1 2 /* @(#)e_hypot.c 5.1 93/09/24 */ 3 /* 4 * ==================================================== 5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 6 * 7 * Developed at SunPro, a Sun Microsystems, Inc. business. 8 * Permission to use, copy, modify, and distribute this 9 * software is freely granted, provided that this notice 10 * is preserved. 11 * ==================================================== 12 */ 13 14 /* 15 FUNCTION 16 <<hypot>>, <<hypotf>>---distance from origin 17 INDEX 18 hypot 19 INDEX 20 hypotf 21 22 ANSI_SYNOPSIS 23 #include <math.h> 24 double hypot(double <[x]>, double <[y]>); 25 float hypotf(float <[x]>, float <[y]>); 26 27 TRAD_SYNOPSIS 28 double hypot(<[x]>, <[y]>) 29 double <[x]>, <[y]>; 30 31 float hypotf(<[x]>, <[y]>) 32 float <[x]>, <[y]>; 33 34 DESCRIPTION 35 <<hypot>> calculates the Euclidean distance 36 @tex 37 $\sqrt{x^2+y^2}$ 38 @end tex 39 @ifnottex 40 <<sqrt(<[x]>*<[x]> + <[y]>*<[y]>)>> 41 @end ifnottex 42 between the origin (0,0) and a point represented by the 43 Cartesian coordinates (<[x]>,<[y]>). <<hypotf>> differs only 44 in the type of its arguments and result. 45 46 RETURNS 47 Normally, the distance value is returned. On overflow, 48 <<hypot>> returns <<HUGE_VAL>> and sets <<errno>> to 49 <<ERANGE>>. 50 51 You can change the error treatment with <<matherr>>. 52 53 PORTABILITY 54 <<hypot>> and <<hypotf>> are not ANSI C. */ 55 56 /* hypot(x,y) 57 * 58 * Method : 59 * If (assume round-to-nearest) z=x*x+y*y 60 * has error less than sqrt(2)/2 ulp, than 61 * sqrt(z) has error less than 1 ulp (exercise). 62 * 63 * So, compute sqrt(x*x+y*y) with some care as 64 * follows to get the error below 1 ulp: 65 * 66 * Assume x>y>0; 67 * (if possible, set rounding to round-to-nearest) 68 * 1. if x > 2y use 69 * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y 70 * where x1 = x with lower 32 bits cleared, x2 = x-x1; else 71 * 2. if x <= 2y use 72 * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) 73 * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, 74 * y1= y with lower 32 bits chopped, y2 = y-y1. 75 * 76 * NOTE: scaling may be necessary if some argument is too 77 * large or too tiny 78 * 79 * Special cases: 80 * hypot(x,y) is INF if x or y is +INF or -INF; else 81 * hypot(x,y) is NAN if x or y is NAN. 82 * 83 * Accuracy: 84 * hypot(x,y) returns sqrt(x^2+y^2) with error less 85 * than 1 ulps (units in the last place) 86 */ 87 88 #include "fdlibm.h" 89 90 #ifndef _DOUBLE_IS_32BITS 91 92 #ifdef __STDC__ hypot(double x,double y)93 double hypot(double x, double y) 94 #else 95 double hypot(x,y) 96 double x, y; 97 #endif 98 { 99 double a=x,b=y,t1,t2,y1,y2,w; 100 __int32_t j,k,ha,hb; 101 102 GET_HIGH_WORD(ha,x); 103 ha &= 0x7fffffff; 104 GET_HIGH_WORD(hb,y); 105 hb &= 0x7fffffff; 106 if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} 107 SET_HIGH_WORD(a,ha); /* a <- |a| */ 108 SET_HIGH_WORD(b,hb); /* b <- |b| */ 109 if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ 110 k=0; 111 if(ha > 0x5f300000) { /* a>2**500 */ 112 if(ha >= 0x7ff00000) { /* Inf or NaN */ 113 __uint32_t low; 114 w = a+b; /* for sNaN */ 115 GET_LOW_WORD(low,a); 116 if(((ha&0xfffff)|low)==0) w = a; 117 GET_LOW_WORD(low,b); 118 if(((hb^0x7ff00000)|low)==0) w = b; 119 return w; 120 } 121 /* scale a and b by 2**-600 */ 122 ha -= 0x25800000; hb -= 0x25800000; k += 600; 123 SET_HIGH_WORD(a,ha); 124 SET_HIGH_WORD(b,hb); 125 } 126 if(hb < 0x20b00000) { /* b < 2**-500 */ 127 if(hb <= 0x000fffff) { /* subnormal b or 0 */ 128 __uint32_t low; 129 GET_LOW_WORD(low,b); 130 if((hb|low)==0) return a; 131 t1=0; 132 SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ 133 b *= t1; 134 a *= t1; 135 k -= 1022; 136 } else { /* scale a and b by 2^600 */ 137 ha += 0x25800000; /* a *= 2^600 */ 138 hb += 0x25800000; /* b *= 2^600 */ 139 k -= 600; 140 SET_HIGH_WORD(a,ha); 141 SET_HIGH_WORD(b,hb); 142 } 143 } 144 /* medium size a and b */ 145 w = a-b; 146 if (w>b) { 147 t1 = 0; 148 SET_HIGH_WORD(t1,ha); 149 t2 = a-t1; 150 w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); 151 } else { 152 a = a+a; 153 y1 = 0; 154 SET_HIGH_WORD(y1,hb); 155 y2 = b - y1; 156 t1 = 0; 157 SET_HIGH_WORD(t1,ha+0x00100000); 158 t2 = a - t1; 159 w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); 160 } 161 if(k!=0) { 162 __uint32_t high; 163 t1 = 1.0; 164 GET_HIGH_WORD(high,t1); 165 SET_HIGH_WORD(t1,high+(k<<20)); 166 return t1*w; 167 } else return w; 168 } 169 170 #endif /* defined(_DOUBLE_IS_32BITS) */ 171