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 __RCSID("$NetBSD: e_fmodl.c,v 1.2 2013/11/14 15:25:22 martin Exp $");
15 #if 0
16 __FBSDID("$FreeBSD: head/lib/msun/src/e_fmodl.c 181063 2008-07-31 20:09:47Z das $");
17 #endif
18
19 #include "namespace.h"
20
21 #include <float.h>
22 #include <stdint.h>
23
24 #include "math.h"
25 #include "math_private.h"
26 #include <machine/ieee.h>
27
28 #ifdef __HAVE_LONG_DOUBLE
29
30 #define BIAS (LDBL_MAX_EXP - 1)
31
32 #if EXT_FRACLBITS > 32
33 typedef uint64_t manl_t;
34 #else
35 typedef uint32_t manl_t;
36 #endif
37
38 #if EXT_FRACHBITS > 32
39 typedef uint64_t manh_t;
40 #else
41 typedef uint32_t manh_t;
42 #endif
43
44 /*
45 * These macros add and remove an explicit integer bit in front of the
46 * fractional mantissa, if the architecture doesn't have such a bit by
47 * default already.
48 */
49 #ifdef LDBL_IMPLICIT_NBIT
50 #define SET_NBIT(hx) ((hx) | (1ULL << EXT_FRACHBITS))
51 #define HFRAC_BITS EXT_FRACHBITS
52 #define LDBL_NBIT 0
53 #else
54 #define SET_NBIT(hx) (hx)
55 #define HFRAC_BITS (EXT_FRACHBITS - 1)
56 #endif
57
58 #define MANL_SHIFT (EXT_FRACLBITS - 1)
59
60 static const long double one = 1.0, Zero[] = {0.0, -0.0,};
61
62 /*
63 * fmodl(x,y)
64 * Return x mod y in exact arithmetic
65 * Method: shift and subtract
66 *
67 * Assumptions:
68 * - The low part of the mantissa fits in a manl_t exactly.
69 * - The high part of the mantissa fits in an int64_t with enough room
70 * for an explicit integer bit in front of the fractional bits.
71 */
72 long double
__ieee754_fmodl(long double x,long double y)73 __ieee754_fmodl(long double x, long double y)
74 {
75 union ieee_ext_u ux = { .extu_ld = x, };
76 union ieee_ext_u uy = { .extu_ld = y, };
77 int64_t hx,hz; /* We need a carry bit even if EXT_FRACHBITS is 32. */
78 manh_t hy;
79 manl_t lx,ly,lz;
80 int ix,iy,n,sx;
81
82 sx = ux.extu_sign;
83
84 /* purge off exception values */
85 if((uy.extu_exp|uy.extu_frach|uy.extu_fracl)==0 || /* y=0 */
86 (ux.extu_exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
87 (uy.extu_exp == BIAS + LDBL_MAX_EXP &&
88 ((uy.extu_frach&~LDBL_NBIT)|uy.extu_fracl)!=0)) /* or y is NaN */
89 return (x*y)/(x*y);
90 if(ux.extu_exp<=uy.extu_exp) {
91 if((ux.extu_exp<uy.extu_exp) ||
92 (ux.extu_frach<=uy.extu_frach &&
93 (ux.extu_frach<uy.extu_frach ||
94 ux.extu_fracl<uy.extu_fracl))) {
95 return x; /* |x|<|y| return x or x-y */
96 }
97 if(ux.extu_frach==uy.extu_frach && ux.extu_fracl==uy.extu_fracl) {
98 return Zero[sx]; /* |x|=|y| return x*0*/
99 }
100 }
101
102 /* determine ix = ilogb(x) */
103 if(ux.extu_exp == 0) { /* subnormal x */
104 ux.extu_ld *= 0x1.0p512;
105 ix = ux.extu_exp - (BIAS + 512);
106 } else {
107 ix = ux.extu_exp - BIAS;
108 }
109
110 /* determine iy = ilogb(y) */
111 if(uy.extu_exp == 0) { /* subnormal y */
112 uy.extu_ld *= 0x1.0p512;
113 iy = uy.extu_exp - (BIAS + 512);
114 } else {
115 iy = uy.extu_exp - BIAS;
116 }
117
118 /* set up {hx,lx}, {hy,ly} and align y to x */
119 hx = SET_NBIT(ux.extu_frach);
120 hy = SET_NBIT(uy.extu_frach);
121 lx = ux.extu_fracl;
122 ly = uy.extu_fracl;
123
124 /* fix point fmod */
125 n = ix - iy;
126
127 while(n--) {
128 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
129 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
130 else {
131 if ((hz|lz)==0) /* return sign(x)*0 */
132 return Zero[sx];
133 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
134 }
135 }
136 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
137 if(hz>=0) {hx=hz;lx=lz;}
138
139 /* convert back to floating value and restore the sign */
140 if((hx|lx)==0) /* return sign(x)*0 */
141 return Zero[sx];
142 while(hx<(1LL<<HFRAC_BITS)) { /* normalize x */
143 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
144 iy -= 1;
145 }
146 ux.extu_frach = hx; /* The mantissa is truncated here if needed. */
147 ux.extu_fracl = lx;
148 if (iy < LDBL_MIN_EXP) {
149 ux.extu_exp = iy + (BIAS + 512);
150 ux.extu_ld *= 0x1p-512;
151 } else {
152 ux.extu_exp = iy + BIAS;
153 }
154 x = ux.extu_ld * one; /* create necessary signal */
155 return x; /* exact output */
156 }
157
158 #endif /* __HAVE_LONG_DOUBLE */
159