xref: /aosp_15_r20/external/musl/src/math/__rem_pio2f.c (revision c9945492fdd68bbe62686c5b452b4dc1be3f8453)
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