1 | #ifdef NOT_NEEDED_ANYMORE |
2 | |
3 | /* |
4 | * ==================================================== |
5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
6 | * |
7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
8 | * Permission to use, copy, modify, and distribute this |
9 | * software is freely granted, provided that this notice |
10 | * is preserved. |
11 | * ==================================================== |
12 | */ |
13 | |
14 | /* __ieee754_rem_pio2(x,y) |
15 | * |
16 | * return the remainder of x rem pi/2 in y[0]+y[1] |
17 | * use __kernel_rem_pio2() |
18 | */ |
19 | |
20 | #include <math.h> |
21 | #include <math_private.h> |
22 | |
23 | /* |
24 | * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
25 | */ |
26 | static const int32_t two_over_pi[] = { |
27 | 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, |
28 | 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, |
29 | 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, |
30 | 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, |
31 | 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, |
32 | 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, |
33 | 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, |
34 | 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, |
35 | 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, |
36 | 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, |
37 | 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, |
38 | }; |
39 | |
40 | static const int32_t npio2_hw[] = { |
41 | 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, |
42 | 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, |
43 | 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, |
44 | 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, |
45 | 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, |
46 | 0x404858EB, 0x404921FB, |
47 | }; |
48 | |
49 | /* |
50 | * invpio2: 53 bits of 2/pi |
51 | * pio2_1: first 33 bit of pi/2 |
52 | * pio2_1t: pi/2 - pio2_1 |
53 | * pio2_2: second 33 bit of pi/2 |
54 | * pio2_2t: pi/2 - (pio2_1+pio2_2) |
55 | * pio2_3: third 33 bit of pi/2 |
56 | * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
57 | */ |
58 | |
59 | static const double |
60 | zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
61 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
62 | two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ |
63 | invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
64 | pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ |
65 | pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ |
66 | pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ |
67 | pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ |
68 | pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ |
69 | pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ |
70 | |
71 | int32_t |
72 | __ieee754_rem_pio2 (double x, double *y) |
73 | { |
74 | double z, w, t, r, fn; |
75 | double tx[3]; |
76 | int32_t e0, i, j, nx, n, ix, hx; |
77 | uint32_t low; |
78 | |
79 | GET_HIGH_WORD (hx, x); /* high word of x */ |
80 | ix = hx & 0x7fffffff; |
81 | if (ix <= 0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ |
82 | { |
83 | y[0] = x; y[1] = 0; return 0; |
84 | } |
85 | if (ix < 0x4002d97c) /* |x| < 3pi/4, special case with n=+-1 */ |
86 | { |
87 | if (hx > 0) |
88 | { |
89 | z = x - pio2_1; |
90 | if (ix != 0x3ff921fb) /* 33+53 bit pi is good enough */ |
91 | { |
92 | y[0] = z - pio2_1t; |
93 | y[1] = (z - y[0]) - pio2_1t; |
94 | } |
95 | else /* near pi/2, use 33+33+53 bit pi */ |
96 | { |
97 | z -= pio2_2; |
98 | y[0] = z - pio2_2t; |
99 | y[1] = (z - y[0]) - pio2_2t; |
100 | } |
101 | return 1; |
102 | } |
103 | else /* negative x */ |
104 | { |
105 | z = x + pio2_1; |
106 | if (ix != 0x3ff921fb) /* 33+53 bit pi is good enough */ |
107 | { |
108 | y[0] = z + pio2_1t; |
109 | y[1] = (z - y[0]) + pio2_1t; |
110 | } |
111 | else /* near pi/2, use 33+33+53 bit pi */ |
112 | { |
113 | z += pio2_2; |
114 | y[0] = z + pio2_2t; |
115 | y[1] = (z - y[0]) + pio2_2t; |
116 | } |
117 | return -1; |
118 | } |
119 | } |
120 | if (ix <= 0x413921fb) /* |x| ~<= 2^19*(pi/2), medium size */ |
121 | { |
122 | t = fabs (x); |
123 | n = (int32_t) (t * invpio2 + half); |
124 | fn = (double) n; |
125 | r = t - fn * pio2_1; |
126 | w = fn * pio2_1t; /* 1st round good to 85 bit */ |
127 | if (n < 32 && ix != npio2_hw[n - 1]) |
128 | { |
129 | y[0] = r - w; /* quick check no cancellation */ |
130 | } |
131 | else |
132 | { |
133 | uint32_t high; |
134 | j = ix >> 20; |
135 | y[0] = r - w; |
136 | GET_HIGH_WORD (high, y[0]); |
137 | i = j - ((high >> 20) & 0x7ff); |
138 | if (i > 16) /* 2nd iteration needed, good to 118 */ |
139 | { |
140 | t = r; |
141 | w = fn * pio2_2; |
142 | r = t - w; |
143 | w = fn * pio2_2t - ((t - r) - w); |
144 | y[0] = r - w; |
145 | GET_HIGH_WORD (high, y[0]); |
146 | i = j - ((high >> 20) & 0x7ff); |
147 | if (i > 49) /* 3rd iteration need, 151 bits acc */ |
148 | { |
149 | t = r; /* will cover all possible cases */ |
150 | w = fn * pio2_3; |
151 | r = t - w; |
152 | w = fn * pio2_3t - ((t - r) - w); |
153 | y[0] = r - w; |
154 | } |
155 | } |
156 | } |
157 | y[1] = (r - y[0]) - w; |
158 | if (hx < 0) |
159 | { |
160 | y[0] = -y[0]; y[1] = -y[1]; return -n; |
161 | } |
162 | else |
163 | return n; |
164 | } |
165 | /* |
166 | * all other (large) arguments |
167 | */ |
168 | if (ix >= 0x7ff00000) /* x is inf or NaN */ |
169 | { |
170 | y[0] = y[1] = x - x; return 0; |
171 | } |
172 | /* set z = scalbn(|x|,ilogb(x)-23) */ |
173 | GET_LOW_WORD (low, x); |
174 | SET_LOW_WORD (z, low); |
175 | e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */ |
176 | SET_HIGH_WORD (z, ix - ((int32_t) (e0 << 20))); |
177 | for (i = 0; i < 2; i++) |
178 | { |
179 | tx[i] = (double) ((int32_t) (z)); |
180 | z = (z - tx[i]) * two24; |
181 | } |
182 | tx[2] = z; |
183 | nx = 3; |
184 | while (tx[nx - 1] == zero) |
185 | nx--; /* skip zero term */ |
186 | n = __kernel_rem_pio2 (tx, y, e0, nx, 2, two_over_pi); |
187 | if (hx < 0) |
188 | { |
189 | y[0] = -y[0]; y[1] = -y[1]; return -n; |
190 | } |
191 | return n; |
192 | } |
193 | #endif |
194 | |