e_rem_pio2l.h revision 176640
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 * Optimized by Bruce D. Evans. 146059Samurai */ 156059Samurai 166059Samurai#include <sys/cdefs.h> 176059Samurai__FBSDID("$FreeBSD: head/lib/msun/src/e_rem_pio2.c 176640 2008-02-28 16:22:36Z bde $"); 186059Samurai 198857Srgrimes/* __ieee754_rem_pio2(x,y) 2026911Sbrian * 218857Srgrimes * return the remainder of x rem pi/2 in y[0]+y[1] 226059Samurai * use __kernel_rem_pio2() 2313379Sphk */ 246059Samurai 256735Samurai#include <float.h> 2613385Speter 2713379Sphk#include "math.h" 2826031Sbrian#include "math_private.h" 2926031Sbrian 3026031Sbrian/* 3126031Sbrian * invpio2: 53 bits of 2/pi 3226031Sbrian * pio2_1: first 33 bit of pi/2 3326031Sbrian * pio2_1t: pi/2 - pio2_1 3426031Sbrian * pio2_2: second 33 bit of pi/2 3526516Sbrian * pio2_2t: pi/2 - (pio2_1+pio2_2) 3626516Sbrian * pio2_3: third 33 bit of pi/2 376059Samurai * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 386059Samurai */ 396059Samurai 406059Samuraistatic const double 416059Samuraizero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 4213389Sphkhalf = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 436059Samuraitwo24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 4426031Sbrianinvpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 456059Samuraipio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 4626142Sbrianpio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 476059Samuraipio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 4825630Sbrianpio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 4925630Sbrianpio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 506059Samuraipio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 5126516Sbrian 526059Samurai#ifdef INLINE_REM_PIO2 536059Samuraiextern inline 546059Samurai#endif 556059Samuraiint 5626031Sbrian__ieee754_rem_pio2(double x, double *y) 576735Samurai{ 586059Samurai double z,w,t,r,fn; 596059Samurai double tx[3],ty[2]; 606059Samurai int32_t e0,i,j,nx,n,ix,hx; 616059Samurai u_int32_t low; 6210528Samurai 636735Samurai GET_HIGH_WORD(hx,x); /* high word of x */ 6414418Sache ix = hx&0x7fffffff; 656059Samurai#if 0 /* Must be handled in caller. */ 6622973Sphk if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 6722973Sphk {y[0] = x; y[1] = 0; return 0;} 686059Samurai#endif 6923603Sache if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ 706059Samurai if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ 716059Samurai goto medium; /* cancellation -- use medium case */ 726059Samurai if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ 736059Samurai if (hx > 0) { 7410528Samurai z = x - pio2_1; /* one round good to 85 bits */ 756059Samurai y[0] = z - pio2_1t; 766059Samurai y[1] = (z-y[0])-pio2_1t; 776059Samurai return 1; 786059Samurai } else { 796059Samurai z = x + pio2_1; 806059Samurai y[0] = z + pio2_1t; 816059Samurai y[1] = (z-y[0])+pio2_1t; 826059Samurai return -1; 836059Samurai } 846059Samurai } else { 856059Samurai if (hx > 0) { 8626516Sbrian z = x - 2*pio2_1; 8726516Sbrian y[0] = z - 2*pio2_1t; 8826516Sbrian y[1] = (z-y[0])-2*pio2_1t; 896059Samurai return 2; 9026516Sbrian } else { 9125566Sbrian z = x + 2*pio2_1; 9226516Sbrian y[0] = z + 2*pio2_1t; 9326516Sbrian y[1] = (z-y[0])+2*pio2_1t; 946059Samurai return -2; 9526516Sbrian } 9626516Sbrian } 976059Samurai } 9826516Sbrian