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 Zero[] = {0.0L, -0.0L};
53 
54 /*
55  * Return the IEEE remainder and set *quo to the last n bits of the
56  * quotient, rounded to the nearest integer.  We choose n=31 because
57  * we wind up computing all the integer bits of the quotient anyway as
58  * a side-effect of computing the remainder by the shift and subtract
59  * method.  In practice, this is far more bits than are needed to use
60  * remquo in reduction algorithms.
61  *
62  * Assumptions:
63  * - The low part of the mantissa fits in a manl_t exactly.
64  * - The high part of the mantissa fits in an int64_t with enough room
65  *   for an explicit integer bit in front of the fractional bits.
66  */
67 long double
remquol(long double x,long double y,int * quo)68 remquol(long double x, long double y, int *quo)
69 {
70 	union IEEEl2bits ux, uy;
71 	int64_t hx,hz;	/* We need a carry bit even if LDBL_MANH_SIZE is 32. */
72 	manh_t hy;
73 	manl_t lx,ly,lz;
74 	int ix,iy,n,q,sx,sxy;
75 
76 	ux.e = x;
77 	uy.e = y;
78 	sx = ux.bits.sign;
79 	sxy = sx ^ uy.bits.sign;
80 	ux.bits.sign = 0;	/* |x| */
81 	uy.bits.sign = 0;	/* |y| */
82 	x = ux.e;
83 
84     /* purge off exception values */
85 	if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
86 	   (ux.bits.exp == BIAS + LDBL_MAX_EXP) ||	 /* or x not finite */
87 	   (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
88 	    ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
89 	    return (x*y)/(x*y);
90 	if(ux.bits.exp<=uy.bits.exp) {
91 	    if((ux.bits.exp<uy.bits.exp) ||
92 	       (ux.bits.manh<=uy.bits.manh &&
93 		(ux.bits.manh<uy.bits.manh ||
94 		 ux.bits.manl<uy.bits.manl))) {
95 		q = 0;
96 		goto fixup;	/* |x|<|y| return x or x-y */
97 	    }
98 	    if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
99 		*quo = (sxy ? -1 : 1);
100 		return Zero[sx];	/* |x|=|y| return x*0*/
101 	    }
102 	}
103 
104     /* determine ix = ilogb(x) */
105 	if(ux.bits.exp == 0) {	/* subnormal x */
106 	    ux.e *= 0x1.0p512;
107 	    ix = ux.bits.exp - (BIAS + 512);
108 	} else {
109 	    ix = ux.bits.exp - BIAS;
110 	}
111 
112     /* determine iy = ilogb(y) */
113 	if(uy.bits.exp == 0) {	/* subnormal y */
114 	    uy.e *= 0x1.0p512;
115 	    iy = uy.bits.exp - (BIAS + 512);
116 	} else {
117 	    iy = uy.bits.exp - BIAS;
118 	}
119 
120     /* set up {hx,lx}, {hy,ly} and align y to x */
121 	hx = SET_NBIT(ux.bits.manh);
122 	hy = SET_NBIT(uy.bits.manh);
123 	lx = ux.bits.manl;
124 	ly = uy.bits.manl;
125 
126     /* fix point fmod */
127 	n = ix - iy;
128 	q = 0;
129 
130 	while(n--) {
131 	    hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
132 	    if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
133 	    else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;}
134 	    q <<= 1;
135 	}
136 	hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
137 	if(hz>=0) {hx=hz;lx=lz;q++;}
138 
139     /* convert back to floating value and restore the sign */
140 	if((hx|lx)==0) {			/* return sign(x)*0 */
141 	    q &= 0x7fffffff;
142 	    *quo = (sxy ? -q : q);
143 	    return Zero[sx];
144 	}
145 	while(hx<(1ULL<<HFRAC_BITS)) {	/* normalize x */
146 	    hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
147 	    iy -= 1;
148 	}
149 	ux.bits.manh = hx; /* The integer bit is truncated here if needed. */
150 	ux.bits.manl = lx;
151 	if (iy < LDBL_MIN_EXP) {
152 	    ux.bits.exp = iy + (BIAS + 512);
153 	    ux.e *= 0x1p-512;
154 	} else {
155 	    ux.bits.exp = iy + BIAS;
156 	}
157 	ux.bits.sign = 0;
158 	x = ux.e;
159 fixup:
160 	y = fabsl(y);
161 	if (y < LDBL_MIN * 2) {
162 	    if (x+x>y || (x+x==y && (q & 1))) {
163 		q++;
164 		x-=y;
165 	    }
166 	} else if (x>0.5*y || (x==0.5*y && (q & 1))) {
167 	    q++;
168 	    x-=y;
169 	}
170 
171 	ux.e = x;
172 	ux.bits.sign ^= sx;
173 	x = ux.e;
174 
175 	q &= 0x7fffffff;
176 	*quo = (sxy ? -q : q);
177 	return x;
178 }
179