bcrc

# scale=6;
pi=4*a(1);
e=e(1);
phi=(1+sqrt(5))/2 # golden ratio
inch=25.4;

define sin(x) {
    if (x == pi/2) {
        return 1;
    }

    return s(x);
}

define cos(x) {
    if (x == pi/2) {
        return 0;
    }

    return c(x);
}

define tan(x) {
    if (x == pi/4) {
        return 1;
    }

    if (x == -pi/4) {
        return -1;
    }

    return s(x)/c(x);
}

define cot(x) {
    if (x == pi/4) {
        return 1;
    }

    if (x == -pi/4) {
        return -1;
    }

    return c(x)/s(x);
}

define sec(x) {
    return 1/cos(x);
}

define csc(x) {
    return 1/sin(x);
}

define asin(x) {
    if (x == 1) {
        return pi/2;
    }

    if (x == -1) {
        return -pi/2;
    }

    return a(x/sqrt(1-x^2));
}

define arcsin(x) {
    return asin(x);
}

define acos(x) {
    if (x == 0) {
        return pi/2;
    }

    if (x == 1) {
        return 0;
    }

    if (x == -1) {
        return pi/1;
    }

    if (x > 0) {
        return a(sqrt(1-x^2)/x);
    }

    return pi/1 - acos(-x);
}

define arccos(x) {
    return acos(x);
}

define atan(x) {
    if (x == 1) {
        return pi/4;
    }

    if (x == -1) {
        return -pi/4;
    }

    return a(x);
}

define arctan(x) {
    return a(x);
}

define acot(x) {
    return pi/2-atan(x);
}

define arccot(x) {
    return acot(x);
}

define asec(x) {
    if (x >= 1) {
        return a(sqrt(x^2-1));
    }

    return pi/1 - a(sqrt(x^2-1));
}

define arcsec(x) {
    return asec(x);
}

define acsc(x) {
    if (x == 1) {
        return pi/2;
    }

    if (x == -1) {
        return -pi/2;
    }

    if (x > 1) {
        return a(1/sqrt(x^2-1));
    }

    return -a(1/sqrt(x^2-1));
}

define arccsc(x) {
    return acsc(x);
}

define ln(x) {
    return l(x);
}

define log(a, b) {
    return l(b)/l(a);
}

define lg(x) {
    return log(10, x);
}

define log10(x) {
    return log(10, x);
}

define log2(x) {
    return log(2, x);
}

define pow(a, b) {
    if (scale(b) == 0) {
        return a ^ b;
    }
    return e(b*l(a));
}

define exp(x) {
    return e(x);
}

define cbrt(x) {
    return pow(x, 1/3);
}

define abs(x) {
    if (x < 0) {
        return -x;
    }
    return x;
}

define bessel(n, x) {
    return j(n,x);
}

define a(m, n) {
    if (n < 0) {
        return 0;
    }

    v = 1;
    for (i = 0; i < n; i++) {
        v *= (m - i);
    }
    return v;
}

define fac(n) {
    return a(n, n);
}

define c(m, n) {
    auto v

    if (n < 0) {
        return 0;
    }

    s = scale;
    scale = 0;
    v = a(m, n) / a(n, n);
    scale = s;
    return v;
}

define rad(deg) {
    return deg/180*pi;
}

define deg(rad) {
    return rad/pi*180;
}

define mod(x, y) {
    s = scale;
    scale = 0;
    ret = x % y;
    scale = s;
    return ret;
}

define min(x, y) {
    if (x < y) {
        return x;
    }
    return y;
}

define max(x, y) {
    if (x > y) {
        return x;
    }
    return y;
}

define time(h, m, s) {
    return 60 * (60 * h + m) + s;
}