1 /* Adapted for Newlib, 2009. (Allow for int < 32 bits; return *quo=0 during
2 * errors to make test scripts easier.) */
3 /* @(#)e_fmod.c 1.3 95/01/18 */
4 /*-
5 * ====================================================
6 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
7 *
8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14 /*
15 FUNCTION
16 <<remquo>>, <<remquof>>---remainder and part of quotient
17 INDEX
18 remquo
19 INDEX
20 remquof
21
22 SYNOPSIS
23 #include <math.h>
24 double remquo(double <[x]>, double <[y]>, int *<[quo]>);
25 float remquof(float <[x]>, float <[y]>, int *<[quo]>);
26
27 DESCRIPTION
28 The <<remquo>> functions compute the same remainder as the <<remainder>>
29 functions; this value is in the range -<[y]>/2 ... +<[y]>/2. In the object
30 pointed to by <<quo>> they store a value whose sign is the sign of <<x>>/<<y>>
31 and whose magnitude is congruent modulo 2**n to the magnitude of the integral
32 quotient of <<x>>/<<y>>. (That is, <<quo>> is given the n lsbs of the
33 quotient, not counting the sign.) This implementation uses n=31 if int is 32
34 bits or more, otherwise, n is 1 less than the width of int.
35
36 For example:
37 . remquo(-29.0, 3.0, &<[quo]>)
38 returns -1.0 and sets <[quo]>=10, and
39 . remquo(-98307.0, 3.0, &<[quo]>)
40 returns -0.0 and sets <[quo]>=-32769, although for 16-bit int, <[quo]>=-1. In
41 the latter case, the actual quotient of -(32769=0x8001) is reduced to -1
42 because of the 15-bit limitation for the quotient.
43
44 RETURNS
45 When either argument is NaN, NaN is returned. If <[y]> is 0 or <[x]> is
46 infinite (and neither is NaN), a domain error occurs (i.e. the "invalid"
47 floating point exception is raised or errno is set to EDOM), and NaN is
48 returned.
49 Otherwise, the <<remquo>> functions return <[x]> REM <[y]>.
50
51 BUGS
52 IEEE754-2008 calls for <<remquo>>(subnormal, inf) to cause the "underflow"
53 floating-point exception. This implementation does not.
54
55 PORTABILITY
56 C99, POSIX.
57
58 */
59
60 #include "fdlibm.h"
61
62 #ifdef _NEED_FLOAT64
63
64 #include <limits.h>
65 #include <math.h>
66
67 /* For quotient, return either all 31 bits that can from calculation (using
68 * int32_t), or as many as can fit into an int that is smaller than 32 bits. */
69 #if INT_MAX > 0x7FFFFFFFL
70 #define QUO_MASK 0x7FFFFFFF
71 # else
72 #define QUO_MASK INT_MAX
73 #endif
74
75 static const __float64 Zero[] = {_F_64(0.0), _F_64(-0.0),};
76
77 /*
78 * Return the IEEE remainder and set *quo to the last n bits of the
79 * quotient, rounded to the nearest integer. We choose n=31--if that many fit--
80 * because we wind up computing all the integer bits of the quotient anyway as
81 * a side-effect of computing the remainder by the shift and subtract
82 * method. In practice, this is far more bits than are needed to use
83 * remquo in reduction algorithms.
