617 lines
25 KiB
Julia
617 lines
25 KiB
Julia
# This file is a part of Julia. License is MIT: https://julialang.org/license
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@testset "clamp" begin
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@test clamp(0, 1, 3) == 1
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@test clamp(1, 1, 3) == 1
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@test clamp(2, 1, 3) == 2
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@test clamp(3, 1, 3) == 3
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@test clamp(4, 1, 3) == 3
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@test clamp(0.0, 1, 3) == 1.0
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@test clamp(1.0, 1, 3) == 1.0
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@test clamp(2.0, 1, 3) == 2.0
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@test clamp(3.0, 1, 3) == 3.0
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@test clamp(4.0, 1, 3) == 3.0
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@test clamp.([0, 1, 2, 3, 4], 1.0, 3.0) == [1.0, 1.0, 2.0, 3.0, 3.0]
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@test clamp.([0 1; 2 3], 1.0, 3.0) == [1.0 1.0; 2.0 3.0]
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begin
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x = [0.0, 1.0, 2.0, 3.0, 4.0]
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clamp!(x, 1, 3)
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@test x == [1.0, 1.0, 2.0, 3.0, 3.0]
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end
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end
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@testset "constants" begin
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@test pi != e
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@test e != 1//2
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@test 1//2 <= e
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@test e <= 15//3
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@test big(1//2) < e
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@test e < big(20//6)
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@test e^pi == exp(pi)
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@test e^2 == exp(2)
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@test e^2.4 == exp(2.4)
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@test e^(2//3) == exp(2//3)
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@test Float16(3.0) < pi
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@test pi < Float16(4.0)
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@test contains(sprint(show,π),"3.14159")
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end
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@testset "frexp,ldexp,significand,exponent" begin
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@testset "$T" for T in (Float16,Float32,Float64)
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for z in (zero(T),-zero(T))
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frexp(z) === (z,0)
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significand(z) === z
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@test_throws DomainError exponent(z)
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end
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for (a,b) in [(T(12.8),T(0.8)),
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(prevfloat(realmin(T)), nextfloat(one(T),-2)),
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(nextfloat(zero(T),3), T(0.75)),
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(nextfloat(zero(T)), T(0.5))]
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n = Int(log2(a/b))
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@test frexp(a) == (b,n)
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@test ldexp(b,n) == a
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@test ldexp(a,-n) == b
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@test significand(a) == 2b
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@test exponent(a) == n-1
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@test frexp(-a) == (-b,n)
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@test ldexp(-b,n) == -a
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@test ldexp(-a,-n) == -b
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@test significand(-a) == -2b
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@test exponent(-a) == n-1
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end
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@test_throws DomainError exponent(convert(T,NaN))
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@test isnan(significand(convert(T,NaN)))
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x,y = frexp(convert(T,NaN))
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@test isnan(x)
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@test y == 0
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@testset "ldexp function" begin
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@test ldexp(T(0.0), 0) === T(0.0)
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@test ldexp(T(-0.0), 0) === T(-0.0)
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@test ldexp(T(Inf), 1) === T(Inf)
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@test ldexp(T(Inf), 10000) === T(Inf)
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@test ldexp(T(-Inf), 1) === T(-Inf)
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@test ldexp(T(NaN), 10) === T(NaN)
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@test ldexp(T(1.0), 0) === T(1.0)
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@test ldexp(T(0.8), 4) === T(12.8)
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@test ldexp(T(-0.854375), 5) === T(-27.34)
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@test ldexp(T(1.0), typemax(Int)) === T(Inf)
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@test ldexp(T(1.0), typemin(Int)) === T(0.0)
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@test ldexp(prevfloat(realmin(T)), typemax(Int)) === T(Inf)
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@test ldexp(prevfloat(realmin(T)), typemin(Int)) === T(0.0)
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@test ldexp(T(0.0), Int128(0)) === T(0.0)
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@test ldexp(T(-0.0), Int128(0)) === T(-0.0)
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@test ldexp(T(1.0), Int128(0)) === T(1.0)
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@test ldexp(T(0.8), Int128(4)) === T(12.8)
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@test ldexp(T(-0.854375), Int128(5)) === T(-27.34)
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@test ldexp(T(1.0), typemax(Int128)) === T(Inf)
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@test ldexp(T(1.0), typemin(Int128)) === T(0.0)
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@test ldexp(prevfloat(realmin(T)), typemax(Int128)) === T(Inf)
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@test ldexp(prevfloat(realmin(T)), typemin(Int128)) === T(0.0)
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@test ldexp(T(0.0), BigInt(0)) === T(0.0)
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@test ldexp(T(-0.0), BigInt(0)) === T(-0.0)
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@test ldexp(T(1.0), BigInt(0)) === T(1.0)
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@test ldexp(T(0.8), BigInt(4)) === T(12.8)
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@test ldexp(T(-0.854375), BigInt(5)) === T(-27.34)
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@test ldexp(T(1.0), BigInt(typemax(Int128))) === T(Inf)
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@test ldexp(T(1.0), BigInt(typemin(Int128))) === T(0.0)
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@test ldexp(prevfloat(realmin(T)), BigInt(typemax(Int128))) === T(Inf)
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@test ldexp(prevfloat(realmin(T)), BigInt(typemin(Int128))) === T(0.0)
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# Test also against BigFloat reference. Needs to be exactly rounded.
