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#if defined(LIBM_SCCS) && !defined(lint)
14static char rcsid[] = "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 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<0x4002d97c) {  /* |x| < 3pi/4, special case with n=+-1 */
103	    if(hx>0) {
104		z = x - pio2_1;
105		if(ix!=0x3ff921fb) { 	/* 33+53 bit pi is good enough */
106		    y[0] = z - pio2_1t;
107		    y[1] = (z-y[0])-pio2_1t;
108		} else {		/* near pi/2, use 33+33+53 bit pi */
109		    z -= pio2_2;
110		    y[0] = z - pio2_2t;
111		    y[1] = (z-y[0])-pio2_2t;
112		}
113		return 1;
114	    } else {	/* negative x */
115		z = x + pio2_1;
116		if(ix!=0x3ff921fb) { 	/* 33+53 bit pi is good enough */
117		    y[0] = z + pio2_1t;
118		    y[1] = (z-y[0])+pio2_1t;
119		} else {		/* near pi/2, use 33+33+53 bit pi */
120		    z += pio2_2;
121		    y[0] = z + pio2_2t;
122		    y[1] = (z-y[0])+pio2_2t;
123		}
124		return -1;
125	    }
126	}
127	if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */
128	    t  = fabs(x);
129	    n  = (int32_t) (t*invpio2+half);
130	    fn = (double)n;
131	    r  = t-fn*pio2_1;
132	    w  = fn*pio2_1t;	/* 1st round good to 85 bit */
133	    if(n<32&&ix!=npio2_hw[n-1]) {
134		y[0] = r-w;	/* quick check no cancellation */
135	    } else {
136	        u_int32_t high;
137	        j  = ix>>20;
138	        y[0] = r-w;
139		GET_HIGH_WORD(high,y[0]);
140	        i = j-((high>>20)&0x7ff);
141	        if(i>16) {  /* 2nd iteration needed, good to 118 */
142		    t  = r;
143		    w  = fn*pio2_2;
144		    r  = t-w;
145		    w  = fn*pio2_2t-((t-r)-w);
146		    y[0] = r-w;
147		    GET_HIGH_WORD(high,y[0]);
148		    i = j-((high>>20)&0x7ff);
149		    if(i>49)  {	/* 3rd iteration need, 151 bits acc */
150		    	t  = r;	/* will cover all possible cases */
151		    	w  = fn*pio2_3;
152		    	r  = t-w;
153		    	w  = fn*pio2_3t-((t-r)-w);
154		    	y[0] = r-w;
155		    }
156		}
157	    }
158	    y[1] = (r-y[0])-w;
159	    if(hx<0) 	{y[0] = -y[0]; y[1] = -y[1]; return -n;}
160	    else	 return n;
161	}
162    /*
163     * all other (large) arguments
164     */
165	if(ix>=0x7ff00000) {		/* x is inf or NaN */
166	    y[0]=y[1]=x-x; return 0;
167	}
168    /* set z = scalbn(|x|,ilogb(x)-23) */
169	GET_LOW_WORD(low,x);
170	SET_LOW_WORD(z,low);
171	e0 	= (ix>>20)-1046;	/* e0 = ilogb(z)-23; */
172	SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20)));
173	for(i=0;i<2;i++) {
174		tx[i] = (double)((int32_t)(z));
175		z     = (z-tx[i])*two24;
176	}
177	tx[2] = z;
178	nx = 3;
179	while(tx[nx-1]==zero) nx--;	/* skip zero term */
180	n  =  __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi);
181	if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
182	return n;
183}
184