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 */ 36static const double 37toint = 1.5/EPS, 38pio4 = 0x1.921fb6p-1, 39invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ 40pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */ 41pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */ 42 43int __rem_pio2f(float x, double *y) 44{ 45 union {float f; uint32_t i;} u = {x}; 46 double tx[1],ty[1]; 47 double_t fn; 48 uint32_t ix; 49 int n, sign, e0; 50 51 ix = u.i & 0x7fffffff; 52 /* 25+53 bit pi is good enough for medium size */ 53 if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */ 54 /* Use a specialized rint() to get fn. */ 55 fn = (double_t)x*invpio2 + toint - toint; 56 n = (int32_t)fn; 57 *y = x - fn*pio2_1 - fn*pio2_1t; 58 /* Matters with directed rounding. */ 59 if (predict_false(*y < -pio4)) { 60 n--; 61 fn--; 62 *y = x - fn*pio2_1 - fn*pio2_1t; 63 } else if (predict_false(*y > pio4)) { 64 n++; 65 fn++; 66 *y = x - fn*pio2_1 - fn*pio2_1t; 67 } 68 return n; 69 } 70 if(ix>=0x7f800000) { /* x is inf or NaN */ 71 *y = x-x; 72 return 0; 73 } 74 /* scale x into [2^23, 2^24-1] */ 75 sign = u.i>>31; 76 e0 = (ix>>23) - (0x7f+23); /* e0 = ilogb(|x|)-23, positive */ 77 u.i = ix - (e0<<23); 78 tx[0] = u.f; 79 n = __rem_pio2_large(tx,ty,e0,1,0); 80 if (sign) { 81 *y = -ty[0]; 82 return -n; 83 } 84 *y = ty[0]; 85 return n; 86} 87