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@test ldexp(realmin(T), -1) == T(ldexp(big(realmin(T)), -1))
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@test ldexp(realmin(T), -2) == T(ldexp(big(realmin(T)), -2))
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@test ldexp(realmin(T)/2, 0) == T(ldexp(big(realmin(T)/2), 0))
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@test ldexp(realmin(T)/3, 0) == T(ldexp(big(realmin(T)/3), 0))
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@test ldexp(realmin(T)/3, -1) == T(ldexp(big(realmin(T)/3), -1))
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@test ldexp(realmin(T)/3, 11) == T(ldexp(big(realmin(T)/3), 11))
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@test ldexp(realmin(T)/11, -10) == T(ldexp(big(realmin(T)/11), -10))
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@test ldexp(-realmin(T)/11, -10) == T(ldexp(big(-realmin(T)/11), -10))
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end
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end
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end
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# We compare to BigFloat instead of hard-coding
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# values, assuming that BigFloat has an independently tested implementation.
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@testset "basic math functions" begin
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@testset "$T" for T in (Float32, Float64)
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x = T(1//3)
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y = T(1//2)
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yi = 4
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@testset "Random values" begin
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@test x^y ≈ big(x)^big(y)
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@test x^1 === x
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@test x^yi ≈ big(x)^yi
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@test acos(x) ≈ acos(big(x))
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@test acosh(1+x) ≈ acosh(big(1+x))
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@test asin(x) ≈ asin(big(x))
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@test asinh(x) ≈ asinh(big(x))
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@test atan(x) ≈ atan(big(x))
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@test atan2(x,y) ≈ atan2(big(x),big(y))
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@test atanh(x) ≈ atanh(big(x))
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@test cbrt(x) ≈ cbrt(big(x))
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@test cos(x) ≈ cos(big(x))
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@test cosh(x) ≈ cosh(big(x))
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@test exp(x) ≈ exp(big(x))
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@test exp10(x) ≈ exp10(big(x))
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@test exp2(x) ≈ exp2(big(x))
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@test expm1(x) ≈ expm1(big(x))
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@test hypot(x,y) ≈ hypot(big(x),big(y))
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@test hypot(x,x,y) ≈ hypot(hypot(big(x),big(x)),big(y))
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@test hypot(x,x,y,y) ≈ hypot(hypot(big(x),big(x)),hypot(big(y),big(y)))
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@test log(x) ≈ log(big(x))
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@test log10(x) ≈ log10(big(x))
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@test log1p(x) ≈ log1p(big(x))
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@test log2(x) ≈ log2(big(x))
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@test sin(x) ≈ sin(big(x))
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@test sinh(x) ≈ sinh(big(x))
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@test sqrt(x) ≈ sqrt(big(x))
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@test tan(x) ≈ tan(big(x))
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@test tanh(x) ≈ tanh(big(x))
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end
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@testset "Special values" begin
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@test isequal(T(1//4)^T(1//2), T(1//2))
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@test isequal(T(1//4)^2, T(1//16))
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@test isequal(acos(T(1)), T(0))
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@test isequal(acosh(T(1)), T(0))
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@test asin(T(1)) ≈ T(pi)/2 atol=eps(T)
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@test atan(T(1)) ≈ T(pi)/4 atol=eps(T)
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@test atan2(T(1),T(1)) ≈ T(pi)/4 atol=eps(T)
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@test isequal(cbrt(T(0)), T(0))
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@test isequal(cbrt(T(1)), T(1))
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@test isequal(cbrt(T(1000000000)), T(1000))
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@test isequal(cos(T(0)), T(1))
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@test cos(T(pi)/2) ≈ T(0) atol=eps(T)
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@test isequal(cos(T(pi)), T(-1))
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@test exp(T(1)) ≈ T(e) atol=10*eps(T)
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@test isequal(exp10(T(1)), T(10))
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@test isequal(exp2(T(1)), T(2))
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@test isequal(expm1(T(0)), T(0))
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@test expm1(T(1)) ≈ T(e)-1 atol=10*eps(T)
