-
-
Notifications
You must be signed in to change notification settings - Fork 5.5k
/
float16.jl
182 lines (159 loc) · 5.95 KB
/
float16.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
# This file is a part of Julia. License is MIT: https://julialang.org/license
using Test
f = Float16(2.)
g = Float16(1.)
@testset "comparisons" begin
@test f >= g
@test f > g
@test g < f
@test g <= g
@test all([g g] .< [f f])
@test all([g g] .<= [f f])
@test all([f f] .> [g g])
@test all([f f] .>= [g g])
@test isless(g, f)
@test !isless(f, g)
@test Float16(2.5) == Float16(2.5)
@test Float16(2.5) != Float16(2.6)
@test isequal(Float16(0.0), Float16(0.0))
@test !isequal(Float16(-0.0), Float16(0.0))
@test !isequal(Float16(0.0), Float16(-0.0))
end
@testset "convert" begin
@test convert(Bool,Float16(0.0)) == false
@test convert(Bool,Float16(1.0)) == true
@test_throws InexactError convert(Bool,Float16(0.1))
@test convert(Int128,Float16(-2.0)) == Int128(-2)
@test convert(UInt128,Float16(2.0)) == UInt128(2)
# convert(::Type{Int128}, x::Float16)
@test convert(Int128, Float16(1.0)) === Int128(1.0)
@test convert(Int128, Float16(-1.0)) === Int128(-1.0)
@test_throws InexactError convert(Int128, Float16(3.5))
# convert(::Type{UInt128}, x::Float16)
@test convert(UInt128, Float16(1.0)) === UInt128(1.0)
@test_throws InexactError convert(UInt128, Float16(3.5))
@test_throws InexactError convert(UInt128, Float16(-1))
@test convert(Int128,Float16(-1.0)) == Int128(-1)
@test convert(UInt128,Float16(5.0)) == UInt128(5)
end
@testset "round, trunc, float, ceil" begin
@test round(Int,Float16(0.5f0)) == round(Int,0.5f0)
@test trunc(Int,Float16(0.9f0)) === trunc(Int,0.9f0) === 0
@test floor(Int,Float16(0.9f0)) === floor(Int,0.9f0) === 0
@test trunc(Int,Float16(1)) === 1
@test floor(Int,Float16(1)) === 1
@test ceil(Int,Float16(0.1f0)) === ceil(Int,0.1f0) === 1
@test ceil(Int,Float16(0)) === ceil(Int,0) === 0
@test round(Float16(0.1f0)) == round(0.1f0) == 0
@test round(Float16(0.9f0)) == round(0.9f0) == 1
@test trunc(Float16(0.9f0)) == trunc(0.9f0) == 0
@test floor(Float16(0.9f0)) == floor(0.9f0) == 0
@test trunc(Float16(1)) === Float16(1)
@test floor(Float16(1)) === Float16(1)
@test ceil(Float16(0.1)) == ceil(0.1)
@test ceil(Float16(0.9)) == ceil(0.9)
@test unsafe_trunc(UInt8, Float16(3)) === 0x03
@test unsafe_trunc(Int16, Float16(3)) === Int16(3)
@test unsafe_trunc(UInt128, Float16(3)) === UInt128(3)
@test unsafe_trunc(Int128, Float16(3)) === Int128(3)
@test unsafe_trunc(Int16, NaN16) === Int16(0) #18771
end
@testset "fma and muladd" begin
@test fma(Float16(0.1),Float16(0.9),Float16(0.5)) ≈ fma(0.1,0.9,0.5)
@test muladd(Float16(0.1),Float16(0.9),Float16(0.5)) ≈ muladd(0.1,0.9,0.5)
end
@testset "unary ops" begin
@test -f === Float16(-2.)
