e_rem_pio2l.h revision 176385
16059Samurai 26059Samurai/* @(#)e_rem_pio2.c 1.4 95/01/18 */ 36059Samurai/* 46059Samurai * ==================================================== 56059Samurai * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 66059Samurai * 76059Samurai * Developed at SunSoft, a Sun Microsystems, Inc. business. 86059Samurai * Permission to use, copy, modify, and distribute this 96059Samurai * software is freely granted, provided that this notice 106059Samurai * is preserved. 116059Samurai * ==================================================== 126059Samurai * 136059Samurai */ 146059Samurai 156059Samurai#include <sys/cdefs.h> 166059Samurai__FBSDID("$FreeBSD: head/lib/msun/src/e_rem_pio2.c 176385 2008-02-18 14:02:12Z bde $"); 176059Samurai 186059Samurai/* __ieee754_rem_pio2(x,y) 198857Srgrimes * 209440Samurai * return the remainder of x rem pi/2 in y[0]+y[1] 218857Srgrimes * use __kernel_rem_pio2() 226059Samurai */ 236059Samurai 246735Samurai#include "math.h" 256059Samurai#include "math_private.h" 266059Samurai 276059Samuraistatic const int32_t npio2_hw[] = { 286059Samurai0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 296059Samurai0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 306059Samurai0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 316059Samurai0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 326059Samurai0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 336735Samurai0x404858EB, 0x404921FB, 346059Samurai}; 356059Samurai 366059Samurai/* 376059Samurai * invpio2: 53 bits of 2/pi 386059Samurai * pio2_1: first 33 bit of pi/2 396059Samurai * pio2_1t: pi/2 - pio2_1 406059Samurai * pio2_2: second 33 bit of pi/2 416059Samurai * pio2_2t: pi/2 - (pio2_1+pio2_2) 426059Samurai * pio2_3: third 33 bit of pi/2 436059Samurai * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 446735Samurai */ 456059Samurai 466059Samuraistatic const double 476059Samuraizero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 486059Samuraihalf = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 496735Samuraitwo24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 506059Samuraiinvpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 516059Samuraipio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 526059Samuraipio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 536059Samuraipio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 546059Samuraipio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 556059Samuraipio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 566059Samuraipio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 576059Samurai 586059Samurai#ifdef INLINE_REM_PIO2 596059Samuraiextern inline 606059Samurai#endif 616059Samuraiint 626059Samurai__ieee754_rem_pio2(double x, double *y) 636059Samurai{ 646059Samurai double z,w,t,r,fn; 656059Samurai double tx[3]; 666059Samurai int32_t e0,i,j,nx,n,ix,hx; 676059Samurai u_int32_t low; 686059Samurai 696059Samurai GET_HIGH_WORD(hx,x); /* high word of x */ 706764Samurai ix = hx&0x7fffffff; 716059Samurai if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 726059Samurai {y[0] = x; y[1] = 0; return 0;} 736059Samurai if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ 746059Samurai if(hx>0) { 756059Samurai z = x - pio2_1; 766059Samurai if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 776059Samurai y[0] = z - pio2_1t; 786059Samurai y[1] = (z-y[0])-pio2_1t; 796764Samurai } else { /* near pi/2, use 33+33+53 bit pi */ 806764Samurai z -= pio2_2; 816059Samurai y[0] = z - pio2_2t; 826059Samurai y[1] = (z-y[0])-pio2_2t; 836059Samurai } 846059Samurai return 1; 856059Samurai } else { /* negative x */ 866059Samurai z = x + pio2_1; 876059Samurai if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 886059Samurai y[0] = z + pio2_1t; 896059Samurai y[1] = (z-y[0])+pio2_1t; 906059Samurai } else { /* near pi/2, use 33+33+53 bit pi */ 916059Samurai z += pio2_2; 926059Samurai y[0] = z + pio2_2t; 936059Samurai y[1] = (z-y[0])+pio2_2t; 946059Samurai } 956059Samurai return -1; 966059Samurai } 976059Samurai } 986059Samurai if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 996059Samurai t = fabs(x); 1006059Samurai n = (int32_t) (t*invpio2+half); 1016059Samurai fn = (double)n; 1026059Samurai r = t-fn*pio2_1; 1036059Samurai w = fn*pio2_1t; /* 1st round good to 85 bit */ 1046059Samurai if(n<32&&ix!=npio2_hw[n-1]) { 1056059Samurai y[0] = r-w; /* quick check no cancellation */ 1066059Samurai } else { 1076059Samurai u_int32_t high; 1086059Samurai j = ix>>20; 1096059Samurai y[0] = r-w; 1106059Samurai GET_HIGH_WORD(high,y[0]); 1116059Samurai i = j-((high>>20)&0x7ff); 1126059Samurai if(i>16) { /* 2nd iteration needed, good to 118 */ 1136059Samurai t = r; 1146059Samurai w = fn*pio2_2; 1156059Samurai r = t-w; 1166059Samurai w = fn*pio2_2t-((t-r)-w); 1176059Samurai y[0] = r-w; 1186059Samurai GET_HIGH_WORD(high,y[0]); 1196059Samurai i = j-((high>>20)&0x7ff); 1206735Samurai if(i>49) { /* 3rd iteration need, 151 bits acc */ 1216735Samurai t = r; /* will cover all possible cases */ 1226735Samurai w = fn*pio2_3; 1236735Samurai r = t-w; 1246735Samurai w = fn*pio2_3t-((t-r)-w); 1256735Samurai y[0] = r-w; 1266059Samurai } 1276059Samurai } 1286059Samurai } 1296059Samurai y[1] = (r-y[0])-w; 1306059Samurai if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 1316059Samurai else return n; 1326059Samurai } 1336059Samurai /* 1346059Samurai * all other (large) arguments 1356059Samurai */ 1366059Samurai if(ix>=0x7ff00000) { /* x is inf or NaN */ 1376059Samurai y[0]=y[1]=x-x; return 0; 1386059Samurai } 1396059Samurai /* set z = scalbn(|x|,ilogb(x)-23) */ 1406059Samurai GET_LOW_WORD(low,x); 1416059Samurai SET_LOW_WORD(z,low); 1426059Samurai e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 1436059Samurai SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 1446059Samurai for(i=0;i<2;i++) { 1456735Samurai tx[i] = (double)((int32_t)(z)); 1466735Samurai z = (z-tx[i])*two24; 1476735Samurai } 1486735Samurai tx[2] = z; 1496735Samurai nx = 3; 1506735Samurai while(tx[nx-1]==zero) nx--; /* skip zero term */ 1516735Samurai n = __kernel_rem_pio2(tx,y,e0,nx,2); 1526735Samurai if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 1536735Samurai return n; 1546735Samurai} 1556735Samurai