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
14
15
16 #define BIAS (LDBL_MAX_EXP - 1)
17
18 /*
19 * These macros add and remove an explicit integer bit in front of the
20 * fractional mantissa, if the architecture doesn't have such a bit by
21 * default already.
22 */
23 #ifdef LDBL_IMPLICIT_NBIT
24 #define LDBL_NBIT 0
25 #define SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE))
26 #define HFRAC_BITS EXT_FRACHBITS
27 #else
28 #define LDBL_NBIT 0x80000000
29 #define SET_NBIT(hx) (hx)
30 #define HFRAC_BITS (EXT_FRACHBITS - 1)
31 #endif
32
33 #define MANL_SHIFT (EXT_FRACLBITS - 1)
34
35 static const long double one = 1.0l, Zero[] = {0.0l, -0.0l,};
36
37 /*
38 * fmodl(x,y)
39 * Return x mod y in exact arithmetic
40 * Method: shift and subtract
41 *
42 * Assumptions:
43 * - The low part of the mantissa fits in a manl_t exactly.
44 * - The high part of the mantissa fits in an int64_t with enough room
45 * for an explicit integer bit in front of the fractional bits.
46 */
47 long double
fmodl(long double x,long double y)48 fmodl(long double x, long double y)
49 {
50 union {
51 long double e;
52 struct ieee_ext bits;
53 } ux, uy;
54 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
55 uint32_t hy;
56 uint32_t lx,ly,lz;
57 int ix,iy,n,sx;
58
59 ux.e = x;
60 uy.e = y;
61 sx = ux.bits.ext_sign;
62
63 if (isnanl(x) || isnanl(y))
64 return x + y;
65
66 if (isinfl(x))
67 return __math_invalidl(x);
68
69 if (y == 0.0L)
70 return __math_invalidl(y);
71
72 if(ux.bits.ext_exp<=uy.bits.ext_exp) {
73 if((ux.bits.ext_exp<uy.bits.ext_exp) ||
74 (ux.bits.ext_frach<=uy.bits.ext_frach &&
75 (ux.bits.ext_frach<uy.bits.ext_frach ||
76 ux.bits.ext_fracl<uy.bits.ext_fracl))) {
77 return x; /* |x|<|y| return x or x-y */
78 }
79 if(ux.bits.ext_frach==uy.bits.ext_frach &&
80 ux.bits.ext_fracl==uy.bits.ext_fracl) {
81 return Zero[sx]; /* |x|=|y| return x*0*/
82 }
83 }
84
85 /* determine ix = ilogb(x) */
86 if(ux.bits.ext_exp == 0) { /* subnormal x */
87 ux.e *= 0x1.0p512l;
88 ix = ux.bits.ext_exp - (BIAS + 512);
89 } else {
90 ix = ux.bits.ext_exp - BIAS;
91 }
92
93 /* determine iy = ilogb(y) */
94 if(uy.bits.ext_exp == 0) { /* subnormal y */
95 uy.e *= 0x1.0p512l;
96 iy = uy.bits.ext_exp - (BIAS + 512);
97 } else {
98 iy = uy.bits.ext_exp - BIAS;
99 }
100
101 /* set up {hx,lx}, {hy,ly} and align y to x */
102 hx = SET_NBIT(ux.bits.ext_frach);
103 hy = SET_NBIT(uy.bits.ext_frach);
104 lx = ux.bits.ext_fracl;
105 ly = uy.bits.ext_fracl;
106
107 /* fix point fmod */
108 n = ix - iy;
109
110 while(n--) {
111 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
112 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
113 else {
114 if ((hz|lz)==0) /* return sign(x)*0 */
115 return Zero[sx];
116 hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz;
117 }
118 }
119 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
120 if(hz>=0) {hx=hz;lx=lz;}
121
122 /* convert back to floating value and restore the sign */
123 if((hx|lx)==0) /* return sign(x)*0 */
124 return Zero[sx];
125 while(hx<(1LL<<HFRAC_BITS)) { /* normalize x */
126 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
127 iy -= 1;
128 }
129 ux.bits.ext_frach = hx; /* The mantissa is truncated here if needed. */
130 ux.bits.ext_fracl = lx;
131 if (iy < LDBL_MIN_EXP) {
132 ux.bits.ext_exp = iy + (BIAS + 512);
133 ux.e *= 0x1p-512l;
134 } else {
135 ux.bits.ext_exp = iy + BIAS;
136 }
137 x = ux.e * one; /* create necessary signal */
138 return x; /* exact output */
139 }
140
