1 /* @(#)e_rem_pio2.c 5.1 93/09/24 */
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
10 * ====================================================
13 #if defined(LIBM_SCCS) && !defined(lint)
14 static const char rcsid[] =
15 "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $";
18 /* __ieee754_rem_pio2(x,y)
20 * return the remainder of x rem pi/2 in y[0]+y[1]
21 * use __kernel_rem_pio2()
24 #include "math_libm.h"
25 #include "math_private.h"
27 libm_hidden_proto(fabs)
30 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
33 static const int32_t two_over_pi[] = {
35 static int32_t two_over_pi[] = {
37 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
38 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
39 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
40 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
41 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
42 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
43 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
44 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
45 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
46 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
47 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
51 static const int32_t npio2_hw[] = {
53 static int32_t npio2_hw[] = {
55 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
56 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
57 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
58 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
59 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
60 0x404858EB, 0x404921FB,
64 * invpio2: 53 bits of 2/pi
65 * pio2_1: first 33 bit of pi/2
66 * pio2_1t: pi/2 - pio2_1
67 * pio2_2: second 33 bit of pi/2
68 * pio2_2t: pi/2 - (pio2_1+pio2_2)
69 * pio2_3: third 33 bit of pi/2
70 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
78 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
79 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
80 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
81 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
82 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
83 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
84 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
85 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
86 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
87 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
90 int32_t attribute_hidden
91 __ieee754_rem_pio2(double x, double *y)
93 int32_t attribute_hidden
94 __ieee754_rem_pio2(x, y)
98 double z = 0.0, w, t, r, fn;
100 int32_t e0, i, j, nx, n, ix, hx;
103 GET_HIGH_WORD(hx, x); /* high word of x */
104 ix = hx & 0x7fffffff;
105 if (ix <= 0x3fe921fb) { /* |x| ~<= pi/4 , no need for reduction */
110 if (ix < 0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
113 if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */
115 y[1] = (z - y[0]) - pio2_1t;
116 } else { /* near pi/2, use 33+33+53 bit pi */
119 y[1] = (z - y[0]) - pio2_2t;
122 } else { /* negative x */
124 if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */
126 y[1] = (z - y[0]) + pio2_1t;
127 } else { /* near pi/2, use 33+33+53 bit pi */
130 y[1] = (z - y[0]) + pio2_2t;
135 if (ix <= 0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
137 n = (int32_t) (t * invpio2 + half);
140 w = fn * pio2_1t; /* 1st round good to 85 bit */
141 if (n < 32 && ix != npio2_hw[n - 1]) {
142 y[0] = r - w; /* quick check no cancellation */
147 GET_HIGH_WORD(high, y[0]);
148 i = j - ((high >> 20) & 0x7ff);
149 if (i > 16) { /* 2nd iteration needed, good to 118 */
153 w = fn * pio2_2t - ((t - r) - w);
155 GET_HIGH_WORD(high, y[0]);
156 i = j - ((high >> 20) & 0x7ff);
157 if (i > 49) { /* 3rd iteration need, 151 bits acc */
158 t = r; /* will cover all possible cases */
161 w = fn * pio2_3t - ((t - r) - w);
166 y[1] = (r - y[0]) - w;
175 * all other (large) arguments
177 if (ix >= 0x7ff00000) { /* x is inf or NaN */
181 /* set z = scalbn(|x|,ilogb(x)-23) */
182 GET_LOW_WORD(low, x);
183 SET_LOW_WORD(z, low);
184 e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */
185 SET_HIGH_WORD(z, ix - ((int32_t) (e0 << 20)));
186 for (i = 0; i < 2; i++) {
187 tx[i] = (double) ((int32_t) (z));
188 z = (z - tx[i]) * two24;
192 while (tx[nx - 1] == zero)
193 nx--; /* skip zero term */
194 n = __kernel_rem_pio2(tx, y, e0, nx, 2, two_over_pi);