[Libclc-dev] [PATCH 1/4] Implement atan builtin
Tom Stellard
tom at stellard.net
Tue Jul 15 08:46:58 PDT 2014
On Wed, Jul 02, 2014 at 04:11:13PM -0400, Tom Stellard wrote:
I'm going to commit these tomorrow if there are no objections.
-Tom
> ---
> generic/include/clc/clc.h | 1 +
> generic/include/clc/math/atan.h | 24 +++++
> generic/include/clc/math/atan.inc | 23 +++++
> generic/lib/SOURCES | 1 +
> generic/lib/math/atan.cl | 182 ++++++++++++++++++++++++++++++++++++++
> generic/lib/math/math.h | 64 ++++++++++++++
> 6 files changed, 295 insertions(+)
> create mode 100644 generic/include/clc/math/atan.h
> create mode 100644 generic/include/clc/math/atan.inc
> create mode 100644 generic/lib/math/atan.cl
> create mode 100644 generic/lib/math/math.h
>
> diff --git a/generic/include/clc/clc.h b/generic/include/clc/clc.h
> index e0cae98..af177dc 100644
> --- a/generic/include/clc/clc.h
> +++ b/generic/include/clc/clc.h
> @@ -32,6 +32,7 @@
> #include <clc/workitem/get_group_id.h>
>
> /* 6.11.2 Math Functions */
> +#include <clc/math/atan.h>
> #include <clc/math/cos.h>
> #include <clc/math/ceil.h>
> #include <clc/math/exp.h>
> diff --git a/generic/include/clc/math/atan.h b/generic/include/clc/math/atan.h
> new file mode 100644
> index 0000000..d969719
> --- /dev/null
> +++ b/generic/include/clc/math/atan.h
> @@ -0,0 +1,24 @@
> +/*
> + * 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.
> + */
> +
> +#define __CLC_BODY <clc/math/atan.inc>
> +#include <clc/math/gentype.inc>
> diff --git a/generic/include/clc/math/atan.inc b/generic/include/clc/math/atan.inc
> new file mode 100644
> index 0000000..d217c95
> --- /dev/null
> +++ b/generic/include/clc/math/atan.inc
> @@ -0,0 +1,23 @@
> +/*
> + * 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.
> + */
> +
> +_CLC_OVERLOAD _CLC_DECL __CLC_GENTYPE atan(__CLC_GENTYPE a);
> diff --git a/generic/lib/SOURCES b/generic/lib/SOURCES
> index 02894d9..ed93084 100644
> --- a/generic/lib/SOURCES
> +++ b/generic/lib/SOURCES
> @@ -27,6 +27,7 @@ integer/sub_sat.cl
> integer/sub_sat_if.ll
> integer/sub_sat_impl.ll
> integer/upsample.cl
> +math/atan.cl
> math/exp.cl
> math/fmax.cl
> math/fmin.cl
> diff --git a/generic/lib/math/atan.cl b/generic/lib/math/atan.cl
> new file mode 100644
> index 0000000..682bff4
> --- /dev/null
> +++ b/generic/lib/math/atan.cl
> @@ -0,0 +1,182 @@
> +/*
> + * 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 "math.h"
> +
> +#include <clc/clc.h>
> +
> +_CLC_OVERLOAD _CLC_DEF float atan(float x)
> +{
> + const float piby2 = 1.5707963267948966f; // 0x3ff921fb54442d18
> +
> + uint ux = as_uint(x);
> + uint aux = ux & EXSIGNBIT_SP32;
> + uint sx = ux ^ aux;
> +
> + float spiby2 = as_float(sx | as_uint(piby2));
> +
> + float v = as_float(aux);
> +
> + // Return for NaN
> + float ret = x;
> +
> + // 2^26 <= |x| <= Inf => atan(x) is close to piby2
> + ret = aux <= PINFBITPATT_SP32 ? spiby2 : ret;
> +
> + // Reduce arguments 2^-19 <= |x| < 2^26
> +
> + // 39/16 <= x < 2^26
> + x = -MATH_RECIP(v);
> + float c = 1.57079632679489655800f; // atan(infinity)
> +
> + // 19/16 <= x < 39/16
> + int l = aux < 0x401c0000;
> + float xx = MATH_DIVIDE(v - 1.5f, mad(v, 1.5f, 1.0f));
> + x = l ? xx : x;
> + c = l ? 9.82793723247329054082e-01f : c; // atan(1.5)
> +
> + // 11/16 <= x < 19/16
> + l = aux < 0x3f980000U;
> + xx = MATH_DIVIDE(v - 1.0f, 1.0f + v);
> + x = l ? xx : x;
> + c = l ? 7.85398163397448278999e-01f : c; // atan(1)
> +
> + // 7/16 <= x < 11/16
> + l = aux < 0x3f300000;
> + xx = MATH_DIVIDE(mad(v, 2.0f, -1.0f), 2.0f + v);
> + x = l ? xx : x;
> + c = l ? 4.63647609000806093515e-01f : c; // atan(0.5)
> +
> + // 2^-19 <= x < 7/16
> + l = aux < 0x3ee00000;
> + x = l ? v : x;
> + c = l ? 0.0f : c;
> +
> + // Core approximation: Remez(2,2) on [-7/16,7/16]
> +
> + float s = x * x;
> + float a = mad(s,
> + mad(s, 0.470677934286149214138357545549e-2f, 0.192324546402108583211697690500f),
> + 0.296528598819239217902158651186f);
> +
> + float b = mad(s,
> + mad(s, 0.299309699959659728404442796915f, 0.111072499995399550138837673349e1f),
> + 0.889585796862432286486651434570f);
> +
> + float q = x * s * MATH_DIVIDE(a, b);
> +
> + float z = c - (q - x);
> + float zs = as_float(sx | as_uint(z));
> +
> + ret = aux < 0x4c800000 ? zs : ret;
> +
> + // |x| < 2^-19
> + ret = aux < 0x36000000 ? as_float(ux) : ret;
> + return ret;
> +}
> +
> +_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atan, float);
> +
> +#ifdef cl_khr_fp64
> +
> +#pragma OPENCL EXTENSION cl_khr_fp64 : enable
> +
> +
> +_CLC_OVERLOAD _CLC_DEF double atan(double x)
> +{
> + const double piby2 = 1.5707963267948966e+00; // 0x3ff921fb54442d18
> +
> + double v = fabs(x);
> +
> + // 2^56 > v > 39/16
> + double a = -1.0;
> + double b = v;
> + // (chi + clo) = arctan(infinity)
> + double chi = 1.57079632679489655800e+00;
> + double clo = 6.12323399573676480327e-17;
> +
> + double ta = v - 1.5;
> + double tb = 1.0 + 1.5 * v;
> + int l = v <= 0x1.38p+1; // 39/16 > v > 19/16
> + a = l ? ta : a;
> + b = l ? tb : b;
> + // (chi + clo) = arctan(1.5)
> + chi = l ? 9.82793723247329054082e-01 : chi;
> + clo = l ? 1.39033110312309953701e-17 : clo;
> +
> + ta = v - 1.0;
> + tb = 1.0 + v;
> + l = v <= 0x1.3p+0; // 19/16 > v > 11/16
> + a = l ? ta : a;
> + b = l ? tb : b;
> + // (chi + clo) = arctan(1.)
