/* * 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 #include "math.h" #include "tables.h" #include "../clcmacro.h" _CLC_OVERLOAD _CLC_DEF float atan2(float y, float x) { const float pi = 0x1.921fb6p+1f; const float piby2 = 0x1.921fb6p+0f; const float piby4 = 0x1.921fb6p-1f; const float threepiby4 = 0x1.2d97c8p+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-32f : 1.0f; float vbyu = s * MATH_DIVIDE(v, s*u); float vbyu2 = vbyu * vbyu; #define USE_2_2_APPROXIMATION #if defined USE_2_2_APPROXIMATION 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); #else float p = mad(vbyu2, mad(vbyu2, -0x1.55cd22p-5f, -0x1.26cf76p-2f), -0x1.55554ep-2f) * vbyu2 * vbyu; float q = mad(vbyu2, mad(vbyu2, mad(vbyu2, 0x1.9f1304p-5f, 0x1.2656fap-1f), 0x1.76b4b8p+0f), 1.0f); #endif // Octant 0 result float a = mad(p, MATH_RECIP(q), vbyu); // Fix up 3 other octants float at = piby2 - a; a = ay > ax ? at : a; at = pi - a; a = x < 0.0F ? at : a; // y == 0 => 0 for x >= 0, pi for x < 0 at = as_int(x) < 0 ? pi : 0.0f; a = y == 0.0f ? at : a; // if (!FINITE_ONLY()) { // x and y are +- Inf at = x > 0.0f ? piby4 : threepiby4; 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, atan2, float, float); #ifdef cl_khr_fp64 #pragma OPENCL EXTENSION cl_khr_fp64 : enable _CLC_OVERLOAD _CLC_DEF double atan2(double y, double x) { const double pi = 3.1415926535897932e+00; /* 0x400921fb54442d18 */ const double piby2 = 1.5707963267948966e+00; /* 0x3ff921fb54442d18 */ const double piby4 = 7.8539816339744831e-01; /* 0x3fe921fb54442d18 */ const double three_piby4 = 2.3561944901923449e+00; /* 0x4002d97c7f3321d2 */ 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 = __amdil_ldexp_f64(u, m); //double vm = __amdil_ldexp_f64(v, m); 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 = q1 + q2; res4 = yneg ? -q1 : q1; res1 = yneg ? -three_piby4 : three_piby4; res2 = yneg ? -piby4 : piby4; res3 = xneg ? res1 : res2; res3 = isinf(x2) & isinf(y2) ? res3 : res4; res1 = yneg ? -pi : pi; // abs(x)/abs(y) > 2^56 and x < 0 res3 = (diffexp < -56 && xneg) ? res1 : res3; res4 = MATH_DIVIDE(y, x); // 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 ? -piby2 : piby2; // 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, atan2, double, double); #endif