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238 lines
7.7 KiB
238 lines
7.7 KiB
/*
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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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