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Fast exp2(::Int) (fixs #17412) #17447

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merged 10 commits into from
Aug 1, 2016
Merged

Fast exp2(::Int) (fixs #17412) #17447

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c202864
=Marked float bit definitions as pure, so they will inline.
Jul 16, 2016
96be3e7
=tests for exp2(int)
Jul 16, 2016
7abae25
=Fast exp2(::Int) definition added
Jul 16, 2016
101e56c
=No Testsets
Jul 16, 2016
02198e3
=retab
Jul 16, 2016
7ab57f5
=Retab.
Jul 16, 2016
278403a
=typos in comments
Jul 16, 2016
920c4b9
=BigInt math returns BigFloat
Jul 16, 2016
d729f94
Made for better branch prediction
oxinabox Jul 27, 2016
b5a8a3d
correct denormal vs zero + microoptimistations
oxinabox Jul 28, 2016
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6 changes: 3 additions & 3 deletions base/float.jl
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Expand Up @@ -519,9 +519,9 @@ exponent_one(::Type{Float32}) = 0x3f80_0000
exponent_half(::Type{Float32}) = 0x3f00_0000
significand_mask(::Type{Float32}) = 0x007f_ffff

significand_bits{T<:AbstractFloat}(::Type{T}) = trailing_ones(significand_mask(T))
exponent_bits{T<:AbstractFloat}(::Type{T}) = sizeof(T)*8 - significand_bits(T) - 1
exponent_bias{T<:AbstractFloat}(::Type{T}) = Int(exponent_one(T) >> significand_bits(T))
@pure significand_bits{T<:AbstractFloat}(::Type{T}) = trailing_ones(significand_mask(T))
@pure exponent_bits{T<:AbstractFloat}(::Type{T}) = sizeof(T)*8 - significand_bits(T) - 1
@pure exponent_bias{T<:AbstractFloat}(::Type{T}) = Int(exponent_one(T) >> significand_bits(T))

## Array operations on floating point numbers ##

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17 changes: 17 additions & 0 deletions base/math.jl
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Expand Up @@ -124,6 +124,23 @@ for f in (:sinh, :cosh, :tanh, :atan, :asinh, :exp, :erf, :erfc, :expm1)
@eval ($f)(x::AbstractFloat) = error("not implemented for ", typeof(x))
end

#functions with special cases for integer arguements
@inline function exp2(x::Integer)
if x > 1023
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no tabs here either

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I'm sorry. I did check that file. But apparently, I fail at using the retab command in vim.

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no big deal, ci is relatively quiet atm

Inf64
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should exp2(x::BigInt) return a BigFloat answer?

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Nice catch.
I've added some test cases to test/bigint.jl to ensure this.

elseif x < -1074
Float64(0.0)
elseif x <= -1023
#Result will be a subnormal number
reinterpret(Float64, Int64(1) << (x + 1074))
else
#If x is a Int128, and is outside the range of Int64, then it is not -123<x<=1023
#We will cast everything to Int64 to avoid errors incase of Int128
reinterpret(Float64, (exponent_bias(Float64) + Int64(x)) << significand_bits(Float64))
end
end


# TODO: GNU libc has exp10 as an extension; should openlibm?
exp10(x::Float64) = 10.0^x
exp10(x::Float32) = 10.0f0^x
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18 changes: 18 additions & 0 deletions test/math.jl
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Expand Up @@ -192,6 +192,24 @@ end
@test exp2(Float16(2.)) ≈ exp2(2.)
@test log(e) == 1

# check exp2(::Integer) matches exp2(::Float)"
for ii in -2048:2048
expected = exp2(float(ii))
@test(exp2(Int16(ii)) == expected)
@test(exp2(Int32(ii)) == expected)
@test(exp2(Int64(ii)) == expected)
@test(exp2(Int128(ii)) == expected)
if ii>=0
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spaces around the >= would be a little easier to read (also [ci skip] worthy)

@test(exp2(UInt16(ii)) == expected)
@test(exp2(UInt32(ii)) == expected)
@test(exp2(UInt64(ii)) == expected)
@test(exp2(UInt128(ii)) == expected)
end
end

@test(exp2(false) == exp2(float(false)))
@test(exp2(true) == exp2(float(true)))

for T in (Int, Float64, BigFloat)
@test deg2rad(T(180)) ≈ 1pi
@test deg2rad(T[45, 60]) ≈ [pi/T(4), pi/T(3)]
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