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^(::Float, ::Integer) #42031

Merged
merged 12 commits into from
Oct 4, 2021
39 changes: 23 additions & 16 deletions base/math.jl
Original file line number Diff line number Diff line change
Expand Up @@ -911,13 +911,17 @@ function modf(x::Float64)
end

@inline function ^(x::Float64, y::Float64)
yint = round(Int, y)
y == yint && return x^yint
z = ccall("llvm.pow.f64", llvmcall, Float64, (Float64, Float64), x, y)
if isnan(z) & !isnan(x+y)
throw_exp_domainerror(x)
end
z
end
@inline function ^(x::Float32, y::Float32)
yint = round(Int, y)
y == yint && return x^yint
z = ccall("llvm.pow.f32", llvmcall, Float32, (Float32, Float32), x, y)
if isnan(z) & !isnan(x+y)
throw_exp_domainerror(x)
Expand All @@ -928,22 +932,25 @@ end

# compensated power by squaring
@inline function ^(x::Float64, n::Integer)
n < 0 && return inv(x^(-n))
y = 1.0
xnlo = ynlo = 0.0
while n > 1
if n&1 > 0
yn = x*y
ynlo = fma(x, y , -yn) + muladd(y, xnlo, x*ynlo)
y = yn
end
xn = x * x
xnlo = muladd(x, 2*xnlo, fma(x, x, -xn))
x = xn
n >>>= 1
end
!isfinite(x) && return x*y
return muladd(x, y, muladd(y, xnlo, x*ynlo))
if n > 0
y = 1.0
xnlo = ynlo = 0.0
while n > 1
if n&1 > 0
yn = x*y
ynlo = fma(x, y , -yn) + muladd(y, xnlo, x*ynlo)
y = yn
end
xn = x * x
xnlo = muladd(x, 2*xnlo, fma(x, x, -xn))
x = xn
n >>>= 1
end
!isfinite(x) && return x*y
return muladd(x, y, muladd(y, xnlo, x*ynlo))
end
n < 0 && return inv(x^(-n))
return one(n) # n == 0
end
@inline function ^(x::Float32, y::Integer)
y < 0 && return inv(x^(-y))
Expand Down