The Android Open Source Project | b07e1d9 | 2009-03-03 19:29:30 -0800 | [diff] [blame] | 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 | /* __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 | /* |
| 24 | * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi |
| 25 | */ |
| 26 | #ifdef __STDC__ |
| 27 | static const int two_over_pi[] = { |
| 28 | #else |
| 29 | static int two_over_pi[] = { |
| 30 | #endif |
| 31 | 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, |
| 32 | 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, |
| 33 | 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, |
| 34 | 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, |
| 35 | 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, |
| 36 | 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, |
| 37 | 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, |
| 38 | 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, |
| 39 | 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, |
| 40 | 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, |
| 41 | 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, |
| 42 | }; |
| 43 | |
| 44 | #ifdef __STDC__ |
| 45 | static const int npio2_hw[] = { |
| 46 | #else |
| 47 | static int npio2_hw[] = { |
| 48 | #endif |
| 49 | 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, |
| 50 | 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, |
| 51 | 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, |
| 52 | 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, |
| 53 | 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, |
| 54 | 0x404858EB, 0x404921FB, |
| 55 | }; |
| 56 | |
| 57 | /* |
| 58 | * invpio2: 53 bits of 2/pi |
| 59 | * pio2_1: first 33 bit of pi/2 |
| 60 | * pio2_1t: pi/2 - pio2_1 |
| 61 | * pio2_2: second 33 bit of pi/2 |
| 62 | * pio2_2t: pi/2 - (pio2_1+pio2_2) |
| 63 | * pio2_3: third 33 bit of pi/2 |
| 64 | * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) |
| 65 | */ |
| 66 | |
| 67 | #ifdef __STDC__ |
| 68 | static const double |
| 69 | #else |
| 70 | static double |
| 71 | #endif |
| 72 | zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ |
| 73 | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
| 74 | two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ |
| 75 | invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ |
| 76 | pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ |
| 77 | pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ |
| 78 | pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ |
| 79 | pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ |
| 80 | pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ |
| 81 | pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ |
| 82 | |
| 83 | #ifdef __STDC__ |
| 84 | int __ieee754_rem_pio2(double x, double *y) |
| 85 | #else |
| 86 | int __ieee754_rem_pio2(x,y) |
| 87 | double x,y[]; |
| 88 | #endif |
| 89 | { |
| 90 | double z,w,t,r,fn; |
| 91 | double tx[3]; |
| 92 | int e0,i,j,nx,n,ix,hx; |
| 93 | |
| 94 | hx = __HI(x); /* high word of x */ |
| 95 | ix = hx&0x7fffffff; |
| 96 | if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ |
| 97 | {y[0] = x; y[1] = 0; return 0;} |
| 98 | if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ |
| 99 | if(hx>0) { |
| 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 | } else { /* negative x */ |
| 111 | z = x + pio2_1; |
| 112 | if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ |
| 113 | y[0] = z + pio2_1t; |
| 114 | y[1] = (z-y[0])+pio2_1t; |
| 115 | } else { /* near pi/2, use 33+33+53 bit pi */ |
| 116 | z += pio2_2; |
| 117 | y[0] = z + pio2_2t; |
| 118 | y[1] = (z-y[0])+pio2_2t; |
| 119 | } |
| 120 | return -1; |
| 121 | } |
| 122 | } |
| 123 | if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ |
| 124 | t = ieee_fabs(x); |
| 125 | n = (int) (t*invpio2+half); |
| 126 | fn = (double)n; |
| 127 | r = t-fn*pio2_1; |
| 128 | w = fn*pio2_1t; /* 1st round good to 85 bit */ |
| 129 | if(n<32&&ix!=npio2_hw[n-1]) { |
| 130 | y[0] = r-w; /* quick check no cancellation */ |
| 131 | } else { |
| 132 | j = ix>>20; |
| 133 | y[0] = r-w; |
| 134 | i = j-(((__HI(y[0]))>>20)&0x7ff); |
| 135 | if(i>16) { /* 2nd iteration needed, good to 118 */ |
| 136 | t = r; |
| 137 | w = fn*pio2_2; |
| 138 | r = t-w; |
| 139 | w = fn*pio2_2t-((t-r)-w); |
| 140 | y[0] = r-w; |
| 141 | i = j-(((__HI(y[0]))>>20)&0x7ff); |
| 142 | if(i>49) { /* 3rd iteration need, 151 bits acc */ |
| 143 | t = r; /* will cover all possible cases */ |
| 144 | w = fn*pio2_3; |
| 145 | r = t-w; |
| 146 | w = fn*pio2_3t-((t-r)-w); |
| 147 | y[0] = r-w; |
| 148 | } |
| 149 | } |
| 150 | } |
| 151 | y[1] = (r-y[0])-w; |
| 152 | if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
| 153 | else return n; |
| 154 | } |
| 155 | /* |
| 156 | * all other (large) arguments |
| 157 | */ |
| 158 | if(ix>=0x7ff00000) { /* x is inf or NaN */ |
| 159 | y[0]=y[1]=x-x; return 0; |
| 160 | } |
| 161 | /* set z = ieee_scalbn(|x|,ilogb(x)-23) */ |
| 162 | __LO(z) = __LO(x); |
| 163 | e0 = (ix>>20)-1046; /* e0 = ieee_ilogb(z)-23; */ |
| 164 | __HI(z) = ix - (e0<<20); |
| 165 | for(i=0;i<2;i++) { |
| 166 | tx[i] = (double)((int)(z)); |
| 167 | z = (z-tx[i])*two24; |
| 168 | } |
| 169 | tx[2] = z; |
| 170 | nx = 3; |
| 171 | while(tx[nx-1]==zero) nx--; /* skip zero term */ |
| 172 | n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); |
| 173 | if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} |
| 174 | return n; |
| 175 | } |