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
83 /* purge off exception values */
84 if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
85 (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
86 (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
87 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
88 return nan_mix_op(x, y, *)/nan_mix_op(x, y, *);
89 if(ux.bits.exp<=uy.bits.exp) {
90 if((ux.bits.exp<uy.bits.exp) ||
91 (ux.bits.manh<=uy.bits.manh &&
92 (ux.bits.manh<uy.bits.manh ||
93 ux.bits.manl<uy.bits.manl))) {
94 q = 0;
95 goto fixup; /* |x|<|y| return x or x-y */
96 }
97 if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
98 *quo = (sxy ? -1 : 1);
99 return Zero[sx]; /* |x|=|y| return x*0*/
100 }
101 }
102
103 /* determine ix = ilogb(x) */
104 if(ux.bits.exp == 0) { /* subnormal x */
105 ux.e *= 0x1.0p512;
106 ix = ux.bits.exp - (BIAS + 512);
107 } else {
108 ix = ux.bits.exp - BIAS;
109 }
110
111 /* determine iy = ilogb(y) */
112 if(uy.bits.exp == 0) { /* subnormal y */
113 uy.e *= 0x1.0p512;
114 iy = uy.bits.exp - (BIAS + 512);
115 } else {
116 iy = uy.bits.exp - BIAS;
117 }
118
119 /* set up {hx,lx}, {hy,ly} and align y to x */
120 hx = SET_NBIT(ux.bits.manh);
121 hy = SET_NBIT(uy.bits.manh);
122 lx = ux.bits.manl;
123 ly = uy.bits.manl;
124
125 /* fix point fmod */
126 n = ix - iy;
127 q = 0;
128 while(n--) {
129 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
130 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
131 else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;}
132 q <<= 1;
133 }
134 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
135 if(hz>=0) {hx=hz;lx=lz;q++;}
136
137 /* convert back to floating value and restore the sign */
138 if((hx|lx)==0) { /* return sign(x)*0 */
139 q &= 0x7fffffff;
140 *quo = (sxy ? -q : q);
141 return Zero[sx];
142 }
143 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */
144 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
145 iy -= 1;
146 }
147 ux.bits.manh = hx; /* The integer bit is truncated here if needed. */
148 ux.bits.manl = lx;
149 if (iy < LDBL_MIN_EXP) {
150 ux.bits.exp = iy + (BIAS + 512);
151 ux.e *= 0x1p-512;
152 } else {
153 ux.bits.exp = iy + BIAS;
154 }
155 fixup:
156 x = ux.e; /* |x| */
157 y = fabsl(y);
158 if (y < LDBL_MIN * 2) {
159 if (x+x>y || (x+x==y && (q & 1))) {
160 q++;
161 x-=y;
162 }
163 } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
164 q++;
165 x-=y;
166 }
167 ux.e = x;
168 ux.bits.sign ^= sx;
169 x = ux.e;
170 q &= 0x7fffffff;
171 *quo = (sxy ? -q : q);
172 return x;
173 }
174