xref: /freebsd/lib/msun/src/e_fmodl.c (revision 4b9d6057)
1 /*-
2  * ====================================================
3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4  *
5  * Developed at SunSoft, a Sun Microsystems, Inc. business.
6  * Permission to use, copy, modify, and distribute this
7  * software is freely granted, provided that this notice
8  * is preserved.
9  * ====================================================
10  */
11 
12 #include <sys/cdefs.h>
13 #include <float.h>
14 #include <stdint.h>
15 
16 #include "fpmath.h"
17 #include "math.h"
18 #include "math_private.h"
19 
20 #define	BIAS (LDBL_MAX_EXP - 1)
21 
22 #if LDBL_MANL_SIZE > 32
23 typedef	uint64_t manl_t;
24 #else
25 typedef	uint32_t manl_t;
26 #endif
27 
28 #if LDBL_MANH_SIZE > 32
29 typedef	uint64_t manh_t;
30 #else
31 typedef	uint32_t manh_t;
32 #endif
33 
34 /*
35  * These macros add and remove an explicit integer bit in front of the
36  * fractional mantissa, if the architecture doesn't have such a bit by
37  * default already.
38  */
39 #ifdef LDBL_IMPLICIT_NBIT
40 #define	SET_NBIT(hx)	((hx) | (1ULL << LDBL_MANH_SIZE))
41 #define	HFRAC_BITS	LDBL_MANH_SIZE
42 #else
43 #define	SET_NBIT(hx)	(hx)
44 #define	HFRAC_BITS	(LDBL_MANH_SIZE - 1)
45 #endif
46 
47 #define	MANL_SHIFT	(LDBL_MANL_SIZE - 1)
48 
49 static const long double one = 1.0, Zero[] = {0.0, -0.0,};
50 
51 /*
52  * fmodl(x,y)
53  * Return x mod y in exact arithmetic
54  * Method: shift and subtract
55  *
56  * Assumptions:
57  * - The low part of the mantissa fits in a manl_t exactly.
58  * - The high part of the mantissa fits in an int64_t with enough room
59  *   for an explicit integer bit in front of the fractional bits.
60  */
61 long double
62 fmodl(long double x, long double y)
63 {
64 	union IEEEl2bits ux, uy;
65 	int64_t hx,hz;	/* We need a carry bit even if LDBL_MANH_SIZE is 32. */
66 	manh_t hy;
67 	manl_t lx,ly,lz;
68 	int ix,iy,n,sx;
69 
70 	ux.e = x;
71 	uy.e = y;
72 	sx = ux.bits.sign;
73 
74     /* purge off exception values */
75 	if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
76 	   (ux.bits.exp == BIAS + LDBL_MAX_EXP) ||	 /* or x not finite */
77 	   (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
78 	    ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
79 	    return nan_mix_op(x, y, *)/nan_mix_op(x, y, *);
80 	if(ux.bits.exp<=uy.bits.exp) {
81 	    if((ux.bits.exp<uy.bits.exp) ||
82 	       (ux.bits.manh<=uy.bits.manh &&
83 		(ux.bits.manh<uy.bits.manh ||
84 		 ux.bits.manl<uy.bits.manl))) {
85 		return x;		/* |x|<|y| return x or x-y */
86 	    }
87 	    if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
88 		return Zero[sx];	/* |x|=|y| return x*0*/
89 	    }
90 	}
91 
92     /* determine ix = ilogb(x) */
93 	if(ux.bits.exp == 0) {	/* subnormal x */
94 	    ux.e *= 0x1.0p512;
95 	    ix = ux.bits.exp - (BIAS + 512);
96 	} else {
97 	    ix = ux.bits.exp - BIAS;
98 	}
99 
100     /* determine iy = ilogb(y) */
101 	if(uy.bits.exp == 0) {	/* subnormal y */
102 	    uy.e *= 0x1.0p512;
103 	    iy = uy.bits.exp - (BIAS + 512);
104 	} else {
105 	    iy = uy.bits.exp - BIAS;
106 	}
107 
108     /* set up {hx,lx}, {hy,ly} and align y to x */
109 	hx = SET_NBIT(ux.bits.manh);
110 	hy = SET_NBIT(uy.bits.manh);
111 	lx = ux.bits.manl;
112 	ly = uy.bits.manl;
113 
114     /* fix point fmod */
115 	n = ix - iy;
116 
117 	while(n--) {
118 	    hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
119 	    if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
120 	    else {
121 		if ((hz|lz)==0)		/* return sign(x)*0 */
122 		    return Zero[sx];
123 		hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
124 	    }
125 	}
126 	hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
127 	if(hz>=0) {hx=hz;lx=lz;}
128 
129     /* convert back to floating value and restore the sign */
130 	if((hx|lx)==0)			/* return sign(x)*0 */
131 	    return Zero[sx];
132 	while(hx<(1ULL<<HFRAC_BITS)) {	/* normalize x */
133 	    hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
134 	    iy -= 1;
135 	}
136 	ux.bits.manh = hx; /* The mantissa is truncated here if needed. */
137 	ux.bits.manl = lx;
138 	if (iy < LDBL_MIN_EXP) {
139 	    ux.bits.exp = iy + (BIAS + 512);
140 	    ux.e *= 0x1p-512;
141 	} else {
142 	    ux.bits.exp = iy + BIAS;
143 	}
144 	x = ux.e * one;		/* create necessary signal */
145 	return x;		/* exact output */
146 }
147