e_rem_pio2l.h revision 176466
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 176466 2008-02-22 17:26:24Z bde $"); 176059Samurai 186059Samurai/* __ieee754_rem_pio2(x,y) 198857Srgrimes * 2049976Sbrian * return the remainder of x rem pi/2 in y[0]+y[1] 218857Srgrimes * use __kernel_rem_pio2() 226059Samurai */ 2343313Sbrian 2430715Sbrian#include <float.h> 2526031Sbrian 2630715Sbrian#include "math.h" 2726031Sbrian#include "math_private.h" 2830715Sbrian 2926031Sbrian/* 3030715Sbrian * invpio2: 53 bits of 2/pi 3136285Sbrian * pio2_1: first 33 bit of pi/2 3230715Sbrian * pio2_1t: pi/2 - pio2_1 3338628Sbrian * pio2_2: second 33 bit of pi/2 3430715Sbrian * pio2_2t: pi/2 - (pio2_1+pio2_2) 3526516Sbrian * pio2_3: third 33 bit of pi/2 3630715Sbrian * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 3730715Sbrian */ 3830715Sbrian 3930715Sbrianstatic const double 4030715Sbrianzero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 4130715Sbrianhalf = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 4230715Sbriantwo24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 4330715Sbrianinvpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 4439395Sbrianpio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 4546086Sbrianpio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 4646086Sbrianpio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 4746086Sbrianpio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 4839395Sbrianpio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 4939395Sbrianpio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 5039395Sbrian 5146686Sbrian#ifdef INLINE_REM_PIO2 5237009Sbrianextern inline 5331343Sbrian#endif 5430715Sbrianint 5530715Sbrian__ieee754_rem_pio2(double x, double *y) 5630715Sbrian{ 576059Samurai double z,w,t,r,fn; 586059Samurai double tx[3]; 5931690Sbrian int32_t e0,i,j,nx,n,ix,hx; 6036285Sbrian u_int32_t low; 6136285Sbrian 6238557Sbrian GET_HIGH_WORD(hx,x); /* high word of x */ 6338557Sbrian ix = hx&0x7fffffff; 646059Samurai#if 0 /* Must be handled in caller. */ 6531343Sbrian if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 6626031Sbrian {y[0] = x; y[1] = 0; return 0;} 6731343Sbrian#endif 6825630Sbrian if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ 6936285Sbrian if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ 7036285Sbrian goto medium; /* cancellation -- use medium case */ 7130715Sbrian if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ 7230715Sbrian if (hx > 0) { 7330715Sbrian z = x - pio2_1; /* one round good to 85 bits */ 7431080Sbrian y[0] = z - pio2_1t; 7536285Sbrian y[1] = (z-y[0])-pio2_1t; 7636285Sbrian return 1; 7736285Sbrian } else { 7836285Sbrian z = x + pio2_1; 7943313Sbrian y[0] = z + pio2_1t; 8043313Sbrian y[1] = (z-y[0])+pio2_1t; 8143313Sbrian return -1; 8236285Sbrian } 8336285Sbrian } else { 8436285Sbrian if (hx > 0) { 8536285Sbrian z = x - 2*pio2_1; 8636285Sbrian y[0] = z - 2*pio2_1t; 8738174Sbrian y[1] = (z-y[0])-2*pio2_1t; 8836285Sbrian return 2; 8940561Sbrian } else { 906059Samurai z = x + 2*pio2_1; 9136285Sbrian y[0] = z + 2*pio2_1t; 9236285Sbrian y[1] = (z-y[0])+2*pio2_1t; 9336285Sbrian return -2; 9436285Sbrian } 9536285Sbrian } 9636285Sbrian } 9736285Sbrian if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ 9836285Sbrian if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ 