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Diffstat (limited to 'libclc/generic/lib/math/atan2.cl')
| -rw-r--r-- | libclc/generic/lib/math/atan2.cl | 237 |
1 files changed, 237 insertions, 0 deletions
diff --git a/libclc/generic/lib/math/atan2.cl b/libclc/generic/lib/math/atan2.cl new file mode 100644 index 0000000..a2f104f --- /dev/null +++ b/libclc/generic/lib/math/atan2.cl @@ -0,0 +1,237 @@ +/* + * 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 <clc/clc.h> + +#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 |