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77a2a8b4 | 1 | /* e_rem_pio2f.c -- float version of e_rem_pio2.c |
688903eb | 2 | Copyright (C) 2011-2018 Free Software Foundation, Inc. |
77a2a8b4 AZ |
3 | This file is part of the GNU C Library. |
4 | Contributed by Adhemerval Zanella <azanella@br.ibm.com>, 2011 | |
5 | ||
6 | The GNU C Library is free software; you can redistribute it and/or | |
7 | modify it under the terms of the GNU Library General Public License as | |
8 | published by the Free Software Foundation; either version 2 of the | |
9 | License, or (at your option) any later version. | |
10 | ||
11 | The GNU C Library is distributed in the hope that it will be useful, | |
12 | but WITHOUT ANY WARRANTY; without even the implied warranty of | |
13 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
14 | Library General Public License for more details. | |
15 | ||
16 | You should have received a copy of the GNU Library General Public | |
59ba27a6 PE |
17 | License along with the GNU C Library; see the file COPYING.LIB. If |
18 | not, see <http://www.gnu.org/licenses/>. */ | |
77a2a8b4 AZ |
19 | |
20 | #include <math.h> | |
21 | ||
1ed0291c | 22 | #include <math_private.h> |
77a2a8b4 AZ |
23 | #include "s_float_bitwise.h" |
24 | ||
25 | /* defined in sysdeps/powerpc/fpu/k_rem_pio2f.c */ | |
26 | int __fp_kernel_rem_pio2f (float *x, float *y, float e0, int32_t nx); | |
27 | ||
28 | /* __ieee754_rem_pio2f(x,y) | |
29 | * | |
30 | * return the remainder of x rem pi/2 in y[0]+y[1] | |
31 | */ | |
32 | ||
33 | static const float npio2_hw[] = { | |
34 | 1.57077026e+00, 3.14154053e+00, 4.71228027e+00, 6.28308105e+00, | |
35 | 7.85388184e+00, 9.42456055e+00, 1.09953613e+01, 1.25661621e+01, | |
36 | 1.41369629e+01, 1.57077637e+01, 1.72783203e+01, 1.88491211e+01, | |
37 | 2.04199219e+01, 2.19907227e+01, 2.35615234e+01, 2.51323242e+01, | |
38 | 2.67031250e+01, 2.82739258e+01, 2.98447266e+01, 3.14155273e+01, | |
39 | 3.29863281e+01, 3.45566406e+01, 3.61279297e+01, 3.76982422e+01, | |
40 | 3.92695312e+01, 4.08398438e+01, 4.24111328e+01, 4.39814453e+01, | |
41 | 4.55527344e+01, 4.71230469e+01, 4.86943359e+01, 5.02646484e+01 | |
42 | }; | |
43 | ||
44 | ||
45 | static const float zero = 0.0000000000e+00; | |
46 | static const float two8 = 2.5600000000e+02; | |
47 | ||
48 | static const float half = 5.0000000000e-01; | |
49 | static const float invpio2 = 6.3661980629e-01; | |
50 | static const float pio2_1 = 1.5707855225e+00; | |
51 | static const float pio2_1t = 1.0804334124e-05; | |
52 | static const float pio2_2 = 1.0804273188e-05; | |
53 | static const float pio2_2t = 6.0770999344e-11; | |
54 | static const float pio2_3 = 6.0770943833e-11; | |
55 | static const float pio2_3t = 6.1232342629e-17; | |
56 | ||
57 | static const float pio4 = 7.8539801e-01; | |
58 | static const float pio3_4 = 2.3561945e+00; | |
59 | static const float pio2_24b = 1.5707951e+00; | |
60 | static const float pio2_2e7 = 2.0106054e+02; | |
61 | ||
62 | ||
63 | int32_t | |
64 | __ieee754_rem_pio2f (float x, float *y) | |
