e_rem_pio2l.h revision 187128
140843Smsmith 240843Smsmith/* @(#)e_rem_pio2.c 1.4 95/01/18 */ 340843Smsmith/* 440843Smsmith * ==================================================== 594290Sdcs * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 651786Sdcs * 751786Sdcs * Developed at SunSoft, a Sun Microsystems, Inc. business. 840843Smsmith * Permission to use, copy, modify, and distribute this 940843Smsmith * software is freely granted, provided that this notice 1040843Smsmith * is preserved. 1140843Smsmith * ==================================================== 1240843Smsmith * 1340843Smsmith * Optimized by Bruce D. Evans. 1440843Smsmith */ 1540843Smsmith 1640843Smsmith#include <sys/cdefs.h> 1740843Smsmith__FBSDID("$FreeBSD: head/lib/msun/src/e_rem_pio2.c 187128 2009-01-13 05:13:20Z das $"); 1840843Smsmith 1940843Smsmith/* __ieee754_rem_pio2(x,y) 2040843Smsmith * 2140843Smsmith * return the remainder of x rem pi/2 in y[0]+y[1] 2240843Smsmith * use __kernel_rem_pio2() 2340843Smsmith */ 2440843Smsmith 2540843Smsmith#include <float.h> 2640843Smsmith 2740843Smsmith#include "math.h" 2840843Smsmith#include "math_private.h" 2940843Smsmith 3040843Smsmith/* 3140843Smsmith * invpio2: 53 bits of 2/pi 3240843Smsmith * pio2_1: first 33 bit of pi/2 3376116Sdcs * pio2_1t: pi/2 - pio2_1 3461584Sdcs * pio2_2: second 33 bit of pi/2 3561584Sdcs * pio2_2t: pi/2 - (pio2_1+pio2_2) 3676116Sdcs * pio2_3: third 33 bit of pi/2 3761584Sdcs * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) 3861584Sdcs */ 3961584Sdcs 4061584Sdcsstatic const double 4161584Sdcszero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 4261584Sdcstwo24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 4376116Sdcsinvpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 4461584Sdcspio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 4561584Sdcspio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ 4661584Sdcspio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ 4761584Sdcspio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ 4876116Sdcspio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ 4976116Sdcspio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ 5076116Sdcs 5176116Sdcs#ifdef INLINE_REM_PIO2 5261584Sdcsextern __gnu89_inline 5340843Smsmith#endif 5440843Smsmithint 5540843Smsmith__ieee754_rem_pio2(double x, double *y) 5676116Sdcs{ 5776116Sdcs double z,w,t,r,fn; 5856718Sdcs double tx[3],ty[2]; 5956718Sdcs int32_t e0,i,j,nx,n,ix,hx; 6040843Smsmith u_int32_t low; 6194290Sdcs 6240843Smsmith GET_HIGH_WORD(hx,x); /* high word of x */ 6394290Sdcs ix = hx&0x7fffffff; 6494290Sdcs#if 0 /* Must be handled in caller. */ 6594290Sdcs if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ 6640843Smsmith {y[0] = x; y[1] = 0; return 0;} 6740843Smsmith#endif 6851786Sdcs if (ix <= 0x400f6a7a) { /* |x| ~<= 5pi/4 */ 6940843Smsmith if ((ix & 0xfffff) == 0x921fb) /* |x| ~= pi/2 or 2pi/2 */ 7051786Sdcs goto medium; /* cancellation -- use medium case */ 7140843Smsmith if (ix <= 0x4002d97c) { /* |x| ~<= 3pi/4 */ 7240843Smsmith if (hx > 0) { 7340843Smsmith z = x - pio2_1; /* one round good to 85 bits */ 7440843Smsmith y[0] = z - pio2_1t; 7540843Smsmith y[1] = (z-y[0])-pio2_1t; 7640843Smsmith return 1; 7740843Smsmith } else { 7840843Smsmith z = x + pio2_1; 7940843Smsmith y[0] = z + pio2_1t; 8040843Smsmith y[1] = (z-y[0])+pio2_1t; 8140843Smsmith return -1; 8240843Smsmith } 8340843Smsmith } else { 8440843Smsmith if (hx > 0) { 8540843Smsmith z = x - 2*pio2_1; 8660959Sdcs y[0] = z - 