e_rem_pio2.c
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 #if defined(LIBM_SCCS) && !defined(lint) 14 static char rcsid[] = "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $"; 15 #endif 16 17 /* __ieee754_rem_pio2(x,y) 18 * 19 * return the remainder of x rem pi/2 in y[0]+y[1] 20 * use __kernel_rem_pio2() 21 */ 22 23 #include "math.h" 24 #include "mathP.h" 25 26 /* 27 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 28 */ 29 #ifdef __STDC__ 30 static const int32_t two_over_pi[] = { 31 #else 32 static int32_t two_over_pi[] = { 33 #endif 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, 45 }; 46 47 #ifdef __STDC__ 48 static const int32_t npio2_hw[] = { 49 #else 50 static int32_t npio2_hw[] = { 51 #endif 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, 58 }; 59 60 /* 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) 68 */ 69 70 #ifdef __STDC__ 71 static const double 72 #else 73 static double 74 #endif 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 */ 85 86 #ifdef __STDC__ 87 int32_t __ieee754_rem_pio2(double x, double *y) 88 #else 89 int32_t __ieee754_rem_pio2(x,y) 90 double x,y[]; 91 #endif 92 { 93 double z,w,t,r,fn; 94 double tx[3]; 95 int32_t e0,i,j,nx,n,ix,hx; 96 u_int32_t low; 97 98 /* XXX z is not properly initialized without this. Is this a 99 * bug? --ds */ 100 z = 0; 101 102 GET_HIGH_WORD(hx,x); /* high word of x */ 103 ix = hx&0x7fffffff; 104 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 105 {y[0] = x; y[1] = 0; return 0;} 106 if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ 107 if(hx>0) { 108 z = x - pio2_1; 109 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 110 y[0] = z - pio2_1t; 111 y[1] = (z-y[0])-pio2_1t; 112 } else { /* near pi/2, use 33+33+53 bit pi */ 113 z -= pio2_2; 114 y[0] = z - pio2_2t; 115 y[1] = (z-y[0])-pio2_2t; 116 } 117 return 1; 118 } else { /* negative x */ 119 z = x + pio2_1; 120 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 121 y[0] = z + pio2_1t; 122 y[1] = (z-y[0])+pio2_1t; 123 } else { /* near pi/2, use 33+33+53 bit pi */ 124 z += pio2_2; 125 y[0] = z + pio2_2t; 126 y[1] = (z-y[0])+pio2_2t; 127 } 128 return -1; 129 } 130 } 131 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 132 t = fabs(x); 133 n = (int32_t) (t*invpio2+half); 134 fn = (double)n; 135 r = t-fn*pio2_1; 136 w = fn*pio2_1t; /* 1st round good to 85 bit */ 137 if(n<32&&ix!=npio2_hw[n-1]) { 138 y[0] = r-w; /* quick check no cancellation */ 139 } else { 140 u_int32_t high; 141 j = ix>>20; 142 y[0] = r-w; 143 GET_HIGH_WORD(high,y[0]); 144 i = j-((high>>20)&0x7ff); 145 if(i>16) { /* 2nd iteration needed, good to 118 */ 146 t = r; 147 w = fn*pio2_2; 148 r = t-w; 149 w = fn*pio2_2t-((t-r)-w); 150 y[0] = r-w; 151 GET_HIGH_WORD(high,y[0]); 152 i = j-((high>>20)&0x7ff); 153 if(i>49) { /* 3rd iteration need, 151 bits acc */ 154 t = r; /* will cover all possible cases */ 155 w = fn*pio2_3; 156 r = t-w; 157 w = fn*pio2_3t-((t-r)-w); 158 y[0] = r-w; 159 } 160 } 161 } 162 y[1] = (r-y[0])-w; 163 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 164 else return n; 165 } 166 /* 167 * all other (large) arguments 168 */ 169 if(ix>=0x7ff00000) { /* x is inf or NaN */ 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 tx[i] = (double)((int32_t)(z)); 179 z = (z-tx[i])*two24; 180 } 181 tx[2] = z; 182 nx = 3; 183 while(tx[nx-1]==zero) nx--; /* skip zero term */ 184 n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); 185 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 186 return n; 187 }