819df11 · urbit.org · git.iko.soy

git.iko.soy/urbit.org

Merge pull request #1218 from tinnus-napbus/update-stdlib-3a-to-3g

update stdlib sections 3a to 3g

commit819df11e645f4cfc2db7644e3b70b1cd9ab9a1c6 authortinnus-napbus <77721746+tinnus-napbus@users.noreply.github.com> dateSun 17 Oct 2021, 00:52 (5 years ago) parentbab05fc 654c074

8 files changed+2948−2822

compare with master

unifiedsplit

content/docs/hoon/reference/stdlib/3a.md+234−232 content/docs/hoon/reference/stdlib/3b.md+1384−1390 content/docs/hoon/reference/stdlib/3c.md+241−242 content/docs/hoon/reference/stdlib/3d.md+437−452 content/docs/hoon/reference/stdlib/3f.md+444−314 content/docs/hoon/reference/stdlib/3g.md+124−134 content/docs/hoon/reference/stdlib/table-of-contents.md+39−34 lib/glossary.js+45−24

content/docs/hoon/reference/stdlib/3a.md+234−232

@@ -8,9 +8,9 @@ template = "doc.html"

99Extended Euclidean algorithm

1010

11−Produces `d`, the

12−[greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor)

13−of `a` and `b`. Also produces `u` and `v` such that `au + bv = GCD(a, b)`.

11+Produces `d`, the [greatest common

12+divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) of `a` and `b`.

13+Also produces `u` and `v` such that `au + bv = GCD(a, b)`.

1414

1515#### Accepts

1616

@@ -29,28 +29,28 @@ of `a` and `b`. Also produces `u` and `v` such that `au + bv = GCD(a, b)`.

2929#### Source

3030

3131```hoon

32− ++ egcd

33− |= [a=@ b=@]

34− =+ si

35− =+ [c=(sun a) d=(sun b)]

36− =+ [u=[c=(sun 1) d=--0] v=[c=--0 d=(sun 1)]]

37− |- ^- [d=@ u=@s v=@s]

38− ?: =(--0 c)

39− [(abs d) d.u d.v]

40− =+ q=(fra d c)

41− %= $

42− c (dif d (pro q c))

43− d c

44− u [(dif d.u (pro q c.u)) c.u]

45− v [(dif d.v (pro q c.v)) c.v]

46− ==

32+++ egcd

33+ |= [a=@ b=@]

34+ =+ si

35+ =+ [c=(sun a) d=(sun b)]

36+ =+ [u=[c=(sun 1) d=--0] v=[c=--0 d=(sun 1)]]

37+ |- ^- [d=@ u=@s v=@s]

38+ ?: =(--0 c)

39+ [(abs d) d.u d.v]

40+ =+ q=(fra d c)

41+ %= $

42+ c (dif d (pro q c))

43+ d c

44+ u [(dif d.u (pro q c.u)) c.u]

45+ v [(dif d.v (pro q c.v)) c.v]

46+ ==

4747```

4848

4949#### Examples

5050

5151```

52− > (egcd 11 2)

53− [d=1 u=--1 v=-5]

52+> (egcd 11 2)

53+[d=1 u=--1 v=-5]

5454```

5555

5656---

@@ -59,14 +59,18 @@ of `a` and `b`. Also produces `u` and `v` such that `au + bv = GCD(a, b)`.

5959

6060Modulo prime

6161

62−Container core for modular arithmetic functions.

62+Container `door` for modular arithmetic functions.

63+

64+#### Accepts

65+

66+`a` is an atom

6367

6468#### Source

6569

6670```hoon

67− ++ fo

68− ^?

69− |_ a=@

71+++ fo

72+ ^|

73+ |_ a=@

7074```

7175

7276---

@@ -79,7 +83,7 @@ Produces the difference between atoms `b` and `c`, with `a` as the modular base.

7983

8084#### Accepts

8185

82−`a` is an atom.

86+`a` is an atom, and is the sample of `+fo`.

8387

8488`b` is an atom.

8589

@@ -92,19 +96,19 @@ An atom.

9296#### Source

9397

9498```hoon

95− ++ dif

96− |= [b=@ c=@]

97− (sit (sub (add a b) (sit c)))

99+++ dif

100+ |= [b=@ c=@]

101+ (sit (sub (add a b) (sit c)))

98102```

99103

100104#### Examples

101105

102106```

103− > (~(dif fo 6) 1 2)

104− 5

107+> (~(dif fo 6) 1 2)

108+5

105109

106− > (~(dif fo 21) 11 45)

107− 8

110+> (~(dif fo 21) 11 45)

111+8

108112```

109113

110114---

@@ -117,7 +121,7 @@ Produces the power of `c` raised to the `b`, with `a` as the modular base.

117121

118122#### Accepts

119123

120−`a` is an atom.

124+`a` is an atom, and is the sample of `+fo`.

121125

122126`b` is an atom.

123127

@@ -130,13 +134,13 @@ An atom.

130134#### Source

131135

132136```hoon

133− ++ exp

134− |= [b=@ c=@]

135− ?: =(0 b)

136− 1

137− =+ d=$(b (rsh 0 1 b))

138− =+ e=(pro d d)

139− ?:(=(0 (end 0 1 b)) e (pro c e))

137+++ exp

138+ |= [b=@ c=@]

139+ ?: =(0 b)

140+ 1

141+ =+ d=$(b (rsh 0 b))

142+ =+ e=(pro d d)

143+ ?:(=(0 (end 0 b)) e (pro c e))

140144```

141145

142146#### Examples

@@ -165,7 +169,7 @@ Produces the quotient of `b` divided by `c`, with `a` as the modular base.

165169

166170#### Accepts

167171

168−`a` is an atom.

172+`a` is an atom, and is the sample of `+fo`.

169173

170174`b` is an atom.

171175

@@ -175,34 +179,28 @@ Produces the quotient of `b` divided by `c`, with `a` as the modular base.

175179

176180An atom.

177181

178−#### Accepts

179−

180−`a` is an atom.

181−

182−`b` is an atom.

183−

184182#### Source

185183

186184```hoon

187− ++ fra

188− |= [b=@ c=@]

189− (pro b (inv c))

185+++ fra

186+ |= [b=@ c=@]

187+ (pro b (inv c))

190188```

191189

192190#### Examples

193191

194192```

195− > (~(fra fo 2) 8 2)

196− 0

193+> (~(fra fo 2) 8 2)

194+0

197195

198− > (~(fra fo 3) 8 2)

199− 1

196+> (~(fra fo 3) 8 2)

197+1

200198

201− > (~(fra fo 4) 8 2)

202− 0

199+> (~(fra fo 4) 8 2)

200+0

203201

204− > (~(fra fo 5) 8 2)

205− 4

202+> (~(fra fo 5) 8 2)

203+4

206204```

207205

208206---

@@ -212,11 +210,11 @@ An atom.

212210Inverse

213211

214212Produces an atom by taking the signed modulus of `a` with the coefficient `u`;

215−`u` is produced by taking the `++egcd` of `a` and `b`.

213+`u` is produced by taking the [`+egcd`](#egcd) of `a` and `b`.

216214

217215#### Accepts

218216

219−`a` is an atom.

217+`a` is an atom, and is the sample of `+fo`.

220218

221219`b` is an atom.

222220

@@ -227,29 +225,29 @@ An atom.

227225#### Source

228226

229227```hoon

230− ++ inv

231− |= b=@

232− =+ c=(dul:si u:(egcd b a) a)

233− c

228+++ inv

229+ |= b=@

230+ =+ c=(dul:si u:(egcd b a) a)

231+ c

234232```

235233

236234#### Examples

237235

238236```

239− > (~(inv fo 11) 2)

240− 6

237+> (~(inv fo 11) 2)

238+6

241239

242− > (~(inv fo 71) 255)

243− 22

240+> (~(inv fo 71) 255)

241+22

244242

245− > (~(inv fo 79) 255)

246− 22

243+> (~(inv fo 79) 255)

244+22

247245

248− > (~(inv fo 78) 255)

249− 67

246+> (~(inv fo 78) 255)

247+67

250248

251− > (~(inv fo 70) 255)

252− 67

249+> (~(inv fo 70) 255)

250+67

253251```

254252

255253---

@@ -262,7 +260,7 @@ Produces the multiplication of `b` and `c` modulo `a`.

262260

263261#### Accepts

264262

265−`a` is an atom.

263+`a` is an atom, and is the sample of `+fo`.

266264

267265`b` is an atom.

268266

@@ -275,19 +273,19 @@ An atom.

275273#### Source

276274

277275```hoon

278− ++ pro

279− |= [b=@ c=@]

280− (sit (mul b c))

276+++ pro

277+ |= [b=@ c=@]

278+ (sit (mul b c))

281279```

282280

283281#### Examples

284282

285283```

286− > (~(pro fo 3) 11 4)

287− 2

284+> (~(pro fo 3) 11 4)

285+2

288286

289− > (mod 44 3)

290− 2

287+> (mod 44 3)

288+2

291289```

292290

293291---

@@ -300,7 +298,7 @@ Produces the remainder of `b` modulo `a`.

300298

301299#### Accepts

302300

303−`a` is an atom.

301+`a` is an atom, and is the sample of `+fo`.

304302

305303`b` is an atom.

306304

@@ -311,16 +309,16 @@ An atom.

311309#### Source

312310

313311```hoon

314− ++ sit

315− |= b=@

316− (mod b a)

312+++ sit

313+ |= b=@

314+ (mod b a)

317315```

318316

319317#### Examples

320318

321319```

322− > (~(sit fo 3) 14)

323− 2

320+> (~(sit fo 3) 14)

321+2

324322```

325323

326324---

@@ -333,7 +331,7 @@ Produces the remainder of `(b + c) mod a`.

333331

334332#### Accepts

335333

336−`a` is an atom.

334+`a` is an atom, and is the sample of `+fo`.

337335

338336`b` is an atom.

339337

@@ -346,20 +344,19 @@ An atom.

346344#### Source

347345

348346```hoon

349− ++ sum

350− |= [b=@ c=@]

351− (sit (add b c))

352− --

347+++ sum

348+ |= [b=@ c=@]

349+ (sit (add b c))

353350```

354351

355352#### Examples

356353

357354```

358− > (~(sum fo 3) 14 3)

359− 2

355+> (~(sum fo 3) 14 3)

356+2

360357

361− > (mod 17 3)

362− 2

358+> (mod 17 3)

359+2

363360```

364361

365362---

@@ -373,9 +370,9 @@ Container core for signed integer functions.

373370#### Source

374371

375372```hoon

376− ++ si

377− ^?

378− |%

373+++ si

374+ ^?

375+ |%

379376```

380377

381378#### Discussion

@@ -390,15 +387,17 @@ signed integers correspond to odd atoms of twice their absolute value minus

390387one. For example:

391388

392389```

393− > `@`--4

394− 8

395− > `@s`8

396− --4

390+> `@`--4

391+8

392+> `@s`8

393+--4

394+```

397395

398− > `@`-4

399− 7

400− > `@s`7

401− -4

396+```

397+> `@`-4

398+7

399+> `@s`7

400+-4

402401```

403402

404403---

@@ -420,17 +419,17 @@ An atom.

420419#### Source

421420

422421```hoon

423− ++ abs |=(a=@s (add (end 0 1 a) (rsh 0 1 a)))

422+++ abs |=(a=@s (add (end 0 a) (rsh 0 a)))

424423```

425424

426425#### Examples

427426

428427```

429− > (abs:si -11)

430− 11

428+> (abs:si -11)

429+11

431430

432− > (abs:si --520)

433− 520

431+> (abs:si --520)

432+520

434433```

435434

436435---

@@ -454,18 +453,18 @@ A signed integer.

454453#### Source

455454

456455```hoon

457− ++ dif |= [a=@s b=@s]

458− (sum a (new !(syn b) (abs b)))

456+++ dif |= [a=@s b=@s]

457+ (sum a (new !(syn b) (abs b)))

459458```

460459

461460#### Examples

462461

463462```

464− > (dif:si --3 -2)

465− --5

463+> (dif:si --3 -2)

464+--5

466465

467− > (dif:si -3 --2)

468− -5

466+> (dif:si -3 --2)

467+-5

469468```

470469

471470---

@@ -489,23 +488,23 @@ An atom.

489488#### Source

490489

491490```hoon

492− ++ dul |= [a=@s b=@]

493− =+(c=(old a) ?:(-.c (mod +.c b) (sub b +.c)))

491+++ dul |= [a=@s b=@]

492+ =+(c=(old a) ?:(-.c (mod +.c b) (sub b +.c)))

494493```

495494

496495#### Examples

497496

498497```

499− > `@s`(dul:si -1 --5)

500− -5

498+> `@s`(dul:si -1 --5)

499+-5

501500

502− > `@`--5

503− 10

504− > `@s`(dul:si -1 10)

505− -5

501+> `@`--5

502+10

503+> `@s`(dul:si -1 10)

504+-5

506505

507− > `@s`(dul:si -11 -61)

508− --55

506+> `@s`(dul:si -11 -61)

507+--55

509508```

510509

511510---

@@ -529,28 +528,28 @@ A signed atom.

529528#### Source

530529

531530```hoon

532− ++ fra |= [a=@s b=@s]

533− (new =(0 (mix (syn a) (syn b))) (div (abs a) (abs b)))

531+++ fra |= [a=@s b=@s]

532+ (new =(0 (mix (syn a) (syn b))) (div (abs a) (abs b)))

534533```

535534

536535#### Examples

537536

538537```

539− > (fra:si -1 -1)

540− --1

538+> (fra:si -1 -1)

539+--1

541540

542− > (fra:si -11 --2)

543− -5

541+> (fra:si -11 --2)

542+-5

544543

545− > (fra:si -0 -1)

546− --0

544+> (fra:si -0 -1)

545+--0

547546```

548547

549548---

550549

551550### `++new:si`

552551

553−Atom to @s

552+Atom to `@s`

554553

555554Produces a signed integer from an atom `b`. The product's sign is determined

556555by the value of flag `a`: `&` will result in a prepending `--`, and `|` will

@@ -569,24 +568,24 @@ A signed integer.

569568#### Source

570569

571570```hoon

572− ++ new |= [a=? b=@]

573− `@s`?:(a (mul 2 b) ?:(=(0 b) 0 +((mul 2 (dec b)))))

571+++ new |= [a=? b=@]

572+ `@s`?:(a (mul 2 b) ?:(=(0 b) 0 +((mul 2 (dec b)))))

574573```

575574

576575#### Examples

577576

578577```

579− > (new:si | 2)

580− -2

578+> (new:si | 2)

579+-2

581580

582− > (new:si & 2)

583− --2

581+> (new:si & 2)

582+--2

584583

585− > (new:si & -2)

586− --3

584+> (new:si & -2)

585+--3

587586

588− > (new:si & --2)

589− --4

587+> (new:si & --2)

588+--4

590589```

591590

592591---

@@ -604,7 +603,7 @@ positive or negative, and the absolute value of `a`.

604603

605604#### Produces

606605

607−A cell composed of a `term` and an atom.

606+A cell composed of a `?` and an atom.

608607

609608#### Source

610609

@@ -612,14 +611,18 @@ A cell composed of a `term` and an atom.

612611 ++ old |=(a=@s [(syn a) (abs a)])

613612```

614613

614+```hoon

615+++ old |=(a=@s [(syn a) (abs a)])

616+```

617+

615618#### Examples

616619

617620```

618− > (old:si -2)

619− [%.n 2]

621+> (old:si -2)

622+[%.n 2]

620623

621− > (old:si --2)

622− [%.y 2]

624+> (old:si --2)

625+[%.y 2]

623626```

624627

625628---

@@ -639,18 +642,18 @@ Produces a signed integer by multiplying `a` and `b`.

639642#### Source

640643

641644```hoon

642− ++ pro |= [a=@s b=@s]

643− (new =(0 (mix (syn a) (syn b))) (mul (abs a) (abs b)))

645+++ pro |= [a=@s b=@s]

646+ (new =(0 (mix (syn a) (syn b))) (mul (abs a) (abs b)))

644647```

645648

646649#### Examples

647650

648651```

649− > (pro:si -3 -3)

650− --9

652+> (pro:si -3 -3)

653+--9

651654

652− > (pro:si -3 --3)

653− -9

655+> (pro:si -3 --3)

656+-9

654657```

655658

656659---

@@ -674,23 +677,23 @@ A signed integer.

674677#### Source

675678

676679```hoon

677− ++ rem |=([a=@s b=@s] (dif a (pro b (fra a b))))

680+++ rem |=([a=@s b=@s] (dif a (pro b (fra a b))))

678681```

679682

680683#### Examples

681684

682685```

683− > (rem:si -17 -3)

684− -2

686+> (rem:si -17 -3)

687+-2

685688

686− > (rem:si --17 -3)

687− --2

689+> (rem:si --17 -3)

690+--2

688691

689− > (rem:si -17 --3)

690− -2

692+> (rem:si -17 --3)

693+-2

691694

692− > (rem:si --17 --3)

693− --2

695+> (rem:si --17 --3)

696+--2

694697```

695698

696699---

@@ -714,36 +717,36 @@ A signed integer.

714717#### Source

715718

716719```hoon

717− ++ sum |= [a=@s b=@s]

718− =+ [c=(old a) d=(old b)]

719− ?: -.c

720− ?: -.d

721− (new & (add +.c +.d))

722− ?: (gte +.c +.d)

723− (new & (sub +.c +.d))

724− (new | (sub +.d +.c))

725− ?: -.d

726− ?: (gte +.c +.d)

727− (new | (sub +.c +.d))

728− (new & (sub +.d +.c))

729− (new | (add +.c +.d))

720+++ sum |= [a=@s b=@s]

721+ =+ [c=(old a) d=(old b)]

722+ ?: -.c

723+ ?: -.d

724+ (new & (add +.c +.d))

725+ ?: (gte +.c +.d)

726+ (new & (sub +.c +.d))

727+ (new | (sub +.d +.c))

728+ ?: -.d

729+ ?: (gte +.c +.d)

730+ (new | (sub +.c +.d))

731+ (new & (sub +.d +.c))

732+ (new | (add +.c +.d))

730733```

731734

732735#### Examples

733736

734737```

735− > (sum:si -11 --2)

736− -9

738+> (sum:si -11 --2)

739+-9

737740

738− > (sum:si --2 --2)

739− --4

741+> (sum:si --2 --2)

742+--4

740743```

741744

742745---

743746

744747### `++sun:si`

745748

746−@u to @s

749+`@u` to `@s`

747750

748751Multiplies the unsigned integer `a` by two, producing an atom.

749752

@@ -758,29 +761,29 @@ An atom.

758761#### Source

759762

760763```hoon

761− ++ sun |=(a=@u (mul 2 a))

764+++ sun |=(a=@u (mul 2 a))

762765```

763766

764767#### Examples

765768

766769```

767− > (sun:si 90)

768− 180

770+> (sun:si 90)

771+180

769772

770− > (sun:si --90)

771− 360

772− > `@u`--90

773− 180

773+> (sun:si --90)

774+360

775+> `@u`--90

776+180

774777

775− > (sun:si --89)

776− 356

777− > `@u`--89

778− 178

778+> (sun:si --89)

779+356

780+> `@u`--89

781+178

779782

780− > (sun:si -89)

781− 354

782− > `@u`-89

783− 177

783+> (sun:si -89)

784+354

785+> `@u`-89

786+177

784787```

785788

786789---

@@ -798,22 +801,22 @@ is positive, and `%.n` is produced if `a` is negative.

798801

799802#### Produces

800803

801−An `term`.

804+A `?`.

802805

803806#### Source

804807

805808```hoon

806− ++ syn |=(a=@s =(0 (end 0 1 a)))

809+++ syn |=(a=@s =(0 (end 0 a)))

807810```

808811

809812#### Examples

810813

811814```

812− > (syn:si -2)

813− %.n

815+> (syn:si -2)

816+%.n

814817

815− > (syn:si --2)

816− %.y

818+> (syn:si --2)

819+%.y

817820```

818821

819822---

@@ -839,41 +842,40 @@ A signed integer.

839842#### Source

840843

841844```hoon

842− ++ cmp |= [a=@s b=@s]

843− ^- @s

844− ?: =(a b)

845− --0

846− ?: (syn a)

847− ?: (syn b)

848− ?: (gth a b)

849− --1

850− -1

851− --1

852− ?: (syn b)

853− -1

854− ?: (gth a b)

855− -1

845+++ cmp |= [a=@s b=@s]

846+ ^- @s

847+ ?: =(a b)

848+ --0

849+ ?: (syn a)

850+ ?: (syn b)

851+ ?: (gth a b)

856852 --1

857− --

853+ -1

854+ --1

855+ ?: (syn b)

856+ -1

857+ ?: (gth a b)

858+ -1

859+ --1

858860```

859861

860862#### Examples

861863

862864```

863− > (cmp:si -2 --1)

864− -1

865+> (cmp:si -2 --1)

866+-1

865867

866− > (cmp:si -2 --1)

867− -1

868+> (cmp:si -2 --1)

869+-1

868870

869− > (cmp:si --2 --1)

870− --1

871+> (cmp:si --2 --1)

872+--1

871873

872− > (cmp:si --2 --2)

873− --0

874+> (cmp:si --2 --2)

875+--0

874876

875− > (cmp:si --2 --5)

876− -1

877+> (cmp:si --2 --5)

878+-1

877879```

878880

879881---

content/docs/hoon/reference/stdlib/3b.md+1384−1390

@@ -11,37 +11,37 @@ Float

1111A mold for the floating-point arithmetic using the base of two, the formula is

1212`(-1)^s * a * 2^e`.

1313

14−Produces either a float (`$f`), an infinity of other sign (`$i`),

15−or not-a-number (`$n`). `s` refers to sign, the `flag`s `&` or `|`; `e` to

14+Produces either a float (`%f`), an infinity of other sign (`%i`),

15+or not-a-number (`%n`). `s` refers to sign, the `flag`s `&` or `|`; `e` to

1616exponent, a signed decimal; and `a` to the significand, an unsigned integer.

1717

1818#### Source

1919

2020```hoon

21− ++ fn

22− $% [$f s=? e=@s a=@u]

23− [$i s=?]

24− [$n ~]

25− ==

21+++ fn

22+ $% [%f s=? e=@s a=@u]

23+ [%i s=?]

24+ [%n ~]

25+ ==

2626```

2727

2828#### Examples

2929

3030```

31− > *fn

32− [%n ~]

31+> *fn

32+[%n ~]

3333

34− > (add:fl [%f & --33 2] [%f | --23 2])

35− [%f s=%.y e=-79 a=10.374.452.512.267.829.421.849.019.032.797.184]

34+> (add:fl [%f & --33 2] [%f | --23 2])

35+[%f s=%.y e=-79 a=10.374.452.512.267.829.421.849.019.032.797.184]

3636

37− > (add:fl [%i &] [%i &])

38− [%i s=%.y]

37+> (add:fl [%i &] [%i &])

38+[%i s=%.y]

3939

40− > (add:fl [%n ~] [%i |])

41− [%n ~]

40+> (add:fl [%n ~] [%i |])

41+[%n ~]

4242

43− > (sun:fl 961.193.554.848.514.048.973.893.027.381.506.219.443)

44− [%f s=%.y e=--17 a=7.333.324.850.834.000.007.430.214.137.126.970]

43+> (sun:fl 961.193.554.848.514.048.973.893.027.381.506.219.443)

44+[%f s=%.y e=--17 a=7.333.324.850.834.000.007.430.214.137.126.970]

4545```

4646

4747---

@@ -53,29 +53,29 @@ Decimal float

5353A mold for the floating-point arithmetic using the base of 10; the formula is

5454`(-1)^s * a *10^e`.

5555

56−Valid values are a float (`$d`), an infinity (`$i`), or a not-a-number (`$n`).

56+Valid values are a float (`%d`), an infinity (`%i`), or a not-a-number (`%n`).

5757`s` refers to sign, the `flag`s `&` or `|`; `e` to exponent, a signed decimal;

5858and `a` to the significand, an unsigned integer.

5959

6060```hoon

61− ++ dn

62− $% [$d s=? e=@s a=@u]

63− [$i s=?]

64− [$n ~]

65− ==

61+++ dn

62+ $% [%d s=? e=@s a=@u]

63+ [%i s=?]

64+ [%n ~]

65+ ==

6666```

6767

6868#### Examples

6969

7070```

71− > `dn`[%d & --0 17.163.091.968]

72− [%d s=%.y e=--0 a=17.163.091.968]

71+> `dn`[%d & --0 17.163.091.968]

72+[%d s=%.y e=--0 a=17.163.091.968]

7373

74− > `dn`[%i s=%.y]

75− [%i s=%.y]

74+> `dn`[%i s=%.y]

75+[%i s=%.y]

7676

77− > `dn`[%n ~]

78− [%n ~]

77+> `dn`[%n ~]

78+[%n ~]

7979```

8080

8181---

@@ -87,23 +87,24 @@ Parsed decimal float

8787A mold for the floating-point arithmetic using the base of 10; the formula is

8888`(-1)^s * a *10^e`.

8989

90−Produces either a parsed float (`$d`), infinity of either sign (`$i`), or

91−not-a-number (`$n`).

90+Produces either a parsed float (`%d`), infinity of either sign (`%i`), or

91+not-a-number (`%n`).

9292

9393#### Source

9494

9595```hoon

96− $% [$d a=? b=[c=@ [d=@ e=@] f=? i=@]]

97− [$i a=?]

98− [$n ~]

99− ==

96+++ rn

97+ $% [%d a=? b=[c=@ [d=@ e=@] f=? i=@]]

98+ [%i a=?]

99+ [%n ~]

100+ ==

100101```

101102

102103#### Examples

103104

104105```

105− > `rn`[%d | [2 [3 4] | 17.163]]

106− [%d a=%.n b=[c=2 [d=3 e=4] f=%.n i=17.163]]

106+> `rn`[%d | [2 [3 4] | 17.163]]

107+[%d a=%.n b=[c=2 [d=3 e=4] f=%.n i=17.163]]

107108```

108109

109110---

@@ -119,25 +120,25 @@ Container arm for floating-point arithmetic functions.

119120- Minimum exponent (`v`): minimum value of e. Default is -16.494.

120121- Width (`w`): Max value of `e` minus min value of `e`. 0 is for fixed-point.

121122 Default is 32.765.

122−- Rounding mode (`r`): Possible modes are nearest (`$n`), up (`$u`),

123− down (`$d`), to zero (`$z`), and away from zero (`$a`). Default value is `%n`.

124−- Behavior (`d`): return denormals (`$d`), flush denormals to zero (`$z`),

125− infinite exponent range (`$i`). Default value is `%d`.

123+- Rounding mode (`r`): Possible modes are nearest (`%n`), up (`%u`),

124+ down (`%d`), to zero (`%z`), and away from zero (`%a`). Default value is `%n`.

125+- Behavior (`d`): return denormals (`%d`), flush denormals to zero (`%z`),

126+ infinite exponent range (`%i`). Default value is `%d`.

126127

127128#### Source

128129

129130```hoon

130− ++ fl

131− =+ ^- [[p=@u v=@s w=@u] r=$?($n $u $d $z $a) d=$?($d $f $i)]

132− [[113 -16.494 32.765] %n %d]

133− =>

134− ~% %cofl +> ~

135− |%

131+++ fl

132+ =/ [[p=@u v=@s w=@u] r=$?(%n %u %d %z %a) d=$?(%d %f %i)]

133+ [[113 -16.494 32.765] %n %d]

134+ =>

135+ ~% %cofl +> ~

136+ |%

136137```

137138

138139---

139140

140−### `++rou:fl`

141+### `^rou:fl`

141142

142143Round

143144

@@ -156,25 +157,25 @@ An `fn`.

156157#### Source

157158

158159```hoon

159− ++ rou

160− |= [a=[e=@s a=@u]] ^- fn (rau a &)

160+++ rou

161+ |= [a=[e=@s a=@u]] ^- fn (rau a &)

161162```

162163

163164#### Examples

164165

165166```

166− > =a 10.161.487.211.429.486.882.397.572.894.294.017.777

167− > (^rou:fl [--12 a])

168− [%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

167+> =a 10.161.487.211.429.486.882.397.572.894.294.017.777

168+> (^rou:fl [--12 a])

169+[%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

169170

170− > (^rou:fl [--12 (add a 1)])

171− [%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

171+> (^rou:fl [--12 (add a 1)])

172+[%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

172173

173− > (^rou:fl [--12 (add a 300)])

174− [%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

174+> (^rou:fl [--12 (add a 300)])

175+[%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

175176

176− > (^rou:fl [--12 (add a 1.000)])

177− [%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.003]

177+> (^rou:fl [--12 (add a 1.000)])

178+[%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.003]

178179```

179180

180181---

@@ -200,29 +201,29 @@ An `fn`.

200201#### Source

201202

202203```hoon

203− ++ rau

204− |= [a=[e=@s a=@u] t=?] ^- fn

205− ?- r

206− $z (lug %fl a t) $d (lug %fl a t)

207− $a (lug %ce a t) $u (lug %ce a t)

208− $n (lug %ne a t)

209− ==

204+++ rau

205+ |= [a=[e=@s a=@u] t=?] ^- fn

206+ ?- r

207+ %z (lug %fl a t) %d (lug %fl a t)

208+ %a (lug %ce a t) %u (lug %ce a t)

209+ %n (lug %ne a t)

210+ ==

210211```

211212

212213#### Examples

213214

214215```

215− > (rau:fl [-18 342.602.577] &)

216− [%f s=%.y e=-102 a=6.626.897.619.228.945.634.459.505.846.648.832]

216+> (rau:fl [-18 342.602.577] &)

217+[%f s=%.y e=-102 a=6.626.897.619.228.945.634.459.505.846.648.832]

217218```

218219

219220#### Discussion

220221

221−See `lug:fl` for possible rounding operations.

222+See [`lug:fl`](#lugfl) for possible rounding operations.

222223

223224---

224225

225−### `++add:fl`

226+### `^add:fl`

226227

227228Add

228229

@@ -247,38 +248,38 @@ An `fn`.

247248#### Source

248249

249250```hoon

250− ++ add

251− |= [a=[e=@s a=@u] b=[e=@s a=@u] e=?] ^- fn

252− =+ q=(dif:si e.a e.b)

253− |- ?. (syn:si q) $(b a, a b, q +(q)) :: a has larger exp

254− ?: e

255− [%f & e.b (^add (lsh 0 (abs:si q) a.a) a.b)]

256− =+ [ma=(met 0 a.a) mb=(met 0 a.b)]

257− =+ ^= w %+ dif:si e.a %- sun:si :: expanded exp of a

258− ?: (gth prc ma) (^sub prc ma) 0

259− =+ ^= x %+ sum:si e.b (sun:si mb) :: highest exp for b

260− ?: =((cmp:si w x) --1) :: don't need to add

261− ?- r

262− $z (lug %fl a &) $d (lug %fl a &)

263− $a (lug %lg a &) $u (lug %lg a &)

264− $n (lug %na a &)

265− ==

266− (rou [e.b (^add (lsh 0 (abs:si q) a.a) a.b)])

251+++ add

252+ |= [a=[e=@s a=@u] b=[e=@s a=@u] e=?] ^- fn

253+ =+ q=(dif:si e.a e.b)

254+ |- ?. (syn:si q) $(b a, a b, q +(q))

255+ ?: e

256+ [%f & e.b (^add (lsh [0 (abs:si q)] a.a) a.b)]

257+ =+ [ma=(met 0 a.a) mb=(met 0 a.b)]

258+ =+ ^= w %+ dif:si e.a %- sun:si

259+ ?: (gth prc ma) (^sub prc ma) 0

260+ =+ ^= x %+ sum:si e.b (sun:si mb)

261+ ?: =((cmp:si w x) --1)

262+ ?- r

263+ %z (lug %fl a &) %d (lug %fl a &)

264+ %a (lug %lg a &) %u (lug %lg a &)

265+ %n (lug %na a &)

266+ ==

267+ (rou [e.b (^add (lsh [0 (abs:si q)] a.a) a.b)])

267268```

268269

269270#### Examples

270271

271272```

272− > (^add:fl [--33 2.718] [--23 11] %.y)

273− [%f s=%.y e=--23 a=2.783.243]

273+> (^add:fl [--33 2.718] [--23 11] %.y)

274+[%f s=%.y e=--23 a=2.783.243]

274275

275− > (^add:fl [--33 2.718] [--23 11] %.n)

276− [%f s=%.y e=-68 a=6.890.975.897.521.519.304.902.126.405.156.864]

276+> (^add:fl [--33 2.718] [--23 11] %.n)

277+[%f s=%.y e=-68 a=6.890.975.897.521.519.304.902.126.405.156.864]

277278```

278279

279280---

280281

281−### `++sub:fl`

282+### `^sub:fl`

282283

283284Subtract

284285

@@ -300,42 +301,42 @@ An `fn`.

300301#### Source

301302

302303```hoon

303− ++ sub

304− |= [a=[e=@s a=@u] b=[e=@s a=@u] e=?] ^- fn

305− =+ q=(dif:si e.a e.b)

306− |- ?. (syn:si q)

307− (fli $(b a, a b, q +(q), r swr))

308− =+ [ma=(met 0 a.a) mb=(met 0 a.b)]

309− =+ ^= w %+ dif:si e.a %- sun:si

310− ?: (gth prc ma) (^sub prc ma) 0

311− =+ ^= x %+ sum:si e.b (sun:si +(mb))

312− ?: &(!e =((cmp:si w x) --1))

313− ?- r

314− $z (lug %sm a &) $d (lug %sm a &)

315− $a (lug %ce a &) $u (lug %ce a &)

316− $n (lug %nt a &)

317− ==

318− =+ j=(lsh 0 (abs:si q) a.a)

319− |- ?. (gte j a.b)

320− (fli $(a.b j, j a.b, r swr))

321− =+ i=(^sub j a.b)

322− ?~ i [%f & zer]

323− ?: e [%f & e.b i] (rou [e.b i])

304+++ sub

305+ |= [a=[e=@s a=@u] b=[e=@s a=@u] e=?] ^- fn

306+ =+ q=(dif:si e.a e.b)

307+ |- ?. (syn:si q)

308+ (fli $(b a, a b, q +(q), r swr))

309+ =+ [ma=(met 0 a.a) mb=(met 0 a.b)]

310+ =+ ^= w %+ dif:si e.a %- sun:si

311+ ?: (gth prc ma) (^sub prc ma) 0

312+ =+ ^= x %+ sum:si e.b (sun:si +(mb))

313+ ?: &(!e =((cmp:si w x) --1))

314+ ?- r

315+ %z (lug %sm a &) %d (lug %sm a &)

316+ %a (lug %ce a &) %u (lug %ce a &)

317+ %n (lug %nt a &)

318+ ==

319+ =+ j=(lsh [0 (abs:si q)] a.a)

320+ |- ?. (gte j a.b)

321+ (fli $(a.b j, j a.b, r swr))

322+ =+ i=(^sub j a.b)

323+ ?~ i [%f & zer]

324+ ?: e [%f & e.b i] (rou [e.b i])

324325```

325326

326327#### Examples

327328

328329```

329− > (^sub:fl [--33 2.718] [--23 11] %.y)

330− [%f s=%.y e=--23 a=2.783.221]

330+> (^sub:fl [--33 2.718] [--23 11] %.y)

331+[%f s=%.y e=--23 a=2.783.221]

331332

332− > (^sub:fl [--33 2.718] [--63 11] %.y)

333− [%f s=%.n e=--33 a=11.811.157.346]

333+> (^sub:fl [--33 2.718] [--63 11] %.y)

334+[%f s=%.n e=--33 a=11.811.157.346]

334335```

335336

336337---

337338

338−### `++mul:fl`

339+### `^mul:fl`

339340

340341Multiply

341342

@@ -355,21 +356,21 @@ An `fn`.

355356#### Source

356357

357358```hoon

358− ++ mul

359− |= [a=[e=@s a=@u] b=[e=@s a=@u]] ^- fn

360− (rou (sum:si e.a e.b) (^mul a.a a.b))

359+++ mul

360+ |= [a=[e=@s a=@u] b=[e=@s a=@u]] ^- fn

361+ (rou (sum:si e.a e.b) (^mul a.a a.b))

361362```

362363

363364#### Examples

364365

365366```

366− > (^mul:fl [--3 2.718] [--23 11])

367− [%f s=%.y e=-72 a=9.475.054.411.405.900.661.487.108.108.582.912]

367+> (^mul:fl [--3 2.718] [--23 11])

368+[%f s=%.y e=-72 a=9.475.054.411.405.900.661.487.108.108.582.912]

368369```

369370

370371---

371372

372−### `++div:fl`

373+### `^div:fl`

373374

374375Divide

375376

@@ -389,26 +390,26 @@ An `fn`.

389390#### Source

390391

391392```hoon

392− ++ div

393− |= [a=[e=@s a=@u] b=[e=@s a=@u]] ^- fn

394− =+ [ma=(met 0 a.a) mb=(met 0 a.b)]

395− =+ v=(dif:si (sun:si ma) (sun:si +((^add mb prc))))

396− =. a ?: (syn:si v) a

397− a(e (sum:si v e.a), a (lsh 0 (abs:si v) a.a))

398− =+ [j=(dif:si e.a e.b) q=(dvr a.a a.b)]

399− (rau [j p.q] =(q.q 0))

393+++ div

394+ |= [a=[e=@s a=@u] b=[e=@s a=@u]] ^- fn

395+ =+ [ma=(met 0 a.a) mb=(met 0 a.b)]

396+ =+ v=(dif:si (sun:si ma) (sun:si +((^add mb prc))))

397+ =. a ?: (syn:si v) a

398+ a(e (sum:si v e.a), a (lsh [0 (abs:si v)] a.a))

399+ =+ [j=(dif:si e.a e.b) q=(dvr a.a a.b)]

400+ (rau [j p.q] =(q.q 0))

400401```

401402

402403#### Examples

403404

404405```

405− > (^div:fl [--13 2.718] [--23 11])

406− [%f s=%.y e=-115 a=10.023.198.055.040.952.765.870.659.817.343.907]

406+> (^div:fl [--13 2.718] [--23 11])

407+[%f s=%.y e=-115 a=10.023.198.055.040.952.765.870.659.817.343.907]

407408```

408409

409410---

410411

411−### `++sqt:fl`

412+### `^sqt:fl`

412413

413414Square root

414415

@@ -425,28 +426,28 @@ An `fn`.

425426#### Source

426427

427428```hoon

428− ++ sqt

429− |= [a=[e=@s a=@u]] ^- fn

430− =. a

431− =+ [w=(met 0 a.a) x=(^mul +(prc) 2)]

432− =+ ?:((^lth w x) (^sub x w) 0)

433− =+ ?: =((dis - 1) (dis (abs:si e.a) 1)) -

434− (^add - 1)

435− a(e (dif:si e.a (sun:si -)), a (lsh 0 - a.a))

436− =+ [y=(^sqt a.a) z=(fra:si e.a --2)]

437− (rau [z p.y] =(q.y 0))

429+++ sqt

430+ |= [a=[e=@s a=@u]] ^- fn

431+ =. a

432+ =+ [w=(met 0 a.a) x=(^mul +(prc) 2)]

433+ =+ ?:((^lth w x) (^sub x w) 0)

434+ =+ ?: =((dis - 1) (dis (abs:si e.a) 1)) -

435+ (^add - 1)

436+ a(e (dif:si e.a (sun:si -)), a (lsh [0 -] a.a))

437+ =+ [y=(^sqt a.a) z=(fra:si e.a --2)]

438+ (rau [z p.y] =(q.y 0))

438439```

439440

440441#### Examples

441442

442443```

443− > (^sqt:fl [-18 342.602.577])

444− [%f s=%.y e=-107 a=5.865.903.143.604.945.574.132.671.852.050.553]

444+> (^sqt:fl [-18 342.602.577])

445+[%f s=%.y e=-107 a=5.865.903.143.604.945.574.132.671.852.050.553]

445446```

446447

447448---

448449

449−### `++lth:fl`

450+### `^lth:fl`

450451

451452Less than

452453

@@ -465,29 +466,29 @@ An `flag`.

465466#### Source

466467

467468```hoon

468− ++ lth

469− |= [a=[e=@s a=@u] b=[e=@s a=@u]] ^- ?

470− ?: =(e.a e.b) (^lth a.a a.b)

471− =+ c=(cmp:si (ibl a) (ibl b))

472− ?: =(c -1) & ?: =(c --1) |

473− ?: =((cmp:si e.a e.b) -1)

474− (^lth (rsh 0 (abs:si (dif:si e.a e.b)) a.a) a.b)

475− (^lth (lsh 0 (abs:si (dif:si e.a e.b)) a.a) a.b)

469+++ lth

470+ |= [a=[e=@s a=@u] b=[e=@s a=@u]] ^- ?

471+ ?: =(e.a e.b) (^lth a.a a.b)

472+ =+ c=(cmp:si (ibl a) (ibl b))

473+ ?: =(c -1) & ?: =(c --1) |

474+ ?: =((cmp:si e.a e.b) -1)

475+ (^lth (rsh [0 (abs:si (dif:si e.a e.b))] a.a) a.b)

476+ (^lth (lsh [0 (abs:si (dif:si e.a e.b))] a.a) a.b)

476477```

477478

478479#### Examples

479480

480481```

481− > (^lth:fl [-4 684] [--0 35])

482− %.n

482+> (^lth:fl [-4 684] [--0 35])

483+%.n

483484

484− > (^lth:fl [-4 684] [--0 90])

485− %.y

485+> (^lth:fl [-4 684] [--0 90])

486+%.y

486487```

487488

488489---

489490

490−### `++equ:fl`

491+### `^equ:fl`

491492

492493Equals

493494

@@ -506,22 +507,22 @@ A `flag`.

506507#### Source

507508

508509```hoon

509− ++ equ

510− |= [a=[e=@s a=@u] b=[e=@s a=@u]] ^- ?

511− ?. =((ibl a) (ibl b)) |

512− ?: =((cmp:si e.a e.b) -1)

513− =((lsh 0 (abs:si (dif:si e.a e.b)) a.b) a.a)

514− =((lsh 0 (abs:si (dif:si e.a e.b)) a.a) a.b)

510+++ equ

511+ |= [a=[e=@s a=@u] b=[e=@s a=@u]] ^- ?

512+ ?. =((ibl a) (ibl b)) |

513+ ?: =((cmp:si e.a e.b) -1)

514+ =((lsh [0 (abs:si (dif:si e.a e.b))] a.b) a.a)

515+ =((lsh [0 (abs:si (dif:si e.a e.b))] a.a) a.b)

515516```

516517

517518#### Examples

518519

519520```

520− > (^equ:fl [-4 480] [-0 50])

521− %.n

521+> (^equ:fl [-4 480] [-0 50])

522+%.n

522523

523− > (^equ:fl [-4 480] [-0 30])

524− %.y

524+> (^equ:fl [-4 480] [-0 30])

525+%.y

525526```

526527

527528---

@@ -544,16 +545,16 @@ A signed integer.

