210 lines
7.1 KiB
Julia
210 lines
7.1 KiB
Julia
# This file is a part of Julia. License is MIT: https://julialang.org/license
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# fast math
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# check expansions
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@test macroexpand(:(@fastmath 1+2)) == :(Base.FastMath.add_fast(1,2))
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@test macroexpand(:(@fastmath +)) == :(Base.FastMath.add_fast)
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@test macroexpand(:(@fastmath min(1))) == :(Base.FastMath.min_fast(1))
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@test macroexpand(:(@fastmath min)) == :(Base.FastMath.min_fast)
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@test macroexpand(:(@fastmath x.min)) == :(x.min)
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# basic arithmetic
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const one32 = one(Float32)
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const eps32 = eps(Float32)
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const eps32_2 = eps32/2
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# Note: Cannot use local functions since these are not yet optimized
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fm_ieee_32(x) = x + eps32_2 + eps32_2
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fm_fast_32(x) = @fastmath x + eps32_2 + eps32_2
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@test fm_ieee_32(one32) == one32
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@test (fm_fast_32(one32) == one32 ||
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fm_fast_32(one32) == one32 + eps32 > one32)
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const one64 = one(Float64)
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const eps64 = eps(Float64)
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const eps64_2 = eps64/2
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# Note: Cannot use local functions since these are not yet optimized
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fm_ieee_64(x) = x + eps64_2 + eps64_2
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fm_fast_64(x) = @fastmath x + eps64_2 + eps64_2
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@test fm_ieee_64(one64) == one64
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@test (fm_fast_64(one64) == one64 ||
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fm_fast_64(one64) == one64 + eps64 > one64)
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# check updating operators
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fm_ieee_64_upd(x) = (r=x; r+=eps64_2; r+=eps64_2)
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fm_fast_64_upd(x) = @fastmath (r=x; r+=eps64_2; r+=eps64_2)
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@test fm_ieee_64_upd(one64) == one64
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@test (fm_fast_64_upd(one64) == one64 ||
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fm_fast_64_upd(one64) == one64 + eps64 > one64)
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let epsf = 1.0f0/2^15, one_epsf = 1+epsf
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@test @fastmath(one_epsf * one_epsf - 1) ≈ Float32(65537/1073741824)
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end
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let eps = 1.0/2^30, one_eps = 1+eps
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@test @fastmath(one_eps * one_eps - 1) ≈ 2147483649/1152921504606846976
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end
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for T in (Float32, Float64, BigFloat)
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zero = convert(T, 0)
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one = convert(T, 1) + eps(T)
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two = convert(T, 2) + 1//10
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three = convert(T, 3) + 1//100
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@test @fastmath(+two) ≈ +two
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@test @fastmath(-two) ≈ -two
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@test @fastmath(zero+one+two) ≈ zero+one+two
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@test @fastmath(zero-one-two) ≈ zero-one-two
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@test @fastmath(one*two*three) ≈ one*two*three
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@test @fastmath(one/two/three) ≈ one/two/three
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@test @fastmath(rem(two,three)) ≈ rem(two,three)
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@test @fastmath(mod(two,three)) ≈ mod(two,three)
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@test @fastmath(cmp(two,two)) == cmp(two,two)
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@test @fastmath(cmp(two,three)) == cmp(two,three)
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@test @fastmath(cmp(three,two)) == cmp(three,two)
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@test @fastmath(one/zero) == convert(T,Inf)
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@test @fastmath(-one/zero) == -convert(T,Inf)
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@test isnan(@fastmath(zero/zero)) # must not throw
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for x in (zero, two, convert(T, Inf), convert(T, NaN))
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@test @fastmath(isfinite(x))
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@test !@fastmath(isinf(x))
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@test !@fastmath(isnan(x))
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@test !@fastmath(issubnormal(x))
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end
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end
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for T in (Complex64, Complex128, Complex{BigFloat})
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zero = convert(T,0)
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one = convert(T,1) + im*eps(real(convert(T,1)))
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two = convert(T,2) + im//10
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three = convert(T,3) + im//100
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@test @fastmath(+two) ≈ +two
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@test @fastmath(-two) ≈ -two
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@test @fastmath(zero+one+two) ≈ zero+one+two
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@test @fastmath(zero-one-two) ≈ zero-one-two
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@test @fastmath(one*two*three) ≈ one*two*three
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@test @fastmath(one/two/three) ≈ one/two/three
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@test @fastmath(three == two) == (three == two)
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@test @fastmath(three != two) == (three != two)
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@test isnan(@fastmath(one/zero)) # must not throw
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@test isnan(@fastmath(-one/zero)) # must not throw
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@test isnan(@fastmath(zero/zero)) # must not throw
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for x in (zero, two, convert(T, Inf), convert(T, NaN))
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@test @fastmath(isfinite(x))
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@test !@fastmath(isinf(x))
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@test !@fastmath(isnan(x))
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@test !@fastmath(issubnormal(x))
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end
