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