e_rem_pio2.c revision 176385
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 176385 2008-02-18 14:02:12Z 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 242116Sjkh#include "math.h" 252116Sjkh#include "math_private.h" 262116Sjkh 272116Sjkhstatic const int32_t npio2_hw[] = { 282116Sjkh0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 292116Sjkh0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 302116Sjkh0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 312116Sjkh0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 322116Sjkh0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 332116Sjkh0x404858EB, 0x404921FB, 342116Sjkh}; 352116Sjkh 362116Sjkh/* 372116Sjkh * invpio2: 53 bits of 2/pi 382116Sjkh * pio2_1: first 33 bit of pi/2 392116Sjkh * pio2_1t: pi/2 - pio2_1 402116Sjkh * pio2_2: second 33 bit of pi/2 412116Sjkh * pio2_2t: pi/2 - (pio2_1+pio2_2) 422116Sjkh * pio2_3: third 33 bit of pi/2 432116Sjkh * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 442116Sjkh */ 452116Sjkh 468870Srgrimesstatic const double 472116Sjkhzero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 482116Sjkhhalf = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 492116Sjkhtwo24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 502116Sjkhinvpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 512116Sjkhpio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 522116Sjkhpio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 532116Sjkhpio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 542116Sjkhpio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 552116Sjkhpio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 562116Sjkhpio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 572116Sjkh 58176385Sbde#ifdef INLINE_REM_PIO2 59176385Sbdeextern inline 60176385Sbde#endif 61176385Sbdeint 62176385Sbde__ieee754_rem_pio2(double x, double *y) 632116Sjkh{ 642116Sjkh double z,w,t,r,fn; 652116Sjkh double tx[3]; 662116Sjkh int32_t e0,i,j,nx,n,ix,hx; 672116Sjkh u_int32_t low; 682116Sjkh 692116Sjkh GET_HIGH_WORD(hx,x); /* high word of x */ 702116Sjkh ix = hx&0x7fffffff; 712116Sjkh if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 722116Sjkh {y[0] = x; y[1] = 0; return 0;} 737659Sbde if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ 74141296Sdas if(hx>0) { 757659Sbde z = x - pio2_1; 767659Sbde if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 777659Sbde y[0] = z - pio2_1t; 787659Sbde y[1] = (z-y[0])-pio2_1t; 797659Sbde } else { /* near pi/2, use 33+33+53 bit pi */ 807659Sbde z -= pio2_2; 817659Sbde y[0] = z - pio2_2t; 827659Sbde y[1] = (z-y[0])-pio2_2t; 837659Sbde } 847659Sbde return 1; 857659Sbde } else { /* negative x */ 867659Sbde z = x + pio2_1; 877659Sbde if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ 887659Sbde y[0] = z + pio2_1t; 897659Sbde y[1] = (z-y[0])+pio2_1t; 907659Sbde } else { /* near pi/2, use 33+33+53 bit pi */ 917659Sbde z += pio2_2; 927659Sbde y[0] = z + pio2_2t; 937659Sbde y[1] = (z-y[0])+pio2_2t; 947659Sbde } 957659Sbde return -1; 967659Sbde } 977659Sbde } 982116Sjkh if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ 992116Sjkh t = fabs(x); 1002116Sjkh n = (int32_t) (t*invpio2+half); 1012116Sjkh fn = (double)n; 1022116Sjkh r = t-fn*pio2_1; 1032116Sjkh w = fn*pio2_1t; /* 1st round good to 85 bit */ 104141296Sdas if(n<32&&ix!=npio2_hw[n-1]) { 1052116Sjkh y[0] = r-w; /* quick check no cancellation */ 1062116Sjkh } else { 1072116Sjkh u_int32_t high; 1082116Sjkh j = ix>>20; 109141296Sdas y[0] = r-w; 1102116Sjkh GET_HIGH_WORD(high,y[0]); 1112116Sjkh i = j-((high>>20)&0x7ff); 1122116Sjkh if(i>16) { /* 2nd iteration needed, good to 118 */ 1132116Sjkh t = r; 114141296Sdas w = fn*pio2_2; 1152116Sjkh r = t-w; 116141296Sdas w = fn*pio2_2t-((t-r)-w); 1172116Sjkh y[0] = r-w; 1182116Sjkh GET_HIGH_WORD(high,y[0]); 1192116Sjkh i = j-((high>>20)&0x7ff); 1202116Sjkh if(i>49) { /* 3rd iteration need, 151 bits acc */ 1212116Sjkh t = r; /* will cover all possible cases */ 122141296Sdas w = fn*pio2_3; 1232116Sjkh r = t-w; 124141296Sdas w = fn*pio2_3t-((t-r)-w); 1252116Sjkh y[0] = r-w; 1262116Sjkh } 1272116Sjkh } 1282116Sjkh } 1292116Sjkh y[1] = (r-y[0])-w; 1302116Sjkh if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 1312116Sjkh else return n; 1322116Sjkh } 133141296Sdas /* 1342116Sjkh * all other (large) arguments 1352116Sjkh */ 1362116Sjkh if(ix>=0x7ff00000) { /* x is inf or NaN */ 1372116Sjkh y[0]=y[1]=x-x; return 0; 1382116Sjkh } 1392116Sjkh /* set z = scalbn(|x|,ilogb(x)-23) */ 1402116Sjkh GET_LOW_WORD(low,x); 1412116Sjkh SET_LOW_WORD(z,low); 1422116Sjkh e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 1432116Sjkh SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 1442116Sjkh for(i=0;i<2;i++) { 1452116Sjkh tx[i] = (double)((int32_t)(z)); 1462116Sjkh z = (z-tx[i])*two24; 1472116Sjkh } 1482116Sjkh tx[2] = z; 1492116Sjkh nx = 3; 1502116Sjkh while(tx[nx-1]==zero) nx--; /* skip zero term */ 151176356Sdas n = __kernel_rem_pio2(tx,y,e0,nx,2); 1522116Sjkh if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 1532116Sjkh return n; 1542116Sjkh} 155