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102 lines
2.9 KiB
C
102 lines
2.9 KiB
C
/* Copyright (C) 1995 DJ Delorie, see COPYING.DJ for details */
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/*
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* hypot() function for DJGPP.
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*
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* hypot() computes sqrt(x^2 + y^2). The problem with the obvious
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* naive implementation is that it might fail for very large or
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* very small arguments. For instance, for large x or y the result
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* might overflow even if the value of the function should not,
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* because squaring a large number might trigger an overflow. For
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* very small numbers, their square might underflow and will be
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* silently replaced by zero; this won't cause an exception, but might
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* have an adverse effect on the accuracy of the result.
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*
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* This implementation tries to avoid the above pitfals, without
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* inflicting too much of a performance hit.
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*
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*/
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#include <precomp.h>
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#if (_MSC_VER >= 1920)
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#pragma function(_hypot)
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#endif
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/* Approximate square roots of DBL_MAX and DBL_MIN. Numbers
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between these two shouldn't neither overflow nor underflow
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when squared. */
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#define __SQRT_DBL_MAX 1.3e+154
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#define __SQRT_DBL_MIN 2.3e-162
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/*
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* @implemented
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*/
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double
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_hypot(double x, double y)
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{
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double abig = fabs(x), asmall = fabs(y);
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double ratio;
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/* Make abig = max(|x|, |y|), asmall = min(|x|, |y|). */
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if (abig < asmall)
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{
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double temp = abig;
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abig = asmall;
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asmall = temp;
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}
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/* Trivial case. */
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if (asmall == 0.)
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return abig;
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/* Scale the numbers as much as possible by using its ratio.
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For example, if both ABIG and ASMALL are VERY small, then
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X^2 + Y^2 might be VERY inaccurate due to loss of
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significant digits. Dividing ASMALL by ABIG scales them
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to a certain degree, so that accuracy is better. */
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if ((ratio = asmall / abig) > __SQRT_DBL_MIN && abig < __SQRT_DBL_MAX)
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return abig * sqrt(1.0 + ratio*ratio);
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else
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{
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/* Slower but safer algorithm due to Moler and Morrison. Never
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produces any intermediate result greater than roughly the
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larger of X and Y. Should converge to machine-precision
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accuracy in 3 iterations. */
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double r = ratio*ratio, t, s, p = abig, q = asmall;
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do {
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t = 4. + r;
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if (t == 4.)
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break;
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s = r / t;
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p += 2. * s * p;
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q *= s;
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r = (q / p) * (q / p);
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} while (1);
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return p;
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}
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}
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#ifdef TEST
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#include <msvcrt/stdio.h>
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int
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main(void)
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{
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printf("hypot(3, 4) =\t\t\t %25.17e\n", _hypot(3., 4.));
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printf("hypot(3*10^150, 4*10^150) =\t %25.17g\n", _hypot(3.e+150, 4.e+150));
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printf("hypot(3*10^306, 4*10^306) =\t %25.17g\n", _hypot(3.e+306, 4.e+306));
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printf("hypot(3*10^-320, 4*10^-320) =\t %25.17g\n",_hypot(3.e-320, 4.e-320));
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printf("hypot(0.7*DBL_MAX, 0.7*DBL_MAX) =%25.17g\n",_hypot(0.7*DBL_MAX, 0.7*DBL_MAX));
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printf("hypot(DBL_MAX, 1.0) =\t\t %25.17g\n", _hypot(DBL_MAX, 1.0));
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printf("hypot(1.0, DBL_MAX) =\t\t %25.17g\n", _hypot(1.0, DBL_MAX));
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printf("hypot(0.0, DBL_MAX) =\t\t %25.17g\n", _hypot(0.0, DBL_MAX));
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return 0;
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}
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#endif
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