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@test isequal(hypot(T(3),T(4)), T(5))
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@test isequal(log(T(1)), T(0))
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@test isequal(log(e,T(1)), T(0))
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@test log(T(e)) ≈ T(1) atol=eps(T)
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@test isequal(log10(T(1)), T(0))
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@test isequal(log10(T(10)), T(1))
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@test isequal(log1p(T(0)), T(0))
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@test log1p(T(e)-1) ≈ T(1) atol=eps(T)
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@test isequal(log2(T(1)), T(0))
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@test isequal(log2(T(2)), T(1))
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@test isequal(sin(T(0)), T(0))
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@test isequal(sin(T(pi)/2), T(1))
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@test sin(T(pi)) ≈ T(0) atol=eps(T)
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@test isequal(sqrt(T(0)), T(0))
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@test isequal(sqrt(T(1)), T(1))
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@test isequal(sqrt(T(100000000)), T(10000))
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@test isequal(tan(T(0)), T(0))
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@test tan(T(pi)/4) ≈ T(1) atol=eps(T)
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end
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@testset "Inverses" begin
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@test acos(cos(x)) ≈ x
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@test acosh(cosh(x)) ≈ x
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@test asin(sin(x)) ≈ x
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@test cbrt(x)^3 ≈ x
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@test cbrt(x^3) ≈ x
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@test asinh(sinh(x)) ≈ x
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@test atan(tan(x)) ≈ x
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@test atan2(x,y) ≈ atan(x/y)
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@test atanh(tanh(x)) ≈ x
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@test cos(acos(x)) ≈ x
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@test cosh(acosh(1+x)) ≈ 1+x
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@test exp(log(x)) ≈ x
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@test exp10(log10(x)) ≈ x
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@test exp2(log2(x)) ≈ x
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@test expm1(log1p(x)) ≈ x
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@test log(exp(x)) ≈ x
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@test log10(exp10(x)) ≈ x
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@test log1p(expm1(x)) ≈ x
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@test log2(exp2(x)) ≈ x
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@test sin(asin(x)) ≈ x
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@test sinh(asinh(x)) ≈ x
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@test sqrt(x)^2 ≈ x
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@test sqrt(x^2) ≈ x
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@test tan(atan(x)) ≈ x
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@test tanh(atanh(x)) ≈ x
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end
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@testset "Relations between functions" begin
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@test cosh(x) ≈ (exp(x)+exp(-x))/2
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@test cosh(x)^2-sinh(x)^2 ≈ 1
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@test hypot(x,y) ≈ sqrt(x^2+y^2)
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@test sin(x)^2+cos(x)^2 ≈ 1
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@test sinh(x) ≈ (exp(x)-exp(-x))/2
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@test tan(x) ≈ sin(x)/cos(x)
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@test tanh(x) ≈ sinh(x)/cosh(x)
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end
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@testset "Edge cases" begin
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@test isinf(log(zero(T)))
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@test isnan(log(convert(T,NaN)))
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@test_throws DomainError log(-one(T))
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@test isinf(log1p(-one(T)))
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@test isnan(log1p(convert(T,NaN)))
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@test_throws DomainError log1p(convert(T,-2.0))
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@test hypot(T(0), T(0)) === T(0)
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@test hypot(T(Inf), T(Inf)) === T(Inf)
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@test hypot(T(Inf), T(x)) === T(Inf)
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@test hypot(T(Inf), T(NaN)) === T(Inf)
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@test isnan(hypot(T(x), T(NaN)))
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end
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end
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end
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@test exp10(5) ≈ exp10(5.0)
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@test exp10(50//10) ≈ exp10(5.0)
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@test log10(exp10(e)) ≈ e
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@test exp2(Float16(2.)) ≈ exp2(2.)
