[Libclc-dev] [PATCH] libclc/math: Add cospi
Jeroen Ketema
j.ketema at imperial.ac.uk
Thu Dec 25 07:34:57 PST 2014
Modulo the math, which I cannot really check, this looks good to me.
Jeroen
> On 18 Dec 2014, at 01:35, Aaron Watry <awatry at gmail.com> wrote:
>
> 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.
>
> Piglit lacks the built-in capability to test double-precision CL builtins
> at the moment. I hacked the cospi(float) tests to use cospi(double) to
> verify that the implementation runs and produces reasonable results, but
> I have NOT added new test cases to piglit which exercise the additional
> precision of the double-precision data type for cospi.
>
> Signed-off-by: Aaron Watry <awatry at gmail.com>
> CC: Tom Stellard <tom at stellard.net>
> CC: Jeroen Ketema <j.ketema at imperial.ac.uk>
> CC: Matt Arsenault <Matthew.Arsenault at amd.com>
> ---
> generic/include/clc/clc.h | 1 +
> generic/include/clc/math/cospi.h | 3 +
> generic/include/clc/math/cospi.inc | 1 +
> generic/lib/SOURCES | 1 +
> generic/lib/math/cospi.cl | 136 +++++++++++++++++++++++++++++++++++++
> generic/lib/math/sincosD_piby4.h | 78 +++++++++++++++++++++
> generic/lib/math/sincospiF_piby4.h | 56 +++++++++++++++
> 7 files changed, 276 insertions(+)
> create mode 100644 generic/include/clc/math/cospi.h
> create mode 100644 generic/include/clc/math/cospi.inc
> create mode 100644 generic/lib/math/cospi.cl
> create mode 100644 generic/lib/math/sincosD_piby4.h
> create mode 100644 generic/lib/math/sincospiF_piby4.h
>
> diff --git a/generic/include/clc/clc.h b/generic/include/clc/clc.h
> index bd92fdb..bff6ddd 100644
> --- a/generic/include/clc/clc.h
> +++ b/generic/include/clc/clc.h
> @@ -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>
> diff --git a/generic/include/clc/math/cospi.h b/generic/include/clc/math/cospi.h
> new file mode 100644
> index 0000000..427733b
> --- /dev/null
> +++ b/generic/include/clc/math/cospi.h
> @@ -0,0 +1,3 @@
> +#define __CLC_BODY <clc/math/cospi.inc>
> +#include <clc/math/gentype.inc>
> +#undef __CLC_BODY
> diff --git a/generic/include/clc/math/cospi.inc b/generic/include/clc/math/cospi.inc
> new file mode 100644
> index 0000000..1e786cf
> --- /dev/null
> +++ b/generic/include/clc/math/cospi.inc
> @@ -0,0 +1 @@
> +_CLC_OVERLOAD _CLC_DECL __CLC_GENTYPE cospi(__CLC_GENTYPE a);
> diff --git a/generic/lib/SOURCES b/generic/lib/SOURCES
> index b76fec9..2b9426e 100644
> --- a/generic/lib/SOURCES
> +++ b/generic/lib/SOURCES
> @@ -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
> diff --git a/generic/lib/math/cospi.cl b/generic/lib/math/cospi.cl
> new file mode 100644
> index 0000000..108b637
> --- /dev/null
> +++ b/generic/lib/math/cospi.cl
> @@ -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
> diff --git a/generic/lib/math/sincosD_piby4.h b/generic/lib/math/sincosD_piby4.h
> new file mode 100644
> index 0000000..a00db85
> --- /dev/null
> +++ b/generic/lib/math/sincosD_piby4.h
> @@ -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;
> +}
> diff --git a/generic/lib/math/sincospiF_piby4.h b/generic/lib/math/sincospiF_piby4.h
> new file mode 100644
> index 0000000..90ecb1d
> --- /dev/null
> +++ b/generic/lib/math/sincospiF_piby4.h
> @@ -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;
> +}
> --
> 2.1.0
>
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