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1+++

2title = "1a: Basic Arithmetic"

3weight = 1

4template = "doc.html"

5+++

7## `++add`

9Add

11Produces the sum of `a` and `b`.

13#### Accepts

15`a` is an [`atom`](/docs/glossary/atom).

17`b` is an [`atom`](/docs/glossary/atom).

19#### Produces

21An [`atom`](/docs/glossary/atom).

23#### Source

25```hoon

26++ add

27 ~/ %add

28 |= [a=@ b=@]

29 ^- @

30 ?: =(0 a) b

31 $(a (dec a), b +(b))

32```

34#### Examples

36```

37> (add 2 2)

384

39```

41```

42> (add 1 1.000.000)

431.000.001

44```

46```

47> (add 1.333 (mul 2 2))

481.337

49```

51```

52> (add 'a' 4)

53101

54```

56```

57> (add 'a' 'b')

58195

59```

61```

62> (add 0xc 0xf)

6327

64```

66```

67> `@ux`(add 0xc 0xf)

680x1b

69```

71---

73## `++dec`

75Decrement

77Decrements `a` by `1`.

79#### Accepts

81`a` is an [`atom`](/docs/glossary/atom).

83#### Produces

85An [`atom`](/docs/glossary/atom).

87#### Source

89```hoon

90++ dec

91 ~/ %dec

92 |= a=@

93 ~_ leaf+"decrement-underflow"

94 ?< =(0 a)

95 =+ b=0

96 |- ^- @

97 ?: =(a +(b)) b

98 $(b +(b))

99```

100

101#### Examples

102

103```

104> (dec 7)

1056

106```

107

108```

109> (dec 0)

110! decrement-underflow

111! exit

112```

113

114```

115> (dec 'b')

11697

117> `@t`(dec 'b')

118'a'

119```

120

121```

122> (dec 0xc)

12311

124> `@ux`(dec 0xc)

1250xb

126```

128---

130## `++div`

132Divide

134Computes `a` divided by `b` without remainder.

135

136#### Accepts

137

138`a` is an [`atom`](/docs/glossary/atom).

139

140`b` is an [`atom`](/docs/glossary/atom).

141

142#### Produces

143

144An [`atom`](/docs/glossary/atom).

145

146#### Source

147

148```hoon

149++ div

150 ~/ %div

151 |: [a=`@`1 b=`@`1]

152 ^- @

153 ~_ leaf+"divide-by-zero"

154 ?< =(0 b)

155 =+ c=0

156 |-

157 ?: (lth a b) c

158 $(a (sub a b), c +(c))

159```

160

161#### Examples

162

163```

164> (div 4 2)

1652

166```

167

168```

169> (div 17 8)

1702

171```

172

173```

174> (div 20 30)

1750

176```

177

178```

179> (div 'ab' 'a')

180259

181> `@`'ab'

18225.185

183> `@`a

18497

185```

186

187```

188> (div 0x9f 0x29)

1896

190```

191

192---

193

194## `++dvr`

195

196Divide with remainder

197

198Computes `a` divided by `b`, producing the quotient and the remainder.

199

200#### Accepts

201

202`a` is an [`atom`](/docs/glossary/atom).

203

204`b` is an [`atom`](/docs/glossary/atom).

205

206#### Produces

207

208A cell of [`atoms`](/docs/glossary/atom).

209

210#### Source

211

212```hoon

213++ dvr

214 ~/ %dvr

215 |= [a=@ b=@]

216 ^- [p=@ q=@]

217 [(div a b) (mod a b)]

218```

219

220#### Examples

221

222```

223> (dvr 17 8)

224[p=2 q=1]

225```

226

227```

228> (dvr 17 6)

229[p=2 q=5]

230```

231

232```

233> (dvr 18 6)

234[p=3 q=0]

235```

236

237```

238> (dvr 4 2)

239[p=2 q=0]

240```

241

242```

243> (dvr 'ab 'a')

244[p=259 q=62]

245> `@`'a'

24697

247> `@`'ab'

24825.185

249```

250

251---

252

253## `++gte`

254

255Greater-than/equal

256

257Tests whether `a` is greater than or equal to `b`.

