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