9936285Sbrian if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ 10036285Sbrian goto medium; 10136285Sbrian if (hx > 0) { 10236285Sbrian z = x - 3*pio2_1; 10336285Sbrian y[0] = z - 3*pio2_1t; 10436285Sbrian y[1] = (z-y[0])-3*pio2_1t; 10536285Sbrian return 3; 10636285Sbrian } else { 10736285Sbrian z = x + 3*pio2_1; 10836285Sbrian y[0] = z + 3*pio2_1t; 10936285Sbrian y[1] = (z-y[0])+3*pio2_1t; 11036285Sbrian return -3; 11136285Sbrian } 11236285Sbrian } else { 11336285Sbrian if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ 11436285Sbrian goto medium; 11536285Sbrian if (hx > 0) { 11638174Sbrian z = x - 4*pio2_1; 11738174Sbrian y[0] = z - 4*pio2_1t; 11838544Sbrian y[1] = (z-y[0])-4*pio2_1t; 11940665Sbrian return 4; 12040665Sbrian } else { 12143313Sbrian z = x + 4*pio2_1; 12244073Sbrian y[0] = z + 4*pio2_1t; 12346686Sbrian y[1] = (z-y[0])+4*pio2_1t; 12446686Sbrian return -4; 1256059Samurai } 12636285Sbrian } 12736285Sbrian } 12836285Sbrian if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 12936285Sbrianmedium: 13036285Sbrian t = fabs(x); 13136285Sbrian#ifdef HAVE_EFFICIENT_IRINT 13244106Sbrian /* Use a specialized rint() to get fn. Assume round-to-nearest. */ 13344106Sbrian STRICT_ASSIGN(double,fn,t*invpio2+0x1.8p52); 13444106Sbrian fn = fn-0x1.8p52; 13544106Sbrian n = irint(fn); 13647858Sbrian#else 13747858Sbrian n = (int32_t) (t*invpio2+half); 13847858Sbrian fn = (double)n; 13947858Sbrian#endif 14047858Sbrian r = t-fn*pio2_1; 14147858Sbrian w = fn*pio2_1t; /* 1st round good to 85 bit */ 14247858Sbrian { 14347858Sbrian u_int32_t high; 14447858Sbrian j = ix>>20; 14536285Sbrian y[0] = r-w; 14649434Sbrian GET_HIGH_WORD(high,y[0]); 14749976Sbrian i = j-((high>>20)&0x7ff); 14836285Sbrian if(i>16) { /* 2nd iteration needed, good to 118 */ 14936285Sbrian t = r; 15036285Sbrian w = fn*pio2_2; 15136285Sbrian r = t-w; 15236285Sbrian w = fn*pio2_2t-((t-r)-w); 15336285Sbrian y[0] = r-w; 15436285Sbrian GET_HIGH_WORD(high,y[0]); 15536285Sbrian i = j-((high>>20)&0x7ff); 15636285Sbrian if(i>49) { /* 3rd iteration need, 151 bits acc */ 15736285Sbrian t = r; /* will cover all possible cases */ 15836285Sbrian w = fn*pio2_3; 15936285Sbrian r = t-w; 16036934Sbrian w = fn*pio2_3t-((t-r)-w); 16140561Sbrian y[0] = r-w; 16240561Sbrian } 16340561Sbrian } 16440561Sbrian } 16540679Sbrian y[1] = (r-y[0])-w; 16631343Sbrian if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 16736285Sbrian else return n; 16836285Sbrian } 16931343Sbrian /* 1706059Samurai * all other (large) arguments 17136285Sbrian */ 17236285Sbrian if(ix>=0x7ff00000) { /* x is inf or NaN */ 17336285Sbrian y[0]=y[1]=x-x; return 0; 17436285Sbrian } 17536285Sbrian /* set z = scalbn(|x|,ilogb(x)-23) */ 17636285Sbrian GET_LOW_WORD(low,x); 17736285Sbrian SET_LOW_WORD(z,low); 17836285Sbrian e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 17936285Sbrian SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 18036285Sbrian for(i=0;i<2;i++) { 18136285Sbrian tx[i] = (double)((int32_t)(z)); 1826059Samurai z = (z-tx[i])*two24; 18331343Sbrian } 1846059Samurai tx[2] = z; 18528679Sbrian nx = 3; 18636285Sbrian while(tx[nx-1]==zero) nx--; /* skip zero term */ 18736285Sbrian n = __kernel_rem_pio2(tx,y,e0,nx,2); 1886059Samurai if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 18936285Sbrian return n; 19036285Sbrian} 19126516Sbrian