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/*
* transcendentals.c
*
* What is the value of acos(1.0000000001)?
* On the Mac you get the intended answer (0.0), but unix returns NaN.
* To guard against this sort of problem, the SnapPea kernel uses
*
* double safe_acos(double x);
* double safe_asin(double x);
* double safe_sqrt(double x);
*
* Incredibly enough, the standard ANSI libraries omit the
* inverse hyperbolic trig functions entirely.
*
* double arcsinh(double x);
* double arccosh(double x);
*
* Many (but not all) standard libraries now provide asinh() and acosh().
* I've changed the names of my homemade versions to arcsinh() and arccosh()
* to avoid conflicts. 2000/02/20 JRW
*/
#include "kernel.h"
#define ERROR_EPSILON 1e-3
double safe_acos(double x)
{
if (x > 1.0)
{
if (x > 1.0 + ERROR_EPSILON)
uFatalError("safe_acos", "transcendentals");
x = 1.0;
}
if (x < -1.0)
{
if (x < -(1.0 + ERROR_EPSILON))
uFatalError("safe_acos", "transcendentals");
x = -1.0;
}
return acos(x);
}
double safe_asin(double x)
{
if (x > 1.0)
{
if (x > 1.0 + ERROR_EPSILON)
uFatalError("safe_asin", "transcendentals");
x = 1.0;
}
if (x < -1.0)
{
if (x < -(1.0 + ERROR_EPSILON))
uFatalError("safe_asin", "transcendentals");
x = -1.0;
}
return asin(x);
}
double safe_sqrt(double x)
{
if (x < 0.0)
{
if (x < -ERROR_EPSILON)
uFatalError("safe_sqrt", "transcendentals");
x = 0.0;
}
return sqrt(x);
}
double arcsinh(
double x)
{
return log(x + sqrt(x*x + 1.0));
}
double arccosh(
double x)
{
if (x < 1.0)
{
if (x < 1.0 - ERROR_EPSILON)
uFatalError("arccosh", "transcendentals");
x = 1.0;
}
return log(x + sqrt(x*x - 1.0));
}
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