@test Float16(0.5f0)^2 ≈ Float16(0.5f0^2)
@test sin(f) ≈ sin(2f0)
@test log10(Float16(100)) == Float16(2.0)
# no domain error is thrown for negative values
@test cbrt(Float16(-1.0)) == -1.0
end
@testset "binary ops" begin
@test f+g === Float16(3f0)
@test f-g === Float16(1f0)
@test f*g === Float16(2f0)
@test f/g === Float16(2f0)
@test f^g === Float16(2f0)
@test f^1 === Float16(2f0)
@test f^-g === Float16(0.5f0)
@test f + 2 === Float16(4f0)
@test f - 2 === Float16(0f0)
@test f*2 === Float16(4f0)
@test f/2 === Float16(1f0)
@test f + 2. === 4.
@test f - 2. === 0.
@test f*2. === 4.
@test f/2. === 1.
end
@testset "NaN16 and Inf16" begin
@test isnan(NaN16)
@test isnan(-NaN16)
@test !isnan(Inf16)
@test !isnan(-Inf16)
@test !isnan(Float16(2.6))
@test NaN16 != NaN16
@test isequal(NaN16, NaN16)
@test repr(NaN16) == "NaN16"
@test sprint(show, NaN16, context=:compact => true) == "NaN"
@test isinf(Inf16)
@test isinf(-Inf16)
@test !isinf(NaN16)
@test !isinf(-NaN16)
@test !isinf(Float16(2.6))
@test Inf16 == Inf16
@test Inf16 != -Inf16
@test -Inf16 < Inf16
@test isequal(Inf16, Inf16)
@test repr(Inf16) == "Inf16"
@test sprint(show, Inf16, context=:compact => true) == "Inf"
@test isnan(reinterpret(Float16,0x7c01))
@test !isinf(reinterpret(Float16,0x7c01))
@test nextfloat(Inf16) === Inf16
@test prevfloat(-Inf16) === -Inf16
end
@test repr(Float16(44099)) == "Float16(4.41e4)"
@testset "signed zeros" begin
for z1 in (Float16(0.0), Float16(-0.0)), z2 in (Float16(0.0), Float16(-0.0))
@test z1 == z2
@test isequal(z1, z1)
@test z1 === z1
for elty in (Float32, Float64)
z3 = convert(elty, z2)
@test z1==z3
end
end
end
@testset "rounding in conversions" begin
for f32 in [.3325f0, -.3325f0]
f16 = Float16(f32)
# need to round away from 0. make sure we picked closest number.
@test abs(f32 - f16) < abs(f32 - nextfloat(f16))
@test abs(f32 - f16) < abs(f32 - prevfloat(f16))
end
# halfway between and last bit is 1
ff = reinterpret(Float32, 0b00111110101010100011000000000000)
@test Float32(Float16(ff)) === reinterpret(Float32, 0b00111110101010100100000000000000)
# halfway between and last bit is 0
ff = reinterpret(Float32, 0b00111110101010100001000000000000)
@test Float32(Float16(ff)) === reinterpret(Float32, 0b00111110101010100000000000000000)
end
# issue #5948
@test string(reinterpret(Float16, 0x7bff)) == "6.55e4"
# #9939 (and #9897)
@test rationalize(Float16(0.1)) == 1//10
# issue #17148
@test rem(Float16(1.2), Float16(one(1.2))) == 0.20019531f0
# issue #32441
const f16eps2 = Float32(eps(Float16(0.0)))/2
const minsubf16 = nextfloat(Float16(0.0))
const minsubf16_32 = Float32(minsubf16)
@test Float16(f16eps2) == Float16(0.0)
@test Float16(nextfloat(f16eps2)) == minsubf16
@test Float16(prevfloat(minsubf16_32)) == minsubf16
# Ties to even, in this case up
@test Float16(minsubf16_32 + f16eps2) == nextfloat(minsubf16)
@test Float16(prevfloat(minsubf16_32 + f16eps2)) == minsubf16
# issues #33076
@test Float16(1f5) == Inf16