7e6a73959a
Increase fp16 support to allow clspv to continue to be OpenCL compliant following the update of the OpenCL-CTS adding more testing on math functions and conversions with half. Math functions are implemented by upscaling to fp32 and using the fp32 implementation. It garantees the accuracy required for half-precision float-point by the CTS.
240 lines
7.8 KiB
Common Lisp
240 lines
7.8 KiB
Common Lisp
/*
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* Copyright (c) 2014 Advanced Micro Devices, Inc.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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* THE SOFTWARE.
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*/
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#include <clc/clc.h>
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#include "math.h"
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#include "tables.h"
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#include "../clcmacro.h"
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_CLC_OVERLOAD _CLC_DEF float atan2(float y, float x)
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{
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const float pi = 0x1.921fb6p+1f;
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const float piby2 = 0x1.921fb6p+0f;
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const float piby4 = 0x1.921fb6p-1f;
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const float threepiby4 = 0x1.2d97c8p+1f;
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float ax = fabs(x);
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float ay = fabs(y);
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float v = min(ax, ay);
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float u = max(ax, ay);
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// Scale since u could be large, as in "regular" divide
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float s = u > 0x1.0p+96f ? 0x1.0p-32f : 1.0f;
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float vbyu = s * MATH_DIVIDE(v, s*u);
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float vbyu2 = vbyu * vbyu;
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#define USE_2_2_APPROXIMATION
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#if defined USE_2_2_APPROXIMATION
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float p = mad(vbyu2, mad(vbyu2, -0x1.7e1f78p-9f, -0x1.7d1b98p-3f), -0x1.5554d0p-2f) * vbyu2 * vbyu;
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float q = mad(vbyu2, mad(vbyu2, 0x1.1a714cp-2f, 0x1.287c56p+0f), 1.0f);
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#else
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float p = mad(vbyu2, mad(vbyu2, -0x1.55cd22p-5f, -0x1.26cf76p-2f), -0x1.55554ep-2f) * vbyu2 * vbyu;
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float q = mad(vbyu2, mad(vbyu2, mad(vbyu2, 0x1.9f1304p-5f, 0x1.2656fap-1f), 0x1.76b4b8p+0f), 1.0f);
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#endif
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// Octant 0 result
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float a = mad(p, MATH_RECIP(q), vbyu);
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// Fix up 3 other octants
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float at = piby2 - a;
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a = ay > ax ? at : a;
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at = pi - a;
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a = x < 0.0F ? at : a;
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// y == 0 => 0 for x >= 0, pi for x < 0
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at = as_int(x) < 0 ? pi : 0.0f;
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a = y == 0.0f ? at : a;
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// if (!FINITE_ONLY()) {
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// x and y are +- Inf
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at = x > 0.0f ? piby4 : threepiby4;
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a = ax == INFINITY & ay == INFINITY ? at : a;
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// x or y is NaN
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a = isnan(x) | isnan(y) ? as_float(QNANBITPATT_SP32) : a;
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// }
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// Fixup sign and return
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return copysign(a, y);
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}
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_CLC_BINARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, atan2, float, float);
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#ifdef cl_khr_fp64
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#pragma OPENCL EXTENSION cl_khr_fp64 : enable
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_CLC_OVERLOAD _CLC_DEF double atan2(double y, double x)
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{
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const double pi = 3.1415926535897932e+00; /* 0x400921fb54442d18 */
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const double piby2 = 1.5707963267948966e+00; /* 0x3ff921fb54442d18 */
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const double piby4 = 7.8539816339744831e-01; /* 0x3fe921fb54442d18 */
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const double three_piby4 = 2.3561944901923449e+00; /* 0x4002d97c7f3321d2 */
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const double pi_head = 3.1415926218032836e+00; /* 0x400921fb50000000 */
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const double pi_tail = 3.1786509547056392e-08; /* 0x3e6110b4611a6263 */
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const double piby2_head = 1.5707963267948965e+00; /* 0x3ff921fb54442d18 */
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const double piby2_tail = 6.1232339957367660e-17; /* 0x3c91a62633145c07 */
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double x2 = x;
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int xneg = as_int2(x).hi < 0;
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int xexp = (as_int2(x).hi >> 20) & 0x7ff;
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double y2 = y;
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int yneg = as_int2(y).hi < 0;
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int yexp = (as_int2(y).hi >> 20) & 0x7ff;
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int cond2 = (xexp < 1021) & (yexp < 1021);
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int diffexp = yexp - xexp;
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// Scale up both x and y if they are both below 1/4
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double x1 = ldexp(x, 1024);
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int xexp1 = (as_int2(x1).hi >> 20) & 0x7ff;
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double y1 = ldexp(y, 1024);
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int yexp1 = (as_int2(y1).hi >> 20) & 0x7ff;
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int diffexp1 = yexp1 - xexp1;
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diffexp = cond2 ? diffexp1 : diffexp;
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x = cond2 ? x1 : x;
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y = cond2 ? y1 : y;
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// General case: take absolute values of arguments
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double u = fabs(x);
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double v = fabs(y);
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// Swap u and v if necessary to obtain 0 < v < u. Compute v/u.