2*pio2_1t; 8760959Sdcs y[1] = (z-y[0])-2*pio2_1t; 8840843Smsmith return 2; 8940843Smsmith } else { 9040843Smsmith z = x + 2*pio2_1; 9140843Smsmith y[0] = z + 2*pio2_1t; 9240843Smsmith y[1] = (z-y[0])+2*pio2_1t; 9340843Smsmith return -2; 9440843Smsmith } 9540843Smsmith } 9640843Smsmith } 9740843Smsmith if (ix <= 0x401c463b) { /* |x| ~<= 9pi/4 */ 9840843Smsmith if (ix <= 0x4015fdbc) { /* |x| ~<= 7pi/4 */ 9940843Smsmith if (ix == 0x4012d97c) /* |x| ~= 3pi/2 */ 10040843Smsmith goto medium; 10140843Smsmith if (hx > 0) { 10276116Sdcs z = x - 3*pio2_1; 10376116Sdcs y[0] = z - 3*pio2_1t; 10476116Sdcs y[1] = (z-y[0])-3*pio2_1t; 10576116Sdcs return 3; 10676116Sdcs } else { 10776116Sdcs z = x + 3*pio2_1; 10876116Sdcs y[0] = z + 3*pio2_1t; 10976116Sdcs y[1] = (z-y[0])+3*pio2_1t; 11040843Smsmith return -3; 11140843Smsmith } 11240843Smsmith } else { 11376116Sdcs if (ix == 0x401921fb) /* |x| ~= 4pi/2 */ 11476116Sdcs goto medium; 11576116Sdcs if (hx > 0) { 11676116Sdcs z = x - 4*pio2_1; 11740843Smsmith y[0] = z - 4*pio2_1t; 11840843Smsmith y[1] = (z-y[0])-4*pio2_1t; 11940843Smsmith return 4; 12040843Smsmith } else { 12140843Smsmith z = x + 4*pio2_1; 12276116Sdcs y[0] = z + 4*pio2_1t; 12376116Sdcs y[1] = (z-y[0])+4*pio2_1t; 12476116Sdcs return -4; 12540843Smsmith } 12676116Sdcs } 12740843Smsmith } 12876116Sdcs if(ix<0x413921fb) { /* |x| ~< 2^20*(pi/2), medium size */ 12976116Sdcsmedium: 13040843Smsmith /* Use a specialized rint() to get fn. Assume round-to-nearest. */ 13176116Sdcs STRICT_ASSIGN(double,fn,x*invpio2+0x1.8p52); 13276116Sdcs fn = fn-0x1.8p52; 13376116Sdcs#ifdef HAVE_EFFICIENT_IRINT 13476116Sdcs n = irint(fn); 13576116Sdcs#else 13676116Sdcs n = (int32_t)fn; 13776116Sdcs#endif 13876116Sdcs r = x-fn*pio2_1; 13976116Sdcs w = fn*pio2_1t; /* 1st round good to 85 bit */ 14076116Sdcs { 14176116Sdcs u_int32_t high; 14240843Smsmith j = ix>>20; 14340843Smsmith y[0] = r-w; 14440843Smsmith GET_HIGH_WORD(high,y[0]); 14540843Smsmith i = j-((high>>20)&0x7ff); 14640843Smsmith if(i>16) { /* 2nd iteration needed, good to 118 */ 14740843Smsmith t = r; 14840843Smsmith w = fn*pio2_2; 14940843Smsmith r = t-w; 15040843Smsmith w = fn*pio2_2t-((t-r)-w); 15140843Smsmith y[0] = r-w; 15240843Smsmith GET_HIGH_WORD(high,y[0]); 15340843Smsmith i = j-((high>>20)&0x7ff); 15440843Smsmith if(i>49) { /* 3rd iteration need, 151 bits acc */ 15540843Smsmith t = r; /* will cover all possible cases */ 15676116Sdcs w = fn*pio2_3; 15776116Sdcs r = t-w; 15876116Sdcs w = fn*pio2_3t-((t-r)-w); 15976116Sdcs y[0] = r-w; 16076116Sdcs } 16176116Sdcs } 16276116Sdcs } 16376116Sdcs y[1] = (r-y[0])-w; 16476116Sdcs return n; 16576116Sdcs } 16676116Sdcs /* 16740843Smsmith * all other (large) arguments 16876116Sdcs */ 16976116Sdcs if(ix>=0x7ff00000) { /* x is inf or NaN */ 17076116Sdcs y[0]=y[1]=x-x; return 0; 17176116Sdcs } 17240843Smsmith /* set z = scalbn(|x|,ilogb(x)-23) */ 17394290Sdcs GET_LOW_WORD(low,x); 17494290Sdcs SET_LOW_WORD(z,low); 17540843Smsmith e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ 17694290Sdcs SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); 17794290Sdcs for(i=0;i<2;i++) { 17894290Sdcs tx[i] = (double)((int32_t)(z)); 17994290Sdcs z = (z-tx[i])*two24; 18094290Sdcs } 18194290Sdcs tx[2] = z; 18294290Sdcs nx = 3; 18394290Sdcs while(tx[nx-1]==zero) nx--; /* skip zero term */ 18494290Sdcs n = __kernel_rem_pio2(tx,ty,e0,nx,1); 18594290Sdcs if(hx<0) {y[0] = -ty[0]; y[1] = -ty[1]; return -n;} 18694290Sdcs y[0] = ty[0]; y[1] = ty[1]; return n; 18794290Sdcs} 18894290Sdcs