if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ 996059Samurai if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ 10026516Sbrian if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ 1016764Samurai goto medium; 10226587Sbrian if (hx > 0) { 1036059Samurai z = x - 3*pio2_1; 1046059Samurai y[0] = z - 3*pio2_1t; 10526516Sbrian y[1] = (z-y[0])-3*pio2_1t; 1066059Samurai return 3; 10726516Sbrian } else { 10826516Sbrian z = x + 3*pio2_1; 10926516Sbrian y[0] = z + 3*pio2_1t; 1106059Samurai y[1] = (z-y[0])+3*pio2_1t; 1116059Samurai return -3; 1126059Samurai } 1136059Samurai } else { 1146059Samurai if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ 1156059Samurai goto medium; 1166059Samurai if (hx > 0) { 11720120Snate z = x - 4*pio2_1; 11820120Snate y[0] = z - 4*pio2_1t; 11925908Sbrian y[1] = (z-y[0])-4*pio2_1t; 12025908Sbrian return 4; 12120120Snate } else { 12210528Samurai z = x + 4*pio2_1; 1236059Samurai y[0] = z + 4*pio2_1t; 12410528Samurai y[1] = (z-y[0])+4*pio2_1t; 1256059Samurai return -4; 12610528Samurai } 1276059Samurai } 12826516Sbrian } 12926516Sbrian if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ 13026516Sbrianmedium: 1316059Samurai /* Use a specialized rint() to get fn. Assume round-to-nearest. */ 13226516Sbrian STRICT_ASSIGN(double,fn,x*invpio2+0x1.8p52); 1336059Samurai fn = fn-0x1.8p52; 1346059Samurai#ifdef HAVE_EFFICIENT_IRINT 1356059Samurai n = irint(fn); 1366059Samurai#else 1376059Samurai n = (int32_t)fn; 1386059Samurai#endif 1396059Samurai r = x-fn*pio2_1; 1406059Samurai w = fn*pio2_1t; /* 1st round good to 85 bit */ 14111336Samurai { 14226858Sbrian u_int32_t high; 14311336Samurai j = ix>>20; 1446059Samurai y[0] = r-w; 14526516Sbrian GET_HIGH_WORD(high,y[0]); 14626516Sbrian i = j-((high>>20)&0x7ff); 14726516Sbrian if(i>16) { /* 2nd iteration needed, good to 118 */ 1486059Samurai t = r; 14926516Sbrian w = fn*pio2_2; 1506059Samurai r = t-w; 1516059Samurai w = fn*pio2_2t-((t-r)-w); 15226516Sbrian y[0] = r-w; 1536735Samurai GET_HIGH_WORD(high,y[0]); 1546735Samurai i = j-((high>>20)&0x7ff); 15526516Sbrian if(i>49) { /* 3rd iteration need, 151 bits acc */ 15626516Sbrian t = r; /* will cover all possible cases */ 15726516Sbrian w = fn*pio2_3; 1586735Samurai r = t-w; 1596735Samurai w = fn*pio2_3t-((t-r)-w); 16026516Sbrian y[0] = r-w; 16111336Samurai } 16211336Samurai } 16326516Sbrian } 16426516Sbrian y[1] = (r-y[0])-w; 16511336Samurai return n; 16611336Samurai } 16726516Sbrian /* 16826516Sbrian * all other (large) arguments 16911336Samurai */ 17011336Samurai if(ix>=0x7ff00000) { /* x is inf or NaN */ 17126858Sbrian y[0]=y[1]=x-x; return 0; 17211336Samurai } 17311336Samurai /* set z = scalbn(|x|,ilogb(x)-23) */ 17411336Samurai GET_LOW_WORD(low,x); 17511336Samurai SET_LOW_WORD(z,low); 17626858Sbrian e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 17726858Sbrian SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 17811336Samurai for(i=0;i<2;i++) { 17926516Sbrian tx[i] = (double)((int32_t)(z)); 18026516Sbrian z = (z-tx[i])*two24; 1816059Samurai } 1826059Samurai tx[2] = z; 18310528Samurai nx = 3; 18410528Samurai while(tx[nx-1]==zero) nx--; /* skip zero term */ 18510528Samurai n = __kernel_rem_pio2(tx,ty,e0,nx,1); 18610528Samurai if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} 18710528Samurai y[0] = ty[0]; y[1] = ty[1]; return n; 18810528Samurai} 18910528Samurai