1 /* @(#)e_rem_pio2.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 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 9 * is preserved. 10 * ==================================================== 11 */ 12 13 #include <sys/cdefs.h> 14 #if defined(LIBM_SCCS) && !defined(lint) 15 __RCSID("$NetBSD: e_rem_pio2.c,v 1.9 1997/10/09 11:29:44 lukem Exp $"); 16 #endif 17 18 /* __ieee754_rem_pio2(x,y) 19 * 20 * return the remainder of x rem pi/2 in y[0]+y[1] 21 * use __kernel_rem_pio2() 22 */ 23 24 #include "math.h" 25 #include "math_private.h" 26 27 /* 28 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 29 */ 30 #ifdef __STDC__ 31 static const int32_t two_over_pi[] = { 32 #else 33 static int32_t two_over_pi[] = { 34 #endif 35 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 36 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 37 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 38 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 39 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 40 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 41 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 42 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 43 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 44 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 45 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 46 }; 47 48 #ifdef __STDC__ 49 static const int32_t npio2_hw[] = { 50 #else 51 static int32_t npio2_hw[] = { 52 #endif 53 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 54 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 55 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 56 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 57 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 58 0x404858EB, 0x404921FB, 59 }; 60 61 /* 62 * invpio2: 53 bits of 2/pi 63 * pio2_1: first 33 bit of pi/2 64 * pio2_1t: pi/2 - pio2_1 65 * pio2_2: second 33 bit of pi/2 66 * pio2_2t: pi/2 - (pio2_1+pio2_2) 67 * pio2_3: third 33 bit of pi/2 68 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 69 */ 70 71 #ifdef __STDC__ 72 static const double 73 #else 74 static double 75 #endif 76 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 77 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 78 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 79 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 80 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 81 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 82 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 83 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 84 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 85 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 86 87 #ifdef __STDC__ 88 int32_t __ieee754_rem_pio2(double x, double *y) 89 #else 90 int32_t __ieee754_rem_pio2(x,y) 91 double x,y[]; 92 #endif 93 { 94 double z,w,t,r,fn; 95 double tx[3]; 96 int32_t e0,i,j,nx,n,ix,hx; 97 u_int32_t low; 98 99 z = 0; 100 GET_HIGH_WORD(hx,x); /* high word of x */ 101 ix = hx&0x7fffffff; 102 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 103 {y[0] = x; y[1] = 0; return 0;} 104 if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ 105 if(hx>0) { 106 z = x - pio2_1; 107 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 108 y[0] = z - pio2_1t; 109 y[1] = (z-y[0])-pio2_1t; 110 } else { /* near pi/2, use 33+33+53 bit pi */ 111 z -= pio2_2; 112 y[0] = z - pio2_2t; 113 y[1] = (z-y[0])-pio2_2t; 114 } 115 return 1; 116 } else { /* negative x */ 117 z = x + pio2_1; 118 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 119 y[0] = z + pio2_1t; 120 y[1] = (z-y[0])+pio2_1t; 121 } else { /* near pi/2, use 33+33+53 bit pi */ 122 z += pio2_2; 123 y[0] = z + pio2_2t; 124 y[1] = (z-y[0])+pio2_2t; 125 } 126 return -1; 127 } 128 } 129 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 130 t = fabs(x); 131 n = (int32_t) (t*invpio2+half); 132 fn = (double)n; 133 r = t-fn*pio2_1; 134 w = fn*pio2_1t; /* 1st round good to 85 bit */ 135 if(n<32&&ix!=npio2_hw[n-1]) { 136 y[0] = r-w; /* quick check no cancellation */ 137 } else { 138 u_int32_t high; 139 j = ix>>20; 140 y[0] = r-w; 141 GET_HIGH_WORD(high,y[0]); 142 i = j-((high>>20)&0x7ff); 143 if(i>16) { /* 2nd iteration needed, good to 118 */ 144 t = r; 145 w = fn*pio2_2; 146 r = t-w; 147 w = fn*pio2_2t-((t-r)-w); 148 y[0] = r-w; 149 GET_HIGH_WORD(high,y[0]); 150 i = j-((high>>20)&0x7ff); 151 if(i>49) { /* 3rd iteration need, 151 bits acc */ 152 t = r; /* will cover all possible cases */ 153 w = fn*pio2_3; 154 r = t-w; 155 w = fn*pio2_3t-((t-r)-w); 156 y[0] = r-w; 157 } 158 } 159 } 160 y[1] = (r-y[0])-w; 161 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 162 else return n; 163 } 164 /* 165 * all other (large) arguments 166 */ 167 if(ix>=0x7ff00000) { /* x is inf or NaN */ 168 y[0]=y[1]=x-x; return 0; 169 } 170 /* set z = scalbn(|x|,ilogb(x)-23) */ 171 GET_LOW_WORD(low,x); 172 SET_LOW_WORD(z,low); 173 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 174 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 175 for(i=0;i<2;i++) { 176 tx[i] = (double)((int32_t)(z)); 177 z = (z-tx[i])*two24; 178 } 179 tx[2] = z; 180 nx = 3; 181 while(tx[nx-1]==zero) nx--; /* skip zero term */ 182 n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); 183 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 184 return n; 185 } 186