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improvements to accuracy/performance for float^integer #24500

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Dec 5, 2017
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improvements to accuracy/performance for float^integer #24500

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14a4677
improvements to accuracy/performance for float^integer
stevengj Nov 6, 2017
0db74f2
eliminate inv(x)^n fallback for all AbstractFloat types
stevengj Nov 6, 2017
a9354df
method ambiguity code no longer needed, add back float^-1 = inv(x)
stevengj Nov 14, 2017
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6 changes: 6 additions & 0 deletions base/intfuncs.jl
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Expand Up @@ -234,6 +234,12 @@ const HWNumber = Union{HWReal, Complex{<:HWReal}, Rational{<:HWReal}}
@inline literal_pow(::typeof(^), x::HWNumber, ::Val{2}) = x*x
@inline literal_pow(::typeof(^), x::HWNumber, ::Val{3}) = x*x*x

# don't use the inv(x) transformation here since float^p is slightly more accurate
@inline literal_pow(::typeof(^), x::AbstractFloat, ::Val{p}) where {p} = x^p
@inline literal_pow(::typeof(^), x::AbstractFloat, ::Val{-1}) = inv(x)

# for other types, define x^-n as inv(x)^n so that negative literal powers can
# be computed in a type-stable way even for e.g. integers.
@inline @generated function literal_pow(f::typeof(^), x, ::Val{p}) where {p}
if p < 0
:(literal_pow(^, inv(x), $(Val{-p}())))
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6 changes: 3 additions & 3 deletions base/math.jl
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Expand Up @@ -732,9 +732,9 @@ end
end
z
end
@inline ^(x::Float64, y::Integer) = x ^ Float64(y)
@inline ^(x::Float32, y::Integer) = x ^ Float32(y)
@inline ^(x::Float16, y::Integer) = Float16(Float32(x) ^ Float32(y))
@inline ^(x::Float64, y::Integer) = ccall("llvm.pow.f64", llvmcall, Float64, (Float64, Float64), x, Float64(y))
@inline ^(x::Float32, y::Integer) = ccall("llvm.pow.f32", llvmcall, Float32, (Float32, Float32), x, Float32(y))
@inline ^(x::Float16, y::Integer) = Float16(Float32(x) ^ y)
@inline literal_pow(::typeof(^), x::Float16, ::Val{p}) where {p} = Float16(literal_pow(^,Float32(x),Val(p)))

function angle_restrict_symm(theta)
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9 changes: 9 additions & 0 deletions test/numbers.jl
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Expand Up @@ -2965,6 +2965,15 @@ module M20889 # do we get the expected behavior without importing Base.^?
Test.@test PR20889(2)^3 == 5
end

@testset "literal negative power accuracy" begin
# a few cases chosen to maximize the error for inv(x)^+n:
@test 0.7130409001548401^-2 === 1.9668494399322154
@test 0.09496527f0^-2 === 110.88438f0
@test 0.20675883960662367^-100 === 2.841786121808917e68
@test 0.6123676f0^-100 === 1.9896729f21
@test 0.004155780785470562^-1 === 240.6286692253353
end

@testset "iszero & isone" begin
# Numeric scalars
for T in [Float16, Float32, Float64, BigFloat,
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