544545#### Source

545546

546547```hoon

547− ++ ibl

548− |= [a=[e=@s a=@u]] ^- @s

549− (sum:si (sun:si (dec (met 0 a.a))) e.a)

548+++ ibl

549+ |= [a=[e=@s a=@u]] ^- @s

550+ (sum:si (sun:si (dec (met 0 a.a))) e.a)

550551```

551552

552553#### Examples

553554

554555```

555− > (ibl:fl [-18 342.602.577])

556− --10

556+> (ibl:fl [-18 342.602.577])

557+--10

557558```

558559

559560---

@@ -577,20 +578,20 @@ A cell of a signed integer and an unsigned integer.

577578#### Source

578579

579580```hoon

580− ++ uni

581− |= [a=[e=@s a=@u]]

582− |- ?: =((end 0 1 a.a) 1) a

583− $(a.a (rsh 0 1 a.a), e.a (sum:si e.a --1))

581+++ uni

582+ |= [a=[e=@s a=@u]]

583+ |- ?: =((end 0 a.a) 1) a

584+ $(a.a (rsh 0 a.a), e.a (sum:si e.a --1))

584585```

585586

586587#### Examples

587588

588589```

589− > (uni:fl [-8 342.602.578])

590− [e=-7 a=171.301.289]

590+> (uni:fl [-8 342.602.578])

591+[e=-7 a=171.301.289]

591592

592− > (uni:fl [-8 342.602.577])

593− [e=-8 a=342.602.577]

593+> (uni:fl [-8 342.602.577])

594+[e=-8 a=342.602.577]

594595```

595596

596597---

@@ -612,29 +613,29 @@ A cell of a signed integer and an unsigned integer.

612613#### Sources

613614

614615```hoon

615− ++ xpd

616− |= [a=[e=@s a=@u]]

617− =+ ma=(met 0 a.a)

618− ?: (gte ma prc) a

619− =+ ?: =(den %i) (^sub prc ma)

620− =+ ^= q

621− =+ w=(dif:si e.a emn)

622− ?: (syn:si w) (abs:si w) 0

623− (min q (^sub prc ma))

624− a(e (dif:si e.a (sun:si -)), a (lsh 0 - a.a))

616+++ xpd

617+ |= [a=[e=@s a=@u]]

618+ =+ ma=(met 0 a.a)

619+ ?: (gte ma prc) a

620+ =+ ?: =(den %i) (^sub prc ma)

621+ =+ ^= q

622+ =+ w=(dif:si e.a emn)

623+ ?: (syn:si w) (abs:si w) 0

624+ (min q (^sub prc ma))

625+ a(e (dif:si e.a (sun:si -)), a (lsh [0 -] a.a))

625626```

626627

627628#### Examples

628629

629630```

630− > (xpd:fl [--3 12])

631− [e=-106 a=7.788.445.287.802.241.442.795.744.493.830.144]

631+> (xpd:fl [--3 12])

632+[e=-106 a=7.788.445.287.802.241.442.795.744.493.830.144]

632633

633− > (xpd:fl [-8 342.602.577])

634− [e=-92 a=6.626.897.619.228.945.634.459.505.846.648.832]

634+> (xpd:fl [-8 342.602.577])

635+[e=-92 a=6.626.897.619.228.945.634.459.505.846.648.832]

635636

636− > (xpd:fl [-92 6.626.897.619.228.945.634.459.505.846.648.832])

637− [e=-92 a=6.626.897.619.228.945.634.459.505.846.648.832]

637+> (xpd:fl [-92 6.626.897.619.228.945.634.459.505.846.648.832])

638+[e=-92 a=6.626.897.619.228.945.634.459.505.846.648.832]

638639```

639640

640641---

@@ -649,16 +650,16 @@ ULP(a) = 2^(e.a)

649650

650651Possible rounding operations:

651652

652−- Floor (`$fl`)

653−- Ceiling (`$ce`)

654−- Smaller (`$sm`)

655−- Larger (`$lg`)

656−- Nearest (`$ne`) -- Rounds ties away from 0 if the number is even, rounds

653+- Floor (`%fl`)

654+- Ceiling (`%ce`)

655+- Smaller (`%sm`)

656+- Larger (`%lg`)

657+- Nearest (`%ne`) -- Rounds ties away from 0 if the number is even, rounds

657658 toward 0 if the number is odd.

658659

659660#### Accepts

660661

661−`t` is one of the following: `$fl`, `$ce`, `$sm`, `$lg`, `$ne`, `$na`, or `$nt`.

662+`t` is one of the following: `%fl`, `%ce`, `%sm`, `%lg`, `%ne`, `%na`, or `%nt`.

662663

663664`a` is a cell of a signed integer and an unsigned integer.

664665

@@ -671,82 +672,75 @@ An `fn`.

671672#### Source

672673

673674```hoon

674− ::

675− :: central rounding mechanism

676− :: can perform: floor, ceiling, smaller, larger,

677− :: nearest (round ties to: even, away from 0, toward 0)

678− :: s is sticky bit: represents a value less than ulp(a) = 2^(e.a)

679− ::

680− ++ lug

681− ~/ %lug

682− |= [t=$?($fl $ce $sm $lg $ne $na $nt) a=[e=@s a=@u] s=?] ^- fn

683− ?< =(a.a 0)

684− =-

685− ?. =(den %f) - :: flush denormals

686− ?. ?=([$f *] -) -

687− ?: =((met 0 ->+>) prc) - [%f & zer]

688− ::

689− =+ m=(met 0 a.a)

690− ?> |(s (gth m prc)) :: require precision

691− =+ ^= q %+ max

692− ?: (gth m prc) (^sub m prc) 0 :: reduce precision

693− %- abs:si ?: =(den %i) --0 :: enforce min. exp

694− ?: =((cmp:si e.a emn) -1) (dif:si emn e.a) --0

695− =^ b a :- (end 0 q a.a)

696− a(e (sum:si e.a (sun:si q)), a (rsh 0 q a.a))

697− ::

698− ?~ a.a

699− ?< =(den %i)

700− ?- t

701− $fl [%f & zer]

702− $sm [%f & zer]

703− $ce [%f & spd]

704− $lg [%f & spd]

705− $ne ?: s [%f & ?:((lte b (bex (dec q))) zer spd)]

706− [%f & ?:((^lth b (bex (dec q))) zer spd)]

707− $nt ?: s [%f & ?:((lte b (bex (dec q))) zer spd)]

708− [%f & ?:((^lth b (bex (dec q))) zer spd)]

709− $na [%f & ?:((^lth b (bex (dec q))) zer spd)]

710− ==

711− ::

712− =. a (xpd a)

713− ::

714− =. a

715− ?- t

716− $fl a

717− $lg a(a +(a.a))

718− $sm ?. &(=(b 0) s) a

719− ?: &(=(e.a emn) !=(den %i)) a(a (dec a.a))

720− =+ y=(dec (^mul a.a 2))

721− ?. (lte (met 0 y) prc) a(a (dec a.a))

722− [(dif:si e.a --1) y]

723− $ce ?: &(=(b 0) s) a a(a +(a.a))

724− $ne ?~ b a

725− =+ y=(bex (dec q))

726− ?: &(=(b y) s) :: round halfs to even

727− ?~ (dis a.a 1) a a(a +(a.a))

728− ?: (^lth b y) a a(a +(a.a))

729− $na ?~ b a

730− =+ y=(bex (dec q))

731− ?: (^lth b y) a a(a +(a.a))

732− $nt ?~ b a

733− =+ y=(bex (dec q))

734− ?: =(b y) ?: s a a(a +(a.a))

735− ?: (^lth b y) a a(a +(a.a))

736− ==

737− ::

738− =. a ?. =((met 0 a.a) +(prc)) a

739− a(a (rsh 0 1 a.a), e (sum:si e.a --1))

740− ?~ a.a [%f & zer]

741− ::

742− ?: =(den %i) [%f & a]

743− ?: =((cmp:si emx e.a) -1) [%i &] [%f & a] :: enforce max. exp

744− ::

675+++ lug

676+ ~/ %lug

677+ |= [t=$?(%fl %ce %sm %lg %ne %na %nt) a=[e=@s a=@u] s=?] ^- fn

678+ ?< =(a.a 0)

679+ =-

680+ ?. =(den %f) - :: flush denormals

681+ ?. ?=([%f *] -) -

682+ ?: =((met 0 ->+>) prc) - [%f & zer]

683+ ::

684+ =+ m=(met 0 a.a)

685+ ?> |(s (gth m prc)) :: require precision

686+ =+ ^= q %+ max

687+ ?: (gth m prc) (^sub m prc) 0 :: reduce precision

688+ %- abs:si ?: =(den %i) --0 :: enforce min. exp

689+ ?: =((cmp:si e.a emn) -1) (dif:si emn e.a) --0

690+ =^ b a :- (end [0 q] a.a)

691+ a(e (sum:si e.a (sun:si q)), a (rsh [0 q] a.a))

692+ ::

693+ ?~ a.a

694+ ?< =(den %i)

695+ ?- t

696+ %fl [%f & zer]

697+ %sm [%f & zer]

698+ %ce [%f & spd]

699+ %lg [%f & spd]

700+ %ne ?: s [%f & ?:((lte b (bex (dec q))) zer spd)]

701+ [%f & ?:((^lth b (bex (dec q))) zer spd)]

702+ %nt ?: s [%f & ?:((lte b (bex (dec q))) zer spd)]

703+ [%f & ?:((^lth b (bex (dec q))) zer spd)]

704+ %na [%f & ?:((^lth b (bex (dec q))) zer spd)]

705+ ==

706+ ::

707+ =. a (xpd a)

708+ ::

709+ =. a

710+ ?- t

711+ %fl a

712+ %lg a(a +(a.a))

713+ %sm ?. &(=(b 0) s) a

714+ ?: &(=(e.a emn) !=(den %i)) a(a (dec a.a))

715+ =+ y=(dec (^mul a.a 2))

716+ ?. (lte (met 0 y) prc) a(a (dec a.a))

717+ [(dif:si e.a --1) y]

718+ %ce ?: &(=(b 0) s) a a(a +(a.a))

719+ %ne ?~ b a

720+ =+ y=(bex (dec q))

721+ ?: &(=(b y) s) :: round halfs to even

722+ ?~ (dis a.a 1) a a(a +(a.a))

723+ ?: (^lth b y) a a(a +(a.a))

724+ %na ?~ b a

725+ =+ y=(bex (dec q))

726+ ?: (^lth b y) a a(a +(a.a))

727+ %nt ?~ b a

728+ =+ y=(bex (dec q))

729+ ?: =(b y) ?: s a a(a +(a.a))

730+ ?: (^lth b y) a a(a +(a.a))

731+ ==

732+ ::

733+ =. a ?. =((met 0 a.a) +(prc)) a

734+ a(a (rsh 0 a.a), e (sum:si e.a --1))

735+ ?~ a.a [%f & zer]

736+ ::

737+ ?: =(den %i) [%f & a]

738+ ?: =((cmp:si emx e.a) -1) [%i &] [%f & a] :: enforce max. exp

745739```

746740

747741---

748742

749−### `++drg:fl`

743+### `^drg:fl`

750744

751745Get printable decimal

752746

@@ -764,74 +758,74 @@ A cell of a signed integer and an unsigned integer.

764758#### Source

765759

766760```hoon

767− ++ drg

768− ~/ %drg

769− |= [a=[e=@s a=@u]] ^- [@s @u]

770− ?< =(a.a 0)

771− =. a (xpd a)

772− =+ r=(lsh 0 ?:((syn:si e.a) (abs:si e.a) 0) a.a)

773− =+ s=(lsh 0 ?.((syn:si e.a) (abs:si e.a) 0) 1)

774− =+ mn=(lsh 0 ?:((syn:si e.a) (abs:si e.a) 0) 1)

775− =+ mp=mn

776− => ?.

777− ?& =(a.a (bex (dec prc))) :: if next smallest

778− |(!=(e.a emn) =(den %i)) :: float is half ULP,

779− == :: tighten lower bound

780− .

781− %= .

782− mp (lsh 0 1 mp)

783− r (lsh 0 1 r)

784− s (lsh 0 1 s)

785− ==

786− =+ [k=--0 q=(^div (^add s 9) 10)]

787− |- ?: (^lth r q)

788− %= $

789− k (dif:si k --1)

790− r (^mul r 10)

791− mn (^mul mn 10)

792− mp (^mul mp 10)

793− ==

794− |- ?: (gte (^add (^mul r 2) mp) (^mul s 2))

795− $(s (^mul s 10), k (sum:si k --1))

796− =+ [u=0 o=0]

797− |- :: r/s+o = a*10^-k

798− =+ v=(dvr (^mul r 10) s)

799− => %= .

800− k (dif:si k --1)

801− u p.v

802− r q.v

803− mn (^mul mn 10)

804− mp (^mul mp 10)

805− ==

806− =+ l=(^lth (^mul r 2) mn) :: in lower bound

807− =+ ^= h :: in upper bound

808− ?| (^lth (^mul s 2) mp)

809− (gth (^mul r 2) (^sub (^mul s 2) mp))

810− ==

811− ?: &(!l !h)

812− $(o (^add (^mul o 10) u))

813− =+ q=&(h |(!l (gth (^mul r 2) s)))

814− =. o (^add (^mul o 10) ?:(q +(u) u))

815− [k o]

816−```

817−

818−#### Examples

819−

820−```

821− > (sun:fl 218.116)

822− [%f s=%.y e=-95 a=8.640.464.947.480.640.129.276.716.135.743.488]

823− > (^drg:fl [e=-95 a=8.640.464.947.480.640.129.276.716.135.743.488])

824− [--0 218.116]

825−

826− > (sun:fl 102.057.673.128.349)

827− [%f s=%.y e=-66 a=7.530.527.107.827.833.883.675.587.233.447.936]

828− > (^drg:fl [e=-66 a=7.530.527.107.827.833.883.675.587.233.447.936])

829− [--0 102.057.673.128.349]

830−```

831−

832−---

833−

834−### `++toj:fl`

761+++ drg :: dragon4; get

762+ ~/ %drg :: printable decimal;

763+ |= [a=[e=@s a=@u]] ^- [@s @u] :: guaranteed accurate

764+ ?< =(a.a 0) :: for rounded floats

765+ =. a (xpd a)

766+ =+ r=(lsh [0 ?:((syn:si e.a) (abs:si e.a) 0)] a.a)

767+ =+ s=(lsh [0 ?.((syn:si e.a) (abs:si e.a) 0)] 1)

768+ =+ mn=(lsh [0 ?:((syn:si e.a) (abs:si e.a) 0)] 1)

769+ =+ mp=mn

770+ => ?.

771+ ?& =(a.a (bex (dec prc))) :: if next smallest

772+ |(!=(e.a emn) =(den %i)) :: float is half ULP,

773+ == :: tighten lower bound

774+ .

775+ %= .

776+ mp (lsh 0 mp)

777+ r (lsh 0 r)

778+ s (lsh 0 s)

779+ ==

780+ =+ [k=--0 q=(^div (^add s 9) 10)]

781+ |- ?: (^lth r q)

782+ %= $

783+ k (dif:si k --1)

784+ r (^mul r 10)

785+ mn (^mul mn 10)

786+ mp (^mul mp 10)

787+ ==

788+ |- ?: (gte (^add (^mul r 2) mp) (^mul s 2))

789+ $(s (^mul s 10), k (sum:si k --1))

790+ =+ [u=0 o=0]

791+ |- :: r/s+o = a*10^-k

792+ =+ v=(dvr (^mul r 10) s)

793+ => %= .

794+ k (dif:si k --1)

795+ u p.v

796+ r q.v

797+ mn (^mul mn 10)

798+ mp (^mul mp 10)

799+ ==

800+ =+ l=(^lth (^mul r 2) mn) :: in lower bound

801+ =+ ^= h :: in upper bound

802+ ?| (^lth (^mul s 2) mp)

803+ (gth (^mul r 2) (^sub (^mul s 2) mp))

804+ ==

805+ ?: &(!l !h)

806+ $(o (^add (^mul o 10) u))

807+ =+ q=&(h |(!l (gth (^mul r 2) s)))

808+ =. o (^add (^mul o 10) ?:(q +(u) u))

809+ [k o]

810+```

811+

812+#### Examples

813+

814+```

815+> (sun:fl 218.116)

816+[%f s=%.y e=-95 a=8.640.464.947.480.640.129.276.716.135.743.488]

817+> (^drg:fl [e=-95 a=8.640.464.947.480.640.129.276.716.135.743.488])

818+[--0 218.116]

819+

820+> (sun:fl 102.057.673.128.349)

821+[%f s=%.y e=-66 a=7.530.527.107.827.833.883.675.587.233.447.936]

822+> (^drg:fl [e=-66 a=7.530.527.107.827.833.883.675.587.233.447.936])

823+[--0 102.057.673.128.349]

824+```

825+

826+---

827+

828+### `^toj:fl`

835829

836830Round to integer

837831

@@ -848,27 +842,27 @@ An `fn`.

848842#### Source

849843

850844```hoon

851− ++ toj

852− |= [a=[e=@s a=@u]] ^- fn

853− ?. =((cmp:si e.a --0) -1) [%f & a]

854− =+ x=(abs:si e.a)

855− =+ y=(rsh 0 x a.a)

856− ?: |(=(r %d) =(r %z)) [%f & --0 y]

857− =+ z=(end 0 x a.a)

858− ?: |(=(r %u) =(r %a)) [%f & --0 ?~(z y +(y))]

859− =+ i=(bex (dec x))

860− ?: &(=(z i) =((dis y 1) 0)) [%f & --0 y]

861− ?: (^lth z i) [%f & --0 y] [%f & --0 +(y)]

845+++ toj

846+ |= [a=[e=@s a=@u]] ^- fn

847+ ?. =((cmp:si e.a --0) -1) [%f & a]

848+ =+ x=(abs:si e.a)

849+ =+ y=(rsh [0 x] a.a)

850+ ?: |(=(r %d) =(r %z)) [%f & --0 y]

851+ =+ z=(end [0 x] a.a)

852+ ?: |(=(r %u) =(r %a)) [%f & --0 ?~(z y +(y))]

853+ =+ i=(bex (dec x))

854+ ?: &(=(z i) =((dis y 1) 0)) [%f & --0 y]

855+ ?: (^lth z i) [%f & --0 y] [%f & --0 +(y)]

862856```

863857

864858#### Examples

865859

866860```

867− > (^toj:fl [-11 7.530.107.827.833.587])

868− [%f s=%.y e=--0 a=3.676.810.462.809]

861+> (^toj:fl [-11 7.530.107.827.833.587])

862+[%f s=%.y e=--0 a=3.676.810.462.809]

869863

870− > (^toj:fl [-11 7.530.107.827.833.589])

871− [%f s=%.y e=--0 a=3.676.810.462.809]

864+> (^toj:fl [-11 7.530.107.827.833.589])

865+[%f s=%.y e=--0 a=3.676.810.462.809]

872866```

873867

874868---

@@ -891,26 +885,26 @@ A cell of a signed integer and an unsigned integer.

891885#### Source

892886

893887```hoon

894− ++ ned

895− |= [a=fn] ^- [$f s=? e=@s a=@u]

896− ?: ?=([$f *] a) a

897− ~_ leaf+"need-float"

898− !!

888+++ ned

889+ |= [a=fn] ^- [%f s=? e=@s a=@u]

890+ ?: ?=([%f *] a) a

891+ ~_ leaf+"need-float"

892+ !!

899893```

900894

901895#### Examples

902896

903897```

904− > (ned:fl [%f s=%.y e=-11 a=7.530.107.827.833.587])

905− [%f s=%.y e=-11 a=7.530.107.827.833.587]

898+> (ned:fl [%f s=%.y e=-11 a=7.530.107.827.833.587])

899+[%f s=%.y e=-11 a=7.530.107.827.833.587]

906900

907− > (ned:fl [%n ~])

908− ! need-float

909− ! exit

901+> (ned:fl [%n ~])

902+! need-float

903+! exit

910904

911− > (ned:fl [%i |])

912− ! need-float

913− ! exit

905+> (ned:fl [%i |])

906+! need-float

907+! exit

914908```

915909

916910---

@@ -935,23 +929,23 @@ An `fn`.

935929#### Source

936930

937931```hoon

938− ++ shf

939− |= [a=fn b=@s]

940− ?: |(?=([$n *] a) ?=([$i *] a)) a

941− a(e (sum:si e.a b))

932+++ shf

933+ |= [a=fn b=@s]

934+ ?: |(?=([%n *] a) ?=([%i *] a)) a

935+ a(e (sum:si e.a b))

942936```

943937

944938#### Examples

945939

946940```

947− > (shf:fl [[%f & -2 7] --2])

948− [%f s=%.y e=--0 a=7]

941+> (shf:fl [[%f & -2 7] --2])

942+[%f s=%.y e=--0 a=7]

949943

950− > (shf:fl [[%f & -2 7] -2])

951− [%f s=%.y e=-4 a=7]

944+> (shf:fl [[%f & -2 7] -2])

945+[%f s=%.y e=-4 a=7]

952946

953− > (shf:fl [%f & -11 7.530.107.827.833.587] --5)

954− [%f s=%.y e=-6 a=7.530.107.827.833.587]

947+> (shf:fl [%f & -11 7.530.107.827.833.587] --5)

948+[%f s=%.y e=-6 a=7.530.107.827.833.587]

955949```

956950

957951---

@@ -973,22 +967,22 @@ An `fn`.

973967#### Source

974968

975969```hoon

976− ++ fli

977− |= [a=fn] ^- fn

978− ?-(-.a $f a(s !s.a), $i a(s !s.a), $n a)

970+++ fli

971+ |= [a=fn] ^- fn

972+ ?-(-.a %f a(s !s.a), %i a(s !s.a), %n a)

979973```

980974

981975#### Examples

982976

983977```

984− > (fli:fl [%f %.y -2 7])

985− [%f s=%.n e=-2 a=7]

978+> (fli:fl [%f %.y -2 7])

979+[%f s=%.n e=-2 a=7]

986980

987− > (fli:fl [%f %.n --2 30.617])

988− [%f s=%.y e=--2 a=30.617]

981+> (fli:fl [%f %.n --2 30.617])

982+[%f s=%.y e=--2 a=30.617]

989983

990− > (fli:fl [%f | --2 30.617])

991− [%f s=%.y e=--2 a=30.617]

984+> (fli:fl [%f | --2 30.617])

985+[%f s=%.y e=--2 a=30.617]

992986```

993987

994988---

@@ -1002,21 +996,21 @@ Switches the rounding mode of `r:fl`.

1002996#### Source

1003997

1004998```hoon

1005− ++ swr ?+(r r $d %u, $u %d)

999+++ swr ?+(r r %d %u, %u %d)

10061000```

10071001

10081002#### Examples

10091003

10101004```

1011− > r:fl

1012− %n

1013− > swr:fl

1014− %n

1005+> r:fl

1006+%n

1007+> swr:fl

1008+%n

10151009

1016− > =new-fl fl :: new fl core with changed state

1017− > =new-fl new-fl(r %u)

1018− > swr:new-fl

1019− %d

1010+> =new-fl fl :: new fl core with changed state

1011+> =new-fl new-fl(r %u)

1012+> swr:new-fl

1013+%d

10201014```

10211015

10221016---

@@ -1031,23 +1025,23 @@ Otherwise, a crash is produced.

10311025#### Source

10321026

10331027```hoon

1034− ++ prc ?>((gth p 1) p)

1028+++ prc ?>((gth p 1) p)

10351029```

10361030

10371031#### Examples

10381032

10391033```

1040− > prc:fl

1041− 113

1034+> prc:fl

1035+113

10421036

1043− > =new-fl fl

1044− > =new-fl new-fl(p 1)

1045− > prc:new-fl

1046− ! exit

1037+> =new-fl fl

1038+> =new-fl new-fl(p 1)

1039+> prc:new-fl

1040+! exit

10471041

1048− > =new-fl new-fl(p 2)

1049− > prc:new-fl

1050− 2

1042+> =new-fl new-fl(p 2)

1043+> prc:new-fl

1044+2

10511045```

10521046

10531047---

@@ -1061,26 +1055,26 @@ Produces `d:fl`. Denormalizes if `d:fl` is `%d`. Flushes denormals to zero if

10611055

10621056- Denormalizes if `d:fl` is `%d`.

10631057- Flushes denormals to zero if `d:fl` is `%f`.

1064−- Infinite exponent range if `$d` is `$i`.

1058+- Infinite exponent range if `%d` is `%i`.

10651059

10661060The default value of `d` is `%d`.

10671061

10681062#### Source

10691063

10701064```hoon

1071− ++ den d

1065+++ den d

10721066```

10731067

10741068#### Examples

10751069

10761070```

1077− > den:fl

1078− %d

1071+> den:fl

1072+%d

10791073

1080− > =new-fl fl

1081− > =new-fl new-fl(d %f)

1082− > den:new-fl

1083− %f

1074+> =new-fl fl

1075+> =new-fl new-fl(d %f)

1076+> den:new-fl

1077+%f

10841078```

10851079

10861080---

@@ -1094,14 +1088,14 @@ Produces `v:fl`, the minimum exponent. The default minimum exponent is -16.494.

10941088#### Source

10951089

10961090```hoon

1097− ++ emn v

1091+++ emn v

10981092```

10991093

11001094#### Examples

11011095

11021096```

1103− > emn:fl

1104− -16.494

1097+> emn:fl

1098+-16.494

11051099```

11061100

11071101---

@@ -1115,17 +1109,17 @@ Returns the maximum exponent of `fl`. The default maximum exponent is --16.271.

11151109#### Source

11161110

11171111```hoon

1118− ++ emx (sum:si emn (sun:si w))

1112+++ emx (sum:si emn (sun:si w))

11191113```

11201114

11211115#### Examples

11221116

11231117```

1124− > emx:fl

1125− --16.271

1118+> emx:fl

1119+--16.271

11261120

1127− > `@u`emx:fl

1128− 32.542

1121+> `@u`emx:fl

1122+32.542

11291123```

11301124

11311125---

@@ -1139,14 +1133,14 @@ Produces the smallest possible denormalized float.

11391133#### Source

11401134

11411135```hoon

1142− ++ spd [e=emn a=1]

1136+++ spd [e=emn a=1]

11431137```

11441138

11451139#### Examples

11461140

11471141```

1148− > spd:fl

1149− [e=-16.494 a=1]

1142+> spd:fl

1143+[e=-16.494 a=1]

11501144```

11511145

11521146---

@@ -1160,14 +1154,14 @@ Produces the smallest representable normal float.

11601154#### Source

11611155

11621156```hoon

1163− ++ spn [e=emn a=(bex (dec prc))]

1157+++ spn [e=emn a=(bex (dec prc))]

11641158```

11651159

11661160#### Examples

11671161

11681162```

1169− > spn:fl

1170− [e=-16.494 a=5.192.296.858.534.827.628.530.496.329.220.096]

1163+> spn:fl

1164+[e=-16.494 a=5.192.296.858.534.827.628.530.496.329.220.096]

11711165```

11721166

11731167---

@@ -1181,14 +1175,14 @@ Produces the largest representable normal float.

11811175#### Source

11821176

11831177```hoon

1184− ++ lfn [e=emx a=(fil 0 prc 1)]

1178+++ lfn [e=emx a=(fil 0 prc 1)]

11851179```

11861180

11871181#### Examples

11881182

11891183```

1190− > lfn:fl

1191− [e=--16.271 a=10.384.593.717.069.655.257.060.992.658.440.191]

1184+> lfn:fl

1185+[e=--16.271 a=10.384.593.717.069.655.257.060.992.658.440.191]

11921186```

11931187

11941188---

@@ -1202,14 +1196,14 @@ Produces the sum of `emx:fl` plus `prc:fl`.

12021196#### Source

12031197

12041198```hoon

1205− ++ lfe (sum:si emx (sun:si prc)) :: 2^lfe is > than all

1199+++ lfe (sum:si emx (sun:si prc))

12061200```

12071201

12081202#### Examples

12091203

12101204```

1211− > lfe:fl

1212− --16.384

1205+> lfe:fl

1206+--16.384

12131207```

12141208

12151209---

@@ -1223,16 +1217,14 @@ Produces zero represented as a float.

12231217#### Source

12241218

12251219```hoon

1226− ++ zer [e=--0 a=0]

1227− --

1228− |%

1220+++ zer [e=--0 a=0]

12291221```

12301222

12311223#### Examples

12321224

12331225```

1234− > zer:fl

1235− [e=--0 a=0]

1226+> zer:fl

1227+[e=--0 a=0]

12361228```

12371229

12381230---

@@ -1254,29 +1246,29 @@ An `fn`.

12541246#### Source

12551247

12561248```hoon

1257− ++ rou

1258− |= [a=fn] ^- fn

1259− ?. ?=([$f *] a) a

1260− ?~ a.a [%f s.a zer]

1261− ?: s.a (^rou +>.a)

1262− =.(r swr (fli (^rou +>.a)))

1249+++ rou

1250+ |= [a=fn] ^- fn

1251+ ?. ?=([%f *] a) a

1252+ ?~ a.a [%f s.a zer]

1253+ ?: s.a (^rou +>.a)

1254+ =.(r swr (fli (^rou +>.a)))

12631255```

12641256

12651257#### Examples

12661258

12671259```

1268− > =a 10.161.487.211.429.486.882.397.572.894.294.017.777

1269− > (rou:fl [%f & --12 a])

1270− [%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

1260+> =a 10.161.487.211.429.486.882.397.572.894.294.017.777

1261+> (rou:fl [%f & --12 a])

1262+[%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

12711263

1272− > (rou:fl [%f & --12 (add a 1)])

1273− [%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

1264+> (rou:fl [%f & --12 (add a 1)])

1265+[%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

12741266

1275− > (rou:fl [%f & --12 (add a 300)])

1276− [%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

1267+> (rou:fl [%f & --12 (add a 300)])

1268+[%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.002]

12771269

1278− > (rou:fl [%f & --12 (add a 1.000)])

1279− [%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.003]

1270+> (rou:fl [%f & --12 (add a 1.000)])

1271+[%f s=%.y e=--22 a=9.923.327.354.911.608.283.591.379.779.584.003]

12801272```

12811273

12821274---

@@ -1298,19 +1290,19 @@ An `fn`.

12981290#### Source

12991291

13001292```hoon

1301− ++ syn

1302− |= [a=fn] ^- ?

1303− ?-(-.a $f s.a, $i s.a, $n &)

1293+++ syn

1294+ |= [a=fn] ^- ?

1295+ ?-(-.a %f s.a, %i s.a, %n &)

13041296```

13051297

13061298#### Examples

13071299

13081300```

1309− > (syn:fl (sun:fl 106))

1310− %.y

1301+> (syn:fl (sun:fl 106))

1302+%.y

13111303

1312− > (syn:fl [%f | --0 106])

1313− %.n

1304+> (syn:fl [%f | --0 106])

1305+%.n

13141306```

13151307

13161308---

@@ -1332,20 +1324,20 @@ An `fn`.

13321324#### Sources

13331325

13341326```hoon

1335− ++ abs

1336− |= [a=fn] ^- fn

1337− ?: ?=([$f *] a) [%f & e.a a.a]

1338− ?: ?=([$i *] a) [%i &] [%n ~]

1327+++ abs

1328+ |= [a=fn] ^- fn

1329+ ?: ?=([%f *] a) [%f & e.a a.a]

1330+ ?: ?=([%i *] a) [%i &] [%n ~]

13391331```

13401332

13411333#### Examples

13421334

13431335```

1344− > (abs:fl [%f | --0 106])

1345− [%f s=%.y e=--0 a=106]

1336+> (abs:fl [%f | --0 106])

1337+[%f s=%.y e=--0 a=106]

13461338

1347− > (abs:fl [%f & --0 106])

1348− [%f s=%.y e=--0 a=106]

1339+> (abs:fl [%f & --0 106])

1340+[%f s=%.y e=--0 a=106]

13491341```

13501342

13511343---

@@ -1369,32 +1361,32 @@ An `fn`.

13691361#### Source

13701362

13711363```hoon

1372− ++ add

1373− |= [a=fn b=fn] ^- fn

1374− ?: |(?=([$n *] a) ?=([$n *] b)) [%n ~]

1375− ?: |(?=([$i *] a) ?=([$i *] b))

1376− ?: &(?=([$i *] a) ?=([$i *] b))

1377− ?: =(a b) a [%n ~]

1378− ?: ?=([$i *] a) a b

1379− ?: |(=(a.a 0) =(a.b 0))

1380− ?. &(=(a.a 0) =(a.b 0)) %- rou ?~(a.a b a)

1381− [%f ?:(=(r %d) &(s.a s.b) |(s.a s.b)) zer]

1382− %- |= [a=fn]

1383− ?. ?=([$f *] a) a

1384− ?. =(a.a 0) a

1385− [%f !=(r %d) zer]

1386− ?: =(s.a s.b)

1387− ?: s.a (^add +>.a +>.b |)

1388− =.(r swr (fli (^add +>.a +>.b |)))

1389− ?: s.a (^sub +>.a +>.b |)

1390− (^sub +>.b +>.a |)

1364+++ add

1365+ |= [a=fn b=fn] ^- fn

1366+ ?: |(?=([%n *] a) ?=([%n *] b)) [%n ~]

1367+ ?: |(?=([%i *] a) ?=([%i *] b))

1368+ ?: &(?=([%i *] a) ?=([%i *] b))

1369+ ?: =(a b) a [%n ~]

1370+ ?: ?=([%i *] a) a b

1371+ ?: |(=(a.a 0) =(a.b 0))

1372+ ?. &(=(a.a 0) =(a.b 0)) %- rou ?~(a.a b a)

1373+ [%f ?:(=(r %d) &(s.a s.b) |(s.a s.b)) zer]

1374+ %- |= [a=fn]

1375+ ?. ?=([%f *] a) a

1376+ ?. =(a.a 0) a

1377+ [%f !=(r %d) zer]

1378+ ?: =(s.a s.b)

1379+ ?: s.a (^add +>.a +>.b |)

1380+ =.(r swr (fli (^add +>.a +>.b |)))

1381+ ?: s.a (^sub +>.a +>.b |)

1382+ (^sub +>.b +>.a |)

13911383```

13921384

13931385#### Examples

13941386

13951387```

1396− > (add:fl [%f & --0 106] [%f | --3 55])

1397− [%f s=%.n e=-104 a=6.774.324.807.619.657.921.598.381.929.529.344]

1388+> (add:fl [%f & --0 106] [%f | --3 55])

1389+[%f s=%.n e=-104 a=6.774.324.807.619.657.921.598.381.929.529.344]

13981390```

13991391

14001392---

@@ -1418,33 +1410,32 @@ An `fn`.

14181410#### Source

14191411

14201412```hoon

1421− ++ ead

1422− |= [a=fn b=fn] ^- fn

1423− ?: |(?=([$n *] a) ?=([$n *] b)) [%n ~]

1424− ?: |(?=([$i *] a) ?=([$i *] b))

1425− ?: &(?=([$i *] a) ?=([$i *] b))

1426− ?: =(a b) a [%n ~]

1427− ?: ?=([$i *] a) a b

1428− ?: |(=(a.a 0) =(a.b 0))

1429− ?. &(=(a.a 0) =(a.b 0)) ?~(a.a b a)

1430− [%f ?:(=(r %d) &(s.a s.b) |(s.a s.b)) zer]

1431− %- |= [a=fn]

1432− ?. ?=([$f *] a) a

1433− ?. =(a.a 0) a

1434− [%f !=(r %d) zer]

1435− ?: =(s.a s.b)

1436− ?: s.a (^add +>.a +>.b &)

1437− (fli (^add +>.a +>.b &))

1438− ?: s.a (^sub +>.a +>.b &)

1439− (^sub +>.b +>.a &)

1440− ::

1413+++ ead

1414+ |= [a=fn b=fn] ^- fn

1415+ ?: |(?=([%n *] a) ?=([%n *] b)) [%n ~]

1416+ ?: |(?=([%i *] a) ?=([%i *] b))

1417+ ?: &(?=([%i *] a) ?=([%i *] b))

1418+ ?: =(a b) a [%n ~]

1419+ ?: ?=([%i *] a) a b

1420+ ?: |(=(a.a 0) =(a.b 0))

1421+ ?. &(=(a.a 0) =(a.b 0)) ?~(a.a b a)

1422+ [%f ?:(=(r %d) &(s.a s.b) |(s.a s.b)) zer]

1423+ %- |= [a=fn]

1424+ ?. ?=([%f *] a) a

1425+ ?. =(a.a 0) a

1426+ [%f !=(r %d) zer]

1427+ ?: =(s.a s.b)

1428+ ?: s.a (^add +>.a +>.b &)

1429+ (fli (^add +>.a +>.b &))

1430+ ?: s.a (^sub +>.a +>.b &)

1431+ (^sub +>.b +>.a &)

14411432```

14421433

14431434#### Examples

14441435

14451436```

1446− > (ead:fl [%f & --0 106] [%f | --3 55])

1447− [%f s=%.n e=--0 a=334]

1437+> (ead:fl [%f & --0 106] [%f | --3 55])

1438+[%f s=%.n e=--0 a=334]

14481439```

14491440

14501441---

@@ -1468,15 +1459,15 @@ An `fn`.

14681459#### Source

14691460

14701461```hoon

1471− ++ sub

1472− |= [a=fn b=fn] ^- fn (add a (fli b))

1462+++ sub

1463+ |= [a=fn b=fn] ^- fn (add a (fli b))

14731464```

14741465

14751466#### Examples

14761467

14771468```

1478− > (sub:fl [%f & --13 2.718] [%f & --23 11])

1479− [%f s=%.n e=-86 a=5.416.671.014.775.224.232.595.412.796.571.648]

1469+> (sub:fl [%f & --13 2.718] [%f & --23 11])

1470+[%f s=%.n e=-86 a=5.416.671.014.775.224.232.595.412.796.571.648]

14801471```

14811472

14821473---

@@ -1500,18 +1491,18 @@ An `fn`.

15001491#### Source

15011492

15021493```hoon

1503− ++ mul

1504− |= [a=fn b=fn] ^- fn

1505− ?: |(?=([$n *] a) ?=([$n *] b)) [%n ~]

1506− ?: ?=([$i *] a)

1507− ?: ?=([$i *] b)

1508− [%i =(s.a s.b)]

1509− ?: =(a.b 0) [%n ~] [%i =(s.a s.b)]

1510− ?: ?=([$i *] b)

1511− ?: =(a.a 0) [%n ~] [%i =(s.a s.b)]

1512− ?: |(=(a.a 0) =(a.b 0)) [%f =(s.a s.b) zer]

1513− ?: =(s.a s.b) (^mul +>.a +>.b)

1514− =.(r swr (fli (^mul +>.a +>.b)))

1494+++ mul

1495+ |= [a=fn b=fn] ^- fn

1496+ ?: |(?=([%n *] a) ?=([%n *] b)) [%n ~]

1497+ ?: ?=([%i *] a)

1498+ ?: ?=([%i *] b)

1499+ [%i =(s.a s.b)]

1500+ ?: =(a.b 0) [%n ~] [%i =(s.a s.b)]

1501+ ?: ?=([%i *] b)

1502+ ?: =(a.a 0) [%n ~] [%i =(s.a s.b)]

1503+ ?: |(=(a.a 0) =(a.b 0)) [%f =(s.a s.b) zer]

1504+ ?: =(s.a s.b) (^mul +>.a +>.b)

1505+ =.(r swr (fli (^mul +>.a +>.b)))

15151506```

15161507

15171508---

@@ -1534,18 +1525,18 @@ An `fn`.

15341525

15351526#### Examples

15361527

1537−```

1538− ++ emu

1539− |= [a=fn b=fn] ^- fn

1540− ?: |(?=([$n *] a) ?=([$n *] b)) [%n ~]

1541− ?: ?=([$i *] a)

1542− ?: ?=([$i *] b)

1543− [%i =(s.a s.b)]

1544− ?: =(a.b 0) [%n ~] [%i =(s.a s.b)]

1545− ?: ?=([$i *] b)

1546− ?: =(a.a 0) [%n ~] [%i =(s.a s.b)]

1547− ?: |(=(a.a 0) =(a.b 0)) [%f =(s.a s.b) zer]

1548− [%f =(s.a s.b) (sum:si e.a e.b) (^^mul a.a a.b)]

1528+```hoon

1529+++ emu

1530+ |= [a=fn b=fn] ^- fn

1531+ ?: |(?=([%n *] a) ?=([%n *] b)) [%n ~]

1532+ ?: ?=([%i *] a)

1533+ ?: ?=([%i *] b)

1534+ [%i =(s.a s.b)]

1535+ ?: =(a.b 0) [%n ~] [%i =(s.a s.b)]

1536+ ?: ?=([%i *] b)

1537+ ?: =(a.a 0) [%n ~] [%i =(s.a s.b)]

1538+ ?: |(=(a.a 0) =(a.b 0)) [%f =(s.a s.b) zer]

1539+ [%f =(s.a s.b) (sum:si e.a e.b) (^^mul a.a a.b)]

15491540```

15501541

15511542---

@@ -1566,19 +1557,19 @@ Produces the quotient of `a` divided by `b`.

15661557

15671558An `fn`.

15681559

1569−#### Divide

1560+#### Source

15701561

15711562```hoon

1572− ++ div

1573− |= [a=fn b=fn] ^- fn

1574− ?: |(?=([$n *] a) ?=([$n *] b)) [%n ~]

1575− ?: ?=([$i *] a)

1576− ?: ?=([$i *] b) [%n ~] [%i =(s.a s.b)]

1577− ?: ?=([$i *] b) [%f =(s.a s.b) zer]

1578− ?: =(a.a 0) ?: =(a.b 0) [%n ~] [%f =(s.a s.b) zer]

1579− ?: =(a.b 0) [%i =(s.a s.b)]

1580− ?: =(s.a s.b) (^div +>.a +>.b)

1581− =.(r swr (fli (^div +>.a +>.b)))

1563+++ div

1564+ |= [a=fn b=fn] ^- fn

1565+ ?: |(?=([%n *] a) ?=([%n *] b)) [%n ~]

1566+ ?: ?=([%i *] a)

1567+ ?: ?=([%i *] b) [%n ~] [%i =(s.a s.b)]

1568+ ?: ?=([%i *] b) [%f =(s.a s.b) zer]

1569+ ?: =(a.a 0) ?: =(a.b 0) [%n ~] [%f =(s.a s.b) zer]

1570+ ?: =(a.b 0) [%i =(s.a s.b)]

1571+ ?: =(s.a s.b) (^div +>.a +>.b)

1572+ =.(r swr (fli (^div +>.a +>.b)))

15821573```

15831574

15841575---

@@ -1605,16 +1596,16 @@ An `fn`.

16051596#### Source

16061597

16071598```hoon

1608− ++ fma

1609− |= [a=fn b=fn c=fn] ^- fn

1610− (add (emu a b) c)

1599+++ fma

1600+ |= [a=fn b=fn c=fn] ^- fn

1601+ (add (emu a b) c)

16111602```

16121603

16131604#### Examples

16141605

16151606```

1616− > (fma:fl [%f & --13 2.718] [%f & --23 11] [%f & --13 2.718])

1617− [%f s=%.y e=-62 a=9.475.054.514.089.037.465.004.673.635.188.736]=

1607+> (fma:fl [%f & --13 2.718] [%f & --23 11] [%f & --13 2.718])

1608+[%f s=%.y e=-62 a=9.475.054.514.089.037.465.004.673.635.188.736]=

16181609```

16191610

16201611---

@@ -1636,19 +1627,19 @@ An `fn`.

