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libclc/math: Add cospi 

Ported from the libclc/amd-builtins branch

v2: Rename sincos_f_piby4 to __libclc__sincosf_piby4
    Add cospi(double) implementation instead of using llvm.cos

Notes:
The sincosD_piby4.h file is mostly the same as the builtin implementation
released by AMD. The inline attribute declaration is changed, and M_PI is
used instead of a constant double. Otherwise, the only difference is that
the header explicitly enables the fp64 pragma.

Signed-off-by: Aaron Watry <awatry@gmail.com>
Reviewed-by: Jeroen Ketema <j.ketema@imperial.ac.uk>
CC: Tom Stellard <tom@stellard.net>
CC: Matt Arsenault <Matthew.Arsenault@amd.com>
llvm-svn: 230641
This commit is contained in:
Aaron Watry 2015-02-26 15:42:00 +00:00
parent f72bdbfbb1
commit f89bcca0b7
7 changed files with 276 additions and 0 deletions
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1
libclc/generic/include/clc/clc.h
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@ -38,6 +38,7 @@
#include <clc/math/atan2.h>
#include <clc/math/copysign.h>
#include <clc/math/cos.h>
#include <clc/math/cospi.h>
#include <clc/math/ceil.h>
#include <clc/math/exp.h>
#include <clc/math/exp10.h>

3
libclc/generic/include/clc/math/cospi.h Normal file
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@ -0,0 +1,3 @@
#define __CLC_BODY <clc/math/cospi.inc>
#include <clc/math/gentype.inc>
#undef __CLC_BODY

1
libclc/generic/include/clc/math/cospi.inc Normal file
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@ -0,0 +1 @@
_CLC_OVERLOAD _CLC_DECL __CLC_GENTYPE cospi(__CLC_GENTYPE a);

1
libclc/generic/lib/SOURCES
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@ -57,6 +57,7 @@ math/atan.cl
math/atan2.cl
math/copysign.cl
math/cos.cl
math/cospi.cl
math/exp.cl
math/exp10.cl
math/fmax.cl

136
libclc/generic/lib/math/cospi.cl Normal file
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@ -0,0 +1,136 @@
/*
* Copyright (c) 2014 Advanced Micro Devices, Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#include <clc/clc.h>
#include "math.h"
#include "sincos_helpers.h"
#include "sincospiF_piby4.h"
#include "../clcmacro.h"
#ifdef cl_khr_fp64
#include "sincosD_piby4.h"
#endif
_CLC_OVERLOAD _CLC_DEF float cospi(float x)
{
int ix = as_int(x) & 0x7fffffff;
float ax = as_float(ix);
int iax = (int)ax;
float r = ax - iax;
int xodd = iax & 0x1 ? 0x80000000 : 0;
// Initialize with return for +-Inf and NaN
int ir = 0x7fc00000;
// 2^24 <= |x| < Inf, the result is always even integer
ir = ix < 0x7f800000 ? 0x3f800000 : ir;
// 2^23 <= |x| < 2^24, the result is always integer
ir = ix < 0x4b800000 ? xodd | 0x3f800000 : ir;
// 0x1.0p-7 <= |x| < 2^23, result depends on which 0.25 interval
// r < 1.0
float a = 1.0f - r;
int e = 1;
int s = xodd ^ 0x80000000;
// r <= 0.75
int c = r <= 0.75f;
a = c ? r - 0.5f : a;
e = c ? 0 : e;
// r < 0.5
c = r < 0.5f;
a = c ? 0.5f - r : a;
s = c ? xodd : s;
// r <= 0.25
c = r <= 0.25f;
a = c ? r : a;
e = c ? 1 : e;
float2 t = __libclc__sincosf_piby4(a * M_PI_F);
int jr = s ^ as_int(e ? t.hi : t.lo);
ir = ix < 0x4b000000 ? jr : ir;
return as_float(ir);
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, cospi, float);
#ifdef cl_khr_fp64
#pragma OPENCL EXTENSION cl_khr_fp64 : enable
_CLC_OVERLOAD _CLC_DEF double cospi(double x) {
long ix = as_long(x) & 0x7fffffffffffffffL;
double ax = as_double(ix);
long iax = (long)ax;
double r = ax - (double)iax;
long xodd = iax & 0x1L ? 0x8000000000000000L : 0L;
// Initialize with return for +-Inf and NaN
long ir = 0x7ff8000000000000L;
// 2^53 <= |x| < Inf, the result is always even integer
ir = ix < 0x7ff0000000000000 ? 0x3ff0000000000000L : ir;
// 2^52 <= |x| < 2^53, the result is always integer
ir = ax < 0x1.0p+53 ? xodd | 0x3ff0000000000000L : ir;
// 0x1.0p-7 <= |x| < 2^52, result depends on which 0.25 interval
// r < 1.0
double a = 1.0 - r;
int e = 1;
long s = xodd ^ 0x8000000000000000L;
// r <= 0.75
int c = r <= 0.75;
double t = r - 0.5;
a = c ? t : a;
e = c ? 0 : e;
// r < 0.5
c = r < 0.5;
t = 0.5 - r;
a = c ? t : a;
s = c ? xodd : s;
// r <= 0.25
c = r <= 0.25;
a = c ? r : a;
e = c ? 1 : e;
double2 sc = __libclc__sincos_piby4(a * M_PI, 0.0);
long jr = s ^ as_long(e ? sc.hi : sc.lo);
ir = ax < 0x1.0p+52 ? jr : ir;
return as_double(ir);
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, cospi, double);
#endif

