1*c9945492SAndroid Build Coastguard Worker /* origin: FreeBSD /usr/src/lib/msun/src/e_rem_pio2f.c */
2*c9945492SAndroid Build Coastguard Worker /*
3*c9945492SAndroid Build Coastguard Worker * Conversion to float by Ian Lance Taylor, Cygnus Support, [email protected].
4*c9945492SAndroid Build Coastguard Worker * Debugged and optimized by Bruce D. Evans.
5*c9945492SAndroid Build Coastguard Worker */
6*c9945492SAndroid Build Coastguard Worker /*
7*c9945492SAndroid Build Coastguard Worker * ====================================================
8*c9945492SAndroid Build Coastguard Worker * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
9*c9945492SAndroid Build Coastguard Worker *
10*c9945492SAndroid Build Coastguard Worker * Developed at SunPro, a Sun Microsystems, Inc. business.
11*c9945492SAndroid Build Coastguard Worker * Permission to use, copy, modify, and distribute this
12*c9945492SAndroid Build Coastguard Worker * software is freely granted, provided that this notice
13*c9945492SAndroid Build Coastguard Worker * is preserved.
14*c9945492SAndroid Build Coastguard Worker * ====================================================
15*c9945492SAndroid Build Coastguard Worker */
16*c9945492SAndroid Build Coastguard Worker /* __rem_pio2f(x,y)
17*c9945492SAndroid Build Coastguard Worker *
18*c9945492SAndroid Build Coastguard Worker * return the remainder of x rem pi/2 in *y
19*c9945492SAndroid Build Coastguard Worker * use double precision for everything except passing x
20*c9945492SAndroid Build Coastguard Worker * use __rem_pio2_large() for large x
21*c9945492SAndroid Build Coastguard Worker */
22*c9945492SAndroid Build Coastguard Worker
23*c9945492SAndroid Build Coastguard Worker #include "libm.h"
24*c9945492SAndroid Build Coastguard Worker
25*c9945492SAndroid Build Coastguard Worker #if FLT_EVAL_METHOD==0 || FLT_EVAL_METHOD==1
26*c9945492SAndroid Build Coastguard Worker #define EPS DBL_EPSILON
27*c9945492SAndroid Build Coastguard Worker #elif FLT_EVAL_METHOD==2
28*c9945492SAndroid Build Coastguard Worker #define EPS LDBL_EPSILON
29*c9945492SAndroid Build Coastguard Worker #endif
30*c9945492SAndroid Build Coastguard Worker
31*c9945492SAndroid Build Coastguard Worker /*
32*c9945492SAndroid Build Coastguard Worker * invpio2: 53 bits of 2/pi
33*c9945492SAndroid Build Coastguard Worker * pio2_1: first 25 bits of pi/2
34*c9945492SAndroid Build Coastguard Worker * pio2_1t: pi/2 - pio2_1
35*c9945492SAndroid Build Coastguard Worker */
36*c9945492SAndroid Build Coastguard Worker static const double
37*c9945492SAndroid Build Coastguard Worker toint = 1.5/EPS,
38*c9945492SAndroid Build Coastguard Worker pio4 = 0x1.921fb6p-1,
39*c9945492SAndroid Build Coastguard Worker invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
40*c9945492SAndroid Build Coastguard Worker pio2_1 = 1.57079631090164184570e+00, /* 0x3FF921FB, 0x50000000 */
41*c9945492SAndroid Build Coastguard Worker pio2_1t = 1.58932547735281966916e-08; /* 0x3E5110b4, 0x611A6263 */
42*c9945492SAndroid Build Coastguard Worker
__rem_pio2f(float x,double * y)43*c9945492SAndroid Build Coastguard Worker int __rem_pio2f(float x, double *y)
44*c9945492SAndroid Build Coastguard Worker {
45*c9945492SAndroid Build Coastguard Worker union {float f; uint32_t i;} u = {x};
46*c9945492SAndroid Build Coastguard Worker double tx[1],ty[1];
47*c9945492SAndroid Build Coastguard Worker double_t fn;
48*c9945492SAndroid Build Coastguard Worker uint32_t ix;
49*c9945492SAndroid Build Coastguard Worker int n, sign, e0;
50*c9945492SAndroid Build Coastguard Worker
51*c9945492SAndroid Build Coastguard Worker ix = u.i & 0x7fffffff;
52*c9945492SAndroid Build Coastguard Worker /* 25+53 bit pi is good enough for medium size */
53*c9945492SAndroid Build Coastguard Worker if (ix < 0x4dc90fdb) { /* |x| ~< 2^28*(pi/2), medium size */
54*c9945492SAndroid Build Coastguard Worker /* Use a specialized rint() to get fn. */
55*c9945492SAndroid Build Coastguard Worker fn = (double_t)x*invpio2 + toint - toint;
56*c9945492SAndroid Build Coastguard Worker n = (int32_t)fn;
57*c9945492SAndroid Build Coastguard Worker *y = x - fn*pio2_1 - fn*pio2_1t;
58*c9945492SAndroid Build Coastguard Worker /* Matters with directed rounding. */
59*c9945492SAndroid Build Coastguard Worker if (predict_false(*y < -pio4)) {
60*c9945492SAndroid Build Coastguard Worker n--;
61*c9945492SAndroid Build Coastguard Worker fn--;
62*c9945492SAndroid Build Coastguard Worker *y = x - fn*pio2_1 - fn*pio2_1t;
63*c9945492SAndroid Build Coastguard Worker } else if (predict_false(*y > pio4)) {
64*c9945492SAndroid Build Coastguard Worker n++;
65*c9945492SAndroid Build Coastguard Worker fn++;
66*c9945492SAndroid Build Coastguard Worker *y = x - fn*pio2_1 - fn*pio2_1t;
67*c9945492SAndroid Build Coastguard Worker }
68*c9945492SAndroid Build Coastguard Worker return n;
69*c9945492SAndroid Build Coastguard Worker }
70*c9945492SAndroid Build Coastguard Worker if(ix>=0x7f800000) { /* x is inf or NaN */
71*c9945492SAndroid Build Coastguard Worker *y = x-x;
72*c9945492SAndroid Build Coastguard Worker return 0;
73*c9945492SAndroid Build Coastguard Worker }
74*c9945492SAndroid Build Coastguard Worker /* scale x into [2^23, 2^24-1] */
75*c9945492SAndroid Build Coastguard Worker sign = u.i>>31;
76*c9945492SAndroid Build Coastguard Worker e0 = (ix>>23) - (0x7f+23); /* e0 = ilogb(|x|)-23, positive */
77*c9945492SAndroid Build Coastguard Worker u.i = ix - (e0<<23);
78*c9945492SAndroid Build Coastguard Worker tx[0] = u.f;
79*c9945492SAndroid Build Coastguard Worker n = __rem_pio2_large(tx,ty,e0,1,0);
80*c9945492SAndroid Build Coastguard Worker if (sign) {
81*c9945492SAndroid Build Coastguard Worker *y = -ty[0];
82*c9945492SAndroid Build Coastguard Worker return -n;
83*c9945492SAndroid Build Coastguard Worker }
84*c9945492SAndroid Build Coastguard Worker *y = ty[0];
85*c9945492SAndroid Build Coastguard Worker return n;
86*c9945492SAndroid Build Coastguard Worker }
87