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@test log(e) == 1
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@testset "exp function" for T in (Float64, Float32)
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@testset "$T accuracy" begin
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X = map(T, vcat(-10:0.0002:10, -80:0.001:80, 2.0^-27, 2.0^-28, 2.0^-14, 2.0^-13))
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for x in X
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y, yb = exp(x), exp(big(x))
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@test abs(y-yb) <= 1.0*eps(T(yb))
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end
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end
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@testset "$T edge cases" begin
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@test isnan(exp(T(NaN)))
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@test exp(T(-Inf)) === T(0.0)
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@test exp(T(Inf)) === T(Inf)
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@test exp(T(0.0)) === T(1.0) # exact
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@test exp(T(5000.0)) === T(Inf)
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@test exp(T(-5000.0)) === T(0.0)
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end
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end
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@testset "test abstractarray trig fxns" begin
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TAA = rand(2,2)
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TAA = (TAA + TAA.')/2.
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STAA = Symmetric(TAA)
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@test full(atanh.(STAA)) == atanh.(TAA)
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@test full(asinh.(STAA)) == asinh.(TAA)
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@test full(acosh.(STAA+Symmetric(ones(TAA)))) == acosh.(TAA+ones(TAA))
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@test full(acsch.(STAA+Symmetric(ones(TAA)))) == acsch.(TAA+ones(TAA))
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@test full(acoth.(STAA+Symmetric(ones(TAA)))) == acoth.(TAA+ones(TAA))
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end
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@testset "check exp2(::Integer) matches exp2(::Float)" begin
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for ii in -2048:2048
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expected = exp2(float(ii))
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@test exp2(Int16(ii)) == expected
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@test exp2(Int32(ii)) == expected
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@test exp2(Int64(ii)) == expected
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@test exp2(Int128(ii)) == expected
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if ii >= 0
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@test exp2(UInt16(ii)) == expected
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@test exp2(UInt32(ii)) == expected
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@test exp2(UInt64(ii)) == expected
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@test exp2(UInt128(ii)) == expected
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end
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end
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end
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@testset "deg2rad/rad2deg" begin
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@testset "$T" for T in (Int, Float64, BigFloat)
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@test deg2rad(T(180)) ≈ 1pi
