[Libclc-dev] [PATCH 07/15] Implement atan2pi builtin
Jan Vesely
jan.vesely at rutgers.edu
Sun Apr 12 12:55:04 PDT 2015
On Tue, 2015-04-07 at 18:05 +0000, Tom Stellard wrote:
> This implementation was ported from the AMD builtin library
> and has been tested with piglit, OpenCV, and the ocl conformance tests.
> ---
> generic/include/clc/clc.h | 1 +
> generic/include/clc/math/atan2pi.h | 24 ++++
> generic/include/clc/math/atan2pi.inc | 23 ++++
> generic/lib/SOURCES | 1 +
> generic/lib/math/atan2pi.cl | 221 +++++++++++++++++++++++++++++++++++
> 5 files changed, 270 insertions(+)
> create mode 100644 generic/include/clc/math/atan2pi.h
> create mode 100644 generic/include/clc/math/atan2pi.inc
> create mode 100644 generic/lib/math/atan2pi.cl
>
> diff --git a/generic/include/clc/clc.h b/generic/include/clc/clc.h
> index 18f7c07..46dd3b7 100644
> --- a/generic/include/clc/clc.h
> +++ b/generic/include/clc/clc.h
> @@ -40,6 +40,7 @@
> #include <clc/math/asinpi.h>
> #include <clc/math/atan.h>
> #include <clc/math/atan2.h>
> +#include <clc/math/atan2pi.h>
> #include <clc/math/atanh.h>
> #include <clc/math/atanpi.h>
> #include <clc/math/copysign.h>
> diff --git a/generic/include/clc/math/atan2pi.h b/generic/include/clc/math/atan2pi.h
> new file mode 100644
> index 0000000..2cf4c53
> --- /dev/null
> +++ b/generic/include/clc/math/atan2pi.h
> @@ -0,0 +1,24 @@
> +/*
> + * Copyright (c) 2014, 2015 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/atan2pi.inc>
> +#include <clc/math/gentype.inc>
> diff --git a/generic/include/clc/math/atan2pi.inc b/generic/include/clc/math/atan2pi.inc
> new file mode 100644
> index 0000000..47a9d44
> --- /dev/null
> +++ b/generic/include/clc/math/atan2pi.inc
> @@ -0,0 +1,23 @@
> +/*
> + * Copyright (c) 2014, 2015 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 atan2pi(__CLC_GENTYPE x, __CLC_GENTYPE y);
> diff --git a/generic/lib/SOURCES b/generic/lib/SOURCES
> index d7caa78..808d72f 100644
> --- a/generic/lib/SOURCES
> +++ b/generic/lib/SOURCES
> @@ -70,6 +70,7 @@ math/asinh.cl
> math/asinpi.cl
> math/atan.cl
> math/atan2.cl
> +math/atan2pi.cl
> math/atanh.cl
> math/atanpi.cl
> math/copysign.cl
> diff --git a/generic/lib/math/atan2pi.cl b/generic/lib/math/atan2pi.cl
> new file mode 100644
> index 0000000..cf51836
> --- /dev/null
> +++ b/generic/lib/math/atan2pi.cl
> @@ -0,0 +1,221 @@
> +/*
> + * Copyright (c) 2014,2015 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 "tables.h"
> +#include "../clcmacro.h"
> +
> +_CLC_OVERLOAD _CLC_DEF float atan2pi(float y, float x) {
> + const float pi = 0x1.921fb6p+1f;
> +
> + float ax = fabs(x);
> + float ay = fabs(y);
> + float v = min(ax, ay);
> + float u = max(ax, ay);
