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
25#include "math.h"
26#include "tables.h"
27#include "../clcmacro.h"
28
29_CLC_OVERLOAD _CLC_DEF float cbrt(float x) {
30
31    uint xi = as_uint(x);
32    uint axi = xi & EXSIGNBIT_SP32;
33    uint xsign = axi ^ xi;
34    xi = axi;
35
36    int m = (xi >> EXPSHIFTBITS_SP32) - EXPBIAS_SP32;
37
38    // Treat subnormals
39    uint xisub = as_uint(as_float(xi | 0x3f800000) - 1.0f);
40    int msub = (xisub >> EXPSHIFTBITS_SP32) - 253;
41    int c = m == -127;
42    xi = c ? xisub : xi;
43    m = c ? msub : m;
44
45    int m3 = m / 3;
46    int rem = m - m3*3;
47    float mf = as_float((m3 + EXPBIAS_SP32) << EXPSHIFTBITS_SP32);
48
49    uint indx = (xi & 0x007f0000) + ((xi & 0x00008000) << 1);
50    float f = as_float((xi & MANTBITS_SP32) | 0x3f000000) - as_float(indx | 0x3f000000);
51
52    indx >>= 16;
53    float r = f * USE_TABLE(log_inv_tbl, indx);
54    float poly = mad(mad(r, 0x1.f9add4p-5f, -0x1.c71c72p-4f), r*r, r * 0x1.555556p-2f);
55
56    // This could also be done with a 5-element table
57    float remH = 0x1.428000p-1f;
58    float remT = 0x1.45f31ap-14f;
59
60    remH = rem == -1 ? 0x1.964000p-1f : remH;
61    remT = rem == -1 ? 0x1.fea53ep-13f : remT;
62
63    remH = rem ==  0 ? 0x1.000000p+0f : remH;
64    remT = rem ==  0 ? 0x0.000000p+0f  : remT;
65
66    remH = rem ==  1 ? 0x1.428000p+0f : remH;
67    remT = rem ==  1 ? 0x1.45f31ap-13f : remT;
68
69    remH = rem ==  2 ? 0x1.964000p+0f : remH;
70    remT = rem ==  2 ? 0x1.fea53ep-12f : remT;
71
72    float2 tv = USE_TABLE(cbrt_tbl, indx);
73    float cbrtH = tv.s0;
74    float cbrtT = tv.s1;
75
76    float bH = cbrtH * remH;
77    float bT = mad(cbrtH, remT, mad(cbrtT, remH, cbrtT*remT));
78
79    float z = mad(poly, bH, mad(poly, bT, bT)) + bH;
80    z *= mf;
81    z = as_float(as_uint(z) | xsign);
82    c = axi >= EXPBITS_SP32 | axi == 0;
83    z = c ? x : z;
84    return z;
85
86}
87
88_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, float, cbrt, float);
89
90#ifdef cl_khr_fp64
91#pragma OPENCL EXTENSION cl_khr_fp64 : enable
92
93_CLC_OVERLOAD _CLC_DEF double cbrt(double x) {
94
95    int return_x = isinf(x) | isnan(x) | x == 0.0;
96    ulong ux = as_ulong(fabs(x));
97    int m = (as_int2(ux).hi >> 20) - 1023;
98
99    // Treat subnormals
100    ulong uxs = as_ulong(as_double(0x3ff0000000000000UL | ux) - 1.0);
101    int ms = m + (as_int2(uxs).hi >> 20) - 1022;
102
103    int c = m == -1023;
104    ux = c ? uxs : ux;
105    m = c ? ms : m;
106
107    int mby3 = m / 3;
108    int rem = m - 3*mby3;
109
110    double mf = as_double((ulong)(mby3 + 1023) << 52);
111
112    ux &= 0x000fffffffffffffUL;
113    double Y = as_double(0x3fe0000000000000UL | ux);
114
115    // nearest integer
116    int index = as_int2(ux).hi >> 11;
117    index = (0x100 | (index >> 1)) + (index & 1);
118    double F = (double)index * 0x1.0p-9;
119
120    double f = Y - F;
121    double r = f * USE_TABLE(cbrt_inv_tbl, index-256);
122
123    double z = r * fma(r,
124                       fma(r,
125                           fma(r,
126                               fma(r,
127                                   fma(r, -0x1.8090d6221a247p-6, 0x1.ee7113506ac13p-6),
128                                   -0x1.511e8d2b3183bp-5),
129                               0x1.f9add3c0ca458p-5),
130                           -0x1.c71c71c71c71cp-4),
131                       0x1.5555555555555p-2);
132
133    double2 tv = USE_TABLE(cbrt_rem_tbl, rem+2);
134    double Rem_h = tv.s0;
135    double Rem_t = tv.s1;
136
137    tv = USE_TABLE(cbrt_dbl_tbl, index-256);
138    double F_h = tv.s0;
139    double F_t = tv.s1;
140
141    double b_h = F_h * Rem_h;
142    double b_t = fma(Rem_t, F_h, fma(F_t, Rem_h, F_t*Rem_t));
143
144    double ans = fma(z, b_h, fma(z, b_t, b_t)) + b_h;
145    ans = copysign(ans*mf, x);
146    return return_x ? x : ans;
147}
148
149_CLC_UNARY_VECTORIZE(_CLC_OVERLOAD _CLC_DEF, double, cbrt, double)
150
151#endif
152