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152 lines
4.7 KiB
152 lines
4.7 KiB
/*
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* Copyright (c) 2014,2015 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 cbrt(float x) {
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uint xi = as_uint(x);
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uint axi = xi & EXSIGNBIT_SP32;
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uint xsign = axi ^ xi;
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xi = axi;
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int m = (xi >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
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// Treat subnormals
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uint xisub = as_uint(as_float(xi | 0x3f800000) - 1.0f);
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int msub = (xisub >> EXPSHIFTBITS_SP32) - 253;
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int c = m == -127;
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xi = c ? xisub : xi;
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m = c ? msub : m;
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int m3 = m / 3;
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int rem = m - m3*3;
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float mf = as_float((m3 + EXPBIAS_SP32) << EXPSHIFTBITS_SP32);
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uint indx = (xi & 0x007f0000) + ((xi & 0x00008000) << 1);
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float f = as_float((xi & MANTBITS_SP32) | 0x3f000000) - as_float(indx | 0x3f000000);
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indx >>= 16;
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float r = f * USE_TABLE(log_inv_tbl, indx);
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float poly = mad(mad(r, 0x1.f9add4p-5f, -0x1.c71c72p-4f), r*r, r * 0x1.555556p-2f);
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// This could also be done with a 5-element table
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float remH = 0x1.428000p-1f;
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float remT = 0x1.45f31ap-14f;
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remH = rem == -1 ? 0x1.964000p-1f : remH;
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remT = rem == -1 ? 0x1.fea53ep-13f : remT;
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remH = rem == 0 ? 0x1.000000p+0f : remH;
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remT = rem == 0 ? 0x0.000000p+0f : remT;
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remH = rem == 1 ? 0x1.428000p+0f : remH;
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remT = rem == 1 ? 0x1.45f31ap-13f : remT;
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remH = rem == 2 ? 0x1.964000p+0f : remH;
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remT = rem == 2 ? 0x1.fea53ep-12f : remT;
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float2 tv = USE_TABLE(cbrt_tbl, indx);
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float cbrtH = tv.s0;
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float cbrtT = tv.s1;
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float bH = cbrtH * remH;
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float bT = mad(cbrtH, remT, mad(cbrtT, remH, cbrtT*remT));
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float z = mad(poly, bH, mad(poly, bT, bT)) + bH;
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z *= mf;
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z = as_float(as_uint(z) | xsign);
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c = axi >= EXPBITS_SP32 | axi == 0;
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z = c ? x : z;
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return z;
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}
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_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, cbrt, 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 cbrt(double x) {
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int return_x = isinf(x) | isnan(x) | x == 0.0;
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ulong ux = as_ulong(fabs(x));
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int m = (as_int2(ux).hi >> 20) - 1023;
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// Treat subnormals
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ulong uxs = as_ulong(as_double(0x3ff0000000000000UL | ux) - 1.0);
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int ms = m + (as_int2(uxs).hi >> 20) - 1022;
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int c = m == -1023;
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ux = c ? uxs : ux;
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m = c ? ms : m;
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int mby3 = m / 3;
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int rem = m - 3*mby3;
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double mf = as_double((ulong)(mby3 + 1023) << 52);
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ux &= 0x000fffffffffffffUL;
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double Y = as_double(0x3fe0000000000000UL | ux);
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// nearest integer
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int index = as_int2(ux).hi >> 11;
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index = (0x100 | (index >> 1)) + (index & 1);
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double F = (double)index * 0x1.0p-9;
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double f = Y - F;
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double r = f * USE_TABLE(cbrt_inv_tbl, index-256);
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double z = r * fma(r,
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fma(r,
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fma(r,
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fma(r,
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fma(r, -0x1.8090d6221a247p-6, 0x1.ee7113506ac13p-6),
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-0x1.511e8d2b3183bp-5),
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0x1.f9add3c0ca458p-5),
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-0x1.c71c71c71c71cp-4),
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0x1.5555555555555p-2);
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double2 tv = USE_TABLE(cbrt_rem_tbl, rem+2);
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double Rem_h = tv.s0;
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double Rem_t = tv.s1;
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tv = USE_TABLE(cbrt_dbl_tbl, index-256);
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double F_h = tv.s0;
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double F_t = tv.s1;
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double b_h = F_h * Rem_h;
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double b_t = fma(Rem_t, F_h, fma(F_t, Rem_h, F_t*Rem_t));
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double ans = fma(z, b_h, fma(z, b_t, b_t)) + b_h;
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ans = copysign(ans*mf, x);
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return return_x ? x : ans;
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}
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_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, cbrt, double)
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#endif
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