16361627#### Source

16371628

16381629```hoon

1639− ++ sqt

1640− |= [a=fn] ^- fn

1641− ?: ?=([$n *] a) [%n ~]

1642− ?: ?=([$i *] a) ?:(s.a a [%n ~])

1643− ?~ a.a [%f s.a zer]

1644− ?: s.a (^sqt +>.a) [%n ~]

1630+++ sqt

1631+ |= [a=fn] ^- fn

1632+ ?: ?=([%n *] a) [%n ~]

1633+ ?: ?=([%i *] a) ?:(s.a a [%n ~])

1634+ ?~ a.a [%f s.a zer]

1635+ ?: s.a (^sqt +>.a) [%n ~]

16451636```

16461637

16471638#### Examples

16481639

16491640```

1650− > (sqt:fl [%f s=%.y e=-18 a=342.602.577])

1651− [%f s=%.y e=-107 a=5.865.903.143.604.945.574.132.671.852.050.553]

1641+> (sqt:fl [%f s=%.y e=-18 a=342.602.577])

1642+[%f s=%.y e=-107 a=5.865.903.143.604.945.574.132.671.852.050.553]

16521643```

16531644

16541645---

@@ -1670,28 +1661,28 @@ An `fn`.

16701661#### Source

16711662

16721663```hoon

1673− ++ inv

1674− |= [a=fn] ^- fn

1675− (div [%f & --0 1] a)

1664+++ inv

1665+ |= [a=fn] ^- fn

1666+ (div [%f & --0 1] a)

16761667```

16771668

16781669#### Examples

16791670

16801671```

1681− > (inv:fl [%f s=%.y e=--0 a=10])

1682− [%f s=%.y e=-116 a=8.307.674.973.655.724.205.648.794.126.752.154]

1683− > (drg:fl [%f s=%.y e=-116 a=8.307.674.973.655.724.205.648.794.126.752.154])

1684− [%d s=%.y e=-1 a=1]

1672+> (inv:fl [%f s=%.y e=--0 a=10])

1673+[%f s=%.y e=-116 a=8.307.674.973.655.724.205.648.794.126.752.154]

1674+> (drg:fl [%f s=%.y e=-116 a=8.307.674.973.655.724.205.648.794.126.752.154])

1675+[%d s=%.y e=-1 a=1]

16851676

1686− > (inv:fl [%f s=%.y e=--1 a=10])

1687− [%f s=%.y e=-117 a=8.307.674.973.655.724.205.648.794.126.752.154]

1688− > (drg:fl [%f s=%.y e=-117 a=8.307.674.973.655.724.205.648.794.126.752.154])

1689− [%d s=%.y e=-2 a=5]

1677+> (inv:fl [%f s=%.y e=--1 a=10])

1678+[%f s=%.y e=-117 a=8.307.674.973.655.724.205.648.794.126.752.154]

1679+> (drg:fl [%f s=%.y e=-117 a=8.307.674.973.655.724.205.648.794.126.752.154])

1680+[%d s=%.y e=-2 a=5]

16901681

1691− > (inv:fl [%f s=%.y e=--2 a=10])

1692− [%f s=%.y e=-118 a=8.307.674.973.655.724.205.648.794.126.752.154]

1693− > (drg:fl [%f s=%.y e=-118 a=8.307.674.973.655.724.205.648.794.126.752.154])

1694− [%d s=%.y e=-3 a=25]

1682+> (inv:fl [%f s=%.y e=--2 a=10])

1683+[%f s=%.y e=-118 a=8.307.674.973.655.724.205.648.794.126.752.154]

1684+> (drg:fl [%f s=%.y e=-118 a=8.307.674.973.655.724.205.648.794.126.752.154])

1685+[%d s=%.y e=-3 a=25]

16951686```

16961687

16971688---

@@ -1713,22 +1704,22 @@ An `fn`.

17131704#### Source

17141705

17151706```hoon

1716− ++ sun

1717− |= [a=@u] ^- fn

1718− (rou [%f & --0 a])

1707+++ sun

1708+ |= [a=@u] ^- fn

1709+ (rou [%f & --0 a])

17191710```

17201711

17211712#### Examples

17221713

17231714```

1724− > (sun:fl 0)

1725− [%f s=%.y e=--0 a=0]

1715+> (sun:fl 0)

1716+[%f s=%.y e=--0 a=0]

17261717

1727− > (sun:fl 5.048.729)

1728− [%f s=%.y e=-90 a=6.250.023.776.601.238.669.911.180.544.311.296]

1718+> (sun:fl 5.048.729)

1719+[%f s=%.y e=-90 a=6.250.023.776.601.238.669.911.180.544.311.296]

17291720

1730− > (sun:fl -100)

1731− ! exit

1721+> (sun:fl -100)

1722+! exit

17321723```

17331724

17341725---

@@ -1750,20 +1741,20 @@ An `fn`.

17501741#### Source

17511742

17521743```hoon

1753− ++ san

1754− |= [a=@s] ^- fn

1755− =+ b=(old:si a)

1756− (rou [%f -.b --0 +.b])

1744+++ san

1745+ |= [a=@s] ^- fn

1746+ =+ b=(old:si a)

1747+ (rou [%f -.b --0 +.b])

17571748```

17581749

17591750#### Examples

17601751

17611752```

1762− > (san:fl --100)

1763− [%f s=%.y e=-106 a=8.112.963.841.460.668.169.578.900.514.406.400]

1753+> (san:fl --100)

1754+[%f s=%.y e=-106 a=8.112.963.841.460.668.169.578.900.514.406.400]

17641755

1765− > (san:fl -100)

1766− [%f s=%.n e=-106 a=8.112.963.841.460.668.169.578.900.514.406.400]

1756+> (san:fl -100)

1757+[%f s=%.n e=-106 a=8.112.963.841.460.668.169.578.900.514.406.400]

17671758```

17681759

17691760---

@@ -1788,29 +1779,29 @@ A `unit` of `flag`.

17881779#### Source

17891780

17901781```hoon

1791− ++ lth

1792− |= [a=fn b=fn] ^- (unit ?)

1793− ?: |(?=([$n *] a) ?=([$n *] b)) ~ :- ~

1794− ?: =(a b) |

1795− ?: ?=([$i *] a) !s.a ?: ?=([$i *] b) s.b

1796− ?: |(=(a.a 0) =(a.b 0))

1797− ?: &(=(a.a 0) =(a.b 0)) |

1798− ?: =(a.a 0) s.b !s.a

1799− ?: !=(s.a s.b) s.b

1800− ?: s.a (^lth +>.a +>.b) (^lth +>.b +>.a)

1782+++ lth

1783+ |= [a=fn b=fn] ^- (unit ?)

1784+ ?: |(?=([%n *] a) ?=([%n *] b)) ~ :- ~

1785+ ?: =(a b) |

1786+ ?: ?=([%i *] a) !s.a ?: ?=([%i *] b) s.b

1787+ ?: |(=(a.a 0) =(a.b 0))

1788+ ?: &(=(a.a 0) =(a.b 0)) |

1789+ ?: =(a.a 0) s.b !s.a

1790+ ?: !=(s.a s.b) s.b

1791+ ?: s.a (^lth +>.a +>.b) (^lth +>.b +>.a)

18011792```

18021793

18031794#### Examples

18041795

18051796```

1806− > (lth:fl (sun:fl 116) (sun:fl 4.820))

1807− [~ u=%.y]

1797+> (lth:fl (sun:fl 116) (sun:fl 4.820))

1798+[~ u=%.y]

18081799

1809− > (lth:fl (sun:fl 218.116) (sun:fl 4.820))

1810− [~ u=%.n]

1800+> (lth:fl (sun:fl 218.116) (sun:fl 4.820))

1801+[~ u=%.n]

18111802

1812− > (lth:fl (sun:fl 218.116) [%n ~])

1813− ~

1803+> (lth:fl (sun:fl 218.116) [%n ~])

1804+~

18141805```

18151806

18161807---

@@ -1835,28 +1826,28 @@ A `unit` of `flag`.

18351826#### Source

18361827

18371828```hoon

1838− ++ lte

1839− |= [a=fn b=fn] ^- (unit ?)

1840− %+ bind (lth b a) |= a=? !a

1829+++ lte

1830+ |= [a=fn b=fn] ^- (unit ?)

1831+ %+ bind (lth b a) |= a=? !a

18411832```

18421833

18431834#### Examples

18441835

18451836```

1846− > (lte:fl (sun:fl 102) [%f %.y -5 973.655.724])

1847− [~ u=%.y]

1837+> (lte:fl (sun:fl 102) [%f %.y -5 973.655.724])

1838+[~ u=%.y]

18481839

1849− > (lte:fl (sun:fl 102) [%f %.y -24 973.655.724])

1850− [~ u=%.n]

1840+> (lte:fl (sun:fl 102) [%f %.y -24 973.655.724])

1841+[~ u=%.n]

18511842

1852− > (lte:fl [%f %.y --2 25] (sun:fl 100))

1853− [~ u=%.y]

1843+> (lte:fl [%f %.y --2 25] (sun:fl 100))

1844+[~ u=%.y]

18541845

1855− > (lte:fl [%f %.y --2 25] [%f %.y --3 2])

1856− [~ u=%.n]

1846+> (lte:fl [%f %.y --2 25] [%f %.y --3 2])

1847+[~ u=%.n]

18571848

1858− > (lte:fl [%f %.y --2 25] [%n ~])

1859− ~

1849+> (lte:fl [%f %.y --2 25] [%n ~])

1850+~

18601851```

18611852

18621853---

@@ -1881,25 +1872,25 @@ An `unit` of `flag`.

18811872#### Source

18821873

18831874```hoon

1884− ++ equ

1885− |= [a=fn b=fn] ^- (unit ?)

1886− ?: |(?=([$n *] a) ?=([$n *] b)) ~ :- ~

1887− ?: =(a b) &

1888− ?: |(?=([$i *] a) ?=([$i *] b)) |

1889− ?: |(=(a.a 0) =(a.b 0))

1890− ?: &(=(a.a 0) =(a.b 0)) & |

1891− ?: |(=(e.a e.b) !=(s.a s.b)) |

1892− (^equ +>.a +>.b)

1875+++ equ

1876+ |= [a=fn b=fn] ^- (unit ?)

1877+ ?: |(?=([%n *] a) ?=([%n *] b)) ~ :- ~

1878+ ?: =(a b) &

1879+ ?: |(?=([%i *] a) ?=([%i *] b)) |

1880+ ?: |(=(a.a 0) =(a.b 0))

1881+ ?: &(=(a.a 0) =(a.b 0)) & |

1882+ ?: |(=(e.a e.b) !=(s.a s.b)) |

1883+ (^equ +>.a +>.b)

18931884```

18941885

18951886#### Examples

18961887

18971888```

1898− > (equ:fl [%f %.y --2 25] (sun:fl 100))

1899− [~ u=%.y]

1889+> (equ:fl [%f %.y --2 25] (sun:fl 100))

1890+[~ u=%.y]

19001891

1901− > (equ:fl [%f %.y --2 25] (sun:fl 101))

1902− [~ u=%.n]

1892+> (equ:fl [%f %.y --2 25] (sun:fl 101))

1893+[~ u=%.n]

19031894```

19041895

19051896---

@@ -1924,21 +1915,21 @@ An `unit` of `flag`.

19241915#### Source

19251916

19261917```hoon

1927− ++ gte

1928− |= [a=fn b=fn] ^- (unit ?) (lte b a)

1918+++ gte

1919+ |= [a=fn b=fn] ^- (unit ?) (lte b a)

19291920```

19301921

19311922#### Examples

19321923

19331924```

1934− > (gte:fl [%f %.y --2 25] (sun:fl 100))

1935− [~ u=%.y]

1925+> (gte:fl [%f %.y --2 25] (sun:fl 100))

1926+[~ u=%.y]

19361927

1937− > (gth:fl [%f %.y --6 73.989] [%f %.y --5 919.599])

1938− [~ u=%.n]

1928+> (gth:fl [%f %.y --6 73.989] [%f %.y --5 919.599])

1929+[~ u=%.n]

19391930

1940− > (gth:fl [%f %.y --6 73.989] [%n ~])

1941− ~

1931+> (gth:fl [%f %.y --6 73.989] [%n ~])

1932+~

19421933```

19431934

19441935---

@@ -1963,18 +1954,18 @@ An `unit` of `flag`.

19631954#### Source

19641955

19651956```hoon

1966− ++ gth

1967− |= [a=fn b=fn] ^- (unit ?) (lth b a)

1957+++ gth

1958+ |= [a=fn b=fn] ^- (unit ?) (lth b a)

19681959```

19691960

19701961#### Examples

19711962

19721963```

1973− > (gth:fl [%f %.y --2 25] (sun:fl 100))

1974− [~ u=%.n]

1964+> (gth:fl [%f %.y --2 25] (sun:fl 100))

1965+[~ u=%.n]

19751966

1976− > (gth:fl [%f %.y --6 73.989] [%f %.y --5 119.599])

1977− [~ u=%.y]

1967+> (gth:fl [%f %.y --6 73.989] [%f %.y --5 119.599])

1968+[~ u=%.y]

19781969```

19791970

19801971---

@@ -1997,19 +1988,19 @@ A `dn`.

19971988#### Source

19981989

19991990```hoon

2000− ++ drg

2001− |= [a=fn] ^- dn

2002− ?: ?=([$n *] a) [%n ~]

2003− ?: ?=([$i *] a) [%i s.a]

2004− ?~ a.a [%d s.a --0 0]

2005− [%d s.a (^drg +>.a)]

1991+++ drg

1992+ |= [a=fn] ^- dn

1993+ ?: ?=([%n *] a) [%n ~]

1994+ ?: ?=([%i *] a) [%i s.a]

1995+ ?~ a.a [%d s.a --0 0]

1996+ [%d s.a (^drg +>.a)]

20061997```

20071998

20081999#### Examples

20092000

20102001```

2011− > (drg:fl [%f | --6 73.989])

2012− [%d s=%.n e=--0 a=4.735.296]

2002+> (drg:fl [%f | --6 73.989])

2003+[%d s=%.n e=--0 a=4.735.296]

20132004```

20142005

20152006---

@@ -2031,25 +2022,25 @@ An `fn`.

20312022#### Source

20322023

20332024```hoon

2034− ++ grd

2035− |= [a=dn] ^- fn

2036− ?: ?=([$n *] a) [%n ~]

2037− ?: ?=([$i *] a) [%i s.a]

2038− => .(r %n)

2039− =+ q=(abs:si e.a)

2040− ?: (syn:si e.a)

2041− (mul [%f s.a --0 a.a] [%f & e.a (pow 5 q)])

2042− (div [%f s.a --0 a.a] [%f & (sun:si q) (pow 5 q)])

2025+++ grd

2026+ |= [a=dn] ^- fn

2027+ ?: ?=([%n *] a) [%n ~]

2028+ ?: ?=([%i *] a) [%i s.a]

2029+ => .(r %n)

2030+ =+ q=(abs:si e.a)

2031+ ?: (syn:si e.a)

2032+ (mul [%f s.a --0 a.a] [%f & e.a (pow 5 q)])

2033+ (div [%f s.a --0 a.a] [%f & (sun:si q) (pow 5 q)])

20432034```

20442035

20452036#### Examples

20462037

20472038```

2048− > (grd:fl [%d s=%.n e=--0 a=73.989])

2049− [%f s=%.n e=-96 a=5.862.012.516.267.904.074.208.723.341.410.304]

2039+> (grd:fl [%d s=%.n e=--0 a=73.989])

2040+[%f s=%.n e=-96 a=5.862.012.516.267.904.074.208.723.341.410.304]

20502041

2051− > (grd:fl [%d s=%.n e=--0 a=100])

2052− [%f s=%.n e=-106 a=8.112.963.841.460.668.169.578.900.514.406.400]

2042+> (grd:fl [%d s=%.n e=--0 a=100])

2043+[%f s=%.n e=-106 a=8.112.963.841.460.668.169.578.900.514.406.400]

20532044```

20542045

20552046---

@@ -2066,24 +2057,24 @@ Rounds `a` to the nearest signed integer.

20662057

20672058#### Produces

20682059

2069−A `unit` of @s.

2060+A `unit` of `@s`.

20702061

20712062#### Source

20722063

20732064```hoon

2074− ++ toi

2075− |= [a=fn] ^- (unit @s)

2076− =+ b=(toj a)

2077− ?. ?=([$f *] b) ~ :- ~

2078− =+ c=(^^mul (bex (abs:si e.b)) a.b)

2079− (new:si s.b c)

2065+++ toi

2066+ |= [a=fn] ^- (unit @s)

2067+ =+ b=(toj a)

2068+ ?. ?=([%f *] b) ~ :- ~

2069+ =+ c=(^^mul (bex (abs:si e.b)) a.b)

2070+ (new:si s.b c)

20802071```

20812072

20822073#### Examples

20832074

20842075```

2085− > (toi:fl [%f s=%.y e=-78 a=8.112.963.841.460.668.169.578.900.514.406.400])

2086− [~ u=--26.843.545.600]

2076+> (toi:fl [%f s=%.y e=-78 a=8.112.963.841.460.668.169.578.900.514.406.400])

2077+[~ u=--26.843.545.600]

20872078```

20882079

20892080---

@@ -2100,34 +2091,33 @@ Rounds `a` to the nearest decimal integer.

21002091

21012092#### Produces

21022093

2103−A `unit` of @s.

2094+A `unit` of `@s`.

21042095

21052096#### Source

21062097

21072098```hoon

2108− ++ toj

2109− |= [a=fn] ^- fn

2110− ?. ?=([$f *] a) a

2111− ?~ a.a [%f s.a zer]

2112− ?: s.a (^toj +>.a)

2113− =.(r swr (fli (^toj +>.a)))

2114− --

2099+++ toj

2100+ |= [a=fn] ^- fn

2101+ ?. ?=([%f *] a) a

2102+ ?~ a.a [%f s.a zer]

2103+ ?: s.a (^toj +>.a)

2104+ =.(r swr (fli (^toj +>.a)))

21152105```

21162106

21172107#### Examples

21182108

21192109```

2120− > (toj:fl [%f s=%.y e=-78 a=8.112.963.841.460.668.169.578.900.514.406.400])

2121− [%f s=%.y e=--0 a=26.843.545.600]

2110+> (toj:fl [%f s=%.y e=-78 a=8.112.963.841.460.668.169.578.900.514.406.400])

2111+[%f s=%.y e=--0 a=26.843.545.600]

21222112

2123− > (toj:fl [%f s=%.y e=-78 a=8.112.963.841.460.668.169.578.900.514])

2124− [%f s=%.y e=--0 a=26.844]

2113+> (toj:fl [%f s=%.y e=-78 a=8.112.963.841.460.668.169.578.900.514])

2114+[%f s=%.y e=--0 a=26.844]

21252115

2126− > (toj:fl [%f s=%.y e=-78 a=8.112.963.841.460])

2127− [%f s=%.y e=--0 a=0]

2116+> (toj:fl [%f s=%.y e=-78 a=8.112.963.841.460])

2117+[%f s=%.y e=--0 a=0]

21282118

2129− > (toj:fl [%f s=%.y e=-9 a=9.002])

2130− [%f s=%.y e=--0 a=16]

2119+> (toj:fl [%f s=%.y e=-9 a=9.002])

2120+[%f s=%.y e=--0 a=16]

21312121```

21322122

21332123---

@@ -2141,23 +2131,22 @@ Container core for IEEE-754 formatting operations.

21412131- `w` is width: The number of bits in the exponent field.

21422132- `p` is precision: The number of bits in the significand field.

21432133- `w` is bias: Added to exponent when storing.

2144−- `r` is rounding mode: Possible modes are nearest (`$n`), up (`$u`),

2145− down (`$d`), to zero (`$z`), and away from zero (`$a`). Default value is `%a`.

2134+- `r` is rounding mode: Possible modes are nearest (`%n`), up (`%u`),

2135+ down (`%d`), to zero (`%z`), and away from zero (`%a`). Default value is `%a`.

21462136

21472137#### Source

21482138

21492139```hoon

2150− ++ ff

2151− |_ [[w=@u p=@u b=@s] r=$?($n $u $d $z $a)]

2140+++ ff

2141+ |_ [[w=@u p=@u b=@s] r=$?(%n %u %d %z %a)]

21522142```

21532143

21542144#### Examples

21552145

21562146```

2157− > =ffcore ~(. ff [8 8 0] %n)

2158− > ffcore

2159− <24.ltg {{{@ud @ud @ud} r/$n} <54.tyv 119.wim 31.ohr 1.jmk $143>}>

2160− >

2147+> =ffcore ~(. ff [8 8 0] %n)

2148+> ffcore

2149+<24.ltg {{{@ud @ud @ud} r/$n} <54.tyv 119.wim 31.ohr 1.jmk $143>}>

21612150```

21622151

21632152---

@@ -2179,14 +2168,14 @@ Produces the sign bit of `++ff`.

21792168#### Source

21802169

21812170```hoon

2182− ++ sb (bex (^add w p))

2171+++ sb (bex (^add w p))

21832172```

21842173

21852174#### Examples

21862175

21872176```

2188− > sb:ff

2189− 1

2177+> sb:ff

2178+1

21902179```

21912180

21922181---

@@ -2200,14 +2189,14 @@ Produces the minimum possible exponent of `ff`.

22002189#### Source

22012190

22022191```hoon

2203− ++ me (dif:si (dif:si --1 b) (sun:si p))

2192+++ me (dif:si (dif:si --1 b) (sun:si p))

22042193```

22052194

22062195#### Examples

22072196

22082197```

2209− > me:ff

2210− --1

2198+> me:ff

2199+--1

22112200```

22122201

22132202---

@@ -2222,20 +2211,20 @@ configuration of the `ff` core.

22222211#### Source

22232212

22242213```hoon

2225− ++ pa

2226− %*(. fl p +(p), v me, w (^sub (bex w) 3), d %d, r r)

2214+++ pa

2215+ %*(. fl p +(p), v me, w (^sub (bex w) 3), d %d, r r)

22272216```

22282217

22292218#### Examples

22302219

22312220```

2232− > ~(pa ff [11 52 --1.023] %n)

2233− < 23.qzd

2234− 28.btz

2235− { {{p/@ v/@s w/@} r/?($n $u $a $d $z) d/$d}

2236− <54.tyv 119.wim 31.ohr 1.jmk $143>

2237− }

2238− >

2221+> ~(pa ff [11 52 --1.023] %n)

2222+< 23.qzd

2223+ 28.btz

2224+ { {{p/@ v/@s w/@} r/?($n $u $a $d $z) d/$d}

2225+ <54.tyv 119.wim 31.ohr 1.jmk $143>

2226+ }

2227+>

22392228```

22402229

22412230#### Discussion

@@ -2257,29 +2246,29 @@ Converts `a` from `@r` to `fn`.

22572246

22582247#### Produces

22592248

2260−A `unit` of @s.

2249+A `unit` of `@s`.

22612250

22622251#### Source

22632252

22642253```hoon

2265− ++ sea

2266− |= [a=@r] ^- fn

2267− =+ [f=(cut 0 [0 p] a) e=(cut 0 [p w] a)]

2268− =+ s=(sig a)

2269− ?: =(e 0)

2270− ?: =(f 0) [%f s --0 0] [%f s me f]

2271− ?: =(e (fil 0 w 1))

2272− ?: =(f 0) [%i s] [%n ~]

2273− =+ q=:(sum:si (sun:si e) me -1)

2274− =+ r=(^add f (bex p))

2275− [%f s q r]

2254+++ sea

2255+ |= [a=@r] ^- fn

2256+ =+ [f=(cut 0 [0 p] a) e=(cut 0 [p w] a)]

2257+ =+ s=(sig a)

2258+ ?: =(e 0)

2259+ ?: =(f 0) [%f s --0 0] [%f s me f]

2260+ ?: =(e (fil 0 w 1))

2261+ ?: =(f 0) [%i s] [%n ~]

2262+ =+ q=:(sum:si (sun:si e) me -1)

2263+ =+ r=(^add f (bex p))

2264+ [%f s q r]

22762265```

22772266

22782267#### Examples

22792268

22802269```

2281− > (sea:ff `@r`0x8)

2282− [%f s=%.y e=--0 a=0]

2270+> (sea:ff `@r`0x8)

2271+[%f s=%.y e=--0 a=0]

22832272```

22842273

22852274---

@@ -2301,14 +2290,14 @@ A `@r`.

23012290#### Source

23022291

23032292```hoon

2304− ++ bit |= [a=fn] (bif (rou:pa a))

2293+++ bit |= [a=fn] (bif (rou:pa a))

23052294```

23062295

23072296#### Examples

23082297

23092298```

2310− > (bit:ma:rd [%f | -6 202])

2311− 0xc009400000000000

2299+> (bit:ma:rd [%f | -6 202])

2300+0xc009400000000000

23122301```

23132302

23142303---

@@ -2330,28 +2319,28 @@ A `flag`.

23302319#### Source

23312320

23322321```hoon

2333− ++ bif

2334− |= [a=fn] ^- @r

2335− ?: ?=([$i *] a)

2336− =+ q=(lsh 0 p (fil 0 w 1))

2337− ?: s.a q (^add q sb)

2338− ?: ?=([$n *] a) (lsh 0 (dec p) (fil 0 +(w) 1))

2339− ?~ a.a ?: s.a `@r`0 sb

2340− =+ ma=(met 0 a.a)

2341− ?. =(ma +(p))

2342− ?> =(e.a me)

2343− ?> (^lth ma +(p))

2344− ?: s.a `@r`a.a (^add a.a sb)

2345− =+ q=(sum:si (dif:si e.a me) --1)

2346− =+ r=(^add (lsh 0 p (abs:si q)) (end 0 p a.a))

2347− ?: s.a r (^add r sb)

2322+++ bif

2323+ |= [a=fn] ^- @r

2324+ ?: ?=([%i *] a)

2325+ =+ q=(lsh [0 p] (fil 0 w 1))

2326+ ?: s.a q (^add q sb)

2327+ ?: ?=([%n *] a) (lsh [0 (dec p)] (fil 0 +(w) 1))

2328+ ?~ a.a ?: s.a `@r`0 sb

2329+ =+ ma=(met 0 a.a)

2330+ ?. =(ma +(p))

2331+ ?> =(e.a me)

2332+ ?> (^lth ma +(p))

2333+ ?: s.a `@r`a.a (^add a.a sb)

2334+ =+ q=(sum:si (dif:si e.a me) --1)

2335+ =+ r=(^add (lsh [0 p] (abs:si q)) (end [0 p] a.a))

2336+ ?: s.a r (^add r sb)

23482337```

23492338

23502339#### Examples

23512340

23522341```

2353− > (bif:ma:rd *fn)

2354− 0x7ff8000000000000

2342+> (bif:ma:rd *fn)

2343+0x7ff8000000000000

23552344```

23562345

23572346---

@@ -2373,16 +2362,16 @@ A `flag`.

23732362#### Source

23742363

23752364```hoon

2376− ++ sig

2377− |= [a=@r] ^- ?

2378− =(0 (cut 0 [(^add p w) 1] a))

2365+++ sig

2366+ |= [a=@r] ^- ?

2367+ =(0 (cut 0 [(^add p w) 1] a))

23792368```

23802369

23812370#### Examples

23822371

23832372```

2384− > (sig:ff `@r`5)

2385− %.n

2373+> (sig:ff `@r`5)

2374+%.n

23862375```

23872376

23882377---

@@ -2404,16 +2393,16 @@ A signed integer.

24042393#### Source

24052394

24062395```hoon

2407− ++ exp

2408− |= [a=@r] ^- @s

2409− (dif:si (sun:si (cut 0 [p w] a)) b)

2396+++ exp

2397+ |= [a=@r] ^- @s

2398+ (dif:si (sun:si (cut 0 [p w] a)) b)

24102399```

24112400

24122401#### Examples

24132402

24142403```

2415− > (exp:ff `@r`5)

2416− --0

2404+> (exp:ff `@r`5)

2405+--0

24172406```

24182407

24192408---

@@ -2437,16 +2426,16 @@ A `@r`, an IEEE float.

24372426#### Source

24382427

24392428```hoon

2440− ++ add

2441− |= [a=@r b=@r]

2442− (bif (add:pa (sea a) (sea b)))

2429+++ add

2430+ |= [a=@r b=@r]

2431+ (bif (add:pa (sea a) (sea b)))

24432432```

24442433

24452434#### Examples

24462435

24472436```

2448− > (add:ma:rd `@r`5 `@r`11)

2449− 0x10

2437+> (add:ma:rd `@r`5 `@r`11)

2438+0x10

24502439```

24512440

24522441---

@@ -2470,16 +2459,16 @@ A `@r`, an IEEE float.

24702459#### Source

24712460

24722461```hoon

2473− ++ sub

2474− |= [a=@r b=@r]

2475− (bif (sub:pa (sea a) (sea b)))

2462+++ sub

2463+ |= [a=@r b=@r]

2464+ (bif (sub:pa (sea a) (sea b)))

24762465```

24772466

24782467#### Examples

24792468

24802469```

2481− > (sub:ma:rd `@r`5 `@r`11)

2482− 0x8000000000000006

2470+> (sub:ma:rd `@r`5 `@r`11)

2471+0x8000000000000006

24832472```

24842473

24852474---

@@ -2503,16 +2492,16 @@ A `@r`, an IEEE float.

25032492#### Multiply

25042493

25052494```hoon

2506− ++ mul

2507− |= [a=@r b=@r]

2508− (bif (mul:pa (sea a) (sea b)))

2495+++ mul

2496+ |= [a=@r b=@r]

2497+ (bif (mul:pa (sea a) (sea b)))

25092498```

25102499

25112500#### Examples

25122501

25132502```

2514− > (mul:ma:rd `@r`11 `@r`2)

2515− 0x0

2503+> (mul:ma:rd `@r`11 `@r`2)

2504+0x0

25162505```

25172506

25182507---

@@ -2536,16 +2525,16 @@ A `@r`, an IEEE float.

25362525#### Source

25372526

25382527```hoon

2539− ++ div

2540− |= [a=@r b=@r]

2541− (bif (div:pa (sea a) (sea b)))

2528+++ div

2529+ |= [a=@r b=@r]

2530+ (bif (div:pa (sea a) (sea b)))

25422531```

25432532

25442533#### Examples

25452534

25462535```

2547− > (div:ma:rd `@r`175 `@r`26)

2548− 0x401aec4ec4ec4ec4

2536+> (div:ma:rd `@r`175 `@r`26)

2537+0x401aec4ec4ec4ec4

25492538```

25502539

25512540---

@@ -2572,16 +2561,16 @@ A `@r`, an IEEE float.

25722561#### Source

25732562

25742563```hoon

2575− ++ fma

2576− |= [a=@r b=@r c=@r]

2577− (bif (fma:pa (sea a) (sea b) (sea c)))

2564+++ fma

2565+ |= [a=@r b=@r c=@r]

2566+ (bif (fma:pa (sea a) (sea b) (sea c)))

25782567```

25792568

25802569#### Examples

25812570

25822571```

2583− > (fma:ma:rd `@r`175 `@r`26 `@r`100)

2584− 0x64

2572+> (fma:ma:rd `@r`175 `@r`26 `@r`100)

2573+0x64

25852574```

25862575

25872576---

@@ -2603,16 +2592,16 @@ A `@r`, an IEEE float.

26032592#### Source

26042593

26052594```hoon

2606− ++ sqt

2607− |= [a=@r]

2608− (bif (sqt:pa (sea a)))

2595+++ sqt

2596+ |= [a=@r]

2597+ (bif (sqt:pa (sea a)))

26092598```

26102599

26112600#### Examples

26122601

26132602```

2614− > (sqt:ma:rd `@r`175)

2615− 0x1e9a751f9447b724

2603+> (sqt:ma:rd `@r`175)

2604+0x1e9a751f9447b724

26162605```

26172606

26182607---

@@ -2636,18 +2625,18 @@ A `flag`.

26362625#### Source

26372626

26382627```hoon

2639− ++ lth

2640− |= [a=@r b=@r] (fall (lth:pa (sea a) (sea b)) |)

2628+++ lth

2629+ |= [a=@r b=@r] (fall (lth:pa (sea a) (sea b)) |)

26412630```

26422631

26432632#### Examples

26442633

26452634```

2646− > (lth:ma:rd `@rd`1 `@rd`2)

2647− %.y

2635+> (lth:ma:rd `@rd`1 `@rd`2)

2636+%.y

26482637

2649− > (lth:ma:rd `@rd`10 `@rd`2)

2650− %.n

2638+> (lth:ma:rd `@rd`10 `@rd`2)

2639+%.n

26512640```

26522641

26532642---

@@ -2671,18 +2660,18 @@ A `flag`.

26712660#### Source

26722661

26732662```hoon

2674− ++ lte

2675− |= [a=@r b=@r] (fall (lte:pa (sea a) (sea b)) |)

2663+++ lte

2664+ |= [a=@r b=@r] (fall (lte:pa (sea a) (sea b)) |)

26762665```

26772666

26782667#### Examples

26792668

26802669```

2681− > (lte:ma:rd `@rd`10 `@rd`2)

2682− %.n

2670+> (lte:ma:rd `@rd`10 `@rd`2)

2671+%.n

26832672

2684− > (lte:ma:rd `@rd`10 `@rd`10)

2685− %.y

2673+> (lte:ma:rd `@rd`10 `@rd`10)

2674+%.y

26862675```

26872676

26882677---

@@ -2706,18 +2695,18 @@ A `flag`.

27062695#### Source

27072696

27082697```hoon

2709− ++ equ

2710− |= [a=@r b=@r] (fall (equ:pa (sea a) (sea b)) |)

2698+++ equ

2699+ |= [a=@r b=@r] (fall (equ:pa (sea a) (sea b)) |)

27112700```

27122701

27132702#### Examples

27142703

27152704```

2716− > (equ:ma:rd `@rd`10 `@rd`2)

2717− %.n

2705+> (equ:ma:rd `@rd`10 `@rd`2)

2706+%.n

27182707

2719− > (equ:ma:rd `@rd`10 `@rd`10)

2720− %.y

2708+> (equ:ma:rd `@rd`10 `@rd`10)

2709+%.y

27212710```

27222711

27232712---

@@ -2741,18 +2730,18 @@ A `flag`.

27412730#### Source

27422731

27432732```hoon

2744− ++ gte

2745− |= [a=@r b=@r] (fall (gte:pa (sea a) (sea b)) |)

2733+++ gte

2734+ |= [a=@r b=@r] (fall (gte:pa (sea a) (sea b)) |)

27462735```

27472736

27482737#### Examples

27492738

27502739```

2751− > (gte:ma:rd `@rd`10 `@rd`10)

2752− %.y

2740+> (gte:ma:rd `@rd`10 `@rd`10)

2741+%.y

27532742

2754− > (gte:ma:rd `@rd`10 `@rd`11)

2755− %.n

2743+> (gte:ma:rd `@rd`10 `@rd`11)

2744+%.n

27562745```

27572746

27582747---

@@ -2776,18 +2765,18 @@ A `flag`.

27762765#### Source

27772766

27782767```hoon

2779− ++ gth

2780− |= [a=@r b=@r] (fall (gth:pa (sea a) (sea b)) |)

2768+++ gth

2769+ |= [a=@r b=@r] (fall (gth:pa (sea a) (sea b)) |)

27812770```

27822771

27832772#### Examples

27842773

27852774```

2786− > (gth:ma:rd `@rd`10 `@rd`10)

2787− %.n

2775+> (gth:ma:rd `@rd`10 `@rd`10)

2776+%.n

27882777

2789− > (gth:ma:rd `@rd`10 `@rd`9)

2790− %.y

2778+> (gth:ma:rd `@rd`10 `@rd`9)

2779+%.y

27912780```

27922781

27932782---

@@ -2809,15 +2798,15 @@ A `@r`, an IEEE float.

28092798#### Source

28102799

28112800```hoon

2812− ++ sun

2813− |= [a=@u] (bit [%f & --0 a])

2801+++ sun

2802+ |= [a=@u] (bit [%f & --0 a])

28142803```

28152804

28162805#### Examples

28172806

28182807```

2819− > (sun:ma:rd 658.149.282)

2820− 0x41c39d47d1000000

2808+> (sun:ma:rd 658.149.282)

2809+0x41c39d47d1000000

28212810```

28222811

28232812---

@@ -2839,15 +2828,15 @@ A `@r`, an IEEE float.

28392828#### Source

28402829

28412830```hoon

2842− ++ san

2843− |= [a=@s] (bit [%f (syn:si a) --0 (abs:si a)])

2831+++ san

2832+ |= [a=@s] (bit [%f (syn:si a) --0 (abs:si a)])

28442833```

28452834

28462835#### Examples

28472836

28482837```

2849− > (san:ma:rd --10)

2850− 0x4024000000000000

2838+> (san:ma:rd --10)

2839+0x4024000000000000

28512840```

28522841

28532842---

@@ -2869,15 +2858,15 @@ A `flag` of `@s`.

28692858#### Source

28702859

28712860```hoon

2872− ++ toi

2873− |= [a=@r] (toi:pa (sea a))

2861+++ toi

2862+ |= [a=@r] (toi:pa (sea a))

28742863```

28752864

28762865#### Examples

28772866

28782867```

2879− > (toi:ma:rd `@r`0x4af)

2880− [~ u=--0]

2868+> (toi:ma:rd `@r`0x4af)

2869+[~ u=--0]

28812870```

28822871

28832872---

@@ -2899,18 +2888,18 @@ A `dn`.

28992888#### Source

29002889

29012890```hoon

2902− ++ drg

2903− |= [a=@r] (drg:pa (sea a))

2891+++ drg

2892+ |= [a=@r] (drg:pa (sea a))

29042893```

29052894

29062895#### Examples

29072896

29082897```

2909− > (drg:ma:rd `@r`0x41c0)

2910− [%d s=%.y e=-323 a=8.316]

2898+> (drg:ma:rd `@r`0x41c0)

2899+[%d s=%.y e=-323 a=8.316]

29112900

2912− > (drg:ma:rd (sun:ma:rd 658.149.282))

2913− [%d s=%.y e=--0 a=658.149.282]

2901+> (drg:ma:rd (sun:ma:rd 658.149.282))

2902+[%d s=%.y e=--0 a=658.149.282]

29142903```

29152904

29162905---

@@ -2932,16 +2921,15 @@ A `@r`, an IEEE float.

29322921#### Source

29332922

29342923```hoon

2935− ++ grd

2936− |= [a=dn] (bif (grd:pa a))

2937− --

2924+++ grd

2925+ |= [a=dn] (bif (grd:pa a))

29382926```

29392927

29402928#### Examples

29412929

29422930```

2943− > (grd:ma:rd [%d s=%.y e=--0 a=658.149.282])

2944− 0x41c39d47d1000000

2931+> (grd:ma:rd [%d s=%.y e=--0 a=658.149.282])

2932+0x41c39d47d1000000

29452933```

29462934

29472935---

@@ -2963,14 +2951,14 @@ A `dn`.

29632951#### Source

29642952

29652953```hoon

2966− ++ rlyd |= a=@rd ^- dn (drg:rd a)

2954+++ rlyd |= a=@rd ^- dn (drg:rd a)

29672955```

29682956

29692957#### Examples

29702958

29712959```

2972− > (rlyd .~2.4703e-320)

2973− [%d s=%.y e=-324 a=24.703]

2960+> (rlyd .~2.4703e-320)

2961+[%d s=%.y e=-324 a=24.703]

29742962```

29752963

29762964---

@@ -2992,14 +2980,14 @@ A `dn`.

29922980#### Source

29932981

29942982```hoon

2995− ++ rlys |= a=@rs ^- dn (drg:rs a)

2983+++ rlys |= a=@rs ^- dn (drg:rs a)

29962984```

29972985

29982986#### Examples

29992987

30002988```

3001− > (rlys .1.681557e-39)

3002− [%d s=%.y e=-45 a=1.681.557]

2989+> (rlys .1.681557e-39)

2990+[%d s=%.y e=-45 a=1.681.557]

30032991```

30042992

30052993---

@@ -3021,14 +3009,14 @@ A `dn`.

30213009#### Source

30223010

30233011```hoon

3024− ++ rlyh |= a=@rh ^- dn (drg:rh a)

3012+++ rlyh |= a=@rh ^- dn (drg:rh a)

30253013```

30263014

30273015#### Examples

30283016

30293017```

3030− > (rlyh .~~3e1)

3031− [%d s=%.y e=--1 a=3]

3018+> (rlyh .~~3e1)

3019+[%d s=%.y e=--1 a=3]

30323020```

30333021

30343022---

@@ -3050,14 +3038,14 @@ A `dn`.

30503038#### Source

30513039

30523040```hoon

3053− ++ rlyq |= a=@rq ^- dn (drg:rq a)

3041+++ rlyq |= a=@rq ^- dn (drg:rq a)

30543042```

30553043

30563044#### Examples

30573045

30583046```

3059− > (rlyq .~~~2.2628017865927756787440310766086816e-4343)

3060− [%d s=%.y e=-4.377 a=22.628.017.865.927.756.787.440.310.766.086.816]

3047+> (rlyq .~~~2.2628017865927756787440310766086816e-4343)

3048+[%d s=%.y e=-4.377 a=22.628.017.865.927.756.787.440.310.766.086.816]

30613049```

30623050

30633051---

@@ -3079,14 +3067,14 @@ A a `@rd`, a double-precision float.

30793067#### Source

30803068

30813069```hoon

3082− ++ ryld |= a=dn ^- @rd (grd:rd a)

3070+++ ryld |= a=dn ^- @rd (grd:rd a)

30833071```

30843072

30853073#### Examples

30863074

30873075```

3088− > (ryld [%d s=%.y e=-324 a=24.703])

3089− .~2.4703e-320

3076+> (ryld [%d s=%.y e=-324 a=24.703])

3077+.~2.4703e-320

30903078```

30913079

30923080---

@@ -3108,17 +3096,17 @@ A a `@rs`, a single-precision float.

31083096#### Source

31093097

31103098```hoon

3111− ++ ryls |= a=dn ^- @rs (grd:rs a)

3099+++ ryls |= a=dn ^- @rs (grd:rs a)

31123100```

31133101

31143102#### Examples

31153103

31163104```

3117− > (ryls [%d s=%.y e=-324 a=24.703])

3118− .0

3105+> (ryls [%d s=%.y e=-324 a=24.703])

3106+.0

31193107

3120− > (ryls [%d s=%.y e=-32 a=24.703])

3121− .2.4703e-28

3108+> (ryls [%d s=%.y e=-32 a=24.703])

3109+.2.4703e-28

31223110```

31233111

31243112---

@@ -3140,20 +3128,20 @@ A a `@rh`, a half-precision float.

