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 Zero[] = {0.0L, -0.0L};
42
43 /*
44 * Return the IEEE remainder and set *quo to the last n bits of the
45 * quotient, rounded to the nearest integer. We choose n=31 because
46 * we wind up computing all the integer bits of the quotient anyway as
47 * a side-effect of computing the remainder by the shift and subtract
48 * method. In practice, this is far more bits than are needed to use
49 * remquo in reduction algorithms.
50 *
51 * Assumptions:
52 * - The low part of the mantissa fits in a manl_t exactly.
53 * - The high part of the mantissa fits in an int64_t with enough room
54 * for an explicit integer bit in front of the fractional bits.
55 */
56 long double
remquol(long double x,long double y,int * quo)57 remquol(long double x, long double y, int *quo)
58 {
59 int64_t hx,hz; /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
60 uint32_t hy;
61 uint32_t lx,ly,lz;
62 uint32_t esx, esy;
63 int ix,iy,n,q,sx,sxy;
64
65 GET_LDOUBLE_WORDS(esx,hx,lx,x);
66 GET_LDOUBLE_WORDS(esy,hy,ly,y);
67 sx = esx & 0x8000;
68 sxy = sx ^ (esy & 0x8000);
69 esx &= 0x7fff; /* |x| */
70 esy &= 0x7fff; /* |y| */
71 SET_LDOUBLE_EXP(x,esx);
72 SET_LDOUBLE_EXP(y,esy);
73
74 /* purge off exception values */
75 if((esy|hy|ly)==0 || /* y=0 */
76 (esx == BIAS + LDBL_MAX_EXP) || /* or x not finite */
77 (esy == BIAS + LDBL_MAX_EXP &&
78 ((hy&~LDBL_NBIT)|ly)!=0)) /* or y is NaN */
79 return (x*y)/(x*y);
80 if(esx<=esy) {
81 if((esx<esy) ||
82 (hx<=hy &&
83 (hx<hy ||
84 lx<ly))) {
85 q = 0;
86 goto fixup; /* |x|<|y| return x or x-y */
87 }
88 if(hx==hy && lx==ly) {
89 *quo = 1;
90 return Zero[sx!=0]; /* |x|=|y| return x*0*/
91 }
92 }
93
94 /* determine ix = ilogb(x) */
95 if(esx == 0) { /* subnormal x */
96 x *= 0x1.0p512;
97 GET_LDOUBLE_WORDS(esx,hx,lx,x);
98 ix = esx - (BIAS + 512);
99 } else {
100 ix = esx - BIAS;
101 }
102
103 /* determine iy = ilogb(y) */
104 if(esy == 0) { /* subnormal y */
105 y *= 0x1.0p512;
106 GET_LDOUBLE_WORDS(esy,hy,ly,y);
107 iy = esy - (BIAS + 512);
108 } else {
109 iy = esy - BIAS;
110 }
111
112 /* set up {hx,lx}, {hy,ly} and align y to x */
113 hx = SET_NBIT(hx);
114 lx = SET_NBIT(lx);
115
116 /* fix point fmod */
117 n = ix - iy;
118 q = 0;
119
120 while(n--) {
121 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
122 if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
123 else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;}
124 q <<= 1;
125 }
126 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
127 if(hz>=0) {hx=hz;lx=lz;q++;}
128
129 /* convert back to floating value and restore the sign */
130 if((hx|lx)==0) { /* return sign(x)*0 */
131 *quo = (sxy ? -q : q);
132 return Zero[sx!=0];
133 }
134 while(hx<(int64_t)(1ULL<<HFRAC_BITS)) { /* normalize x */
135 hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
136 iy -= 1;
137 }
138 if (iy < LDBL_MIN_EXP) {
139 esx = (iy + BIAS + 512) & 0x7fff;
140 SET_LDOUBLE_WORDS(x,esx,hx,lx);
141 x *= 0x1p-512;
142 GET_LDOUBLE_WORDS(esx,hx,lx,x);
143 } else {
144 esx = (iy + BIAS) & 0x7fff;
145 }
146 SET_LDOUBLE_WORDS(x,esx,hx,lx);
147 fixup:
148 y = fabsl(y);
149 if (y < LDBL_MIN * 2) {
150 if (x+x>y || (x+x==y && (q & 1))) {
151 q++;
152 x-=y;
153 }
154 } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
155 q++;
156 x-=y;
157 }
158
159 GET_LDOUBLE_EXP(esx,x);
160 esx ^= sx;
161 SET_LDOUBLE_EXP(x,esx);
162
163 q &= 0x7fffffff;
164 *quo = (sxy ? -q : q);
165 return x;
166 }
167