258

259#### Accepts

260

261`a` is an [`atom`](/docs/glossary/atom).

262

263`b` is an [`atom`](/docs/glossary/atom).

265#### Produces

267A flag.

269#### Source

271```hoon

272++ gte

273 ~/ %gte

274 |= [a=@ b=@]

275 ^- ?

276 !(lth a b)

277```

278

279#### Examples

280

281```

282> (gte 100 10)

283%.y

284```

285

286```

287> (gte 4 4)

288%.y

289```

290

291```

292> (gte 3 4)

293%.n

294```

296---

298## `++gth`

300Greater-than

302Tests whether `a` is greater than `b`.

303

304#### Accepts

305

306`a` is an [`atom`](/docs/glossary/atom).

307

308`b` is an [`atom`](/docs/glossary/atom).

310#### Produces

312A flag.

314#### Source

316```hoon

317++ gth

318 ~/ %gth

319 |= [a=@ b=@]

320 ^- ?

321 !(lte a b)

322```

323

324#### Examples

325

326```

327> (gth 'd' 'c')

328%.y

329```

330

331```

332> (gth ~h1 ~m61)

333%.n

334```

335

336```

337> (gth 'steak' 'brisket')

338%.n

339```

341---

343## `++lte`

345Less-than/equal

347Tests whether `a` is less than or equal to `b`.

348

349#### Accepts

350

351`a` is an [`atom`](/docs/glossary/atom).

352

353`b` is an [`atom`](/docs/glossary/atom).

355#### Produces

357A flag.

359#### Source

361```hoon

362++ lte

363 ~/ %lte

364 |= [a=@ b=@]

365 |(=(a b) (lth a b))

366```

367

368#### Examples

369

370```

371> (lte 4 5)

372%.y

373```

374

375```

376> (lte 5 4)

377%.n

378```

379

380```

381> (lte 5 5)

382%.y

383```

384

385```

386> (lte 0 0)

387%.y

388```

389

390```

391> (lte 'a' 'b')

392%.y

393> `@`'a'

39497

395> `@`'b'

39698

397```

398

399```

400> (lte 'abraham' 'bob')

401%.n

402```

403

404```

405> (lte ~m61 ~h1)

406%.n

407```

409---

411## `++lth`

413Less-than

415Tests whether `a` is less than `b`.

416

417#### Accepts

418

419`a` is an [`atom`](/docs/glossary/atom).

420

421`b` is an [`atom`](/docs/glossary/atom).

423#### Produces

425A flag.

427#### Source

429```hoon

430++ lth

431 ~/ %lth

432 |= [a=@ b=@]

433 ^- ?

434 ?& !=(a b)

435 |-

436 ?| =(0 a)

437 ?& !=(0 b)

438 $(a (dec a), b (dec b))

439 == == ==

440```

441

442#### Examples

443

444```

445> (lth 4 5)

446%.y

447```

448

449```

450> (lth 5 4)

451%.n

452```

453

454```

455> (lth 5 5)

456%.n

457```

458

459```

460> (lth 5 0)

461%.n

462```

463

464```

465> (lth 'a' 'b')

466%.y

467> `@`'a'

46897

469> `@`'b'

47098

471```

472

473```

474> (lth 'abraham' 'bob')

475%.n

476```

478---

480## `++max`

482Maximum

484Computes the greater of `a` and `b`.

485

486#### Accepts

487

488`a` is an [`atom`](/docs/glossary/atom).

489

490`b` is an [`atom`](/docs/glossary/atom).

491

492#### Produces

493

494An [`atom`](/docs/glossary/atom).

495

496#### Source

497

498```hoon

499++ max

500 ~/ %max

501 |= [a=@ b=@]

502 ^- @

503 ?: (gth a b) a

504 b

505```

506

507#### Examples

508

509```

510> (max 10 100)

511100

512```

513

514```

515> (max 10.443 9)

51610.443

517```

518

519```

520> (max 1 1)

5211

522```

523

524```

525> (max 'abraham' 'bob')

52630.787.873.400.840.801

527```

528

529```

530> `@t`(max 'abraham' 'bob')

531'abraham'

532```

533

534```

535> `@t`(max 'abraham' 'benjamin')

536'benjamin'

537```

538

539```

540> `@dr`(max ~m6 ~h1)

541~h1

542```

543

544```

545>`@ux`(max 0xe1 0x1e)

5460xe1

547```

549---

551## `++min`

553Minimum

555Computes the lesser of `a` and `b`.

