#include "misc.h"
#include <math.h>
#include <stdlib.h> /* for size_t */

double kahan_sum(double *x, size_t n)
{
    /* Returns the sum of the elements of `x` using the Kahan summation algorithm.
     *
     * See https://en.wikipedia.org/wiki/Kahan_summation_algorithm. */
    size_t i;
    double sum, c, y, t;

    sum = 0.0;
    c = 0.0;
    for (i = 0; i < n; i++) {
        y = x[i] - c;
        t = sum + y;
        c = (t - sum) - y;
        sum = t;
    }

    return sum;
}

double interp1d(double x, double *xp, double *yp, size_t n)
{
    /* A fast interpolation routine which assumes that the values in `xp` are
     * evenly spaced.
     *
     * If x < xp[0] returns yp[0] and if x > xp[n-1] returns yp[n-1].  */
    size_t i;

    if (x < xp[0]) return yp[0];
    if (x > xp[n-1]) return yp[n-1];

    i = (x-xp[0])/(xp[1]-xp[0]);

    return yp[i] + (yp[i+1]-yp[i])*(x-xp[i])/(xp[i+1]-xp[i]);
}

int isclose(double a, double b, double rel_tol, double abs_tol)
{
    /* Returns 1 if a and b are "close". This algorithm is taken from Python's
     * math.isclose() function.
     *
     * See https://www.python.org/dev/peps/pep-0485/. */
    return fabs(a-b) <= fmax(rel_tol*fmax(fabs(a),fabs(b)),abs_tol);
}

int allclose(double *a, double *b, size_t n, double rel_tol, double abs_tol)
{
    /* Returns 1 if all the elements of a and b are "close". This algorithm is
     * taken from Python's math.isclose() function.
     *
     * See https://www.python.org/dev/peps/pep-0485/. */
    size_t i;

    for (i = 0; i < n; i++) {
        if (!isclose(a[i],b[i],rel_tol,abs_tol)) return 0;
    }

    return 1;
}

double logsumexp(double *a, size_t n)
{
    /* Returns the log of the sum of the exponentials of the array `a`.
     *
     * This function is designed to reduce underflow when the exponentials of
     * `a` are very small, for example when computing probabilities. */
    size_t i;
    double amax, sum;

    amax = a[0];
    for (i = 0; i < n; i++) {
        if (a[i] > amax) amax = a[i];
    }

    sum = 0.0;

    for (i = 0; i < n; i++) {
        sum += exp(a[i]-amax);
    }

    sum = log(sum);

    return amax + sum;
}

double norm(double x, double mu, double sigma)
{
    /* Returns the PDF for a gaussian random variable with mean `mu` and
     * standard deviation `sigma`. */
    return exp(-pow(x-mu,2)/(2*pow(sigma,2)))/(sqrt(2*M_PI)*sigma);
}

double norm_cdf(double x, double mu, double sigma)
{
    /* Returns the CDF for a gaussian random variable with mean `mu` and
     * standard deviation `sigma`. */
    return erfc(-(x-mu)/(sqrt(2)*sigma))/2.0;
}