> + chi = l ? 7.85398163397448278999e-01 : chi;
> + clo = l ? 3.06161699786838240164e-17 : clo;
> +
> + ta = 2.0 * v - 1.0;
> + tb = 2.0 + v;
> + l = v <= 0x1.6p-1; // 11/16 > v > 7/16
> + a = l ? ta : a;
> + b = l ? tb : b;
> + // (chi + clo) = arctan(0.5)
> + chi = l ? 4.63647609000806093515e-01 : chi;
> + clo = l ? 2.26987774529616809294e-17 : clo;
> +
> + l = v <= 0x1.cp-2; // v < 7/16
> + a = l ? v : a;
> + b = l ? 1.0 : b;;
> + chi = l ? 0.0 : chi;
> + clo = l ? 0.0 : clo;
> +
> + // Core approximation: Remez(4,4) on [-7/16,7/16]
> + double r = a / b;
> + double s = r * r;
> + double qn = fma(s,
> + fma(s,
> + fma(s,
> + fma(s, 0.142316903342317766e-3,
> + 0.304455919504853031e-1),
> + 0.220638780716667420e0),
> + 0.447677206805497472e0),
> + 0.268297920532545909e0);
> +
> + double qd = fma(s,
> + fma(s,
> + fma(s,
> + fma(s, 0.389525873944742195e-1,
> + 0.424602594203847109e0),
> + 0.141254259931958921e1),
> + 0.182596787737507063e1),
> + 0.804893761597637733e0);
> +
> + double q = r * s * qn / qd;
> + r = chi - ((q - clo) - r);
> +
> + double z = isnan(x) ? x : piby2;
> + z = v <= 0x1.0p+56 ? r : z;
> + z = v < 0x1.0p-26 ? v : z;
> + return x == v ? z : -z;
> +}
> +
> +_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atan, double);
> +
> +#endif // cl_khr_fp64
> diff --git a/generic/lib/math/math.h b/generic/lib/math/math.h
> new file mode 100644
> index 0000000..53ed38a
> --- /dev/null
> +++ b/generic/lib/math/math.h
> @@ -0,0 +1,64 @@
> +/*
> + * 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.
> + */
> +
> +#define SNAN 0x001
> +#define QNAN 0x002
> +#define NINF 0x004
> +#define NNOR 0x008
> +#define NSUB 0x010
> +#define NZER 0x020
> +#define PZER 0x040
> +#define PSUB 0x080
> +#define PNOR 0x100
> +#define PINF 0x200
> +
> +#define HAVE_HW_FMA32() (1)
> +#define HAVE_BITALIGN() (0)
> +#define HAVE_FAST_FMA32() (0)
> +
> +#define MATH_DIVIDE(X, Y) ((X) / (Y))
> +#define MATH_RECIP(X) (1.0f / (X))
> +#define MATH_SQRT(X) sqrt(X)
> +
> +#define SIGNBIT_SP32 0x80000000
> +#define EXSIGNBIT_SP32 0x7fffffff
> +#define EXPBITS_SP32 0x7f800000
> +#define MANTBITS_SP32 0x007fffff
> +#define ONEEXPBITS_SP32 0x3f800000
> +#define TWOEXPBITS_SP32 0x40000000
> +#define HALFEXPBITS_SP32 0x3f000000
> +#define IMPBIT_SP32 0x00800000
> +#define QNANBITPATT_SP32 0x7fc00000
> +#define INDEFBITPATT_SP32 0xffc00000
> +#define PINFBITPATT_SP32 0x7f800000
> +#define NINFBITPATT_SP32 0xff800000
> +#define EXPBIAS_SP32 127
> +#define EXPSHIFTBITS_SP32 23
> +#define BIASEDEMIN_SP32 1
> +#define EMIN_SP32 -126
> +#define BIASEDEMAX_SP32 254
> +#define EMAX_SP32 127
> +#define LAMBDA_SP32 1.0e30
> +#define MANTLENGTH_SP32 24
> +#define BASEDIGITS_SP32 7
> +
> +#define ALIGNED(x) __attribute__((aligned(x)))
> --
> 1.8.1.5
>
>
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