1 /* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */
2 /*
3 * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
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 pio4 = 0x1.921fb6p-1,
39 invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
40 pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
41 pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
42
__rem_pio2f(float x,double * y)43 int __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