1 /* e_rem_pio2f.c -- float version of e_rem_pio2.c 2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian (at) cygnus.com. 3 * Debugged and optimized by Bruce D. Evans. 4 */ 5 6 /* 7 * ==================================================== 8 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 9 * 10 * Developed at SunPro, a Sun Microsystems, Inc. business. 11 * Permission to use, copy, modify, and distribute this 12 * software is freely granted, provided that this notice 13 * is preserved. 14 * ==================================================== 15 */ 16 17 #ifndef lint 18 static char rcsid[] = "$FreeBSD: src/lib/msun/src/e_rem_pio2f.c,v 1.19 2005/11/23 03:03:09 bde Exp $"; 19 #endif 20 21 /* __ieee754_rem_pio2f(x,y) 22 * 23 * return the remainder of x rem pi/2 in y[0]+y[1] 24 * use double precision internally 25 * use __kernel_rem_pio2() for large x 26 */ 27 28 #include "math.h" 29 #include "math_private.h" 30 31 /* 32 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi 33 */ 34 static const int32_t two_over_pi[] = { 35 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, 36 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, 37 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, 38 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, 39 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, 40 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, 41 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, 42 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, 43 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, 44 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, 45 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, 46 }; 47 48 /* 49 * invpio2: 53 bits of 2/pi 50 * pio2_1: first 33 bit of pi/2 51 * pio2_1t: pi/2 - pio2_1 52 */ 53 54 static const double 55 zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ 56 half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ 57 two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ 58 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 59 pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ 60 pio2_1t = 6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */ 61 62 int32_t __ieee754_rem_pio2f(float x, float *y) 63 { 64 double w,t,r,fn; 65 double tx[1],ty[2]; 66 float z; 67 int32_t e0,n,ix,hx; 68 69 GET_FLOAT_WORD(hx,x); 70 ix = hx&0x7fffffff; 71 /* 33+53 bit pi is good enough for medium size */ 72 if(ix<=0x49490f80) { /* |x| ~<= 2^19*(pi/2), medium size */ 73 t = fabsf(x); 74 n = (int32_t) (t*invpio2+half); 75 fn = (double)n; 76 r = t-fn*pio2_1; 77 w = fn*pio2_1t; 78 y[0] = r-w; 79 y[1] = (r-y[0])-w; 80 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 81 else return n; 82 } 83 /* 84 * all other (large) arguments 85 */ 86 if(ix>=0x7f800000) { /* x is inf or NaN */ 87 y[0]=y[1]=x-x; return 0; 88 } 89 /* set z = scalbn(|x|,ilogb(|x|)-23) */ 90 e0 = (ix>>23)-150; /* e0 = ilogb(|x|)-23; */ 91 SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23))); 92 tx[0] = z; 93 n = __kernel_rem_pio2(tx,ty,e0,1,1,two_over_pi); 94 y[0] = ty[0]; 95 y[1] = ty[0] - y[0]; 96 if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} 97 return n; 98 } 99
