e_rem_pio2.c revision 176465
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 15176385Sbde#include <sys/cdefs.h> 16176385Sbde__FBSDID("$FreeBSD: head/lib/msun/src/e_rem_pio2.c 176465 2008-02-22 15:55:14Z bde $"); 172116Sjkh 182116Sjkh/* __ieee754_rem_pio2(x,y) 19141296Sdas * 20141296Sdas * return the remainder of x rem pi/2 in y[0]+y[1] 212116Sjkh * use __kernel_rem_pio2() 222116Sjkh */ 232116Sjkh 24176465Sbde#include <float.h> 25176465Sbde 262116Sjkh#include "math.h" 272116Sjkh#include "math_private.h" 282116Sjkh 292116Sjkhstatic const int32_t npio2_hw[] = { 302116Sjkh0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 312116Sjkh0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 322116Sjkh0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 332116Sjkh0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 342116Sjkh0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 352116Sjkh0x404858EB, 0x404921FB, 362116Sjkh}; 372116Sjkh 382116Sjkh/* 392116Sjkh * invpio2: 53 bits of 2/pi 402116Sjkh * pio2_1: first 33 bit of pi/2 412116Sjkh * pio2_1t: pi/2 - pio2_1 422116Sjkh * pio2_2: second 33 bit of pi/2 432116Sjkh * pio2_2t: pi/2 - (pio2_1+pio2_2) 442116Sjkh * pio2_3: third 33 bit of pi/2 452116Sjkh * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 462116Sjkh */ 472116Sjkh 488870Srgrimesstatic const double 492116Sjkhzero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 502116Sjkhhalf = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 512116Sjkhtwo24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 522116Sjkhinvpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 532116Sjkhpio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 542116Sjkhpio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 552116Sjkhpio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 562116Sjkhpio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 572116Sjkhpio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 582116Sjkhpio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 592116Sjkh 60176385Sbde#ifdef INLINE_REM_PIO2 61176385Sbdeextern inline 62176385Sbde#endif 63176385Sbdeint 64176385Sbde__ieee754_rem_pio2(double x, double *y) 652116Sjkh{ 662116Sjkh double z,w,t,r,fn; 672116Sjkh double tx[3]; 682116Sjkh int32_t e0,i,j,nx,n,ix,hx; 692116Sjkh u_int32_t low; 702116Sjkh 712116Sjkh GET_HIGH_WORD(hx,x); /* high word of x */ 722116Sjkh ix = hx&0x7fffffff; 73176409Sbde#if 0 /* Must be handled in caller. */ 742116Sjkh if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 752116Sjkh {y[0] = x; y[1] = 0; return 0;} 76176409Sbde#endif 77176409Sbde if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ 78176409Sbde if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ 79176409Sbde goto medium; /* cancellation -- use medium case */ 80176409Sbde if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ 81176409Sbde if (hx > 0) { 82176409Sbde z = x - pio2_1; /* one round good to 85 bits */ 837659Sbde y[0] = z - pio2_1t; 847659Sbde y[1] = (z-y[0])-pio2_1t; 85176409Sbde return 1; 86176409Sbde } else { 87176409Sbde z = x + pio2_1; 887659Sbde y[0] = z + pio2_1t; 897659Sbde y[1] = (z-y[0])+pio2_1t; 90176409Sbde return -1; 917659Sbde } 92176409Sbde } else { 93176409Sbde if (hx > 0) { 94176409Sbde z = x - 2*pio2_1; 95176409Sbde y[0] = z - 2*pio2_1t; 96176409Sbde y[1] = (z-y[0])-2*pio2_1t; 97176409Sbde return 2; 98176409Sbde } else { 99176409Sbde z = x + 2*pio2_1; 100176409Sbde y[0] = z + 2*pio2_1t; 101176409Sbde