e_rem_pio2l.h revision 221234 
1/* From: @(#)e_rem_pio2.c 1.4 95/01/18 */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
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/ld80/e_rem_pio2l.h 221234 2011-04-29 23:13:43Z kargl $");
18
19/* ld80 version of __ieee754_rem_pio2l(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#include "fpmath.h"
30
31#define	BIAS	(LDBL_MAX_EXP - 1)
32
33/*
34 * invpio2:  64 bits of 2/pi
35 * pio2_1:   first  39 bits of pi/2
36 * pio2_1t:  pi/2 - pio2_1
37 * pio2_2:   second 39 bits of pi/2
38 * pio2_2t:  pi/2 - (pio2_1+pio2_2)
39 * pio2_3:   third  39 bits of pi/2
40 * pio2_3t:  pi/2 - (pio2_1+pio2_2+pio2_3)
41 */
42
43static const double
44zero =  0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */
45two24 =  1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */
46pio2_1  =  1.57079632679597125389e+00,	/* 0x3FF921FB, 0x54444000 */
47pio2_2  = -1.07463465549783099519e-12,	/* -0x12e7b967674000.0p-92 */
48pio2_3  =  6.36831716351370313614e-25;	/*  0x18a2e037074000.0p-133 */
49
50#if defined(__amd64__) || defined(__i386__)
51/* Long double constants are slow on these arches, and broken on i386. */
52static const volatile double
53invpio2hi =  6.3661977236758138e-01,	/*  0x145f306dc9c883.0p-53 */
54invpio2lo = -3.9356538861223811e-17,	/* -0x16b00000000000.0p-107 */
55pio2_1thi = -1.0746346554971943e-12,	/* -0x12e7b9676733af.0p-92 */
56pio2_1tlo =  8.8451028997905949e-29,	/*  0x1c080000000000.0p-146 */
57pio2_2thi =  6.3683171635109499e-25,	/*  0x18a2e03707344a.0p-133 */
58pio2_2tlo =  2.3183081793789774e-41,	/*  0x10280000000000.0p-187 */
59pio2_3thi = -2.7529965190440717e-37,	/* -0x176b7ed8fbbacc.0p-174 */
60pio2_3tlo = -4.2006647512740502e-54;	/* -0x19c00000000000.0p-230 */
61#define	invpio2	((long double)invpio2hi + invpio2lo)
62#define	pio2_1t	((long double)pio2_1thi + pio2_1tlo)
63#define	pio2_2t	((long double)pio2_2thi + pio2_2tlo)
64#define	pio2_3t	((long double)pio2_3thi + pio2_3tlo)
65#else
66static const long double
67invpio2 =  6.36619772367581343076e-01L,	/*  0xa2f9836e4e44152a.0p-64 */
68pio2_1t = -1.07463465549719416346e-12L,	/* -0x973dcb3b399d747f.0p-103 */
69pio2_2t =  6.36831716351095013979e-25L,	/*  0xc51701b839a25205.0p-144 */
70pio2_3t = -2.75299651904407171810e-37L;	/* -0xbb5bf6c7ddd660ce.0p-185 */
71#endif
72
73#ifdef INLINE_REM_PIO2L
74static inline __always_inline
75#endif
76int
77__ieee754_rem_pio2l(long double x, long double *y)
78{
79	union IEEEl2bits u,u1;
80	long double z,w,t,r,fn;
81	double tx[3],ty[2];
82	int e0,ex,i,j,nx,n;
83	int16_t expsign;
84
85	u.e = x;
86	expsign = u.xbits.expsign;
87	ex = expsign & 0x7fff;
88	if (ex < BIAS + 25 || ex == BIAS + 25 && u.bits.manh < 0xc90fdaa2) {
89	    /* |x| ~< 2^25*(pi/2), medium size */
90	    /* Use a specialized rint() to get fn.  Assume round-to-nearest. */
91	    fn = x*invpio2+0x1.8p63;
92	    fn = fn-0x1.8p63;
93#ifdef HAVE_EFFICIENT_IRINT
94	    n  = irint(fn);
95#else
96	    n  = fn;
97#endif
98	    r  = x-fn*pio2_1;
99	    w  = fn*pio2_1t;	/* 1st round good to 102 bit */
100	    {
101		union IEEEl2bits u2;
102	        int ex1;
103	        j  = ex;
104	        y[0] = r-w;
105		u2.e = y[0];
106		ex1 = u2.xbits.expsign & 0x7fff;
107	        i = j-ex1;
108	        if(i>22) {  /* 2nd iteration needed, good to 141 */
109		    t  = r;
110		    w  = fn*pio2_2;
111		    r  = t-w;
112		    w  = fn*pio2_2t-((t-r)-w);
113		    y[0] = r-w;
114		    u2.e = y[0];
115		    ex1 = u2.xbits.expsign & 0x7fff;
116		    i = j-ex1;
117		    if(i>61) {	/* 3rd iteration need, 180 bits acc */
118		    	t  = r;	/* will cover all possible cases */
119		    	w  = fn*pio2_3;
120		    	r  = t-w;
121		    	w  = fn*pio2_3t-((t-r)-w);
122		    	y[0] = r-w;
123		    }
124		}
125	    }
126	    y[1] = (r-y[0])-w;
127	    return n;
128	}
129    /*
130     * all other (large) arguments
131     */
132	if(ex==0x7fff) {		/* x is inf or NaN */
133	    y[0]=y[1]=x-x; return 0;
134	}
135    /* set z = scalbn(|x|,ilogb(x)-23) */
136	u1.e = x;
137	e0 = ex - BIAS - 23;		/* e0 = ilogb(|x|)-23; */
138	u1.xbits.expsign = ex - e0;
139	z = u1.e;
140	for(i=0;i<2;i++) {
141		tx[i] = (double)((int32_t)(z));
142		z     = (z-tx[i])*two24;
143	}
144	tx[2] = z;
145	nx = 3;
146	while(tx[nx-1]==zero) nx--;	/* skip zero term */
147	n  =  __kernel_rem_pio2(tx,ty,e0,nx,2);
148	r = (long double)ty[0] + ty[1];
149	w = ty[1] - (r - ty[0]);
150	if(expsign<0) {y[0] = -r; y[1] = -w; return -n;}
151	y[0] = r; y[1] = w; return n;
152}
153