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 28 remquo(double x, double y, int *quo) 29 { 30 int32_t hx,hy,hz,ix,iy,n,sx; 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) 57 ix = subnormal_ilogb(hx, lx); 58 else 59 ix = (hx>>20)-1023; 60 61 /* determine iy = ilogb(y) */ 62 if(hy<0x00100000) 63 iy = subnormal_ilogb(hy, ly); 64 else 65 iy = (hy>>20)-1023; 66 67 /* set up {hx,lx}, {hy,ly} and align y to x */ 68 if(ix >= -1022) 69 hx = 0x00100000|(0x000fffff&hx); 70 else { /* subnormal x, shift x to normal */ 71 n = -1022-ix; 72 if(n<=31) { 73 hx = (hx<<n)|(lx>>(32-n)); 74 lx <<= n; 75 } else { 76 hx = lx<<(n-32); 77 lx = 0; 78 } 79 } 80 if(iy >= -1022) 81 hy = 0x00100000|(0x000fffff&hy); 82 else { /* subnormal y, shift y to normal */ 83 n = -1022-iy; 84 if(n<=31) { 85 hy = (hy<<n)|(ly>>(32-n)); 86 ly <<= n; 87 } else { 88 hy = ly<<(n-32); 89 ly = 0; 90 } 91 } 92 93 /* fix point fmod */ 94 n = ix - iy; 95 q = 0; 96 while(n--) { 97 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 98 if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} 99 else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;} 100 q <<= 1; 101 } 102 hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; 103 if(hz>=0) {hx=hz;lx=lz;q++;} 104 105 /* convert back to floating value and restore the sign */ 106 if((hx|lx)==0) { /* return sign(x)*0 */ 107 q &= 0x7fffffff; 108 *quo = (sxy ? -q : q); 109 return Zero[(u_int32_t)sx>>31]; 110 } 111 while(hx<0x00100000) { /* normalize x */ 112 hx = hx+hx+(lx>>31); lx = lx+lx; 113 iy -= 1; 114 } 115 if(iy>= -1022) { /* normalize output */ 116 hx = ((hx-0x00100000)|((iy+1023)<<20)); 117 } else { /* subnormal output */ 118 n = -1022 - iy; 119 if(n<=20) { 120 lx = (lx>>n)|((u_int32_t)hx<<(32-n)); 121 hx >>= n; 122 } else if (n<=31) { 123 lx = (hx<<(32-n))|(lx>>n); hx = 0; 124 } else { 125 lx = hx>>(n-32); hx = 0; 126 } 127 } 128 fixup: 129 INSERT_WORDS(x,hx,lx); 130 y = fabs(y); 131 if (y < 0x1p-1021) { 132 if (x+x>y || (x+x==y && (q & 1))) { 133 q++; 134 x-=y; 135 } 136 } else if (x>0.5*y || (x==0.5*y && (q & 1))) { 137 q++; 138 x-=y; 139 } 140 GET_HIGH_WORD(hx,x); 141 SET_HIGH_WORD(x,hx^sx); 142 q &= 0x7fffffff; 143 *quo = (sxy ? -q : q); 144 return x; 145 } 146 147 #if LDBL_MANT_DIG == 53 148 __weak_reference(remquo, remquol); 149 #endif 150