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 
41 static 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  */
56 long double
57 remquol(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<(int64_t)(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);
147 fixup:
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 }
167