1 2 /* @(#)e_rem_pio2.c 1.4 95/01/18 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunSoft, 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 #ifndef lint 16 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_rem_pio2.c,v 1.8 2005/02/04 18:26:06 das Exp $"; 17 #endif 18 19 /* __ieee754_rem_pio2(x,y) 20 * 21 * return the remainder of x rem pi/2 in y[0]+y[1] 22 * use __kernel_rem_pio2() 23 */ 24 25 #include "math.h" 26 #include "math_private.h" 27 28 /* 29 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 30 */ 31 static const int32_t two_over_pi[] = { 32 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 33 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 34 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 35 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 36 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 37 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 38 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 39 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 40 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 41 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 42 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 43 }; 44 45 static const int32_t npio2_hw[] = { 46 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 47 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 48 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 49 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 50 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 51 0x404858EB, 0x404921FB, 52 }; 53 54 /* 55 * invpio2: 53 bits of 2/pi 56 * pio2_1: first 33 bit of pi/2 57 * pio2_1t: pi/2 - pio2_1 58 * pio2_2: second 33 bit of pi/2 59 * pio2_2t: pi/2 - (pio2_1+pio2_2) 60 * pio2_3: third 33 bit of pi/2 61 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 62 */ 63 64 static const double 65 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 66 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 67 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 68 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 69 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 70 pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 71 pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 72 pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 73 pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 74 pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 75 76 int32_t __ieee754_rem_pio2(double x, double *y) 77 { 78 double z,w,t,r,fn; 79 double tx[3]; 80 int32_t e0,i,j,nx,n,ix,hx; 81 u_int32_t low; 82 83 GET_HIGH_WORD(hx,x); /* high word of x */ 84 ix = hx&0x7fffffff; 85 if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 86 {y[0] = x; y[1] = 0; return 0;} 87 if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ 88 if(hx>0) { 89 z = x - pio2_1; 90 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 91 y[0] = z - pio2_1t; 92 y[1] = (z-y[0])-pio2_1t; 93 } else { /* near pi/2, use 33+33+53 bit pi */ 94 z -= pio2_2; 95 y[0] = z - pio2_2t; 96 y[1] = (z-y[0])-pio2_2t; 97 } 98 return 1; 99 } else { /* negative x */ 100 z = x + pio2_1; 101 if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 102 y[0] = z + pio2_1t; 103 y[1] = (z-y[0])+pio2_1t; 104 } else { /* near pi/2, use 33+33+53 bit pi */ 105 z += pio2_2; 106 y[0] = z + pio2_2t; 107 y[1] = (z-y[0])+pio2_2t; 108 } 109 return -1; 110 } 111 } 112 if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 113 t = fabs(x); 114 n = (int32_t) (t*invpio2+half); 115 fn = (double)n; 116 r = t-fn*pio2_1; 117 w = fn*pio2_1t; /* 1st round good to 85 bit */ 118 if(n<32&&ix!=npio2_hw[n-1]) { 119 y[0] = r-w; /* quick check no cancellation */ 120 } else { 121 u_int32_t high; 122 j = ix>>20; 123 y[0] = r-w; 124 GET_HIGH_WORD(high,y[0]); 125 i = j-((high>>20)&0x7ff); 126 if(i>16) { /* 2nd iteration needed, good to 118 */ 127 t = r; 128 w = fn*pio2_2; 129 r = t-w; 130 w = fn*pio2_2t-((t-r)-w); 131 y[0] = r-w; 132 GET_HIGH_WORD(high,y[0]); 133 i = j-((high>>20)&0x7ff); 134 if(i>49) { /* 3rd iteration need, 151 bits acc */ 135 t = r; /* will cover all possible cases */ 136 w = fn*pio2_3; 137 r = t-w; 138 w = fn*pio2_3t-((t-r)-w); 139 y[0] = r-w; 140 } 141 } 142 } 143 y[1] = (r-y[0])-w; 144 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 145 else return n; 146 } 147 /* 148 * all other (large) arguments 149 */ 150 if(ix>=0x7ff00000) { /* x is inf or NaN */ 151 y[0]=y[1]=x-x; return 0; 152 } 153 /* set z = scalbn(|x|,ilogb(x)-23) */ 154 GET_LOW_WORD(low,x); 155 SET_LOW_WORD(z,low); 156 e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 157 SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 158 for(i=0;i<2;i++) { 159 tx[i] = (double)((int32_t)(z)); 160 z = (z-tx[i])*two24; 161 } 162 tx[2] = z; 163 nx = 3; 164 while(tx[nx-1]==zero) nx--; /* skip zero term */ 165 n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); 166 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 167 return n; 168 } 169
