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 SET_NBIT(hx) ((hx) | (1ULL << LDBL_MANH_SIZE))
25 #define HFRAC_BITS EXT_FRACHBITS
26 #else
27 #define SET_NBIT(hx) (hx)
28 #define HFRAC_BITS (EXT_FRACHBITS - 1)
29 #endif
30
31 #define MANL_SHIFT (EXT_FRACLBITS - 1)
32
33 static const long double Zero[] = {0.0L, -0.0L};
34
35 /*
36 * Return the IEEE remainder and set *quo to the last n bits of the
37 * quotient, rounded to the nearest integer. We choose n=31 because
38 * we wind up computing all the integer bits of the quotient anyway as
39 * a side-effect of computing the remainder by the shift and subtract
40 * method. In practice, this is far more bits than are needed to use
41 * remquo in reduction algorithms.
42 *
43 * Assumptions:
44 * - The low part of the mantissa fits in a manl_t exactly.
45 * - The high part of the mantissa fits in an int64_t with enough room
46 * for an explicit integer bit in front of the fractional bits.
47 */
48 long double
remquol(long double x,long double y,int * quo)49 remquol(long double x, long double y, int *quo)
50 {
51 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
52 uint32_t hy;
53 uint32_t lx,ly,lz;
54 uint32_t esx, esy;
55 int ix,iy,n,q,sx,sxy;
56
57 GET_LDOUBLE_WORDS(esx,hx,lx,x);
58 GET_LDOUBLE_WORDS(esy,hy,ly,y);
59 sx = esx & 0x8000;
60 sxy = sx ^ (esy & 0x8000);
61 esx &= 0x7fff; /* |x| */
62 esy &= 0x7fff; /* |y| */
63 SET_LDOUBLE_EXP(x,esx);
64 SET_LDOUBLE_EXP(y,esy);
65
66 /* purge off exception values */
67 if((esy|hy|ly)==0 || /* y=0 */
68 (esx == BIAS + LDBL_MAX_EXP) || /* or x not finite */
69 (esy == BIAS + LDBL_MAX_EXP &&
70 ((hy&~LDBL_NBIT)|ly)!=0)) { /* or y is NaN */
71 *quo = 0;
72 return (x*y)/(x*y);
73 }
74 if(esx<=esy) {
75 if((esx<esy) ||
76 (hx<=hy &&
77 (hx<hy ||
78 lx<ly))) {
79 q = 0;
80 goto fixup; /* |x|<|y| return x or x-y */
81 }
82 if(hx==hy && lx==ly) {
83 *quo = 1;
84 return Zero[sx!=0]; /* |x|=|y| return x*0*/
85 }
86 }
87
88 /* determine ix = ilogb(x) */
89 if(esx == 0) { /* subnormal x */
90 x *= 0x1.0p512L;
91 GET_LDOUBLE_WORDS(esx,hx,lx,x);
92 ix = esx - (BIAS + 512);
93 } else {
94 ix = esx - BIAS;
95 }
96
97 /* determine iy = ilogb(y) */
98 if(esy == 0) { /* subnormal y */
99 y *= 0x1.0p512L;
100 GET_LDOUBLE_WORDS(esy,hy,ly,y);
101 iy = esy - (BIAS + 512);
102 } else {
103 iy = esy - BIAS;
104 }
105
106 /* set up {hx,lx}, {hy,ly} and align y to x */
107 hx = SET_NBIT(hx);
108 lx = SET_NBIT(lx);
109
110 /* fix point fmod */
111 n = ix - iy;
112 q = 0;
113
114 while(n--) {
115 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
116 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
117 else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;}
118 q <<= 1;
119 }
120 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
121 if(hz>=0) {hx=hz;lx=lz;q++;}
122
123 /* convert back to floating value and restore the sign */
124 if((hx|lx)==0) { /* return sign(x)*0 */
125 *quo = (sxy ? -q : q);
126 return Zero[sx!=0];
127 }
128 while(hx<(1LL<<HFRAC_BITS)) { /* normalize x */
129 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
130 iy -= 1;
131 }
132 if (iy < LDBL_MIN_EXP) {
133 esx = (iy + BIAS + 512) & 0x7fff;
134 SET_LDOUBLE_WORDS(x,esx,hx,lx);
135 x *= 0x1p-512L;
136 GET_LDOUBLE_WORDS(esx,hx,lx,x);
137 } else {
138 esx = (iy + BIAS) & 0x7fff;
139 }
140 SET_LDOUBLE_WORDS(x,esx,hx,lx);
141 fixup:
142 y = fabsl(y);
143 if (y < LDBL_MIN * 2) {
144 if (x+x>y || (x+x==y && (q & 1))) {
145 q++;
146 x-=y;
147 }
148 } else if (x>0.5L*y || (x==0.5L*y && (q & 1))) {
149 q++;
150 x-=y;
151 }
152
153 GET_LDOUBLE_EXP(esx,x);
154 esx ^= sx;
155 SET_LDOUBLE_EXP(x,esx);
156
157 q &= 0x7fffffff;
158 *quo = (sxy ? -q : q);
159 return x;
160 }
161
