e_rem_pio2.c revision 176466 
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 176466 2008-02-22 17:26:24Z 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 <float.h>
25
26#include "math.h"
27#include "math_private.h"
28
29/*
30 * invpio2:  53 bits of 2/pi
31 * pio2_1:   first  33 bit of pi/2
32 * pio2_1t:  pi/2 - pio2_1
33 * pio2_2:   second 33 bit of pi/2
34 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
35 * pio2_3:   third  33 bit of pi/2
36 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
37 */
38
39static const double
40zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
41half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
42two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
43invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
44pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
45pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
46pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
47pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
48pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
49pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
50
51#ifdef INLINE_REM_PIO2
52extern inline
53#endif
54int
55__ieee754_rem_pio2(double x, double *y)
56{
57	double z,w,t,r,fn;
58	double tx[3];
59	int32_t e0,i,j,nx,n,ix,hx;
60	u_int32_t low;
61
62	GET_HIGH_WORD(hx,x);		/* high word of x */
63	ix = hx&0x7fffffff;
64#if 0 /* Must be handled in caller. */
65	if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
66	    {y[0] = x; y[1] = 0; return 0;}
67#endif
68	if (ix <= 0x400f6a7a) {		/* |x| ~<= 5pi/4 */
69	    if ((ix & 0xfffff) == 0x921fb)  /* |x| ~= pi/2 or 2pi/2 */
70		goto medium;		/* cancellation -- use medium case */
71	    if (ix <= 0x4002d97c) {	/* |x| ~<= 3pi/4 */
72		if (hx > 0) {
73		    z = x - pio2_1;	/* one round good to 85 bits */
74		    y[0] = z - pio2_1t;
75		    y[1] = (z-y[0])-pio2_1t;
76		    return 1;
77		} else {
78		    z = x + pio2_1;
79		    y[0] = z + pio2_1t;
80		    y[1] = (z-y[0])+pio2_1t;
81		    return -1;
82		}
83	    } else {
84		if (hx > 0) {
85		    z = x - 2*pio2_1;
86		    y[0] = z - 2*pio2_1t;
87		    y[1] = (z-y[0])-2*pio2_1t;
88		    return 2;
89		} else {
90		    z = x + 2*pio2_1;
91		    y[0] = z + 2*pio2_1t;
92		    y[1] = (z-y[0])+2*pio2_1t;
93		    return -2;
94		}
95	    }
96	}
97	if (ix <= 0x401c463b) {		/* |x| ~<= 9pi/4 */
98	    if (ix <= 0x4015fdbc) {	/* |x| ~<= 7pi/4 */
99		if (ix == 0x4012d97c)	/* |x| ~= 3pi/2 */
100		    goto medium;
101		if (hx > 0) {
102		    z = x - 3*pio2_1;
103		    y[0] = z - 3*pio2_1t;
104		    y[1] = (z-y[0])-3*pio2_1t;
105		    return 3;
106		} else {
107		    z = x + 3*pio2_1;
108		    y[0] = z + 3*pio2_1t;
109		    y[1] = (z-y[0])+3*pio2_1t;
110		    return -3;
111		}
112	    } else {
113		if (ix == 0x401921fb)	/* |x| ~= 4pi/2 */
114		    goto medium;
115		if (hx > 0) {
116		    z = x - 4*pio2_1;
117		    y[0] = z - 4*pio2_1t;
118		    y[1] = (z-y[0])-4*pio2_1t;
119		    return 4;
120		} else {
121		    z = x + 4*pio2_1;
122		    y[0] = z + 4*pio2_1t;
123		    y[1] = (z-y[0])+4*pio2_1t;
124		    return -4;
125		}
126	    }
127	}
128	if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
129medium:
130	    t  = fabs(x);
131#ifdef HAVE_EFFICIENT_IRINT
132	    /* Use a specialized rint() to get fn.  Assume round-to-nearest. */
133	    STRICT_ASSIGN(double,fn,t*invpio2+0x1.8p52);
134	    fn = fn-0x1.8p52;
135	    n  = irint(fn);
136#else
137	    n  = (int32_t) (t*invpio2+half);
138	    fn = (double)n;
139#endif
140	    r  = t-fn*pio2_1;
141	    w  = fn*pio2_1t;	/* 1st round good to 85 bit */
142	    {
143	        u_int32_t high;
144	        j  = ix>>20;
145	        y[0] = r-w;
146		GET_HIGH_WORD(high,y[0]);
147	        i = j-((high>>20)&0x7ff);
148	        if(i>16) {  /* 2nd iteration needed, good to 118 */
149		    t  = r;
150		    w  = fn*pio2_2;
151		    r  = t-w;
152		    w  = fn*pio2_2t-((t-r)-w);
153		    y[0] = r-w;
154		    GET_HIGH_WORD(high,y[0]);
155		    i = j-((high>>20)&0x7ff);
156		    if(i>49)  {	/* 3rd iteration need, 151 bits acc */
157		    	t  = r;	/* will cover all possible cases */
158		    	w  = fn*pio2_3;
159		    	r  = t-w;
160		    	w  = fn*pio2_3t-((t-r)-w);
161		    	y[0] = r-w;
162		    }
163		}
164	    }
165	    y[1] = (r-y[0])-w;
166	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
167	    else	 return n;
168	}
169    /*
170     * all other (large) arguments
171     */
172	if(ix>=0x7ff00000) {		/* x is inf or NaN */
173	    y[0]=y[1]=x-x; return 0;
174	}
175    /* set z = scalbn(|x|,ilogb(x)-23) */
176	GET_LOW_WORD(low,x);
177	SET_LOW_WORD(z,low);
178	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
179	SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
180	for(i=0;i<2;i++) {
181		tx[i] = (double)((int32_t)(z));
182		z     = (z-tx[i])*two24;
183	}
184	tx[2] = z;
185	nx = 3;
186	while(tx[nx-1]==zero) nx--;	/* skip zero term */
187	n  =  __kernel_rem_pio2(tx,y,e0,nx,2);
188	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
189	return n;
190}
191