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 Zero[] = {0.0L, -0.0L};
36
37 /*
38 * Return the IEEE remainder and set *quo to the last n bits of the
39 * quotient, rounded to the nearest integer. We choose n=31 because
40 * we wind up computing all the integer bits of the quotient anyway as
41 * a side-effect of computing the remainder by the shift and subtract
42 * method. In practice, this is far more bits than are needed to use
43 * remquo in reduction algorithms.
44 *
45 * Assumptions:
46 * - The low part of the mantissa fits in a manl_t exactly.
47 * - The high part of the mantissa fits in an int64_t with enough room
48 * for an explicit integer bit in front of the fractional bits.
49 */
50 long double
remquol(long double x,long double y,int * quo)51 remquol(long double x, long double y, int *quo)
52 {
53 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
54 uint32_t hy;
55 uint32_t lx,ly,lz;
56 uint32_t esx, esy;
57 int ix,iy,n,q,sx,sxy;
58
59 GET_LDOUBLE_WORDS(esx,hx,lx,x);
60 GET_LDOUBLE_WORDS(esy,hy,ly,y);
61 sx = esx & 0x8000;
62 sxy = sx ^ (esy & 0x8000);
63 esx &= 0x7fff; /* |x| */
64 esy &= 0x7fff; /* |y| */
65 SET_LDOUBLE_EXP(x,esx);
66 SET_LDOUBLE_EXP(y,esy);
67
68 /* purge off exception values */
69 if((esy|hy|ly)==0 || /* y=0 */
70 (esx == BIAS + LDBL_MAX_EXP) || /* or x not finite */
71 (esy == BIAS + LDBL_MAX_EXP &&
72 ((hy&~LDBL_NBIT)|ly)!=0)) { /* or y is NaN */
73 *quo = 0;
74 return (x*y)/(x*y);
75 }
76 if(esx<=esy) {
77 if((esx<esy) ||
78 (hx<=hy &&
79 (hx<hy ||
80 lx<ly))) {
81 q = 0;
82 goto fixup; /* |x|<|y| return x or x-y */
83 }
84 if(hx==hy && lx==ly) {
85 *quo = 1;
86 return Zero[sx!=0]; /* |x|=|y| return x*0*/
87 }
88 }
89
90 /* determine ix = ilogb(x) */
91 if(esx == 0) { /* subnormal x */
92 x *= 0x1.0p512L;
93 GET_LDOUBLE_WORDS(esx,hx,lx,x);
94 ix = esx - (BIAS + 512);
95 } else {
96 ix = esx - BIAS;
97 }
98
99 /* determine iy = ilogb(y) */
100 if(esy == 0) { /* subnormal y */
101 y *= 0x1.0p512L;
102 GET_LDOUBLE_WORDS(esy,hy,ly,y);
103 iy = esy - (BIAS + 512);
104 } else {
105 iy = esy - BIAS;
106 }
107
108 /* set up {hx,lx}, {hy,ly} and align y to x */
109 hx = SET_NBIT(hx);
110 lx = SET_NBIT(lx);
111
112 /* fix point fmod */
113 n = ix - iy;
114 q = 0;
115
116 while(n--) {
117 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
118 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
119 else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;}
120 q <<= 1;
121 }
122 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
123 if(hz>=0) {hx=hz;lx=lz;q++;}
124
125 /* convert back to floating value and restore the sign */
126 if((hx|lx)==0) { /* return sign(x)*0 */
127 *quo = (sxy ? -q : q);
128 return Zero[sx!=0];
129 }
130 while(hx<(1LL<<HFRAC_BITS)) { /* normalize x */
131 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
132 iy -= 1;
133 }
134 if (iy < LDBL_MIN_EXP) {
135 esx = (iy + BIAS + 512) & 0x7fff;
136 SET_LDOUBLE_WORDS(x,esx,hx,lx);
137 x *= 0x1p-512L;
138 GET_LDOUBLE_WORDS(esx,hx,lx,x);
139 } else {
140 esx = (iy + BIAS) & 0x7fff;
141 }
142 SET_LDOUBLE_WORDS(x,esx,hx,lx);
143 fixup:
144 y = fabsl(y);
145 if (y < LDBL_MIN * 2) {
146 if (x+x>y || (x+x==y && (q & 1))) {
147 q++;
148 x-=y;
149 }
150 } else if (x>0.5L*y || (x==0.5L*y && (q & 1))) {
151 q++;
152 x-=y;
153 }
154
155 GET_LDOUBLE_EXP(esx,x);
156 esx ^= sx;
157 SET_LDOUBLE_EXP(x,esx);
158
159 q &= 0x7fffffff;
160 *quo = (sxy ? -q : q);
161 return x;
162 }
163
