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/types.h>
14 #include <machine/ieee.h>
15
16 #include <float.h>
17 #include <math.h>
18 #include <stdint.h>
19
20 #include "math_private.h"
21
22 #define BIAS (LDBL_MAX_EXP - 1)
23
24 /*
25 * These macros add and remove an explicit integer bit in front of the
26 * fractional mantissa, if the architecture doesn't have such a bit by
27 * default already.
28 */
29 #ifdef LDBL_IMPLICIT_NBIT
30 #define LDBL_NBIT 0
31 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE))
32 #define HFRAC_BITS EXT_FRACHBITS
33 #else
34 #define LDBL_NBIT 0x80000000
35 #define SET_NBIT(hx) (hx)
36 #define HFRAC_BITS (EXT_FRACHBITS - 1)
37 #endif
38
39 #define MANL_SHIFT (EXT_FRACLBITS - 1)
40
41 static const long double one = 1.0, Zero[] = {0.0, -0.0,};
42
43 /*
44 * fmodl(x,y)
45 * Return x mod y in exact arithmetic
46 * Method: shift and subtract
47 *
48 * Assumptions:
49 * - The low part of the mantissa fits in a manl_t exactly.
50 * - The high part of the mantissa fits in an int64_t with enough room
51 * for an explicit integer bit in front of the fractional bits.
52 */
53 long double
fmodl(long double x,long double y)54 fmodl(long double x, long double y)
55 {
56 union {
57 long double e;
58 struct ieee_ext bits;
59 } ux, uy;
60 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
61 uint32_t hy;
62 uint32_t lx,ly,lz;
63 int ix,iy,n,sx;
64
65 ux.e = x;
66 uy.e = y;
67 sx = ux.bits.ext_sign;
68
69 /* purge off exception values */
70 if((uy.bits.ext_exp|uy.bits.ext_frach|uy.bits.ext_fracl)==0 || /* y=0 */
71 (ux.bits.ext_exp == BIAS + LDBL_MAX_EXP) || /* or x not finite */
72 (uy.bits.ext_exp == BIAS + LDBL_MAX_EXP &&
73 ((uy.bits.ext_frach&~LDBL_NBIT)|uy.bits.ext_fracl)!=0)) /* or y is NaN */
74 return (x*y)/(x*y);
75 if(ux.bits.ext_exp<=uy.bits.ext_exp) {
76 if((ux.bits.ext_exp<uy.bits.ext_exp) ||
77 (ux.bits.ext_frach<=uy.bits.ext_frach &&
78 (ux.bits.ext_frach<uy.bits.ext_frach ||
79 ux.bits.ext_fracl<uy.bits.ext_fracl))) {
80 return x; /* |x|<|y| return x or x-y */
81 }
82 if(ux.bits.ext_frach==uy.bits.ext_frach &&
83 ux.bits.ext_fracl==uy.bits.ext_fracl) {
84 return Zero[sx]; /* |x|=|y| return x*0*/
85 }
86 }
87
88 /* determine ix = ilogb(x) */
89 if(ux.bits.ext_exp == 0) { /* subnormal x */
90 ux.e *= 0x1.0p512;
91 ix = ux.bits.ext_exp - (BIAS + 512);
92 } else {
93 ix = ux.bits.ext_exp - BIAS;
94 }
95
96 /* determine iy = ilogb(y) */
97 if(uy.bits.ext_exp == 0) { /* subnormal y */
98 uy.e *= 0x1.0p512;
99 iy = uy.bits.ext_exp - (BIAS + 512);
100 } else {
101 iy = uy.bits.ext_exp - BIAS;
102 }
103
104 /* set up {hx,lx}, {hy,ly} and align y to x */
105 hx = SET_NBIT(ux.bits.ext_frach);
106 hy = SET_NBIT(uy.bits.ext_frach);
107 lx = ux.bits.ext_fracl;
108 ly = uy.bits.ext_fracl;
109
110 /* fix point fmod */
111 n = ix - iy;
112
113 while(n--) {
114 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
115 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
116 else {
117 if ((hz|lz)==0) /* return sign(x)*0 */
118 return Zero[sx];
119 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
120 }
121 }
122 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
123 if(hz>=0) {hx=hz;lx=lz;}
124
125 /* convert back to floating value and restore the sign */
126 if((hx|lx)==0) /* return sign(x)*0 */
127 return Zero[sx];
128 while(hx<(int64_t)(1ULL<<HFRAC_BITS)) { /* normalize x */
129 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
130 iy -= 1;
131 }
132 ux.bits.ext_frach = hx; /* The mantissa is truncated here if needed. */
133 ux.bits.ext_fracl = lx;
134 if (iy < LDBL_MIN_EXP) {
135 ux.bits.ext_exp = iy + (BIAS + 512);
136 ux.e *= 0x1p-512;
137 } else {
138 ux.bits.ext_exp = iy + BIAS;
139 }
140 x = ux.e * one; /* create necessary signal */
141 return x; /* exact output */
142 }
143