e_rem_pio2.c revision 176476 
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 * Optimized by Bruce D. Evans.
14 */
15
16#include <sys/cdefs.h>
17__FBSDID("$FreeBSD: head/lib/msun/src/e_rem_pio2.c 176476 2008-02-23 12:53:21Z bde $");
18
19/* __ieee754_rem_pio2(x,y)
20 *
21 * return the remainder of x rem pi/2 in y[0]+y[1]
22 * use __kernel_rem_pio2()
23 */
24
25#include <float.h>
26
27#include "math.h"
28#include "math_private.h"
29
30/*
31 * invpio2:  53 bits of 2/pi
32 * pio2_1:   first  33 bit of pi/2
33 * pio2_1t:  pi/2 - pio2_1
34 * pio2_2:   second 33 bit of pi/2
35 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
36 * pio2_3:   third  33 bit of pi/2
37 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
38 */
39
40static const double
41zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
42half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
43two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
44invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
45pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
46pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
47pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
48pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
49pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
50pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
51
52#ifdef INLINE_REM_PIO2
53extern inline
54#endif
55int
56__ieee754_rem_pio2(double x, double *y)
57{
58	double z,w,t,r,fn;
59	double tx[3];
60	int32_t e0,i,j,nx,n,ix,hx;
61	u_int32_t low;
62
63	GET_HIGH_WORD(hx,x);		/* high word of x */
64	ix = hx&0x7fffffff;
65#if 0 /* Must be handled in caller. */
66	if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
67	    {y[0] = x; y[1] = 0; return 0;}
68#endif
69	if (ix <= 0x400f6a7a) {		/* |x| ~<= 5pi/4 */
70	    if ((ix & 0xfffff) == 0x921fb)  /* |x| ~= pi/2 or 2pi/2 */
71		goto medium;		/* cancellation -- use medium case */
72	    if (ix <= 0x4002d97c) {	/* |x| ~<= 3pi/4 */
73		if (hx > 0) {
74		    z = x - pio2_1;	/* one round good to 85 bits */
75		    y[0] = z - pio2_1t;
76		    y[1] = (z-y[0])-pio2_1t;
77		    return 1;
78		} else {
79		    z = x + pio2_1;
80		    y[0] = z + pio2_1t;
81		    y[1] = (z-y[0])+pio2_1t;
82		    return -1;
83		}
84	    } else {
85		if (hx > 0) {
86		    z = x - 2*pio2_1;
87		    y[0] = z - 2*pio2_1t;
88		    y[1] = (z-y[0])-2*pio2_1t;
89		    return 2;
90		} else {
91		    z = x + 2*pio2_1;
92		    y[0] = z + 2*pio2_1t;
93		    y[1] = (z-y[0])+2*pio2_1t;
94		    return -2;
95		}
96	    }
97	}
98	if (ix <= 0x401c463b) {		/* |x| ~<= 9pi/4 */
99	    if (ix <= 0x4015fdbc) {	/* |x| ~<= 7pi/4 */
100		if (ix == 0x4012d97c)	/* |x| ~= 3pi/2 */
101		    goto medium;
102		if (hx > 0) {
103		    z = x - 3*pio2_1;
104		    y[0] = z - 3*pio2_1t;
105		    y[1] = (z-y[0])-3*pio2_1t;
106		    return 3;
107		} else {
108		    z = x + 3*pio2_1;
109		    y[0] = z + 3*pio2_1t;
110		    y[1] = (z-y[0])+3*pio2_1t;
111		    return -3;
112		}
113	    } else {
114		if (ix == 0x401921fb)	/* |x| ~= 4pi/2 */
115		    goto medium;
116		if (hx > 0) {
117		    z = x - 4*pio2_1;
118		    y[0] = z - 4*pio2_1t;
119		    y[1] = (z-y[0])-4*pio2_1t;
120		    return 4;
121		} else {
122		    z = x + 4*pio2_1;
123		    y[0] = z + 4*pio2_1t;
124		    y[1] = (z-y[0])+4*pio2_1t;
125		    return -4;
126		}
127	    }
128	}
129	if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
130medium:
131	    /* Use a specialized rint() to get fn.  Assume round-to-nearest. */
132	    STRICT_ASSIGN(double,fn,x*invpio2+0x1.8p52);
133	    fn = fn-0x1.8p52;
134#ifdef HAVE_EFFICIENT_IRINT
135	    n  = irint(fn);
136#else
137	    n  = (int32_t)fn;
138#endif
139	    r  = x-fn*pio2_1;
140	    w  = fn*pio2_1t;	/* 1st round good to 85 bit */
141	    {
142	        u_int32_t high;
143	        j  = ix>>20;
144	        y[0] = r-w;
145		GET_HIGH_WORD(high,y[0]);
146	        i = j-((high>>20)&0x7ff);
147	        if(i>16) {  /* 2nd iteration needed, good to 118 */
148		    t  = r;
149		    w  = fn*pio2_2;
150		    r  = t-w;
151		    w  = fn*pio2_2t-((t-r)-w);
152		    y[0] = r-w;
153		    GET_HIGH_WORD(high,y[0]);
154		    i = j-((high>>20)&0x7ff);
155		    if(i>49)  {	/* 3rd iteration need, 151 bits acc */
156		    	t  = r;	/* will cover all possible cases */
157		    	w  = fn*pio2_3;
158		    	r  = t-w;
159		    	w  = fn*pio2_3t-((t-r)-w);
160		    	y[0] = r-w;
161		    }
162		}
163	    }
164	    y[1] = (r-y[0])-w;
165	    return n;
166	}
167    /*
168     * all other (large) arguments
169     */
170	if(ix>=0x7ff00000) {		/* x is inf or NaN */
171	    y[0]=y[1]=x-x; return 0;
172	}
173    /* set z = scalbn(|x|,ilogb(x)-23) */
174	GET_LOW_WORD(low,x);
175	SET_LOW_WORD(z,low);
176	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
177	SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
178	for(i=0;i<2;i++) {
179		tx[i] = (double)((int32_t)(z));
180		z     = (z-tx[i])*two24;
181	}
182	tx[2] = z;
183	nx = 3;
184	while(tx[nx-1]==zero) nx--;	/* skip zero term */
185	n  =  __kernel_rem_pio2(tx,y,e0,nx,2);
186	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
187	return n;
188}
189