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feat: monotonic sqrt big dec (#6053)
* feat: monotonic sqrt big dec * changelog
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,149 @@ | ||
| package osmomath | ||
|
|
||
| import ( | ||
| "math/big" | ||
| "math/rand" | ||
| "testing" | ||
|
|
||
| sdk "github.com/cosmos/cosmos-sdk/types" | ||
| "github.com/stretchr/testify/assert" | ||
| "github.com/stretchr/testify/require" | ||
| ) | ||
|
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||
| func generateRandomDecForEachBitlenBigDec(r *rand.Rand, numPerBitlen int) []BigDec { | ||
| return generateRandomDecForEachBitlen[BigDec](r, numPerBitlen, NewDecFromBigIntWithPrec, Precision) | ||
| } | ||
|
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||
| func TestSdkApproxSqrtVectors_BigDec(t *testing.T) { | ||
| testCases := []struct { | ||
| input BigDec | ||
| expected BigDec | ||
| }{ | ||
| {OneDec(), OneDec()}, // 1.0 => 1.0 | ||
| {NewDecWithPrec(25, 2), NewDecWithPrec(5, 1)}, // 0.25 => 0.5 | ||
| {NewDecWithPrec(4, 2), NewDecWithPrec(2, 1)}, // 0.09 => 0.3 | ||
| {NewDecFromInt(NewInt(9)), NewDecFromInt(NewInt(3))}, // 9 => 3 | ||
| {NewDecFromInt(NewInt(2)), MustNewDecFromStr("1.414213562373095048801688724209698079")}, // 2 => 1.414213562373095048801688724209698079 | ||
| {smallestBigDec, NewDecWithPrec(1, 18)}, // 10^-36 => 10^-18 | ||
| {smallestBigDec.MulInt64(3), NewDecWithPrec(1732050807568877294, 36)}, // 3*10^-36 => sqrt(3)*10^-18 | ||
| } | ||
|
|
||
| for i, tc := range testCases { | ||
| res, err := MonotonicSqrtBigDec(tc.input) | ||
| require.NoError(t, err) | ||
| require.Equal(t, tc.expected, res, "unexpected result for test case %d, input: %v", i, tc.input) | ||
| } | ||
| } | ||
|
|
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| func testMonotonicityAroundBigDec(t *testing.T, x BigDec) { | ||
| // test that sqrt(x) is monotonic around x | ||
| // i.e. sqrt(x-1) <= sqrt(x) <= sqrt(x+1) | ||
| sqrtX, err := MonotonicSqrtBigDec(x) | ||
| require.NoError(t, err) | ||
| sqrtXMinusOne, err := MonotonicSqrtBigDec(x.Sub(smallestBigDec)) | ||
| require.NoError(t, err) | ||
| sqrtXPlusOne, err := MonotonicSqrtBigDec(x.Add(smallestBigDec)) | ||
| require.NoError(t, err) | ||
| assert.True(t, sqrtXMinusOne.LTE(sqrtX), "sqrtXMinusOne: %s, sqrtX: %s", sqrtXMinusOne, sqrtX) | ||
| assert.True(t, sqrtX.LTE(sqrtXPlusOne), "sqrtX: %s, sqrtXPlusOne: %s", sqrtX, sqrtXPlusOne) | ||
| } | ||
|
|
||
| func TestSqrtMonotinicity_BigDec(t *testing.T) { | ||
| type testcase struct { | ||
| smaller BigDec | ||
| bigger BigDec | ||
| } | ||
| testCases := []testcase{ | ||
| {MustNewDecFromStr("120.120060020005000000"), MustNewDecFromStr("120.120060020005000001")}, | ||
| {smallestBigDec, smallestBigDec.MulInt64(2)}, | ||
| } | ||
| // create random test vectors for every bit-length | ||
| r := rand.New(rand.NewSource(rand.Int63())) | ||
| for i := 0; i < 255+sdk.DecimalPrecisionBits; i++ { | ||
| upperbound := big.NewInt(1) | ||
| upperbound.Lsh(upperbound, uint(i)) | ||
| for j := 0; j < 100; j++ { | ||
| v := big.NewInt(0).Rand(r, upperbound) | ||
| d := NewDecFromBigIntWithPrec(v, 36) | ||
| testCases = append(testCases, testcase{d, d.Add(smallestBigDec)}) | ||
| } | ||
| } | ||
| for i := 0; i < 1024; i++ { | ||
| d := NewDecWithPrec(int64(i), 18) | ||
| testCases = append(testCases, testcase{d, d.Add(smallestBigDec)}) | ||
| } | ||
|
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||
| for _, i := range testCases { | ||
