e_rem_pio2l.h revision 176409 
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 176409 2008-02-19 15:30:58Z 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 0 /* Must be handled in caller. */
72	if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
73	    {y[0] = x; y[1] = 0; return 0;}
74#endif
75	if (ix <= 0x400f6a7a) {		/* |x| ~<= 5pi/4 */
76	    if ((ix & 0xfffff) == 0x921fb)  /* |x| ~= pi/2 or 2pi/2 */
77		goto medium;		/* cancellation -- use medium case */
78	    if (ix <= 0x4002d97c) {	/* |x| ~<= 3pi/4 */
79		if (hx > 0) {
80		    z = x - pio2_1;	/* one round good to 85 bits */
81		    y[0] = z - pio2_1t;
82		    y[1] = (z-y[0])-pio2_1t;
83		    return 1;
84		} else {
85		    z = x + pio2_1;
86		    y[0] = z + pio2_1t;
87		    y[1] = (z-y[0])+pio2_1t;
88		    return -1;
89		}
90	    } else {
91		if (hx > 0) {
92		    z = x - 2*pio2_1;
93		    y[0] = z - 2*pio2_1t;
94		    y[1] = (z-y[0])-2*pio2_1t;
95		    return 2;
96		} else {
97		    z = x + 2*pio2_1;
98		    y[0] = z + 2*pio2_1t;
99		    y[1] = (z-y[0])+2*pio2_1t;
100		    return -2;
101		}
102	    }
103	}
104	if (ix <= 0x401c463b) {		/* |x| ~<= 9pi/4 */
105	    if (ix <= 0x4015fdbc) {	/* |x| ~<= 7pi/4 */
106		if (ix == 0x4012d97c)	/* |x| ~= 3pi/2 */
107		    goto medium;
108		if (hx > 0) {
109		    z = x - 3*pio2_1;
110		    y[0] = z - 3*pio2_1t;
111		    y[1] = (z-y[0])-3*pio2_1t;
112		    return 3;
113		} else {
114		    z = x + 3*pio2_1;
115		    y[0] = z + 3*pio2_1t;
116		    y[1] = (z-y[0])+3*pio2_1t;
117		    return -3;
118		}
119	    } else {
120		if (ix == 0x401921fb)	/* |x| ~= 4pi/2 */
121		    goto medium;
122		if (hx > 0) {
123		    z = x - 4*pio2_1;
124		    y[0] = z - 4*pio2_1t;
125		    y[1] = (z-y[0])-4*pio2_1t;
126		    return 4;
127		} else {
128		    z = x + 4*pio2_1;
129		    y[0] = z + 4*pio2_1t;
130		    y[1] = (z-y[0])+4*pio2_1t;
131		    return -4;
132		}
133	    }
134	}
135	if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
136medium:
137	    t  = fabs(x);
138	    n  = (int32_t) (t*invpio2+half);
139	    fn = (double)n;
140	    r  = t-fn*pio2_1;
141	    w  = fn*pio2_1t;	/* 1st round good to 85 bit */
142	    if(n<32&&ix!=npio2_hw[n-1]) {
143		y[0] = r-w;	/* quick check no cancellation */
144	    } else {
145	        u_int32_t high;
146	        j  = ix>>20;
147	        y[0] = r-w;
148		GET_HIGH_WORD(high,y[0]);
149	        i = j-((high>>20)&0x7ff);
150	        if(i>16) {  /* 2nd iteration needed, good to 118 */
151		    t  = r;
152		    w  = fn*pio2_2;
153		    r  = t-w;
154		    w  = fn*pio2_2t-((t-r)-w);
155		    y[0] = r-w;
156		    GET_HIGH_WORD(high,y[0]);
157		    i = j-((high>>20)&0x7ff);
158		    if(i>49)  {	/* 3rd iteration need, 151 bits acc */
159		    	t  = r;	/* will cover all possible cases */
160		    	w  = fn*pio2_3;
161		    	r  = t-w;
162		    	w  = fn*pio2_3t-((t-r)-w);
163		    	y[0] = r-w;
164		    }
165		}
166	    }
167	    y[1] = (r-y[0])-w;
168	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
169	    else	 return n;
170	}
171    /*
172     * all other (large) arguments
173     */
174	if(ix>=0x7ff00000) {		/* x is inf or NaN */
175	    y[0]=y[1]=x-x; return 0;
176	}
177    /* set z = scalbn(|x|,ilogb(x)-23) */
178	GET_LOW_WORD(low,x);
179	SET_LOW_WORD(z,low);
180	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
181	SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
182	for(i=0;i<2;i++) {
183		tx[i] = (double)((int32_t)(z));
184		z     = (z-tx[i])*two24;
185	}
186	tx[2] = z;
187	nx = 3;
188	while(tx[nx-1]==zero) nx--;	/* skip zero term */
189	n  =  __kernel_rem_pio2(tx,y,e0,nx,2);
190	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
191	return n;
192}
193