e_rem_pio2l.h revision 141296
1117395Skan 2169689Skan/* @(#)e_rem_pio2.c 1.4 95/01/18 */ 3169689Skan/* 4117395Skan * ==================================================== 5132718Skan * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6117395Skan * 7132718Skan * Developed at SunSoft, a Sun Microsystems, Inc. business. 8117395Skan * Permission to use, copy, modify, and distribute this 9117395Skan * software is freely granted, provided that this notice 10117395Skan * is preserved. 11117395Skan * ==================================================== 12132718Skan * 13117395Skan */ 14117395Skan 15117395Skan#ifndef lint 16117395Skanstatic char rcsid[] = "$FreeBSD: head/lib/msun/src/e_rem_pio2.c 141296 2005-02-04 18:26:06Z das $"; 17117395Skan#endif 18132718Skan 19169689Skan/* __ieee754_rem_pio2(x,y) 20169689Skan * 21117395Skan * return the remainder of x rem pi/2 in y[0]+y[1] 22169689Skan * use __kernel_rem_pio2() 23169689Skan */ 24169689Skan 25169689Skan#include "math.h" 26169689Skan#include "math_private.h" 27169689Skan 28117395Skan/* 29169689Skan * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 30117395Skan */ 31169689Skanstatic const int32_t two_over_pi[] = { 32169689Skan0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 33117395Skan0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 34169689Skan0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 35169689Skan0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 36169689Skan0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 37169689Skan0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 38169689Skan0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 39169689Skan0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 40169689Skan0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 41169689Skan0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 42169689Skan0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 43169689Skan}; 44169689Skan 45169689Skanstatic const int32_t npio2_hw[] = { 46169689Skan0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 47169689Skan0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 48169689Skan0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 49169689Skan0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 50169689Skan0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 51169689Skan0x404858EB, 0x404921FB, 52169689Skan}; 53169689Skan 54169689Skan/* 55169689Skan * invpio2: 53 bits of 2/pi 56169689Skan * pio2_1: first 33 bit of pi/2 57169689Skan * pio2_1t: pi/2 - pio2_1 58117395Skan * pio2_2: second 33 bit of pi/2 59117395Skan * pio2_2t: pi/2 - (pio2_1+pio2_2) 60169689Skan * pio2_3: third 33 bit of pi/2 61117395Skan * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 62169689Skan */ 63169689Skan 64169689Skanstatic const double 65169689Skanzero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 66169689Skanhalf = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 67169689Skantwo24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 68169689Skaninvpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 69169689Skanpio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 70169689Skanpio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 71169689Skanpio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 72169689Skanpio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 73117395Skanpio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 74169689Skanpio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 75169689Skan 76169689Skan int32_t __ieee754_rem_pio2(double x, double *y) 77169689Skan{ 78169689Skan double z,w,t,r,fn; 79117395Skan double tx[3]; 80169689Skan int32_t e0,i,j,nx,n,ix,hx; 81169689Skan u_int32_t low; 82169689Skan 83169689Skan GET_HIGH_WORD(hx,x); /* high word of x */ 84169689Skan ix = hx&0x7fffffff; 85169689Skan if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 86117395Skan {y[0] = x; y[1] = 0; return 0;} 87169689Skan if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ 88169689Skan if(hx>0) { 89169689Skan z = x - pio2_1; 90169689Skan if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 91169689Skan y[0] = z - pio2_1t; 92117395Skan y[1] = (z-y[0])-pio2_1t; 93169689Skan } else { /* near pi/2, use 33+33+53 bit pi */ 94169689Skan z -= pio2_2; 95169689Skan y[0] = z - pio2_2t; 96169689Skan y[1] = (z-y[0])-pio2_2t; 97169689Skan } 98117395Skan return 1; 99169689Skan } else { /* negative x */ 100169689Skan z = x + pio2_1; 101169689Skan if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 102169689Skan y[0] = z + pio2_1t; 103169689Skan y[1] = (z-y[0])+pio2_1t; 104117395Skan } else { /* near pi/2, use 33+33+53 bit pi */ 105169689Skan z += pio2_2; 106169689Skan y[0] = z + pio2_2t; 107169689Skan y[1] = (z-y[0])+pio2_2t; 108169689Skan } 109169689Skan return -1; 110117395Skan } 111169689Skan } 112169689Skan if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 113169689Skan t = fabs(x); 114169689Skan n = (int32_t) (t*invpio2+half); 115169689Skan fn = (double)n; 116117395Skan r = t-fn*pio2_1; 117169689Skan w = fn*pio2_1t; /* 1st round good to 85 bit */ 118169689Skan if(n<32&&ix!=npio2_hw[n-1]) { 119169689Skan y[0] = r-w; /* quick check no cancellation */ 120169689Skan } else { 121169689Skan u_int32_t high; 122169689Skan j = ix>>20; 123117395Skan y[0] = r-w; 124169689Skan GET_HIGH_WORD(high,y[0]); 125169689Skan i = j-((high>>20)&0x7ff); 126169689Skan if(i>16) { /* 2nd iteration needed, good to 118 */ 127169689Skan t = r; 128169689Skan w = fn*pio2_2; 129117395Skan r = t-w; 130169689Skan w = fn*pio2_2t-((t-r)-w); 131169689Skan y[0] = r-w; 132169689Skan GET_HIGH_WORD(high,y[0]); 133169689Skan i = j-((high>>20)&0x7ff); 134169689Skan if(i>49) { /* 3rd iteration need, 151 bits acc */ 135169689Skan t = r; /* will cover all possible cases */ 136117395Skan w = fn*pio2_3; 137169689Skan r = t-w; 138169689Skan w = fn*pio2_3t-((t-r)-w); 139169689Skan y[0] = r-w; 140169689Skan } 141169689Skan } 142117395Skan } 143169689Skan y[1] = (r-y[0])-w; 144169689Skan if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 145169689Skan else return n; 146169689Skan } 147169689Skan /* 148117395Skan * all other (large) arguments 149169689Skan */ 150169689Skan if(ix>=0x7ff00000) { /* x is inf or NaN */ 151169689Skan y[0]=y[1]=x-x; return 0; 152169689Skan } 153169689Skan /* set z = scalbn(|x|,ilogb(x)-23) */ 154169689Skan GET_LOW_WORD(low,x); 155169689Skan SET_LOW_WORD(z,low); 156169689Skan e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 157117395Skan SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 158169689Skan for(i=0;i<2;i++) { 159169689Skan tx[i] = (double)((int32_t)(z)); 160169689Skan z = (z-tx[i])*two24; 161169689Skan } 162169689Skan tx[2] = z; 163169689Skan nx = 3; 164117395Skan while(tx[nx-1]==zero) nx--; /* skip zero term */ 165169689Skan n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); 166169689Skan if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 167169689Skan return n; 168169689Skan} 169169689Skan