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 #ifndef lint 14 static char rcsid[] = "$Id: e_rem_pio2.c,v 1.5 1994/08/18 23:05:56 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 "math_private.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 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<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 103 t = fabs(x); 104 n = (int32_t) (t*invpio2+half); 105 fn = (double)n; 106 r = t-fn*pio2_1; 107 w = fn*pio2_1t; /* 1st round good to 85 bit */ 108 if(n<32&&ix!=npio2_hw[n-1]) { 109 y[0] = r-w; /* quick check no cancellation */ 110 } else { 111 u_int32_t high; 112 j = ix>>20; 113 y[0] = r-w; 114 GET_HIGH_WORD(high,y[0]); 115 i = j-((high>>20)&0x7ff); 116 if(i>16) { /* 2nd iteration needed, good to 118 */ 117 t = r; 118 w = fn*pio2_2; 119 r = t-w; 120 w = fn*pio2_2t-((t-r)-w); 121 y[0] = r-w; 122 GET_HIGH_WORD(high,y[0]); 123 i = j-((high>>20)&0x7ff); 124 if(i>49) { /* 3rd iteration need, 151 bits acc */ 125 t = r; /* will cover all possible cases */ 126 w = fn*pio2_3; 127 r = t-w; 128 w = fn*pio2_3t-((t-r)-w); 129 y[0] = r-w; 130 } 131 } 132 } 133 y[1] = (r-y[0])-w; 134 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 135 else return n; 136 } 137 /* 138 * all other (large) arguments 139 */ 140 if(ix>=0x7ff00000) { /* x is inf or NaN */ 141 y[0]=y[1]=x-x; return 0; 142 } 143 /* set z = scalbn(|x|,ilogb(x)-23) */ 144 GET_LOW_WORD(low,x); 145 SET_LOW_WORD(z,low); 146 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 147 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 148 for(i=0;i<2;i++) { 149 tx[i] = (double)((int32_t)(z)); 150 z = (z-tx[i])*two24; 151 } 152 tx[2] = z; 153 nx = 3; 154 while(tx[nx-1]==zero) nx--; /* skip zero term */ 155 n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); 156 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 157 return n; 158 } 159