/*
* Copyright (c) 2014,2015 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 cbrt(float x) {
uint xi = as_uint(x);
uint axi = xi & EXSIGNBIT_SP32;
uint xsign = axi ^ xi;
xi = axi;
int m = (xi >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
// Treat subnormals
uint xisub = as_uint(as_float(xi | 0x3f800000) - 1.0f);
int msub = (xisub >> EXPSHIFTBITS_SP32) - 253;
int c = m == -127;
xi = c ? xisub : xi;
m = c ? msub : m;
int m3 = m / 3;
int rem = m - m3*3;
float mf = as_float((m3 + EXPBIAS_SP32) << EXPSHIFTBITS_SP32);
uint indx = (xi & 0x007f0000) + ((xi & 0x00008000) << 1);
float f = as_float((xi & MANTBITS_SP32) | 0x3f000000) - as_float(indx | 0x3f000000);
indx >>= 16;
float r = f * USE_TABLE(log_inv_tbl, indx);
float poly = mad(mad(r, 0x1.f9add4p-5f, -0x1.c71c72p-4f), r*r, r * 0x1.555556p-2f);
// This could also be done with a 5-element table
float remH = 0x1.428000p-1f;
float remT = 0x1.45f31ap-14f;
remH = rem == -1 ? 0x1.964000p-1f : remH;
remT = rem == -1 ? 0x1.fea53ep-13f : remT;
remH = rem == 0 ? 0x1.000000p+0f : remH;
remT = rem == 0 ? 0x0.000000p+0f : remT;
remH = rem == 1 ? 0x1.428000p+0f : remH;
remT = rem == 1 ? 0x1.45f31ap-13f : remT;
remH = rem == 2 ? 0x1.964000p+0f : remH;
remT = rem == 2 ? 0x1.fea53ep-12f : remT;
float2 tv = USE_TABLE(cbrt_tbl, indx);
float cbrtH = tv.s0;
float cbrtT = tv.s1;
float bH = cbrtH * remH;
float bT = mad(cbrtH, remT, mad(cbrtT, remH, cbrtT*remT));
float z = mad(poly, bH, mad(poly, bT, bT)) + bH;
z *= mf;
z = as_float(as_uint(z) | xsign);
c = axi >= EXPBITS_SP32 | axi == 0;
z = c ? x : z;
return z;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, cbrt, float);
#ifdef cl_khr_fp64
#pragma OPENCL EXTENSION cl_khr_fp64 : enable
_CLC_OVERLOAD _CLC_DEF double cbrt(double x) {
int return_x = isinf(x) | isnan(x) | x == 0.0;
ulong ux = as_ulong(fabs(x));
int m = (as_int2(ux).hi >> 20) - 1023;
// Treat subnormals
ulong uxs = as_ulong(as_double(0x3ff0000000000000UL | ux) - 1.0);
int ms = m + (as_int2(uxs).hi >> 20) - 1022;
int c = m == -1023;
ux = c ? uxs : ux;
m = c ? ms : m;
int mby3 = m / 3;
int rem = m - 3*mby3;
double mf = as_double((ulong)(mby3 + 1023) << 52);
ux &= 0x000fffffffffffffUL;
double Y = as_double(0x3fe0000000000000UL | ux);
// nearest integer
int index = as_int2(ux).hi >> 11;
index = (0x100 | (index >> 1)) + (index & 1);
double F = (double)index * 0x1.0p-9;
double f = Y - F;
double r = f * USE_TABLE(cbrt_inv_tbl, index-256);
double z = r * fma(r,
fma(r,
fma(r,
fma(r,
fma(r, -0x1.8090d6221a247p-6, 0x1.ee7113506ac13p-6),
-0x1.511e8d2b3183bp-5),
0x1.f9add3c0ca458p-5),
-0x1.c71c71c71c71cp-4),
0x1.5555555555555p-2);
double2 tv = USE_TABLE(cbrt_rem_tbl, rem+2);
double Rem_h = tv.s0;
double Rem_t = tv.s1;
tv = USE_TABLE(cbrt_dbl_tbl, index-256);
double F_h = tv.s0;
double F_t = tv.s1;
double b_h = F_h * Rem_h;
double b_t = fma(Rem_t, F_h, fma(F_t, Rem_h, F_t*Rem_t));
double ans = fma(z, b_h, fma(z, b_t, b_t)) + b_h;
ans = copysign(ans*mf, x);
return return_x ? x : ans;
}
_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, cbrt, double)
#endif
_CLC_DEFINE_UNARY_BUILTIN_FP16(cbrt)
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