1/* 2 * Copyright (c) 2014,2015 Advanced Micro Devices, Inc. 3 * 4 * Permission is hereby granted, free of charge, to any person obtaining a copy 5 * of this software and associated documentation files (the "Software"), to deal 6 * in the Software without restriction, including without limitation the rights 7 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 8 * copies of the Software, and to permit persons to whom the Software is 9 * furnished to do so, subject to the following conditions: 10 * 11 * The above copyright notice and this permission notice shall be included in 12 * all copies or substantial portions of the Software. 13 * 14 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 15 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 16 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 17 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 18 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 19 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN 20 * THE SOFTWARE. 21 */ 22 23#include <clc/clc.h> 24#include <clc/clcmacro.h> 25#include <clc/math/math.h> 26#include <clc/math/tables.h> 27 28_CLC_OVERLOAD _CLC_DEF float cbrt(float x) { 29 30 uint xi = as_uint(x); 31 uint axi = xi & EXSIGNBIT_SP32; 32 uint xsign = axi ^ xi; 33 xi = axi; 34 35 int m = (xi >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32; 36 37 // Treat subnormals 38 uint xisub = as_uint(as_float(xi | 0x3f800000) - 1.0f); 39 int msub = (xisub >> EXPSHIFTBITS_SP32) - 253; 40 int c = m == -127; 41 xi = c ? xisub : xi; 42 m = c ? msub : m; 43 44 int m3 = m / 3; 45 int rem = m - m3*3; 46 float mf = as_float((m3 + EXPBIAS_SP32) << EXPSHIFTBITS_SP32); 47 48 uint indx = (xi & 0x007f0000) + ((xi & 0x00008000) << 1); 49 float f = as_float((xi & MANTBITS_SP32) | 0x3f000000) - as_float(indx | 0x3f000000); 50 51 indx >>= 16; 52 float r = f * USE_TABLE(log_inv_tbl, indx); 53 float poly = mad(mad(r, 0x1.f9add4p-5f, -0x1.c71c72p-4f), r*r, r * 0x1.555556p-2f); 54 55 // This could also be done with a 5-element table 56 float remH = 0x1.428000p-1f; 57 float remT = 0x1.45f31ap-14f; 58 59 remH = rem == -1 ? 0x1.964000p-1f : remH; 60 remT = rem == -1 ? 0x1.fea53ep-13f : remT; 61 62 remH = rem == 0 ? 0x1.000000p+0f : remH; 63 remT = rem == 0 ? 0x0.000000p+0f : remT; 64 65 remH = rem == 1 ? 0x1.428000p+0f : remH; 66 remT = rem == 1 ? 0x1.45f31ap-13f : remT; 67 68 remH = rem == 2 ? 0x1.964000p+0f : remH; 69 remT = rem == 2 ? 0x1.fea53ep-12f : remT; 70 71 float2 tv = USE_TABLE(cbrt_tbl, indx); 72 float cbrtH = tv.s0; 73 float cbrtT = tv.s1; 74 75 float bH = cbrtH * remH; 76 float bT = mad(cbrtH, remT, mad(cbrtT, remH, cbrtT*remT)); 77 78 float z = mad(poly, bH, mad(poly, bT, bT)) + bH; 79 z *= mf; 80 z = as_float(as_uint(z) | xsign); 81 c = axi >= EXPBITS_SP32 | axi == 0; 82 z = c ? x : z; 83 return z; 84 85} 86 87_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, cbrt, float); 88 89#ifdef cl_khr_fp64 90#pragma OPENCL EXTENSION cl_khr_fp64 : enable 91 92_CLC_OVERLOAD _CLC_DEF double cbrt(double x) { 93 94 int return_x = isinf(x) | isnan(x) | x == 0.0; 95 ulong ux = as_ulong(fabs(x)); 96 int m = (as_int2(ux).hi >> 20) - 1023; 97 98 // Treat subnormals 99 ulong uxs = as_ulong(as_double(0x3ff0000000000000UL | ux) - 1.0); 100 int ms = m + (as_int2(uxs).hi >> 20) - 1022; 101 102 int c = m == -1023; 103 ux = c ? uxs : ux; 104 m = c ? ms : m; 105 106 int mby3 = m / 3; 107 int rem = m - 3*mby3; 108 109 double mf = as_double((ulong)(mby3 + 1023) << 52); 110 111 ux &= 0x000fffffffffffffUL; 112 double Y = as_double(0x3fe0000000000000UL | ux); 113 114 // nearest integer 115 int index = as_int2(ux).hi >> 11; 116 index = (0x100 | (index >> 1)) + (index & 1); 117 double F = (double)index * 0x1.0p-9; 118 119 double f = Y - F; 120 double r = f * USE_TABLE(cbrt_inv_tbl, index-256); 121 122 double z = r * fma(r, 123 fma(r, 124 fma(r, 125 fma(r, 126 fma(r, -0x1.8090d6221a247p-6, 0x1.ee7113506ac13p-6), 127 -0x1.511e8d2b3183bp-5), 128 0x1.f9add3c0ca458p-5), 129 -0x1.c71c71c71c71cp-4), 130 0x1.5555555555555p-2); 131 132 double2 tv = USE_TABLE(cbrt_rem_tbl, rem+2); 133 double Rem_h = tv.s0; 134 double Rem_t = tv.s1; 135 136 tv = USE_TABLE(cbrt_dbl_tbl, index-256); 137 double F_h = tv.s0; 138 double F_t = tv.s1; 139 140 double b_h = F_h * Rem_h; 141 double b_t = fma(Rem_t, F_h, fma(F_t, Rem_h, F_t*Rem_t)); 142 143 double ans = fma(z, b_h, fma(z, b_t, b_t)) + b_h; 144 ans = copysign(ans*mf, x); 145 return return_x ? x : ans; 146} 147 148_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, cbrt, double) 149 150#endif 151 152#ifdef cl_khr_fp16 153 154#pragma OPENCL EXTENSION cl_khr_fp16 : enable 155 156_CLC_DEFINE_UNARY_BUILTIN_FP16(cbrt) 157 158#endif 159