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int swap_vu = u < v;
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double uu = u;
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u = swap_vu ? v : u;
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v = swap_vu ? uu : v;
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double vbyu = v / u;
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double q1, q2;
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// General values of v/u. Use a look-up table and series expansion.
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{
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double val = vbyu > 0.0625 ? vbyu : 0.063;
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int index = convert_int(fma(256.0, val, 0.5));
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double2 tv = USE_TABLE(atan_jby256_tbl, index - 16);
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q1 = tv.s0;
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q2 = tv.s1;
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double c = (double)index * 0x1.0p-8;
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// We're going to scale u and v by 2^(-u_exponent) to bring them close to 1
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// u_exponent could be EMAX so we have to do it in 2 steps
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int m = -((int)(as_ulong(u) >> EXPSHIFTBITS_DP64) - EXPBIAS_DP64);
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//double um = __amdil_ldexp_f64(u, m);
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//double vm = __amdil_ldexp_f64(v, m);
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double um = ldexp(u, m);
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double vm = ldexp(v, m);
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// 26 leading bits of u
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double u1 = as_double(as_ulong(um) & 0xfffffffff8000000UL);
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double u2 = um - u1;
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double r = MATH_DIVIDE(fma(-c, u2, fma(-c, u1, vm)), fma(c, vm, um));
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// Polynomial approximation to atan(r)
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double s = r * r;
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q2 = q2 + fma((s * fma(-s, 0.19999918038989143496, 0.33333333333224095522)), -r, r);
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}
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double q3, q4;
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{
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q3 = 0.0;
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q4 = vbyu;
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}
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double q5, q6;
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{
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double u1 = as_double(as_ulong(u) & 0xffffffff00000000UL);
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double u2 = u - u1;
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double vu1 = as_double(as_ulong(vbyu) & 0xffffffff00000000UL);
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double vu2 = vbyu - vu1;
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q5 = 0.0;
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double s = vbyu * vbyu;
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q6 = vbyu + fma(-vbyu * s,
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fma(-s,
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fma(-s,
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fma(-s,
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fma(-s, 0.90029810285449784439E-01,
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0.11110736283514525407),
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0.14285713561807169030),
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0.19999999999393223405),
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0.33333333333333170500),
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MATH_DIVIDE(fma(-u, vu2, fma(-u2, vu1, fma(-u1, vu1, v))), u));
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}
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q3 = vbyu < 0x1.d12ed0af1a27fp-27 ? q3 : q5;
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q4 = vbyu < 0x1.d12ed0af1a27fp-27 ? q4 : q6;
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q1 = vbyu > 0.0625 ? q1 : q3;
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q2 = vbyu > 0.0625 ? q2 : q4;
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// Tidy-up according to which quadrant the arguments lie in
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double res1, res2, res3, res4;
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q1 = swap_vu ? piby2_head - q1 : q1;
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q2 = swap_vu ? piby2_tail - q2 : q2;
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q1 = xneg ? pi_head - q1 : q1;
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q2 = xneg ? pi_tail - q2 : q2;
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q1 = q1 + q2;
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res4 = yneg ? -q1 : q1;
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res1 = yneg ? -three_piby4 : three_piby4;
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res2 = yneg ? -piby4 : piby4;
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res3 = xneg ? res1 : res2;
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res3 = isinf(x2) & isinf(y2) ? res3 : res4;
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res1 = yneg ? -pi : pi;
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// abs(x)/abs(y) > 2^56 and x < 0
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res3 = (diffexp < -56 && xneg) ? res1 : res3;
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res4 = MATH_DIVIDE(y, x);
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// x positive and dominant over y by a factor of 2^28
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res3 = diffexp < -28 & xneg == 0 ? res4 : res3;
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// abs(y)/abs(x) > 2^56
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res4 = yneg ? -piby2 : piby2; // atan(y/x) is insignificant compared to piby2
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res3 = diffexp > 56 ? res4 : res3;
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res3 = x2 == 0.0 ? res4 : res3; // Zero x gives +- pi/2 depending on sign of y
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res4 = xneg ? res1 : y2;
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res3 = y2 == 0.0 ? res4 : res3; // Zero y gives +-0 for positive x and +-pi for negative x
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res3 = isnan(y2) ? y2 : res3;
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res3 = isnan(x2) ? x2 : res3;
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return res3;
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}
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_CLC_BINARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, atan2, double, double);
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#endif
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_CLC_DEFINE_BINARY_BUILTIN_FP16(atan2)
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