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/cdefs.h>
14__FBSDID("$FreeBSD$");
15
16#include <float.h>
17#include <stdint.h>
18
19#include "fpmath.h"
20#include "math.h"
21#include "math_private.h"
22
23#define	BIAS (LDBL_MAX_EXP - 1)
24
25#if LDBL_MANL_SIZE > 32
26typedef	uint64_t manl_t;
27#else
28typedef	uint32_t manl_t;
29#endif
30
31#if LDBL_MANH_SIZE > 32
32typedef	uint64_t manh_t;
33#else
34typedef	uint32_t manh_t;
35#endif
36
37/*
38 * These macros add and remove an explicit integer bit in front of the
39 * fractional mantissa, if the architecture doesn't have such a bit by
40 * default already.
41 */
42#ifdef LDBL_IMPLICIT_NBIT
43#define	SET_NBIT(hx)	((hx) | (1ULL << LDBL_MANH_SIZE))
44#define	HFRAC_BITS	LDBL_MANH_SIZE
45#else
46#define	SET_NBIT(hx)	(hx)
47#define	HFRAC_BITS	(LDBL_MANH_SIZE - 1)
48#endif
49
50#define	MANL_SHIFT	(LDBL_MANL_SIZE - 1)
51
52static const long double one = 1.0, Zero[] = {0.0, -0.0,};
53
54/*
55 * fmodl(x,y)
56 * Return x mod y in exact arithmetic
57 * Method: shift and subtract
58 *
59 * Assumptions:
60 * - The low part of the mantissa fits in a manl_t exactly.
61 * - The high part of the mantissa fits in an int64_t with enough room
62 *   for an explicit integer bit in front of the fractional bits.
63 */
64long double
65fmodl(long double x, long double y)
66{
67	union IEEEl2bits ux, uy;
68	int64_t hx,hz;	/* We need a carry bit even if LDBL_MANH_SIZE is 32. */
69	manh_t hy;
70	manl_t lx,ly,lz;
71	int ix,iy,n,sx;
72
73	ux.e = x;
74	uy.e = y;
75	sx = ux.bits.sign;
76
77    /* purge off exception values */
78	if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
79	   (ux.bits.exp == BIAS + LDBL_MAX_EXP) ||	 /* or x not finite */
80	   (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
81	    ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
82	    return (x*y)/(x*y);
83	if(ux.bits.exp<=uy.bits.exp) {
84	    if((ux.bits.exp<uy.bits.exp) ||
85	       (ux.bits.manh<=uy.bits.manh &&
86		(ux.bits.manh<uy.bits.manh ||
87		 ux.bits.manl<uy.bits.manl))) {
88		return x;		/* |x|<|y| return x or x-y */
89	    }
90	    if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
91		return Zero[sx];	/* |x|=|y| return x*0*/
92	    }
93	}
94
95    /* determine ix = ilogb(x) */
96	if(ux.bits.exp == 0) {	/* subnormal x */
97	    ux.e *= 0x1.0p512;
98	    ix = ux.bits.exp - (BIAS + 512);
99	} else {
100	    ix = ux.bits.exp - BIAS;
101	}
102
103    /* determine iy = ilogb(y) */
104	if(uy.bits.exp == 0) {	/* subnormal y */
105	    uy.e *= 0x1.0p512;
106	    iy = uy.bits.exp - (BIAS + 512);
107	} else {
108	    iy = uy.bits.exp - BIAS;
109	}
110
111    /* set up {hx,lx}, {hy,ly} and align y to x */
112	hx = SET_NBIT(ux.bits.manh);
113	hy = SET_NBIT(uy.bits.manh);
114	lx = ux.bits.manl;
115	ly = uy.bits.manl;
116
117    /* fix point fmod */
118	n = ix - iy;
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 {
124		if ((hz|lz)==0)		/* return sign(x)*0 */
125		    return Zero[sx];
126		hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
127	    }
128	}
129	hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
130	if(hz>=0) {hx=hz;lx=lz;}
131
132    /* convert back to floating value and restore the sign */
133	if((hx|lx)==0)			/* return sign(x)*0 */
134	    return Zero[sx];
135	while(hx<(1ULL<<HFRAC_BITS)) {	/* normalize x */
136	    hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
137	    iy -= 1;
138	}
139	ux.bits.manh = hx; /* The mantissa is truncated here if needed. */
140	ux.bits.manl = lx;
141	if (iy < LDBL_MIN_EXP) {
142	    ux.bits.exp = iy + (BIAS + 512);
143	    ux.e *= 0x1p-512;
144	} else {
145	    ux.bits.exp = iy + BIAS;
146	}
147	x = ux.e * one;		/* create necessary signal */
148	return x;		/* exact output */
149}
150