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 <float.h>
14 #include <math.h>
15
16 #include "math_private.h"
17
18 static const double Zero[] = {0.0, -0.0,};
19
20 /*
21 * Return the IEEE remainder and set *quo to the last n bits of the
22 * quotient, rounded to the nearest integer. We choose n=31 because
23 * we wind up computing all the integer bits of the quotient anyway as
24 * a side-effect of computing the remainder by the shift and subtract
25 * method. In practice, this is far more bits than are needed to use
26 * remquo in reduction algorithms.
27 */
28 double
remquo(double x,double y,int * quo)29 remquo(double x, double y, int *quo)
30 {
31 int32_t n,hx,hy,hz,ix,iy,sx,i;
32 u_int32_t lx,ly,lz,q,sxy;
33
34 EXTRACT_WORDS(hx,lx,x);
35 EXTRACT_WORDS(hy,ly,y);
36 sxy = (hx ^ hy) & 0x80000000;
37 sx = hx&0x80000000; /* sign of x */
38 hx ^=sx; /* |x| */
39 hy &= 0x7fffffff; /* |y| */
40
41 /* purge off exception values */
42 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
43 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
44 return (x*y)/(x*y);
45 if(hx<=hy) {
46 if((hx<hy)||(lx<ly)) {
47 q = 0;
48 goto fixup; /* |x|<|y| return x or x-y */
49 }
50 if(lx==ly) {
51 *quo = 1;
52 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
53 }
54 }
55
56 /* determine ix = ilogb(x) */
57 if(hx<0x00100000) { /* subnormal x */
58 if(hx==0) {
59 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
60 } else {
61 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
62 }
63 } else ix = (hx>>20)-1023;
64
65 /* determine iy = ilogb(y) */
66 if(hy<0x00100000) { /* subnormal y */
67 if(hy==0) {
68 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
69 } else {
70 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
71 }
72 } else iy = (hy>>20)-1023;
73
74 /* set up {hx,lx}, {hy,ly} and align y to x */
75 if(ix >= -1022)
76 hx = 0x00100000|(0x000fffff&hx);
77 else { /* subnormal x, shift x to normal */
78 n = -1022-ix;
79 if(n<=31) {
80 hx = (hx<<n)|(lx>>(32-n));
81 lx <<= n;
82 } else {
83 hx = lx<<(n-32);
84 lx = 0;
85 }
86 }
87 if(iy >= -1022)
88 hy = 0x00100000|(0x000fffff&hy);
89 else { /* subnormal y, shift y to normal */
90 n = -1022-iy;
91 if(n<=31) {
92 hy = (hy<<n)|(ly>>(32-n));
93 ly <<= n;
94 } else {
95 hy = ly<<(n-32);
96 ly = 0;
97 }
98 }
99
100 /* fix point fmod */
101 n = ix - iy;
102 q = 0;
103 while(n--) {
104 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
105 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
106 else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
107 q <<= 1;
108 }
109 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
110 if(hz>=0) {hx=hz;lx=lz;q++;}
111
112 /* convert back to floating value and restore the sign */
113 if((hx|lx)==0) { /* return sign(x)*0 */
114 *quo = (sxy ? -q : q);
115 return Zero[(u_int32_t)sx>>31];
116 }
117 while(hx<0x00100000) { /* normalize x */
118 hx = hx+hx+(lx>>31); lx = lx+lx;
119 iy -= 1;
120 }
121 if(iy>= -1022) { /* normalize output */
122 hx = ((hx-0x00100000)|((iy+1023)<<20));
123 } else { /* subnormal output */
124 n = -1022 - iy;
125 if(n<=20) {
126 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
127 hx >>= n;
128 } else if (n<=31) {
129 lx = (hx<<(32-n))|(lx>>n); hx = sx;
130 } else {
131 lx = hx>>(n-32); hx = sx;
132 }
133 }
134 fixup:
135 INSERT_WORDS(x,hx,lx);
136 y = fabs(y);
137 if (y < 0x1p-1021) {
138 if (x+x>y || (x+x==y && (q & 1))) {
139 q++;
140 x-=y;
141 }
142 } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
143 q++;
144 x-=y;
145 }
146 GET_HIGH_WORD(hx,x);
147 SET_HIGH_WORD(x,hx^sx);
148 q &= 0x7fffffff;
149 *quo = (sxy ? -q : q);
150 return x;
151 }
152
153 #if LDBL_MANT_DIG == DBL_MANT_DIG
154 __strong_alias(remquol, remquo);
155 #endif /* LDBL_MANT_DIG == DBL_MANT_DIG */
156