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@test deg2rad.(T[45, 60]) ≈ [pi/T(4), pi/T(3)]
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@test rad2deg.([pi/T(4), pi/T(3)]) ≈ [45, 60]
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@test rad2deg(T(1)*pi) ≈ 180
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@test rad2deg(T(1)) ≈ rad2deg(true)
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@test deg2rad(T(1)) ≈ deg2rad(true)
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end
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end
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@testset "degree-based trig functions" begin
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@testset "$T" for T = (Float32,Float64,Rational{Int})
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fT = typeof(float(one(T)))
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for x = -400:40:400
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@test sind(convert(T,x))::fT ≈ convert(fT,sin(pi/180*x)) atol=eps(deg2rad(convert(fT,x)))
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@test cosd(convert(T,x))::fT ≈ convert(fT,cos(pi/180*x)) atol=eps(deg2rad(convert(fT,x)))
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end
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@testset "sind" begin
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@test sind(convert(T,0.0))::fT === zero(fT)
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@test sind(convert(T,180.0))::fT === zero(fT)
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@test sind(convert(T,360.0))::fT === zero(fT)
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T != Rational{Int} && @test sind(convert(T,-0.0))::fT === -zero(fT)
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@test sind(convert(T,-180.0))::fT === -zero(fT)
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@test sind(convert(T,-360.0))::fT === -zero(fT)
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end
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@testset "cosd" begin
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@test cosd(convert(T,90))::fT === zero(fT)
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@test cosd(convert(T,270))::fT === zero(fT)
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@test cosd(convert(T,-90))::fT === zero(fT)
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@test cosd(convert(T,-270))::fT === zero(fT)
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end
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@testset "sinpi and cospi" begin
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for x = -3:0.3:3
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@test sinpi(convert(T,x))::fT ≈ convert(fT,sin(pi*x)) atol=eps(pi*convert(fT,x))
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@test cospi(convert(T,x))::fT ≈ convert(fT,cos(pi*x)) atol=eps(pi*convert(fT,x))
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end
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@test sinpi(convert(T,0.0))::fT === zero(fT)
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@test sinpi(convert(T,1.0))::fT === zero(fT)
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@test sinpi(convert(T,2.0))::fT === zero(fT)
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T != Rational{Int} && @test sinpi(convert(T,-0.0))::fT === -zero(fT)
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@test sinpi(convert(T,-1.0))::fT === -zero(fT)
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@test sinpi(convert(T,-2.0))::fT === -zero(fT)
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@test_throws DomainError sinpi(convert(T,Inf))
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@test cospi(convert(T,0.5))::fT === zero(fT)
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@test cospi(convert(T,1.5))::fT === zero(fT)
