Published
Edited
Jul 19, 2019
4 stars
RationalAngleAccumulator = () => {
const
running_angle = Ratio(0, 1),
running_angle_int = running_angle[int32buffer],
angle = Ratio(0, 1),
angle_int = angle[int32buffer],
compose_angle = (numerator, denominator=1, half_turns=0) => {
angle[0] = numerator;
angle[1] = denominator;
angle_int[4] = half_turns;
normalize_ratio(angle);
const rp = running_angle[0], rq = running_angle[1]; // temporary copy
running_angle[0] = angle[0] * rq + rp * angle[1];
running_angle[1] = rq * angle[1] - angle[0] * rp;
running_angle_int[4] += angle_int[4]; // sum winding numbers
normalize_ratio(running_angle);
},
unit_complex = () => {
const
out = new Float64Array(2),
half_turn = 1 - ((running_angle_int[4] & 1) << 1),
scale = half_turn / Math.hypot(running_angle[0], running_angle[1]);
out[0] = running_angle[1] * scale, out[1] = running_angle[0] * scale;
return out;
},
tangent = () => {
return running_angle[0] / running_angle[1];
},
angle_measure = () => {
return (
Math.PI * running_angle_int[4] +
Math.atan2(running_angle[0], running_angle[1]));
},
angle_measure_degrees = () => {
return (
180 * running_angle_int[4] +
DEGREES * Math.atan2(running_angle[0], running_angle[1]));
};
return {
running_angle,
compose_angle,
unit_complex,
tangent,
angle_measure,
angle_measure_degrees,
}
}
{ // Example
const running_angle = RationalAngleAccumulator();
for (let i = 0; i < 15; i++) {
running_angle.compose_angle(1,1);
}
return [running_angle.angle_measure_degrees(), running_angle.tangent(), running_angle.unit_complex()];
}
normalize_ratio(Ratio(0x10000000000000,1))
normalize_ratio = {
const
EMASK = 0x7ff00000, // 0111 1111 1111 0000 0000 0000 0000 0000
ETOP = 0x7f000000, // 0111 1111 0000 0000 0000 0000 0000 0000
SMASK = 0x80000000, // 1000 0000 0000 0000 0000 0000 0000 0000
ONE = 0x3ff00000, // 0011 1111 1111 0000 0000 0000 0000 0000
offset_float = new Float64Array([1.0]),
offset_int = new Int32Array(offset_float.buffer);
return function normalize_ratio(ratio) {
const
intbuf = ratio[int32buffer],
p = ratio[0],
q = ratio[1],
pe = intbuf[1] & EMASK, // p exponent
qe = intbuf[3] & EMASK, // q exponent
ps = intbuf[1] & SMASK, // p sign
qs = intbuf[3] & SMASK; // q sign
if ((pe === EMASK) | (q === 0)) { // Check for x:0, ∞:x, NaN:x
if (isNaN(p) | (qe === EMASK) | (p === 0)) {
ratio[0] = NaN, ratio[1] = NaN;
return ratio; }
intbuf[0] = 0, intbuf[1] = ONE; // set ratio to 1:0
intbuf[2] = 0, intbuf[3] = 0;
intbuf[4] -= ps >>> 31; // subtract 1 from winding number in -1:0 case
return ratio;
}
intbuf[4] += (qs >>> 31) * (1 - (ps >>> 30)) // add sign of p to winding number if q < 0
if ((qe === EMASK) | (p === 0)) { // Check for 0:x, x:∞, x:NaN
if (isNaN(q) | (pe === EMASK) | (q === 0)) {
ratio[0] = NaN, ratio[1] = NaN;
return ratio; }
intbuf[0] = 0, intbuf[1] = 0;
intbuf[2] = 0, intbuf[3] = ONE; // set ratio to 0:1
return ratio;
}
offset_int[1] = ((ETOP - (pe + qe >>> 1)) & EMASK) + qs;
ratio[0] *= offset_float[0];
ratio[1] *= offset_float[0];
return ratio;
}
}
int32buffer = Symbol('int32buffer');
Ratio = (p, q, half_turns=0) => {
const
intbuf = new Int32Array(5),
ratio = new Float64Array(intbuf.buffer, 0, 2);
ratio[0] = p;
ratio[1] = q;
intbuf[4] = half_turns;
ratio[int32buffer] = intbuf;
return ratio;
}
DEGREES = 180 / Math.PI
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