1 /* derived from /netlib/fdlibm */ 2 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 /* 16 * __ieee754_fmod(x,y) 17 * Return x mod y in exact arithmetic 18 * Method: shift and subtract 19 */ 20 21 #include "fdlibm.h" 22 23 static const double one = 1.0, Zero[] = {0.0, -0.0,}; 24 __ieee754_fmod(double x,double y)25 double __ieee754_fmod(double x, double y) 26 { 27 int n,hx,hy,hz,ix,iy,sx,i; 28 unsigned lx,ly,lz; 29 30 hx = __HI(x); /* high word of x */ 31 lx = __LO(x); /* low word of x */ 32 hy = __HI(y); /* high word of y */ 33 ly = __LO(y); /* low word of y */ 34 sx = hx&0x80000000; /* sign of x */ 35 hx ^=sx; /* |x| */ 36 hy &= 0x7fffffff; /* |y| */ 37 38 /* purge off exception values */ 39 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ 40 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ 41 return (x*y)/(x*y); 42 if(hx<=hy) { 43 if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ 44 if(lx==ly) 45 return Zero[(unsigned)sx>>31]; /* |x|=|y| return x*0*/ 46 } 47 48 /* determine ix = ilogb(x) */ 49 if(hx<0x00100000) { /* subnormal x */ 50 if(hx==0) { 51 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; 52 } else { 53 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; 54 } 55 } else ix = (hx>>20)-1023; 56 57 /* determine iy = ilogb(y) */ 58 if(hy<0x00100000) { /* subnormal y */ 59 if(hy==0) { 60 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; 61 } else { 62 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; 63 } 64 } else iy = (hy>>20)-1023; 65 66 /* set up {hx,lx}, {hy,ly} and align y to x */ 67 if(ix >= -1022) 68 hx = 0x00100000|(0x000fffff&hx); 69 else { /* subnormal x, shift x to normal */ 70 n = -1022-ix; 71 if(n<=31) { 72 hx = (hx<<n)|(lx>>(32-n)); 73 lx <<= n; 74 } else { 75 hx = lx<<(n-32); 76 lx = 0; 77 } 78 } 79 if(iy >= -1022) 80 hy = 0x00100000|(0x000fffff&hy); 81 else { /* subnormal y, shift y to normal */ 82 n = -1022-iy; 83 if(n<=31) { 84 hy = (hy<<n)|(ly>>(32-n)); 85 ly <<= n; 86 } else { 87 hy = ly<<(n-32); 88 ly = 0; 89 } 90 } 91 92 /* fix point fmod */ 93 n = ix - iy; 94 while(n--) { 95 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 96 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} 97 else { 98 if((hz|lz)==0) /* return sign(x)*0 */ 99 return Zero[(unsigned)sx>>31]; 100 hx = hz+hz+(lz>>31); lx = lz+lz; 101 } 102 } 103 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 104 if(hz>=0) {hx=hz;lx=lz;} 105 106 /* convert back to floating value and restore the sign */ 107 if((hx|lx)==0) /* return sign(x)*0 */ 108 return Zero[(unsigned)sx>>31]; 109 while(hx<0x00100000) { /* normalize x */ 110 hx = hx+hx+(lx>>31); lx = lx+lx; 111 iy -= 1; 112 } 113 if(iy>= -1022) { /* normalize output */ 114 hx = ((hx-0x00100000)|((iy+1023)<<20)); 115 __HI(x) = hx|sx; 116 __LO(x) = lx; 117 } else { /* subnormal output */ 118 n = -1022 - iy; 119 if(n<=20) { 120 lx = (lx>>n)|((unsigned)hx<<(32-n)); 121 hx >>= n; 122 } else if (n<=31) { 123 lx = (hx<<(32-n))|(lx>>n); hx = sx; 124 } else { 125 lx = hx>>(n-32); hx = sx; 126 } 127 __HI(x) = hx|sx; 128 __LO(x) = lx; 129 x *= one; /* create necessary signal */ 130 } 131 return x; /* exact output */ 132 } 133