1 /*-
2 * ====================================================
3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
4 *
5 * Developed at SunSoft, a Sun Microsystems, Inc. business.
6 * Permission to use, copy, modify, and distribute this
7 * software is freely granted, provided that this notice
8 * is preserved.
9 * ====================================================
10 */
11
12 #include <float.h>
13
14 #include "math.h"
15 #include "math_private.h"
16
17 static const double Zero[] = {0.0, -0.0,};
18
19 /*
20 * Return the IEEE remainder and set *quo to the last n bits of the
21 * quotient, rounded to the nearest integer. We choose n=31 because
22 * we wind up computing all the integer bits of the quotient anyway as
23 * a side-effect of computing the remainder by the shift and subtract
24 * method. In practice, this is far more bits than are needed to use
25 * remquo in reduction algorithms.
26 */
27 double
remquo(double x,double y,int * quo)28 remquo(double x, double y, int *quo)
29 {
30 int32_t n,hx,hy,hz,ix,iy,sx,i;
31 u_int32_t lx,ly,lz,q,sxy;
32
33 EXTRACT_WORDS(hx,lx,x);
34 EXTRACT_WORDS(hy,ly,y);
35 sxy = (hx ^ hy) & 0x80000000;
36 sx = hx&0x80000000; /* sign of x */
37 hx ^=sx; /* |x| */
38 hy &= 0x7fffffff; /* |y| */
39
40 /* purge off exception values */
41 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
42 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */
43 return nan_mix_op(x, y, *)/nan_mix_op(x, y, *);
44 if(hx<=hy) {
45 if((hx<hy)||(lx<ly)) {
46 q = 0;
47 goto fixup; /* |x|<|y| return x or x-y */
48 }
49 if(lx==ly) {
50 *quo = (sxy ? -1 : 1);
51 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
52 }
53 }
54
55 /* determine ix = ilogb(x) */
56 if(hx<0x00100000) { /* subnormal x */
57 if(hx==0) {
58 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
59 } else {
60 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
61 }
62 } else ix = (hx>>20)-1023;
63
64 /* determine iy = ilogb(y) */
65 if(hy<0x00100000) { /* subnormal y */
66 if(hy==0) {
67 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
68 } else {
69 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
70 }
71 } else iy = (hy>>20)-1023;
72
73 /* set up {hx,lx}, {hy,ly} and align y to x */
74 if(ix >= -1022)
75 hx = 0x00100000|(0x000fffff&hx);
76 else { /* subnormal x, shift x to normal */
77 n = -1022-ix;
78 if(n<=31) {
79 hx = (hx<<n)|(lx>>(32-n));
80 lx <<= n;
81 } else {
82 hx = lx<<(n-32);
83 lx = 0;
84 }
85 }
86 if(iy >= -1022)
87 hy = 0x00100000|(0x000fffff&hy);
88 else { /* subnormal y, shift y to normal */
89 n = -1022-iy;
90 if(n<=31) {
91 hy = (hy<<n)|(ly>>(32-n));
92 ly <<= n;
93 } else {
94 hy = ly<<(n-32);
95 ly = 0;
96 }
97 }
98
99 /* fix point fmod */
100 n = ix - iy;
101 q = 0;
102 while(n--) {
103 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
104 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
105 else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
106 q <<= 1;
107 }
108 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
109 if(hz>=0) {hx=hz;lx=lz;q++;}
110
111 /* convert back to floating value and restore the sign */
112 if((hx|lx)==0) { /* return sign(x)*0 */
113 q &= 0x7fffffff;
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 = 0;
130 } else {
131 lx = hx>>(n-32); hx = 0;
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 == 53
154 __weak_reference(remquo, remquol);
155 #endif
156