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@test cospi(convert(T,-0.5))::fT === zero(fT)
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@test cospi(convert(T,-1.5))::fT === zero(fT)
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@test_throws DomainError cospi(convert(T,Inf))
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end
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@testset "Check exact values" begin
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@test sind(convert(T,30)) == 0.5
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@test cosd(convert(T,60)) == 0.5
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@test sind(convert(T,150)) == 0.5
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@test sinpi(one(T)/convert(T,6)) == 0.5
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@test_throws DomainError sind(convert(T,Inf))
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@test_throws DomainError cosd(convert(T,Inf))
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T != Float32 && @test cospi(one(T)/convert(T,3)) == 0.5
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T == Rational{Int} && @test sinpi(5//6) == 0.5
|
|
end
|
|
end
|
|
end
|
|
|
|
@testset "Integer args to sinpi/cospi/sinc/cosc" begin
|
|
@test sinpi(1) == 0
|
|
@test sinpi(-1) == -0
|
|
@test cospi(1) == -1
|
|
@test cospi(2) == 1
|
|
|
|
@test sinc(1) == 0
|
|
@test sinc(complex(1,0)) == 0
|
|
@test sinc(0) == 1
|
|
@test sinc(Inf) == 0
|
|
@test cosc(1) == -1
|
|
@test cosc(0) == 0
|
|
@test cosc(complex(1,0)) == -1
|
|
@test cosc(Inf) == 0
|
|
end
|
|
|
|
@testset "trig function type stability" begin
|
|
@testset "$T $f" for T = (Float32,Float64,BigFloat), f = (sind,cosd,sinpi,cospi)
|
|
@test Base.return_types(f,Tuple{T}) == [T]
|
|
end
|
|
end
|
|
|
|
@testset "beta, lbeta" begin
|
|
@test beta(3/2,7/2) ≈ 5π/128
|
|
@test beta(3,5) ≈ 1/105
|
|
@test lbeta(5,4) ≈ log(beta(5,4))
|
|
@test beta(5,4) ≈ beta(4,5)
|
|
@test beta(-1/2, 3) ≈ beta(-1/2 + 0im, 3 + 0im) ≈ -16/3
|
|
@test lbeta(-1/2, 3) ≈ log(16/3)
|
|
@test beta(Float32(5),Float32(4)) == beta(Float32(4),Float32(5))
|
|
@test beta(3,5) ≈ beta(3+0im,5+0im)
|
|
@test(beta(3.2+0.1im,5.3+0.3im) ≈ exp(lbeta(3.2+0.1im,5.3+0.3im)) ≈
|
|
0.00634645247782269506319336871208405439180447035257028310080 -
|
|
0.00169495384841964531409376316336552555952269360134349446910im)
|
|
end
|
|
|
|
# useful test functions for relative error, which differ from isapprox (≈)
|
|
# in that relerrc separately looks at the real and imaginary parts
|
|
relerr(z, x) = z == x ? 0.0 : abs(z - x) / abs(x)
|
|
relerrc(z, x) = max(relerr(real(z),real(x)), relerr(imag(z),imag(x)))
|
|
≅(a,b) = relerrc(a,b) ≤ 1e-13
|
|
|
|
@testset "gamma and friends" begin
|
|
@testset "gamma, lgamma (complex argument)" begin
|
|
if Base.Math.libm == "libopenlibm"
|
|
@test gamma.(Float64[1:25;]) == gamma.(1:25)
|
|
else
|
|
@test gamma.(Float64[1:25;]) ≈ gamma.(1:25)
|
|
end
|
|
for elty in (Float32, Float64)
|
|
@test gamma(convert(elty,1/2)) ≈ convert(elty,sqrt(π))
|
|
@test gamma(convert(elty,-1/2)) ≈ convert(elty,-2sqrt(π))
|
|
@test lgamma(convert(elty,-1/2)) ≈ convert(elty,log(abs(gamma(-1/2))))
|
|
end
|
|
@test lgamma(1.4+3.7im) ≈ -3.7094025330996841898 + 2.4568090502768651184im
|
|
@test lgamma(1.4+3.7im) ≈ log(gamma(1.4+3.7im))
|
|
@test lgamma(-4.2+0im) ≈ lgamma(-4.2)-5pi*im
|
|
@test factorial(3.0) == gamma(4.0) == factorial(3)
|
|
for x in (3.2, 2+1im, 3//2, 3.2+0.1im)
|
|
@test factorial(x) == gamma(1+x)
|
|
end
|
|
@test lfact(0) == lfact(1) == 0
|
|
@test lfact(2) == lgamma(3)
|
|
# Ensure that the domain of lfact matches that of factorial (issue #21318)
|
|
@test_throws DomainError lfact(-3)
|
|
@test_throws MethodError lfact(1.0)
|
|
end
|
|
|
|
# lgamma test cases (from Wolfram Alpha)
|
|
