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perf: Speedup Dec.Sqrt() (#16141)

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Dev Ojha 2023-05-15 12:34:13 +02:00 committed by GitHub
parent 793cbe5bfd
commit fb8ff071ca
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3 changed files with 47 additions and 13 deletions
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1
math/CHANGELOG.md
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@ -43,6 +43,7 @@ Ref: https://github.com/commitizen/conventional-commit-types/blob/v3.0.0/index.j
### Improvements
* [#15768](https://github.com/cosmos/cosmos-sdk/pull/15768) Removed the second call to the `init` method for the global variable `grand`.
* [#16141](https://github.com/cosmos/cosmos-sdk/pull/16141) Speedup `LegacyDec.ApproxRoot` and `LegacyDec.ApproxSqrt`.
## [math/v1.0.0](https://github.com/cosmos/cosmos-sdk/releases/tag/math/v1.0.0) - 2023-03-23

29
math/dec.go
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@ -220,6 +220,7 @@ func (d LegacyDec) LTE(d2 LegacyDec) bool { return (d.i).Cmp(d2.i) <= 0 }
func (d LegacyDec) Neg() LegacyDec { return LegacyDec{new(big.Int).Neg(d.i)} } // reverse the decimal sign
func (d LegacyDec) NegMut() LegacyDec { d.i.Neg(d.i); return d } // reverse the decimal sign, mutable
func (d LegacyDec) Abs() LegacyDec { return LegacyDec{new(big.Int).Abs(d.i)} } // absolute value
func (d LegacyDec) AbsMut() LegacyDec { d.i.Abs(d.i); return d } // absolute value, mutable
func (d LegacyDec) Set(d2 LegacyDec) LegacyDec { d.i.Set(d2.i); return d } // set to existing dec value
func (d LegacyDec) Clone() LegacyDec { return LegacyDec{new(big.Int).Set(d.i)} } // clone new dec
@ -442,24 +443,38 @@ func (d LegacyDec) ApproxRoot(root uint64) (guess LegacyDec, err error) {
return absRoot.NegMut(), err
}
if root == 1 || d.IsZero() || d.Equal(LegacyOneDec()) {
// One decimal, that we invalidate later. Helps us save a heap allocation.
scratchOneDec := LegacyOneDec()
if root == 1 || d.IsZero() || d.Equal(scratchOneDec) {
return d, nil
}
if root == 0 {
return LegacyOneDec(), nil
return scratchOneDec, nil
}
guess, delta := LegacyOneDec(), LegacyOneDec()
guess, delta := scratchOneDec, LegacyOneDec()
smallestDec := LegacySmallestDec()
for iter := 0; delta.Abs().GT(LegacySmallestDec()) && iter < maxApproxRootIterations; iter++ {
prev := guess.Power(root - 1)
for iter := 0; delta.AbsMut().GT(smallestDec) && iter < maxApproxRootIterations; iter++ {
// Set prev = guess^{root - 1}, with an optimization for sqrt
// where root=2 => prev = guess. (And thus no extra heap allocations)
prev := guess
if root != 2 {
prev = guess.Power(root - 1)
}
if prev.IsZero() {
prev = LegacySmallestDec()
prev = smallestDec
}
delta.Set(d).QuoMut(prev)
delta.SubMut(guess)
delta.QuoInt64Mut(int64(root))
// delta = delta / root.
// We optimize for sqrt, where root=2 => delta = delta >> 1
if root == 2 {
delta.i.Rsh(delta.i, 1)
} else {
delta.QuoInt64Mut(int64(root))
}
guess.AddMut(delta)
}

30
math/dec_test.go
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@ -453,12 +453,16 @@ func (s *decimalTestSuite) TestApproxSqrt() {
input math.LegacyDec
expected math.LegacyDec
}{
{math.LegacyOneDec(), math.LegacyOneDec()}, // 1.0 => 1.0
{math.LegacyNewDecWithPrec(25, 2), math.LegacyNewDecWithPrec(5, 1)}, // 0.25 => 0.5
{math.LegacyNewDecWithPrec(4, 2), math.LegacyNewDecWithPrec(2, 1)}, // 0.09 => 0.3
{math.LegacyNewDecFromInt(math.NewInt(9)), math.LegacyNewDecFromInt(math.NewInt(3))}, // 9 => 3
{math.LegacyNewDecFromInt(math.NewInt(-9)), math.LegacyNewDecFromInt(math.NewInt(-3))}, // -9 => -3
{math.LegacyNewDecFromInt(math.NewInt(2)), math.LegacyNewDecWithPrec(1414213562373095049, 18)}, // 2 => 1.414213562373095049
{math.LegacyOneDec(), math.LegacyOneDec()}, // 1.0 => 1.0
{math.LegacyNewDecWithPrec(25, 2), math.LegacyNewDecWithPrec(5, 1)}, // 0.25 => 0.5
{math.LegacyNewDecWithPrec(4, 2), math.LegacyNewDecWithPrec(2, 1)}, // 0.09 => 0.3
{math.LegacyNewDec(9), math.LegacyNewDecFromInt(math.NewInt(3))}, // 9 => 3
{math.LegacyNewDec(-9), math.LegacyNewDecFromInt(math.NewInt(-3))}, // -9 => -3
{math.LegacyNewDec(2), math.LegacyNewDecWithPrec(1414213562373095049, 18)}, // 2 => 1.414213562373095049
{ // 2^127 - 1 => 13043817825332782212.3495718062525083688 which rounds to 13043817825332782212.3495718062525083689
math.LegacyNewDec(2).Power(127).Sub(math.LegacyOneDec()),
math.LegacyMustNewDecFromStr("13043817825332782212.349571806252508369"),
},
}
for i, tc := range testCases {
@ -651,6 +655,20 @@ func BenchmarkLegacyQuoTruncateMut(b *testing.B) {
sink = (interface{})(nil)
}
func BenchmarkLegacySqrtOnMersennePrime(b *testing.B) {
b1 := math.LegacyNewDec(2).Power(127).Sub(math.LegacyOneDec())
b.ReportAllocs()
b.ResetTimer()
for i := 0; i < b.N; i++ {
sink, _ = b1.ApproxSqrt()
}
if sink == nil {
b.Fatal("Benchmark did not run")
}
sink = (interface{})(nil)
}
func BenchmarkLegacyQuoRoundupMut(b *testing.B) {
b1 := math.LegacyNewDec(17e2 + 8371)
b2 := math.LegacyNewDec(4371)