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
26 typedef	uint64_t manl_t;
27 #else
28 typedef	uint32_t manl_t;
29 #endif
30 
31 #if LDBL_MANH_SIZE > 32
32 typedef	uint64_t manh_t;
33 #else
34 typedef	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 
52 static 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  */
64 long double
fmodl(long double x,long double y)65 fmodl(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