31403128#### Source

31413129

31423130```hoon

3143− ++ rylh |= a=dn ^- @rh (grd:rh a)

3131+++ rylh |= a=dn ^- @rh (grd:rh a)

31443132```

31453133

31463134#### Examples

31473135

31483136```

3149− > (rylh [%d s=%.y e=--1 a=703])

3150− .~~7.032e3

3137+> (rylh [%d s=%.y e=--1 a=703])

3138+.~~7.032e3

31513139

3152− > (rylh [%d s=%.y e=--3 a=56])

3153− .~~5.6e4

3140+> (rylh [%d s=%.y e=--3 a=56])

3141+.~~5.6e4

31543142

3155− > (rylh [%d s=%.y e=--4 a=56])

3156− .~~inf

3143+> (rylh [%d s=%.y e=--4 a=56])

3144+.~~inf

31573145```

31583146

31593147---

@@ -3175,14 +3163,14 @@ A a `@rq`, a quad-precision float.

31753163#### Source

31763164

31773165```hoon

3178− ++ rylq |= a=dn ^- @rq (grd:rq a)

3166+++ rylq |= a=dn ^- @rq (grd:rq a)

31793167```

31803168

31813169#### Examples

31823170

31833171```

3184− > (rylq [%d s=%.y e=-324 a=24.703])

3185− .~~~2.4703e-320

3172+> (rylq [%d s=%.y e=-324 a=24.703])

3173+.~~~2.4703e-320

31863174```

31873175

31883176---

@@ -3199,10 +3187,10 @@ down (`$d`), and round to zero (`$z`).

31993187#### Source

32003188

32013189```hoon

3202− ++ rd

3203− ^?

3204− ~% %rd +> ~

3205− |_ r=$?($n $u $d $z)

3190+++ rd

3191+ ^|

3192+ ~% %rd +> ~

3193+ |_ r=$?(%n %u %d %z)

32063194```

32073195

32083196---

@@ -3217,17 +3205,17 @@ configuration of the `rd` core.

32173205#### Source

32183206

32193207```hoon

3220− ++ ma

3221− %*(. ff w 11, p 52, b --1.023, r r)

3208+++ ma

3209+ %*(. ff w 11, p 52, b --1.023, r r)

32223210```

32233211

32243212#### Examples

32253213

32263214```

3227− > ~(ma rd %n)

3228− < 24.ltg

3229− {{{w/@ud p/@ud b/@sd} r/?($n $u $d $z)} <54.tyv 119.wim 31.ohr 1.jmk $143>}

3230− >

3215+> ~(ma rd %n)

3216+< 24.ltg

3217+ {{{w/@ud p/@ud b/@sd} r/?($n $u $d $z)} <54.tyv 119.wim 31.ohr 1.jmk $143>}

3218+>

32313219```

32323220

32333221---

@@ -3238,16 +3226,18 @@ configuration of the `rd` core.

32383226

32393227Converts `a` from a double-precision binary float to `fn`.

32403228

3229+#### Source

3230+

32413231```hoon

3242− ++ sea :: @rd to fn

3243− |= [a=@rd] (sea:ma a)

3232+++ sea

3233+ |= [a=@rd] (sea:ma a)

32443234```

32453235

32463236#### Examples

32473237

32483238```

3249− > (sea:rd .~4.94066e-319)

3250− [%f s=%.y e=-1.074 a=100.000]

3239+> (sea:rd .~4.94066e-319)

3240+[%f s=%.y e=-1.074 a=100.000]

32513241```

32523242

32533243---

@@ -3269,15 +3259,15 @@ A `@rd`, a double-precision float.

32693259#### Source

32703260

32713261```hoon

3272− ++ bit

3273− |= [a=fn] ^- @rd (bit:ma a)

3262+++ bit

3263+ |= [a=fn] ^- @rd (bit:ma a)

32743264```

32753265

32763266#### Examples

32773267

32783268```

3279− > (bit:rd [%f s=%.y e=-1.074 a=100.000])

3280− .~4.94066e-319

3269+> (bit:rd [%f s=%.y e=-1.074 a=100.000])

3270+.~4.94066e-319

32813271```

32823272

32833273---

@@ -3301,17 +3291,17 @@ A `@rd`.

33013291#### Source

33023292

33033293```hoon

3304− ++ add ~/ %add

3305− |= [a=@rd b=@rd] ^- @rd

3306− ~_ leaf+"rd-fail"

3307− (add:ma a b)

3294+++ add ~/ %add

3295+ |= [a=@rd b=@rd] ^- @rd

3296+ ~_ leaf+"rd-fail"

3297+ (add:ma a b)

33083298```

33093299

33103300#### Examples

33113301

33123302```

3313− > (add:rd .~3.94066e12 .~9.2846e11)

3314− .~4.86912e12

3303+> (add:rd .~3.94066e12 .~9.2846e11)

3304+.~4.86912e12

33153305```

33163306

33173307---

@@ -3335,17 +3325,17 @@ A `@rd`.

33353325#### Source

33363326

33373327```hoon

3338− ++ sub ~/ %sub

3339− |= [a=@rd b=@rd] ^- @rd

3340− ~_ leaf+"rd-fail"

3341− (sub:ma a b)

3328+++ sub ~/ %sub

3329+ |= [a=@rd b=@rd] ^- @rd

3330+ ~_ leaf+"rd-fail"

3331+ (sub:ma a b)

33423332```

33433333

33443334#### Examples

33453335

33463336```

3347− > (sub:rd .~7.94069e2 .~1.2846e3)

3348− .~-4.9053099999999995e2

3337+> (sub:rd .~7.94069e2 .~1.2846e3)

3338+.~-4.9053099999999995e2

33493339```

33503340

33513341---

@@ -3369,17 +3359,17 @@ A `@rd`.

33693359#### Source

33703360

33713361```hoon

3372− ++ mul ~/ %mul

3373− |= [a=@rd b=@rd] ^- @rd

3374− ~_ leaf+"rd-fail"

3375− (mul:ma a b)

3362+++ mul ~/ %mul

3363+ |= [a=@rd b=@rd] ^- @rd

3364+ ~_ leaf+"rd-fail"

3365+ (mul:ma a b)

33763366```

33773367

33783368#### Examples

33793369

33803370```

3381− > (mul:rd .~7.94069e2 .~1.2246e3)

3382− .~9.724168973999998e5

3371+> (mul:rd .~7.94069e2 .~1.2246e3)

3372+.~9.724168973999998e5

33833373```

33843374

33853375---

@@ -3403,17 +3393,17 @@ A `@rd`.

34033393#### Source

34043394

34053395```hoon

3406− ++ div ~/ %div

3407− |= [a=@rd b=@rd] ^- @rd

3408− ~_ leaf+"rd-fail"

3409− (div:ma a b)

3396+++ div ~/ %div

3397+ |= [a=@rd b=@rd] ^- @rd

3398+ ~_ leaf+"rd-fail"

3399+ (div:ma a b)

34103400```

34113401

34123402#### Examples

34133403

34143404```

3415− > (div:rd .~7.94099e2 .~1.2246e3)

3416− .~6.484558223093255e-1

3405+> (div:rd .~7.94099e2 .~1.2246e3)

3406+.~6.484558223093255e-1

34173407```

34183408

34193409---

@@ -3439,20 +3429,18 @@ A `@rd`.

34393429

34403430#### Source

34413431

3442−#### Source

3443−

34443432```hoon

3445− ++ fma ~/ %fma

3446− |= [a=@rd b=@rd c=@rd] ^- @rd

3447− ~_ leaf+"rd-fail"

3448− (fma:ma a b c)

3433+++ fma ~/ %fma

3434+ |= [a=@rd b=@rd c=@rd] ^- @rd

3435+ ~_ leaf+"rd-fail"

3436+ (fma:ma a b c)

34493437```

34503438

34513439#### Examples

34523440

34533441```

3454− > (fma:rd .~7.94099e2 .~1.2246e3 .~3.94066e3)

3455− .~9.763942954e5

3442+> (fma:rd .~7.94099e2 .~1.2246e3 .~3.94066e3)

3443+.~9.763942954e5

34563444```

34573445

34583446---

@@ -3474,16 +3462,16 @@ A `@rd`.

34743462#### Source

34753463

34763464```hoon

3477− ++ sqt ~/ %sqt

3478− |= [a=@rd] ^- @rd ~_ leaf+"rd-fail"

3479− (sqt:ma a)

3465+++ sqt ~/ %sqt

3466+ |= [a=@rd] ^- @rd ~_ leaf+"rd-fail"

3467+ (sqt:ma a)

34803468```

34813469

34823470#### Examples

34833471

34843472```

3485− > (sqt:rd .~3.94066e3)

3486− .~6.2774676422901614e1

3473+> (sqt:rd .~3.94066e3)

3474+.~6.2774676422901614e1

34873475```

34883476

34893477---

@@ -3507,23 +3495,23 @@ A `@rd`.

35073495#### Source

35083496

35093497```hoon

3510− ++ lth ~/ %lth

3511− |= [a=@rd b=@rd]

3512− ~_ leaf+"rd-fail"

3513− (lth:ma a b)

3498+++ lth ~/ %lth

3499+ |= [a=@rd b=@rd]

3500+ ~_ leaf+"rd-fail"

3501+ (lth:ma a b)

35143502```

35153503

35163504#### Examples

35173505

35183506```

3519− > (lth:rd .~7.94099e2 .~1.2246e3)

3520− %.y

3507+> (lth:rd .~7.94099e2 .~1.2246e3)

3508+%.y

35213509

3522− > (lth:rd .~7.94099e2 .~1.2246e2)

3523− %.n

3510+> (lth:rd .~7.94099e2 .~1.2246e2)

3511+%.n

35243512

3525− > (lth:rd .~1.2246e2 .~1.2246e2)

3526− %.n

3513+> (lth:rd .~1.2246e2 .~1.2246e2)

3514+%.n

35273515```

35283516

35293517---

@@ -3547,23 +3535,23 @@ A `@rd`.

35473535#### Source

35483536

35493537```hoon

3550− ++ lte ~/ %lte :: less-equals

3551− |= [a=@rd b=@rd]

3552− ~_ leaf+"rd-fail"

3553− (lte:ma a b)

3538+++ lte ~/ %lte

3539+ |= [a=@rd b=@rd]

3540+ ~_ leaf+"rd-fail"

3541+ (lte:ma a b)

35543542```

35553543

35563544#### Examples

35573545

35583546```

3559− > (lte:rd .~7.94099e2 .~1.2246e3)

3560− %.y

3547+> (lte:rd .~7.94099e2 .~1.2246e3)

3548+%.y

35613549

3562− > (lte:rd .~7.94099e2 .~1.2246e2)

3563− %.n

3550+> (lte:rd .~7.94099e2 .~1.2246e2)

3551+%.n

35643552

3565− > (lte:rd .~1.2246e2 .~1.2246e2)

3566− %.y

3553+> (lte:rd .~1.2246e2 .~1.2246e2)

3554+%.y

35673555```

35683556

35693557---

@@ -3587,23 +3575,23 @@ A `@rd`.

35873575#### Source

35883576

35893577```hoon

3590− ++ equ ~/ %equ

3591− |= [a=@rd b=@rd]

3592− ~_ leaf+"rd-fail"

3593− (equ:ma a b)

3578+++ equ ~/ %equ

3579+ |= [a=@rd b=@rd]

3580+ ~_ leaf+"rd-fail"

3581+ (equ:ma a b)

35943582```

35953583

35963584#### Examples

35973585

35983586```

3599− > (equ:rd .~7.94099e2 .~1.2246e3)

3600− %.n

3587+> (equ:rd .~7.94099e2 .~1.2246e3)

3588+%.n

36013589

3602− > (equ:rd .~7.94099e2 .~1.2246e2)

3603− %.n

3590+> (equ:rd .~7.94099e2 .~1.2246e2)

3591+%.n

36043592

3605− > (equ:rd .~1.2246e2 .~1.2246e2)

3606− %.y

3593+> (equ:rd .~1.2246e2 .~1.2246e2)

3594+%.y

36073595```

36083596

36093597---

@@ -3627,23 +3615,23 @@ A `@rd`.

36273615#### Source

36283616

36293617```hoon

3630− ++ gte ~/ %gte

3631− |= [a=@rd b=@rd]

3632− ~_ leaf+"rd-fail"

3633− (gte:ma a b)

3618+++ gte ~/ %gte

3619+ |= [a=@rd b=@rd]

3620+ ~_ leaf+"rd-fail"

3621+ (gte:ma a b)

36343622```

36353623

36363624#### Examples

36373625

36383626```

3639− > (gte:rd .~7.94099e2 .~1.2246e3)

3640− %.n

3627+> (gte:rd .~7.94099e2 .~1.2246e3)

3628+%.n

36413629

3642− > (gte:rd .~7.94099e2 .~1.2246e2)

3643− %.y

3630+> (gte:rd .~7.94099e2 .~1.2246e2)

3631+%.y

36443632

3645− > (gte:rd .~1.2246e2 .~1.2246e2)

3646− %.y

3633+> (gte:rd .~1.2246e2 .~1.2246e2)

3634+%.y

36473635```

36483636

36493637---

@@ -3667,23 +3655,23 @@ A `@rd`.

36673655#### Source

36683656

36693657```hoon

3670− ++ gth ~/ %gth

3671− |= [a=@rd b=@rd]

3672− ~_ leaf+"rd-fail"

3673− (gth:ma a b)

3658+++ gth ~/ %gth

3659+ |= [a=@rd b=@rd]

3660+ ~_ leaf+"rd-fail"

3661+ (gth:ma a b)

36743662```

36753663

36763664#### Examples

36773665

36783666```

3679− > (gth:rd .~7.94099e2 .~1.2246e3)

3680− %.n

3667+> (gth:rd .~7.94099e2 .~1.2246e3)

3668+%.n

36813669

3682− > (gth:rd .~7.94099e2 .~1.2246e2)

3683− %.y

3670+> (gth:rd .~7.94099e2 .~1.2246e2)

3671+%.y

36843672

3685− > (gth:rd .~1.2246e2 .~1.2246e2)

3686− %.n

3673+> (gth:rd .~1.2246e2 .~1.2246e2)

3674+%.n

36873675```

36883676

36893677---

@@ -3705,14 +3693,14 @@ A `@rd`.

37053693#### Source

37063694

37073695```hoon

3708− ++ sun |= [a=@u] ^- @rd (sun:ma a)

3696+++ sun |= [a=@u] ^- @rd (sun:ma a)

37093697```

37103698

37113699#### Examples

37123700

37133701```

3714− > (sun:rd 511)

3715− .~5.11e2

3702+> (sun:rd 511)

3703+.~5.11e2

37163704```

37173705

37183706---

@@ -3734,14 +3722,14 @@ A `@rd`.

37343722#### Source

37353723

37363724```hoon

3737− ++ san |= [a=@s] ^- @rd (san:ma a)

3725+++ san |= [a=@s] ^- @rd (san:ma a)

37383726```

37393727

37403728#### Examples

37413729

37423730```

3743− > (san:rd -511)

3744− .~-5.11e2

3731+> (san:rd -511)

3732+.~-5.11e2

37453733```

37463734

37473735---

@@ -3763,14 +3751,14 @@ A `flag`.

37633751#### Source

37643752

37653753```hoon

3766− ++ sig |= [a=@rd] ^- ? (sig:ma a)

3754+++ sig |= [a=@rd] ^- ? (sig:ma a)

37673755```

37683756

37693757#### Examples

37703758

37713759```

3772− > (sig:rd .~1.2246e3)

3773− %.y

3760+> (sig:rd .~1.2246e3)

3761+%.y

37743762```

37753763

37763764---

@@ -3792,14 +3780,14 @@ A `@s`.

37923780#### Source

37933781

37943782```hoon

3795− ++ exp |= [a=@rd] ^- @s (exp:ma a) :: get exponent

3783+++ exp |= [a=@rd] ^- @s (exp:ma a)

37963784```

37973785

37983786#### Examples

37993787

38003788```

3801− > (exp:rd .~1.2246e3)

3802− --10

3789+> (exp:rd .~1.2246e3)

3790+--10

38033791```

38043792

38053793---

@@ -3821,14 +3809,14 @@ A `unit` of `@s`.

38213809#### Source

38223810

38233811```hoon

3824− ++ toi |= [a=@rd] ^- (unit @s) (toi:ma a)

3812+++ toi |= [a=@rd] ^- (unit @s) (toi:ma a)

38253813```

38263814

38273815#### Examples

38283816

38293817```

3830− > (toi:rd .~1.2246e3)

3831− [~ u=--1.224]

3818+> (toi:rd .~1.2246e3)

3819+[~ u=--1.224]

38323820```

38333821

38343822---

@@ -3851,14 +3839,14 @@ A `dn`.

38513839#### Source

38523840

38533841```hoon

3854− ++ drg |= [a=@rd] ^- dn (drg:ma a)

3842+++ drg |= [a=@rd] ^- dn (drg:ma a)

38553843```

38563844

38573845#### Examples

38583846

38593847```

3860− > (drg:rd .~1.2246e3)

3861− [%d s=%.y e=-1 a=12.246]

3848+> (drg:rd .~1.2246e3)

3849+[%d s=%.y e=-1 a=12.246]

38623850```

38633851

38643852---

@@ -3880,15 +3868,14 @@ A `@rd`.

38803868#### Source

38813869

38823870```hoon

3883− ++ grd |= [a=dn] ^- @rd (grd:ma a) :: decimal float to @rd

3884− --

3871+++ grd |= [a=dn] ^- @rd (grd:ma a)

38853872```

38863873

38873874#### Examples

38883875

38893876```

3890− > (grd:rd [%d s=%.y e=-1 a=12.246])

3891− .~1.2246e3

3877+> (grd:rd [%d s=%.y e=-1 a=12.246])

3878+.~1.2246e3

38923879```

38933880

38943881---

@@ -3905,10 +3892,10 @@ down (`$d`), and round to zero (`$z`).

39053892#### Source

39063893

39073894```hoon

3908− ++ rs

3909− ~% %rs +> ~

3910− ^?

3911− |_ r=$?($n $u $d $z)

3895+++ rs

3896+ ~% %rs +> ~

3897+ ^|

3898+ |_ r=$?(%n %u %d %z)

39123899```

39133900

39143901---

@@ -3923,17 +3910,17 @@ configuration of the `rs` core.

39233910#### Source

39243911

39253912```hoon

3926− ++ ma

3927− %*(. ff w 8, p 23, b --127, r r)

3913+++ ma

3914+ %*(. ff w 8, p 23, b --127, r r)

39283915```

39293916

39303917#### Examples

39313918

39323919```

3933− > ~(ma rs %n)

3934− < 24.ltg

3935− {{{w/@ud p/@ud b/@sd} r/?($n $u $d $z)} <54.tyv 119.wim 31.ohr 1.jmk $143>}

3936− >

3920+> ~(ma rs %n)

3921+< 24.ltg

3922+ {{{w/@ud p/@ud b/@sd} r/?($n $u $d $z)} <54.tyv 119.wim 31.ohr 1.jmk $143>}

3923+>

39373924```

39383925

39393926---

@@ -3955,15 +3942,15 @@ An `fn`.

39553942#### Source

39563943

39573944```hoon

3958− ++ sea

3959− |= [a=@rs] (sea:ma a)

3945+++ sea

3946+ |= [a=@rs] (sea:ma a)

39603947```

39613948

39623949#### Examples

39633950

39643951```

3965− > (sea:rs .1.4e-43)

3966− [%f s=%.y e=-149 a=100]

3952+> (sea:rs .1.4e-43)

3953+[%f s=%.y e=-149 a=100]

39673954```

39683955

39693956---

@@ -3985,15 +3972,15 @@ A `@rs`, a single-precision float.

39853972#### Source

39863973

39873974```hoon

3988− ++ bit

3989− |= [a=fn] ^- @rs (bit:ma a)

3975+++ bit

3976+ |= [a=fn] ^- @rs (bit:ma a)

39903977```

39913978

39923979#### Examples

39933980

39943981```

3995− > (bit:rs [%f & -2 1.000])

3996− .2.5e2

3982+> (bit:rs [%f & -2 1.000])

3983+.2.5e2

39973984```

39983985

39993986---

@@ -4017,17 +4004,17 @@ A `@rs`.

40174004#### Source

40184005

40194006```hoon

4020− ++ add ~/ %add

4021− |= [a=@rs b=@rs] ^- @rs

4022− ~_ leaf+"rs-fail"

4023− (add:ma a b)

4007+++ add ~/ %add

4008+ |= [a=@rs b=@rs] ^- @rs

4009+ ~_ leaf+"rs-fail"

4010+ (add:ma a b)

40244011```

40254012

40264013#### Examples

40274014

40284015```

4029− > (add:rs .2.5e1 .2.5e2)

4030− .2.75e2

4016+> (add:rs .2.5e1 .2.5e2)

4017+.2.75e2

40314018```

40324019

40334020---

@@ -4038,20 +4025,26 @@ Subtract

40384025

40394026Subtracts `a` from `b`.

40404027

4028+#### Accepts

4029+

4030+`a` is a `@rs`.

4031+

4032+`b` is a `@rs`.

4033+

40414034#### Source

40424035

40434036```hoon

4044− ++ sub ~/ %sub

4045− |= [a=@rs b=@rs] ^- @rs

4046− ~_ leaf+"rs-fail"

4047− (sub:ma a b)

4037+++ sub ~/ %sub

4038+ |= [a=@rs b=@rs] ^- @rs

4039+ ~_ leaf+"rs-fail"

4040+ (sub:ma a b)

40484041```

40494042

40504043#### Examples

40514044

40524045```

4053− > (sub:rs .2.5e1 .2.5e2)

4054− .-2.25e2

4046+> (sub:rs .2.5e1 .2.5e2)

4047+.-2.25e2

40554048```

40564049

40574050---

@@ -4075,17 +4068,17 @@ A `@rs`.

40754068#### Source

40764069

40774070```hoon

4078− ++ mul ~/ %mul

4079− |= [a=@rs b=@rs] ^- @rs

4080− ~_ leaf+"rs-fail"

4081− (mul:ma a b)

4071+++ mul ~/ %mul

4072+ |= [a=@rs b=@rs] ^- @rs

4073+ ~_ leaf+"rs-fail"

4074+ (mul:ma a b)

40824075```

40834076

40844077#### Examples

40854078

40864079```

4087− > (mul:rs .2.5e1 .2.5e2)

4088− .6.25e3

4080+> (mul:rs .2.5e1 .2.5e2)

4081+.6.25e3

40894082```

40904083

40914084---

@@ -4109,17 +4102,17 @@ A `@rs`.

41094102#### Source

41104103

41114104```hoon

4112− ++ div ~/ %div

4113− |= [a=@rs b=@rs] ^- @rs

4114− ~_ leaf+"rs-fail"

4115− (div:ma a b)

4105+++ div ~/ %div

4106+ |= [a=@rs b=@rs] ^- @rs

4107+ ~_ leaf+"rs-fail"

4108+ (div:ma a b)

41164109```

41174110

41184111#### Examples

41194112

41204113```

4121− > (div:rs .4.5e1 .2.2e2)

4122− .2.0454545e-1

4114+> (div:rs .4.5e1 .2.2e2)

4115+.2.0454545e-1

41234116```

41244117

41254118---

@@ -4146,17 +4139,17 @@ A `@rs`.

41464139#### Source

41474140

41484141```hoon

4149− ++ fma ~/ %fma

4150− |= [a=@rs b=@rs c=@rs] ^- @rs

4151− ~_ leaf+"rs-fail"

4152− (fma:ma a b c)

4142+++ fma ~/ %fma

4143+ |= [a=@rs b=@rs c=@rs] ^- @rs

4144+ ~_ leaf+"rs-fail"

4145+ (fma:ma a b c)

41534146```

41544147

41554148#### Examples

41564149

41574150```

4158− > (fma:rs .2.5e1 .2.5e2 .8.2e1)

4159− .6.332e3

4151+> (fma:rs .2.5e1 .2.5e2 .8.2e1)

4152+.6.332e3

41604153```

41614154

41624155---

@@ -4178,17 +4171,17 @@ A `@rs`.

41784171#### Source

41794172

41804173```hoon

4181− ++ sqt ~/ %sqt

4182− |= [a=@rs] ^- @rs

4183− ~_ leaf+"rs-fail"

4184− (sqt:ma a)

4174+++ sqt ~/ %sqt

4175+ |= [a=@rs] ^- @rs

4176+ ~_ leaf+"rs-fail"

4177+ (sqt:ma a)

41854178```

41864179

41874180#### Examples

41884181

41894182```

4190− > (sqt:rs .2.5e2)

4191− .1.5811388e1

4183+> (sqt:rs .2.5e2)

4184+.1.5811388e1

41924185```

41934186

41944187---

@@ -4212,20 +4205,20 @@ A `@rs`.

42124205#### Source

42134206

42144207```hoon

4215− ++ lth ~/ %lth

4216− |= [a=@rs b=@rs]

4217− ~_ leaf+"rs-fail"

4218− (lth:ma a b)

4208+++ lth ~/ %lth

4209+ |= [a=@rs b=@rs]

4210+ ~_ leaf+"rs-fail"

4211+ (lth:ma a b)

42194212```

42204213

42214214#### Examples

42224215

42234216```

4224− > (lth:rs .9.9e1 .1.1e2)

4225− %.y

4217+> (lth:rs .9.9e1 .1.1e2)

4218+%.y

42264219

4227− > (lth:rs .9.9e1 .9.9e1)

4228− %.n

4220+> (lth:rs .9.9e1 .9.9e1)

4221+%.n

42294222```

42304223

42314224---

@@ -4249,20 +4242,20 @@ A `@rs`.

42494242#### Source

42504243

42514244```hoon

4252− ++ lte ~/ %lte

4253− |= [a=@rs b=@rs]

4254− ~_ leaf+"rs-fail"

4255− (lte:ma a b)

4245+++ lte ~/ %lte

4246+ |= [a=@rs b=@rs]

4247+ ~_ leaf+"rs-fail"

4248+ (lte:ma a b)

42564249```

42574250

42584251#### Examples

42594252

42604253```

4261− > (lte:rs .9.9e1 .1.1e2)

4262− %.y

4254+> (lte:rs .9.9e1 .1.1e2)

4255+%.y

42634256

4264− > (lte:rs .9.9e1 .9.9e1)

4265− %.y

4257+> (lte:rs .9.9e1 .9.9e1)

4258+%.y

42664259```

42674260

42684261---

@@ -4286,20 +4279,20 @@ A `@rs`.

42864279#### Source

42874280

42884281```hoon

4289− ++ equ ~/ %equ

4290− |= [a=@rs b=@rs]

4291− ~_ leaf+"rs-fail"

4292− (equ:ma a b)

4282+++ equ ~/ %equ

4283+ |= [a=@rs b=@rs]

4284+ ~_ leaf+"rs-fail"

4285+ (equ:ma a b)

42934286```

42944287

42954288#### Examples

42964289

42974290```

4298− > (equ:rs .9.9e1 .1.1e2)

4299− %.n

4291+> (equ:rs .9.9e1 .1.1e2)

4292+%.n

43004293

4301− > (equ:rs .9.9e1 .9.9e1)

4302− %.y

4294+> (equ:rs .9.9e1 .9.9e1)

4295+%.y

43034296```

43044297

43054298---

@@ -4323,20 +4316,20 @@ A `@rs`.

43234316#### Source

43244317

43254318```hoon

4326− ++ gte ~/ %gte

4327− |= [a=@rs b=@rs]

4328− ~_ leaf+"rs-fail"

4329− (gte:ma a b)

4319+++ gte ~/ %gte

4320+ |= [a=@rs b=@rs]

4321+ ~_ leaf+"rs-fail"

4322+ (gte:ma a b)

43304323```

43314324

43324325#### Examples

43334326

43344327```

4335− > (gte:rs .9.9e1 .9.9e1)

4336− %.y

4328+> (gte:rs .9.9e1 .9.9e1)

4329+%.y

43374330

4338− > (gte:rs .9.9e1 .9.2e2)

4339− %.n

4331+> (gte:rs .9.9e1 .9.2e2)

4332+%.n

43404333```

43414334

43424335---

@@ -4360,23 +4353,23 @@ A `@rs`.

43604353#### Source

43614354

43624355```hoon

4363− ++ gth ~/ %gth

4364− |= [a=@rs b=@rs]

4365− ~_ leaf+"rs-fail"

4366− (gth:ma a b)

4356+++ gth ~/ %gth

4357+ |= [a=@rs b=@rs]

4358+ ~_ leaf+"rs-fail"

4359+ (gth:ma a b)

43674360```

43684361

43694362#### Examples

43704363

43714364```

4372− > (gth:rs .9.9e1 .9.2e2)

4373− %.n

4365+> (gth:rs .9.9e1 .9.2e2)

4366+%.n

43744367

4375− > (gth:rs .9.9e1 .9.9e1)

4376− %.n

4368+> (gth:rs .9.9e1 .9.9e1)

4369+%.n

43774370

4378− > (gth:rs .9.9e1 .1.9e1)

4379− %.y

4371+> (gth:rs .9.9e1 .1.9e1)

4372+%.y

43804373```

43814374

43824375---

@@ -4398,14 +4391,14 @@ A `@rs`.

43984391#### Source

43994392

44004393```hoon

4401− ++ sun |= [a=@u] ^- @rs (sun:ma a)

4394+++ sun |= [a=@u] ^- @rs (sun:ma a)

44024395```

44034396

44044397#### Examples

44054398

44064399```

4407− > (sun:rs 343)

4408− .3.43e2

4400+> (sun:rs 343)

4401+.3.43e2

44094402```

44104403

44114404---

@@ -4427,16 +4420,18 @@ A `@rs`.

44274420#### Source

44284421

44294422```hoon

4430− ++ san |= [a=@s] ^- @rs (san:ma a)

4423+++ san |= [a=@s] ^- @rs (san:ma a)

44314424```

44324425

44334426#### Examples

44344427

44354428```

4436− > (san:rs -343)

4437− .-3.43e2'

4429+> (san:rs -343)

4430+.-3.43e2'

44384431```

44394432

4433+---

4434+

44404435### `++sig:rs`

44414436

44424437Get sign

@@ -4454,17 +4449,17 @@ A `flag`.

44544449#### Source

44554450

44564451```hoon

4457− ++ sig |= [a=@rs] ^- ? (sig:ma a)

4452+++ sig |= [a=@rs] ^- ? (sig:ma a)

44584453```

44594454

44604455#### Examples

44614456

44624457```

4463− > (sig:rs .3.43e2)

4464− %.y

4458+> (sig:rs .3.43e2)

4459+%.y

44654460

4466− > (sig:rs .-3.43e2)

4467− %.n

4461+> (sig:rs .-3.43e2)

4462+%.n

44684463```

44694464

44704465---

@@ -4486,14 +4481,14 @@ A signed integer.

44864481#### Source

44874482

44884483```hoon

4489− ++ exp |= [a=@rs] ^- @s (exp:ma a)

4484+++ exp |= [a=@rs] ^- @s (exp:ma a)

44904485```

44914486

44924487#### Examples

44934488

44944489```

4495− > (exp:rs .-3.43e2)

4496− --8

4490+> (exp:rs .-3.43e2)

4491+--8

44974492```

44984493

44994494---

@@ -4515,14 +4510,14 @@ A `unit` of `@s`.

45154510#### Source

45164511

45174512```hoon

4518− ++ toi |= [a=@rs] ^- (unit @s) (toi:ma a)

4513+++ toi |= [a=@rs] ^- (unit @s) (toi:ma a)

45194514```

45204515

45214516#### Examples

45224517

45234518```

4524− > (toi:rs .-3.43e2)

4525− [~ u=-343]

4519+> (toi:rs .-3.43e2)

4520+[~ u=-343]

45264521```

45274522

45284523---

@@ -4545,14 +4540,14 @@ A `dn`.

45454540#### Source

45464541

45474542```hoon

4548− ++ drg |= [a=@rs] ^- dn (drg:ma a)

4543+++ drg |= [a=@rs] ^- dn (drg:ma a)

45494544```

45504545

45514546#### Examples

45524547

45534548```

4554− > (drg:rs .-3.43e2)

4555− [%d s=%.n e=--0 a=343]

4549+> (drg:rs .-3.43e2)

4550+[%d s=%.n e=--0 a=343]

45564551```

45574552

45584553---

@@ -4574,15 +4569,14 @@ A `@rs`.

45744569#### Source

45754570

45764571```hoon

4577− ++ grd |= [a=dn] ^- @rs (grd:ma a)

4578− --

4572+++ grd |= [a=dn] ^- @rs (grd:ma a)

45794573```

45804574

45814575#### Examples

45824576

45834577```

4584− > (grd:rs [%d s=%.n e=--0 a=343])

4585− .-3.43e2

4578+> (grd:rs [%d s=%.n e=--0 a=343])

4579+.-3.43e2

45864580```

45874581

45884582---

@@ -4593,16 +4587,16 @@ Quadruple-precision fp

45934587

45944588A container core for operations related to quadruple-precision binary floats.

45954589

4596−`++rq` has four rounding modes: round to nearest (`$n`), round up (`$u`), round

4597−down (`$d`), and round to zero (`$z`).

4590+`++rq` has four rounding modes: round to nearest (`%n`), round up (`%u`), round

4591+down (`%d`), and round to zero (`%z`).

45984592

45994593#### Source

46004594

46014595```hoon

4602− ++ rq

4603− ~% %rq +> ~

4604− ^?

4605− |_ r=$?($n $u $d $z)

4596+++ rq

4597+ ~% %rq +> ~

4598+ ^|

4599+ |_ r=$?(%n %u %d %z)

46064600```

46074601

46084602### `++ma:rq`

@@ -4615,8 +4609,8 @@ configuration of the `rq` core.

46154609#### Source

46164610

46174611```hoon

4618− ++ ma

4619− %*(. ff w 15, p 112, b --16.383, r r)

4612+++ ma

4613+ %*(. ff w 15, p 112, b --16.383, r r)

46204614```

46214615

46224616---

@@ -4638,15 +4632,15 @@ An `fn`.

46384632#### Source

46394633

46404634```hoon

4641− ++ sea

4642− |= [a=@rq] (sea:ma a)

4635+++ sea

4636+ |= [a=@rq] (sea:ma a)

46434637```

46444638

46454639#### Examples

46464640

46474641```

4648− > (sea:rq .~~~1.05102e5)

4649− [%f s=%.y e=-96 a=8.327.038.336.574.210.409.756.656.268.214.272]

4642+> (sea:rq .~~~1.05102e5)

4643+[%f s=%.y e=-96 a=8.327.038.336.574.210.409.756.656.268.214.272]

46504644```

46514645

46524646---

@@ -4668,15 +4662,15 @@ A `@rq`, a quad-precision float.

46684662#### Source

46694663

46704664```hoon

4671− ++ bit

4672− |= [a=n] ^- @rq (bit:ma a)

4665+++ bit

4666+ |= [a=fn] ^- @rq (bit:ma a)

46734667```

46744668

46754669#### Examples

46764670

46774671```

4678− > (bit:rq [%f s=%.y e=-96 a=8.327.038.336.574.210.409.756.656.268.214.272])

4679− .~~~1.05102e5

4672+> (bit:rq [%f s=%.y e=-96 a=8.327.038.336.574.210.409.756.656.268.214.272])

4673+.~~~1.05102e5

46804674```

46814675

46824676---

@@ -4700,17 +4694,17 @@ A `@rq`.

47004694#### Source

47014695

47024696```hoon

4703− ++ add ~/ %add

4704− |= [a=@rq b=@rq] ^- @rq

4705− ~_ leaf+"rq-fail"

4706− (add:ma a b)

4697+++ add ~/ %add

4698+ |= [a=@rq b=@rq] ^- @rq

4699+ ~_ leaf+"rq-fail"

4700+ (add:ma a b)

47074701```

47084702

47094703#### Examples

47104704

47114705```

4712− > (add:rq .~~~-1.821e5 .~~~1.05102e5)

4713− .~~~-7.6998e4

4706+> (add:rq .~~~-1.821e5 .~~~1.05102e5)

4707+.~~~-7.6998e4

47144708```

47154709

47164710---

@@ -4734,20 +4728,20 @@ A `@rq`.

47344728#### Source

47354729

47364730```hoon

4737− ++ sub ~/ %sub

4738− |= [a=@rq b=@rq] ^- @rq

4739− ~_ leaf+"rq-fail"

4740− (sub:ma a b)

4731+++ sub ~/ %sub

4732+ |= [a=@rq b=@rq] ^- @rq

4733+ ~_ leaf+"rq-fail"

4734+ (sub:ma a b)

47414735```

47424736

47434737#### Examples

47444738

47454739```

4746− > (sub:rq .~~~1.821e5 .~~~1.05102e5)

4747− .~~~7.6998e4

4740+> (sub:rq .~~~1.821e5 .~~~1.05102e5)

4741+.~~~7.6998e4

47484742

4749− > (sub:rq .~~~1.821e5 .~~~-1.05102e5)

4750− .~~~2.87202e5

4743+> (sub:rq .~~~1.821e5 .~~~-1.05102e5)

4744+.~~~2.87202e5

47514745```

47524746

47534747---

@@ -4771,17 +4765,17 @@ A `@rq`.

47714765#### Source

47724766

47734767```hoon

4774− ++ mul ~/ %mul

4775− |= [a=@rq b=@rq] ^- @rq

4776− ~_ leaf+"rq-fail"

4777− (mul:ma a b)

4768+++ mul ~/ %mul

4769+ |= [a=@rq b=@rq] ^- @rq

4770+ ~_ leaf+"rq-fail"

4771+ (mul:ma a b)

47784772```

47794773

47804774#### Examples

47814775

47824776```

4783− > (mul:rq .~~~1.821e5 .~~~-1.05102e5)

4784− .~~~-1.91390742e10

4777+> (mul:rq .~~~1.821e5 .~~~-1.05102e5)

4778+.~~~-1.91390742e10

47854779```

47864780

47874781---

@@ -4805,17 +4799,17 @@ A `@rq`.

48054799#### Source

48064800

48074801```hoon

4808− ++ div ~/ %div

4809− |= [a=@rq b=@rq] ^- @rq

4810− ~_ leaf+"rq-fail"

4811− (div:ma a b)

4802+++ div ~/ %div

4803+ |= [a=@rq b=@rq] ^- @rq

4804+ ~_ leaf+"rq-fail"

4805+ (div:ma a b)

48124806```

48134807

48144808#### Examples

48154809

48164810```

4817− > (div:rq .~~~1.821e5 .~~~1.05102e3)

4818− .~~~1.732602614602957127361991208540275e2

4811+> (div:rq .~~~1.821e5 .~~~1.05102e3)

4812+.~~~1.732602614602957127361991208540275e2

48194813```

48204814

48214815---

@@ -4842,17 +4836,17 @@ A `@rq`.

48424836#### Source

48434837

48444838```hoon

4845− ++ fma ~/ %fma

4846− |= [a=@rq b=@rq c=@rq] ^- @rq

4847− ~_ leaf+"rq-fail"

4848− (fma:ma a b c)

4839+++ fma ~/ %fma

4840+ |= [a=@rq b=@rq c=@rq] ^- @rq

4841+ ~_ leaf+"rq-fail"

4842+ (fma:ma a b c)

48494843```

48504844

48514845#### Examples

48524846

48534847```

4854− > (fma:rq .~~~1.821e5 .~~~-1.05102e2 .~~~6.2044e7)

4855− .~~~4.29049258e7

4848+> (fma:rq .~~~1.821e5 .~~~-1.05102e2 .~~~6.2044e7)

4849+.~~~4.29049258e7

48564850```

48574851

48584852---

@@ -4874,17 +4868,17 @@ A `@rq`.

48744868#### Source

48754869

48764870```hoon

4877− ++ sqt ~/ %sqt

4878− |= [a=@rq] ^- @rq

4879− ~_ leaf+"rq-fail"

4880− (sqt:ma a)

4871+++ sqt ~/ %sqt

4872+ |= [a=@rq] ^- @rq

4873+ ~_ leaf+"rq-fail"

4874+ (sqt:ma a)

48814875```

48824876

48834877#### Examples

48844878

48854879```

4886− > (sqt:rq .~~~6.2044e7)

4887− .~~~7.876801381271461258959876570289002e3

4880+> (sqt:rq .~~~6.2044e7)

4881+.~~~7.876801381271461258959876570289002e3

48884882```

48894883

48904884---

@@ -4908,20 +4902,20 @@ A `@rq`.

49084902#### Source

49094903

49104904```hoon

4911− ++ lth ~/ %lth

4912− |= [a=@rq b=@rq]

4913− ~_ leaf+"rq-fail"

4914− (lth:ma a b)

4905+++ lth ~/ %lth

4906+ |= [a=@rq b=@rq]

4907+ ~_ leaf+"rq-fail"

4908+ (lth:ma a b)

49154909```

49164910

49174911#### Examples

49184912

49194913```

4920− > (lth:rq .~~~1.2044e7 (mul:rq .~~~9.02e2 .~~~7.114e3))

4921− %.n

4914+> (lth:rq .~~~1.2044e7 (mul:rq .~~~9.02e2 .~~~7.114e3))

4915+%.n

49224916

4923− > (lth:rq .~~~1.2044e7 (mul:rq .~~~9.02e3 .~~~7.114e3))

4924− %.y

4917+> (lth:rq .~~~1.2044e7 (mul:rq .~~~9.02e3 .~~~7.114e3))

4918+%.y

49254919```

49264920

49274921---

@@ -4945,23 +4939,23 @@ A `@rq`.

49454939#### Source

49464940

49474941```hoon

4948− ++ lte ~/ %lte

4949− |= [a=@rq b=@rq]

4950− ~_ leaf+"rq-fail"

4951− (lte:ma a b)

4942+++ lte ~/ %lte

4943+ |= [a=@rq b=@rq]

4944+ ~_ leaf+"rq-fail"

4945+ (lte:ma a b)

49524946```

49534947

49544948#### Examples

49554949

49564950```

4957− > (lte:rq .~~~1.2044e7 (mul:rq .~~~9.02e2 .~~~7.114e3))

4958− %.n

4951+> (lte:rq .~~~1.2044e7 (mul:rq .~~~9.02e2 .~~~7.114e3))

4952+%.n

49594953

4960− > (lte:rq .~~~1.2044e7 (mul:rq .~~~9.02e3 .~~~7.114e3))

4961− %.y

4954+> (lte:rq .~~~1.2044e7 (mul:rq .~~~9.02e3 .~~~7.114e3))

4955+%.y

49624956

4963− > (lte:rq .~~~1.2044e7 .~~~1.2044e7)

4964− %.y

4957+> (lte:rq .~~~1.2044e7 .~~~1.2044e7)

4958+%.y

49654959```

49664960

49674961---

@@ -4985,20 +4979,20 @@ A `@rq`.

