e_rem_pio2.c revision 176385 
1
2/* @(#)e_rem_pio2.c 1.4 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 *
13 */
14
15#include <sys/cdefs.h>
16__FBSDID("$FreeBSD: head/lib/msun/src/e_rem_pio2.c 176385 2008-02-18 14:02:12Z bde $");
17
18/* __ieee754_rem_pio2(x,y)
19 *
20 * return the remainder of x rem pi/2 in y[0]+y[1]
21 * use __kernel_rem_pio2()
22 */
23
24#include "math.h"
25#include "math_private.h"
26
27static const int32_t npio2_hw[] = {
280x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
290x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
300x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
310x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
320x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
330x404858EB, 0x404921FB,
34};
35
36/*
37 * invpio2:  53 bits of 2/pi
38 * pio2_1:   first  33 bit of pi/2
39 * pio2_1t:  pi/2 - pio2_1
40 * pio2_2:   second 33 bit of pi/2
41 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
42 * pio2_3:   third  33 bit of pi/2
43 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
44 */
45
46static const double
47zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
48half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
49two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
50invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
51pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
52pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
53pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
54pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
55pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
56pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
57
58#ifdef INLINE_REM_PIO2
59extern inline
60#endif
61int
62__ieee754_rem_pio2(double x, double *y)
63{
64	double z,w,t,r,fn;
65	double tx[3];
66	int32_t e0,i,j,nx,n,ix,hx;
67	u_int32_t low;
68
69	GET_HIGH_WORD(hx,x);		/* high word of x */
70	ix = hx&0x7fffffff;
71	if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
72	    {y[0] = x; y[1] = 0; return 0;}
73	if(ix<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
74	    if(hx>0) {
75		z = x - pio2_1;
76		if(ix!=0x3ff921fb) { 	/* 33+53 bit pi is good enough */
77		    y[0] = z - pio2_1t;
78		    y[1] = (z-y[0])-pio2_1t;
79		} else {		/* near pi/2, use 33+33+53 bit pi */
80		    z -= pio2_2;
81		    y[0] = z - pio2_2t;
82		    y[1] = (z-y[0])-pio2_2t;
83		}
84		return 1;
85	    } else {	/* negative x */
86		z = x + pio2_1;
87		if(ix!=0x3ff921fb) { 	/* 33+53 bit pi is good enough */
88		    y[0] = z + pio2_1t;
89		    y[1] = (z-y[0])+pio2_1t;
90		} else {		/* near pi/2, use 33+33+53 bit pi */
91		    z += pio2_2;
92		    y[0] = z + pio2_2t;
93		    y[1] = (z-y[0])+pio2_2t;
94		}
95		return -1;
96	    }
97	}
98	if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
99	    t  = fabs(x);
100	    n  = (int32_t) (t*invpio2+half);
101	    fn = (double)n;
102	    r  = t-fn*pio2_1;
103	    w  = fn*pio2_1t;	/* 1st round good to 85 bit */
104	    if(n<32&&ix!=npio2_hw[n-1]) {
105		y[0] = r-w;	/* quick check no cancellation */
106	    } else {
107	        u_int32_t high;
108	        j  = ix>>20;
109	        y[0] = r-w;
110		GET_HIGH_WORD(high,y[0]);
111	        i = j-((high>>20)&0x7ff);
112	        if(i>16) {  /* 2nd iteration needed, good to 118 */
113		    t  = r;
114		    w  = fn*pio2_2;
115		    r  = t-w;
116		    w  = fn*pio2_2t-((t-r)-w);
117		    y[0] = r-w;
118		    GET_HIGH_WORD(high,y[0]);
119		    i = j-((high>>20)&0x7ff);
120		    if(i>49)  {	/* 3rd iteration need, 151 bits acc */
121		    	t  = r;	/* will cover all possible cases */
122		    	w  = fn*pio2_3;
123		    	r  = t-w;
124		    	w  = fn*pio2_3t-((t-r)-w);
125		    	y[0] = r-w;
126		    }
127		}
128	    }
129	    y[1] = (r-y[0])-w;
130	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
131	    else	 return n;
132	}
133    /*
134     * all other (large) arguments
135     */
136	if(ix>=0x7ff00000) {		/* x is inf or NaN */
137	    y[0]=y[1]=x-x; return 0;
138	}
139    /* set z = scalbn(|x|,ilogb(x)-23) */
140	GET_LOW_WORD(low,x);
141	SET_LOW_WORD(z,low);
142	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
143	SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
144	for(i=0;i<2;i++) {
145		tx[i] = (double)((int32_t)(z));
146		z     = (z-tx[i])*two24;
147	}
148	tx[2] = z;
149	nx = 3;
150	while(tx[nx-1]==zero) nx--;	/* skip zero term */
151	n  =  __kernel_rem_pio2(tx,y,e0,nx,2);
152	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
153	return n;
154}
155