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refactor(math) refactor ApproxRoot() for better read and perf #22226

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refactor(math) refactor ApproxRoot() for better read and perf #22226

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refactor:(ApproxRoot) refact ApproxRoot() for better read and perform…
Oct 11, 2024
4acafb5
Merge branch 'main' into main
shdhsj Oct 11, 2024
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38 changes: 27 additions & 11 deletions math/dec.go
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Original file line number Diff line number Diff line change
Expand Up @@ -472,28 +472,44 @@ func (d LegacyDec) ApproxRoot(root uint64) (guess LegacyDec, err error) {
return absRoot.NegMut(), err
}

// One decimal, that we invalidate later. Helps us save a heap allocation.
scratchOneDec := LegacyOneDec()
if root == 1 || d.IsZero() || d.Equal(scratchOneDec) {
// Special cases
if root == 1 || d.IsZero() {
return d, nil
}

// Handle d == 1 case
if d.Equal(LegacyOneDec()) {
return LegacyOneDec(), nil
}

if root == 0 {
return scratchOneDec, nil
return LegacyOneDec(), nil
}

guess, delta := scratchOneDec, LegacyOneDec()
// Initial guess (could improve with better heuristics)
guess = LegacyOneDec() // start with 1
// Constants
rootDec := LegacyDecFromInt64(int64(root))
rootMinusOne := root - 1

for iter := 0; iter < maxApproxRootIterations && delta.Abs().GT(smallestDec); iter++ {
prev := guess.Power(root - 1)
// Iteratively apply Newton's method
for iter := 0; iter < maxApproxRootIterations; iter++ {
// Compute guess^(root-1)
prev := guess.Power(rootMinusOne)
if prev.IsZero() {
prev = smallestDec
prev = smallestDec // avoid division by zero
}
delta.Set(d).QuoMut(prev)
delta.SubMut(guess)
delta.QuoInt64Mut(int64(root))

// delta = (d / guess^(root-1) - guess) / root
delta := d.Quo(prev).Sub(guess).Quo(rootDec)

// Update guess: guess = guess + delta
guess.AddMut(delta)

// If delta is small enough, break early (convergence)
if delta.Abs().LT(smallestDec) {
break
}
}
Comment on lines +495 to 513
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🛠️ Refactor suggestion

Refactored Newton's method improves performance and readability

The iterative application of Newton's method has been streamlined. Simplifying the calculation of delta and adding an effective convergence check with smallestDec enhances both performance and readability. The handling of potential division by zero with prev.IsZero() is appropriate.

Suggestion: To further align with the Uber Golang style guide, consider adding comments explaining the choice of smallestDec to avoid division by zero, and clarifying the convergence criteria.

Code Improvement: You might consider encapsulating the convergence criteria and the division by zero handling into separate helper functions to enhance modularity and readability.


return guess, nil
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