e_rem_pio2f.c revision 152132 
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 * Conversion to not use float except for the arg by Bruce 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 152132 2005-11-06 17:48:02Z 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 __kernel_rem_pio2f()
25 */
26
27#include "math.h"
28#include "math_private.h"
29
30/*
31 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
32 */
33static const int32_t two_over_pi[] = {
340xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62,
350x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A,
360x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129,
370xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41,
380x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8,
390x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF,
400x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5,
410xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08,
420x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3,
430x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880,
440x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B,
45};
46
47/*
48 * invpio2:  53 bits of 2/pi
49 * pio2_1:   first  33 bit of pi/2
50 * pio2_1t:  pi/2 - pio2_1
51 */
52
53static const double
54zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
55half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
56two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
57invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
58pio2    =  1.57079632679489655700e+00, /* 0x3FF921FB, 0x54442d18 */
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];
66	int32_t e0,i,nx,n,ix,hx;
67
68	GET_FLOAT_WORD(hx,x);
69	ix = hx&0x7fffffff;
70	if(ix<=0x3f490fd8)   /* |x| ~<= pi/4 , no need for reduction */
71	    {y[0] = x; y[1] = 0; return 0;}
72	/* 33+53 bit pi is good enough for special and medium size cases */
73	if(ix<0x4016cbe4) {  /* |x| < 3pi/4, special case with n=+-1 */
74	    if(hx>0) {
75		z = x - pio2;
76		n = 1;
77	    } else {
78		z = x + pio2;
79		n = 3;
80	    }
81	    y[0] = z;
82	    y[1] = z - y[0];
83	    return n;
84	}
85	if(ix<0x407b53d1) {  /* |x| < 5*pi/4, special case with n=+-2 */
86	    if(hx>0)
87		z = x - 2*pio2;
88	    else
89		z = x + 2*pio2;
90	    y[0] = z;
91	    y[1] = z - y[0];
92	    return 2;
93	}
94	if(ix<0x40afeddf) {  /* |x| < 7*pi/4, special case with n=+-3 */
95	    if(hx>0) {
96		z = x - 3*pio2;
97		n = 3;
98	    } else {
99		z = x + 3*pio2;
100		n = 1;
101	    }
102	    y[0] = z;
103	    y[1] = z - y[0];
104	    return n;
105	}
106	if(ix<0x40e231d6) {  /* |x| < 9*pi/4, special case with n=+-4 */
107	    if(hx>0)
108		z = x - 4*pio2;
109	    else
110		z = x + 4*pio2;
111	    y[0] = z;
112	    y[1] = z - y[0];
113	    return 0;
114	}
115	if(ix<=0x49490f80) { /* |x| ~<= 2^19*(pi/2), medium size */
116	    t  = fabsf(x);
117	    n  = (int32_t) (t*invpio2+half);
118	    fn = (double)n;
119	    r  = t-fn*pio2_1;
120	    w  = fn*pio2_1t;
121	    y[0] = r-w;
122	    y[1] = (r-y[0])-w;
123	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
124	    else	 return n;
125	}
126    /*
127     * all other (large) arguments
128     */
129	if(ix>=0x7f800000) {		/* x is inf or NaN */
130	    y[0]=y[1]=x-x; return 0;
131	}
132    /* set z = scalbn(|x|,ilogb(x)-23) */
133	z = x;
134	GET_HIGH_WORD(hx,z);
135	ix = hx&0x7fffffff;
136	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
137	SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
138	for(i=0;i<2;i++) {
139		tx[i] = (double)((int32_t)(z));
140		z     = (z-tx[i])*two24;
141	}
142	tx[2] = z;
143	nx = 3;
144	while(tx[nx-1]==zero) nx--;	/* skip zero term */
145	n  =  __kernel_rem_pio2(tx,&z,e0,nx,1,two_over_pi);
146	y[0] = z;
147	y[1] = z - y[0];
148	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
149	return n;
150}
151