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 * ====================================================
14 static char rcsid[] = "$FreeBSD$";
17 /* __ieee754_rem_pio2(x,y)
19 * return the remainder of x rem pi/2 in y[0]+y[1]
20 * use __kernel_rem_pio2()
24 #include "math_private.h"
27 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
30 static const int32_t two_over_pi[] = {
32 static int32_t two_over_pi[] = {
34 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
35 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
36 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
37 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
38 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
39 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
40 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
41 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
42 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
43 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
44 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
48 static const int32_t npio2_hw[] = {
50 static int32_t npio2_hw[] = {
52 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
53 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
54 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
55 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
56 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
57 0x404858EB, 0x404921FB,
61 * invpio2: 53 bits of 2/pi
62 * pio2_1: first 33 bit of pi/2
63 * pio2_1t: pi/2 - pio2_1
64 * pio2_2: second 33 bit of pi/2
65 * pio2_2t: pi/2 - (pio2_1+pio2_2)
66 * pio2_3: third 33 bit of pi/2
67 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
75 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
76 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
77 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
78 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
79 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
80 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
81 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
82 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
83 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
84 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
87 int32_t __ieee754_rem_pio2(double x, double *y)
89 int32_t __ieee754_rem_pio2(x,y)
95 int32_t e0,i,j,nx,n,ix,hx;
98 GET_HIGH_WORD(hx,x); /* high word of x */
100 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */
101 {y[0] = x; y[1] = 0; return 0;}
102 if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */
105 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
107 y[1] = (z-y[0])-pio2_1t;
108 } else { /* near pi/2, use 33+33+53 bit pi */
111 y[1] = (z-y[0])-pio2_2t;
114 } else { /* negative x */
116 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */
118 y[1] = (z-y[0])+pio2_1t;
119 } else { /* near pi/2, use 33+33+53 bit pi */
122 y[1] = (z-y[0])+pio2_2t;
127 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
129 n = (int32_t) (t*invpio2+half);
132 w = fn*pio2_1t; /* 1st round good to 85 bit */
133 if(n<32&&ix!=npio2_hw[n-1]) {
134 y[0] = r-w; /* quick check no cancellation */
139 GET_HIGH_WORD(high,y[0]);
140 i = j-((high>>20)&0x7ff);
141 if(i>16) { /* 2nd iteration needed, good to 118 */
145 w = fn*pio2_2t-((t-r)-w);
147 GET_HIGH_WORD(high,y[0]);
148 i = j-((high>>20)&0x7ff);
149 if(i>49) { /* 3rd iteration need, 151 bits acc */
150 t = r; /* will cover all possible cases */
153 w = fn*pio2_3t-((t-r)-w);
159 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
163 * all other (large) arguments
165 if(ix>=0x7ff00000) { /* x is inf or NaN */
166 y[0]=y[1]=x-x; return 0;
168 /* set z = scalbn(|x|,ilogb(x)-23) */
171 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */
172 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
174 tx[i] = (double)((int32_t)(z));
179 while(tx[nx-1]==zero) nx--; /* skip zero term */
180 n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
181 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}