65 | { | |
66 | float ax, z, n, r, w, t, e0; | |
67 | float tx[3]; | |
68 | int32_t i, nx; | |
69 | ||
70 | ax = __builtin_fabsf (x); | |
71 | if (ax <= pio4) | |
72 | { | |
73 | y[0] = x; | |
74 | y[1] = 0; | |
75 | return 0; | |
76 | } | |
77 | if (ax < pio3_4) | |
78 | { | |
79 | if (x > 0) | |
80 | { | |
81 | z = x - pio2_1; | |
82 | if (!__float_and_test28 (ax, pio2_24b)) | |
83 | { | |
84 | y[0] = z - pio2_1t; | |
85 | y[1] = (z - y[0]) - pio2_1t; | |
86 | } | |
87 | else | |
88 | { | |
89 | z -= pio2_2; | |
90 | y[0] = z - pio2_2t; | |
91 | y[1] = (z - y[0]) - pio2_2t; | |
92 | } | |
93 | return 1; | |
94 | } | |
95 | else | |
96 | { | |
97 | z = x + pio2_1; | |
98 | if (!__float_and_test28 (ax, pio2_24b)) | |
99 | { | |
100 | y[0] = z + pio2_1t; | |
101 | y[1] = (z - y[0]) + pio2_1t; | |
102 | } | |
103 | else | |
104 | { | |
105 | z += pio2_2; | |
106 | y[0] = z + pio2_2t; | |
107 | y[1] = (z - y[0]) + pio2_2t; | |
108 | } | |
109 | return -1; | |
110 | } | |
111 | } | |
112 | if (ax <= pio2_2e7) | |
113 | { | |
edc121be | 114 | n = __floorf (ax * invpio2 + half); |
77a2a8b4 AZ |
115 | i = (int32_t) n; |
116 | r = ax - n * pio2_1; | |
117 | w = n * pio2_1t; /* 1st round good to 40 bit */ | |
118 | if (i < 32 && !__float_and_test24 (ax, npio2_hw[i - 1])) | |
119 | { | |
120 | y[0] = r - w; | |
121 | } | |
122 | else | |
123 | { | |
124 | float i, j; | |
125 | j = __float_and8 (ax); | |
126 | y[0] = r - w; | |
127 | i = __float_and8 (y[0]); | |
128 | if (j / i > 256.0 || j / i < 3.9062500e-3) | |
129 | { /* 2nd iterations needed, good to 57 */ | |
130 | t = r; | |
131 | w = n * pio2_2; | |
132 | r = t - w; | |
133 | w = n * pio2_2t - ((t - r) - w); | |
134 | y[0] = r - w; | |
135 | i = __float_and8 (y[0]); | |
136 | if (j / i > 33554432 || j / i < 2.9802322e-8) | |
137 | { /* 3rd iteration needed, 74 bits acc */ | |
138 | t = r; | |
139 | w = n * pio2_3; | |
140 | r = t - w; | |
141 | w = n * pio2_3t - ((t - r) - w); | |
142 | y[0] = r - w; | |
143 | } | |
144 | } | |
145 | } | |
146 | y[1] = (r - y[0]) - w; | |
147 | if (x < 0) | |
148 | { | |
149 | y[0] = -y[0]; | |
150 | y[1] = -y[1]; | |
151 | return -i; | |
152 | } | |
153 | else | |
154 | { | |
155 | return i; | |
156 | } | |
157 | } | |
158 | ||
159 | /* all other (large) arguments */ | |
160 | if (isnanf (x) || isinff (x)) | |
161 | { | |
162 | y[0] = y[1] = x - x; | |
163 | return 0; | |
164 | } | |
165 | ||
166 | /* set z = scalbn(|x|,ilogb(x)-7) */ | |
167 | e0 = __float_and8 (ax / 128.0); | |
168 | z = ax / e0; | |
169 | ||
edc121be | 170 | tx[0] = __floorf (z); |
77a2a8b4 | 171 | z = (z - tx[0]) * two8; |
edc121be | 172 | tx[1] = __floorf (z); |
77a2a8b4 | 173 | z = (z - tx[1]) * two8; |
edc121be | 174 | tx[2] = __floorf (z); |
77a2a8b4 AZ |
175 | |
176 | nx = 3; | |
177 | while (tx[nx - 1] == zero) | |
178 | nx--; | |
179 | ||
180 | i = __fp_kernel_rem_pio2f (tx, y, e0, nx); | |
181 | if (x < 0) | |
182 | { | |
183 | y[0] = -y[0]; | |
184 | y[1] = -y[1]; | |
185 | return -i; | |
186 | } | |
187 | return i; | |
188 | } |