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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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12 changes: 7 additions & 5 deletions base/math.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -128,15 +128,17 @@ end
@inline function exp2(x::Base.BitInteger)
if x > 1023
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))
if x < -1074
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Shouldn't this be x >= -1074?

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Actually, you might not need this branch at all (if x < -1074, the bitshift should still give the correct answer).

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Shouldn't this be x >= -1074?
yes

Actually, you might not need this branch at all (if x < -1074, the bitshift should still give the correct answer).

Yes. Tested and confirmed

# Result will be a subnormal number
reinterpret(Float64, (1 % Int64) << (x + 1074))
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You could convert the shift count to unsigned via %; otherwise Julia will have to check the sign.

else #-1073 < x <= -1023
0.0
end
else
# If x is a Int128, and is outside the range of Int64, then it is not -1023<x<=1023
# We will cast everything to Int64 to avoid errors in case of Int128
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Since you cast everything to Int64, you could also restrict the argument type to Int, and have a generic version that accepts Integer and calls the main function with argument converted to Int.

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I think it is a bit cleaner not to.
Not all paths have the cast, on x
only line 141

The cast on the 1 in line 134, is to make sure things work on 32 bit machines where 1 is a 32bit.
Perhaps cleaner, I change that one to 0x0000_0000_0000_0001

reinterpret(Float64, (exponent_bias(Float64) + Int64(x)) << significand_bits(Float64))
reinterpret(Float64, (exponent_bias(Float64) + (x % Int64)) << significand_bits(Float64))
end
end

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