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floatfuncs.jl
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floatfuncs.jl
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# This file is a part of Julia. License is MIT: https://julialang.org/license
using Test, Random
# test the basic floating point functions
@testset "flipsign" begin
for elty in (Float32,Float64)
x = convert(elty,-2.0)
x = flipsign(x,-1.0)
@test flipsign(x,big(-1.0)) == convert(elty,-2.0)
end
end
@testset "maxintfloat" begin
@test maxintfloat(Float16) === Float16(2048f0)
for elty in (Float16,Float32,Float64)
@test maxintfloat(rand(elty)) === maxintfloat(elty)
end
@test maxintfloat() === maxintfloat(Float64)
@test maxintfloat(Float64, Int32) === 2147483647.0
@test maxintfloat(Float32, Int32) === maxintfloat(Float32)
@test maxintfloat(Float64, Int16) === 32767.0
@test maxintfloat(Float64, Int64) === maxintfloat(Float64)
end
@testset "isinteger" begin
for elty in (Float16, Float32, Float64)
@test !isinteger(elty(1.2))
@test isinteger(elty(12))
@test isinteger(zero(elty))
@test isinteger(-zero(elty))
@test !isinteger(nextfloat(zero(elty)))
@test !isinteger(prevfloat(zero(elty)))
@test isinteger(maxintfloat(elty))
@test isinteger(-maxintfloat(elty))
@test !isinteger(elty(Inf))
@test !isinteger(-elty(Inf))
@test !isinteger(elty(NaN))
end
end
@testset "ispow2 and iseven/isodd" begin
for T in (Float16,Float32,Float64,BigFloat)
for x in (0.25, 1.0, 4.0, exp2(T(exponent(floatmax(T)))), exp2(T(exponent(floatmin(T)))))
@test ispow2(T(x))
end
for x in (1.5, 0.0, 7.0, NaN, Inf)
@test !ispow2(T(x))
end
for x in (0, 134)
@test iseven(T(x)) && iseven(T(-x))
@test isodd(T(x+1)) && isodd(T(-x-1))
end
let x = maxintfloat(T) * π
@test iseven(x) && iseven(-x)
@test !isodd(x) && !isodd(-x)
end
@test !iseven(0.5) && !isodd(0.5)
end
end
@testset "round" begin
for elty in (Float32, Float64)
x = rand(elty)
A = fill(x,(10,10))
@test round.(A,RoundToZero) == fill(trunc(x),(10,10))
@test round.(A,RoundUp) == fill(ceil(x),(10,10))
@test round.(A,RoundDown) == fill(floor(x),(10,10))
A = fill(x,(10,10,10))
@test round.(A,RoundToZero) == fill(trunc(x),(10,10,10))
@test round.(A,RoundUp) == fill(ceil(x),(10,10,10))
@test round.(A,RoundDown) == fill(floor(x),(10,10,10))
for elty2 in (Int32,Int64)
A = fill(x,(10,))
@test round.(elty2,A,RoundToZero) == fill(trunc(elty2,x),(10,))
@test round.(elty2,A,RoundUp) == fill(ceil(elty2,x),(10,))
@test round.(elty2,A,RoundDown) == fill(floor(elty2,x),(10,))
A = fill(x,(10,10))
@test round.(elty2,A,RoundToZero) == fill(trunc(elty2,x),(10,10))
@test round.(elty2,A,RoundUp) == fill(ceil(elty2,x),(10,10))
@test round.(elty2,A,RoundDown) == fill(floor(elty2,x),(10,10))
A = fill(x,(10,10,10))
@test round.(elty2,A,RoundToZero) == fill(trunc(elty2,x),(10,10,10))
@test round.(elty2,A,RoundUp) == fill(ceil(elty2,x),(10,10,10))
@test round.(elty2,A,RoundDown) == fill(floor(elty2,x),(10,10,10))
@test round.(elty2,A) == fill(round(elty2,x),(10,10,10))
end
end
end
@testset "Types" begin
for x in (Int16(0), 1, 2f0, pi, 3//4, big(5//6), 7.8, big(9), big(ℯ))
@test float(typeof(x)) == typeof(float(x))
@test float(typeof(complex(x, x))) == typeof(float(complex(x, x)))
end
end
@testset "significant digits" begin
# (would be nice to have a smart vectorized
# version of signif)
@test round(123.456, sigdigits=1) ≈ 100.
