| The Android Open Source Project | b07e1d9 | 2009-03-03 19:29:30 -0800 | [diff] [blame] | 1 | |
| 2 | /* @(#)e_hypot.c 1.3 95/01/18 */ |
| 3 | /* |
| 4 | * ==================================================== |
| 5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| 6 | * |
| 7 | * Developed at SunSoft, 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 | /* __ieee754_hypot(x,y) |
| 15 | * |
| 16 | * Method : |
| 17 | * If (assume round-to-nearest) z=x*x+y*y |
| 18 | * has error less than ieee_sqrt(2)/2 ulp, than |
| 19 | * sqrt(z) has error less than 1 ulp (exercise). |
| 20 | * |
| 21 | * So, compute ieee_sqrt(x*x+y*y) with some care as |
| 22 | * follows to get the error below 1 ulp: |
| 23 | * |
| 24 | * Assume x>y>0; |
| 25 | * (if possible, set rounding to round-to-nearest) |
| 26 | * 1. if x > 2y use |
| 27 | * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y |
| 28 | * where x1 = x with lower 32 bits cleared, x2 = x-x1; else |
| 29 | * 2. if x <= 2y use |
| 30 | * t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) |
| 31 | * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, |
| 32 | * y1= y with lower 32 bits chopped, y2 = y-y1. |
| 33 | * |
| 34 | * NOTE: scaling may be necessary if some argument is too |
| 35 | * large or too tiny |
| 36 | * |
| 37 | * Special cases: |
| 38 | * hypot(x,y) is INF if x or y is +INF or -INF; else |
| 39 | * hypot(x,y) is NAN if x or y is NAN. |
| 40 | * |
| 41 | * Accuracy: |
| 42 | * hypot(x,y) returns ieee_sqrt(x^2+y^2) with error less |
| 43 | * than 1 ulps (units in the last place) |
| 44 | */ |
| 45 | |
| 46 | #include "fdlibm.h" |
| 47 | |
| 48 | #ifdef __STDC__ |
| 49 | double __ieee754_hypot(double x, double y) |
| 50 | #else |
| 51 | double __ieee754_hypot(x,y) |
| 52 | double x, y; |
| 53 | #endif |
| 54 | { |
| 55 | double a=x,b=y,t1,t2,y1,y2,w; |
| 56 | int j,k,ha,hb; |
| 57 | |
| 58 | ha = __HI(x)&0x7fffffff; /* high word of x */ |
| 59 | hb = __HI(y)&0x7fffffff; /* high word of y */ |
| 60 | if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} |
| 61 | __HI(a) = ha; /* a <- |a| */ |
| 62 | __HI(b) = hb; /* b <- |b| */ |
| 63 | if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ |
| 64 | k=0; |
| 65 | if(ha > 0x5f300000) { /* a>2**500 */ |
| 66 | if(ha >= 0x7ff00000) { /* Inf or NaN */ |
| 67 | w = a+b; /* for sNaN */ |
| 68 | if(((ha&0xfffff)|__LO(a))==0) w = a; |
| 69 | if(((hb^0x7ff00000)|__LO(b))==0) w = b; |
| 70 | return w; |
| 71 | } |
| 72 | /* scale a and b by 2**-600 */ |
| 73 | ha -= 0x25800000; hb -= 0x25800000; k += 600; |
| 74 | __HI(a) = ha; |
| 75 | __HI(b) = hb; |
| 76 | } |
| 77 | if(hb < 0x20b00000) { /* b < 2**-500 */ |
| 78 | if(hb <= 0x000fffff) { /* subnormal b or 0 */ |
| 79 | if((hb|(__LO(b)))==0) return a; |
| 80 | t1=0; |
| 81 | __HI(t1) = 0x7fd00000; /* t1=2^1022 */ |
| 82 | b *= t1; |
| 83 | a *= t1; |
| 84 | k -= 1022; |
| 85 | } else { /* scale a and b by 2^600 */ |
| 86 | ha += 0x25800000; /* a *= 2^600 */ |
| 87 | hb += 0x25800000; /* b *= 2^600 */ |
| 88 | k -= 600; |
| 89 | __HI(a) = ha; |
| 90 | __HI(b) = hb; |
| 91 | } |
| 92 | } |
| 93 | /* medium size a and b */ |
| 94 | w = a-b; |
| 95 | if (w>b) { |
| 96 | t1 = 0; |
| 97 | __HI(t1) = ha; |
| 98 | t2 = a-t1; |
| 99 | w = ieee_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); |
| 100 | } else { |
| 101 | a = a+a; |
| 102 | y1 = 0; |
| 103 | __HI(y1) = hb; |
| 104 | y2 = b - y1; |
| 105 | t1 = 0; |
| 106 | __HI(t1) = ha+0x00100000; |
| 107 | t2 = a - t1; |
| 108 | w = ieee_sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); |
| 109 | } |
| 110 | if(k!=0) { |
| 111 | t1 = 1.0; |
| 112 | __HI(t1) += (k<<20); |
| 113 | return t1*w; |
| 114 | } else return w; |
| 115 | } |