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 <float.h>
14 #include <stdint.h>
15
16 #include "fpmath.h"
17 #include "math.h"
18 #include "math_private.h"
19
20 #define BIAS (LDBL_MAX_EXP - 1)
21
22 #if LDBL_MANL_SIZE > 32
23 typedef uint64_t manl_t;
24 #else
25 typedef uint32_t manl_t;
26 #endif
27
28 #if LDBL_MANH_SIZE > 32
29 typedef uint64_t manh_t;
30 #else
31 typedef uint32_t manh_t;
32 #endif
33
34 /*
35 * These macros add and remove an explicit integer bit in front of the
36 * fractional mantissa, if the architecture doesn't have such a bit by
37 * default already.
38 */
39 #ifdef LDBL_IMPLICIT_NBIT
40 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE))
41 #define HFRAC_BITS LDBL_MANH_SIZE
42 #else
43 #define SET_NBIT(hx) (hx)
44 #define HFRAC_BITS (LDBL_MANH_SIZE - 1)
45 #endif
46
47 #define MANL_SHIFT (LDBL_MANL_SIZE - 1)
48
49 static const long double one = 1.0, Zero[] = {0.0, -0.0,};
50
51 /*
52 * fmodl(x,y)
53 * Return x mod y in exact arithmetic
54 * Method: shift and subtract
55 *
56 * Assumptions:
57 * - The low part of the mantissa fits in a manl_t exactly.
58 * - The high part of the mantissa fits in an int64_t with enough room
59 * for an explicit integer bit in front of the fractional bits.
60 */
61 long double
fmodl(long double x,long double y)62 fmodl(long double x, long double y)
63 {
64 union IEEEl2bits ux, uy;
65 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
66 manh_t hy;
67 manl_t lx,ly,lz;
68 int ix,iy,n,sx;
69
70 ux.e = x;
71 uy.e = y;
72 sx = ux.bits.sign;
73
74 /* purge off exception values */
75 if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
76 (ux.bits.exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
77 (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
78 ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
79 return nan_mix_op(x, y, *)/nan_mix_op(x, y, *);
80 if(ux.bits.exp<=uy.bits.exp) {
81 if((ux.bits.exp<uy.bits.exp) ||
82 (ux.bits.manh<=uy.bits.manh &&
83 (ux.bits.manh<uy.bits.manh ||
84 ux.bits.manl<uy.bits.manl))) {
85 return x; /* |x|<|y| return x or x-y */
86 }
87 if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
88 return Zero[sx]; /* |x|=|y| return x*0*/
89 }
90 }
91
92 /* determine ix = ilogb(x) */
93 if(ux.bits.exp == 0) { /* subnormal x */
94 ux.e *= 0x1.0p512;
95 ix = ux.bits.exp - (BIAS + 512);
96 } else {
97 ix = ux.bits.exp - BIAS;
98 }
99
100 /* determine iy = ilogb(y) */
101 if(uy.bits.exp == 0) { /* subnormal y */
102 uy.e *= 0x1.0p512;
103 iy = uy.bits.exp - (BIAS + 512);
104 } else {
105 iy = uy.bits.exp - BIAS;
106 }
107
108 /* set up {hx,lx}, {hy,ly} and align y to x */
109 hx = SET_NBIT(ux.bits.manh);
110 hy = SET_NBIT(uy.bits.manh);
111 lx = ux.bits.manl;
112 ly = uy.bits.manl;
113
114 /* fix point fmod */
115 n = ix - iy;
116
117 while(n--) {
118 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
119 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
120 else {
121 if ((hz|lz)==0) /* return sign(x)*0 */
122 return Zero[sx];
123 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
124 }
125 }
126 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
127 if(hz>=0) {hx=hz;lx=lz;}
128
129 /* convert back to floating value and restore the sign */
130 if((hx|lx)==0) /* return sign(x)*0 */
131 return Zero[sx];
132 while(hx<(1ULL<<HFRAC_BITS)) { /* normalize x */
133 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
134 iy -= 1;
135 }
136 ux.bits.manh = hx; /* The mantissa is truncated here if needed. */
137 ux.bits.manl = lx;
138 if (iy < LDBL_MIN_EXP) {
139 ux.bits.exp = iy + (BIAS + 512);
140 ux.e *= 0x1p-512;
141 } else {
142 ux.bits.exp = iy + BIAS;
143 }
144 x = ux.e * one; /* create necessary signal */
145 return x; /* exact output */
146 }
147