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4a8cb4a49c
The extra-clever code in Sincos is trying to do
if v&2 == 0 {
mask = 0xffffffffffffffff
} else {
mask = 0
}
It does this by turning v&2 into a float64 X0 and then using
MOVSD $0.0, X3
CMPSD X0, X3, 0
That CMPSD is defined to behave like:
if X0 == X3 {
X3 = 0xffffffffffffffff
} else {
X3 = 0
}
which gives the desired mask in X3. The goal in using the
CMPSD was to avoid a conditional branch.
This code fails when called from a PortAudio callback.
In particular, the failure behavior is exactly as if the
CMPSD always chose the 'true' execution.
Notice that the comparison X0 == X3 is comparing as
floating point values the 64-bit pattern v&2 and the actual
floating point value zero. The only possible values for v&2
are 0x0000000000000000 (floating point zero)
and 0x0000000000000002 (floating point 1e-323, a denormal).
If they are both comparing equal to zero, I conclude that
in a PortAudio callback (whatever that means), the processor
is running in "denormals are zero" mode.
I confirmed this by placing the processor into that mode
and running the test case in the bug; it produces the
incorrect output reported in the bug.
In general, if a Go program changes the floating point math
modes to something other than what Go expects, the math
library is not going to work exactly as intended, so we might
be justified in not fixing this at all.
However, it seems reasonable that the client code might
have expected "denormals are zero" mode to only affect
actual processing of denormals. This code has produced
what is in effect a gratuitous denormal by being extra clever.
There is nothing about the computation being requested
that fundamentally requires a denormal.
It is also easy to do this computation in integer math instead:
mask = ((v&2)>>1)-1
Do that.
For the record, the other math tests that fail if you put the
processor in "denormals are zero" mode are the tests for
Frexp, Ilogb, Ldexp, Logb, Log2, and FloatMinMax, but all
fail processing denormal inputs. Sincos was the only function
for which that mode causes incorrect behavior on non-denormal inputs.
The existing tests check that the new assembly is correct.
There is no test for behavior in "denormals are zero" mode,
because I don't want to add assembly to change that.
Fixes #8623.
LGTM=josharian
R=golang-codereviews, josharian
CC=golang-codereviews, iant, r
https://golang.org/cl/151750043
143 lines
3.8 KiB
ArmAsm
143 lines
3.8 KiB
ArmAsm
// Copyright 2010 The Go Authors. All rights reserved.
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// Use of this source code is governed by a BSD-style
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// license that can be found in the LICENSE file.
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#include "textflag.h"
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// The method is based on a paper by Naoki Shibata: "Efficient evaluation
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// methods of elementary functions suitable for SIMD computation", Proc.
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// of International Supercomputing Conference 2010 (ISC'10), pp. 25 -- 32
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// (May 2010). The paper is available at
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// http://www.springerlink.com/content/340228x165742104/
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//
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// The original code and the constants below are from the author's
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// implementation available at http://freshmeat.net/projects/sleef.
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// The README file says, "The software is in public domain.
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// You can use the software without any obligation."
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//
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// This code is a simplified version of the original.
