1 /* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */ 2 /* 3 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. 4 * Debugged and optimized by Bruce D. Evans. 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 /* __rem_pio2f(x,y) 17 * 18 * return the remainder of x rem pi/2 in *y 19 * use double precision for everything except passing x 20 * use __rem_pio2_large() for large x 21 */ 22 23 #include "libm.h" 24 25 #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1 26 #define EPS DBL_EPSILON 27 #elif FLT_EVAL_METHOD==2 28 #define EPS LDBL_EPSILON 29 #endif 30 31 /* 32 * invpio2: 53 bits of 2/pi 33 * pio2_1: first 25 bits of pi/2 34 * pio2_1t: pi/2 - pio2_1 35 */ 36 static const double 37 toint = 1.5/EPS, 38 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 39 pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */ 40 pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */ 41 42 int __rem_pio2f(float x, double *y) 43 { 44 union {float f; uint32_t i;} u = {x}; 45 double tx[1],ty[1]; 46 double_t fn; 47 uint32_t ix; 48 int n, sign, e0; 49 50 ix = u.i & 0x7fffffff; 51 /* 25+53 bit pi is good enough for medium size */ 52 if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */ 53 /* Use a specialized rint() to get fn. Assume round-to-nearest. */ 54 fn = (double_t)x*invpio2 + toint - toint; 55 n = (int32_t)fn; 56 *y = x - fn*pio2_1 - fn*pio2_1t; 57 return n; 58 } 59 if(ix>=0x7f800000) { /* x is inf or NaN */ 60 *y = x-x; 61 return 0; 62 } 63 /* scale x into [2^23, 2^24-1] */ 64 sign = u.i>>31; 65 e0 = (ix>>23) - (0x7f+23); /* e0 = ilogb(|x|)-23, positive */ 66 u.i = ix - (e0<<23); 67 tx[0] = u.f; 68 n = __rem_pio2_large(tx,ty,e0,1,0); 69 if (sign) { 70 *y = -ty[0]; 71 return -n; 72 } 73 *y = ty[0]; 74 return n; 75 } 76