1*eac90eaaSmartynas /* @(#)e_fmod.c 1.3 95/01/18 */
2*eac90eaaSmartynas /*-
3*eac90eaaSmartynas * ====================================================
4*eac90eaaSmartynas * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5*eac90eaaSmartynas *
6*eac90eaaSmartynas * Developed at SunSoft, a Sun Microsystems, Inc. business.
7*eac90eaaSmartynas * Permission to use, copy, modify, and distribute this
8*eac90eaaSmartynas * software is freely granted, provided that this notice
9*eac90eaaSmartynas * is preserved.
10*eac90eaaSmartynas * ====================================================
11*eac90eaaSmartynas */
12*eac90eaaSmartynas
13*eac90eaaSmartynas #include "math.h"
14*eac90eaaSmartynas #include "math_private.h"
15*eac90eaaSmartynas
16*eac90eaaSmartynas static const float Zero[] = {0.0, -0.0,};
17*eac90eaaSmartynas
18*eac90eaaSmartynas /*
19*eac90eaaSmartynas * Return the IEEE remainder and set *quo to the last n bits of the
20*eac90eaaSmartynas * quotient, rounded to the nearest integer. We choose n=31 because
21*eac90eaaSmartynas * we wind up computing all the integer bits of the quotient anyway as
22*eac90eaaSmartynas * a side-effect of computing the remainder by the shift and subtract
23*eac90eaaSmartynas * method. In practice, this is far more bits than are needed to use
24*eac90eaaSmartynas * remquo in reduction algorithms.
25*eac90eaaSmartynas */
26*eac90eaaSmartynas float
remquof(float x,float y,int * quo)27*eac90eaaSmartynas remquof(float x, float y, int *quo)
28*eac90eaaSmartynas {
29*eac90eaaSmartynas int32_t n,hx,hy,hz,ix,iy,sx,i;
30*eac90eaaSmartynas u_int32_t q,sxy;
31*eac90eaaSmartynas
32*eac90eaaSmartynas GET_FLOAT_WORD(hx,x);
33*eac90eaaSmartynas GET_FLOAT_WORD(hy,y);
34*eac90eaaSmartynas sxy = (hx ^ hy) & 0x80000000;
35*eac90eaaSmartynas sx = hx&0x80000000; /* sign of x */
36*eac90eaaSmartynas hx ^=sx; /* |x| */
37*eac90eaaSmartynas hy &= 0x7fffffff; /* |y| */
38*eac90eaaSmartynas
39*eac90eaaSmartynas /* purge off exception values */
40*eac90eaaSmartynas if(hy==0||hx>=0x7f800000||hy>0x7f800000) /* y=0,NaN;or x not finite */
41*eac90eaaSmartynas return (x*y)/(x*y);
42*eac90eaaSmartynas if(hx<hy) {
43*eac90eaaSmartynas q = 0;
44*eac90eaaSmartynas goto fixup; /* |x|<|y| return x or x-y */
45*eac90eaaSmartynas } else if(hx==hy) {
46*eac90eaaSmartynas *quo = 1;
47*eac90eaaSmartynas return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
48*eac90eaaSmartynas }
49*eac90eaaSmartynas
50*eac90eaaSmartynas /* determine ix = ilogb(x) */
51*eac90eaaSmartynas if(hx<0x00800000) { /* subnormal x */
52*eac90eaaSmartynas for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1;
53*eac90eaaSmartynas } else ix = (hx>>23)-127;
54*eac90eaaSmartynas
55*eac90eaaSmartynas /* determine iy = ilogb(y) */
56*eac90eaaSmartynas if(hy<0x00800000) { /* subnormal y */
57*eac90eaaSmartynas for (iy = -126,i=(hy<<8); i>0; i<<=1) iy -=1;
58*eac90eaaSmartynas } else iy = (hy>>23)-127;
59*eac90eaaSmartynas
60*eac90eaaSmartynas /* set up {hx,lx}, {hy,ly} and align y to x */
61*eac90eaaSmartynas if(ix >= -126)
62*eac90eaaSmartynas hx = 0x00800000|(0x007fffff&hx);
63*eac90eaaSmartynas else { /* subnormal x, shift x to normal */
64*eac90eaaSmartynas n = -126-ix;
65*eac90eaaSmartynas hx <<= n;
66*eac90eaaSmartynas }
67*eac90eaaSmartynas if(iy >= -126)
68*eac90eaaSmartynas hy = 0x00800000|(0x007fffff&hy);
69*eac90eaaSmartynas else { /* subnormal y, shift y to normal */
70*eac90eaaSmartynas n = -126-iy;
71*eac90eaaSmartynas hy <<= n;
72*eac90eaaSmartynas }
73*eac90eaaSmartynas
74*eac90eaaSmartynas /* fix point fmod */
75*eac90eaaSmartynas n = ix - iy;
76*eac90eaaSmartynas q = 0;
77*eac90eaaSmartynas while(n--) {
78*eac90eaaSmartynas hz=hx-hy;
79*eac90eaaSmartynas if(hz<0) hx = hx << 1;
80*eac90eaaSmartynas else {hx = hz << 1; q++;}
81*eac90eaaSmartynas q <<= 1;
82*eac90eaaSmartynas }
83*eac90eaaSmartynas hz=hx-hy;
84*eac90eaaSmartynas if(hz>=0) {hx=hz;q++;}
85*eac90eaaSmartynas
86*eac90eaaSmartynas /* convert back to floating value and restore the sign */
87*eac90eaaSmartynas if(hx==0) { /* return sign(x)*0 */
88*eac90eaaSmartynas *quo = (sxy ? -q : q);
89*eac90eaaSmartynas return Zero[(u_int32_t)sx>>31];
90*eac90eaaSmartynas }
91*eac90eaaSmartynas while(hx<0x00800000) { /* normalize x */
92*eac90eaaSmartynas hx <<= 1;
93*eac90eaaSmartynas iy -= 1;
94*eac90eaaSmartynas }
95*eac90eaaSmartynas if(iy>= -126) { /* normalize output */
96*eac90eaaSmartynas hx = ((hx-0x00800000)|((iy+127)<<23));
97*eac90eaaSmartynas } else { /* subnormal output */
98*eac90eaaSmartynas n = -126 - iy;
99*eac90eaaSmartynas hx >>= n;
100*eac90eaaSmartynas }
101*eac90eaaSmartynas fixup:
102*eac90eaaSmartynas SET_FLOAT_WORD(x,hx);
103*eac90eaaSmartynas y = fabsf(y);
104*eac90eaaSmartynas if (y < 0x1p-125f) {
105*eac90eaaSmartynas if (x+x>y || (x+x==y && (q & 1))) {
106*eac90eaaSmartynas q++;
107*eac90eaaSmartynas x-=y;
108*eac90eaaSmartynas }
109*eac90eaaSmartynas } else if (x>0.5f*y || (x==0.5f*y && (q & 1))) {
110*eac90eaaSmartynas q++;
111*eac90eaaSmartynas x-=y;
112*eac90eaaSmartynas }
113*eac90eaaSmartynas GET_FLOAT_WORD(hx,x);
114*eac90eaaSmartynas SET_FLOAT_WORD(x,hx^sx);
115*eac90eaaSmartynas q &= 0x7fffffff;
116*eac90eaaSmartynas *quo = (sxy ? -q : q);
117*eac90eaaSmartynas return x;
118*eac90eaaSmartynas }
119