author | Jan Vrany <jan.vrany@fit.cvut.cz> |
Tue, 11 Jun 2019 22:03:11 +0100 | |
changeset 3914 | 35aa88fa58c1 |
parent 2380 | 9195eccdcbd9 |
permissions | -rw-r--r-- |
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1 |
|
fa7400d022a0
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/* @(#)e_hypot.c 1.3 95/01/18 */ |
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/* |
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* ==================================================== |
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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* |
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* Developed at SunSoft, a Sun Microsystems, Inc. business. |
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8 |
* Permission to use, copy, modify, and distribute this |
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* software is freely granted, provided that this notice |
fa7400d022a0
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10 |
* is preserved. |
fa7400d022a0
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* ==================================================== |
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*/ |
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|
fa7400d022a0
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/* __ieee754_hypot(x,y) |
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* |
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* Method : |
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* If (assume round-to-nearest) z=x*x+y*y |
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* has error less than sqrt(2)/2 ulp, than |
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* sqrt(z) has error less than 1 ulp (exercise). |
fa7400d022a0
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20 |
* |
fa7400d022a0
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21 |
* So, compute sqrt(x*x+y*y) with some care as |
fa7400d022a0
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22 |
* follows to get the error below 1 ulp: |
fa7400d022a0
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* |
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24 |
* Assume x>y>0; |
fa7400d022a0
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* (if possible, set rounding to round-to-nearest) |
fa7400d022a0
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26 |
* 1. if x > 2y use |
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* x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y |
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* where x1 = x with lower 32 bits cleared, x2 = x-x1; else |
fa7400d022a0
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* 2. if x <= 2y use |
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30 |
* t1*y1+((x-y)*(x-y)+(t1*y2+t2*y)) |
fa7400d022a0
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31 |
* where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, |
fa7400d022a0
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32 |
* y1= y with lower 32 bits chopped, y2 = y-y1. |
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* |
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34 |
* NOTE: scaling may be necessary if some argument is too |
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* large or too tiny |
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36 |
* |
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37 |
* Special cases: |
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38 |
* hypot(x,y) is INF if x or y is +INF or -INF; else |
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39 |
* hypot(x,y) is NAN if x or y is NAN. |
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40 |
* |
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41 |
* Accuracy: |
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42 |
* hypot(x,y) returns sqrt(x^2+y^2) with error less |
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* than 1 ulps (units in the last place) |
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44 |
*/ |
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45 |
|
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46 |
#include "fdlibm.h" |
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47 |
|
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#ifdef __STDC__ |
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double __ieee754_hypot(double x, double y) |
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#else |
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double __ieee754_hypot(x,y) |
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double x, y; |
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53 |
#endif |
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{ |
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double a=x,b=y,t1,t2,y1,y2,w; |
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56 |
int j,k,ha,hb; |
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|
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ha = __HI(x)&0x7fffffff; /* high word of x */ |
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59 |
hb = __HI(y)&0x7fffffff; /* high word of y */ |
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if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} |
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__HI(a) = ha; /* a <- |a| */ |
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__HI(b) = hb; /* b <- |b| */ |
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if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ |
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64 |
k=0; |
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if(ha > 0x5f300000) { /* a>2**500 */ |
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66 |
if(ha >= 0x7ff00000) { /* Inf or NaN */ |
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w = a+b; /* for sNaN */ |
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if(((ha&0xfffff)|__LO(a))==0) w = a; |
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if(((hb^0x7ff00000)|__LO(b))==0) w = b; |
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return w; |
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71 |
} |
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72 |
/* scale a and b by 2**-600 */ |
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ha -= 0x25800000; hb -= 0x25800000; k += 600; |
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__HI(a) = ha; |
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__HI(b) = hb; |
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76 |
} |
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if(hb < 0x20b00000) { /* b < 2**-500 */ |
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if(hb <= 0x000fffff) { /* subnormal b or 0 */ |
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if((hb|(__LO(b)))==0) return a; |
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t1=0; |
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__HI(t1) = 0x7fd00000; /* t1=2^1022 */ |
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b *= t1; |
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a *= t1; |
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84 |
k -= 1022; |
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85 |
} else { /* scale a and b by 2^600 */ |
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86 |
ha += 0x25800000; /* a *= 2^600 */ |
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87 |
hb += 0x25800000; /* b *= 2^600 */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
88 |
k -= 600; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
89 |
__HI(a) = ha; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
90 |
__HI(b) = hb; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
91 |
} |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
92 |
} |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
93 |
/* medium size a and b */ |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
94 |
w = a-b; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
95 |
if (w>b) { |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
96 |
t1 = 0; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
97 |
__HI(t1) = ha; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
98 |
t2 = a-t1; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
99 |
w = sqrt(t1*t1-(b*(-b)-t2*(a+t1))); |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
100 |
} else { |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
101 |
a = a+a; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
102 |
y1 = 0; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
103 |
__HI(y1) = hb; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
104 |
y2 = b - y1; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
105 |
t1 = 0; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
106 |
__HI(t1) = ha+0x00100000; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
107 |
t2 = a - t1; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
108 |
w = sqrt(t1*y1-(w*(-w)-(t1*y2+t2*b))); |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
109 |
} |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
110 |
if(k!=0) { |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
111 |
t1 = 1.0; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
112 |
__HI(t1) += (k<<20); |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
113 |
return t1*w; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
114 |
} else return w; |
fa7400d022a0
Updated to https://swing.fit.cvut.cz/hg/stx.libjava/rev/31f8b995905e
Jan Vrany <jan.vrany@fit.cvut.cz>
parents:
diff
changeset
|
115 |
} |