49854979#### Source

49864980

49874981```hoon

4988− ++ equ ~/ %equ

4989− |= [a=@rq b=@rq]

4990− ~_ leaf+"rq-fail"

4991− (equ:ma a b)

4982+++ equ ~/ %equ

4983+ |= [a=@rq b=@rq]

4984+ ~_ leaf+"rq-fail"

4985+ (equ:ma a b)

49924986```

49934987

49944988#### Examples

49954989

49964990```

4997− > (equ:rq .~~~1.2044e7 .~~~1.2044e7)

4998− %.y

4991+> (equ:rq .~~~1.2044e7 .~~~1.2044e7)

4992+%.y

49994993

5000− > (equ:rq .~~~2.2044e7 .~~~1.2044e7)

5001− %.n

4994+> (equ:rq .~~~2.2044e7 .~~~1.2044e7)

4995+%.n

50024996```

50034997

50044998---

@@ -5022,23 +5016,23 @@ A `@rq`.

50225016#### Source

50235017

50245018```hoon

5025− ++ gte ~/ %gte

5026− |= [a=@rq b=@rq]

5027− ~_ leaf+"rq-fail"

5028− (gte:ma a b)

5019+++ gte ~/ %gte

5020+ |= [a=@rq b=@rq]

5021+ ~_ leaf+"rq-fail"

5022+ (gte:ma a b)

50295023```

50305024

50315025#### Examples

50325026

50335027```

5034− > (gte:rq .~~~1.2044e7 .~~~1.2044e7)

5035− %.y

5028+> (gte:rq .~~~1.2044e7 .~~~1.2044e7)

5029+%.y

50365030

5037− > (gte:rq .~~~2.2044e7 .~~~1.2044e7)

5038− %.y

5031+> (gte:rq .~~~2.2044e7 .~~~1.2044e7)

5032+%.y

50395033

5040− > (gte:rq .~~~1.2044e7 .~~~2.2044e7)

5041− %.n

5034+> (gte:rq .~~~1.2044e7 .~~~2.2044e7)

5035+%.n

50425036```

50435037

50445038---

@@ -5060,23 +5054,23 @@ A `@rq`.

50605054#### Source

50615055

50625056```hoon

5063− ++ gth ~/ %gth

5064− |= [a=@rq b=@rq]

5065− ~_ leaf+"rq-fail"

5066− (gth:ma a b)

5057+++ gth ~/ %gth

5058+ |= [a=@rq b=@rq]

5059+ ~_ leaf+"rq-fail"

5060+ (gth:ma a b)

50675061```

50685062

50695063#### Examples

50705064

50715065```

5072− > (gth:rq .~~~1.2044e7 .~~~1.2044e7)

5073− %.n

5066+> (gth:rq .~~~1.2044e7 .~~~1.2044e7)

5067+%.n

50745068

5075− > (gth:rq .~~~2.2044e7 .~~~1.2044e7)

5076− %.y

5069+> (gth:rq .~~~2.2044e7 .~~~1.2044e7)

5070+%.y

50775071

5078− > (gth:rq .~~~1.2044e7 .~~~2.2044e7)

5079− %.n

5072+> (gth:rq .~~~1.2044e7 .~~~2.2044e7)

5073+%.n

50805074```

50815075

50825076---

@@ -5098,14 +5092,14 @@ A `@rq`, a quad-precision float.

50985092#### Source

50995093

51005094```hoon

5101− ++ sun |= [a=@u] ^- @rq (sun:ma a)

5095+++ sun |= [a=@u] ^- @rq (sun:ma a)

51025096```

51035097

51045098#### Examples

51055099

51065100```

5107− > (sun:rq 205)

5108− .~~~2.05e2

5101+> (sun:rq 205)

5102+.~~~2.05e2

51095103```

51105104

51115105---

@@ -5127,14 +5121,14 @@ A `@rq`, a quad-precision float.

51275121#### Source

51285122

51295123```hoon

5130− ++ san |= [a=@s] ^- @rq (san:ma a)

5124+++ san |= [a=@s] ^- @rq (san:ma a)

51315125```

51325126

51335127#### Examples

51345128

51355129```

5136− > (san:rq -205)

5137− .~~~-2.05e2

5130+> (san:rq -205)

5131+.~~~-2.05e2

51385132```

51395133

51405134---

@@ -5156,14 +5150,14 @@ A `flag`.

51565150#### Source

51575151

51585152```hoon

5159− ++ sig |= [a=@rq] ^- ? (sig:ma a)

5153+++ sig |= [a=@rq] ^- ? (sig:ma a)

51605154```

51615155

51625156#### Examples

51635157

51645158```

5165− > (sig:rq .~~~-2.05e2)

5166− %.n

5159+> (sig:rq .~~~-2.05e2)

5160+%.n

51675161```

51685162

51695163---

@@ -5185,14 +5179,14 @@ A `@s`, a signed integer.

51855179#### Source

51865180

51875181```hoon

5188− ++ exp |= [a=@rq] ^- @s (exp:ma a)

5182+++ exp |= [a=@rq] ^- @s (exp:ma a)

51895183```

51905184

51915185#### Examples

51925186

51935187```

5194− > (exp:rq .~~~-2.05e2)

5195− --7

5188+> (exp:rq .~~~-2.05e2)

5189+--7

51965190```

51975191

51985192---

@@ -5214,17 +5208,17 @@ A `unit` of `@s`.

52145208#### Source

52155209

52165210```hoon

5217− ++ toi |= [a=@rq] ^- (unit @s) (toi:ma a)

5211+++ toi |= [a=@rq] ^- (unit @s) (toi:ma a)

52185212```

52195213

52205214#### Examples

52215215

52225216```

5223− > (toi:rq .~~~-2.085e2)

5224− [~ u=-208]

5217+> (toi:rq .~~~-2.085e2)

5218+[~ u=-208]

52255219

5226− > (toi:rq .~~~-2.08e2)

5227− [~ u=-208]

5220+> (toi:rq .~~~-2.08e2)

5221+[~ u=-208]

52285222```

52295223

52305224---

@@ -5247,17 +5241,17 @@ A `dn`.

52475241#### Source

52485242

52495243```hoon

5250− ++ drg |= [a=@rq] ^- dn (drg:ma a) :: @rq to decimal float

5244+++ drg |= [a=@rq] ^- dn (drg:ma a)

52515245```

52525246

52535247#### Examples

52545248

52555249```

5256− > (drg:rq .~~~-2.085e2)

5257− [%d s=%.n e=-1 a=2.085]

5250+> (drg:rq .~~~-2.085e2)

5251+[%d s=%.n e=-1 a=2.085]

52585252

5259− > (drg:rq .~~~-2.08e2)

5260− [%d s=%.n e=--0 a=208]

5253+> (drg:rq .~~~-2.08e2)

5254+[%d s=%.n e=--0 a=208]

52615255```

52625256

52635257---

@@ -5281,15 +5275,14 @@ A `@rq`, a quad-precision float.

52815275#### Source

52825276

52835277```hoon

5284− ++ grd |= [a=dn] ^- @rq (grd:ma a)

5285− --

5278+++ grd |= [a=dn] ^- @rq (grd:ma a)

52865279```

52875280

52885281#### Examples

52895282

52905283```

5291− > (grd:rq [%d s=%.n e=--0 a=343])

5292− .~~~-3.43e2

5284+> (grd:rq [%d s=%.n e=--0 a=343])

5285+.~~~-3.43e2

52935286```

52945287

52955288---

@@ -5300,16 +5293,16 @@ Half-precision fp

53005293

53015294A container core for operations related to half-precision binary floats.

53025295

5303−`++rh` has four rounding modes: round to nearest (`$n`), round up (`$u`), round

5304−down (`$d`), and round to zero (`$z`).

5296+`++rh` has four rounding modes: round to nearest (`%n`), round up (`%u`), round

5297+down (`%d`), and round to zero (`%z`).

53055298

53065299#### Source

53075300

53085301```hoon

5309− ++ rh

5310− ~% %rh +> ~

5311− ^?

5312− |_ r=$?($n $u $d $z)

5302+++ rh

5303+ ~% %rh +> ~

5304+ ^|

5305+ |_ r=$?(%n %u %d %z)

53135306```

53145307

53155308---

@@ -5324,8 +5317,8 @@ configuration of the `rh` core.

53245317#### Source

53255318

53265319```hoon

5327− ++ ma

5328− %*(. ff w 5, p 10, b --15, r r)

5320+++ ma

5321+ %*(. ff w 5, p 10, b --15, r r)

53295322```

53305323

53315324---

@@ -5347,15 +5340,15 @@ An `fn`.

53475340#### Source

53485341

53495342```hoon

5350− ++ sea

5351− |= [a=@rh] (sea:ma a)

5343+++ sea

5344+ |= [a=@rh] (sea:ma a)

53525345```

53535346

53545347#### Examples

53555348

53565349```

5357− > (sea:rh .~~1.22e-5)

5358− [%f s=%.y e=-24 a=205]

5350+> (sea:rh .~~1.22e-5)

5351+[%f s=%.y e=-24 a=205]

53595352```

53605353

53615354---

@@ -5377,15 +5370,15 @@ A `@rh`, a half-precision float.

53775370#### Source

53785371

53795372```hoon

5380− ++ bit

5381− |= [a=fn] ^- @rh (bit:ma a)

5373+++ bit

5374+ |= [a=fn] ^- @rh (bit:ma a)

53825375```

53835376

53845377#### Examples

53855378

53865379```

5387− > (bit:rh [%f s=%.y e=-24 a=205])

5388− .~~1.22e-5

5380+> (bit:rh [%f s=%.y e=-24 a=205])

5381+.~~1.22e-5

53895382```

53905383

53915384---

@@ -5407,17 +5400,17 @@ A `@rh`.

54075400#### Source

54085401

54095402```hoon

5410− ++ add ~/ %add

5411− |= [a=@rh b=@rh] ^- @rh

5412− ~_ leaf+"rh-fail"

5413− (add:ma a b)

5403+++ add ~/ %add

5404+ |= [a=@rh b=@rh] ^- @rh

5405+ ~_ leaf+"rh-fail"

5406+ (add:ma a b)

54145407```

54155408

54165409#### Examples

54175410

54185411```

5419− > (add:rh .~~1.82e2 .~~1.02e2)

5420− .~~2.84e2

5412+> (add:rh .~~1.82e2 .~~1.02e2)

5413+.~~2.84e2

54215414```

54225415

54235416---

@@ -5441,20 +5434,20 @@ A `@rh`.

54415434#### Source

54425435

54435436```hoon

5444− ++ sub ~/ %sub

5445− |= [a=@rh b=@rh] ^- @rh

5446− ~_ leaf+"rh-fail"

5447− (sub:ma a b)

5437+++ sub ~/ %sub

5438+ |= [a=@rh b=@rh] ^- @rh

5439+ ~_ leaf+"rh-fail"

5440+ (sub:ma a b)

54485441```

54495442

54505443#### Examples

54515444

54525445```

5453− > (sub:rh .~~1.821e2 .~~1.051e2)

5454− .~~7.7e1

5446+> (sub:rh .~~1.821e2 .~~1.051e2)

5447+.~~7.7e1

54555448

5456− > (sub:rh .~~1.821e2 .~~6.051e2)

5457− .~~-4.228e2

5449+> (sub:rh .~~1.821e2 .~~6.051e2)

5450+.~~-4.228e2

54585451```

54595452

54605453---

@@ -5478,17 +5471,17 @@ A `@rh`.

54785471#### Source

54795472

54805473```hoon

5481− ++ mul ~/ %mul

5482− |= [a=@rh b=@rh] ^- @rh

5483− ~_ leaf+"rh-fail"

5484− (mul:ma a b)

5474+++ mul ~/ %mul

5475+ |= [a=@rh b=@rh] ^- @rh

5476+ ~_ leaf+"rh-fail"

5477+ (mul:ma a b)

54855478```

54865479

54875480#### Examples

54885481

54895482```

5490− > (mul:rh .~~1.821e1 .~~-1.05102e2)

5491− .~~-1.913e3

5483+> (mul:rh .~~1.821e1 .~~-1.05102e2)

5484+.~~-1.913e3

54925485```

54935486

54945487---

@@ -5512,17 +5505,17 @@ A `@rh`.

55125505#### Source

55135506

55145507```hoon

5515− ++ div ~/ %div

5516− |= [a=@rh b=@rh] ^- @rh

5517− ~_ leaf+"rh-fail"

5518− (div:ma a b)

5508+++ div ~/ %div

5509+ |= [a=@rh b=@rh] ^- @rh

5510+ ~_ leaf+"rh-fail"

5511+ (div:ma a b)

55195512```

55205513

55215514#### examples

55225515

55235516```

5524− > (div:rh .~~1.821e3 .~~1.05102e2)

5525− .~~1.731e1

5517+> (div:rh .~~1.821e3 .~~1.05102e2)

5518+.~~1.731e1

55265519```

55275520

55285521---

@@ -5549,17 +5542,17 @@ A `@rh`.

55495542#### Source

55505543

55515544```hoon

5552− ++ fma ~/ %fma

5553− |= [a=@rh b=@rh c=@rh] ^- @rh

5554− ~_ leaf+"rh-fail"

5555− (fma:ma a b c)

5545+++ fma ~/ %fma

5546+ |= [a=@rh b=@rh c=@rh] ^- @rh

5547+ ~_ leaf+"rh-fail"

5548+ (fma:ma a b c)

55565549```

55575550

55585551#### Examples

55595552

55605553```

5561− > (fma:rh .~~1.821e4 .~~-1.05102e2 .~~6.2044e3)

5562− .~~-6.55e4

5554+> (fma:rh .~~1.821e4 .~~-1.05102e2 .~~6.2044e3)

5555+.~~-6.55e4

55635556```

55645557

55655558---

@@ -5581,17 +5574,17 @@ A `@rh`.

55815574#### Source

55825575

55835576```hoon

5584− ++ sqt ~/ %sqt

5585− |= [a=@rh] ^- @rh

5586− ~_ leaf+"rh-fail"

5587− (sqt:ma a)

5577+++ sqt ~/ %sqt

5578+ |= [a=@rh] ^- @rh

5579+ ~_ leaf+"rh-fail"

5580+ (sqt:ma a)

55885581```

55895582

5590−#### Source

5583+#### Example

55915584

55925585```hoon

5593− > (sqt:rh .~~6.24e4)

5594− .~~2.498e2

5586+> (sqt:rh .~~6.24e4)

5587+.~~2.498e2

55955588```

55965589

55975590---

@@ -5615,20 +5608,20 @@ A `@rh`.

56155608#### Source

56165609

56175610```hoon

5618− ++ lth ~/ %lth

5619− |= [a=@rh b=@rh]

5620− ~_ leaf+"rh-fail"

5621− (lth:ma a b)

5611+++ lth ~/ %lth

5612+ |= [a=@rh b=@rh]

5613+ ~_ leaf+"rh-fail"

5614+ (lth:ma a b)

56225615```

56235616

56245617#### Examples

56255618

56265619```

5627− > (lth:rh .~~1.2e5 (mul:rh .~~9.02e2 .~~7.114e2))

5628− %.n

5620+> (lth:rh .~~1.2e5 (mul:rh .~~9.02e2 .~~7.114e2))

5621+%.n

56295622

5630− > (lth:rh .~~1.2e3 (mul:rh .~~9.02e1 .~~7.114e2))

5631− %.y

5623+> (lth:rh .~~1.2e3 (mul:rh .~~9.02e1 .~~7.114e2))

5624+%.y

56325625```

56335626

56345627---

@@ -5652,23 +5645,23 @@ A `@rh`.

56525645#### Source

56535646

56545647```hoon

5655− ++ lte ~/ %lte

5656− |= [a=@rh b=@rh]

5657− ~_ leaf+"rh-fail"

5658− (lte:ma a b)

5648+++ lte ~/ %lte

5649+ |= [a=@rh b=@rh]

5650+ ~_ leaf+"rh-fail"

5651+ (lte:ma a b)

56595652```

56605653

56615654#### Examples

56625655

56635656```

5664− > (lte:rh .~~1.2e5 (mul:rh .~~9.02e2 .~~7.114e2))

5665− %.n

5657+> (lte:rh .~~1.2e5 (mul:rh .~~9.02e2 .~~7.114e2))

5658+%.n

56665659

5667− > (lte:rh .~~1.2e3 (mul:rh .~~9.02e1 .~~7.114e2))

5668− %.y

5660+> (lte:rh .~~1.2e3 (mul:rh .~~9.02e1 .~~7.114e2))

5661+%.y

56695662

5670− > (lte:rh .~~1.2e3 .~~1.2e3)

5671− %.y

5663+> (lte:rh .~~1.2e3 .~~1.2e3)

5664+%.y

56725665```

56735666

56745667---

@@ -5692,20 +5685,20 @@ A `@rh`.

56925685#### Source

56935686

56945687```hoon

5695− ++ equ ~/ %equ

5696− |= [a=@rh b=@rh]

5697− ~_ leaf+"rh-fail"

5698− (equ:ma a b)

5688+++ equ ~/ %equ

5689+ |= [a=@rh b=@rh]

5690+ ~_ leaf+"rh-fail"

5691+ (equ:ma a b)

56995692```

57005693

57015694#### Examples

57025695

57035696```

5704− > (equ:rh .~~1.24e4 .~~1.24e4)

5705− %.y

5697+> (equ:rh .~~1.24e4 .~~1.24e4)

5698+%.y

57065699

5707− > (equ:rh .~~2.24e4 .~~1.24e4)

5708− %.n

5700+> (equ:rh .~~2.24e4 .~~1.24e4)

5701+%.n

57095702```

57105703

57115704---

@@ -5729,23 +5722,23 @@ A `@rh`.

57295722#### Source

57305723

57315724```hoon

5732− ++ gte ~/ %gte

5733− |= [a=@rh b=@rh]

5734− ~_ leaf+"rh-fail"

5735− (gte:ma a b)

5725+++ gte ~/ %gte

5726+ |= [a=@rh b=@rh]

5727+ ~_ leaf+"rh-fail"

5728+ (gte:ma a b)

57365729```

57375730

57385731#### Examples

57395732

57405733```

5741− > (gte:rh .~~1.24e4 .~~1.24e4)

5742− %.y

5734+> (gte:rh .~~1.24e4 .~~1.24e4)

5735+%.y

57435736

5744− > (gte:rh .~~2.24e4 .~~1.24e4)

5745− %.y

5737+> (gte:rh .~~2.24e4 .~~1.24e4)

5738+%.y

57465739

5747− > (gte:rh .~~1.24e4 .~~2.24e4)

5748− %.n

5740+> (gte:rh .~~1.24e4 .~~2.24e4)

5741+%.n

57495742```

57505743

57515744---

@@ -5767,23 +5760,23 @@ A `@rh`.

57675760#### Source

57685761

57695762```hoon

5770− ++ gth ~/ %gth

5771− |= [a=@rh b=@rh]

5772− ~_ leaf+"rh-fail"

5773− (gth:ma a b)

5763+++ gth ~/ %gth

5764+ |= [a=@rh b=@rh]

5765+ ~_ leaf+"rh-fail"

5766+ (gth:ma a b)

57745767```

57755768

57765769#### Examples

57775770

57785771```

5779− > (gth:rh .~~1.24e4 .~~1.244e4)

5780− %.n

5772+> (gth:rh .~~1.24e4 .~~1.244e4)

5773+%.n

57815774

5782− > (gth:rh .~~2.24e4 .~~1.24e4)

5783− %.y

5775+> (gth:rh .~~2.24e4 .~~1.24e4)

5776+%.y

57845777

5785− > (gth:rh .~~1.24e4 .~~2.24e4)

5786− %.n

5778+> (gth:rh .~~1.24e4 .~~2.24e4)

5779+%.n

57875780```

57885781

57895782---

@@ -5805,14 +5798,15 @@ A `@rs`, a single-precision float.

58055798#### Source

58065799

58075800```hoon

5808− ++ tos |= {a/@rh} (bit:rs (sea a))

5801+++ tos

5802+ |= [a=@rh] (bit:rs (sea a))

58095803```

58105804

58115805#### Examples

58125806

58135807```

5814− > (tos:rh .~~2.5e2)

5815− .2.5e2

5808+> (tos:rh .~~2.5e2)

5809+.2.5e2

58165810```

58175811

58185812---

@@ -5834,14 +5828,15 @@ A `@rh`, a half-precision float.

58345828#### Source

58355829

58365830```hoon

5837− ++ fos |= {a/@rs} (bit (sea:rs a))

5831+++ fos

5832+ |= [a=@rs] (bit (sea:rs a))

58385833```

58395834

58405835#### Examples

58415836

58425837```

5843− > (fos:rh .2.5e2)

5844− .~~2.5e2

5838+> (fos:rh .2.5e2)

5839+.~~2.5e2

58455840```

58465841

58475842---

@@ -5863,14 +5858,14 @@ A `@rh`, a half-precision float.

58635858#### Source

58645859

58655860```hoon

5866− ++ sun |= [a=@u] ^- @rh (sun:ma a)

5861+++ sun |= [a=@u] ^- @rh (sun:ma a)

58675862```

58685863

58695864#### Examples

58705865

58715866```

5872− > (sun:rh 205)

5873− .~~2.05e2

5867+> (sun:rh 205)

5868+.~~2.05e2

58745869```

58755870

58765871---

@@ -5892,14 +5887,14 @@ A `@rh`, a half-precision float.

58925887#### Source

58935888

58945889```hoon

5895− ++ san |= [a=@s] ^- @rh (san:ma a)

5890+++ san |= [a=@s] ^- @rh (san:ma a)

58965891```

58975892

58985893#### Examples

58995894

59005895```

5901− > (san:rh -205)

5902− .~~-2.05e2

5896+> (san:rh -205)

5897+.~~-2.05e2

59035898```

59045899

59055900---

@@ -5921,14 +5916,14 @@ A `flag`.

59215916#### Source

59225917

59235918```hoon

5924− ++ sig |= [a=@rh] ^- ? (sig:ma a)

5919+++ sig |= [a=@rh] ^- ? (sig:ma a)

59255920```

59265921

59275922#### Examples

59285923

59295924```

5930− > (sig:rh .~~-2.05e2)

5931− %.n

5925+> (sig:rh .~~-2.05e2)

5926+%.n

59325927```

59335928

59345929---

@@ -5950,14 +5945,14 @@ A `@s`, a signed integer.

59505945#### Source

59515946

59525947```hoon

5953− ++ exp |= [a=@rh] ^- @s (exp:ma a)

5948+++ exp |= [a=@rh] ^- @s (exp:ma a)

59545949```

59555950

59565951#### Examples

59575952

59585953```

5959− > (exp:rh .~~-2.05e2)

5960− --7

5954+> (exp:rh .~~-2.05e2)

5955+--7

59615956```

59625957

59635958---

@@ -5979,17 +5974,17 @@ A `unit` of `@s`.

59795974#### Source

59805975

59815976```hoon

5982− ++ toi |= [a=@rh] ^- (unit @s) (toi:ma a)

5977+++ toi |= [a=@rh] ^- (unit @s) (toi:ma a)

59835978```

59845979

59855980#### Examples

59865981

59875982```

5988− > (toi:rh .~~-2.085e2)

5989− [~ u=-208]

5983+> (toi:rh .~~-2.085e2)

5984+[~ u=-208]

59905985

5991− > (toi:rh .~~-2.08e2)

5992− [~ u=-208]

5986+> (toi:rh .~~-2.08e2)

5987+[~ u=-208]

59935988```

59945989

59955990---

@@ -6012,17 +6007,17 @@ A `dn`.

60126007#### Source

60136008

60146009```hoon

6015− ++ drg |= [a=@rh] ^- dn (drg:ma a)

6010+++ drg |= [a=@rh] ^- dn (drg:ma a)

60166011```

60176012

60186013#### Examples

60196014

60206015```

6021− > (drg:rh .~~-2.085e2)

6022− [%d s=%.n e=-1 a=2.085]

6016+> (drg:rh .~~-2.085e2)

6017+[%d s=%.n e=-1 a=2.085]

60236018

6024− > (drg:rh .~~-2.08e2)

6025− [%d s=%.n e=--0 a=208]

6019+> (drg:rh .~~-2.08e2)

6020+[%d s=%.n e=--0 a=208]

60266021```

60276022

60286023---

@@ -6046,15 +6041,14 @@ A `@rh`, a a half-precision float.

60466041#### Source

60476042

60486043```hoon

6049− ++ grd |= [a=dn] ^- @rh (grd:ma a)

6050− --

6044+++ grd |= [a=dn] ^- @rh (grd:ma a)

60516045```

60526046

60536047#### Examples

60546048

60556049```

6056− > (grd:rh [%d s=%.n e=--0 a=343])

6057− .~~-3.43e2

6050+> (grd:rh [%d s=%.n e=--0 a=343])

6051+.~~-3.43e2

60586052```

60596053

60606054---

content/docs/hoon/reference/stdlib/3c.md+241−242

@@ -4,353 +4,352 @@ weight = 23

44template = "doc.html"

55+++

7−## `++yall`

7+## `++year`

9−Time since beginning of time

9+Date to `@da`

1010

11−Produce the date tuple of `[y=@ud m=@ud d=@ud]` of the year, month, and

12−day from a number of days from the beginning of the Gregorian calendar.

11+Accept a parsed date of form `[[a=? y=@ud] m=@ud t=tarp]` and produce

12+its `@da` representation.

1313

1414#### Accepts

1515

16−`day` is a an unsigned decimal.

16+`det` is a `date`

1717

1818#### Produces

1919

20−A cell of unsigned decimals.

20+A `@da`.

2121

2222#### Source

2323

2424```hoon

25− ++ yall

26− |= day=@ud

27− ^- [y=@ud m=@ud d=@ud]

28− =+ [era=0 cet=0 lep=*?]

29− => .(era (div day era:yo), day (mod day era:yo))

30− => ^+ .

31− ?: (lth day +(cet:yo))

32− .(lep &, cet 0)

33− => .(lep |, cet 1, day (sub day +(cet:yo)))

34− .(cet (add cet (div day cet:yo)), day (mod day cet:yo))

35− =+ yer=(add (mul 400 era) (mul 100 cet))

36− |- ^- [y=@ud m=@ud d=@ud]

37− =+ dis=?:(lep 366 365)

38− ?. (lth day dis)

39− =+ ner=+(yer)

40− $(yer ner, day (sub day dis), lep =(0 (end 0 2 ner)))

41− |- ^- [y=@ud m=@ud d=@ud]

42− =+ [mot=0 cah=?:(lep moy:yo moh:yo)]

43− |- ^- [y=@ud m=@ud d=@ud]

44− =+ zis=(snag mot cah)

45− ?: (lth day zis)

46− [yer +(mot) +(day)]

47− $(mot +(mot), day (sub day zis))

25+++ year

26+ |= det=date

27+ ^- @da

28+ =+ ^= yer

29+ ?: a.det

30+ (add 292.277.024.400 y.det)

31+ (sub 292.277.024.400 (dec y.det))

32+ =+ day=(yawn yer m.det d.t.det)

33+ (yule day h.t.det m.t.det s.t.det f.t.det)

4834```

4935

5036#### Examples

5137

5238```

53− > (yall 198)

54− [y=0 m=7 d=17]

55−

56− > (yall 90.398)

57− [y=247 m=7 d=3]

58−

59− > (yall 0)

60− [y=0 m=1 d=1]

39+> (year [[a=%.y y=2.014] m=8 t=[d=4 h=20 m=4 s=57 f=~[0xd940]]])

40+~2014.8.4..20.04.57..d940

6141```

6242

6343---

6444

65−## `++yawn`

45+## `++yore`

6646

67−Days since beginning of time

47+Date from atomic date

6848

69−Inverse of `yall`, computes number of days A.D. from y/m/d date as the

70−tuple `[yer=@ud mot=@ud day=@ud]`.

49+Produces a `date` from a `@da`.

7150

7251#### Accepts

7352

74−`yer` is an unsigned decimal.

75−

76−`mon` is an unsigned decimal.

77−

78−`day` is an unsigned decimal.

53+`now` is a time atom, `@da`.

7954

8055#### Produces

8156

82−An unsigned decimal.

57+A `date`.

8358

8459#### Source

8560

8661```hoon

87− ++ yawn

88− |= [yer=@ud mot=@ud day=@ud]

89− ^- @ud

90− => .(mot (dec mot), day (dec day))

91− => ^+ .

92− %= .

93− day

94− =+ cah=?:((yelp yer) moy:yo moh:yo)

95− |- ^- @ud

96− ?: =(0 mot)

97− day

98− $(mot (dec mot), cah (slag 1 cah), day (add day (snag 0 cah)))

99− ==

100− |- ^- @ud

101− ?. =(0 (mod yer 4))

102− =+ ney=(dec yer)

103− $(yer ney, day (add day ?:((yelp ney) 366 365)))

104− ?. =(0 (mod yer 100))

105− =+ nef=(sub yer 4)

106− $(yer nef, day (add day ?:((yelp nef) 1.461 1.460)))

107− ?. =(0 (mod yer 400))

108− =+ nec=(sub yer 100)

109− $(yer nec, day (add day ?:((yelp nec) 36.525 36.524)))

110− (add day (mul (div yer 400) (add 1 (mul 4 36.524))))

62+++ yore

63+ |= now=@da

64+ ^- date

65+ =+ rip=(yell now)

66+ =+ ger=(yall d.rip)

67+ :- ?: (gth y.ger 292.277.024.400)

68+ [a=& y=(sub y.ger 292.277.024.400)]

69+ [a=| y=+((sub 292.277.024.400 y.ger))]

70+ [m.ger d.ger h.rip m.rip s.rip f.rip]

11171```

11272

11373#### Examples

11474

11575```

116− > (yawn 2.018 7 4)

117− 737.244

118−

119− > (yawn 1.776 7 4)

120− 648.856

121−

122− > (yawn 1.990 10 11)

123− 727.116

76+> (yore ~2014.6.6..21.09.15..0a16)

77+[[a=%.y y=2.014] m=6 t=[d=6 h=21 m=9 s=15 f=~[0xa16]]]

12478```

12579

12680---

12781

128−## `++year`

82+## `++yell`

12983

130−Date to @d

84+Tarp from atomic date

13185

132−Accept a parsed date of form `[[a=? y=@ud] m=@ud t=tarp]` and produce

133−its `@d` representation.

86+Produce a [`$tarp`](/docs/hoon/reference/stdlib/2q#tarp) time format from a`@da`.

13487

13588#### Accepts

13689

137−`det` is a `date`

90+`now` is a `@da`.

13891

13992#### Produces

14093

141−A `@d`.

94+A `tarp`.

14295

14396#### Source

14497

14598```hoon

146− ++ year

147− |= det=date

148− ^- @da

149− =+ ^= yer

150− ?: a.det

151− (add 292.277.024.400 y.det)

152− (sub 292.277.024.400 (dec y.det))

153− =+ day=(yawn yer m.det d.t.det)

154− (yule day h.t.det m.t.det s.t.det f.t.det)

99+++ yell

100+ |= now=@d

101+ ^- tarp

102+ =+ sec=(rsh 6 now)

103+ =+ ^= fan

104+ =+ [muc=4 raw=(end 6 now)]

105+ |- ^- (list @ux)

106+ ?: |(=(0 raw) =(0 muc))

107+ ~

108+ => .(muc (dec muc))

109+ [(cut 4 [muc 1] raw) $(raw (end [4 muc] raw))]

110+ =+ day=(div sec day:yo)

111+ => .(sec (mod sec day:yo))

112+ =+ hor=(div sec hor:yo)

113+ => .(sec (mod sec hor:yo))

114+ =+ mit=(div sec mit:yo)

115+ => .(sec (mod sec mit:yo))

116+ [day hor mit sec fan]

155117```

156118

157119#### Examples

158120

159121```

160− > (year [[a=%.y y=2.014] m=8 t=[d=4 h=20 m=4 s=57 f=~[0xd940]]])

161− 0x8000000d227df4e9d940000000000000

122+> (yell ~2014.3.20..05.42.53..7456)

123+[d=106.751.991.820.094 h=5 m=42 s=53 f=~[0x7456]]

124+

125+> (yell ~2014.6.9..19.09.40..8b66)

126+[d=106.751.991.820.175 h=19 m=9 s=40 f=~[0x8b66]]

127+

128+> (yell ~1776.7.4)

129+[d=106.751.991.733.273 h=0 m=0 s=0 f=~]

162130```

163131

164132---

165133

166−## `++yell`

134+## `++yule`

167135

168−Tarp from atomic date

136+Daily time to time atom

169137

170−Produce a parsed daily time format from, `@d`, an atomic date.

138+Accepts a [`$tarp`](/docs/hoon/reference/stdlib/2q#tarp), a parsed daily time,

139+and produces a `@da`.

171140

172141#### Accepts

173142

174−`now` is a `@d`.

143+`rip` is a `tarp`.

175144

176145#### Produces

177146

178−A `tarp`.

147+A time atom, `@da`.

179148

180149#### Source

181150

182151```hoon

183− ++ yell

184− |= now=@d

185− ^- tarp

186− =+ sec=(rsh 6 1 now)

187− =+ ^= fan

188− =+ [muc=4 raw=(end 6 1 now)]

189− |- ^- (list @ux)

190− ?: |(=(0 raw) =(0 muc))

191− ~

192− => .(muc (dec muc))

193− [(cut 4 [muc 1] raw) $(raw (end 4 muc raw))]

194− =+ day=(div sec day:yo)

195− => .(sec (mod sec day:yo))

196− =+ hor=(div sec hor:yo)

197− => .(sec (mod sec hor:yo))

198− =+ mit=(div sec mit:yo)

199− => .(sec (mod sec mit:yo))

200− [day hor mit sec fan]

152+++ yule

153+ |= rip=tarp

154+ ^- @d

155+ =+ ^= sec ;: add

156+ (mul d.rip day:yo)

157+ (mul h.rip hor:yo)

158+ (mul m.rip mit:yo)

159+ s.rip

160+ ==

161+ =+ ^= fac =+ muc=4

162+ |- ^- @

163+ ?~ f.rip

164+ 0

165+ => .(muc (dec muc))

166+ (add (lsh [4 muc] i.f.rip) $(f.rip t.f.rip))

167+ (con (lsh 6 sec) fac)

201168```

202169

203170#### Examples

204171

205172```

206− > (yell ~2014.3.20..05.42.53..7456)

207− [d=106.751.991.820.094 h=5 m=42 s=53 f=~[0x7456]]

173+> =murica (yell ~1776.7.4)

174+

175+> murica

176+[d=106.751.991.733.273 h=0 m=0 s=0 f=~]

177+

178+> (yule murica)

179+0x8000000b62aaf5800000000000000000

180+

181+> `@da`(yule murica)

182+~1776.7.4

183+

184+> `@da`(yule (yell ~2014.3.20..05.42.53..7456))

185+~2014.3.20..05.42.53..7456

208186

209− > (yell ~2014.6.9..19.09.40..8b66)

210− [d=106.751.991.820.175 h=19 m=9 s=40 f=~[0x8b66]]

187+> `tarp`[31 12 30 0 ~]

188+[d=31 h=12 m=30 s=0 f=~]

211189

212− > (yell ~1776.7.4)

213− [d=106.751.991.733.273 h=0 m=0 s=0 f=~]

190+> `@dr`(yule `tarp`[31 12 30 0 ~])

191+~d31.h12.m30

214192```

215193

216194---

217195

218−## `++yelp`

196+## `++yall`

219197

220−Leap-week?

198+Time since beginning of time

221199

222−Determines whether a year contains an ISO 8601 leap-week. Produces a flag.

200+Produce the date tuple of `[y=@ud m=@ud d=@ud]` of the year, month, and

201+day from a number of days from the beginning of the Gregorian calendar.

223202

224203#### Accepts

225204

226−`yer` is an unsigned decimal.

205+`day` is a `@ud`.

227206

228207#### Produces

229208

230−A flag.

209+A cell of unsigned decimals.

231210

232211#### Source

233212

234213```hoon

235− ++ yelp

236− |= yer=@ud ^- ?

237− &(=(0 (mod yer 4)) |(!=(0 (mod yer 100)) =(0 (mod yer 400))))

214+++ yall

215+ |= day=@ud

216+ ^- [y=@ud m=@ud d=@ud]

217+ =+ [era=0 cet=0 lep=*?]

218+ => .(era (div day era:yo), day (mod day era:yo))

219+ => ^+ .

220+ ?: (lth day +(cet:yo))

221+ .(lep &, cet 0)

222+ => .(lep |, cet 1, day (sub day +(cet:yo)))

223+ .(cet (add cet (div day cet:yo)), day (mod day cet:yo))

224+ =+ yer=(add (mul 400 era) (mul 100 cet))

225+ |- ^- [y=@ud m=@ud d=@ud]

226+ =+ dis=?:(lep 366 365)

227+ ?. (lth day dis)

228+ =+ ner=+(yer)

229+ $(yer ner, day (sub day dis), lep =(0 (end [0 2] ner)))

230+ |- ^- [y=@ud m=@ud d=@ud]

231+ =+ [mot=0 cah=?:(lep moy:yo moh:yo)]

232+ |- ^- [y=@ud m=@ud d=@ud]

233+ =+ zis=(snag mot cah)

234+ ?: (lth day zis)

235+ [yer +(mot) +(day)]

236+ $(mot +(mot), day (sub day zis))

238237```

239238

240239#### Examples

241240

242241```

243− > (yelp 2.014)

244− %.n

242+> (yall 198)

243+[y=0 m=7 d=17]

245244

246− > (yelp 2.008)

247− %.y

245+> (yall 90.398)

246+[y=247 m=7 d=3]

248247

249− > (yelp 0)

250− %.y

251−

252− > (yelp 14.011)

253− %.n

248+> (yall 0)

249+[y=0 m=1 d=1]

254250```

255251

256252---

257253

258−## `++yore`

254+## `++yawn`

259255

260−Date from atomic date

256+Days since beginning of time

261257

262−Produces a `date` from a `@d`.

258+Inverse of `yall`, computes number of days A.D. from y/m/d date as the

259+tuple `[yer=@ud mot=@ud day=@ud]`.

263260

264261#### Accepts

265262

266−`now` is a time atom, `@d`.

263+`yer` is an unsigned decimal.

264+

265+`mon` is an unsigned decimal.

266+

267+`day` is an unsigned decimal.

267268

268269#### Produces

269270

270−A `date`.

271+An unsigned decimal.

271272

272273#### Source

273274

274275```hoon

275− ++ yore

276− |= now=@da

277− ^- date

278− =+ rip=(yell now)

279− =+ ger=(yall d.rip)

280− :- ?: (gth y.ger 292.277.024.400)

281− [a=& y=(sub y.ger 292.277.024.400)]

282− [a=| y=+((sub 292.277.024.400 y.ger))]

283− [m.ger d.ger h.rip m.rip s.rip f.rip]

276+++ yawn

277+ |= [yer=@ud mot=@ud day=@ud]

278+ ^- @ud

279+ => .(mot (dec mot), day (dec day))

280+ => ^+ .

281+ %= .

282+ day

283+ =+ cah=?:((yelp yer) moy:yo moh:yo)

284+ |- ^- @ud

285+ ?: =(0 mot)

286+ day

287+ $(mot (dec mot), cah (slag 1 cah), day (add day (snag 0 cah)))

288+ ==

289+ |- ^- @ud

290+ ?. =(0 (mod yer 4))

291+ =+ ney=(dec yer)

292+ $(yer ney, day (add day ?:((yelp ney) 366 365)))

293+ ?. =(0 (mod yer 100))

294+ =+ nef=(sub yer 4)

295+ $(yer nef, day (add day ?:((yelp nef) 1.461 1.460)))

296+ ?. =(0 (mod yer 400))

297+ =+ nec=(sub yer 100)

298+ $(yer nec, day (add day ?:((yelp nec) 36.525 36.524)))

299+ (add day (mul (div yer 400) (add 1 (mul 4 36.524))))

284300```

285301

286302#### Examples

287303

288304```

289− > (yore ~2014.6.6..21.09.15..0a16)

290− [[a=%.y y=2.014] m=6 t=[d=6 h=21 m=9 s=15 f=~[0xa16]]]

305+> (yawn 2.018 7 4)

306+737.244

307+

308+> (yawn 1.776 7 4)

309+648.856

310+

311+> (yawn 1.990 10 11)

312+727.116

291313```

292314

293315---

294316

295−## `++yule`

317+## `++yelp`

296318

297−Daily time to time atom

319+Leap year?

298320

299−Accepts a `tarp`, a parsed daily time, and produces a time atom,

300−`@d`.

321+Determines whether a year is a leap year. Produces a flag.

301322

302323#### Accepts

303324

304−`rip` is a `tarp`.

325+`yer` is an unsigned decimal.

305326

306327#### Produces

307328

308−A time atom, `@d`.

329+A flag.

309330

310331#### Source

311332

312333```hoon

313− ++ yule :: time atom

314− |= rip=tarp

315− ^- @d

316− =+ ^= sec ;: add

317− (mul d.rip day:yo)

318− (mul h.rip hor:yo)

319− (mul m.rip mit:yo)

320− s.rip

321− ==

322− =+ ^= fac =+ muc=4

323− |- ^- @

324− ?~ f.rip

325− 0

326− => .(muc (dec muc))

327− (add (lsh 4 muc i.f.rip) $(f.rip t.f.rip))

328− (con (lsh 6 1 sec) fac)

329− ::

334+++ yelp

335+ |= yer=@ud ^- ?

336+ &(=(0 (mod yer 4)) |(!=(0 (mod yer 100)) =(0 (mod yer 400))))

330337```

331338

332339#### Examples

333340

334341```

335− > =murica (yell ~1776.7.4)

336−

337− > murica

338− [d=106.751.991.733.273 h=0 m=0 s=0 f=~]

339−

340− > (yule murica)

341− 0x8000000b62aaf5800000000000000000

342−

343− > `@da`(yule murica)

344− ~1776.7.4

342+> (yelp 2.014)

343+%.n

345344

346− > `@da`(yule (yell ~2014.3.20..05.42.53..7456))

347− ~2014.3.20..05.42.53..7456

345+> (yelp 2.008)

346+%.y

348347

349− > `tarp`[31 12 30 0 ~]

350− [d=31 h=12 m=30 s=0 f=~]

348+> (yelp 0)

349+%.y

351350

352− > `@dr`(yule `tarp`[31 12 30 0 ~])

353− ~d31.h12.m30

351+> (yelp 14.011)

352+%.n

354353```

355354

356355---

@@ -364,7 +363,7 @@ Core whose arms contain constants for interacting with earth time.

364363#### Source

365364

366365```hoon

367− ++ yo

366+++ yo

368367```

369368

370369---

@@ -384,20 +383,20 @@ An atom.

384383#### Source

385384

386385```hoon

387− |% ++ cet 36.524

386+++ cet 36.524

388387```

389388

390389#### Examples

391390

392391```

393− > cet:yo

394− 36.524

392+> cet:yo

393+36.524

395394

396− > (add 365 cet:yo)

397− 36.889

395+> (add 365 cet:yo)

396+36.889

398397

399− > (sub (add 24 (mul 100 365)) cet:yo)

400− 0

398+> (sub (add 24 (mul 100 365)) cet:yo)

399+0

401400```

402401

403402---

@@ -415,17 +414,17 @@ An atom.

