1 2 /* @(#)e_rem_pio2.c 5.1 93/09/24 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunPro, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 * 13 */ 14 15 /* __ieee754_rem_pio2(x,y) 16 * 17 * return the remainder of x rem pi/2 in y[0]+y[1] 18 * use __kernel_rem_pio2() 19 */ 20 21 #include "fdlibm.h" 22 23 #ifndef _DOUBLE_IS_32BITS 24 25 /* 26 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 27 */ 28 #ifdef __STDC__ 29 static const __int32_t two_over_pi[] = { 30 #else 31 static __int32_t two_over_pi[] = { 32 #endif 33 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 34 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 35 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 36 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 37 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 38 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 39 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 40 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 41 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 42 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 43 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 44 }; 45 46 #ifdef __STDC__ 47 static const __int32_t npio2_hw[] = { 48 #else 49 static __int32_t npio2_hw[] = { 50 #endif 51 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 52 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 53 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 54 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 55 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 56 0x404858EB, 0x404921FB, 57 }; 58 59 /* 60 * invpio2: 53 bits of 2/pi 61 * pio2_1: first 33 bit of pi/2 62 * pio2_1t: pi/2 - pio2_1 63 * pio2_2: second 33 bit of pi/2 64 * pio2_2t: pi/2 - (pio2_1+pio2_2) 65 * pio2_3: third 33 bit of pi/2 66 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 67 */ 68 69 #ifdef __STDC__ 70 static const double 71 #else 72 static double 73 #endif 74 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 75 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 76 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 77 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 78 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 79 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 80 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 81 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 82 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 83 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 84 85 #ifdef __STDC__ __ieee754_rem_pio2(double x,double * y)86 __int32_t __ieee754_rem_pio2(double x, double *y) 87 #else 88 __int32_t __ieee754_rem_pio2(x,y) 89 double x,y[]; 90 #endif 91 { 92 double z,w,t,r,fn; 93 double tx[3]; 94 __int32_t i,j,n,ix,hx; 95 int e0,nx; 96 __uint32_t low; 97 98 GET_HIGH_WORD(hx,x); /* high word of x */ 99 ix = hx&0x7fffffff; 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 */ 103 if(hx>0) { 104 z = x - pio2_1; 105 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 106 y[0] = z - pio2_1t; 107 y[1] = (z-y[0])-pio2_1t; 108 } else { /* near pi/2, use 33+33+53 bit pi */ 109 z -= pio2_2; 110 y[0] = z - pio2_2t; 111 y[1] = (z-y[0])-pio2_2t; 112 } 113 return 1; 114 } else { /* negative x */ 115 z = x + pio2_1; 116 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 117 y[0] = z + pio2_1t; 118 y[1] = (z-y[0])+pio2_1t; 119 } else { /* near pi/2, use 33+33+53 bit pi */ 120 z += pio2_2; 121 y[0] = z + pio2_2t; 122 y[1] = (z-y[0])+pio2_2t; 123 } 124 return -1; 125 } 126 } 127 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 128 t = fabs(x); 129 n = (__int32_t) (t*invpio2+half); 130 fn = (double)n; 131 r = t-fn*pio2_1; 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 */ 135 } else { 136 __uint32_t high; 137 j = ix>>20; 138 y[0] = r-w; 139 GET_HIGH_WORD(high,y[0]); 140 i = j-((high>>20)&0x7ff); 141 if(i>16) { /* 2nd iteration needed, good to 118 */ 142 t = r; 143 w = fn*pio2_2; 144 r = t-w; 145 w = fn*pio2_2t-((t-r)-w); 146 y[0] = 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 */ 151 w = fn*pio2_3; 152 r = t-w; 153 w = fn*pio2_3t-((t-r)-w); 154 y[0] = r-w; 155 } 156 } 157 } 158 y[1] = (r-y[0])-w; 159 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 160 else return n; 161 } 162 /* 163 * all other (large) arguments 164 */ 165 if(ix>=0x7ff00000) { /* x is inf or NaN */ 166 y[0]=y[1]=x-x; return 0; 167 } 168 /* set z = scalbn(|x|,ilogb(x)-23) */ 169 GET_LOW_WORD(low,x); 170 SET_LOW_WORD(z,low); 171 e0 = (int)((ix>>20)-1046); /* e0 = ilogb(z)-23; */ 172 SET_HIGH_WORD(z, ix - ((__int32_t)e0<<20)); 173 for(i=0;i<2;i++) { 174 tx[i] = (double)((__int32_t)(z)); 175 z = (z-tx[i])*two24; 176 } 177 tx[2] = z; 178 nx = 3; 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;} 182 return n; 183 } 184 185 #endif /* defined(_DOUBLE_IS_32BITS) */ 186