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float16.jl
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float16.jl
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# 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))
for T = Base.BitInteger_types
@test -Inf16 < typemin(T)
@test -Inf16 <= typemin(T)
@test typemin(T) > -Inf16
@test typemin(T) >= -Inf16
@test typemin(T) != -Inf16
@test Inf16 > typemax(T)
@test Inf16 >= typemax(T)
@test typemax(T) < Inf16
@test typemax(T) <= Inf16
@test typemax(T) != Inf16
end
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)
@test sin(ComplexF16(f)) ≈ sin(complex(2f0))
# no domain error is thrown for negative values
@test cbrt(Float16(-1.0)) == -1.0
# test zero and Inf
@test cbrt(Float16(0.0)) == Float16(0.0)
@test cbrt(Inf16) == Inf16
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)
for x = (typemin(Int64), typemin(Int128)), R = (RoundUp, RoundToZero)
@test Float16(x, R) == nextfloat(-Inf16)
end
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
@testset "conversion to Float16 from" begin
for T in (Float32, Float64, BigFloat)
@testset "conversion from $T" begin
for i in 1:2^16
f = reinterpret(Float16, UInt16(i-1))
isfinite(f) || continue
if f < 0
epsdown = T(eps(f))/2
epsup = issubnormal(f) ? epsdown : T(eps(nextfloat(f)))/2
else
epsup = T(eps(f))/2
epsdown = issubnormal(f) ? epsup : T(eps(prevfloat(f)))/2
end
@test isequal(f*(-1)^(f === Float16(0)), Float16(nextfloat(T(f) - epsdown)))
@test isequal(f*(-1)^(f === -Float16(0)), Float16(prevfloat(T(f) + epsup)))
@test isequal(prevfloat(f), Float16(prevfloat(T(f) - epsdown)))
@test isequal(nextfloat(f), Float16(nextfloat(T(f) + epsup)))
end
end
end
end