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 one = 1.0, Zero[] = {0.0, -0.0,};
53
54 /*
55 * fmodl(x,y)
56 * Return x mod y in exact arithmetic
57 * Method: shift and subtract
58 *
59 * Assumptions:
60 * - The low part of the mantissa fits in a manl_t exactly.
61 * - The high part of the mantissa fits in an int64_t with enough room
62 * for an explicit integer bit in front of the fractional bits.
63 */
64 long double
fmodl(long double x,long double y)65 fmodl(long double x, long double y)
66 {
67 union IEEEl2bits ux, uy;
68 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
69 manh_t hy;
70 manl_t lx,ly,lz;
71 int ix,iy,n,sx;
72
73 ux.e = x;
74 uy.e = y;
75 sx = ux.bits.sign;
76
77 /* purge off exception values */
78 if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
79 (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
80 (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
81 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
82 return (x*y)/(x*y);
83 if(ux.bits.exp<=uy.bits.exp) {
84 if((ux.bits.exp<uy.bits.exp) ||
85 (ux.bits.manh<=uy.bits.manh &&
86 (ux.bits.manh<uy.bits.manh ||
87 ux.bits.manl<uy.bits.manl))) {
88 return x; /* |x|<|y| return x or x-y */
89 }
90 if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
91 return Zero[sx]; /* |x|=|y| return x*0*/
92 }
93 }
94
95 /* determine ix = ilogb(x) */
96 if(ux.bits.exp == 0) { /* subnormal x */
97 ux.e *= 0x1.0p512;
98 ix = ux.bits.exp - (BIAS + 512);
99 } else {
100 ix = ux.bits.exp - BIAS;
101 }
102
103 /* determine iy = ilogb(y) */
104 if(uy.bits.exp == 0) { /* subnormal y */
105 uy.e *= 0x1.0p512;
106 iy = uy.bits.exp - (BIAS + 512);
107 } else {
108 iy = uy.bits.exp - BIAS;
109 }
110
111 /* set up {hx,lx}, {hy,ly} and align y to x */
112 hx = SET_NBIT(ux.bits.manh);
113 hy = SET_NBIT(uy.bits.manh);
114 lx = ux.bits.manl;
115 ly = uy.bits.manl;
116
117 /* fix point fmod */
118 n = ix - iy;
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 {
124 if ((hz|lz)==0) /* return sign(x)*0 */
125 return Zero[sx];
126 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
127 }
128 }
129 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
130 if(hz>=0) {hx=hz;lx=lz;}
131
132 /* convert back to floating value and restore the sign */
133 if((hx|lx)==0) /* return sign(x)*0 */
134 return Zero[sx];
135 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */
136 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
137 iy -= 1;
138 }
139 ux.bits.manh = hx; /* The mantissa is truncated here if needed. */
140 ux.bits.manl = lx;
141 if (iy < LDBL_MIN_EXP) {
142 ux.bits.exp = iy + (BIAS + 512);
143 ux.e *= 0x1p-512;
144 } else {
145 ux.bits.exp = iy + BIAS;
146 }
147 x = ux.e * one; /* create necessary signal */
148 return x; /* exact output */
149 }
150