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end
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# math functions
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# real arithmetic
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for T in (Float32, Float64, BigFloat)
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half = 1/convert(T,2)
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third = 1/convert(T,3)
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for f in (:+, :-, :abs, :abs2, :conj, :inv, :sign,
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:acos, :asin, :asinh, :atan, :atanh, :cbrt, :cos, :cosh,
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:exp10, :exp2, :exp, :expm1, :lgamma, :log10, :log1p,
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:log2, :log, :sin, :sinh, :sqrt, :tan, :tanh)
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@eval begin
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@test @fastmath($f($half)) ≈ $f($half)
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@test @fastmath($f($third)) ≈ $f($third)
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end
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end
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for f in (:acosh,)
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@eval begin
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@test @fastmath($f(1+$half)) ≈ $f(1+$half)
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@test @fastmath($f(1+$third)) ≈ $f(1+$third)
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end
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end
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for f in (:+, :-, :*, :/, :%, :(==), :!=, :<, :<=, :>, :>=, :^,
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:atan2, :hypot, :max, :min)
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@eval begin
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@test @fastmath($f($half, $third)) ≈ $f($half, $third)
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@test @fastmath($f($third, $half)) ≈ $f($third, $half)
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end
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end
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for f in (:minmax,)
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@eval begin
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@test @fastmath($f($half, $third)[1]) ≈ $f($half, $third)[1]
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@test @fastmath($f($half, $third)[2]) ≈ $f($half, $third)[2]
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@test @fastmath($f($third, $half)[1]) ≈ $f($third, $half)[1]
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@test @fastmath($f($third, $half)[2]) ≈ $f($third, $half)[2]
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end
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end
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end
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# complex arithmetic
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for T in (Complex64, Complex128, Complex{BigFloat})
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half = (1+1im)/T(2)
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third = (1-1im)/T(3)
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# some of these functions promote their result to double
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# precision, but we want to check equality at precision T
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rtol = Base.rtoldefault(real(T))
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for f in (:+, :-, :abs, :abs2, :conj, :inv, :sign,
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:acos, :acosh, :asin, :asinh, :atan, :atanh, :cis, :cos,
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:cosh, :exp10, :exp2, :exp, :expm1, :log10, :log1p,
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:log2, :log, :sin, :sinh, :sqrt, :tan, :tanh)
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@eval begin
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@test @fastmath($f($half)) ≈ $f($half) rtol=$rtol
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@test @fastmath($f($third)) ≈ $f($third) rtol=$rtol
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end
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end
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for f in (:+, :-, :*, :/, :(==), :!=, :^)
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@eval begin
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@test @fastmath($f($half, $third)) ≈ $f($half, $third) rtol=$rtol
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@test @fastmath($f($third, $half)) ≈ $f($third, $half) rtol=$rtol
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end
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end
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end
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# mixed real/complex arithmetic
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for T in (Float32, Float64, BigFloat)
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CT = Complex{T}
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half = 1/T(2)
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third = 1/T(3)
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chalf = (1+1im)/CT(2)
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cthird = (1-1im)/CT(3)
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for f in (:+, :-, :*, :/, :(==), :!=, :^)
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@eval begin
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@test @fastmath($f($chalf, $third)) ≈ $f($chalf, $third)
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@test @fastmath($f($half, $cthird)) ≈ $f($half, $cthird)
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@test @fastmath($f($cthird, $half)) ≈ $f($cthird, $half)
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@test @fastmath($f($third, $chalf)) ≈ $f($third, $chalf)
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end
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end
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@test @fastmath(third^3) ≈ third^3
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@test @fastmath(chalf/third) ≈ chalf/third
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@test @fastmath(chalf^3) ≈ chalf^3
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@test @fastmath(cis(third)) ≈ cis(third)
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end
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# issue #10544
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let a = ones(2,2), b = ones(2,2)
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@test @fastmath(a[1] += 2.0) ≈ (b[1] += 2.0)
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@test @fastmath(a[2] -= 2.0) ≈ (b[2] -= 2.0)
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@test @fastmath(a[1,1] *= 2.0) ≈ (b[1,1] *= 2.0)
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@test @fastmath(a[2,2] /= 2.0) ≈ (b[2,2] /= 2.0)
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@test @fastmath(a[1,2] ^= 2.0) ≈ (b[1,2] ^= 2.0)
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# test fallthrough for unsupported ops
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local c = 0
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@test @fastmath(c |= 1) == 1
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end
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# issue #23218
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let a = zeros(1), b = ones(1), idx = (1,)
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@fastmath a[idx...] += b[idx...]
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@test a == b
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end
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