415414#### Source

416415

417416```hoon

418− ++ day 86.400

417+++ day 86.400

419418```

420419

421420#### Examples

422421

423422```

424− > day:yo

425− 86.400

423+> day:yo

424+86.400

426425

427− > (add 60 day:yo)

428− 86.460

426+> (add 60 day:yo)

427+86.460

429428```

430429

431430---

@@ -445,17 +444,17 @@ An atom.

445444#### Source

446445

447446```hoon

448− ++ era 146.097

447+++ era 146.097

449448```

450449

451450#### Examples

452451

453452```

454− > era:yo

455− 146.097

453+> era:yo

454+146.097

456455

457− > (sub era:yo (mul 4 cet:yo))

458− 1

456+> (sub era:yo (mul 4 cet:yo))

457+1

459458```

460459

461460#### Discussion

@@ -482,17 +481,17 @@ An atom.

482481#### Source

483482

484483```hoon

485− ++ hor 3.600

484+++ hor 3.600

486485```

487486

488487#### Examples

489488

490489```

491− > hor:yo

492− 3.600

490+> hor:yo

491+3.600

493492

494− > (div hor:yo 60)

495− 60

493+> (div hor:yo 60)

494+60

496495```

497496

498497---

@@ -511,14 +510,14 @@ An atom.

511510#### Source

512511

513512```hoon

514− ++ jes 106.751.991.084.417

513+++ jes 106.751.991.084.417

515514```

516515

517516#### Examples

518517

519518```

520− > jes:yo

521− 106.751.991.084.417

519+> jes:yo

520+106.751.991.084.417

522521```

523522

524523#### Discussion

@@ -540,14 +539,14 @@ An atom.

540539#### Source

541540

542541```hoon

543− ++ mit 60

542+++ mit 60

544543```

545544

546545#### Examples

547546

548547```

549− > mit:yo

550− 60

548+> mit:yo

549+60

551550```

552551

553552---

@@ -567,17 +566,17 @@ A `list` of `@ud`

567566#### Source

568567

569568```hoon

570− ++ moh `(list @ud)`[31 28 31 30 31 30 31 31 30 31 30 31 ~]

569+++ moh `(list @ud)`[31 28 31 30 31 30 31 31 30 31 30 31 ~]

571570```

572571

573572#### Examples

574573

575574```

576− > moh:yo

577− ~[31 28 31 30 31 30 31 31 30 31 30 31]

575+> moh:yo

576+~[31 28 31 30 31 30 31 31 30 31 30 31]

578577

579− > (snag 4 moh:yo)

580− 31

578+> (snag 4 moh:yo)

579+31

581580```

582581

583582---

@@ -597,17 +596,17 @@ A `list` of `@ud`.

597596#### Source

598597

599598```hoon

600− ++ moy `(list @ud)`[31 29 31 30 31 30 31 31 30 31 30 31 ~]

599+++ moy `(list @ud)`[31 29 31 30 31 30 31 31 30 31 30 31 ~]

601600```

602601

603602#### Examples

604603

605604```

606− > moy:yo

607− ~[31 29 31 30 31 30 31 31 30 31 30 31]

605+> moy:yo

606+~[31 29 31 30 31 30 31 31 30 31 30 31]

608607

609− > (snag 1 moy:yo)

610− 29

608+> (snag 1 moy:yo)

609+29

611610```

612611

613612---

@@ -626,14 +625,14 @@ An atom.

626625#### Source

627626

628627```hoon

629− ++ qad 126.144.001

628+++ qad 126.144.001

630629```

631630

632631#### Examples

633632

634633```

635− > qad:yo

636− 126.144.001

634+> qad:yo

635+126.144.001

637636```

638637

639638---

@@ -652,14 +651,14 @@ An atom.

652651#### Source

653652

654653```hoon

655− ++ yer 31.536.000

654+++ yer 31.536.000

656655```

657656

658657#### Examples

659658

660659```

661− > yer:yo

662− 31.536.000

660+> yer:yo

661+31.536.000

663662```

664663

665664---

content/docs/hoon/reference/stdlib/3d.md+437−452

@@ -22,15 +22,14 @@ An atom.

2222#### Source

2323

2424```hoon

25− ++ shad |=(ruz=@ (shax (shax ruz)))

25+++ shad |=(ruz=@ (shax (shax ruz)))

2626```

2727

2828#### Examples

2929

3030```

31− > (shad 11)

32− \/20.519.637.820.582.103.109.435.907.615.585.653.479.776.629.591.855.451.248.\/

33− 718.295.626.625.655.417.234

31+> `@uw`(shad 11)

32+0w2Rt.J1gzO.JjsQc.0Komy.DYUUO.27koh.QxwE0.Qgwt7.EPGCi

3433```

3534

3635---

@@ -39,8 +38,9 @@ An atom.

3938

4039Half SHA-256

4140

42−Produces a 128-bit atom by performing the [bitwise XOR](/docs/hoon/reference/stdlib/2d) on the

43−first and last halves of the 256-bit salted hash `shas`.

41+Produces a 128-bit atom by performing the [bitwise

42+XOR](/docs/hoon/reference/stdlib/2d) on the first and last halves of the 256-bit

43+salted hash `shas`.

4444

4545#### Accepts

4646

@@ -51,350 +51,238 @@ first and last halves of the 256-bit salted hash `shas`.

5151#### Source

5252

5353```hoon

54− ++ shaf :: half sha-256

55− |= [sal=@ ruz=@]

56− =+ haz=(shas sal ruz)

57− (mix (end 7 1 haz) (rsh 7 1 haz))

54+++ shaf

55+ |= [sal=@ ruz=@]

56+ =+ haz=(shas sal ruz)

57+ (mix (end 7 haz) (rsh 7 haz))

5858```

5959

6060#### Examples

6161

6262```

63− > (shaf 17 8)

64− 52.667.672.807.485.289.251.324.336.639.183.409.041

65−

66− > `@ub`(shaf 17 8)

67− \/0b1011.1111.1101.0110.1110.1000.0100.1110.1100.1000.0010.0100.1111.0001.0010.0010\/

68− .0100.1110.1110.0011.1100.1111.0001.1101.1101.1100.1110.1111.0100.0101.0001.0100

69− \/

63+> `@uw`(shaf 17 8)

64+0wD.DSP0L.WUuQg.-A765.4RY-h

7065```

7166

7267---

7368

74−## `++shal`

69+## `++sham`

7570

76−SHA-512 with length

71+128-bit noun hash

7772

78−Produces an atom by hashing an atom `ruz` with SHA-512. Another atom, `len`, is

79−the byte-length of the theoretical buffer represented by the atom.

73+Produces a 128-bit atom by hashing a noun `yux` with the [`+shaf`](#shaf)

74+function. If that noun is a cell, then it is passed to the

75+[`jam`](/docs/hoon/reference/stdlib/2p#jam) function to produce an atom to be

76+hashed.

8077

8178#### Accepts

8279

83−`len` is an atom.

84−

85−`ruz` is an atom.

80+`yux` is a noun.

8681

8782#### Produces

8883

89−An atom.

84+A `@uvH`.

9085

9186#### Source

9287

9388```hoon

94− ++ shal

95− ~/ %shal

96− |= [len=@ ruz=@] ^- @

97− => .(ruz (cut 3 [0 len] ruz))

98− =+ [few==>(fe .(a 6)) wac=|=([a=@ b/@] (cut 6 [a 1] b))]

99− =+ [sum=sum.few ror=ror.few net=net.few inv=inv.few]

100− =+ ral=(lsh 0 3 len)

101− =+ ^= ful

102− %+ can 0

103− :~ [ral ruz]

104− [8 128]

105− [(mod (sub 1.920 (mod (add 8 ral) 1.024)) 1.024) 0]

106− [128 (~(net fe 7) ral)]

107− ==

108− =+ lex=(met 10 ful)

109− =+ ^= kbx 0x6c44.198c.4a47.5817.5fcb.6fab.3ad6.faec.

110− 597f.299c.fc65.7e2a.4cc5.d4be.cb3e.42b6.

111− 431d.67c4.9c10.0d4c.3c9e.be0a.15c9.bebc.

112− 32ca.ab7b.40c7.2493.28db.77f5.2304.7d84.

113− 1b71.0b35.131c.471b.113f.9804.bef9.0dae.

114− 0a63.7dc5.a2c8.98a6.06f0.67aa.7217.6fba.

115− f57d.4f7f.ee6e.d178.eada.7dd6.cde0.eb1e.

116− d186.b8c7.21c0.c207.ca27.3ece.ea26.619c.

117− c671.78f2.e372.532b.bef9.a3f7.b2c6.7915.

118− a450.6ceb.de82.bde9.90be.fffa.2363.1e28.

119− 8cc7.0208.1a64.39ec.84c8.7814.a1f0.ab72.

120− 78a5.636f.4317.2f60.748f.82ee.5def.b2fc.

121− 682e.6ff3.d6b2.b8a3.5b9c.ca4f.7763.e373.

122− 4ed8.aa4a.e341.8acb.391c.0cb3.c5c9.5a63.

123− 34b0.bcb5.e19b.48a8.2748.774c.df8e.eb99.

124− 1e37.6c08.5141.ab53.19a4.c116.b8d2.d0c8.

125− 106a.a070.32bb.d1b8.f40e.3585.5771.202a.

126− d699.0624.5565.a910.d192.e819.d6ef.5218.

127− c76c.51a3.0654.be30.c24b.8b70.d0f8.9791.

128− a81a.664b.bc42.3001.a2bf.e8a1.4cf1.0364.

129− 9272.2c85.1482.353b.81c2.c92e.47ed.aee6.

130− 766a.0abb.3c77.b2a8.650a.7354.8baf.63de.

131− 5338.0d13.9d95.b3df.4d2c.6dfc.5ac4.2aed.

132− 2e1b.2138.5c26.c926.27b7.0a85.46d2.2ffc.

133− 1429.2967.0a0e.6e70.06ca.6351.e003.826f.

134− d5a7.9147.930a.a725.c6e0.0bf3.3da8.8fc2.

135− bf59.7fc7.beef.0ee4.b003.27c8.98fb.213f.

136− a831.c66d.2db4.3210.983e.5152.ee66.dfab.

137− 76f9.88da.8311.53b5.5cb0.a9dc.bd41.fbd4.

138− 4a74.84aa.6ea6.e483.2de9.2c6f.592b.0275.

139− 240c.a1cc.77ac.9c65.0fc1.9dc6.8b8c.d5b5.

140− efbe.4786.384f.25e3.e49b.69c1.9ef1.4ad2.

141− c19b.f174.cf69.2694.9bdc.06a7.25c7.1235.

142− 80de.b1fe.3b16.96b1.72be.5d74.f27b.896f.

143− 550c.7dc3.d5ff.b4e2.2431.85be.4ee4.b28c.

144− 1283.5b01.4570.6fbe.d807.aa98.a303.0242.

145− ab1c.5ed5.da6d.8118.923f.82a4.af19.4f9b.

146− 59f1.11f1.b605.d019.3956.c25b.f348.b538.

147− e9b5.dba5.8189.dbbc.b5c0.fbcf.ec4d.3b2f.

148− 7137.4491.23ef.65cd.428a.2f98.d728.ae22

149− =+ ^= hax 0x5be0.cd19.137e.2179.1f83.d9ab.fb41.bd6b.

150− 9b05.688c.2b3e.6c1f.510e.527f.ade6.82d1.

151− a54f.f53a.5f1d.36f1.3c6e.f372.fe94.f82b.

152− bb67.ae85.84ca.a73b.6a09.e667.f3bc.c908

153− =+ i=0

154− |- ^- @

155− ?: =(i lex)

156− (rep 6 (turn (rip 6 hax) net))

157− =+ ^= wox

158− =+ dux=(cut 10 [i 1] ful)

159− =+ wox=(rep 6 (turn (rip 6 dux) net))

160− =+ j=16

161− |- ^- @

162− ?: =(80 j)

163− wox

164− =+ :* l=(wac (sub j 15) wox)

165− m=(wac (sub j 2) wox)

166− n=(wac (sub j 16) wox)

167− o=(wac (sub j 7) wox)

168− ==

169− =+ x=:(mix (ror 0 1 l) (ror 0 8 l) (rsh 0 7 l))

170− =+ y=:(mix (ror 0 19 m) (ror 0 61 m) (rsh 0 6 m))

171− =+ z=:(sum n x o y)

172− $(wox (con (lsh 6 j z) wox), j +(j))

173− =+ j=0

174− =+ :* a=(wac 0 hax)

175− b=(wac 1 hax)

176− c=(wac 2 hax)

177− d=(wac 3 hax)

178− e=(wac 4 hax)

179− f=(wac 5 hax)

180− g=(wac 6 hax)

181− h=(wac 7 hax)

182− ==

183− |- ^- @

184− ?: =(80 j)

185− %= ^$

186− i +(i)

187− hax %+ rep 6

188− :~ (sum a (wac 0 hax))

189− (sum b (wac 1 hax))

190− (sum c (wac 2 hax))

191− (sum d (wac 3 hax))

192− (sum e (wac 4 hax))

193− (sum f (wac 5 hax))

194− (sum g (wac 6 hax))

195− (sum h (wac 7 hax))

196− ==

197− ==

198− =+ l=:(mix (ror 0 28 a) (ror 0 34 a) (ror 0 39 a)) :: S0

199− =+ m=:(mix (dis a b) (dis a c) (dis b c)) :: maj

200− =+ n=(sum l m) :: t2

201− =+ o=:(mix (ror 0 14 e) (ror 0 18 e) (ror 0 41 e)) :: S1

202− =+ p=(mix (dis e f) (dis (inv e) g)) :: ch

203− =+ q=:(sum h o p (wac j kbx) (wac j wox)) :: t1

204− $(j +(j), a (sum q n), b a, c b, d c, e (sum d q), f e, g f, h g)

89+++ sham

90+ |= yux=* ^- @uvH ^- @

91+ ?@ yux

92+ (shaf %mash yux)

93+ (shaf %sham (jam yux))

20594```

20695

20796#### Examples

20897

20998```

210− > (shal 1 'hello')

211− \/7.956.615.373.791.575.273.027.009.123.631.914.645.972.441.264.528.176.292.399.908\/

212− .424.469.676.078.106.561.839.264.176.650.109.335.825.608.088.511.266.620.100.157.

213− 847.055.280.028.606.252.747.432.021.213.474

214− \/

99+> (sham [2 4])

100+0v3.71s52.4bqnp.ki2b8.9hhsp.2ufgg

215101

216− > (shal 1 'hello')

217− \/7.956.615.373.791.575.273.027.009.123.631.914.645.972.441.264.528.176.292.399.908\/

218− .424.469.676.078.106.561.839.264.176.650.109.335.825.608.088.511.266.620.100.157.

219− 847.055.280.028.606.252.747.432.021.213.474

220− \/

102+> (sham "hello")

103+0v1.hg8mv.t7s3f.u4f8a.q5noe.dvqvh

221104```

222105

223−#### Discussion

224−

225−Because byte-strings can have leading zeros, but atoms cannot, we use `len`

226−as a way of saying that the atom `ruz` is shorter than its representative

227−byte-string.

228−

229106---

230107

231−## `++sham`

108+## `++shas`

232109

233−128-bit noun hash

110+Salted hash

234111

235−Produces a 128-bit atom by hashing a noun `yux` with the `shah` function. If

236−that noun is a cell, then it is passed to the [`jam`](/docs/hoon/reference/stdlib/2p) function to produce

237−an atom to be hashed.

112+Produces an atom by using SHA-256 plus a salt input. The [bitwise

113+XOR](/docs/hoon/reference/stdlib/2d) is performed on salt `sal` and the product

114+of atom `ruz` hashed with SHA-256. The product of that logical operation is then

115+itself hashed with SHA-256.

238116

239117#### Accepts

240118

241−`yux` is a noun.

242−

243−#### Produces

119+`sal` is an atom.

244120

245−An atom.

121+`ruz` is an atom.

246122

247123#### Source

248124

249125```hoon

250− ++ sham

251− |= yux=* ^- @uvH ^- @

252− ?@ yux

253− (shaf %mash yux)

254− (shaf %sham (jam yux))

255− ::

126+++ shas

127+ ~/ %shas

128+ |= [sal=@ ruz=@]

129+ (shax (mix sal (shax ruz)))

256130```

257131

258132#### Examples

259133

260134```

261− > (sham [2 4])

262− 0v3.71s52.4bqnp.ki2b8.9hhsp.2ufgg

263−

264− > (sham "hello")

265− 0v1.hg8mv.t7s3f.u4f8a.q5noe.dvqvh

135+> `@uw`(shas 1 1)

136+0w5hZ.Gim4L.9xKlU.jJJQr.2Bgi~.RHd5s.IwXuV.p43at.ZdsTY

266137```

267138

268139---

269140

270−## `++shan`

271−

272−SHA-1

273−

274−Produces an atom by hashing an atom `ruz` with SHA-1.

275−

276−#### Accepts

277−

278−`ruz` is an atom.

141+## `++shax`

279142

280−#### Produces

143+SHA-256

281144

282−An atom.

145+Produces an atom by hashing an atom `ruz` with SHA-256.

283146

284−#### Source

147+#### Sources

285148

286149```hoon

287− ++ shan

288− |= ruz=@

289− =+ [few==>(fe .(a 5)) wac=|=([a=@ b=@] (cut 5 [a 1] b))]

290− =+ [sum=sum.few ror=ror.few rol=rol.few net=net.few inv=inv.few]

291− =+ ral=(lsh 0 3 (met 3 ruz))

292− =+ ^= ful

293− %+ can 0

294− :~ [ral ruz]

295− [8 128]

296− [(mod (sub 960 (mod (add 8 ral) 512)) 512) 0]

297− [64 (~(net fe 6) ral)]

298− ==

299− =+ lex=(met 9 ful)

300− =+ kbx=0xca62.c1d6.8f1b.bcdc.6ed9.eba1.5a82.7999

301− =+ hax=0xc3d2.e1f0.1032.5476.98ba.dcfe.efcd.ab89.6745.2301

302− =+ i=0

303− |-

304− ?: =(i lex)

305− (rep 5 (flop (rip 5 hax)))

306− =+ ^= wox

307− =+ dux=(cut 9 [i 1] ful)

308− =+ wox=(rep 5 (turn (rip 5 dux) net))

309− =+ j=16

310− |- ^- @

311− ?: =(80 j)

312− wox

313− =+ :* l=(wac (sub j 3) wox)

314− m=(wac (sub j 8) wox)

315− n=(wac (sub j 14) wox)

316− o=(wac (sub j 16) wox)

317− ==

318− =+ z=(rol 0 1 :(mix l m n o))

319− $(wox (con (lsh 5 j z) wox), j +(j))

320− =+ j=0

321− =+ :* a=(wac 0 hax)

322− b=(wac 1 hax)

323− c=(wac 2 hax)

324− d=(wac 3 hax)

325− e=(wac 4 hax)

326− ==

327− |- ^- @

328− ?: =(80 j)

329− %= ^$

330− i +(i)

331− hax %+ rep 5

332− :~

333− (sum a (wac 0 hax))

334− (sum b (wac 1 hax))

335− (sum c (wac 2 hax))

336− (sum d (wac 3 hax))

337− (sum e (wac 4 hax))

338− ==

339− ==

340− =+ fx=(con (dis b c) (dis (not 5 1 b) d))

341− =+ fy=:(mix b c d)

342− =+ fz=:(con (dis b c) (dis b d) (dis c d))

343− =+ ^= tem

344− ?: &((gte j 0) (lte j 19))

345− :(sum (rol 0 5 a) fx e (wac 0 kbx) (wac j wox))

346− ?: &((gte j 20) (lte j 39))

347− :(sum (rol 0 5 a) fy e (wac 1 kbx) (wac j wox))

348− ?: &((gte j 40) (lte j 59))

349− :(sum (rol 0 5 a) fz e (wac 2 kbx) (wac j wox))

350− :(sum (rol 0 5 a) fy e (wac 3 kbx) (wac j wox))

351− $(j +(j), a tem, b a, c (rol 0 30 b), d c, e d)

150+++ shax

151+ ~/ %shax

152+ |= ruz=@ ^- @

153+ (shay [(met 3 ruz) ruz])

352154```

353155

354156#### Examples

355157

356158```

357− > (shan 'hello')

358− 975.987.071.262.755.080.377.722.350.727.279.193.143.145.743.181

159+> `@uw`(shax 'foo')

160+0waXD.pCa8n.EHVEb.-3p70.JgxcQ.gj0tf.4mr-o.~6~Sx.HJ2oI

359161```

360162

361−#### Discussion

362−

363−SHA-1 is a deprecated function; it is not considered secure.

364−

365163---

366164

367−## `++shas`

165+## `++shay`

368166

369−Salted hash

167+SHA-256 with length

370168

371−Produces an atom by using SHA-256 plus a salt input. The [bitwise XOR](/docs/hoon/reference/stdlib/2d)

372−is performed on `sal` and the product of `ruz` hashed with SHA-256. The product

373−of that logical operation is then itself hashed with SHA-256.

169+Produces an atom by hashing an atom `ruz` with SHA-512. Another atom, `len`, is

170+the byte-length of the theoretical buffer represented by the atom.

374171

375172#### Accepts

376173

377−`sal` is an atom.

174+`len` is an atom.

378175

379176`ruz` is an atom.

380177

381178#### Source

382179

383180```hoon

384− ++ shas

385− |= [sal=@ ruz=@]

386− (shax (mix sal (shax ruz)))

181+++ shay

182+ ~/ %shay

183+ |= [len=@u ruz=@] ^- @

184+ => .(ruz (cut 3 [0 len] ruz))

185+ =+ [few==>(fe .(a 5)) wac=|=([a=@ b=@] (cut 5 [a 1] b))]

186+ =+ [sum=sum.few ror=ror.few net=net.few inv=inv.few]

187+ =+ ral=(lsh [0 3] len)

188+ =+ ^= ful

189+ %+ can 0

190+ :~ [ral ruz]

191+ [8 128]

192+ [(mod (sub 960 (mod (add 8 ral) 512)) 512) 0]

193+ [64 (~(net fe 6) ral)]

194+ ==

195+ =+ lex=(met 9 ful)

196+ =+ ^= kbx 0xc671.78f2.bef9.a3f7.a450.6ceb.90be.fffa.

197+ 8cc7.0208.84c8.7814.78a5.636f.748f.82ee.

198+ 682e.6ff3.5b9c.ca4f.4ed8.aa4a.391c.0cb3.

199+ 34b0.bcb5.2748.774c.1e37.6c08.19a4.c116.

200+ 106a.a070.f40e.3585.d699.0624.d192.e819.

201+ c76c.51a3.c24b.8b70.a81a.664b.a2bf.e8a1.

202+ 9272.2c85.81c2.c92e.766a.0abb.650a.7354.

203+ 5338.0d13.4d2c.6dfc.2e1b.2138.27b7.0a85.

204+ 1429.2967.06ca.6351.d5a7.9147.c6e0.0bf3.

205+ bf59.7fc7.b003.27c8.a831.c66d.983e.5152.

206+ 76f9.88da.5cb0.a9dc.4a74.84aa.2de9.2c6f.

207+ 240c.a1cc.0fc1.9dc6.efbe.4786.e49b.69c1.

208+ c19b.f174.9bdc.06a7.80de.b1fe.72be.5d74.

209+ 550c.7dc3.2431.85be.1283.5b01.d807.aa98.

210+ ab1c.5ed5.923f.82a4.59f1.11f1.3956.c25b.

211+ e9b5.dba5.b5c0.fbcf.7137.4491.428a.2f98

212+ =+ ^= hax 0x5be0.cd19.1f83.d9ab.9b05.688c.510e.527f.

213+ a54f.f53a.3c6e.f372.bb67.ae85.6a09.e667

214+ =+ i=0

215+ |- ^- @

216+ ?: =(i lex)

217+ (run 5 hax net)

218+ =+ ^= wox

219+ =+ dux=(cut 9 [i 1] ful)

220+ =+ wox=(run 5 dux net)

221+ =+ j=16

222+ |- ^- @

223+ ?: =(64 j)

224+ wox

225+ =+ :* l=(wac (sub j 15) wox)

226+ m=(wac (sub j 2) wox)

227+ n=(wac (sub j 16) wox)

228+ o=(wac (sub j 7) wox)

229+ ==

230+ =+ x=:(mix (ror 0 7 l) (ror 0 18 l) (rsh [0 3] l))

231+ =+ y=:(mix (ror 0 17 m) (ror 0 19 m) (rsh [0 10] m))

232+ =+ z=:(sum n x o y)

233+ $(wox (con (lsh [5 j] z) wox), j +(j))

234+ =+ j=0

235+ =+ :* a=(wac 0 hax)

236+ b=(wac 1 hax)

237+ c=(wac 2 hax)

238+ d=(wac 3 hax)

239+ e=(wac 4 hax)

240+ f=(wac 5 hax)

241+ g=(wac 6 hax)

242+ h=(wac 7 hax)

243+ ==

244+ |- ^- @

245+ ?: =(64 j)

246+ %= ^$

247+ i +(i)

248+ hax %+ rep 5

249+ :~ (sum a (wac 0 hax))

250+ (sum b (wac 1 hax))

251+ (sum c (wac 2 hax))

252+ (sum d (wac 3 hax))

253+ (sum e (wac 4 hax))

254+ (sum f (wac 5 hax))

255+ (sum g (wac 6 hax))

256+ (sum h (wac 7 hax))

257+ ==

258+ ==

259+ =+ l=:(mix (ror 0 2 a) (ror 0 13 a) (ror 0 22 a)) :: s0

260+ =+ m=:(mix (dis a b) (dis a c) (dis b c)) :: maj

261+ =+ n=(sum l m) :: t2

262+ =+ o=:(mix (ror 0 6 e) (ror 0 11 e) (ror 0 25 e)) :: s1

263+ =+ p=(mix (dis e f) (dis (inv e) g)) :: ch

264+ =+ q=:(sum h o p (wac j kbx) (wac j wox)) :: t1

265+ $(j +(j), a (sum q n), b a, c b, d c, e (sum d q), f e, g f, h g)

387266```

388267

389268#### Examples

390269

391270```

392− > (shas 12.845 6)

393− \/111.115.941.493.032.291.043.932.789.632.248.509.108.945.255.494.251.860.287\/

394− .707.279.709.200.349.471.936

395− \/

271+> `@uw`(shay 1 'hello')

272+0w2eN.jupNe.OyGTU.-l0Co.SWSGS.fFD9k.HPHg1.-AYmg.CgaCG

396273```

397274

275+```

276+> `@uw`(shay 2 'hello')

277+0wdUu.vKccX.fhjYt.tY2a4.B~sqA.KWNOM.1TnEu.8sQd8.LvyYT

278+```

279+

280+#### Discussion

281+

282+Because byte-strings can have leading zeros, but atoms cannot, we use `len`

283+as a way of saying that the atom `ruz` is shorter than its representative

284+byte-string.

285+

398286---

399287

400288## `++shaw`

@@ -419,52 +307,57 @@ An atom.

419307#### Source

420308

421309```hoon

422− ++ shaw

423− |= [sal=@ len=@ ruz=@]

424− (~(raw og (shas sal (mix len ruz))) len)

310+++ shaw

311+ |= [sal=@ len=@ ruz=@]

312+ (~(raw og (shas sal (mix len ruz))) len)

425313```

426314

427315#### Examples

428316

429317```

430− > `@ub`(shaw 3 6 98)

431− 0b11.0111

318+> `@ub`(shaw 3 6 98)

319+0b11.0111

432320

433− > `@ub`(shaw 2 6 98)

434− 0b11

321+> `@ub`(shaw 2 6 98)

322+0b11

435323```

436324

437325---

438326

439−## `++shax`

327+## `++shaz`

440328

441−SHA-256

329+SHA-512

442330

443−Produces an atom by hashing an atom `ruz` with SHA-256.

331+Produces an atom by hashing an atom `ruz` with SHA-512.

444332

445−#### Sources

333+#### Accepts

334+

335+`ruz` is an atom.

336+

337+#### Produces

338+

339+An atom.

340+

341+#### Source

446342

447343```hoon

448− ++ shax

449− ~/ %shax

450− |= ruz=@ ^- @

451− (shay [(met 3 ruz) ruz])

344+++ shaz

345+ |= ruz=@ ^- @

346+ (shal [(met 3 ruz) ruz])

452347```

453348

454349#### Examples

455350

456351```

457− > (shax 'hello')

458− \/16.552.786.619.039.860.277.601.417.878.457.384.195.409.020.923.835.016.617.984.82\/

459− 0.774.431.701.725.740

460− \/

352+`@uw`(shaz 'hello')

353+0w1.3MdWY.sS~QT.zFsbB.N7oQo.cSImU.56Xcu.DMtMq.mrSsc.z8WsY.pNABZ.Z~ySG.Ecysb.XCP5P.fuHjq.Jimnn.zPoHQ.AQD6r

461354```

462355

463356---

464357

465−## `++shay`

358+## `++shal`

466359

467−SHA-256 with length

360+SHA-512 with length

468361

469362Produces an atom by hashing an atom `ruz` with SHA-512. Another atom, `len`, is

470363the byte-length of the theoretical buffer represented by the atom.

@@ -475,108 +368,136 @@ the byte-length of the theoretical buffer represented by the atom.

475368

476369`ruz` is an atom.

477370

371+#### Produces

372+

373+An atom.

374+

478375#### Source

479376

480377```hoon

481− ++ shay

482− ~/ %shay

483− |= [len=@u ruz=@] ^- @

484− => .(ruz (cut 3 [0 len] ruz))

485− =+ [few==>(fe .(a 5)) wac=|=([a=@ b=@] (cut 5 [a 1] b))]

486− =+ [sum=sum.few ror=ror.few net=net.few inv=inv.few]

487− =+ ral=(lsh 0 3 len)

488− =+ ^= ful

489− %+ can 0

490− :~ [ral ruz]

491− [8 128]

492− [(mod (sub 960 (mod (add 8 ral) 512)) 512) 0]

493− [64 (~(net fe 6) ral)]

494− ==

495− =+ lex=(met 9 ful)

496− =+ ^= kbx 0xc671.78f2.bef9.a3f7.a450.6ceb.90be.fffa.

497− 8cc7.0208.84c8.7814.78a5.636f.748f.82ee.

498− 682e.6ff3.5b9c.ca4f.4ed8.aa4a.391c.0cb3.

499− 34b0.bcb5.2748.774c.1e37.6c08.19a4.c116.

500− 106a.a070.f40e.3585.d699.0624.d192.e819.

501− c76c.51a3.c24b.8b70.a81a.664b.a2bf.e8a1.

502− 9272.2c85.81c2.c92e.766a.0abb.650a.7354.

503− 5338.0d13.4d2c.6dfc.2e1b.2138.27b7.0a85.

504− 1429.2967.06ca.6351.d5a7.9147.c6e0.0bf3.

505− bf59.7fc7.b003.27c8.a831.c66d.983e.5152.

506− 76f9.88da.5cb0.a9dc.4a74.84aa.2de9.2c6f.

507− 240c.a1cc.0fc1.9dc6.efbe.4786.e49b.69c1.

508− c19b.f174.9bdc.06a7.80de.b1fe.72be.5d74.

509− 550c.7dc3.2431.85be.1283.5b01.d807.aa98.

510− ab1c.5ed5.923f.82a4.59f1.11f1.3956.c25b.

511− e9b5.dba5.b5c0.fbcf.7137.4491.428a.2f98

512− =+ ^= hax 0x5be0.cd19.1f83.d9ab.9b05.688c.510e.527f.

513− a54f.f53a.3c6e.f372.bb67.ae85.6a09.e667

514− =+ i=0

378+++ shal

379+ ~/ %shal

380+ |= [len=@ ruz=@] ^- @

381+ => .(ruz (cut 3 [0 len] ruz))

382+ =+ [few==>(fe .(a 6)) wac=|=([a=@ b=@] (cut 6 [a 1] b))]

383+ =+ [sum=sum.few ror=ror.few net=net.few inv=inv.few]

384+ =+ ral=(lsh [0 3] len)

385+ =+ ^= ful

386+ %+ can 0

387+ :~ [ral ruz]

388+ [8 128]

389+ [(mod (sub 1.920 (mod (add 8 ral) 1.024)) 1.024) 0]

390+ [128 (~(net fe 7) ral)]

391+ ==

392+ =+ lex=(met 10 ful)

393+ =+ ^= kbx 0x6c44.198c.4a47.5817.5fcb.6fab.3ad6.faec.

394+ 597f.299c.fc65.7e2a.4cc5.d4be.cb3e.42b6.

395+ 431d.67c4.9c10.0d4c.3c9e.be0a.15c9.bebc.

396+ 32ca.ab7b.40c7.2493.28db.77f5.2304.7d84.

397+ 1b71.0b35.131c.471b.113f.9804.bef9.0dae.

398+ 0a63.7dc5.a2c8.98a6.06f0.67aa.7217.6fba.

399+ f57d.4f7f.ee6e.d178.eada.7dd6.cde0.eb1e.

400+ d186.b8c7.21c0.c207.ca27.3ece.ea26.619c.

401+ c671.78f2.e372.532b.bef9.a3f7.b2c6.7915.

402+ a450.6ceb.de82.bde9.90be.fffa.2363.1e28.

403+ 8cc7.0208.1a64.39ec.84c8.7814.a1f0.ab72.

404+ 78a5.636f.4317.2f60.748f.82ee.5def.b2fc.

405+ 682e.6ff3.d6b2.b8a3.5b9c.ca4f.7763.e373.

406+ 4ed8.aa4a.e341.8acb.391c.0cb3.c5c9.5a63.

407+ 34b0.bcb5.e19b.48a8.2748.774c.df8e.eb99.

408+ 1e37.6c08.5141.ab53.19a4.c116.b8d2.d0c8.

409+ 106a.a070.32bb.d1b8.f40e.3585.5771.202a.

410+ d699.0624.5565.a910.d192.e819.d6ef.5218.

411+ c76c.51a3.0654.be30.c24b.8b70.d0f8.9791.

412+ a81a.664b.bc42.3001.a2bf.e8a1.4cf1.0364.

413+ 9272.2c85.1482.353b.81c2.c92e.47ed.aee6.

414+ 766a.0abb.3c77.b2a8.650a.7354.8baf.63de.

415+ 5338.0d13.9d95.b3df.4d2c.6dfc.5ac4.2aed.

416+ 2e1b.2138.5c26.c926.27b7.0a85.46d2.2ffc.

417+ 1429.2967.0a0e.6e70.06ca.6351.e003.826f.

418+ d5a7.9147.930a.a725.c6e0.0bf3.3da8.8fc2.

419+ bf59.7fc7.beef.0ee4.b003.27c8.98fb.213f.

420+ a831.c66d.2db4.3210.983e.5152.ee66.dfab.

421+ 76f9.88da.8311.53b5.5cb0.a9dc.bd41.fbd4.

422+ 4a74.84aa.6ea6.e483.2de9.2c6f.592b.0275.

423+ 240c.a1cc.77ac.9c65.0fc1.9dc6.8b8c.d5b5.

424+ efbe.4786.384f.25e3.e49b.69c1.9ef1.4ad2.

425+ c19b.f174.cf69.2694.9bdc.06a7.25c7.1235.

426+ 80de.b1fe.3b16.96b1.72be.5d74.f27b.896f.

427+ 550c.7dc3.d5ff.b4e2.2431.85be.4ee4.b28c.

428+ 1283.5b01.4570.6fbe.d807.aa98.a303.0242.

429+ ab1c.5ed5.da6d.8118.923f.82a4.af19.4f9b.

430+ 59f1.11f1.b605.d019.3956.c25b.f348.b538.

431+ e9b5.dba5.8189.dbbc.b5c0.fbcf.ec4d.3b2f.

432+ 7137.4491.23ef.65cd.428a.2f98.d728.ae22

433+ =+ ^= hax 0x5be0.cd19.137e.2179.1f83.d9ab.fb41.bd6b.

434+ 9b05.688c.2b3e.6c1f.510e.527f.ade6.82d1.

435+ a54f.f53a.5f1d.36f1.3c6e.f372.fe94.f82b.

436+ bb67.ae85.84ca.a73b.6a09.e667.f3bc.c908

437+ =+ i=0

438+ |- ^- @

439+ ?: =(i lex)

440+ (run 6 hax net)

441+ =+ ^= wox

442+ =+ dux=(cut 10 [i 1] ful)

443+ =+ wox=(run 6 dux net)

444+ =+ j=16

515445 |- ^- @

516− ?: =(i lex)

517− (rep 5 (turn (rip 5 hax) net))

518− =+ ^= wox

519− =+ dux=(cut 9 [i 1] ful)

520− =+ wox=(rep 5 (turn (rip 5 dux) net))

521− =+ j=16

522− |- ^- @

523− ?: =(64 j)

524− wox

525− =+ :* l=(wac (sub j 15) wox)

526− m=(wac (sub j 2) wox)

527− n=(wac (sub j 16) wox)

528− o=(wac (sub j 7) wox)

529− ==

530− =+ x=:(mix (ror 0 7 l) (ror 0 18 l) (rsh 0 3 l))

531− =+ y=:(mix (ror 0 17 m) (ror 0 19 m) (rsh 0 10 m))

532− =+ z=:(sum n x o y)

533− $(wox (con (lsh 5 j z) wox), j +(j))

534− =+ j=0

535− =+ :* a=(wac 0 hax)

536− b=(wac 1 hax)

537− c=(wac 2 hax)

538− d=(wac 3 hax)

539− e=(wac 4 hax)

540− f=(wac 5 hax)

541− g=(wac 6 hax)

542− h=(wac 7 hax)

446+ ?: =(80 j)

447+ wox

448+ =+ :* l=(wac (sub j 15) wox)

449+ m=(wac (sub j 2) wox)

450+ n=(wac (sub j 16) wox)

451+ o=(wac (sub j 7) wox)

543452 ==

544− |- ^- @

545− ?: =(64 j)

546− %= ^$

547− i +(i)

548− hax %+ rep 5

549− :~ (sum a (wac 0 hax))

550− (sum b (wac 1 hax))

551− (sum c (wac 2 hax))

552− (sum d (wac 3 hax))

553− (sum e (wac 4 hax))

554− (sum f (wac 5 hax))

555− (sum g (wac 6 hax))

556− (sum h (wac 7 hax))

557− ==

558− ==

559− =+ l=:(mix (ror 0 2 a) (ror 0 13 a) (ror 0 22 a)) :: s0

560− =+ m=:(mix (dis a b) (dis a c) (dis b c)) :: maj

561− =+ n=(sum l m) :: t2

562− =+ o=:(mix (ror 0 6 e) (ror 0 11 e) (ror 0 25 e)) :: s1

563− =+ p=(mix (dis e f) (dis (inv e) g)) :: ch

564− =+ q=:(sum h o p (wac j kbx) (wac j wox)) :: t1

565− $(j +(j), a (sum q n), b a, c b, d c, e (sum d q), f e, g f, h g)

453+ =+ x=:(mix (ror 0 1 l) (ror 0 8 l) (rsh [0 7] l))

454+ =+ y=:(mix (ror 0 19 m) (ror 0 61 m) (rsh [0 6] m))

455+ =+ z=:(sum n x o y)

456+ $(wox (con (lsh [6 j] z) wox), j +(j))

457+ =+ j=0

458+ =+ :* a=(wac 0 hax)

459+ b=(wac 1 hax)

460+ c=(wac 2 hax)

461+ d=(wac 3 hax)

462+ e=(wac 4 hax)

463+ f=(wac 5 hax)

464+ g=(wac 6 hax)

465+ h=(wac 7 hax)

466+ ==

467+ |- ^- @

468+ ?: =(80 j)

469+ %= ^$

470+ i +(i)

471+ hax %+ rep 6

472+ :~ (sum a (wac 0 hax))

473+ (sum b (wac 1 hax))

474+ (sum c (wac 2 hax))

475+ (sum d (wac 3 hax))

476+ (sum e (wac 4 hax))

477+ (sum f (wac 5 hax))

478+ (sum g (wac 6 hax))

479+ (sum h (wac 7 hax))

480+ ==

481+ ==

482+ =+ l=:(mix (ror 0 28 a) (ror 0 34 a) (ror 0 39 a)) :: S0

483+ =+ m=:(mix (dis a b) (dis a c) (dis b c)) :: maj

484+ =+ n=(sum l m) :: t2

485+ =+ o=:(mix (ror 0 14 e) (ror 0 18 e) (ror 0 41 e)) :: S1

486+ =+ p=(mix (dis e f) (dis (inv e) g)) :: ch

487+ =+ q=:(sum h o p (wac j kbx) (wac j wox)) :: t1

488+ $(j +(j), a (sum q n), b a, c b, d c, e (sum d q), f e, g f, h g)

566489```

567490

568491#### Examples

569492

570493```

571− > (shay 1 'hello')

572− \/16.144.219.278.061.159.438.339.586.294.967.166.038.336.988.797.862.808.055.174.98\/

573− 7.398.597.302.069.674

574− \/

494+> `@uw`(shal 1 'hello')

495+0w2.nWO0R.zMAzH.OSWU1.apOje.19Mta.RE24o.4u~MB.wQuj4.NDdG6.0QZA0.w21Br.yQVhu.pFBII.Cdgvd.WT-bH.g51Yu.fL44y

496+```

575497

576− > (shay 2 'hello')

577− \/100.467.333.538.737.303.691.714.735.404.408.035.555.613.179.595.938.688.113.300.8\/

578− 01.974.878.934.544.183

579− \/

498+```

499+> `@uw`(shal 2 'hello')

500+0w1.r3W4g.hae37.8YUFp.ntryr.DsQuY.rPsdm.p3Xjv.rayLz.DslEc.Lxvll.OJUc3.tZeLZ.TjUnu.XMyGr.82qPA.zl1y0.HbSpT

580501```

581502

582503#### Discussion

@@ -587,11 +508,11 @@ byte-string.

587508

588509---

589510

590−## `++shaz`

511+## `++shan`

591512

592−SHA-512

513+SHA-1

593514

594−Produces an atom by hashing an atom `ruz` with SHA-512.

515+Produces an atom by hashing an atom `ruz` with SHA-1.

595516

596517#### Accepts

597518

@@ -604,21 +525,84 @@ An atom.