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#define PosOne 0x3FF0000000000000
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#define PosInf 0x7FF0000000000000
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#define NaN 0x7FF8000000000001
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#define PI4A 0.7853981554508209228515625 // pi/4 split into three parts
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#define PI4B 0.794662735614792836713604629039764404296875e-8
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#define PI4C 0.306161699786838294306516483068750264552437361480769e-16
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#define M4PI 1.273239544735162542821171882678754627704620361328125 // 4/pi
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#define T0 1.0
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#define T1 -8.33333333333333333333333e-02 // (-1.0/12)
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#define T2 2.77777777777777777777778e-03 // (+1.0/360)
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#define T3 -4.96031746031746031746032e-05 // (-1.0/20160)
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#define T4 5.51146384479717813051146e-07 // (+1.0/1814400)
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// func Sincos(d float64) (sin, cos float64)
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TEXT ·Sincos(SB),NOSPLIT,$0
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// test for special cases
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MOVQ $~(1<<63), DX // sign bit mask
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MOVQ x+0(FP), BX
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ANDQ BX, DX
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JEQ isZero
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MOVQ $PosInf, AX
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CMPQ AX, DX
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JLE isInfOrNaN
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// Reduce argument
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MOVQ BX, X7 // x7= d
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MOVQ DX, X0 // x0= |d|
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MOVSD $M4PI, X2
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MULSD X0, X2
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CVTTSD2SQ X2, BX // bx= q
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MOVQ $1, AX
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ANDQ BX, AX
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ADDQ BX, AX
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CVTSQ2SD AX, X2
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MOVSD $PI4A, X3
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MULSD X2, X3
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SUBSD X3, X0
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MOVSD $PI4B, X3
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MULSD X2, X3
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SUBSD X3, X0
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MOVSD $PI4C, X3
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MULSD X2, X3
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SUBSD X3, X0
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MULSD $0.125, X0 // x0= x, x7= d, bx= q
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// Evaluate Taylor series
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MULSD X0, X0
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MOVSD $T4, X2
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MULSD X0, X2
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ADDSD $T3, X2
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MULSD X0, X2
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ADDSD $T2, X2
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MULSD X0, X2
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ADDSD $T1, X2
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MULSD X0, X2
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ADDSD $T0, X2
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MULSD X2, X0 // x0= x, x7= d, bx= q
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// Apply double angle formula
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MOVSD $4.0, X2
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SUBSD X0, X2
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MULSD X2, X0
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MOVSD $4.0, X2
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SUBSD X0, X2
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MULSD X2, X0
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MOVSD $4.0, X2
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SUBSD X0, X2
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MULSD X2, X0
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MULSD $0.5, X0 // x0= x, x7= d, bx= q
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// sin = sqrt((2 - x) * x)
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MOVSD $2.0, X2
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SUBSD X0, X2
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MULSD X0, X2
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SQRTSD X2, X2 // x0= x, x2= z, x7= d, bx= q
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// cos = 1 - x
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MOVSD $1.0, X1
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SUBSD X0, X1 // x1= x, x2= z, x7= d, bx= q
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// if ((q + 1) & 2) != 0 { sin, cos = cos, sin }
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MOVQ $1, DX
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ADDQ BX, DX
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ANDQ $2, DX
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SHRQ $1, DX
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SUBQ $1, DX
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MOVQ DX, X3
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// sin = (y & z) | (^y & x)
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MOVAPD X2, X0
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ANDPD X3, X0 // x0= sin
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MOVAPD X3, X4
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ANDNPD X1, X4
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ORPD X4, X0 // x0= sin, x1= x, x2= z, x3= y, x7= d, bx= q
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// cos = (y & x) | (^y & z)
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ANDPD X3, X1 // x1= cos
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ANDNPD X2, X3
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ORPD X3, X1 // x0= sin, x1= cos, x7= d, bx= q
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// if ((q & 4) != 0) != (d < 0) { sin = -sin }
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MOVQ BX, AX
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MOVQ $61, CX
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SHLQ CX, AX
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MOVQ AX, X3
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XORPD X7, X3
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MOVQ $(1<<63), AX
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MOVQ AX, X2 // x2= -0.0
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ANDPD X2, X3
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ORPD X3, X0 // x0= sin, x1= cos, x2= -0.0, bx= q
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// if ((q + 2) & 4) != 0 { cos = -cos }
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MOVQ $2, AX
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ADDQ AX, BX
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MOVQ $61, CX
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SHLQ CX, BX
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MOVQ BX, X3
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ANDPD X2, X3
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ORPD X3, X1 // x0= sin, x1= cos
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// return (sin, cos)
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MOVSD X0, sin+8(FP)
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MOVSD X1, cos+16(FP)
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RET
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isZero: // return (±0.0, 1.0)
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MOVQ BX, sin+8(FP)
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MOVQ $PosOne, AX
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MOVQ AX, cos+16(FP)
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RET
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isInfOrNaN: // return (NaN, NaN)
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MOVQ $NaN, AX
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MOVQ AX, sin+8(FP)
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MOVQ AX, cos+16(FP)
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RET
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