@test round(123.456, sigdigits=3) ≈ 123.
@test round(123.456, sigdigits=5) ≈ 123.46
@test round(123.456, sigdigits=8, base = 2) ≈ 123.5
@test round(123.456, sigdigits=2, base = 4) ≈ 128.0
@test round(0.0, sigdigits=1) === 0.0
@test round(-0.0, sigdigits=1) === -0.0
@test round(1.2, sigdigits=2) === 1.2
@test round(1.0, sigdigits=6) === 1.0
@test round(0.6, sigdigits=1) === 0.6
@test round(7.262839104539736, sigdigits=2) === 7.3
@test isinf(round(Inf, sigdigits=3))
@test isnan(round(NaN, sigdigits=3))
@test round(1.12312, sigdigits=1000) === 1.12312
@test round(Float32(7.262839104539736), sigdigits=3) === Float32(7.26)
@test round(Float32(7.262839104539736), sigdigits=4) === Float32(7.263)
@test round(Float32(1.2), sigdigits=3) === Float32(1.2)
@test round(Float32(1.2), sigdigits=5) === Float32(1.2)
@test round(Float16(0.6), sigdigits=2) === Float16(0.6)
@test round(Float16(1.1), sigdigits=70) === Float16(1.1)
end
@testset "literal pow matches runtime pow matches optimized pow" begin
two = 2
@test 1.0000000105367122^2 == 1.0000000105367122^two
@test 1.0041504f0^2 == 1.0041504f0^two
function g2(start, two, N)
x = start
n = 0
for _ in 1:N
n += (x^2 !== x^two)
x = nextfloat(x)
end
return n
end
@test g2(1.0, 2, 100_000_000) == 0
@test g2(1.0f0, 2, 100_000_000) == 0
g2′(start, N) = g2(start, 2, N)
@test g2′(1.0, 100_000_000) == 0
@test g2′(1.0f0, 100_000_000) == 0
function g3(start, three, N)
x = start
n = 0
for _ in 1:N
n += (x^3 !== x^three)
x = nextfloat(x)
end
return n
end
@test g3(1.0, 3, 100_000_000) == 0
@test g3(1.0f0, 3, 100_000_000) == 0
g3′(start, N) = g3(start, 3, N)
@test g3′(1.0, 100_000_000) == 0
@test g3′(1.0f0, 100_000_000) == 0
function ginv(start, inv, N)
x = start
n = 0
for _ in 1:N
n += (x^-1 !== x^inv)
x = nextfloat(x)
end
return n
end
@test ginv(1.0, -1, 100_000_000) == 0
@test ginv(1.0f0, -1, 100_000_000) == 0
ginv′(start, N) = ginv(start, -1, N)
@test ginv′(1.0, 100_000_000) == 0
@test ginv′(1.0f0, 100_000_000) == 0
f(x, p) = x^p
finv(x) = f(x, -1)
f2(x) = f(x, 2)
f3(x) = f(x, 3)
x = 1.0000000105367122
@test x^2 == f(x, 2) == f2(x) == x*x == Float64(big(x)*big(x))
@test x^3 == f(x, 3) == f3(x) == x*x*x == Float64(big(x)*big(x)*big(x))
x = 1.000000007393669
@test x^-1 == f(x, -1) == finv(x) == 1/x == inv(x) == Float64(1/big(x)) == Float64(inv(big(x)))
end
@testset "curried approximation" begin
@test ≈(1.0; atol=1).(1.0:3.0) == [true, true, false]
end
@testset "isnan for Number" begin
struct CustomNumber <: Number end
@test !isnan(CustomNumber())
end