y[1] = (z-y[0])+2*pio2_1t; 102176409Sbde return -2; 103176409Sbde } 1047659Sbde } 1057659Sbde } 106176409Sbde if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ 107176409Sbde if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ 108176409Sbde if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ 109176409Sbde goto medium; 110176409Sbde if (hx > 0) { 111176409Sbde z = x - 3*pio2_1; 112176409Sbde y[0] = z - 3*pio2_1t; 113176409Sbde y[1] = (z-y[0])-3*pio2_1t; 114176409Sbde return 3; 115176409Sbde } else { 116176409Sbde z = x + 3*pio2_1; 117176409Sbde y[0] = z + 3*pio2_1t; 118176409Sbde y[1] = (z-y[0])+3*pio2_1t; 119176409Sbde return -3; 120176409Sbde } 121176409Sbde } else { 122176409Sbde if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ 123176409Sbde goto medium; 124176409Sbde if (hx > 0) { 125176409Sbde z = x - 4*pio2_1; 126176409Sbde y[0] = z - 4*pio2_1t; 127176409Sbde y[1] = (z-y[0])-4*pio2_1t; 128176409Sbde return 4; 129176409Sbde } else { 130176409Sbde z = x + 4*pio2_1; 131176409Sbde y[0] = z + 4*pio2_1t; 132176409Sbde y[1] = (z-y[0])+4*pio2_1t; 133176409Sbde return -4; 134176409Sbde } 135176409Sbde } 136176409Sbde } 1372116Sjkh if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 138176409Sbdemedium: 1392116Sjkh t = fabs(x); 140176465Sbde#ifdef HAVE_EFFICIENT_IRINT 141176465Sbde /* Use a specialized rint() to get fn. Assume round-to-nearest. */ 142176465Sbde STRICT_ASSIGN(double,fn,t*invpio2+0x1.8p52); 143176465Sbde fn = fn-0x1.8p52; 144176465Sbde n = irint(fn); 145176465Sbde#else 1462116Sjkh n = (int32_t) (t*invpio2+half); 1472116Sjkh fn = (double)n; 148176465Sbde#endif 1492116Sjkh r = t-fn*pio2_1; 1502116Sjkh w = fn*pio2_1t; /* 1st round good to 85 bit */ 151141296Sdas if(n<32&&ix!=npio2_hw[n-1]) { 1522116Sjkh y[0] = r-w; /* quick check no cancellation */ 1532116Sjkh } else { 1542116Sjkh u_int32_t high; 1552116Sjkh j = ix>>20; 156141296Sdas y[0] = r-w; 1572116Sjkh GET_HIGH_WORD(high,y[0]); 1582116Sjkh i = j-((high>>20)&0x7ff); 1592116Sjkh if(i>16) { /* 2nd iteration needed, good to 118 */ 1602116Sjkh t = r; 161141296Sdas w = fn*pio2_2; 1622116Sjkh r = t-w; 163141296Sdas w = fn*pio2_2t-((t-r)-w); 1642116Sjkh y[0] = r-w; 1652116Sjkh GET_HIGH_WORD(high,y[0]); 1662116Sjkh i = j-((high>>20)&0x7ff); 1672116Sjkh if(i>49) { /* 3rd iteration need, 151 bits acc */ 1682116Sjkh t = r; /* will cover all possible cases */ 169141296Sdas w = fn*pio2_3; 1702116Sjkh r = t-w; 171141296Sdas w = fn*pio2_3t-((t-r)-w); 1722116Sjkh y[0] = r-w; 1732116Sjkh } 1742116Sjkh } 1752116Sjkh } 1762116Sjkh y[1] = (r-y[0])-w; 1772116Sjkh if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 1782116Sjkh else return n; 1792116Sjkh } 180141296Sdas /* 1812116Sjkh * all other (large) arguments 1822116Sjkh */ 1832116Sjkh if(ix>=0x7ff00000) { /* x is inf or NaN */ 1842116Sjkh y[0]=y[1]=x-x; return 0; 1852116Sjkh } 1862116Sjkh /* set z = scalbn(|x|,ilogb(x)-23) */ 1872116Sjkh GET_LOW_WORD(low,x); 1882116Sjkh SET_LOW_WORD(z,low); 1892116Sjkh e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 1902116Sjkh SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 1912116Sjkh for(i=0;i<2;i++) { 1922116Sjkh tx[i] = (double)((int32_t)(z)); 1932116Sjkh z = (z-tx[i])*two24; 1942116Sjkh } 1952116Sjkh tx[2] = z; 1962116Sjkh nx = 3; 1972116Sjkh while(tx[nx-1]==zero) nx--; /* skip zero term */ 198176356Sdas n = __kernel_rem_pio2(tx,y,e0,nx,2); 1992116Sjkh if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 2002116Sjkh return n; 2012116Sjkh} 202