e_rem_pio2l.h revision 141296
1141296Sdas 2141296Sdas/* @(#)e_rem_pio2.c 1.4 95/01/18 */ 32116Sjkh/* 42116Sjkh * ==================================================== 52116Sjkh * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 62116Sjkh * 7141296Sdas * Developed at SunSoft, a Sun Microsystems, Inc. business. 82116Sjkh * Permission to use, copy, modify, and distribute this 9141296Sdas * software is freely granted, provided that this notice 102116Sjkh * is preserved. 112116Sjkh * ==================================================== 12141296Sdas * 132116Sjkh */ 142116Sjkh 152116Sjkh#ifndef lint 1650476Speterstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/e_rem_pio2.c 141296 2005-02-04 18:26:06Z das $"; 172116Sjkh#endif 182116Sjkh 192116Sjkh/* __ieee754_rem_pio2(x,y) 20141296Sdas * 21141296Sdas * return the remainder of x rem pi/2 in y[0]+y[1] 222116Sjkh * use __kernel_rem_pio2() 232116Sjkh */ 242116Sjkh 252116Sjkh#include "math.h" 262116Sjkh#include "math_private.h" 272116Sjkh 282116Sjkh/* 29141296Sdas * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 302116Sjkh */ 312116Sjkhstatic const int32_t two_over_pi[] = { 32141296Sdas0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 33141296Sdas0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 34141296Sdas0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 35141296Sdas0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 36141296Sdas0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 37141296Sdas0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 38141296Sdas0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 39141296Sdas0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 40141296Sdas0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 41141296Sdas0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 42141296Sdas0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 432116Sjkh}; 442116Sjkh 452116Sjkhstatic const int32_t npio2_hw[] = { 462116Sjkh0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 472116Sjkh0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 482116Sjkh0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 492116Sjkh0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 502116Sjkh0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 512116Sjkh0x404858EB, 0x404921FB, 522116Sjkh}; 532116Sjkh 542116Sjkh/* 552116Sjkh * invpio2: 53 bits of 2/pi 562116Sjkh * pio2_1: first 33 bit of pi/2 572116Sjkh * pio2_1t: pi/2 - pio2_1 582116Sjkh * pio2_2: second 33 bit of pi/2 592116Sjkh * pio2_2t: pi/2 - (pio2_1+pio2_2) 602116Sjkh * pio2_3: third 33 bit of pi/2 612116Sjkh * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 622116Sjkh */ 632116Sjkh 648870Srgrimesstatic const double 652116Sjkhzero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 662116Sjkhhalf = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 672116Sjkhtwo24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 682116Sjkhinvpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 692116Sjkhpio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 702116Sjkhpio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 712116Sjkhpio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 722116Sjkhpio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 732116Sjkhpio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 742116Sjkhpio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 752116Sjkh 762116Sjkh int32_t __ieee754_rem_pio2(double x, double *y) 772116Sjkh{ 782116Sjkh double z,w,t,r,fn; 792116Sjkh double tx[3]; 802116Sjkh int32_t e0,i,j,nx,n,ix,hx; 812116Sjkh u_int32_t low; 822116Sjkh 832116Sjkh GET_HIGH_WORD(hx,x); /* high word of x */ 842116Sjkh ix = hx&0x7fffffff; 852116Sjkh if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 862116Sjkh {y[0] = x; y[1] = 0; return 0;} 877659Sbde if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ 88141296Sdas if(hx>0) { 897659Sbde z = x - pio2_1; 907659Sbde if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 917659Sbde y[0] = z - pio2_1t; 927659Sbde y[1] = (z-y[0])-pio2_1t; 937659Sbde } else { /* near pi/2, use 33+33+53 bit pi */ 947659Sbde z -= pio2_2; 957659Sbde y[0] = z - pio2_2t; 967659Sbde y[1] = (z-y[0])-pio2_2t; 977659Sbde } 987659Sbde return 1; 997659Sbde } else { /* negative x */ 1007659Sbde z = x + pio2_1; 1017659Sbde if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 1027659Sbde y[0] = z + pio2_1t; 1037659Sbde y[1] = (z-y[0])+pio2_1t; 1047659Sbde } else { /* near pi/2, use 33+33+53 bit pi */ 1057659Sbde z += pio2_2; 1067659Sbde y[0] = z + pio2_2t; 1077659Sbde y[1] = (z-y[0])+pio2_2t; 1087659Sbde } 1097659Sbde return -1; 1107659Sbde } 1117659Sbde } 1122116Sjkh if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 1132116Sjkh t = fabs(x); 1142116Sjkh n = (int32_t) (t*invpio2+half); 1152116Sjkh fn = (double)n; 1162116Sjkh r = t-fn*pio2_1; 1172116Sjkh w = fn*pio2_1t; /* 1st round good to 85 bit */ 118141296Sdas if(n<32&&ix!=npio2_hw[n-1]) { 1192116Sjkh y[0] = r-w; /* quick check no cancellation */ 1202116Sjkh } else { 1212116Sjkh u_int32_t high; 1222116Sjkh j = ix>>20; 123141296Sdas y[0] = r-w; 1242116Sjkh GET_HIGH_WORD(high,y[0]); 1252116Sjkh i = j-((high>>20)&0x7ff); 1262116Sjkh if(i>16) { /* 2nd iteration needed, good to 118 */ 1272116Sjkh t = r; 128141296Sdas w = fn*pio2_2; 1292116Sjkh r = t-w; 130141296Sdas w = fn*pio2_2t-((t-r)-w); 1312116Sjkh y[0] = r-w; 1322116Sjkh GET_HIGH_WORD(high,y[0]); 1332116Sjkh i = j-((high>>20)&0x7ff); 1342116Sjkh if(i>49) { /* 3rd iteration need, 151 bits acc */ 1352116Sjkh t = r; /* will cover all possible cases */ 136141296Sdas w = fn*pio2_3; 1372116Sjkh r = t-w; 138141296Sdas w = fn*pio2_3t-((t-r)-w); 1392116Sjkh y[0] = r-w; 1402116Sjkh } 1412116Sjkh } 1422116Sjkh } 1432116Sjkh y[1] = (r-y[0])-w; 1442116Sjkh if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 1452116Sjkh else return n; 1462116Sjkh } 147141296Sdas /* 1482116Sjkh * all other (large) arguments 1492116Sjkh */ 1502116Sjkh if(ix>=0x7ff00000) { /* x is inf or NaN */ 1512116Sjkh y[0]=y[1]=x-x; return 0; 1522116Sjkh } 1532116Sjkh /* set z = scalbn(|x|,ilogb(x)-23) */ 1542116Sjkh GET_LOW_WORD(low,x); 1552116Sjkh SET_LOW_WORD(z,low); 1562116Sjkh e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 1572116Sjkh SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 1582116Sjkh for(i=0;i<2;i++) { 1592116Sjkh tx[i] = (double)((int32_t)(z)); 1602116Sjkh z = (z-tx[i])*two24; 1612116Sjkh } 1622116Sjkh tx[2] = z; 1632116Sjkh nx = 3; 1642116Sjkh while(tx[nx-1]==zero) nx--; /* skip zero term */ 1652116Sjkh n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); 1662116Sjkh if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 1672116Sjkh return n; 1682116Sjkh} 169