604525#### Source

605526

606527```hoon

607− ++ shaz

608− |= ruz=@ ^- @

609− (shal [(met 3 ruz) ruz])

528+++ shan

529+ |= ruz=@

530+ =+ [few==>(fe .(a 5)) wac=|=([a=@ b=@] (cut 5 [a 1] b))]

531+ =+ [sum=sum.few ror=ror.few rol=rol.few net=net.few inv=inv.few]

532+ =+ ral=(lsh [0 3] (met 3 ruz))

533+ =+ ^= ful

534+ %+ can 0

535+ :~ [ral ruz]

536+ [8 128]

537+ [(mod (sub 960 (mod (add 8 ral) 512)) 512) 0]

538+ [64 (~(net fe 6) ral)]

539+ ==

540+ =+ lex=(met 9 ful)

541+ =+ kbx=0xca62.c1d6.8f1b.bcdc.6ed9.eba1.5a82.7999

542+ =+ hax=0xc3d2.e1f0.1032.5476.98ba.dcfe.efcd.ab89.6745.2301

543+ =+ i=0

544+ |-

545+ ?: =(i lex)

546+ (rep 5 (flop (rip 5 hax)))

547+ =+ ^= wox

548+ =+ dux=(cut 9 [i 1] ful)

549+ =+ wox=(rep 5 (turn (rip 5 dux) net))

550+ =+ j=16

551+ |- ^- @

552+ ?: =(80 j)

553+ wox

554+ =+ :* l=(wac (sub j 3) wox)

555+ m=(wac (sub j 8) wox)

556+ n=(wac (sub j 14) wox)

557+ o=(wac (sub j 16) wox)

558+ ==

559+ =+ z=(rol 0 1 :(mix l m n o))

560+ $(wox (con (lsh [5 j] z) wox), j +(j))

561+ =+ j=0

562+ =+ :* a=(wac 0 hax)

563+ b=(wac 1 hax)

564+ c=(wac 2 hax)

565+ d=(wac 3 hax)

566+ e=(wac 4 hax)

567+ ==

568+ |- ^- @

569+ ?: =(80 j)

570+ %= ^$

571+ i +(i)

572+ hax %+ rep 5

573+ :~

574+ (sum a (wac 0 hax))

575+ (sum b (wac 1 hax))

576+ (sum c (wac 2 hax))

577+ (sum d (wac 3 hax))

578+ (sum e (wac 4 hax))

579+ ==

580+ ==

581+ =+ fx=(con (dis b c) (dis (not 5 1 b) d))

582+ =+ fy=:(mix b c d)

583+ =+ fz=:(con (dis b c) (dis b d) (dis c d))

584+ =+ ^= tem

585+ ?: &((gte j 0) (lte j 19))

586+ :(sum (rol 0 5 a) fx e (wac 0 kbx) (wac j wox))

587+ ?: &((gte j 20) (lte j 39))

588+ :(sum (rol 0 5 a) fy e (wac 1 kbx) (wac j wox))

589+ ?: &((gte j 40) (lte j 59))

590+ :(sum (rol 0 5 a) fz e (wac 2 kbx) (wac j wox))

591+ :(sum (rol 0 5 a) fy e (wac 3 kbx) (wac j wox))

592+ $(j +(j), a tem, b a, c (rol 0 30 b), d c, e d)

610593```

611594

612595#### Examples

613596

614597```

615− > (shaz 'hello')

616− \/3.548.533.422.469.437.734.729.094.584.175.910.682.076.656.883.559.953.324.378.007\/

617− .735.849.386.038.666.450.748.109.671.344.747.196.048.200.348.948.408.339.256.384.

618− 360.070.359.656.053.016.948.640.159.265.179

619− \/

598+> `@uw`(shan 'hello')

599+0waH.QNxTs.NuyyS.HXu3P.J8bdC.KGkdd

620600```

621601

602+#### Discussion

603+

604+SHA-1 is a deprecated function; it is not considered secure.

605+

622606---

623607

624608## `++og`

@@ -637,16 +621,16 @@ A core.

637621#### Source

638622

639623```hoon

640− ++ og

641− ~/ %og

642− |_ a=@

624+++ og

625+ ~/ %og

626+ |_ a=@

643627```

644628

645629#### Examples

646630

647631```

648− > ~(. og 919)

649− <4.wmp {a/@ud <54.tyv 119.olq 31.ohr 1.jmk $143>}>

632+> ~(. og 919)

633+<4.wmp {a/@ud <54.tyv 119.olq 31.ohr 1.jmk $143>}>

650634```

651635

652636#### Discussion

@@ -675,26 +659,28 @@ An atom.

675659#### Source

676660

677661```hoon

678− ++ rad

679− |= b=@ ^- @

680− =+ c=(raw (met 0 b))

681− ?:((lth c b) c $(a +(a)))

662+++ rad

663+ |= b=@ ^- @

664+ ~_ leaf+"rad-zero"

665+ ?< =(0 b)

666+ =+ c=(raw (met 0 b))

667+ ?:((lth c b) c $(a +(a)))

682668```

683669

684670#### Examples

685671

686672```

687− > (~(rad og 5) 11)

688− 4

673+> (~(rad og 5) 11)

674+4

689675

690− > (~(rad og 758.716.593) 11)

691− 2

676+> (~(rad og 758.716.593) 11)

677+2

692678

693− > (~(rad og 1) 100.000)

694− 71.499

679+> (~(rad og 1) 100.000)

680+71.499

695681

696− > (~(rad og eny) 11) :: `eny` acts as a random sample

697− 7

682+> (~(rad og eny) 11) :: `eny` acts as a random sample

683+7

698684```

699685

700686---

@@ -718,23 +704,23 @@ A cell.

718704#### Source

719705

720706```hoon

721− ++ rads

722− |= b=@

723− =+ r=(rad b)

724− [r +>.$(a (shas %og-s (mix a r)))]

707+++ rads

708+ |= b=@

709+ =+ r=(rad b)

710+ [r +>.$(a (shas %og-s (mix a r)))]

725711```

726712

727713#### Examples

728714

729715```

730− > (~(rads og 4) 10)

731− [2 <4.wmp {a/@ <54.tyv 119.olq 31.ohr 1.jmk $143>}>]

716+> (~(rads og 4) 10)

717+[2 <4.wmp {a/@ <54.tyv 119.olq 31.ohr 1.jmk $143>}>]

732718

733− > =/ rng ~(. og 7)

734− =^ a rng (rads:rng 10)

735− =^ b rng (rads:rng 10)

736− [a b]

737− [2 8]

719+> =/ rng ~(. og 7)

720+ =^ a rng (rads:rng 10)

721+ =^ b rng (rads:rng 10)

722+ [a b]

723+[2 8]

738724```

739725

740726#### Discussion

@@ -762,35 +748,35 @@ An atom.

762748#### Source

763749

764750```hoon

765− ++ raw

766− ~/ %raw

767− |= b=@ ^- @

768− %+ can

769− 0

770− =+ c=(shas %og-a (mix b a))

771− |- ^- (list [@ @])

772− ?: =(0 b)

773− ~

774− =+ d=(shas %og-b (mix b (mix a c)))

775− ?: (lth b 256)

776− [[b (end 0 b d)] ~]

777− [[256 d] $(c d, b (sub b 256))]

751+++ raw

752+ ~/ %raw

753+ |= b=@ ^- @

754+ %+ can

755+ 0

756+ =+ c=(shas %og-a (mix b a))

757+ |- ^- (list [@ @])

758+ ?: =(0 b)

759+ ~

760+ =+ d=(shas %og-b (mix b (mix a c)))

761+ ?: (lth b 256)

762+ [[b (end [0 b] d)] ~]

763+ [[256 d] $(c d, b (sub b 256))]

778764```

779765

780766#### Examples

781767

782768```

783− > `@ud`(~(raw og 27) 4)

784− 0b1001

769+> `@ud`(~(raw og 27) 4)

770+0b1001

785771

786− > `@ub`(~(raw og 27) 3)

787− 0b0

772+> `@ub`(~(raw og 27) 3)

773+0b0

788774

789− > `@ub`(~(raw og 11) 4)

790− 0b1111

775+> `@ub`(~(raw og 11) 4)

776+0b1111

791777

792− > `@ub`(~(raw og 11) 3)

793− 0b100

778+> `@ub`(~(raw og 11) 3)

779+0b100

794780```

795781

796782---

@@ -806,24 +792,23 @@ parent core with `(raw b)`.

806792#### Source

807793

808794```hoon

809− ++ raws

810− |= b=@

811− =+ r=(raw b)

812− [r +>.$(a (shas %og-s r))]

813− --

795+++ raws

796+ |= b=@

797+ =+ r=(raw b)

798+ [r +>.$(a (shas %og-s (mix a r)))]

814799```

815800

816801#### Examples

817802

818803```

819− > `[@ub _og]`(~(raws og 7) 4)

820− [0b1100 <4.wmp {a/@ <54.tyv 119.olq 31.ohr 1.jmk $143>}>]

804+> `[@ub _og]`(~(raws og 7) 4)

805+[0b1100 <4.wmp {a/@ <54.tyv 119.olq 31.ohr 1.jmk $143>}>]

821806

822− > =/ rng ~(. og 7)

823− =^ a rng (rads:rng 4)

824− =^ b rng (rads:rng 4)

825− [`@ub`a `@ub`b]

826− [0b10 0b1]

807+> =/ rng ~(. og 7)

808+ =^ a rng (rads:rng 4)

809+ =^ b rng (rads:rng 4)

810+ [`@ub`a `@ub`b]

811+[0b10 0b1]

827812```

828813

829814#### Discussion

content/docs/hoon/reference/stdlib/3f.md+444−314

@@ -14,8 +14,8 @@ Used in the `@p` phonetic base.

1414#### Source

1515

1616```hoon

17− ++ un

18− |%

17+++ un

18+ |%

1919```

2020

2121---

@@ -39,36 +39,35 @@ An atom.

3939#### Source

4040

4141```hoon

42− ++ wren

43− |= pyn=@ ^- @

44− =+ len=(met 3 pyn)

45− ?: =(0 len)

46− 0

47− => .(len (dec len))

48− =+ mig=(zaft (xafo len (cut 3 [len 1] pyn)))

49− %+ can 3

50− %- flop ^- (list [@ @])

51− :- [1 mig]

52− |- ^- (list [@ @])

53− ?: =(0 len)

54− ~

55− => .(len (dec len))

56− =+ mog=(zyft :(mix mig (end 3 1 len) (cut 3 [len 1] pyn)))

57− [[1 mog] $(mig mog)]

58− ::

42+++ wren

43+ |= pyn=@ ^- @

44+ =+ len=(met 3 pyn)

45+ ?: =(0 len)

46+ 0

47+ => .(len (dec len))

48+ =+ mig=(zaft (xafo len (cut 3 [len 1] pyn)))

49+ %+ can 3

50+ %- flop ^- (list [@ @])

51+ :- [1 mig]

52+ |- ^- (list [@ @])

53+ ?: =(0 len)

54+ ~

55+ => .(len (dec len))

56+ =+ mog=(zyft :(mix mig (end 3 len) (cut 3 [len 1] pyn)))

57+ [[1 mog] $(mig mog)]

5958```

6059

6160#### Examples

6261

6362```

64− > `@ux`(wren:un 'testing')

65− 0x30.bf6a.b9fe.7d8f

63+> `@ux`(wren:un 'testing')

64+0x30.bf6a.b9fe.7d8f

6665

67− > `@ux`'testing'

68− 0x67.6e69.7473.6574

66+> `@ux`'testing'

67+0x67.6e69.7473.6574

6968

70− > `@da`(wred:un (wren:un ~2001.2.5))

71− ~2001.2.5

69+> `@da`(wred:un (wren:un ~2001.2.5))

70+~2001.2.5

7271```

7372

7473---

@@ -92,36 +91,35 @@ An atom.

9291#### Source

9392

9493```hoon

95− ++ wred

96− |= cry=@ ^- @

97− =+ len=(met 3 cry)

98− ?: =(0 len)

99− 0

100− => .(len (dec len))

101− =+ mig=(cut 3 [len 1] cry)

102− %+ can 3

103− %- flop ^- (list [@ @])

104− :- [1 (xaro len (zart mig))]

105− |- ^- (list [@ @])

106− ?: =(0 len)

107− ~

108− => .(len (dec len))

109− =+ mog=(cut 3 [len 1] cry)

110− [[1 :(mix mig (end 3 1 len) (zyrt mog))] $(mig mog)]

111− ::

94+++ wred

95+ |= cry=@ ^- @

96+ =+ len=(met 3 cry)

97+ ?: =(0 len)

98+ 0

99+ => .(len (dec len))

100+ =+ mig=(cut 3 [len 1] cry)

101+ %+ can 3

102+ %- flop ^- (list [@ @])

103+ :- [1 (xaro len (zart mig))]

104+ |- ^- (list [@ @])

105+ ?: =(0 len)

106+ ~

107+ => .(len (dec len))

108+ =+ mog=(cut 3 [len 1] cry)

109+ [[1 :(mix mig (end 3 len) (zyrt mog))] $(mig mog)]

112110```

113111

114112#### Examples

115113

116114```

117− > (wred:un 0x30.bf6a.b9fe.7d8f)

118− 29.113.321.805.538.676

115+> (wred:un 0x30.bf6a.b9fe.7d8f)

116+29.113.321.805.538.676

119117

120− > `@t`(wred:un 0x30.bf6a.b9fe.7d8f)

121− 'testing'

118+> `@t`(wred:un 0x30.bf6a.b9fe.7d8f)

119+'testing'

122120

123− > (wred:un (wren:un 200.038.426))

124− 200.038.426

121+> (wred:un (wren:un 200.038.426))

122+200.038.426

125123```

126124

127125---

@@ -146,20 +144,20 @@ An atom.

146144#### Source

147145

148146```hoon

149− ++ xafo |=([a=@ b=@] +((mod (add (dec b) a) 255)))

147+++ xafo |=([a=@ b=@] +((mod (add (dec b) a) 255)))

150148```

151149

152150#### Examples

153151

154152```

155− > (xafo:un 5 6)

156− 11

153+> (xafo:un 5 6)

154+11

157155

158− > (xafo:un 256 20)

159− 21

156+> (xafo:un 256 20)

157+21

160158

161− > (xafo:un 256 (xaro:un 256 20))

162− 20

159+> (xafo:un 256 (xaro:un 256 20))

160+20

163161```

164162

165163---

@@ -184,20 +182,20 @@ An atom.

184182#### Source

185183

186184```hoon

187− ++ xaro |=([a=@ b=@] +((mod (add (dec b) (sub 255 (mod a 255))) 255)))

185+++ xaro |=([a=@ b=@] +((mod (add (dec b) (sub 255 (mod a 255))) 255)))

188186```

189187

190188#### Examples

191189

192190```

193− > (xaro:un 17 57)

194− 40

191+> (xaro:un 17 57)

192+40

195193

196− > (xaro:un 265 12)

197− 2

194+> (xaro:un 265 12)

195+2

198196

199− > (xaro:un 256 (xafo:un 256 20))

200− 20

197+> (xaro:un 256 (xafo:un 256 20))

198+20

201199```

202200

203201---

@@ -220,37 +218,37 @@ An atom.

220218#### Source

221219

222220```hoon

223− ++ zaft

224− |= a=@D

225− =+ ^= b

226− 0xcc.75bc.86c8.2fb1.9a42.f0b3.79a0.92ca.21f6.1e41.cde5.fcc0.

227− 7e85.51ae.1005.c72d.1246.07e8.7c64.a914.8d69.d9f4.59c2.8038.

228− 1f4a.dca2.6fdf.66f9.f561.a12e.5a16.f7b0.a39f.364e.cb70.7318.

229− 1de1.ad31.63d1.abd4.db68.6a33.134d.a760.edee.5434.493a.e323.

230− 930d.8f3d.3562.bb81.0b24.43cf.bea5.a6eb.52b4.0229.06b2.6704.

231− 78c9.45ec.d75e.58af.c577.b7b9.c40e.017d.90c3.87f8.96fa.1153.

232− 0372.7f30.1c32.ac83.ff17.c6e4.d36d.6b55.e2ce.8c71.8a5b.b6f3.

233− 9d4b.eab5.8b3c.e7f2.a8fe.9574.5de0.bf20.3f15.9784.9939.5f9c.

234− e609.564f.d8a4.b825.9819.94aa.2c08.8e4c.9b22.477a.2840.3ed6.

235− 3750.6ef1.44dd.89ef.6576.d00a.fbda.9ed2.3b6c.7b0c.bde9.2ade.

236− 5c88.c182.481a.1b0f.2bfd.d591.2726.57ba

237− (cut 3 [(dec a) 1] b)

221+++ zaft

222+ |= a=@D

223+ =+ ^= b

224+ 0xcc.75bc.86c8.2fb1.9a42.f0b3.79a0.92ca.21f6.1e41.cde5.fcc0.

225+ 7e85.51ae.1005.c72d.1246.07e8.7c64.a914.8d69.d9f4.59c2.8038.

226+ 1f4a.dca2.6fdf.66f9.f561.a12e.5a16.f7b0.a39f.364e.cb70.7318.

227+ 1de1.ad31.63d1.abd4.db68.6a33.134d.a760.edee.5434.493a.e323.

228+ 930d.8f3d.3562.bb81.0b24.43cf.bea5.a6eb.52b4.0229.06b2.6704.

229+ 78c9.45ec.d75e.58af.c577.b7b9.c40e.017d.90c3.87f8.96fa.1153.

230+ 0372.7f30.1c32.ac83.ff17.c6e4.d36d.6b55.e2ce.8c71.8a5b.b6f3.

231+ 9d4b.eab5.8b3c.e7f2.a8fe.9574.5de0.bf20.3f15.9784.9939.5f9c.

232+ e609.564f.d8a4.b825.9819.94aa.2c08.8e4c.9b22.477a.2840.3ed6.

233+ 3750.6ef1.44dd.89ef.6576.d00a.fbda.9ed2.3b6c.7b0c.bde9.2ade.

234+ 5c88.c182.481a.1b0f.2bfd.d591.2726.57ba

235+ (cut 3 [(dec a) 1] b)

238236```

239237

240238#### Examples

241239

242240```

243− > (zaft:un 0x12)

244− 42

241+> (zaft:un 0x12)

242+42

245243

246− > (zaft:un 0xff)

247− 204

248− > `@ux`(zart:un 204)

249− 0xff

244+> (zaft:un 0xff)

245+204

246+> `@ux`(zart:un 204)

247+0xff

250248

251− > (zaft:un 0x0)

252− ! decrement-underflow

253− ! exit

249+> (zaft:un 0x0)

250+! decrement-underflow

251+! exit

254252```

255253

256254---

@@ -273,35 +271,34 @@ An atom.

273271#### Source

274272

275273```hoon

276− ++ zart :: reverse 255-sbox

277− |= a=@D

278− =+ ^= b

279− 0x68.4f07.ea1c.73c9.75c2.efc8.d559.5125.f621.a7a8.8591.5613.

280− dd52.40eb.65a2.60b7.4bcb.1123.ceb0.1bd6.3c84.2906.b164.19b3.

281− 1e95.5fec.ffbc.f187.fbe2.6680.7c77.d30e.e94a.9414.fd9a.017d.

282− 3a7e.5a55.8ff5.8bf9.c181.e5b6.6ab2.35da.50aa.9293.3bc0.cdc6.

283− f3bf.1a58.4130.f844.3846.744e.36a0.f205.789e.32d8.5e54.5c22.

284− 0f76.fce7.4569.0d99.d26e.e879.dc16.2df4.887f.1ffe.4dba.6f5d.

285− bbcc.2663.1762.aed7.af8a.ca20.dbb4.9bc7.a942.834c.105b.c4d4.

286− 8202.3e61.a671.90e6.273d.bdab.3157.cfa4.0c2e.df86.2496.f7ed.

287− 2b48.2a9d.5318.a343.d128.be9c.a5ad.6bb5.6dfa.c5e1.3408.128d.

288− 2c04.0339.97a1.2ff0.49d0.eeb8.6c0a.0b37.b967.c347.d9ac.e072.

289− e409.7b9f.1598.1d3f.33de.8ce3.8970.8e7a

290− (cut 3 [(dec a) 1] b)

291− ::

274+++ zart

275+ |= a=@D

276+ =+ ^= b

277+ 0x68.4f07.ea1c.73c9.75c2.efc8.d559.5125.f621.a7a8.8591.5613.

278+ dd52.40eb.65a2.60b7.4bcb.1123.ceb0.1bd6.3c84.2906.b164.19b3.

279+ 1e95.5fec.ffbc.f187.fbe2.6680.7c77.d30e.e94a.9414.fd9a.017d.

280+ 3a7e.5a55.8ff5.8bf9.c181.e5b6.6ab2.35da.50aa.9293.3bc0.cdc6.

281+ f3bf.1a58.4130.f844.3846.744e.36a0.f205.789e.32d8.5e54.5c22.

282+ 0f76.fce7.4569.0d99.d26e.e879.dc16.2df4.887f.1ffe.4dba.6f5d.

283+ bbcc.2663.1762.aed7.af8a.ca20.dbb4.9bc7.a942.834c.105b.c4d4.

284+ 8202.3e61.a671.90e6.273d.bdab.3157.cfa4.0c2e.df86.2496.f7ed.

285+ 2b48.2a9d.5318.a343.d128.be9c.a5ad.6bb5.6dfa.c5e1.3408.128d.

286+ 2c04.0339.97a1.2ff0.49d0.eeb8.6c0a.0b37.b967.c347.d9ac.e072.

287+ e409.7b9f.1598.1d3f.33de.8ce3.8970.8e7a

288+ (cut 3 [(dec a) 1] b)

292289```

293290

294291#### Examples

295292

296293```

297− > `@ux`(zart:un 204)

298− 0xff

294+> `@ux`(zart:un 204)

295+0xff

299296

300− > `@ux`(zart:un 42)

301− 0x12

297+> `@ux`(zart:un 42)

298+0x12

302299

303− > (zaft:un 0x12)

304− 42

300+> (zaft:un 0x12)

301+42

305302```

306303

307304---

@@ -324,38 +321,37 @@ An atom.

324321#### Source

325322

326323```hoon

327− ++ zyft :: forward 256-sbox

328− |= a=@D

329− =+ ^= b

330− 0xbb49.b71f.b881.b402.17e4.6b86.69b5.1647.115f.dddb.7ca5.

331− 8371.4bd5.19a9.b092.605d.0d9b.e030.a0cc.78ba.5706.4d2d.

332− 986a.768c.f8e8.c4c7.2f1c.effe.3cae.01c0.253e.65d3.3872.

333− ce0e.7a74.8ac6.daac.7e5c.6479.44ec.4143.3d20.4af0.ee6c.

334− c828.deca.0377.249f.ffcd.7b4f.eb7d.66f2.8951.042e.595a.

335− 8e13.f9c3.a79a.f788.6199.9391.7fab.6200.4ce5.0758.e2f1.

336− 7594.c945.d218.4248.afa1.e61a.54fb.1482.bea4.96a2.3473.

337− 63c2.e7cb.155b.120a.4ed7.bfd8.b31b.4008.f329.fca3.5380.

338− 9556.0cb2.8722.2bea.e96e.3ac5.d1bc.10e3.2c52.a62a.b1d6.

339− 35aa.d05e.f6a8.0f3b.31ed.559d.09ad.f585.6d21.fd1d.8d67.

340− 370b.26f4.70c1.b923.4684.6fbd.cf8b.5036.0539.9cdc.d93f.

341− 9068.1edf.8f33.b632.d427.97fa.9ee1

342− (cut 3 [a 1] b)

343− ::

324+++ zyft

325+ |= a=@D

326+ =+ ^= b

327+ 0xbb49.b71f.b881.b402.17e4.6b86.69b5.1647.115f.dddb.7ca5.

328+ 8371.4bd5.19a9.b092.605d.0d9b.e030.a0cc.78ba.5706.4d2d.

329+ 986a.768c.f8e8.c4c7.2f1c.effe.3cae.01c0.253e.65d3.3872.

330+ ce0e.7a74.8ac6.daac.7e5c.6479.44ec.4143.3d20.4af0.ee6c.

331+ c828.deca.0377.249f.ffcd.7b4f.eb7d.66f2.8951.042e.595a.

332+ 8e13.f9c3.a79a.f788.6199.9391.7fab.6200.4ce5.0758.e2f1.

333+ 7594.c945.d218.4248.afa1.e61a.54fb.1482.bea4.96a2.3473.

334+ 63c2.e7cb.155b.120a.4ed7.bfd8.b31b.4008.f329.fca3.5380.

335+ 9556.0cb2.8722.2bea.e96e.3ac5.d1bc.10e3.2c52.a62a.b1d6.

336+ 35aa.d05e.f6a8.0f3b.31ed.559d.09ad.f585.6d21.fd1d.8d67.

337+ 370b.26f4.70c1.b923.4684.6fbd.cf8b.5036.0539.9cdc.d93f.

338+ 9068.1edf.8f33.b632.d427.97fa.9ee1

339+ (cut 3 [a 1] b)

344340```

345341

346342#### Examples

347343

348344```

349− > (zyft:un 0x12)

350− 57

345+> (zyft:un 0x12)

346+57

351347

352− > (zyft:un 0x0)

353− 225

348+> (zyft:un 0x0)

349+225

354350

355− > (zyft:un 0xff)

356− 187

357− > `@ux`(zyrt:un 187)

358− 0xff

351+> (zyft:un 0xff)

352+187

353+> `@ux`(zyrt:un 187)

354+0xff

359355```

360356

361357---

@@ -378,66 +374,76 @@ An atom.

378374#### Source

379375

380376```hoon

381− ++ zyrt :: reverse 256-sbox

382− |= a=@D

383− =+ ^= b

384− 0x9fc8.2753.6e02.8fcf.8b35.2b20.5598.7caa.c9a9.30b0.9b48.

385− 47ce.6371.80f6.407d.00dd.0aa5.ed10.ecb7.0f5a.5c3a.e605.

386− c077.4337.17bd.9eda.62a4.79a7.ccb8.44cd.8e64.1ec4.5b6b.

387− 1842.ffd8.1dfb.fd07.f2f9.594c.3be3.73c6.2cb6.8438.e434.

388− 8d3d.ea6a.5268.72db.a001.2e11.de8c.88d3.0369.4f7a.87e2.

389− 860d.0991.25d0.16b9.978a.4bf4.2a1a.e96c.fa50.85b5.9aeb.

390− 9dbb.b2d9.a2d1.7bba.66be.e81f.1946.29a8.f5d2.f30c.2499.

391− c1b3.6583.89e1.ee36.e0b4.6092.937e.d74e.2f6f.513e.9615.

392− 9c5d.d581.e7ab.fe74.f01b.78b1.ae75.af57.0ec2.adc7.3245.

393− 12bf.2314.3967.0806.31dc.cb94.d43f.493c.54a6.0421.c3a1.

394− 1c4a.28ac.fc0b.26ca.5870.e576.f7f1.616d.905f.ef41.33bc.

395− df4d.225e.2d56.7fd6.1395.a3f8.c582

396− (cut 3 [a 1] b)

377+++ zyrt

378+ |= a=@D

379+ =+ ^= b

380+ 0x9fc8.2753.6e02.8fcf.8b35.2b20.5598.7caa.c9a9.30b0.9b48.

381+ 47ce.6371.80f6.407d.00dd.0aa5.ed10.ecb7.0f5a.5c3a.e605.

382+ c077.4337.17bd.9eda.62a4.79a7.ccb8.44cd.8e64.1ec4.5b6b.

383+ 1842.ffd8.1dfb.fd07.f2f9.594c.3be3.73c6.2cb6.8438.e434.

384+ 8d3d.ea6a.5268.72db.a001.2e11.de8c.88d3.0369.4f7a.87e2.

385+ 860d.0991.25d0.16b9.978a.4bf4.2a1a.e96c.fa50.85b5.9aeb.

386+ 9dbb.b2d9.a2d1.7bba.66be.e81f.1946.29a8.f5d2.f30c.2499.

387+ c1b3.6583.89e1.ee36.e0b4.6092.937e.d74e.2f6f.513e.9615.

388+ 9c5d.d581.e7ab.fe74.f01b.78b1.ae75.af57.0ec2.adc7.3245.

389+ 12bf.2314.3967.0806.31dc.cb94.d43f.493c.54a6.0421.c3a1.

390+ 1c4a.28ac.fc0b.26ca.5870.e576.f7f1.616d.905f.ef41.33bc.

391+ df4d.225e.2d56.7fd6.1395.a3f8.c582

392+ (cut 3 [a 1] b)

397393```

398394

399395#### Examples

400396

401397```

402− > `@ux`(zyrt:un 57)

403− 0x12

398+> `@ux`(zyrt:un 57)

399+0x12

404400

405− > `@ux`(zyrt:un 225)

406− 0x0

401+> `@ux`(zyrt:un 225)

402+0x0

407403

408− > `@ux`(zyrt:un 187)

409− 0xff

410− > (zyft:un 0xff)

411− 187

404+> `@ux`(zyrt:un 187)

405+0xff

406+> (zyft:un 0xff)

407+187

412408```

413409

414410---

415411

416412## `++ob`

417413

418−Reversible scrambling, v2

419−

420−```hoon

421− ++ ob

422− |%

423−```

414+Reversible scrambling, v3

424415

425416A core for performing reversible scrambling operations for the `@p` phonetic

426417base.

427418

419+#### Source

420+

421+```hoon

422+++ ob

423+ ~% %ob ..ob

424+ ==

425+ %fein fein

426+ %fynd fynd

427+ ==

428+ |%

429+```

430+

428431---

429432

430−### `++feen:ob`

433+### `++fein:ob`

431434

432−Conceal structure, v2

435+conceal structure, v3

433436

434−Randomly permutes atoms that fit into 17 to 32 bits into one another. If the

435−atom fits into 33 to 64 bits, does the same permutation on the low 32 bits

436−only. Otherwise, passes the atom through unchanged.

437+`+fein` conceals planet-sized atoms. The idea is that it should not be trivial

438+to tell which planet a star has spawned under.

439+

440+Permutes atom `pyn` which fits into 17 to 32 bits, or if `pyn` fits

441+into 33 to 64 bits, does the same permutation on the low 32 bits only.

442+Otherwise, passes `pyn` through unchanged.

437443

438444#### Accepts

439445

440−An atom.

446+`pyn` is an atom.

441447

442448#### Produces

443449

@@ -446,49 +452,44 @@ An atom.

446452#### Source

447453

448454```hoon

449− ++ feen

450− |= pyn=@ ^- @

451− ?: &((gte pyn 0x1.0000) (lte pyn 0xffff.ffff))

452− (add 0x1.0000 (fice (sub pyn 0x1.0000)))

453− ?: &((gte pyn 0x1.0000.0000) (lte pyn 0xffff.ffff.ffff.ffff))

454− =+ lo=(dis pyn 0xffff.ffff)

455− =+ hi=(dis pyn 0xffff.ffff.0000.0000)

456− %+ con hi

457− (add 0x1.0000 (fice (sub lo 0x1.0000)))

458− pyn

459− ::

455+++ fein

456+ ~/ %fein

457+ |= pyn=@ ^- @

458+ ?: &((gte pyn 0x1.0000) (lte pyn 0xffff.ffff))

459+ (add 0x1.0000 (feis (sub pyn 0x1.0000)))

460+ ?: &((gte pyn 0x1.0000.0000) (lte pyn 0xffff.ffff.ffff.ffff))

461+ =/ lo (dis pyn 0xffff.ffff)

462+ =/ hi (dis pyn 0xffff.ffff.0000.0000)

463+ %+ con hi

464+ $(pyn lo)

465+ pyn

460466```

461467

462468#### Examples

463469

464470```

465− > `@p`(feen:ob 111.103)

466− ~mophul-pagwyx

471+> (fein:ob 111.103)

472+2.783.373.008

467473

468− > `@p`(feen:ob ~mophul-pagwyx)

469− ~wisfed-lonwes

470−

471− > `@p`(feen:ob (fend:ob ~mophul-pagwyx))

472− ~mophul-pagwyx

473−

474− > `@p`(feen:ob ~wex)

475− ~wex

474+> (fynd:ob 2.783.373.008)

475+111.103

476476```

477477

478478---

479479

480−### `++fend:ob`

480+### `++fynd:ob`

481+

482+Restore structure, v3

481483

482−Restore structure, v2

484+Restores obfuscated values that have been enciphered with [+fein](feinob).

483485

484−Randomly permutes atoms that fit into 17 to 32 bits into one another, and

485−randomly permutes the low 32 bits of atoms that fit into 33 to 64 bits;

486−otherwise, passes the atom through unchanged. The inverse of the one applied

487−by `feen`.

486+Permutes atom `cry` that fits into 17 to 32 bits, or permutes the low 32 bits of

487+`cry` if it fits into 33 to 64 bits. Otherwise, passes the atom through

488+unchanged. The inverse of the one applied by [`+fein`](#feinob).

488489

489490#### Accepts

490491

491−An atom.

492+`cry` is an atom.

492493

493494#### Produces

494495

@@ -497,52 +498,42 @@ An atom.

497498#### Source

498499

499500```hoon

500− ++ fend

501− |= cry=@ ^- @

502− ?: &((gte cry 0x1.0000) (lte cry 0xffff.ffff))

503− (add 0x1.0000 (teil (sub cry 0x1.0000)))

504− ?: &((gte cry 0x1.0000.0000) (lte cry 0xffff.ffff.ffff.ffff))

505− =+ lo=(dis cry 0xffff.ffff)

506− =+ hi=(dis cry 0xffff.ffff.0000.0000)

507− %+ con hi

508− (add 0x1.0000 (teil (sub lo 0x1.0000)))

509− cry

510− ::

501+++ fynd

502+ ~/ %fynd

503+ |= cry=@ ^- @

504+ ?: &((gte cry 0x1.0000) (lte cry 0xffff.ffff))

505+ (add 0x1.0000 (tail (sub cry 0x1.0000)))

506+ ?: &((gte cry 0x1.0000.0000) (lte cry 0xffff.ffff.ffff.ffff))

507+ =/ lo (dis cry 0xffff.ffff)

508+ =/ hi (dis cry 0xffff.ffff.0000.0000)

509+ %+ con hi

510+ $(cry lo)

511+ cry

511512```

512513

513514#### Examples

514515

515516```

516− > `@p`(fend:ob 111.103)

517− ~doznec-sapfes

518−

519− > `@p`(fend:ob ~doznec-sapfes)

520− ~hanrud-widwyc

521−

522− > `@p`(fend:ob ~wisfed-lonwes)

523− ~mophul-pagwyx

524−

525− > `@p`(fend:ob (feen:ob ~wisfed-lonwes))

526− ~wisfed-lonwes

517+> (fein:ob 111.103)

518+2.783.373.008

527519

528− > `@p`(fend:ob ~tarmed)

529− ~tarmed

520+> (fynd:ob 2.783.373.008)

521+111.103

530522```

531523

532524---

533525

534−### `++fice:ob`

526+### `++feis:ob`

535527

536−Feistel-like cipher

528+Four-round generalised Feistel cipher over the domain [0, 2^32 - 2^16 - 1]

537529

538−Produces an atom by applying a variant of the Feistel cipher. Unlike

539−a conventional Feistel cipher that is its own inverse if keys are used in

540−reverse order, this Feistel-like cipher uses two moduli that must be swapped

541−when applying the reverse transformation. The inverse of `teil`.

530+See: Black & Rogaway (2002), Ciphers for arbitrary finite domains.

531+

532+Inverse of [`+tail`](#tailob).

542533

543534#### Accepts

544535

545−`nor` is an atom.

536+`m` is an atom.

546537

547538#### Produces

548539

@@ -551,42 +542,33 @@ An atom.

551542#### Source

552543

553544```hoon

554− ++ fice :: adapted from

555− |= nor=@ :: black and rogaway

556− ^- @ :: "ciphers with

557− =+ ^= sel :: arbitrary finite

558− %+ rynd 2 :: domains", 2002

559− %+ rynd 1

560− %+ rynd 0

561− [(mod nor 65.535) (div nor 65.535)]

562− (add (mul 65.535 -.sel) +.sel)

563− ::

545+++ feis

546+ |= m=@

547+ ^- @

548+ (fee 4 0xffff 0x1.0000 (mul 0xffff 0x1.0000) eff m)

564549```

565550

566551#### Examples

567552

568553```

569− > (fice:ob 11)

570− 776.343.932

554+> (feis:ob 11)

555+776.343.932

571556

572− > (fice:ob (teil:ob 11))

573− 11

557+> (tail:ob 776.343.932)

558+11

574559```

575560

576561---

577562

578−### `++teil:ob`

563+### `++tail:ob`

579564

580−Reverse Feistel-like cipher

565+Reverse [`+feis`](#feisob)

581566

582−Applies the reverse of the Feistel-like cipher applied by `fice`. Unlike

583−a conventional Feistel cipher that is its own inverse if keys are used in

584−reverse order, this Feistel-like cipher uses two moduli that must be swapped

585−when applying the reverse transformation.

567+Applies the reverse of the Feistel cipher applied by `+feis`.

586568

587569#### Accepts

588570

589−`vip` is an atom.

571+`m` is an atom.

590572

591573#### Produces

592574

@@ -595,112 +577,261 @@ An atom.

595577#### Source

596578

597579```hoon

598− ++ teil :: reverse ++fice

599− |= vip=@

600− ^- @

601− =+ ^= sel

602− %+ rund 0

603− %+ rund 1

604− %+ rund 2

605− [(mod vip 65.535) (div vip 65.535)]

606− (add (mul 65.535 -.sel) +.sel)

607− ::

580+++ tail

581+ |= m=@

582+ ^- @

583+ (feen 4 0xffff 0x1.0000 (mul 0xffff 0x1.0000) eff m)

608584```

609585

610586#### Examples

611587

612588```

613− > (teil:ob 11)

614− 514.230.493

589+> (feis:ob 11)

590+776.343.932

615591

616− > (teil:ob (fice:ob 11))

617− 11

592+> (tail:ob 776.343.932)

593+11

618594```

619595

620596---

621597

622−### `++rynd:ob`

598+### `++fee:ob`

599+

600+"Fe" in B&R (2002)

623601

624−Reverse Feistel-like cipher

602+A Feistel cipher given the following parameters:

625603

626−A single round of the Feistel-like cipher `fice`. AES ([`aesc`](/docs/hoon/reference/stdlib/3f)) is

627−used as the round function. The inverse of `rund`.

604+- `r`: Number of Feistel rounds.

605+- `a`, `b`: Parameters such that `ab` >= `k`.

606+- `k`: Value such that the domain of the cipher is [0, k - 1].

607+- `prf`: A gate denoting a family of pseudorandom functions indexed by its first argument and taking its second argument as input.

608+- `m`: An input value in the domain [0, k - 1].

628609

629610#### Accepts

630611

631−`n` is an atom.

612+`r`, `a`, `b`, `k` are an atoms.

632613

633−`l` is an atom.

614+`prft` is a gate: `$-([j=@ r=@] @)`.

634615

635−`r` is an atom.

616+`m` is an atom.

636617

637618#### Produces

638619

639−A cell of two atoms.

620+An atom.

640621

641622#### Source

642623

643624```hoon

644− ++ rynd

645− |= [n=@ l=@ r=@]

646− ^- [@ @]

647− :- r

648− ?~ (mod n 2)

649− (~(sum fo 65.535) l (en:aesc (snag n raku) r))

650− (~(sum fo 65.536) l (en:aesc (snag n raku) r))

625+++ fee

626+ |= [r=@ a=@ b=@ k=@ prf=$-([j=@ r=@] @) m=@]

627+ ^- @

628+ =/ c (fe r a b prf m)

629+ ?: (lth c k)

630+ c

631+ (fe r a b prf c)

651632```

652633

653−#### Examples

634+---

635+

636+### `++feen:ob`

637+

638+Reverse [`+fee`](#feeob)

639+

640+"Fe^-1" in B&R (2002). Reverses a Feistel cipher constructed with parameters as

641+described in `+fee`.

642+

643+#### Accepts

644+

645+`r`, `a`, `b`, and `k` are atoms.

646+

647+`prf` is a gate: `$-([j=@ r=@] @)`.

648+

649+`m` is an atom.

650+

651+#### Produces

652+

653+An atom.

654+

655+#### Source

654656

657+```hoon

658+++ feen

659+ |= [r=@ a=@ b=@ k=@ prf=$-([j=@ r=@] @) m=@]

660+ ^- @

661+ =/ c (fen r a b prf m)

662+ ?: (lth c k)

663+ c

664+ (fen r a b prf c)

655665```

656− > (rynd:ob 2 261 9)

657− [9 37.422]

658666

659− > (rynd:ob 2 (rund:ob 2 37.422 9))

660− [261 32.902]

667+---

668+

669+### `+fe:ob`

670+

671+An internal function to [`+fee`](#feeob).

672+

673+Note that this implementation differs slightly from the reference paper to

674+support some legacy behaviour.

675+

676+#### Accepts

677+

678+`r`, `a`, and `b` are atoms.

679+

680+`prf` is a gate: `$-([j=@ r=@] @)`.

681+

682+`m` is an atom.

683+

684+#### Produces

685+

686+An atom.

687+

688+#### Source

689+

690+```hoon

691+++ fe

692+ |= [r=@ a=@ b=@ prf=$-([j=@ r=@] @) m=@]

693+ =/ j 1

694+ =/ ell (mod m a)

695+ =/ arr (div m a)

696+ |- ^- @

697+ ::

698+ ?: (gth j r)

699+ ?. =((mod r 2) 0)

700+ (add (mul arr a) ell)

701+ ::

702+ :: Note that +fe differs from B&R (2002)'s "fe" below, as a previous

703+ :: implementation of this cipher contained a bug such that certain inputs

704+ :: could encipher to the same output.

705+ ::

706+ :: To correct these problem cases while also preserving the cipher's

707+ :: legacy behaviour on most inputs, we check for a problem case (which

708+ :: occurs when 'arr' is equal to 'a') and, if detected, use an alternate

709+ :: permutation instead.

710+ ::

711+ ?: =(arr a)

712+ (add (mul arr a) ell)

713+ (add (mul ell a) arr)

714+ ::

715+ =/ f (prf (sub j 1) arr)

716+ ::

717+ =/ tmp

718+ ?. =((mod j 2) 0)

719+ (mod (add f ell) a)

720+ (mod (add f ell) b)

721+ ::

722+ $(j +(j), ell arr, arr tmp)

661723```

662724

663725---

664726

665−### `++rund:ob`

727+### `++fen:ob`

728+

729+Reverse [`+fe`](#feob)

666730

667−Reverse single Feistel-like

731+This is an internal function to [`+feen`](#feenob)

668732

669−A single round of the Feistel-like reverse cipher `teil`. AES ([`aesc`](/docs/hoon/reference/stdlib/3f))

670−is used as the round function. The inverse of `rynd`.

733+Note that this implementation differs slightly from the reference paper

734+to support some legacy behaviour.

671735

672736#### Accepts

673737

674−`n` is an atom.

738+`r`, `a` and `b` are atoms.

675739

676−`l` is an atom.

740+`prf` is a gate: `$-([j=@ r=@] @)`.

677741

678−`r` is an atom.

742+`m` is an atom.

679743

680744#### Produces

681745

682−A cell of two atoms.

746+An atom.

683747

684748#### Source

685749

686750```hoon

687− ++ rund

688− |= [n=@ l=@ r=@]

689− ^- [@ @]

690− :- r

691− ?~ (mod n 2)

692− (~(dif fo 65.535) l (muk (snag n raku) 2 r))

693− (~(dif fo 65.536) l (muk (snag n raku) 2 r))

751+++ fen

752+ |= [r=@ a=@ b=@ prf=$-([j=@ r=@] @) m=@]

753+ =/ j r

754+ ::

755+ =/ ahh

756+ ?. =((mod r 2) 0)

757+ (div m a)

758+ (mod m a)

759+ ::

760+ =/ ale

761+ ?. =((mod r 2) 0)

762+ (mod m a)

763+ (div m a)

764+ ::

765+ :: Similar to the comment in +fe, +fen differs from B&R (2002)'s "fe^-1"

766+ :: here in order to preserve the legacy cipher's behaviour on most inputs.

