e_rem_pio2.c revision 2116 
1/* @(#)e_rem_pio2.c 5.1 93/09/24 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunPro, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 */
12
13#ifndef lint
14static char rcsid[] = "$Id: e_rem_pio2.c,v 1.5 1994/08/18 23:05:56 jtc Exp $";
15#endif
16
17/* __ieee754_rem_pio2(x,y)
18 *
19 * return the remainder of x rem pi/2 in y[0]+y[1]
20 * use __kernel_rem_pio2()
21 */
22
23#include "math.h"
24#include "math_private.h"
25
26/*
27 * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
28 */
29#ifdef __STDC__
30static const int32_t two_over_pi[] = {
31#else
32static int32_t two_over_pi[] = {
33#endif
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#ifdef __STDC__
48static const int32_t npio2_hw[] = {
49#else
50static int32_t npio2_hw[] = {
51#endif
520x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C,
530x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C,
540x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A,
550x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C,
560x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB,
570x404858EB, 0x404921FB,
58};
59
60/*
61 * invpio2:  53 bits of 2/pi
62 * pio2_1:   first  33 bit of pi/2
63 * pio2_1t:  pi/2 - pio2_1
64 * pio2_2:   second 33 bit of pi/2
65 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
66 * pio2_3:   third  33 bit of pi/2
67 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
68 */
69
70#ifdef __STDC__
71static const double
72#else
73static double
74#endif
75zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
76half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
77two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
78invpio2 =  6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */
79pio2_1  =  1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */
80pio2_1t =  6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */
81pio2_2  =  6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */
82pio2_2t =  2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */
83pio2_3  =  2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */
84pio2_3t =  8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */
85
86#ifdef __STDC__
87	int32_t __ieee754_rem_pio2(double x, double *y)
88#else
89	int32_t __ieee754_rem_pio2(x,y)
90	double x,y[];
91#endif
92{
93	double z,w,t,r,fn;
94	double tx[3];
95	int32_t e0,i,j,nx,n,ix,hx;
96	u_int32_t low;
97
98	GET_HIGH_WORD(hx,x);		/* high word of x */
99	ix = hx&0x7fffffff;
100	if(ix<=0x3fe921fb)   /* |x| ~<= pi/4 , no need for reduction */
101	    {y[0] = x; y[1] = 0; return 0;}
102	if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
103	    t  = fabs(x);
104	    n  = (int32_t) (t*invpio2+half);
105	    fn = (double)n;
106	    r  = t-fn*pio2_1;
107	    w  = fn*pio2_1t;	/* 1st round good to 85 bit */
108	    if(n<32&&ix!=npio2_hw[n-1]) {
109		y[0] = r-w;	/* quick check no cancellation */
110	    } else {
111	        u_int32_t high;
112	        j  = ix>>20;
113	        y[0] = r-w;
114		GET_HIGH_WORD(high,y[0]);
115	        i = j-((high>>20)&0x7ff);
116	        if(i>16) {  /* 2nd iteration needed, good to 118 */
117		    t  = r;
118		    w  = fn*pio2_2;
119		    r  = t-w;
120		    w  = fn*pio2_2t-((t-r)-w);
121		    y[0] = r-w;
122		    GET_HIGH_WORD(high,y[0]);
123		    i = j-((high>>20)&0x7ff);
124		    if(i>49)  {	/* 3rd iteration need, 151 bits acc */
125		    	t  = r;	/* will cover all possible cases */
126		    	w  = fn*pio2_3;
127		    	r  = t-w;
128		    	w  = fn*pio2_3t-((t-r)-w);
129		    	y[0] = r-w;
130		    }
131		}
132	    }
133	    y[1] = (r-y[0])-w;
134	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
135	    else	 return n;
136	}
137    /*
138     * all other (large) arguments
139     */
140	if(ix>=0x7ff00000) {		/* x is inf or NaN */
141	    y[0]=y[1]=x-x; return 0;
142	}
143    /* set z = scalbn(|x|,ilogb(x)-23) */
144	GET_LOW_WORD(low,x);
145	SET_LOW_WORD(z,low);
146	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
147	SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
148	for(i=0;i<2;i++) {
149		tx[i] = (double)((int32_t)(z));
150		z     = (z-tx[i])*two24;
151	}
152	tx[2] = z;
153	nx = 3;
154	while(tx[nx-1]==zero) nx--;	/* skip zero term */
155	n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
156	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
157	return n;
158}
159