@test lgamma(-300im) ≅ -473.17185074259241355733179182866544204963885920016823743 - 1410.3490664555822107569308046418321236643870840962522425im
|
|
@test lgamma(3.099) ≅ lgamma(3.099+0im) ≅ 0.786413746900558058720665860178923603134125854451168869796
|
|
@test lgamma(1.15) ≅ lgamma(1.15+0im) ≅ -0.06930620867104688224241731415650307100375642207340564554
|
|
@test lgamma(0.89) ≅ lgamma(0.89+0im) ≅ 0.074022173958081423702265889979810658434235008344573396963
|
|
@test lgamma(0.91) ≅ lgamma(0.91+0im) ≅ 0.058922567623832379298241751183907077883592982094770449167
|
|
@test lgamma(0.01) ≅ lgamma(0.01+0im) ≅ 4.599479878042021722513945411008748087261001413385289652419
|
|
@test lgamma(-3.4-0.1im) ≅ -1.1733353322064779481049088558918957440847715003659143454 + 12.331465501247826842875586104415980094316268974671819281im
|
|
@test lgamma(-13.4-0.1im) ≅ -22.457344044212827625152500315875095825738672314550695161 + 43.620560075982291551250251193743725687019009911713182478im
|
|
@test lgamma(-13.4+0.0im) ≅ conj(lgamma(-13.4-0.0im)) ≅ -22.404285036964892794140985332811433245813398559439824988 - 43.982297150257105338477007365913040378760371591251481493im
|
|
@test lgamma(-13.4+8im) ≅ -44.705388949497032519400131077242200763386790107166126534 - 22.208139404160647265446701539526205774669649081807864194im
|
|
@test lgamma(1+exp2(-20)) ≅ lgamma(1+exp2(-20)+0im) ≅ -5.504750066148866790922434423491111098144565651836914e-7
|
|
@test lgamma(1+exp2(-20)+exp2(-19)*im) ≅ -5.5047799872835333673947171235997541985495018556426e-7 - 1.1009485171695646421931605642091915847546979851020e-6im
|
|
@test lgamma(-300+2im) ≅ -1419.3444991797240659656205813341478289311980525970715668 - 932.63768120761873747896802932133229201676713644684614785im
|
|
@test lgamma(300+2im) ≅ 1409.19538972991765122115558155209493891138852121159064304 + 11.4042446282102624499071633666567192538600478241492492652im
|
|
@test lgamma(1-6im) ≅ -7.6099596929506794519956058191621517065972094186427056304 - 5.5220531255147242228831899544009162055434670861483084103im
|
|
@test lgamma(1-8im) ≅ -10.607711310314582247944321662794330955531402815576140186 - 9.4105083803116077524365029286332222345505790217656796587im
|
|
@test lgamma(1+6.5im) ≅ conj(lgamma(1-6.5im)) ≅ -8.3553365025113595689887497963634069303427790125048113307 + 6.4392816159759833948112929018407660263228036491479825744im
|
|
@test lgamma(1+1im) ≅ conj(lgamma(1-1im)) ≅ -0.6509231993018563388852168315039476650655087571397225919 - 0.3016403204675331978875316577968965406598997739437652369im
|
|
@test lgamma(-pi*1e7 + 6im) ≅ -5.10911758892505772903279926621085326635236850347591e8 - 9.86959420047365966439199219724905597399295814979993e7im
|
|
@test lgamma(-pi*1e7 + 8im) ≅ -5.10911765175690634449032797392631749405282045412624e8 - 9.86959074790854911974415722927761900209557190058925e7im
|
|
@test lgamma(-pi*1e14 + 6im) ≅ -1.0172766411995621854526383224252727000270225301426e16 - 9.8696044010873714715264929863618267642124589569347e14im
|
|
@test lgamma(-pi*1e14 + 8im) ≅ -1.0172766411995628137711690403794640541491261237341e16 - 9.8696044010867038531027376655349878694397362250037e14im
|
|
@test lgamma(2.05 + 0.03im) ≅ conj(lgamma(2.05 - 0.03im)) ≅ 0.02165570938532611215664861849215838847758074239924127515 + 0.01363779084533034509857648574107935425251657080676603919im
|
|
@test lgamma(2+exp2(-20)+exp2(-19)*im) ≅ 4.03197681916768997727833554471414212058404726357753e-7 + 8.06398296652953575754782349984315518297283664869951e-7im
|
|
|
|
@testset "lgamma for non-finite arguments" begin
|
|
@test lgamma(Inf + 0im) === Inf + 0im
|
|
@test lgamma(Inf - 0.0im) === Inf - 0.0im
|
|
@test lgamma(Inf + 1im) === Inf + Inf*im
|
|
@test lgamma(Inf - 1im) === Inf - Inf*im
|
|
@test lgamma(-Inf + 0.0im) === -Inf - Inf*im
|
|
@test lgamma(-Inf - 0.0im) === -Inf + Inf*im
|
|
@test lgamma(Inf*im) === -Inf + Inf*im
|
|
@test lgamma(-Inf*im) === -Inf - Inf*im
|
|
