Published
Edited
Oct 15, 2020
md`# ExtrapolateCumSumRatio`
ExtrapolateCumSumRatio(1000, 1e15, {PositionEstimate: 4e6, VelocityEstimate: 0}, {PositionEstimate: 1, VelocityEstimate: 0}) === 4e9
ExtrapolatedCumSumRatioEpsilon = BigInt(302231454903657293676544)
Ln = (v) => Math.log(10 + v.toString())
function ExtrapolateCumSumRatio (delta, relativeStart, estimateNum, estimateDenom) {
const deltaT = delta << 128
const t0 = relativeStart << 128
const position1 = estimateNum.PositionEstimate
const position2 = estimateDenom.PositionEstimate
const velocity1 = estimateNum.VelocityEstimate
const velocity2 = estimateDenom.VelocityEstimate
const squaredVelocity2 = (velocity1 * velocity2) >> 128
if (squaredVelocity2 > ExtrapolatedCumSumRatioEpsilon) {
let x2a = ((t0 * velocity2) >> 128) + position2
let x2b = ((deltaT * velocity2) >> 128) + x2a
x2a = Ln(x2a) // Q.128
x2b = Ln(x2b) // Q.128
let m1 = x2b - x2a
m1 = velocity2 * position1 * m1 // Q.128 * Q.128 * Q.128 => Q.384
m1 = m1 >> 128
let m2L = (x2a - x2b)
m2L = position2 * m2L // Q.128 * Q.128 => Q.256
let m2R = velocity2 * deltaT // Q.128 * Q.128 => Q.256
let m2 = m2L + m2R
m2 = velocity1 * m2 // Q.256 => Q.384
m2 = m2 >> 128 //Q.384 => Q.256
return (m1 + m2) / squaredVelocity2 // Q.256 / Q.128 => Q.128
}
let halfDeltaT = deltaT >> 1 // Q.128 / Q.0 => Q.128
let x1m = velocity1 * (t0 + halfDeltaT) // Q.128 * Q.128 => Q.256
x1m = x1m >> 128 // Q.256 => Q.128
x1m = position1 + x1m
let cumsumRatio = (x1m * deltaT) // Q.128 * Q.128 => Q.256
cumsumRatio = (cumsumRatio / position2) // Q.256 / Q.128 => Q.128
return cumsumRatio
}
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