767+ ::

768+ :: Here problem cases can be identified by 'ahh' equating with 'a'; we

769+ :: correct those cases by swapping the values of 'ahh' and 'ale'.

770+ ::

771+ =/ ell

772+ ?: =(ale a)

773+ ahh

774+ ale

775+ ::

776+ =/ arr

777+ ?: =(ale a)

778+ ale

779+ ahh

780+ ::

781+ |- ^- @

782+ ?: (lth j 1)

783+ (add (mul arr a) ell)

784+ =/ f (prf (sub j 1) ell)

785+ ::

786+ :: Note that there is a slight deviation here to avoid dealing with

787+ :: negative values. We add 'a' or 'b' to arr as appropriate and reduce

788+ :: 'f' modulo the same number before performing subtraction.

789+ ::

790+ =/ tmp

791+ ?. =((mod j 2) 0)

792+ (mod (sub (add arr a) (mod f a)) a)

793+ (mod (sub (add arr b) (mod f b)) b)

794+ ::

795+ $(j (sub j 1), ell tmp, arr ell)

694796```

695797

696−#### Examples

798+---

799+

800+### `++eff:ob`

801+

802+murmur3-based pseudorandom function.

803+

804+'F' in B&R (2002).

805+

806+- `j` is a number between 0 and 3, selecting the seed with that index in

807+ [+raku](#rakuob).

808+- `r` is an atom with a maximum length of two bytes. This is an internal

809+ function of [`+feis`](#feisob) and [`+tail`](#tailob).

810+

811+#### Accepts

812+

813+`j` is an atom.

814+

815+`r` is an atom.

697816

817+#### Produces

818+

819+An atom.

820+

821+#### Source

822+

823+```hoon

824+++ eff

825+ |= [j=@ r=@]

826+ ^- @

827+ (muk (snag j raku) 2 r)

698828```

699− > (rund:ob 2 261 9)

700− [9 28.635]

701829

702− > (rund:ob 2 (rynd:ob 2 28.635 9))

703− [261 32.651]

830+#### Example

831+

832+```

833+> (eff:ob 0 'ab')

834+1.178.819.349

704835```

705836

706837---

@@ -709,7 +840,7 @@ A cell of two atoms.

709840

710841Key list

711842

712−Produces a list of arbitrary hexademical keys for use with [`aesc`](/docs/hoon/reference/stdlib/3f).

843+Produces a list of arbitrary hexademical keys for use with [`+eff`](#effob).

713844

714845#### Produces

715846

@@ -718,21 +849,20 @@ A list of atoms of aura `@ux` (hexadecimal).

718849#### Source

719850

720851```hoon

721− ++ raku

722− ^- (list @ux)

723− :~ 0xb76d.5eed

724− 0xee28.1300

725− 0x85bc.ae01

726− 0x4b38.7af7

727− ==

728− --

852+++ raku

853+ ^- (list @ux)

854+ :~ 0xb76d.5eed

855+ 0xee28.1300

856+ 0x85bc.ae01

857+ 0x4b38.7af7

858+ ==

729859```

730860

731861#### Examples

732862

733863```

734− > raku:ob

735− ~[0xb76d.5eed 0xee28.1300 0x85bc.ae01 0x4b38.7af7]

864+> raku:ob

865+~[0xb76d.5eed 0xee28.1300 0x85bc.ae01 0x4b38.7af7]

736866```

737867

738868---

content/docs/hoon/reference/stdlib/3g.md+124−134

@@ -4,7 +4,7 @@ weight = 27

44template = "doc.html"

55+++

7−## `++coin`

7+## `+$coin`

99Noun-literal syntax cases

1010

@@ -14,91 +14,92 @@ and printed using `++so` and `++co` cores.

1414#### Source

1515

1616```hoon

17− ++ coin $% [$$ p=dime]

18− [$blob p=*]

19− [$many p=(list coin)]

20− ==

17++$ coin $~ [%$ %ud 0]

18+ $% [%$ p=dime]

19+ [%blob p=*]

20+ [%many p=(list coin)]

2121```

2222

23−---

24−

2523#### Examples

2624

2725```

28− > `coin`(need (slay '~s1'))

29− [%$ p=[p=~.dr q=18.446.744.073.709.551.616]]

26+> `coin`(need (slay '~s1'))

27+[%$ p=[p=~.dr q=18.446.744.073.709.551.616]]

3028

31− > `coin`(need (slay '0x2b59'))

32− [%$ p=[p=~.ux q=11.097]]

29+> `coin`(need (slay '0x2b59'))

30+[%$ p=[p=~.ux q=11.097]]

3331

34− > ~(rend co [%many ~[[%$ %ud 1] [%$ %tas 'a'] [%$ %s -2]]])

35− "._1_a_-2__"

36− > ._1_a_-2__

37− [1 %a -2]

32+> ~(rend co [%many ~[[%$ %ud 1] [%$ %tas 'a'] [%$ %s -2]]])

33+"._1_a_-2__"

34+> ._1_a_-2__

35+[1 %a -2]

3836

39− > `@uv`(jam [3 4])

40− 0v2cd1

37+> `@uv`(jam [3 4])

38+0v2cd1

4139

42− > (slay '~02cd1')

43− [~ u=[%blob p=[3 4]]]

40+> (slay '~02cd1')

41+[~ u=[%blob p=[3 4]]]

4442

45− > ~02cd1

46− [3 4]

43+> ~02cd1

44+[3 4]

4745```

4846

4947---

5048

51−## `++dime`

49+## `+$dime`

5250

5351Aura-atom pair

5452

55−Used in `++coin`. Convenience methods [`++scot`](/docs/hoon/reference/stdlib/4m) and

56−[`++scow`](/docs/hoon/reference/stdlib/4m) print dimes as `++cord` and `++tape`, respectively.

57−[`++slat`](/docs/hoon/reference/stdlib/4m), [`++slav`](/docs/hoon/reference/stdlib/4m), and [`++slaw`](/docs/hoon/reference/stdlib/4m) are used

58−to parse atoms of specific auras.

53+Used in `++coin`. Convenience methods

54+[`++scot`](/docs/hoon/reference/stdlib/4m#scot) and

55+[`++scow`](/docs/hoon/reference/stdlib/4m#scow) print dimes as `++cord` and

56+`++tape`, respectively. [`++slat`](/docs/hoon/reference/stdlib/4m#slat),

57+[`++slav`](/docs/hoon/reference/stdlib/4m#slav), and

58+[`++slaw`](/docs/hoon/reference/stdlib/4m#slaw) are used to parse atoms of

59+specific auras.

5960

6061#### Source

6162

6263```hoon

63− ++ dime [p=@ta q=@]

64++$ dime [p=@ta q=@]

6465```

6566

6667#### Examples

6768

6869```

69− > +>:(slay '0x123')

70− p=[p=~.ux q=291]

70+> +>:(slay '0x123')

71+p=[p=~.ux q=291]

7172```

7273

7374---

7475

75−## `++edge`

76+## `+$edge`

7677

7778Parsing location metadata. Parsing location input `p` and optional result `p.q` and parsing continuation `q.q`.

7879

7980#### Source

8081

8182```hoon

82− ++ edge [p=hair q=(unit [p=* q=nail])] :: parsing output

83++$ edge [p=hair q=(unit [p=* q=nail])]

8384```

8485

8586#### Examples

8687

8788```

88− > *edge

89− [p=[p=0 q=0] q=~]

89+> *edge

90+[p=[p=0 q=0] q=~]

9091

91− > (tall:vast [1 1] "a b")

92− [p=[p=1 q=3] q=[~ u=[p=[%wing p=~[%a]] q=[p=[p=1 q=2] q=" b"]]]]

92+> (tall:vast [1 1] "a b")

93+[p=[p=1 q=3] q=[~ u=[p=[%wing p=~[%a]] q=[p=[p=1 q=2] q=" b"]]]]

9394```

9495

9596#### Discussion

9697

97−See also: [Section 3g](/docs/hoon/reference/stdlib/3g#rule), `++rule`

98+See also: [$rule](#rule).

9899

99100---

100101

101−## `++hair`

102+## `+$hair`

102103

103104Parsing line and column

104105

@@ -107,23 +108,23 @@ A pair of two `@ud` used in parsing indicating line and column number.

107108#### Source

108109

109110```hoon

110− ++ hair [p=@ud q=@ud]

111++$ hair [p=@ud q=@ud]

111112```

112113

113114#### Examples

114115

115116```

116− > *hair

117− [p=0 q=0]

117+> *hair

118+[p=0 q=0]

118119

119− > `hair`[1 1] :: parsing starts at [1 1] as a convention.

120− [p=1 q=1]

120+> `hair`[1 1] :: parsing starts at [1 1] as a convention.

121+[p=1 q=1]

121122

122− > ((plus ace) [1 1] " --")

123− [p=[p=1 q=4] q=[~ u=[p=[~~. " "] q=[p=[p=1 q=4] q="--"]]]]

123+> ((plus ace) [1 1] " --")

124+[p=[p=1 q=4] q=[~ u=[p=[~~. " "] q=[p=[p=1 q=4] q="--"]]]]

124125

125− > `hair`p:((plus ace) [1 1] " --")

126− [p=1 q=4]

126+> `hair`p:((plus ace) [1 1] " --")

127+[p=1 q=4]

127128```

128129

129130---

@@ -132,38 +133,39 @@ A pair of two `@ud` used in parsing indicating line and column number.

132133

133134Generic edge

134135

135−Generates an `++edge` with a parsed result set to a specific type.

136+Generates an [`$edge`](#edge) with a parsed result set to a specific type.

136137

137138#### Source

138139

139140```hoon

140− ++ like |* a=gate

141− |= b=_`*`[(hair) ~]

142− :- p=(hair -.b)

143− ^= q

144− :- ~

145− u=[p=(a +>-.b) q=[p=(hair -.b) q=(tape +.b)]]

141+++ like |* a=$-(* *)

142+ |: b=`*`[(hair) ~]

143+ :- p=(hair -.b)

144+ ^= q

145+ ?@ +.b ~

146+ :- ~

147+ u=[p=(a +>-.b) q=[p=(hair -.b) q=(tape +.b)]]

146148```

147149

148150#### Examples

149151

150152```

151− > *(like char)

152− [p=[p=0 q=0] q=~]

153+> *(like char)

154+[p=[p=0 q=0] q=~]

153155

154− > (ace [1 1] " a")

155− [p=[p=1 q=2] q=[~ u=[p=' ' q=[p=[p=1 q=2] q="a"]]]]

156+> (ace [1 1] " a")

157+[p=[p=1 q=2] q=[~ u=[p=' ' q=[p=[p=1 q=2] q="a"]]]]

156158

157− > `(like char)`(ace [1 1] " a")

158− [p=[p=1 q=2] q=[~ [p=~~. q=[p=[p=1 q=2] q="a"]]]]

159+> `(like char)`(ace [1 1] " a")

160+[p=[p=1 q=2] q=[~ [p=~~. q=[p=[p=1 q=2] q="a"]]]]

159161

160− > `(like ,@)`(ace [1 1] " a")

161− [p=[p=1 q=2] q=[~ u=[p=32 q=[p=[p=1 q=2] q="a"]]]]

162+> `(like ,@)`(ace [1 1] " a")

163+[p=[p=1 q=2] q=[~ u=[p=32 q=[p=[p=1 q=2] q="a"]]]]

162164```

163165

164166---

165167

166−## `++nail`

168+## `+$nail`

167169

168170Location, remainder of parsed text

169171

@@ -172,44 +174,44 @@ Indicates parsing position `p`, and remaining text to be parsed `q`.

172174#### Source

173175

174176```hoon

175− ++ nail [p=hair q=tape]

177++$ nail [p=hair q=tape]

176178```

177179

178180#### Examples

179181

180182```

181− > +<:;~(plug cab cab)

182− c=[p=[p=0 q=0] q=""]

183+> +<:;~(plug cab cab)

184+c=[p=[p=0 q=0] q=""]

183185```

184186

185187---

186188

187−## `++pint`

189+## `+$pint`

188190

189191Parsing range

190192

191−A `++pint` is a pair of `++hair`, indicating from `p` to `q`. Mostly used for

193+A `$pint` is a pair of [`$hair`](#hair), indicating from `p` to `q`. Mostly used for

192194stack traces.

193195

194196#### Source

195197

196198```hoon

197− ++ pint [p=[p=@ q=@] q=[p=@ q=@]]

199++$ pint [p=[p=@ q=@] q=[p=@ q=@]]

198200```

199201

200202#### Examples

201203

202204```

203− > !:(!!) :: !! always produces a crash

204− /~zod/home/~2014.9.20..01.22.04..52e3/:<[1 4].[1 6]>

205+> !:(!!) :: !! always produces a crash

206+/~zod/home/~2014.9.20..01.22.04..52e3/:<[1 4].[1 6]>

205207

206− > `pint`[[1 4] [1 6]]

207− [p=[p=1 q=4] q=[p=1 q=6]]

208+> `pint`[[1 4] [1 6]]

209+[p=[p=1 q=4] q=[p=1 q=6]]

208210```

209211

210212---

211213

212−## `++rule`

214+## `+$rule`

213215

214216Parsing rule

215217

@@ -218,19 +220,19 @@ An empty parsing rule, but used to check that parsing rules match this with `_`.

218220#### Source

219221

220222```hoon

221− ++ rule _|=(nail *edge)

223++$ rule _|:($:nail $:edge)

222224```

223225

224226#### Examples

225227

226228```

227− > ([|=(a=nail [p.a ~ u=['a' a]])]:|6 [1 1] "hi")

228− [[p=1 q=1] ~ u=['a' p=[p=1 q=1] q="hi"]]

229+> ([|=(a=nail [p.a ~ u=['a' a]])]:|6 [1 1] "hi")

230+[[p=1 q=1] ~ u=['a' p=[p=1 q=1] q="hi"]]

229231```

230232

231233---

232234

233−## `++spot`

235+## `+$spot`

234236

235237Stack trace line

236238

@@ -245,14 +247,14 @@ The stack trace that is printed after crashing.

245247#### Examples

246248

247249```

248− > !: !! :: !! always produces a crash

249− /~zod/home/~2018.8.8..21.42.40..7852:<[1 5].[1 7]>

250− ! exit

250+> !: !! :: !! always produces a crash

251+/~zod/home/~2018.8.8..21.42.40..7852:<[1 5].[1 7]>

252+! exit

251253```

252254

253255---

254256

255−## `++tone`

257+## `+$tone`

256258

257259Nock result, error report

258260

@@ -262,45 +264,27 @@ or failure with an error report (`%2`).

262264#### Source

263265

264266```hoon

265− ++ tone $% [$0 p=*] :: success

266− [$1 p=(list)] :: blocks

267− [$2 p=(list [@ta *])] :: error report

268− ==

267++$ tone $% [%0 product=*]

268+ [%1 block=*]

269+ [%2 trace=(list [@ta *])]

270+ ==

269271```

270272

271273#### Examples

272274

273275```

274− > (mink [[20 21] 0 3] $~)

275− [%0 p=21]

276−

277−

278− > (mink [[1 2] !=(!:(+(.)))] ,~)

279− [ %2

280− p

281− ~[

282− [ ~.spot

283− [ [ \/72.245.008.048.359.254.300.063.028.130.093.488.830.539.186.242.06\/

284− 3.318.457.928.725.368.447.417.075.673.617.723.940.025.940.705.343

285− .057.601.925.133.611.559.292.046.932.324.629.048.702

286− \/ \/

287− 1.701.670.760

288− \/347.698.068.472.453.194.464.038.059.283.550.210.118.689.128.761.6\/

289− 88.459.326.078

290− \/ \/

291− 0

292− ]

293− [1 20]

294− 1

295− 24

296− ]

297− ]

298− ]

276+> (mink [[20 21] 0 3] $~)

277+[%0 product=21]

278+```

279+

280+```

281+> (mink [[1 2] !=(!:(+(.)))] ,~)

282+[%2 trace=~[[~.spot [[1.685.027.454 1.702.060.386 20.241.306.789.072.368.304.935.424.358.627.395.315.601.229.215.400.789.787.861.332.606 0] [1 20] 1 24]]]]

299283```

300284

301285---

302286

303−## `++toon`

287+## `+$toon`

304288

305289Nock result, stack trace

306290

@@ -310,20 +294,30 @@ or failure with a stack trace (`%2`).

310294#### Source

311295

312296```hoon

313− ++ toon $% [$0 p=*] :: success

314− [$1 p=(list)] :: blocks

315− [$2 p=(list tank)] :: stack trace

316− ==

297++$ toon $% [%0 p=*] :: success

298+ [%1 p=*] :: block

299+ [%2 p=(list tank)] :: stack trace

300+ == ::

317301```

318302

319303#### Examples

320304

321305```

322− > (mock [[20 21] 0 3] $~)

323− [%0 p=21]

306+> (mock [[20 21] 0 3] $~)

307+[%0 p=21]

308+```

324309

325− > (mock [[1 2] !=(!:(+(.)))] ,~)

326− [%2 p=~[[%leaf p="/~zod/try/~2014.9.23..18.34.32..d3c5/:<[1 20].[1 24]>"]]]

310+```

311+> (mock [[1 2] !=(!:(+(.)))] ,~)

312+[ %2

313+ p

314+ ~[

315+ [ %rose

316+ p=[p=":" q="" r=""]

317+ q=[i=[%rose p=[p="/" q="/" r=""] q=[i=[%leaf p="~zod"] t=[i=[%leaf p="base"] t=[i=[%leaf p="~2021.10.16..10.03.16..59ee"] t=~]]]] t=[i=[%leaf p="<[1 20].[1 24]>"] t=~]]

318+ ]

319+ ]

320+]

327321```

328322

329323---

@@ -332,34 +326,30 @@ or failure with a stack trace (`%2`).

332326

333327Product from edge

334328

335−Pull result out of a `++edge`, or crash if there's no result.

329+Pull result out of a [`$edge`](#edge), or crash if there's no result.

336330

337331#### Source

338332

339333```hoon

340− ++ wonk |*(veq=edge ?~(q.veq !! p.u.q.veq))

334+++ wonk =+ veq=$:edge

335+ |@ ++ $ ?~(q.veq !! p.u.q.veq)

336+ --

341337```

342338

343339#### Examples

344340

345341```

346− > (wide:vast [1 1] "(add 2 2)")

347− [ p=[p=1 q=10]

348− q

349− [ ~

350− u

351− [ p=[%cnhp p=[%wing p=~[%add]] q=~[[%sand p=%ud q=2] [%sand p=%ud q=2]]]

352− q=[p=[p=1 q=10] q=""]

353− ]

354− ]

355− ]

342+> (wide:vast [1 1] "(add 2 2)")

343+[p=[p=1 q=10] q=[~ [p=[%cncl p=[%wing p=~[%add]] q=~[[%sand p=%ud q=2] [%sand p=%ud q=2]]] q=[p=[p=1 q=10] q=""]]]]

344+```

356345

357− > (wonk (wide:vast [1 1] "(add 2 2)"))

358− [%cnhp p=[%wing p=~[%add]] q=~[[%sand p=%ud q=2] [%sand p=%ud q=2]]]

346+```

347+> (wonk (wide:vast [1 1] "(add 2 2)"))

348+[%cncl p=[%wing p=~[%add]] q=~[[%sand p=%ud q=2] [%sand p=%ud q=2]]]

359349```

360350

361351#### Discussion

362352

363−See also: `++edge`

353+See also: [`$edge`](#edge)

364354

365355---

content/docs/hoon/reference/stdlib/table-of-contents.md+39−34

@@ -99,7 +99,7 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

9999<a class="tooltip" href='/docs/hoon/reference/stdlib/3a/#cmpsi' title="Compare (signed integer)"><code>++cmp:si</code></a>

100100<a class="tooltip" href='/docs/hoon/reference/stdlib/4k/#co' title="Literal rendering engine"><code>++co</code></a>

101101<a class="tooltip" href='/docs/hoon/reference/stdlib/4o/#coil' title="Tuple of core information"><code>++coil</code></a>

102−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#coin' title="Nounliteral syntax cases"><code>++coin</code></a>

102+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#coin' title="Nounliteral syntax cases"><code>+$coin</code></a>

103103<a class="tooltip" href='/docs/hoon/reference/stdlib/4h/#col' title="Parse : (col)"><code>++col</code></a>

104104<a class="tooltip" href='/docs/hoon/reference/stdlib/4f/#cold' title="Replace with constant"><code>++cold</code></a>

105105<a class="tooltip" href='/docs/hoon/reference/stdlib/4h/#com' title="Parse , (com)"><code>++com</code></a>

@@ -138,7 +138,7 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

138138<a class="tooltip" href='/docs/hoon/reference/stdlib/2i/#digby' title="Address of key (map)"><code>++dig:by</code></a>

139139<a class="tooltip" href='/docs/hoon/reference/stdlib/2h/#digin' title="Address of a in set"><code>++dig:in</code></a>

140140<a class="tooltip" href='/docs/hoon/reference/stdlib/4j/#dimag' title="Parse decimal number"><code>++dim:ag</code></a>

141−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#dime' title="Auraatom pair"><code>++dime</code></a>

141+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#dime' title="Auraatom pair"><code>+$dime</code></a>

142142<a class="tooltip" href='/docs/hoon/reference/stdlib/4c/#dinre' title="(Undocumented)"><code>++din:re</code></a>

143143<a class="tooltip" href='/docs/hoon/reference/stdlib/2d/#dis' title="Binary AND (atoms)"><code>++dis</code></a>

144144<a class="tooltip" href='/docs/hoon/reference/stdlib/4i/#dit' title="Decimal digit"><code>++dit</code></a>

@@ -172,7 +172,8 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

172172<a class="tooltip" href='/docs/hoon/reference/stdlib/3b/#eadfl' title="Exact add"><code>++ead:fl</code></a>

173173<a class="tooltip" href='/docs/hoon/reference/stdlib/1c/#each' title="Mold of fork between two types"><code>++each</code></a>

174174<a class="tooltip" href='/docs/hoon/reference/stdlib/4f/#easy' title="Always parse"><code>++easy</code></a>

175−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#edge' title="Parsing location metadata"><code>++edge</code></a>

175+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#edge' title="Parsing location metadata"><code>+$edge</code></a>

176+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#effob' title="murmur3-based pseudorandom function"><code>++eff:ob</code></a>

176177<a class="tooltip" href='/docs/hoon/reference/stdlib/3a/#egcd' title="Extended Euclidean algorithm"><code>++egcd</code></a>

177178<a class="tooltip" href='/docs/hoon/reference/stdlib/3b/#emnfl' title="Minimum exponent"><code>++emn:fl</code></a>

178179<a class="tooltip" href='/docs/hoon/reference/stdlib/3b/#emufl' title="Exact multiply"><code>++emu:fl</code></a>

@@ -200,9 +201,12 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

200201<a class="tooltip" href='/docs/hoon/reference/stdlib/4h/#fas' title="Parse / (fas)"><code>++fas</code></a>

201202<a class="tooltip" href='/docs/hoon/reference/stdlib/2c/#fe' title="Modulo bloq"><code>++fe</code></a>

202203<a class="tooltip" href='/docs/hoon/reference/stdlib/4j/#fedag' title="Parse @p"><code>++fed:ag</code></a>

203−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feenob' title="Conceal structure v2"><code>++feen:ob</code></a>

204−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#fendob' title="Restore structure v2"><code>++fend:ob</code></a>

205−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#ficeob' title="Feistellike cipher"><code>++fice:ob</code></a>

204+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feob' title="Internal function to +fee"><code>++fe:ob</code></a>

205+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feeob' title="Feistel cipher Fe in B&R (2002)"><code>++fee:ob</code></a>

206+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feenob' title="Reverse +fee"><code>++feen:ob</code></a>

207+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feinob' title="Conceal structure v3"><code>++fein:ob</code></a>

208+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feisob' title="Four-round generalised Feistel cipher over the domain [0, 2^32 - 2^16 - 1]"><code>++feis:ob</code></a>

209+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#fenob' title="Reverse +fe"><code>++fen:ob</code></a>

206210<a class="tooltip" href='/docs/hoon/reference/stdlib/2c/#fil' title="Fill bloqstream"><code>++fil</code></a>

207211<a class="tooltip" href='/docs/hoon/reference/stdlib/2b/#find' title="First index in list"><code>++find</code></a>

208212<a class="tooltip" href='/docs/hoon/reference/stdlib/4c/#fitre' title="Fit on one line test"><code>++fit:re</code></a>

@@ -224,6 +228,7 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

224228<a class="tooltip" href='/docs/hoon/reference/stdlib/3a/#frasi' title="Divide (signed integer)"><code>++fra:si</code></a>

225229<a class="tooltip" href='/docs/hoon/reference/stdlib/4f/#full' title="Parse to end"><code>++full</code></a>

226230<a class="tooltip" href='/docs/hoon/reference/stdlib/4f/#funk' title="Add to tape"><code>++funk</code></a>

231+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#fyndob' title="Restore structure v3"><code>++fynd:ob</code></a>

227232

228233### g

229234

@@ -272,7 +277,7 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

272277

273278### h

274279

275−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#hair' title="Parsing line and column"><code>++hair</code></a>

280+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#hair' title="Parsing line and column"><code>+$hair</code></a>

276281<a class="tooltip" href='/docs/hoon/reference/stdlib/2i/#hasby' title="Key existence check (map)"><code>++has:by</code></a>

277282<a class="tooltip" href='/docs/hoon/reference/stdlib/2h/#hasin' title="Key existence check (set)"><code>++has:in</code></a>

278283<a class="tooltip" href='/docs/hoon/reference/stdlib/2j/#hasju' title="Check contents (jug)"><code>++has:ju</code></a>

@@ -420,7 +425,7 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

420425

421426### n

422427

423−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#nail' title="Location, remainder of parsed text"><code>++nail</code></a>

428+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#nail' title="Location, remainder of parsed text"><code>+$nail</code></a>

424429<a class="tooltip" href='/docs/hoon/reference/stdlib/2k/#napto' title="Remove head of queue"><code>++nap:to</code></a>

425430<a class="tooltip" href='/docs/hoon/reference/stdlib/4j/#ne' title="Digit rendering engine"><code>++ne</code></a>

426431<a class="tooltip" href='/docs/hoon/reference/stdlib/3b/#nedfl' title="Require float"><code>++ned:fl</code></a>

@@ -461,7 +466,7 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

461466<a class="tooltip" href='/docs/hoon/reference/stdlib/4j/#pevab' title="Parse <=5 in base 32"><code>++pev:ab</code></a>

462467<a class="tooltip" href='/docs/hoon/reference/stdlib/4j/#pewab' title="Parse <= 5 in base 64"><code>++pew:ab</code></a>

463468<a class="tooltip" href='/docs/hoon/reference/stdlib/4e/#pfix' title="Discard first rule"><code>++pfix</code></a>

464−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#pint' title="Parsing range"><code>++pint</code></a>

469+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#pint' title="Parsing range"><code>+$pint</code></a>

465470<a class="tooltip" href='/docs/hoon/reference/stdlib/4j/#pivab' title="Parse 5 digits in base 32"><code>++piv:ab</code></a>

466471<a class="tooltip" href='/docs/hoon/reference/stdlib/4j/#piwab' title="Parse 5 digits in base 64"><code>++piw:ab</code></a>

467472<a class="tooltip" href='/docs/hoon/reference/stdlib/4e/#plug' title="Parse to tuple"><code>++plug</code></a>

@@ -535,11 +540,10 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

535540<a class="tooltip" href='/docs/hoon/reference/stdlib/2p/#rub' title="Lengthdecode"><code>++rub</code></a>

536541<a class="tooltip" href='/docs/hoon/reference/stdlib/4b/#rubat' title="(Undocumented)"><code>++rub:at</code></a>

537542<a class="tooltip" href='/docs/hoon/reference/stdlib/4b/#rudat' title="(Undocumented)"><code>++rud:at</code></a>

538−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#rule' title="Parsing rule (match this with _)"><code>++rule</code></a>

543+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#rule' title="Parsing rule (match this with _)"><code>+$rule</code></a>

539544<a class="tooltip" href='/docs/hoon/reference/stdlib/4b/#rumat' title="(Undocumented)"><code>++rum:at</code></a>

540545<a class="tooltip" href='/docs/hoon/reference/stdlib/2i/#runby' title="Transform values (map)"><code>++run:by</code></a>

541546<a class="tooltip" href='/docs/hoon/reference/stdlib/2h/#runin' title="Apply gate to set"><code>++run:in</code></a>

542−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#rundob' title="Reverse single Feistellike"><code>++rund:ob</code></a>

543547<a class="tooltip" href='/docs/hoon/reference/stdlib/4b/#runt' title="Prepend n times"><code>++runt</code></a>

544548<a class="tooltip" href='/docs/hoon/reference/stdlib/4b/#rupat' title="(Undocumented)"><code>++rup:at</code></a>

545549<a class="tooltip" href='/docs/hoon/reference/stdlib/4g/#rush' title="Parse or null"><code>++rush</code></a>

@@ -547,7 +551,6 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

547551<a class="tooltip" href='/docs/hoon/reference/stdlib/2i/#rutby' title="Transform nodes (map)"><code>++rut:by</code></a>

548552<a class="tooltip" href='/docs/hoon/reference/stdlib/4b/#ruvat' title="(Undocumented)"><code>++ruv:at</code></a>

549553<a class="tooltip" href='/docs/hoon/reference/stdlib/4b/#ruxat' title="(Undocumented)"><code>++rux:at</code></a>

550−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#ryndob' title="Reverse Feistellike cipher"><code>++rynd:ob</code></a>

551554

552555### s

553556

@@ -642,7 +645,7 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

642645<a class="tooltip" href='/docs/hoon/reference/stdlib/3b/#spdfl' title="Produce smallest denormalized float"><code>++spd:fl</code></a>

643646<a class="tooltip" href='/docs/hoon/reference/stdlib/2b/#spin' title="Gate to list (with state)"><code>++spin</code></a>

644647<a class="tooltip" href='/docs/hoon/reference/stdlib/3b/#spnfl' title="Produce smallest normal float"><code>++spn:fl</code></a>

645−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#spot' title="Stack trace line"><code>++spot</code></a>

648+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#spot' title="Stack trace line"><code>+$spot</code></a>

646649<a class="tooltip" href='/docs/hoon/reference/stdlib/4m/#spud' title="Render path as tape"><code>++spud</code></a>

647650<a class="tooltip" href='/docs/hoon/reference/stdlib/2b/#spun' title="Gate to list (with state)"><code>++spun</code></a>

648651<a class="tooltip" href='/docs/hoon/reference/stdlib/2g/#sqt' title="Compute square root with remainder"><code>++sqt</code></a>

@@ -702,7 +705,7 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

702705<a class="tooltip" href='/docs/hoon/reference/stdlib/4h/#tec' title="Parse ` (tec)"><code>++tec</code></a>

703706<a class="tooltip" href='/docs/hoon/reference/stdlib/4j/#tedab' title="Parse decimal number with <= 3 digits"><code>++ted:ab</code></a>

704707<a class="tooltip" href='/docs/hoon/reference/stdlib/4b/#teff' title="UTF8 length"><code>++teff</code></a>

705−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#teilob' title="Reverse Feistellike cipher"><code>++teil:ob</code></a>

708+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#tailob' title="Reverse +feis"><code>++tail:ob</code></a>

706709<a class="tooltip" href='/docs/hoon/reference/stdlib/2q/#term' title="Hoon constant"><code>+$term</code></a>

707710<a class="tooltip" href='/docs/hoon/reference/stdlib/2n/#test' title="Test for equality"><code>++test</code></a>

708711<a class="tooltip" href='/docs/hoon/reference/stdlib/4j/#tidab' title="Parse 3 decimal digits"><code>++tid:ab</code></a>

@@ -721,8 +724,8 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

721724<a class="tooltip" href='/docs/hoon/reference/stdlib/3b/#toirs' title="Round singleprecision float to nearest signed integer"><code>++toi:rs</code></a>

722725<a class="tooltip" href='/docs/hoon/reference/stdlib/3b/#toirq' title="Round quadprecision float to nearest signed integer"><code>++toi:rq</code></a>

723726<a class="tooltip" href='/docs/hoon/reference/stdlib/3b/#tojfl' title="Round unsigned and signed integer to float"><code>++toj:fl</code></a>

724−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#tone' title="Nock result (error report)"><code>++tone</code></a>

725−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#toon' title="Nock result (stack trace)"><code>++toon</code></a>

727+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#tone' title="Nock result (error report)"><code>+$tone</code></a>

728+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#toon' title="Nock result (stack trace)"><code>+$toon</code></a>

726729<a class="tooltip" href='/docs/hoon/reference/stdlib/2k/#topto' title="Produce head of queue"><code>++top:to</code></a>

727730<a class="tooltip" href='/docs/hoon/reference/stdlib/4a/#tospo' title="Fetch prefix"><code>++tos:po</code></a>

728731<a class="tooltip" href='/docs/hoon/reference/stdlib/3b/#tosrh' title="Convert halfprecision float to singleprecision float"><code>++tos:rh</code></a>

@@ -1372,14 +1375,16 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

13721375### 3f: scrambling

13731376

13741377<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#ob' title="Reversible scrambling v2"><code>++ob</code></a>

1375−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feenob' title="Conceal structure v2"><code>++feen:ob</code></a>

1376−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#fendob' title="Restore structure v2"><code>++fend:ob</code></a>

1377−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#ficeob' title="Feistellike cipher"><code>++fice:ob</code></a>

1378+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feinob' title="Conceal structure v3"><code>++fein:ob</code></a>

1379+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#fyndob' title="Restore structure v3"><code>++fynd:ob</code></a>

1380+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feisob' title="Four-round generalised Feistel cipher over the domain [0, 2^32 - 2^16 - 1]"><code>++feis:ob</code></a>

13781381<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#rakuob' title="Key list"><code>++raku:ob</code></a>

1379−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#rundob' title="Reverse single Feistellike"><code>++rund:ob</code></a>

1380−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#ryndob' title="Reverse Feistellike cipher"><code>++rynd:ob</code></a>

1381−<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#teilob' title="Reverse Feistellike cipher"><code>++teil:ob</code></a>

1382−

1382+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#tailob' title="Reverse +feis"><code>++tail:ob</code></a>

1383+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feeob' title="Feistel cipher Fe in B&R (2002)"><code>++fee:ob</code></a>

1384+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feenob' title="Reverse +fee"><code>++feen:ob</code></a>

1385+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#feob' title="Internal function to +fee"><code>++fe:ob</code></a>

1386+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#fenob' title="Reverse +fe"><code>++fen:ob</code></a>

1387+<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#effob' title="murmur3-based pseudorandom function"><code>++eff:ob</code></a>

13831388<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#un' title="Reversible scrambling"><code>++un</code></a>

13841389<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#wredun' title="Restore structure"><code>++wred:un</code></a>

13851390<a class="tooltip" href='/docs/hoon/reference/stdlib/3f/#wrenun' title="Conceal structure"><code>++wren:un</code></a>

@@ -1392,17 +1397,17 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

13921397

13931398### 3g: molds and mold builders

13941399

1395−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#coin' title="Nounliteral syntax cases"><code>++coin</code></a>

1396−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#dime' title="Auraatom pair"><code>++dime</code></a>

1397−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#edge' title="Parsing location metadata"><code>++edge</code></a>

1398−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#hair' title="Parsing line and column"><code>++hair</code></a>

1400+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#coin' title="Nounliteral syntax cases"><code>+$coin</code></a>

1401+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#dime' title="Auraatom pair"><code>+$dime</code></a>

1402+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#edge' title="Parsing location metadata"><code>+$edge</code></a>

1403+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#hair' title="Parsing line and column"><code>+$hair</code></a>

13991404<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#like' title="Generic edge"><code>++like</code></a>

1400−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#nail' title="Location, remainder of parsed text"><code>++nail</code></a>

1401−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#pint' title="Parsing range"><code>++pint</code></a>

1402−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#rule' title="Parsing rule (match this with _)"><code>++rule</code></a>

1403−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#spot' title="Stack trace line"><code>++spot</code></a>

1404−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#tone' title="Nock result (error report)"><code>++tone</code></a>

1405−<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#toon' title="Nock result (stack trace)"><code>++toon</code></a>

1405+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#nail' title="Location, remainder of parsed text"><code>+$nail</code></a>

1406+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#pint' title="Parsing range"><code>+$pint</code></a>

1407+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#rule' title="Parsing rule (match this with _)"><code>+$rule</code></a>

1408+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#spot' title="Stack trace line"><code>+$spot</code></a>

1409+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#tone' title="Nock result (error report)"><code>+$tone</code></a>

1410+<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#toon' title="Nock result (stack trace)"><code>+$toon</code></a>

14061411<a class="tooltip" href='/docs/hoon/reference/stdlib/3g/#wonk' title="Product from edge"><code>++wonk</code></a>

14071412

14081413### 4a: exotic bases

@@ -1716,7 +1721,7 @@ Can be navigated [alphabetically](#alphabetical) or [by section](#by-section).

17161721<a class="tooltip" href='/docs/hoon/reference/stdlib/4o/#span' title="ASCII atom"><code>++span</code></a>

17171722<a class="tooltip" href='/docs/hoon/reference/stdlib/4o/#tiki' title="(Undocumented)"><code>++tiki</code></a>

17181723<a class="tooltip" href='/docs/hoon/reference/stdlib/4o/#toga' title="Tree of faces"><code>++toga</code></a>

1719−<a class="tooltip" href='/docs/hoon/reference/stdlib/4o/#tone'><code>++tone</code></a>

1724+<a class="tooltip" href='/docs/hoon/reference/stdlib/4o/#tone'><code>+$tone</code></a>

17201725<a class="tooltip" href='/docs/hoon/reference/stdlib/4o/#tuna' title="XML template tree"><code>++tuna</code></a>

17211726<a class="tooltip" href='/docs/hoon/reference/stdlib/4o/#tusk' title="List of expressions"><code>++tusk</code></a>

17221727<a class="tooltip" href='/docs/hoon/reference/stdlib/4o/#tyke' title="List of 'maybe' hoons"><code>++tyke</code></a>

lib/glossary.js+45−24

@@ -2431,6 +2431,13 @@ export const glossary = [

24312431 slug: "https://urbit.org/docs/reference/library/3g/#edge",

24322432 desc: "Used in the Hoon standard library.",

24332433 },

2434+ {

2435+ name: "murmur3-based pseudorandom function",

2436+ symbol: "eff:ob",

2437+ usage: "stdlib",

2438+ slug: "https://urbit.org/docs/reference/library/3f/#effob",

2439+ desc: "Used in the Hoon standard library.",

2440+ },

24342441 {

24352442 name: "Extended Euclidean algorithm",

24362443 symbol: "egcd",

@@ -2600,24 +2607,52 @@ export const glossary = [

26002607 desc: "Used in the Hoon standard library.",

26012608 },

26022609 {

2603− name: "Conceal structure v2",

2610+ name: "Internal function to +fee",

2611+ symbol: "fe:ob",

2612+ usage: "stdlib",

2613+ slug: "https://urbit.org/docs/reference/library/3f/#feob",

2614+ desc: "Used in the Hoon standard library.",

2615+ },

2616+ {

2617+ name: "Feistel cipher Fe in B&R (2002)",

2618+ symbol: "fee:ob",

2619+ usage: "stdlib",

2620+ slug: "https://urbit.org/docs/reference/library/3f/#feeob",

2621+ desc: "Used in the Hoon standard library.",

2622+ },

2623+ {

2624+ name: "Reverse +fee",

26042625 symbol: "feen:ob",

26052626 usage: "stdlib",

26062627 slug: "https://urbit.org/docs/reference/library/3f/#feenob",

26072628 desc: "Used in the Hoon standard library.",

26082629 },

26092630 {

2610− name: "Restore structure v2",

2611− symbol: "fend:ob",

2631+ name: "Conceal structure v3",

2632+ symbol: "fein:ob",

2633+ usage: "stdlib",

2634+ slug: "https://urbit.org/docs/reference/library/3f/#feinob",

2635+ desc: "Used in the Hoon standard library.",

2636+ },

2637+ {

2638+ name: "Reverse +fe",

2639+ symbol: "fen:ob",

26122640 usage: "stdlib",

2613− slug: "https://urbit.org/docs/reference/library/3f/#fendob",

2641+ slug: "https://urbit.org/docs/reference/library/3f/#fenob",

26142642 desc: "Used in the Hoon standard library.",

26152643 },

26162644 {

2617− name: "Feistel-like cipher",

2618− symbol: "fice:ob",

2645+ name: "Restore structure v3",

2646+ symbol: "fynd:ob",

26192647 usage: "stdlib",

2620− slug: "https://urbit.org/docs/reference/library/3f/#ficeob",

2648+ slug: "https://urbit.org/docs/reference/library/3f/#fyndob",

2649+ desc: "Used in the Hoon standard library.",

2650+ },

2651+ {

2652+ name: "Four-round generalised Feistel cipher over the domain [0, 2^32 - 2^16 - 1]",

2653+ symbol: "feis:ob",

2654+ usage: "stdlib",

2655+ slug: "https://urbit.org/docs/reference/library/3f/#feisob",

26212656 desc: "Used in the Hoon standard library.",

26222657 },

26232658 {

@@ -4713,13 +4748,6 @@ export const glossary = [

47134748 slug: "https://urbit.org/docs/reference/library/2h/#runin",

47144749 desc: "Used in the Hoon standard library.",

47154750 },

4716− {

4717− name: "Reverse single Feistel-like",

4718− symbol: "rund:ob",

4719− usage: "stdlib",

4720− slug: "https://urbit.org/docs/reference/library/3f/#rundob",

4721− desc: "Used in the Hoon standard library.",

4722− },

47234751 {

47244752 name: "Prepend n times",

47254753 symbol: "runt",

@@ -4769,13 +4797,6 @@ export const glossary = [

47694797 slug: "https://urbit.org/docs/reference/library/4b/#ruxat",

47704798 desc: "Used in the Hoon standard library.",

47714799 },

4772− {

4773− name: "Reverse Feistel-like cipher",

4774− symbol: "rynd:ob",

4775− usage: "stdlib",

4776− slug: "https://urbit.org/docs/reference/library/3f/#ryndob",

4777− desc: "Used in the Hoon standard library.",

4778− },

47794800 {

47804801 name: "Identity (produces same value)",

47814802 symbol: "same",

@@ -5813,10 +5834,10 @@ export const glossary = [

58135834 desc: "Used in the Hoon standard library.",

58145835 },

58155836 {

5816− name: "Reverse Feistel-like cipher",

5817− symbol: "teil:ob",

5837+ name: "Reverse +feis",

5838+ symbol: "tail:ob",

58185839 usage: "stdlib",

5819− slug: "https://urbit.org/docs/reference/library/3f/#teilob",

5840+ slug: "https://urbit.org/docs/reference/library/3f/#tailob",

58205841 desc: "Used in the Hoon standard library.",

58215842 },

58225843 {