135 lines
3.0 KiB
JavaScript
135 lines
3.0 KiB
JavaScript
Math.cos = function(a)
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{
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// Bring a into the 0 to +pi range without expensive branching.
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// Uses the symmetry that cos is even.
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a = (a + Math.PI) % (2*Math.PI);
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a = Math.abs((2*Math.PI + a) % (2*Math.PI) - Math.PI);
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// make b = 0 if a < pi/2 and b=1 if a > pi/2
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var b = (a-Math.PI/2) + Math.abs(a-Math.PI/2);
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b = b/(b+1e-30); // normalize b to one while avoiding divide by zero errors.
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// if a > pi/2 send a to pi-a, otherwise just send a to -a which has no effect
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// Using the symmetry cos(x) = -cos(pi-x) to bring a to the 0 to pi/2 range.
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a = b*Math.PI - a;
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var c = 1 - 2*b; // sign of the output
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// Taylor expansion about 0 with a correction term in the quadratic to make cos(pi/2)=0
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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))))));
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};
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Math.sin = function(a)
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{
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return Math.cos(a - Math.PI/2);
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};
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// Returns angle from -pi/2 to pi/2
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Math.atan = function(a)
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{
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var tanPiBy6 = 0.5773502691896257;
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var tanPiBy12 = 0.2679491924311227;
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var sign = 1;
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var inverted = false;
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var tanPiBy6Shift = 0;
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if (a < 0){
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// tan(x) = -tan(-x) so remove sign now and put it back at the end
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sign = -1;
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a *= -1;
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}
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if (a > 1)
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{
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// tan(pi/2 - x) = 1/tan(x)
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inverted = true;
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a = 1/a;
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}
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if (a > tanPiBy12)
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{
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// tan(x-pi/6) = (tan(x) - tan(pi/6)) / (1 + tan(pi/6)tan(x))
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tanPiBy6Shift = Math.PI/6;
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a = (a - tanPiBy6) / (1 + tanPiBy6*a);
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}
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// Now a will be in the range [-tan(pi/12), tan(pi/12)]
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// Use the taylor expansion around 0 with a correction to the linear term to match the pi/12 boundary
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// atan(x) = x - x^3/3 + x^5/5 - ...
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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)))))));
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// shift the result back where necessary
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r += tanPiBy6Shift;
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if (inverted)
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r = Math.PI/2 - r;
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return sign * r;
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};
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Math.atan2 = function(y,x)
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{
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// get unsigned x,y for ease of calculation, this means all angles are in the range [0, pi/2]
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var ux = Math.abs(x);
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var uy = Math.abs(y);
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// holds the result in the upper right quadrant
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var r;
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// Handle all edges cases to match the spec
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if (uy === 0)
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{
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r = 0;
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}
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else
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{
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if (ux === 0)
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{
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r = Math.PI / 2;
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}
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if (uy === Infinity)
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{
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if (ux === Infinity)
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r = Math.PI / 4;
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else
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r = Math.PI / 2;
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}
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else
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{
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if (ux === Infinity)
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r = 0;
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else
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r = Math.atan(uy/ux);
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}
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}
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// puts the result into the correct quadrant
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// 1/(-0) is the only way to determine the sign for a 0 value
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if (x < 0 || 1/x === -Infinity)
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{
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if (y < 0 || 1/y === -Infinity)
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return -Math.PI + r;
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else
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return Math.PI - r;
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}
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else
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{
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if (y < 0 || 1/y === -Infinity)
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return -r;
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else
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return r;
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}
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};
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Math.acos = function()
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{
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error("Math.acos() does not have a synchronization safe implementation");
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};
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Math.asin = function()
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{
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error("Math.asin() does not have a synchronization safe implementation");
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};
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Math.tan = function()
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{
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error("Math.tan() does not have a synchronization safe implementation");
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};
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