@test lgamma(Inf + Inf*im) === lgamma(NaN + 0im) === lgamma(NaN*im) === NaN + NaN*im
|
|
end
|
|
end
|
|
|
|
@testset "subnormal flags" begin
|
|
# Ensure subnormal flags functions don't segfault
|
|
@test any(set_zero_subnormals(true) .== [false,true])
|
|
@test any(get_zero_subnormals() .== [false,true])
|
|
@test set_zero_subnormals(false)
|
|
@test !get_zero_subnormals()
|
|
end
|
|
|
|
@testset "evalpoly" begin
|
|
@test @evalpoly(2,3,4,5,6) == 3+2*(4+2*(5+2*6)) == @evalpoly(2+0im,3,4,5,6)
|
|
@test let evalcounts=0
|
|
@evalpoly(begin
|
|
evalcounts += 1
|
|
4
|
|
end, 1,2,3,4,5)
|
|
evalcounts
|
|
end == 1
|
|
a0 = 1
|
|
a1 = 2
|
|
c = 3
|
|
@test @evalpoly(c, a0, a1) == 7
|
|
end
|
|
|
|
@testset "cis" begin
|
|
for z in (1.234, 1.234 + 5.678im)
|
|
@test cis(z) ≈ exp(im*z)
|
|
end
|
|
let z = [1.234, 5.678]
|
|
@test cis.(z) ≈ exp.(im*z)
|
|
end
|
|
end
|
|
|
|
@testset "modf" begin
|
|
@testset "$elty" for elty in (Float16, Float32, Float64)
|
|
@test modf( convert(elty,1.2) )[1] ≈ convert(elty,0.2)
|
|
@test modf( convert(elty,1.2) )[2] ≈ convert(elty,1.0)
|
|
@test modf( convert(elty,1.0) )[1] ≈ convert(elty,0.0)
|
|
@test modf( convert(elty,1.0) )[2] ≈ convert(elty,1.0)
|
|
end
|
|
end
|
|
|
|
@testset "frexp" begin
|
|
@testset "$elty" for elty in (Float16, Float32, Float64)
|
|
@test frexp( convert(elty,0.5) ) == (0.5, 0)
|
|
@test frexp( convert(elty,4.0) ) == (0.5, 3)
|
|
@test frexp( convert(elty,10.5) ) == (0.65625, 4)
|
|
end
|
|
end
|
|
|
|
@testset "log/log1p" begin
|
|
# if using Tang's algorithm, should be accurate to within 0.56 ulps
|
|
X = rand(100)
|
|
for x in X
|
|
for n = -5:5
|
|
xn = ldexp(x,n)
|
|
|
|
for T in (Float32,Float64)
|
|
xt = T(x)
|
|
|
|
y = Base.Math.JuliaLibm.log(xt)
|
|
yb = log(big(xt))
|
|
@test abs(y-yb) <= 0.56*eps(T(yb))
|
|
|
|
y = Base.Math.JuliaLibm.log1p(xt)
|
|
yb = log1p(big(xt))
|
|
@test abs(y-yb) <= 0.56*eps(T(yb))
|
|
|
|
if n <= 0
|
|
y = Base.Math.JuliaLibm.log1p(-xt)
|
|
yb = log1p(big(-xt))
|
|
@test abs(y-yb) <= 0.56*eps(T(yb))
|
|
end
|
|
end
|
|
end
|
|
end
|
|
|
|
for n = 0:28
|
|
@test log(2,2^n) == n
|
|
end
|
|
setprecision(10_000) do
|
|
@test log(2,big(2)^100) == 100
|
|
@test log(2,big(2)^200) == 200
|
|
@test log(2,big(2)^300) == 300
|
|
@test log(2,big(2)^400) == 400
|
|
end
|
|
|
|
for T in (Float32,Float64)
|
|
@test log(zero(T)) == -Inf
|
|
@test isnan(log(NaN))
|
|
@test_throws DomainError log(-one(T))
|
|
@test log1p(-one(T)) == -Inf
|
|
@test isnan(log1p(NaN))
|
|
@test_throws DomainError log1p(-2*one(T))
|
|
end
|
|
end
|
|
|
|
@testset "vectorization of 2-arg functions" begin
|
|
binary_math_functions = [
|
|
copysign, flipsign, log, atan2, hypot, max, min,
|
|
beta, lbeta,
|
|
]
|
|
@testset "$f" for f in binary_math_functions
|
|
x = y = 2
|
|
v = [f(x,y)]
|
|
@test f.([x],y) == v
|
|
@test f.(x,[y]) == v
|
|
@test f.([x],[y]) == v
|
|
end
|
|
end
|
|
|
|
@testset "issues #3024, #12822" begin
|
|
@test_throws DomainError 2 ^ -2
|
|
@test_throws DomainError (-2)^(2.2)
|
|
@test_throws DomainError (-2.0)^(2.2)
|
|
@test_throws DomainError false ^ -2
|
|
@test 1 ^ -2 === (-1) ^ -2 === 1
|
|
@test (-1) ^ -3 === -1
|
|
@test true ^ -2 === true
|
|
end
|
|
|
|
@testset "issue #13748" begin
|
|
let A = [1 2; 3 4]; B = [5 6; 7 8]; C = [9 10; 11 12]
|
|
@test muladd(A,B,C) == A*B + C
|
|
end
|
|
end
|
|
|
|
@testset "issue #19872" begin
|
|
f19872a(x) = x ^ 5
|
|
f19872b(x) = x ^ (-1024)
|
|
@test 0 < f19872b(2.0) < 1e-300
|
|
@test issubnormal(2.0 ^ (-1024))
|
|
@test issubnormal(f19872b(2.0))
|
|
@test !issubnormal(f19872b(0.0))
|
|
@test f19872a(2.0) === 32.0
|
|
@test !issubnormal(f19872a(2.0))
|
|
@test !issubnormal(0.0)
|
|
end
|
|
|
|
# no domain error is thrown for negative values
|
|
@test invoke(cbrt, Tuple{AbstractFloat}, -1.0) == -1.0
|
|
|
|
@testset "promote Float16 irrational #15359" begin
|
|
@test typeof(Float16(.5) * pi) == Float16
|
|
end
|