1 /* @(#)e_fmod.c 5.1 93/09/24 */ 2 /* 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunPro, 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 <sys/cdefs.h> 14 #if defined(LIBM_SCCS) && !defined(lint) 15 __RCSID("$NetBSD: e_fmod.c,v 1.12 2013/11/19 14:02:59 joerg Exp $"); 16 #endif 17 18 /* 19 * __ieee754_fmod(x,y) 20 * Return x mod y in exact arithmetic 21 * Method: shift and subtract 22 */ 23 24 #include "math.h" 25 #include "math_private.h" 26 27 static const double one = 1.0, Zero[] = {0.0, -0.0,}; 28 29 #ifndef __HAVE_LONG_DOUBLE 30 __strong_alias(__ieee754_fmodl, __ieee754_fmod) 31 #endif 32 33 double 34 __ieee754_fmod(double x, double y) 35 { 36 int32_t n,hx,hy,hz,ix,iy,sx,i; 37 u_int32_t lx,ly,lz; 38 39 EXTRACT_WORDS(hx,lx,x); 40 EXTRACT_WORDS(hy,ly,y); 41 sx = hx&0x80000000; /* sign of x */ 42 hx ^=sx; /* |x| */ 43 hy &= 0x7fffffff; /* |y| */ 44 45 /* purge off exception values */ 46 if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ 47 ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ 48 return (x*y)/(x*y); 49 if(hx<=hy) { 50 if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ 51 if(lx==ly) 52 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ 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 while(n--) { 102 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 103 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} 104 else { 105 if((hz|lz)==0) /* return sign(x)*0 */ 106 return Zero[(u_int32_t)sx>>31]; 107 hx = hz+hz+(lz>>31); lx = lz+lz; 108 } 109 } 110 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 111 if(hz>=0) {hx=hz;lx=lz;} 112 113 /* convert back to floating value and restore the sign */ 114 if((hx|lx)==0) /* return sign(x)*0 */ 115 return Zero[(u_int32_t)sx>>31]; 116 while(hx<0x00100000) { /* normalize x */ 117 hx = hx+hx+(lx>>31); lx = lx+lx; 118 iy -= 1; 119 } 120 if(iy>= -1022) { /* normalize output */ 121 hx = ((hx-0x00100000)|((iy+1023)<<20)); 122 INSERT_WORDS(x,hx|sx,lx); 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 INSERT_WORDS(x,hx|sx,lx); 134 x *= one; /* create necessary signal */ 135 } 136 return x; /* exact output */ 137 } 138