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[/] [openrisc/] [trunk/] [gnu-src/] [newlib-1.17.0/] [newlib/] [libm/] [math/] [e_rem_pio2.c] - Rev 414
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/* @(#)e_rem_pio2.c 5.1 93/09/24 */ /* * ==================================================== * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. * * Developed at SunPro, a Sun Microsystems, Inc. business. * Permission to use, copy, modify, and distribute this * software is freely granted, provided that this notice * is preserved. * ==================================================== * */ /* __ieee754_rem_pio2(x,y) * * return the remainder of x rem pi/2 in y[0]+y[1] * use __kernel_rem_pio2() */ #include "fdlibm.h" #ifndef _DOUBLE_IS_32BITS /* * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi */ #ifdef __STDC__ static const __int32_t two_over_pi[] = { #else static __int32_t two_over_pi[] = { #endif 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, }; #ifdef __STDC__ static const __int32_t npio2_hw[] = { #else static __int32_t npio2_hw[] = { #endif 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, 0x404858EB, 0x404921FB, }; /* * invpio2: 53 bits of 2/pi * pio2_1: first 33 bit of pi/2 * pio2_1t: pi/2 - pio2_1 * pio2_2: second 33 bit of pi/2 * pio2_2t: pi/2 - (pio2_1+pio2_2) * pio2_3: third 33 bit of pi/2 * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) */ #ifdef __STDC__ static const double #else static double #endif zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ #ifdef __STDC__ __int32_t __ieee754_rem_pio2(double x, double *y) #else __int32_t __ieee754_rem_pio2(x,y) double x,y[]; #endif { double z,w,t,r,fn; double tx[3]; __int32_t i,j,n,ix,hx; int e0,nx; __uint32_t low; GET_HIGH_WORD(hx,x); /* high word of x */ ix = hx&0x7fffffff; if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ {y[0] = x; y[1] = 0; return 0;} if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ if(hx>0) { z = x - pio2_1; if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ y[0] = z - pio2_1t; y[1] = (z-y[0])-pio2_1t; } else { /* near pi/2, use 33+33+53 bit pi */ z -= pio2_2; y[0] = z - pio2_2t; y[1] = (z-y[0])-pio2_2t; } return 1; } else { /* negative x */ z = x + pio2_1; if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ y[0] = z + pio2_1t; y[1] = (z-y[0])+pio2_1t; } else { /* near pi/2, use 33+33+53 bit pi */ z += pio2_2; y[0] = z + pio2_2t; y[1] = (z-y[0])+pio2_2t; } return -1; } } if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ t = fabs(x); n = (__int32_t) (t*invpio2+half); fn = (double)n; r = t-fn*pio2_1; w = fn*pio2_1t; /* 1st round good to 85 bit */ if(n<32&&ix!=npio2_hw[n-1]) { y[0] = r-w; /* quick check no cancellation */ } else { __uint32_t high; j = ix>>20; y[0] = r-w; GET_HIGH_WORD(high,y[0]); i = j-((high>>20)&0x7ff); if(i>16) { /* 2nd iteration needed, good to 118 */ t = r; w = fn*pio2_2; r = t-w; w = fn*pio2_2t-((t-r)-w); y[0] = r-w; GET_HIGH_WORD(high,y[0]); i = j-((high>>20)&0x7ff); if(i>49) { /* 3rd iteration need, 151 bits acc */ t = r; /* will cover all possible cases */ w = fn*pio2_3; r = t-w; w = fn*pio2_3t-((t-r)-w); y[0] = r-w; } } } y[1] = (r-y[0])-w; if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} else return n; } /* * all other (large) arguments */ if(ix>=0x7ff00000) { /* x is inf or NaN */ y[0]=y[1]=x-x; return 0; } /* set z = scalbn(|x|,ilogb(x)-23) */ GET_LOW_WORD(low,x); SET_LOW_WORD(z,low); e0 = (int)((ix>>20)-1046); /* e0 = ilogb(z)-23; */ SET_HIGH_WORD(z, ix - ((__int32_t)e0<<20)); for(i=0;i<2;i++) { tx[i] = (double)((__int32_t)(z)); z = (z-tx[i])*two24; } tx[2] = z; nx = 3; while(tx[nx-1]==zero) nx--; /* skip zero term */ n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} return n; } #endif /* defined(_DOUBLE_IS_32BITS) */
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