1 /* @(#)e_fmod.c 1.3 95/01/18 */ 2 /*- 3 * ==================================================== 4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 5 * 6 * Developed at SunSoft, 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 __FBSDID("$FreeBSD$"); 15 16 #include "math.h" 17 #include "math_private.h" 18 19 static const float Zero[] = {0.0, -0.0,}; 20 21 /* 22 * Return the IEEE remainder and set *quo to the last n bits of the 23 * quotient, rounded to the nearest integer. We choose n=31 because 24 * we wind up computing all the integer bits of the quotient anyway as 25 * a side-effect of computing the remainder by the shift and subtract 26 * method. In practice, this is far more bits than are needed to use 27 * remquo in reduction algorithms. 28 */ 29 float 30 remquof(float x, float y, int *quo) 31 { 32 int32_t n,hx,hy,hz,ix,iy,sx,i; 33 u_int32_t q,sxy; 34 35 GET_FLOAT_WORD(hx,x); 36 GET_FLOAT_WORD(hy,y); 37 sxy = (hx ^ hy) & 0x80000000; 38 sx = hx&0x80000000; /* sign of x */ 39 hx ^=sx; /* |x| */ 40 hy &= 0x7fffffff; /* |y| */ 41 42 /* purge off exception values */ 43 if(hy==0||hx>=0x7f800000||hy>0x7f800000) /* y=0,NaN;or x not finite */ 44 return (x*y)/(x*y); 45 if(hx<hy) { 46 q = 0; 47 goto fixup; /* |x|<|y| return x or x-y */ 48 } else if(hx==hy) { 49 *quo = (sxy ? -1 : 1); 50 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/ 51 } 52 53 /* determine ix = ilogb(x) */ 54 if(hx<0x00800000) { /* subnormal x */ 55 for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1; 56 } else ix = (hx>>23)-127; 57 58 /* determine iy = ilogb(y) */ 59 if(hy<0x00800000) { /* subnormal y */ 60 for (iy = -126,i=(hy<<8); i>0; i<<=1) iy -=1; 61 } else iy = (hy>>23)-127; 62 63 /* set up {hx,lx}, {hy,ly} and align y to x */ 64 if(ix >= -126) 65 hx = 0x00800000|(0x007fffff&hx); 66 else { /* subnormal x, shift x to normal */ 67 n = -126-ix; 68 hx <<= n; 69 } 70 if(iy >= -126) 71 hy = 0x00800000|(0x007fffff&hy); 72 else { /* subnormal y, shift y to normal */ 73 n = -126-iy; 74 hy <<= n; 75 } 76 77 /* fix point fmod */ 78 n = ix - iy; 79 q = 0; 80 while(n--) { 81 hz=hx-hy; 82 if(hz<0) hx = hx << 1; 83 else {hx = hz << 1; q++;} 84 q <<= 1; 85 } 86 hz=hx-hy; 87 if(hz>=0) {hx=hz;q++;} 88 89 /* convert back to floating value and restore the sign */ 90 if(hx==0) { /* return sign(x)*0 */ 91 q &= 0x7fffffff; 92 *quo = (sxy ? -q : q); 93 return Zero[(u_int32_t)sx>>31]; 94 } 95 while(hx<0x00800000) { /* normalize x */ 96 hx <<= 1; 97 iy -= 1; 98 } 99 if(iy>= -126) { /* normalize output */ 100 hx = ((hx-0x00800000)|((iy+127)<<23)); 101 } else { /* subnormal output */ 102 n = -126 - iy; 103 hx >>= n; 104 } 105 fixup: 106 SET_FLOAT_WORD(x,hx); 107 y = fabsf(y); 108 if (y < 0x1p-125f) { 109 if (x+x>y || (x+x==y && (q & 1))) { 110 q++; 111 x-=y; 112 } 113 } else if (x>0.5f*y || (x==0.5f*y && (q & 1))) { 114 q++; 115 x-=y; 116 } 117 GET_FLOAT_WORD(hx,x); 118 SET_FLOAT_WORD(x,hx^sx); 119 q &= 0x7fffffff; 120 *quo = (sxy ? -q : q); 121 return x; 122 } 123
