1 /* ef_rem_pio2.c -- float version of e_rem_pio2.c
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 */
4
5 /*
6 * ====================================================
7 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
8 *
9 * Developed at SunPro, a Sun Microsystems, Inc. business.
10 * Permission to use, copy, modify, and distribute this
11 * software is freely granted, provided that this notice
12 * is preserved.
13 * ====================================================
14 *
15 */
16
17 /* __rem_pio2f(x,y)
18 *
19 * return the remainder of x rem pi/2 in y[0]+y[1]
20 * use __kernel_rem_pio2_32()
21 */
22
23 #include "fdlibm.h"
24
25 /*
26 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
27 */
28 static const __int32_t two_over_pi[] = {
29 0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, 0x27, 0x57, 0xD1,
30 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, 0x95, 0x99, 0x3C, 0x43, 0x90, 0x41,
31 0xFE, 0x51, 0x63, 0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
32 0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, 0xD1, 0x92, 0x1C,
33 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, 0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5,
34 0x2E, 0xBB, 0x44, 0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
35 0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, 0x84, 0x5F, 0x8B,
36 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, 0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F,
37 0xEF, 0x2F, 0x11, 0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
38 0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, 0x5F, 0xEA, 0x2D,
39 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, 0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7,
40 0x8A, 0x52, 0x92, 0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
41 0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, 0xCF, 0xBC, 0x20,
42 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, 0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08,
43 0x65, 0x99, 0x85, 0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
44 0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, 0x73, 0xA8, 0xC9,
45 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
46 };
47
48 /* This array is like the one in e_rem_pio2.c, but the numbers are
49 single precision and the last 8 bits are forced to 0. */
50 static const __uint32_t npio2_hw[] = {
51 0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
52 0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
53 0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
54 0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
55 0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
56 0x4242c700, 0x42490f00
57 };
58
59 /*
60 * invpio2: 24 bits of 2/pi
61 * pio2_1: first 17 bit of pi/2
62 * pio2_1t: pi/2 - pio2_1
63 * pio2_2: second 17 bit of pi/2
64 * pio2_2t: pi/2 - (pio2_1+pio2_2)
65 * pio2_3: third 17 bit of pi/2
66 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
67 */
68
69 static const float zero = 0.0000000000e+00, /* 0x00000000 */
70 half = 5.0000000000e-01, /* 0x3f000000 */
71 two8 = 2.5600000000e+02, /* 0x43800000 */
72 invpio2 = 6.3661980629e-01, /* 0x3f22f984 */
73 pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */
74 pio2_1t = 1.0804334124e-05, /* 0x37354443 */
75 pio2_2 = 1.0804273188e-05, /* 0x37354400 */
76 pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */
77 pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */
78 pio2_3t = 6.1232342629e-17; /* 0x248d3132 */
79
80 __int32_t
__rem_pio2f(float x,float * y)81 __rem_pio2f(float x, float *y)
82 {
83 float z, w, t, r, fn;
84 float tx[3];
85 __int32_t i, j, n, ix, hx;
86 int e0, nx;
87
88 GET_FLOAT_WORD(hx, x);
89 ix = hx & 0x7fffffff;
90 if (ix <= 0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
91 {
92 y[0] = x;
93 y[1] = 0;
94 return 0;
95 }
96 if (ix < 0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
97 if (hx > 0) {
98 z = x - pio2_1;
99 if ((ix & 0xfffffff0) != 0x3fc90fd0) { /* 24+24 bit pi OK */
100 y[0] = z - pio2_1t;
101 y[1] = (z - y[0]) - pio2_1t;
102 } else { /* near pi/2, use 24+24+24 bit pi */
103 z -= pio2_2;
104 y[0] = z - pio2_2t;
105 y[1] = (z - y[0]) - pio2_2t;
106 }
107 return 1;
108 } else { /* negative x */
109 z = x + pio2_1;
110 if ((ix & 0xfffffff0) != 0x3fc90fd0) { /* 24+24 bit pi OK */
111 y[0] = z + pio2_1t;
112 y[1] = (z - y[0]) + pio2_1t;
113 } else { /* near pi/2, use 24+24+24 bit pi */
114 z += pio2_2;
115 y[0] = z + pio2_2t;
116 y[1] = (z - y[0]) + pio2_2t;
117 }
118 return -1;
119 }
120 }
121 if (ix <= 0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
122 t = fabsf(x);
123 n = (__int32_t)(t * invpio2 + half);
124 fn = (float)n;
125 r = t - fn * pio2_1;
126 w = fn * pio2_1t; /* 1st round good to 40 bit */
127 if (n < 32 && (ix & 0xffffff00) != npio2_hw[n - 1]) {
128 y[0] = r - w; /* quick check no cancellation */
129 } else {
130 __uint32_t high;
131 j = ix >> 23;
132 y[0] = r - w;
133 GET_FLOAT_WORD(high, y[0]);
134 i = j - ((high >> 23) & 0xff);
135 if (i > 8) { /* 2nd iteration needed, good to 57 */
136 t = r;
137 w = fn * pio2_2;
138 r = t - w;
139 w = fn * pio2_2t - ((t - r) - w);
140 y[0] = r - w;
141 GET_FLOAT_WORD(high, y[0]);
142 i = j - ((high >> 23) & 0xff);
143 if (i > 25) { /* 3rd iteration need, 74 bits acc */
144 t = r; /* will cover all possible cases */
145 w = fn * pio2_3;
146 r = t - w;
147 w = fn * pio2_3t - ((t - r) - w);
148 y[0] = r - w;
149 }
150 }
151 }
152 y[1] = (r - y[0]) - w;
153 if (hx < 0) {
154 y[0] = -y[0];
155 y[1] = -y[1];
156 return -n;
157 } else
158 return n;
159 }
160 /*
161 * all other (large) arguments
162 */
163 if (!FLT_UWORD_IS_FINITE(ix)) {
164 y[0] = y[1] = x - x;
165 return 0;
166 }
167 /* set z = scalbn(|x|,ilogb(x)-7) */
168 e0 = (int)((ix >> 23) - 134); /* e0 = ilogb(z)-7; */
169 SET_FLOAT_WORD(z, ix - ((__int32_t)e0 << 23));
170 for (i = 0; i < 2; i++) {
171 tx[i] = (float)((__int32_t)(z));
172 z = (z - tx[i]) * two8;
173 }
174 tx[2] = z;
175 nx = 3;
176 while (tx[nx - 1] == zero)
177 nx--; /* skip zero term */
178 n = __kernel_rem_pio2f(tx, y, e0, nx, 2, two_over_pi);
179 if (hx < 0) {
180 y[0] = -y[0];
181 y[1] = -y[1];
182 return -n;
183 }
184 return n;
185 }
186