> +
> + // Scale since u could be large, as in "regular" divide
> + float s = u > 0x1.0p+96f ? 0x1.0p-32 : 1.0f;
needs an 'f' suffix ^
> + float vbyu = s * MATH_DIVIDE(v, s*u);
> +
> + float vbyu2 = vbyu * vbyu;
> +
> + float p = mad(vbyu2, mad(vbyu2, -0x1.7e1f78p-9f, -0x1.7d1b98p-3f), -0x1.5554d0p-2f) * vbyu2 * vbyu;
> + float q = mad(vbyu2, mad(vbyu2, 0x1.1a714cp-2f, 0x1.287c56p+0f), 1.0f);
> +
> + // Octant 0 result
> + float a = MATH_DIVIDE(mad(p, MATH_RECIP(q), vbyu), pi);
> +
> + // Fix up 3 other octants
> + float at = 0.5f - a;
> + a = ay > ax ? at : a;
> + at = 1.0f - a;
> + a = x < 0.0F ? at : a;
> +
> + // y == 0 => 0 for x >= 0, pi for x < 0
> + at = as_int(x) < 0 ? 1.0f : 0.0f;
> + a = y == 0.0f ? at : a;
> +
> + // if (!FINITE_ONLY()) {
> + // x and y are +- Inf
> + at = x > 0.0f ? 0.25f : 0.75f;
> + a = ax == INFINITY & ay == INFINITY ? at : a;
> +
> + // x or y is NaN
> + a = isnan(x) | isnan(y) ? as_float(QNANBITPATT_SP32) : a;
> + // }
> +
> + // Fixup sign and return
> + return copysign(a, y);
> +}
> +
> +_CLC_BINARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atan2pi, float, float)
> +
> +#ifdef cl_khr_fp64
> +#pragma OPENCL EXTENSION cl_khr_fp64 : enable
> +
> +_CLC_OVERLOAD _CLC_DEF double atan2pi(double y, double x) {
> + const double pi = 3.1415926535897932e+00; /* 0x400921fb54442d18 */
> + const double pi_head = 3.1415926218032836e+00; /* 0x400921fb50000000 */
> + const double pi_tail = 3.1786509547056392e-08; /* 0x3e6110b4611a6263 */
> + const double piby2_head = 1.5707963267948965e+00; /* 0x3ff921fb54442d18 */
> + const double piby2_tail = 6.1232339957367660e-17; /* 0x3c91a62633145c07 */
> +
> + double x2 = x;
> + int xneg = as_int2(x).hi < 0;
> + int xexp = (as_int2(x).hi >> 20) & 0x7ff;
> +
> + double y2 = y;
> + int yneg = as_int2(y).hi < 0;
> + int yexp = (as_int2(y).hi >> 20) & 0x7ff;
> +
> + int cond2 = (xexp < 1021) & (yexp < 1021);
> + int diffexp = yexp - xexp;
> +
> + // Scale up both x and y if they are both below 1/4
> + double x1 = ldexp(x, 1024);
> + int xexp1 = (as_int2(x1).hi >> 20) & 0x7ff;
> + double y1 = ldexp(y, 1024);
> + int yexp1 = (as_int2(y1).hi >> 20) & 0x7ff;
> + int diffexp1 = yexp1 - xexp1;
> +
> + diffexp = cond2 ? diffexp1 : diffexp;
> + x = cond2 ? x1 : x;
> + y = cond2 ? y1 : y;
> +
> + // General case: take absolute values of arguments
> + double u = fabs(x);
> + double v = fabs(y);
> +
> + // Swap u and v if necessary to obtain 0 < v < u. Compute v/u.
> + int swap_vu = u < v;
> + double uu = u;
> + u = swap_vu ? v : u;
> + v = swap_vu ? uu : v;
> +
> + double vbyu = v / u;
> + double q1, q2;
> +
> + // General values of v/u. Use a look-up table and series expansion.