84 */
85 __float64
remquo64(__float64 x,__float64 y,int * quo)86 remquo64(__float64 x, __float64 y, int *quo)
87 {
88 __int32_t n,hx,hy,hz,ix,iy,sx,i;
89 __uint32_t lx,ly,lz,q,sxy;
90
91 EXTRACT_WORDS(hx,lx,x);
92 EXTRACT_WORDS(hy,ly,y);
93 sxy = (hx ^ hy) & 0x80000000;
94 sx = hx&0x80000000; /* sign of x */
95 hx ^=sx; /* |x| */
96 hy &= 0x7fffffff; /* |y| */
97
98 /* purge off exception values */
99 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */
100 ((hy|((ly|-ly)>>31))>0x7ff00000)) { /* or y is NaN */
101 *quo = 0; /* Not necessary, but return consistent value */
102 return (x*y)/(x*y);
103 }
104 if(hx<=hy) {
105 if((hx<hy)||(lx<ly)) {
106 q = 0;
107 goto fixup; /* |x|<|y| return x or x-y */
108 }
109 if(lx==ly) {
110 *quo = (sxy ? -1 : 1);
111 return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0 */
112 }
113 }
114
115 /* determine ix = ilogb(x) */
116 if(hx<0x00100000) { /* subnormal x */
117 if(hx==0) {
118 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
119 } else {
120 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
121 }
122 } else ix = (hx>>20)-1023;
123
124 /* determine iy = ilogb(y) */
125 if(hy<0x00100000) { /* subnormal y */
126 if(hy==0) {
127 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
128 } else {
129 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
130 }
131 } else iy = (hy>>20)-1023;
132
133 /* set up {hx,lx}, {hy,ly} and align y to x */
134 if(ix >= -1022)
135 hx = 0x00100000|(0x000fffff&hx);
136 else { /* subnormal x, shift x to normal */
137 n = -1022-ix;
138 if(n<=31) {
139 hx = (hx<<n)|(lx>>(32-n));
140 lx <<= n;
141 } else {
142 hx = lx<<(n-32);
143 lx = 0;
144 }
145 }
146 if(iy >= -1022)
147 hy = 0x00100000|(0x000fffff&hy);
148 else { /* subnormal y, shift y to normal */
149 n = -1022-iy;
150 if(n<=31) {
151 hy = (hy<<n)|(ly>>(32-n));
152 ly <<= n;
153 } else {
154 hy = ly<<(n-32);
155 ly = 0;
156 }
157 }
158
159 /* fix point fmod */
160 n = ix - iy;
161 q = 0;
162 while(n--) {
163 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
164 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
165 else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
166 q <<= 1;
167 }
168 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
169 if(hz>=0) {hx=hz;lx=lz;q++;}
170
171 /* convert back to floating value and restore the sign */
172 if((hx|lx)==0) { /* return sign(x)*0 */
173 q &= QUO_MASK;
174 *quo = (sxy ? -q : q);
175 return Zero[(__uint32_t)sx>>31];
176 }
177 while(hx<0x00100000) { /* normalize x */
178 hx = hx+hx+(lx>>31); lx = lx+lx;
179 iy -= 1;
180 }
181 if(iy>= -1022) { /* normalize output */
182 hx = ((hx-0x00100000)|((iy+1023)<<20));
183 } else { /* subnormal output */
184 n = -1022 - iy;
185 if(n<=20) {
186 lx = (lx>>n)|((__uint32_t)hx<<(32-n));
187 hx >>= n;
188 } else if (n<=31) {
189 lx = (hx<<(32-n))|(lx>>n); hx = sx;
190 } else {
191 lx = hx>>(n-32); hx = sx;
192 }
193 }
194 fixup:
195 INSERT_WORDS(x,hx,lx);
196 y = fabs64(y);
197 if (y < _F_64(0x1p-1021)) {
198 if (x+x>y || (x+x==y && (q & 1))) {
199 q++;
200 x-=y;
201 }
202 } else if (x>_F_64(0.5)*y || (x==_F_64(0.5)*y && (q & 1))) {
203 q++;
204 x-=y;
205 }
206 GET_HIGH_WORD(hx,x);
207 SET_HIGH_WORD(x,hx^sx);
208 q &= QUO_MASK;
209 *quo = (sxy ? -q : q);
210 return x;
211 }
212
213 _MATH_ALIAS_d_ddI(remquo)
214
215 #endif /* _NEED_FLOAT64 */
216