556

557#### Accepts

558

559`a` is an [`atom`](/docs/glossary/atom).

560

561`b` is an [`atom`](/docs/glossary/atom).

562

563#### Produces

564

565An [`atom`](/docs/glossary/atom).

566

567#### Source

568

569```hoon

570++ min

571 ~/ %min

572 |= [a=@ b=@]

573 ^- @

574 ?: (lth a b) a

575 b

576```

577

578#### Examples

579

580```

581> (min 10 100)

58210

583```

584

585```

586> (min 10.443 9)

5879

588```

589

590```

591> (min 1 1)

5921

593```

594

595```

596> (min 'abraham' 'bob')

5976.451.042

598```

599

600```

601> `@t`(min 'abraham' 'bob')

602'bob'

603```

604

605```

606> `@t`(min 'abraham' 'benjamin')

607'abraham'

608```

609

610```

611> `@dr`(min ~m6 ~h1)

612~m6

613```

615---

617## `++mod`

619Modulus

621Computes the remainder of dividing `a` by `b`.

622

623#### Accepts

624

625`a` is an [`atom`](/docs/glossary/atom).

626

627`b` is an [`atom`](/docs/glossary/atom).

628

629#### Produces

630

631An [`atom`](/docs/glossary/atom).

632

633#### Source

634

635```hoon

636++ mod

637 ~/ %mod

638 |: [a=`@`1 b=`@`1]

639 ^- @

640 ?< =(0 b)

641 (sub a (mul b (div a b)))

642```

643

644#### Examples

645

646```

647> (mod 5 2)

6481

649```

650

651```

652> (mod 5 5)

6530

654```

655

656```

657> (mod 2 5)

6582

659```

660

661```

662> (mod 40 20)

6630

664```

665

666```

667> `@`'c'

66899

669>`@`'a'

67097

671> (mod 'c' 'a')

6722

673```

675---

677## `++mul`

679Multiply

681Multiplies `a` by `b`.

682

683#### Accepts

684

685`a` is an [`atom`](/docs/glossary/atom).

686

687`b` is an [`atom`](/docs/glossary/atom).

688

689#### Produces

690

691An [`atom`](/docs/glossary/atom).

692

693#### Source

694

695```hoon

696++ mul

697 ~/ %mul

698 |: [a=`@`1 b=`@`1]

699 ^- @

700 =+ c=0

701 |-

702 ?: =(0 a) c

703 $(a (dec a), c (add b c))

704```

705

706#### Examples

707

708```

709> (mul 3 4)

71012

711```

712

713```

714> (mul 0 1)

7150

716```

717

718```

719> `@`'a'

72097

721> `@`'b'

72298

723> (mul 'a' 'b')

7249.506

725```

726

727```

728>`@ux`(mul 0x1f 0xe)

7290x1b2

730```

732---

734## `++sub`

736Subtract

738Subtracts `b` from `a`.

739

740#### Accepts

741

742`a` is an [`atom`](/docs/glossary/atom).

743

744`b` is an [`atom`](/docs/glossary/atom).

745

746#### Produces

747

748An [`atom`](/docs/glossary/atom).

749

750#### Source

751

752```hoon

753++ sub

754 ~/ %sub

755 |= [a=@ b=@]

756 ~_ leaf+"subtract-underflow"

757 ^- @

758 ?: =(0 b) a

759 $(a (dec a), b (dec b))

760```

761

762#### Examples

763

764```

765> (sub 10 5)

7665

767```

768

769```

770> (sub 243 44)

771199

772```

773

774```

775> (sub 5 0)

7765

777```

778

779```

780> (sub 0 5)

781! subtract-underflow

782! exit

783```

784

785```

786> (sub 'c' 'a')

7872

788> `@`'c'

78999

790> `@`'a'

79197

792```

793

794```

795> (sub 0x1f 0xe)

79617

797> `@ux`(sub 0x1f 0xe)

7980x11

799```