78
libclc/generic/lib/math/sincosD_piby4.h Normal file
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@ -0,0 +1,78 @@
/*
* Copyright (c) 2014 Advanced Micro Devices, Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
#pragma OPENCL EXTENSION cl_khr_fp64 : enable
_CLC_INLINE double2
__libclc__sincos_piby4(double x, double xx)
{
// Taylor series for sin(x) is x - x^3/3! + x^5/5! - x^7/7! ...
// = x * (1 - x^2/3! + x^4/5! - x^6/7! ...
// = x * f(w)
// where w = x*x and f(w) = (1 - w/3! + w^2/5! - w^3/7! ...
// We use a minimax approximation of (f(w) - 1) / w
// because this produces an expansion in even powers of x.
// If xx (the tail of x) is non-zero, we add a correction
// term g(x,xx) = (1-x*x/2)*xx to the result, where g(x,xx)
// is an approximation to cos(x)*sin(xx) valid because
// xx is tiny relative to x.
// Taylor series for cos(x) is 1 - x^2/2! + x^4/4! - x^6/6! ...
// = f(w)
// where w = x*x and f(w) = (1 - w/2! + w^2/4! - w^3/6! ...
// We use a minimax approximation of (f(w) - 1 + w/2) / (w*w)
// because this produces an expansion in even powers of x.
// If xx (the tail of x) is non-zero, we subtract a correction
// term g(x,xx) = x*xx to the result, where g(x,xx)
// is an approximation to sin(x)*sin(xx) valid because
// xx is tiny relative to x.
const double sc1 = -0.166666666666666646259241729;
const double sc2 = 0.833333333333095043065222816e-2;
const double sc3 = -0.19841269836761125688538679e-3;
const double sc4 = 0.275573161037288022676895908448e-5;
const double sc5 = -0.25051132068021699772257377197e-7;
const double sc6 = 0.159181443044859136852668200e-9;
const double cc1 = 0.41666666666666665390037e-1;
const double cc2 = -0.13888888888887398280412e-2;
const double cc3 = 0.248015872987670414957399e-4;
const double cc4 = -0.275573172723441909470836e-6;
const double cc5 = 0.208761463822329611076335e-8;
const double cc6 = -0.113826398067944859590880e-10;
double x2 = x * x;
double x3 = x2 * x;
double r = 0.5 * x2;
double t = 1.0 - r;
double sp = fma(fma(fma(fma(sc6, x2, sc5), x2, sc4), x2, sc3), x2, sc2);
double cp = t + fma(fma(fma(fma(fma(fma(cc6, x2, cc5), x2, cc4), x2, cc3), x2, cc2), x2, cc1),
x2*x2, fma(x, xx, (1.0 - t) - r));
double2 ret;
ret.lo = x - fma(-x3, sc1, fma(fma(-x3, sp, 0.5*xx), x2, -xx));
ret.hi = cp;
return ret;
}

56
libclc/generic/lib/math/sincospiF_piby4.h Normal file
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@ -0,0 +1,56 @@
/*
* Copyright (c) 2014 Advanced Micro Devices, Inc.
*
* Permission is hereby granted, free of charge, to any person obtaining a copy
* of this software and associated documentation files (the "Software"), to deal
* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*/
// Evaluate single precisions in and cos of value in interval [-pi/4, pi/4]
_CLC_INLINE float2
__libclc__sincosf_piby4(float x)
{
// Taylor series for sin(x) is x - x^3/3! + x^5/5! - x^7/7! ...
// = x * (1 - x^2/3! + x^4/5! - x^6/7! ...
// = x * f(w)
// where w = x*x and f(w) = (1 - w/3! + w^2/5! - w^3/7! ...
// We use a minimax approximation of (f(w) - 1) / w
// because this produces an expansion in even powers of x.
// Taylor series for cos(x) is 1 - x^2/2! + x^4/4! - x^6/6! ...
// = f(w)
// where w = x*x and f(w) = (1 - w/2! + w^2/4! - w^3/6! ...
// We use a minimax approximation of (f(w) - 1 + w/2) / (w*w)
// because this produces an expansion in even powers of x.
const float sc1 = -0.166666666638608441788607926e0F;
const float sc2 = 0.833333187633086262120839299e-2F;
const float sc3 = -0.198400874359527693921333720e-3F;
const float sc4 = 0.272500015145584081596826911e-5F;
const float cc1 = 0.41666666664325175238031e-1F;
const float cc2 = -0.13888887673175665567647e-2F;
const float cc3 = 0.24800600878112441958053e-4F;
const float cc4 = -0.27301013343179832472841e-6F;
float x2 = x * x;
float2 ret;
ret.x = mad(x*x2, mad(x2, mad(x2, mad(x2, sc4, sc3), sc2), sc1), x);
ret.y = mad(x2*x2, mad(x2, mad(x2, mad(x2, cc4, cc3), cc2), cc1), mad(x2, -0.5f, 1.0f));
return ret;
}