e_rem_pio2f.c revision 152706 
1/* e_rem_pio2f.c -- float version of e_rem_pio2.c
2 * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
3 * Debugged and optimized by Bruce D. Evans.
4 */
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
17#ifndef lint
18static char rcsid[] = "$FreeBSD: head/lib/msun/src/e_rem_pio2f.c 152706 2005-11-23 02:06:06Z bde $";
19#endif
20
21/* __ieee754_rem_pio2f(x,y)
22 *
23 * return the remainder of x rem pi/2 in y[0]+y[1]
24 * use double precision internally
25 * use __kernel_rem_pio2() for large x
26 */
27
28#include "math.h"
29#include "math_private.h"
30
31/*
32 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
33 */
34static const int32_t two_over_pi[] = {
350xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
360x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
370x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
380xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
390x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
400x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
410x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
420xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
430x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
440x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
450x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
46};
47
48/*
49 * invpio2:  53 bits of 2/pi
50 * pio2_1:   first  33 bit of pi/2
51 * pio2_1t:  pi/2 - pio2_1
52 */
53
54static const double
55zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
56half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
57two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
58invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
59pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
60pio2_1t =  6.07710050650619224932e-11; /* 0x3DD0B461, 0x1A626331 */
61
62	int32_t __ieee754_rem_pio2f(float x, float *y)
63{
64	double z,w,t,r,fn;
65	double tx[3],ty[2];
66	int32_t e0,i,nx,n,ix,hx;
67
68	GET_FLOAT_WORD(hx,x);
69	ix = hx&0x7fffffff;
70    /* 33+53 bit pi is good enough for medium size */
71	if(ix<=0x49490f80) {		/* |x| ~<= 2^19*(pi/2), medium size */
72	    t  = fabsf(x);
73	    n  = (int32_t) (t*invpio2+half);
74	    fn = (double)n;
75	    r  = t-fn*pio2_1;
76	    w  = fn*pio2_1t;
77	    y[0] = r-w;
78	    y[1] = (r-y[0])-w;
79	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
80	    else	 return n;
81	}
82    /*
83     * all other (large) arguments
84     */
85	if(ix>=0x7f800000) {		/* x is inf or NaN */
86	    y[0]=y[1]=x-x; return 0;
87	}
88    /* set z = scalbn(|x|,ilogb(x)-23) */
89	z = x;
90	GET_HIGH_WORD(hx,z);
91	ix = hx&0x7fffffff;
92	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
93	SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
94	for(i=0;i<2;i++) {
95		tx[i] = (double)((int32_t)(z));
96		z     = (z-tx[i])*two24;
97	}
98	tx[2] = z;
99	nx = 3;
100	while(tx[nx-1]==zero) nx--;	/* skip zero term */
101	n  =  __kernel_rem_pio2(tx,ty,e0,nx,1,two_over_pi);
102	y[0] = ty[0];
103	y[1] = ty[0] - y[0];
104	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
105	return n;
106}
107