Math.cos = function(a)
{
    // Bring a into the 0 to +pi range without expensive branching.
    // Uses the symmetry that cos is even.
    a = (a + Math.PI) % (2*Math.PI);
    a = Math.abs((2*Math.PI + a) % (2*Math.PI) - Math.PI);

    // make b = 0 if a < pi/2 and b=1 if a > pi/2
    var b = (a-Math.PI/2) + Math.abs(a-Math.PI/2);
    b = b/(b+1e-30); // normalize b to one while avoiding divide by zero errors.

    // if a > pi/2 send a to pi-a, otherwise just send a to -a which has no effect
    // Using the symmetry cos(x) = -cos(pi-x) to bring a to the 0 to pi/2 range.
    a = b*Math.PI - a;

    var c = 1 - 2*b; // sign of the output

    // Taylor expansion about 0 with a correction term in the quadratic to make cos(pi/2)=0
    return c * (1 - a*a*(0.5000000025619951 - a*a*(1/24 - a*a*(1/720 - a*a*(1/40320 - a*a*(1/3628800 - a*a/479001600))))));
};

Math.sin = function(a)
{
    return Math.cos(a - Math.PI/2);
};

// Returns angle from -pi/2 to pi/2
Math.atan = function(a)
{
    var tanPiBy6 = 0.5773502691896257;
    var tanPiBy12 = 0.2679491924311227;
    var sign = 1;
    var inverted = false;
    var tanPiBy6Shift = 0;

    if (a < 0){
        // tan(x) = -tan(-x) so remove sign now and put it back at the end
        sign = -1;
        a *= -1;
    }

    if (a > 1)
    {
        // tan(pi/2 - x) = 1/tan(x)
        inverted = true;
        a = 1/a;
    }

    if (a > tanPiBy12)
    {
        // tan(x-pi/6) = (tan(x) - tan(pi/6)) / (1 + tan(pi/6)tan(x))
        tanPiBy6Shift = Math.PI/6;
        a = (a - tanPiBy6) / (1 + tanPiBy6*a);
    }
    // Now a will be in the range [-tan(pi/12), tan(pi/12)]

    // Use the taylor expansion around 0 with a correction to the linear term to match the pi/12 boundary
    // atan(x) = x - x^3/3 + x^5/5 - ...
    var r = a*(1.0000000000390272 - a*a*(1/3 - a*a*(1/5 - a*a*(1/7 - a*a*(1/9 - a*a*(1/11 - a*a*(1/13 - a*a/15)))))));

    // shift the result back where necessary
    r += tanPiBy6Shift;
    if (inverted)
        r = Math.PI/2 - r;
    return sign * r;
};

Math.atan2 = function(y,x)
{
    // get unsigned x,y for ease of calculation, this means all angles are in the range [0, pi/2]
    var ux = Math.abs(x);
    var uy = Math.abs(y);
    // holds the result in the upper right quadrant
    var r;

    // Handle all edges cases to match the spec
    if (uy === 0)
    {
        r = 0;
    }
    else
    {
        if (ux === 0)
        {
            r = Math.PI / 2;
        }
        if (uy === Infinity)
        {
            if (ux === Infinity)
                r = Math.PI / 4;
            else
                r = Math.PI / 2;
        }
        else
        {
            if (ux === Infinity)
                r = 0;
            else
                r = Math.atan(uy/ux);
        }
    }

    // puts the result into the correct quadrant
    // 1/(-0) is the only way to determine the sign for a 0 value
    if (x < 0 || 1/x === -Infinity)
    {
        if (y < 0 || 1/y === -Infinity)
            return -Math.PI + r;
        else
            return Math.PI - r;
    }
    else
    {
        if (y < 0 || 1/y === -Infinity)
            return -r;
        else
            return r;
    }
};

Math.acos = function()
{
    error("Math.acos() does not have a synchronization safe implementation");
};

Math.asin = function()
{
    error("Math.asin() does not have a synchronization safe implementation");
};

Math.tan = function()
{
    error("Math.tan() does not have a synchronization safe implementation");
};

Math.pow = function(base, e)
{
    if (Math.round(e) == e)
    {
        if (e >= 0)
        {
            var a = Math.intPow(base, e);
        }
        else
        {
            var a = 1 / Math.intPow(base, -e);
        }
    }
    else
    {
        var a = Math.exp(e*Math.ln(base));
    }
    warn(base+" ^ "+e+" = "+a);
    return a;
}

Math.exp = function(x)
{
    if (x < 0)
    {
        var iPart = 1/Math.intPow(Math.E, -Math.floor(x));
    }
    else
    {
        var iPart = Math.intPow(Math.E, Math.floor(x));
    }

    x = x - Math.floor(x);
    // x \in [0,1)

    if (x == 0)
        // no need to loop if we know the answer
        return iPart;

    // taylor series around 0
    var fPart =1+x*(1+x*(1+x*(1+x*(1+x*(1+x*(1+x*(1+x*(1+x*(1+x/10)/9)/8)/7)/6)/5)/4)/3)/2);

    return iPart*fPart;
}

Math.ln = function(x)
{
    // the binary logarithm of e
    var lb_e = 1.442695040888963407359924681001892137426645954152985934135449;
    return Math.lb(x) / lb_e;
}

/**
 * binary log implementation
 *
 * based on http://en.wikipedia.org/wiki/Binary_logarithm#Real_number
 */
Math.lb = function(x)
{
    if (x <= 0)
    {
        return -Infinity;
    }

    // calculate to 20 fractional bits
    var precisionBits = 20;

    // calculate integer log, rounded down
    // when implemented in C, just count the number of bits before the fraction
    // without leading zeros. This may be negative.
    var log = 0;
    if (x >= 1)
    {
        for (var i = 1; i <= x; i *= 2)
        {
            log++;
        }
        log--;
        i /= 2;
    }
    else
    {
        for (var i = 1; i > x; i /= 2)
        {
            log--;
        }
    }
    // now lb(x) = log + lb(y) with y = x/i. So y \in [1,2)

    var y = x/i;

    if (y <= 1)
        // we're done, or there's a minimal rounding error, and we should be done
        return log;

    var m = 0;
    var add = 1;
    while (true)
    {
        while (m <= precisionBits && y < 4)
        {
            m++;
            y *= y;
            add /= 2;
        }
        if (m > precisionBits)
            break;
        log += add;
        y /= 2;
    }

    return log;

}
/**
 * calculate the power for positive integer exponents
 */
Math.intPow = function(base, exp)
{
    var powers = [base];
    var binary = [1];
    var i = 0;
    for (var e = 2; e <= exp; e *= 2)
    {
        // calculate base^i, using base^(i/2)
        powers.push(powers[i]*powers[i]);
        binary.push(e);
        i++;
    }

    var result = 1;

    var i = binary.length;

    while (exp > 0)
    {
        if (binary[--i] <= exp)
        {
            result *= powers[i];
            exp -= binary[i];
        }
    }

    return result;

}