> +
> + {
> + double val = vbyu > 0.0625 ? vbyu : 0.063;
> + int index = convert_int(fma(256.0, val, 0.5));
> + double2 tv = USE_TABLE(atan_jby256_tbl, (index - 16));
> + q1 = tv.s0;
> + q2 = tv.s1;
> + double c = (double)index * 0x1.0p-8;
> +
> + // We're going to scale u and v by 2^(-u_exponent) to bring them close to 1
> + // u_exponent could be EMAX so we have to do it in 2 steps
> + int m = -((int)(as_ulong(u) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64);
> + double um = ldexp(u, m);
> + double vm = ldexp(v, m);
> +
> + // 26 leading bits of u
> + double u1 = as_double(as_ulong(um) & 0xfffffffff8000000UL);
> + double u2 = um - u1;
> +
> + double r = MATH_DIVIDE(fma(-c, u2, fma(-c, u1, vm)), fma(c, vm, um));
> +
> + // Polynomial approximation to atan(r)
> + double s = r * r;
> + q2 = q2 + fma((s * fma(-s, 0.19999918038989143496, 0.33333333333224095522)), -r, r);
> + }
> +
> +
> + double q3, q4;
> + {
> + q3 = 0.0;
> + q4 = vbyu;
> + }
> +
> + double q5, q6;
> + {
> + double u1 = as_double(as_ulong(u) & 0xffffffff00000000UL);
> + double u2 = u - u1;
> + double vu1 = as_double(as_ulong(vbyu) & 0xffffffff00000000UL);
> + double vu2 = vbyu - vu1;
> +
> + q5 = 0.0;
> + double s = vbyu * vbyu;
> + q6 = vbyu + fma(-vbyu * s,
> + fma(-s,
> + fma(-s,
> + fma(-s,
> + fma(-s, 0.90029810285449784439E-01,
> + 0.11110736283514525407),
> + 0.14285713561807169030),
> + 0.19999999999393223405),
> + 0.33333333333333170500),
> + MATH_DIVIDE(fma(-u, vu2, fma(-u2, vu1, fma(-u1, vu1, v))), u));
> + }
> +
> +
> + q3 = vbyu < 0x1.d12ed0af1a27fp-27 ? q3 : q5;
> + q4 = vbyu < 0x1.d12ed0af1a27fp-27 ? q4 : q6;
> +
> + q1 = vbyu > 0.0625 ? q1 : q3;
> + q2 = vbyu > 0.0625 ? q2 : q4;
> +
> + // Tidy-up according to which quadrant the arguments lie in
> + double res1, res2, res3, res4;
> + q1 = swap_vu ? piby2_head - q1 : q1;
> + q2 = swap_vu ? piby2_tail - q2 : q2;
> + q1 = xneg ? pi_head - q1 : q1;
> + q2 = xneg ? pi_tail - q2 : q2;
> + q1 = MATH_DIVIDE(q1 + q2, pi);
> + res4 = yneg ? -q1 : q1;
> +
> + res1 = yneg ? -0.75 : 0.75;
> + res2 = yneg ? -0.25 : 0.25;
> + res3 = xneg ? res1 : res2;
> +
> + res3 = isinf(y2) & isinf(x2) ? res3 : res4;
> + res1 = yneg ? -1.0 : 1.0;
> +
> + // abs(x)/abs(y) > 2^56 and x < 0
> + res3 = (diffexp < -56 && xneg) ? res1 : res3;
> +
> + res4 = MATH_DIVIDE(MATH_DIVIDE(y, x), pi);
> + // x positive and dominant over y by a factor of 2^28
> + res3 = diffexp < -28 & xneg == 0 ? res4 : res3;
> +
> + // abs(y)/abs(x) > 2^56
> + res4 = yneg ? -0.5 : 0.5; // atan(y/x) is insignificant compared to piby2
> + res3 = diffexp > 56 ? res4 : res3;
> +
> + res3 = x2 == 0.0 ? res4 : res3; // Zero x gives +- pi/2 depending on sign of y
> + res4 = xneg ? res1 : y2;
> +
> + res3 = y2 == 0.0 ? res4 : res3; // Zero y gives +-0 for positive x and +-pi for negative x
> + res3 = isnan(y2) ? y2 : res3;
> + res3 = isnan(x2) ? x2 : res3;
> +
> + return res3;
> +}
> +
> +
> +_CLC_BINARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atan2pi, double, double)
> +
> +#endif
--
Jan Vesely <jan.vesely at rutgers.edu>
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