:module FloatTests
:set ascii=on

section "Float Formatting"
:help :set fp-base
:help :set fp-format

:set fp-base=2
10.25 : Medium

:set fp-base=8
10.25 : Medium

:set fp-base=10
10.25       : Medium
1.0 /. 3.0  : Small
0.4         : Small

:set fp-base=16
10.25       : Medium
1.0 /.  3.0 : Small

:set fp-base=16
:set fp-format=free+exp
0x12.34 : Medium
:set fp-format=.1
0x12.34 : Medium
:set fp-format=2
0x12.34 : Medium
:set fp-format=2+exp
0x12.34 : Medium


section "Float Type"
:help Float
zero : Float 0 0            // Too small
zero : Float 80 1000        // Too large
zero : Small
zero : Medium
zero : Large

section "Literals"
:set fp-base=10
1.0         : Medium
1.25        : Medium
1.25e2      : Medium
:set fp-base=16
0x1.25      : Medium
0xFF.FFp3   : Medium
0xFF.FFp-4  : Medium
0xFF.FFe3   : Medium     // This is NOT AN EXPONENT
5.0         : Small      // Not checked
0x5.0       : Small      // Checked
1.2         : Medium
0x0.2       : Small      // Subnormal
fpFromBits 1 : Small     // Subnormal

section "NaN"
:help fpNaN
fpNaN : Medium
:set base=2
fpToBits    (fpNaN : Small)
fpToBits    (fpNaN : Medium)
roundTrip   (fpNaN : Large)
eqRefl1     (fpNaN : Medium)
eqRefl2     (fpNaN : Medium)
leqRefl     (fpNaN : Medium)

section "Arithmetic"

:set fp-base=10
1.0 + 1.0    : Medium
1.0 - 1.0    : Medium
3.0 * 2.0    : Medium
3.0 /. 2.0   : Medium

1.0  /. 0.0  : Medium
-1.0 /. 0.0  : Medium
-0.0 /. 0.0  : Medium
1.0  /. -0.0 : Medium
-1.0 /. -0.0 : Medium
-0.0 /. -0.0 : Medium

2.0 + 3.0    : Small
2.0 + 8.0    : Small

fpAdd rne 2.0 3.0         : Small
fpAdd rne 2.0 8.0         : Small
fpAdd rne (-2.0) (-3.0)   : Small
fpAdd rne (-2.0) (-8.0)   : Small
fpAdd rna 2.0 3.0         : Small
fpAdd rna 2.0 8.0         : Small
fpAdd rna (-2.0) (-3.0)   : Small
fpAdd rna (-2.0) (-8.0)   : Small
fpAdd rtp 2.0 3.0         : Small
fpAdd rtp 2.0 8.0         : Small
fpAdd rtp (-2.0) (-3.0)   : Small
fpAdd rtp (-2.0) (-8.0)   : Small
fpAdd rtn 2.0 3.0         : Small
fpAdd rtn 2.0 8.0         : Small
fpAdd rtn (-2.0) (-3.0)   : Small
fpAdd rtn (-2.0) (-8.0)   : Small
fpAdd rtz 2.0 3.0         : Small
fpAdd rtz 2.0 8.0         : Small
fpAdd rtz (-2.0) (-3.0)   : Small
fpAdd rtz (-2.0) (-8.0)   : Small


section "Proofs"
:set prover=w4-z3
:set show-examples = off
:prove \(x : Medium) -> x == 0.0 \/ x =.= fpNaN     // False
:set show-examples = on
:prove \(x : Medium) -> x == x                      // False
:prove \(x : Medium) -> eqRefl1 x
:prove \(x : Medium) -> eqRefl2 x
:prove \(x : Medium) -> roundTrip x
:prove roundTrip2`{3,2}
:prove roundTrip2`{11,53}
:prove \(x : Medium) -> leqRefl x
:prove \(x : Medium) y -> eqProp x y

section "Random Testing"
:check \(x : Medium) -> eqRefl1 x
:check \(x : Medium) -> eqRefl2 x
:check \(x : Medium) -> roundTrip x
:prove roundTrip2`{3,2}
:prove roundTrip2`{11,53}
:check \(x : Medium) -> leqRefl x
:check \(x : Medium) y -> eqProp x y