e_rem_pio2.c revision 239195
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 * 13176476Sbde * Optimized by Bruce D. Evans. 142116Sjkh */ 152116Sjkh 16176385Sbde#include <sys/cdefs.h> 17176385Sbde__FBSDID("$FreeBSD: head/lib/msun/src/e_rem_pio2.c 239195 2012-08-11 15:47:22Z dim $"); 182116Sjkh 192116Sjkh/* __ieee754_rem_pio2(x,y) 20141296Sdas * 21141296Sdas * return the remainder of x rem pi/2 in y[0]+y[1] 222116Sjkh * use __kernel_rem_pio2() 232116Sjkh */ 242116Sjkh 25176465Sbde#include <float.h> 26176465Sbde 272116Sjkh#include "math.h" 282116Sjkh#include "math_private.h" 292116Sjkh 302116Sjkh/* 312116Sjkh * invpio2: 53 bits of 2/pi 322116Sjkh * pio2_1: first 33 bit of pi/2 332116Sjkh * pio2_1t: pi/2 - pio2_1 342116Sjkh * pio2_2: second 33 bit of pi/2 352116Sjkh * pio2_2t: pi/2 - (pio2_1+pio2_2) 362116Sjkh * pio2_3: third 33 bit of pi/2 372116Sjkh * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 382116Sjkh */ 392116Sjkh 408870Srgrimesstatic const double 412116Sjkhzero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 422116Sjkhtwo24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 432116Sjkhinvpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 442116Sjkhpio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 452116Sjkhpio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 462116Sjkhpio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 472116Sjkhpio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 482116Sjkhpio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 492116Sjkhpio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 502116Sjkh 51239192Sdim#ifdef INLINE_REM_PIO2 52239195Sdimstatic __inline __always_inline 53176385Sbde#endif 54239192Sdimint 55176385Sbde__ieee754_rem_pio2(double x, double *y) 562116Sjkh{ 572116Sjkh double z,w,t,r,fn; 58176558Sbde double tx[3],ty[2]; 592116Sjkh int32_t e0,i,j,nx,n,ix,hx; 602116Sjkh u_int32_t low; 612116Sjkh 622116Sjkh GET_HIGH_WORD(hx,x); /* high word of x */ 632116Sjkh ix = hx&0x7fffffff; 64176409Sbde#if 0 /* Must be handled in caller. */ 652116Sjkh if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 662116Sjkh {y[0] = x; y[1] = 0; return 0;} 67176409Sbde#endif 68176409Sbde if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ 69176409Sbde if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ 70176409Sbde goto medium; /* cancellation -- use medium case */ 71176409Sbde if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ 72176409Sbde if (hx > 0) { 73176409Sbde z = x - pio2_1; /* one round good to 85 bits */ 747659Sbde y[0] = z - pio2_1t; 757659Sbde y[1] = (z-y[0])-pio2_1t; 76176409Sbde return 1; 77176409Sbde } else { 78176409Sbde z = x + pio2_1; 797659Sbde y[0] = z + pio2_1t; 807659Sbde y[1] = (z-y[0])+pio2_1t; 81176409Sbde return -1; 827659Sbde } 83176409Sbde } else { 84176409Sbde if (hx > 0) { 85176409Sbde z = x - 2*pio2_1; 86176409Sbde y[0] = z - 2*pio2_1t; 87176409Sbde y[1] = (z-y[0])-2*pio2_1t; 88176409Sbde return 2; 89176409Sbde } else { 90176409Sbde z = x + 2*pio2_1; 91176409Sbde y[0] = z + 2*pio2_1t; 92176409Sbde y[1] = (z-y[0])+2*pio2_1t; 93176409Sbde return -2; 94176409Sbde } 957659Sbde } 967659Sbde } 97176409Sbde if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ 98176409Sbde if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ 99176409Sbde if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ 100176409Sbde goto medium; 101176409Sbde if (hx > 0) { 102176409Sbde z = x - 3*pio2_1; 103176409Sbde y[0] = z - 3*pio2_1t; 104176409Sbde y[1] = (z-y[0])-3*pio2_1t; 105176409Sbde return 3; 106176409Sbde } else { 107176409Sbde z = x + 3*pio2_1; 108176409Sbde y[0] = z + 3*pio2_1t; 109176409Sbde y[1] = (z-y[0])+3*pio2_1t; 110176409Sbde return -3; 111176409Sbde } 112176409Sbde } else { 113176409Sbde if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ 114176409Sbde goto medium; 115176409Sbde if (hx > 0) { 116176409Sbde z = x - 4*pio2_1; 117176409Sbde y[0] = z - 4*pio2_1t; 118176409Sbde y[1] = (z-y[0])-4*pio2_1t; 119176409Sbde return 4; 120176409Sbde } else { 121176409Sbde z = x + 4*pio2_1; 122176409Sbde y[0] = z + 4*pio2_1t; 123176409Sbde y[1] = (z-y[0])+4*pio2_1t; 124176409Sbde return -4; 125176409Sbde } 126176409Sbde } 127176409Sbde } 128176640Sbde if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ 129176409Sbdemedium: 130176465Sbde /* Use a specialized rint() to get fn. Assume round-to-nearest. */ 131176476Sbde STRICT_ASSIGN(double,fn,x*invpio2+0x1.8p52); 132176465Sbde fn = fn-0x1.8p52; 133176467Sbde#ifdef HAVE_EFFICIENT_IRINT 134176465Sbde n = irint(fn); 135176465Sbde#else 136176467Sbde n = (int32_t)fn; 137176465Sbde#endif 138176476Sbde r = x-fn*pio2_1; 1392116Sjkh w = fn*pio2_1t; /* 1st round good to 85 bit */ 140176466Sbde { 1412116Sjkh u_int32_t high; 1422116Sjkh j = ix>>20; 143141296Sdas y[0] = r-w; 1442116Sjkh GET_HIGH_WORD(high,y[0]); 1452116Sjkh i = j-((high>>20)&0x7ff); 1462116Sjkh if(i>16) { /* 2nd iteration needed, good to 118 */ 1472116Sjkh t = r; 148141296Sdas w = fn*pio2_2; 1492116Sjkh r = t-w; 150141296Sdas w = fn*pio2_2t-((t-r)-w); 1512116Sjkh y[0] = r-w; 1522116Sjkh GET_HIGH_WORD(high,y[0]); 1532116Sjkh i = j-((high>>20)&0x7ff); 1542116Sjkh if(i>49) { /* 3rd iteration need, 151 bits acc */ 1552116Sjkh t = r; /* will cover all possible cases */ 156141296Sdas w = fn*pio2_3; 1572116Sjkh r = t-w; 158141296Sdas w = fn*pio2_3t-((t-r)-w); 1592116Sjkh y[0] = r-w; 1602116Sjkh } 1612116Sjkh } 1622116Sjkh } 1632116Sjkh y[1] = (r-y[0])-w; 164176476Sbde return n; 1652116Sjkh } 166141296Sdas /* 1672116Sjkh * all other (large) arguments 1682116Sjkh */ 1692116Sjkh if(ix>=0x7ff00000) { /* x is inf or NaN */ 1702116Sjkh y[0]=y[1]=x-x; return 0; 1712116Sjkh } 1722116Sjkh /* set z = scalbn(|x|,ilogb(x)-23) */ 1732116Sjkh GET_LOW_WORD(low,x); 1742116Sjkh e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 175223302Skargl INSERT_WORDS(z, ix - ((int32_t)(e0<<20)), low); 1762116Sjkh for(i=0;i<2;i++) { 1772116Sjkh tx[i] = (double)((int32_t)(z)); 1782116Sjkh z = (z-tx[i])*two24; 1792116Sjkh } 1802116Sjkh tx[2] = z; 1812116Sjkh nx = 3; 1822116Sjkh while(tx[nx-1]==zero) nx--; /* skip zero term */ 183176558Sbde n = __kernel_rem_pio2(tx,ty,e0,nx,1); 184176558Sbde if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} 185176558Sbde y[0] = ty[0]; y[1] = ty[1]; return n; 1862116Sjkh} 187