1/* @(#)e_fmod.c 1.3 95/01/18 */
2/*-
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, 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#include <sys/types.h>
14#include <machine/ieee.h>
15
16#include <float.h>
17#include <math.h>
18#include <stdint.h>
19
20#include "math_private.h"
21
22#define	BIAS (LDBL_MAX_EXP - 1)
23
24/*
25 * These macros add and remove an explicit integer bit in front of the
26 * fractional mantissa, if the architecture doesn't have such a bit by
27 * default already.
28 */
29#ifdef LDBL_IMPLICIT_NBIT
30#define	LDBL_NBIT	0
31#define	SET_NBIT(hx)	((hx) | (1ULL << LDBL_MANH_SIZE))
32#define	HFRAC_BITS	EXT_FRACHBITS
33#else
34#define	LDBL_NBIT	0x80000000
35#define	SET_NBIT(hx)	(hx)
36#define	HFRAC_BITS	(EXT_FRACHBITS - 1)
37#endif
38
39#define	MANL_SHIFT	(EXT_FRACLBITS - 1)
40
41static const long double Zero[] = {0.0L, -0.0L};
42
43/*
44 * Return the IEEE remainder and set *quo to the last n bits of the
45 * quotient, rounded to the nearest integer.  We choose n=31 because
46 * we wind up computing all the integer bits of the quotient anyway as
47 * a side-effect of computing the remainder by the shift and subtract
48 * method.  In practice, this is far more bits than are needed to use
49 * remquo in reduction algorithms.
50 *
51 * Assumptions:
52 * - The low part of the mantissa fits in a manl_t exactly.
53 * - The high part of the mantissa fits in an int64_t with enough room
54 *   for an explicit integer bit in front of the fractional bits.
55 */
56long double
57remquol(long double x, long double y, int *quo)
58{
59	int64_t hx,hz;	/* We need a carry bit even if LDBL_MANH_SIZE is 32. */
60	uint32_t hy;
61	uint32_t lx,ly,lz;
62	uint32_t esx, esy;
63	int ix,iy,n,q,sx,sxy;
64
65	GET_LDOUBLE_WORDS(esx,hx,lx,x);
66	GET_LDOUBLE_WORDS(esy,hy,ly,y);
67	sx = esx & 0x8000;
68	sxy = sx ^ (esy & 0x8000);
69	esx &= 0x7fff;				/* |x| */
70	esy &= 0x7fff;				/* |y| */
71	SET_LDOUBLE_EXP(x,esx);
72	SET_LDOUBLE_EXP(y,esy);
73
74    /* purge off exception values */
75	if((esy|hy|ly)==0 ||			/* y=0 */
76	   (esx == BIAS + LDBL_MAX_EXP) ||	/* or x not finite */
77	   (esy == BIAS + LDBL_MAX_EXP &&
78	    ((hy&~LDBL_NBIT)|ly)!=0))		/* or y is NaN */
79	    return (x*y)/(x*y);
80	if(esx<=esy) {
81	    if((esx<esy) ||
82	       (hx<=hy &&
83		(hx<hy ||
84		 lx<ly))) {
85		q = 0;
86		goto fixup;			/* |x|<|y| return x or x-y */
87	    }
88	    if(hx==hy && lx==ly) {
89		*quo = 1;
90		return Zero[sx!=0];		/* |x|=|y| return x*0*/
91	    }
92	}
93
94    /* determine ix = ilogb(x) */
95	if(esx == 0) {				/* subnormal x */
96	    x *= 0x1.0p512;
97	    GET_LDOUBLE_WORDS(esx,hx,lx,x);
98	    ix = esx - (BIAS + 512);
99	} else {
100	    ix = esx - BIAS;
101	}
102
103    /* determine iy = ilogb(y) */
104	if(esy == 0) {				/* subnormal y */
105	    y *= 0x1.0p512;
106	    GET_LDOUBLE_WORDS(esy,hy,ly,y);
107	    iy = esy - (BIAS + 512);
108	} else {
109	    iy = esy - BIAS;
110	}
111
112    /* set up {hx,lx}, {hy,ly} and align y to x */
113	hx = SET_NBIT(hx);
114	lx = SET_NBIT(lx);
115
116    /* fix point fmod */
117	n = ix - iy;
118	q = 0;
119
120	while(n--) {
121	    hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
122	    if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
123	    else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;}
124	    q <<= 1;
125	}
126	hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
127	if(hz>=0) {hx=hz;lx=lz;q++;}
128
129    /* convert back to floating value and restore the sign */
130	if((hx|lx)==0) {			/* return sign(x)*0 */
131	    *quo = (sxy ? -q : q);
132	    return Zero[sx!=0];
133	}
134	while(hx<(1ULL<<HFRAC_BITS)) {	/* normalize x */
135	    hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
136	    iy -= 1;
137	}
138	if (iy < LDBL_MIN_EXP) {
139	    esx = (iy + BIAS + 512) & 0x7fff;
140	    SET_LDOUBLE_WORDS(x,esx,hx,lx);
141	    x *= 0x1p-512;
142	    GET_LDOUBLE_WORDS(esx,hx,lx,x);
143	} else {
144	    esx = (iy + BIAS) & 0x7fff;
145	}
146	SET_LDOUBLE_WORDS(x,esx,hx,lx);
147fixup:
148	y = fabsl(y);
149	if (y < LDBL_MIN * 2) {
150	    if (x+x>y || (x+x==y && (q & 1))) {
151		q++;
152		x-=y;
153	    }
154	} else if (x>0.5*y || (x==0.5*y && (q & 1))) {
155	    q++;
156	    x-=y;
157	}
158
159	GET_LDOUBLE_EXP(esx,x);
160	esx ^= sx;
161	SET_LDOUBLE_EXP(x,esx);
162
163	q &= 0x7fffffff;
164	*quo = (sxy ? -q : q);
165	return x;
166}
167DEF_STD(remquol);
168