Exp.cpp

#include "Headers.h"
#include "Exp.h"

int ExpMultErr(const double x, const double dx, const double y, const double dy, MathResult * result)
{
    const double ay  = fabs(y);

    if(y == 0.0)
    {
        result->val = 0.0;
        result->err = fabs(dy * exp(x));
        return MATH_SUCCESS;
    }
    else if((x < 0.5*MATH_LOG_DBL_MAX && x > 0.5*MATH_LOG_DBL_MIN) && (ay < 0.8*MATH_SQRT_DBL_MAX && ay > 1.2*MATH_SQRT_DBL_MIN))
    {
        double ex = exp(x);
        result->val  = y * ex;
        result->err  = ex * (fabs(dy) + fabs(y*dx));
        result->err += 2.0 * MATH_DBL_EPSILON * fabs(result->val);
        return MATH_SUCCESS;
    }
    else
    {
        const double ly  = log(ay);
        const double lnr = x + ly;

        if(lnr > MATH_LOG_DBL_MAX - 0.01)
        {
            OVERFLOW_ERROR(result);
        }
        else if(lnr < MATH_LOG_DBL_MIN + 0.01)
        {
            UNDERFLOW_ERROR(result);
        }
        else
        {
            const double sy  = MATH_SIGN(y);
            const double M   = floor(x);
            const double N   = floor(ly);
            const double a   = x  - M;
            const double b   = ly - N;
            const double eMN = exp(M+N);
            const double eab = exp(a+b);
            result->val  = sy * eMN * eab;
            result->err  = eMN * eab * 2.0*MATH_DBL_EPSILON;
            result->err += eMN * eab * fabs(dy/y);
            result->err += eMN * eab * fabs(dx);
            return MATH_SUCCESS;
        }
    }
}