| sqrtSmaller, err := MonotonicSqrtBigDec(i.smaller) | ||
| require.NoError(t, err, "smaller: %s", i.smaller) | ||
| sqrtBigger, err := MonotonicSqrtBigDec(i.bigger) | ||
| require.NoError(t, err, "bigger: %s", i.bigger) | ||
| assert.True(t, sqrtSmaller.LTE(sqrtBigger), "sqrtSmaller: %s, sqrtBigger: %s", sqrtSmaller, sqrtBigger) | ||
|
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||
| // separately sanity check that sqrt * sqrt >= input | ||
| sqrtSmallerSquared := sqrtSmaller.Mul(sqrtSmaller) | ||
| assert.True(t, sqrtSmallerSquared.GTE(i.smaller), "sqrt %s, sqrtSmallerSquared: %s, smaller: %s", sqrtSmaller, sqrtSmallerSquared, i.smaller) | ||
| } | ||
| } | ||
|
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||
| // Test that square(sqrt(x)) = x when x is a perfect square. | ||
| // We do this by sampling sqrt(v) from the set of numbers `a.b`, where a in [0, 2^128], b in [0, 10^9]. | ||
| // and then setting x = sqrt(v) | ||
| // this is because this is the set of values whose squares are perfectly representable. | ||
| func TestPerfectSquares_BigDec(t *testing.T) { | ||
| cases := []BigDec{ | ||
| NewBigDec(100), | ||
| } | ||
| r := rand.New(rand.NewSource(rand.Int63())) | ||
| tenToMin9 := big.NewInt(1_000_000_000) | ||
| for i := 0; i < 128; i++ { | ||
| upperbound := big.NewInt(1) | ||
| upperbound.Lsh(upperbound, uint(i)) | ||
| for j := 0; j < 100; j++ { | ||
| v := big.NewInt(0).Rand(r, upperbound) | ||
| dec := big.NewInt(0).Rand(r, tenToMin9) | ||
| d := NewDecFromBigInt(v).Add(NewDecFromBigIntWithPrec(dec, 9)) | ||
| cases = append(cases, d.MulMut(d)) | ||
| } | ||
| } | ||
|
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||
| for _, i := range cases { | ||
| sqrt, err := MonotonicSqrtBigDec(i) | ||
| require.NoError(t, err, "smaller: %s", i) | ||
| assert.Equal(t, i, sqrt.MulMut(sqrt)) | ||
| if !i.IsZero() { | ||
| testMonotonicityAroundBigDec(t, i) | ||
| } | ||
| } | ||
| } | ||
|
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||
| func TestSqrtRounding_BigDec(t *testing.T) { | ||
| testCases := []BigDec{ | ||
| MustNewDecFromStr("11662930532952632574132537947829685675668532938920838254939577167671385459971.396347723368091000"), | ||
| } | ||
| r := rand.New(rand.NewSource(rand.Int63())) | ||
| testCases = append(testCases, generateRandomDecForEachBitlenBigDec(r, 10)...) | ||
| for _, i := range testCases { | ||
| sqrt, err := MonotonicSqrtBigDec(i) | ||
| require.NoError(t, err, "smaller: %s", i) | ||
| // Sanity check that sqrt * sqrt >= input | ||
| sqrtSquared := sqrt.Mul(sqrt) | ||
| assert.True(t, sqrtSquared.GTE(i), "sqrt %s, sqrtSquared: %s, original: %s", sqrt, sqrtSquared, i) | ||
| // (aside) check that (sqrt - 1ulp)^2 <= input | ||
| sqrtMin1 := sqrt.Sub(smallestBigDec) | ||
| sqrtSquared = sqrtMin1.Mul(sqrtMin1) | ||
| assert.True(t, sqrtSquared.LTE(i), "sqrtMin1ULP %s, sqrtSquared: %s, original: %s", sqrt, sqrtSquared, i) | ||
| } | ||
| } | ||
|
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||
| // benchmarks the new square root across bit-lengths, for comparison with the SDK square root. | ||
| func BenchmarkMonotonicSqrt_BigDec(b *testing.B) { | ||
| r := rand.New(rand.NewSource(1)) | ||
| vectors := generateRandomDecForEachBitlenBigDec(r, 1) | ||
| for i := 0; i < b.N; i++ { | ||
| for j := 0; j < len(vectors); j++ { | ||
| a, _ := MonotonicSqrtBigDec(vectors[j]) | ||
| _ = a | ||
| } | ||
| } | ||
| } |
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