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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,145 @@ | ||
| package types | ||
|
|
||
| import ( | ||
| "errors" | ||
| "math/big" | ||
| "strings" | ||
|
|
||
| "github.com/shopspring/decimal" | ||
| ) | ||
|
|
||
| // DecimalFractional constant for decimal calculations | ||
| var DecimalFractional = decimal.NewFromBigInt(big.NewInt(1_000_000_000_000_000_000), 0) | ||
|
|
||
| // SubSign returns mod subtraction and boolean indicating if the result is negative | ||
| func SubSign(a, b decimal.Decimal) (decimal.Decimal, bool) { | ||
| if a.GreaterThanOrEqual(b) { | ||
| return a.Sub(b), false | ||
| } | ||
| return b.Sub(a), true | ||
| } | ||
|
|
||
| // Sqrt computes the square root of a decimal number using Newton's method. | ||
| func Sqrt(value decimal.Decimal, precision decimal.Decimal) (decimal.Decimal, error) { | ||
| if value.LessThan(decimal.Zero) { | ||
| return decimal.Decimal{}, errors.New("square root of negative number") | ||
| } | ||
|
|
||
| x := value.DivRound(decimal.NewFromInt(2), precision.Exponent()) | ||
| lastX := decimal.Zero | ||
|
|
||
| for x.Sub(lastX).Abs().GreaterThan(precision) { | ||
| lastX = x | ||
| x = decimal.Avg(x, value.Div(x)) | ||
| } | ||
|
|
||
| return x, nil | ||
| } | ||
|
|
||
| // CalculatePow computes base^(exp) using an approximation algorithm | ||
| func ApproximatePow(baseS, expS string, precisionS string) (decimal.Decimal, error) { | ||
| // Convert string to Decimal | ||
| base, err := decimal.NewFromString(baseS) | ||
| if err != nil { | ||
| return decimal.Decimal{}, err | ||
| } | ||
|
|
||
| exp, err := decimal.NewFromString(expS) | ||
| if err != nil { | ||
| return decimal.Decimal{}, err | ||
| } | ||
|
|
||
| precision, err := decimal.NewFromString(precisionS) | ||
| if err != nil { | ||
| return decimal.Decimal{}, err | ||
| } | ||
|
|
||
| if base.IsZero() && !exp.IsZero() { | ||
| return base, nil | ||
| } | ||
|
|
||
| if base.GreaterThan(decimal.NewFromInt(2)) { | ||
| return decimal.Decimal{}, errors.New("calculatePow: base must be less than 2") | ||
| } | ||
|
|
||
| integer := exp.Div(DecimalFractional).Floor() | ||
| fractional := exp.Mod(DecimalFractional) | ||
| integerPow := base.Pow(integer) | ||
|
|
||
| if fractional.IsZero() { | ||
| return integerPow, nil | ||
| } | ||
|
|
||
| fractionalPow, err := PowApprox(base, fractional, precision) | ||
| if err != nil { | ||
| return decimal.Decimal{}, err | ||
| } | ||
|
|
||
| result := integerPow.Mul(fractionalPow) | ||
| return result, nil | ||
| } | ||
|
|
||
| // PowApprox approximates power for fractional exponents | ||
| func PowApprox(base, exp, precision decimal.Decimal) (decimal.Decimal, error) { | ||
| if exp.Equals(decimal.NewFromInt(1).Div(decimal.NewFromInt(2))) { | ||
| sqrtBase, err := Sqrt(base, precision) | ||
| if err != nil { | ||
| return decimal.Decimal{}, err | ||
| } | ||
| return sqrtBase, nil | ||
| } | ||
|
|
||
| x, xNeg := SubSign(base, decimal.NewFromInt(1)) | ||
| term := decimal.NewFromInt(1) | ||
| sum := decimal.NewFromInt(1) | ||
| negative := false | ||
|
|
||
| a := exp | ||
| bigK := decimal.Zero | ||
| i := decimal.NewFromInt(1) | ||
|
|
||
| for term.GreaterThanOrEqual(precision) { | ||
| c, cNeg := SubSign(a, bigK) | ||
| bigK = i | ||
|
|
||
| newTerm := term.Mul(c).Mul(x).Div(bigK) | ||
| term = newTerm | ||
|
|
||
| if term.IsZero() { | ||
| break | ||
| } | ||
|
|
||
| if xNeg { | ||
| negative = !negative | ||
| } | ||
|
|
||
| if cNeg { | ||
| negative = !negative | ||
| } | ||
|
|
||
| if negative { | ||
| sum = sum.Sub(term) | ||
| } else { | ||
| sum = sum.Add(term) | ||
| } | ||
|
|
||
| i = i.Add(decimal.NewFromInt(1)) | ||
| } | ||
| fixedPoint := DecimalPlacesFromPrecision(precision) | ||
| return sum.RoundDown(fixedPoint), nil | ||
| } | ||
|
|
||
| // DecimalPlacesFromPrecision calculates the number of decimal places based on the precision decimal. | ||
| // DecimalPlacesFromPrecision calculates the number of decimal places based on the precision decimal. | ||
| func DecimalPlacesFromPrecision(precision decimal.Decimal) int32 { | ||
| // Convert precision to string using no fixed decimal places to avoid trailing zeros. | ||
| str := precision.String() | ||
| dotIndex := strings.IndexRune(str, '.') | ||
| if dotIndex != -1 { | ||
| // Remove trailing zeros to get the correct count of significant decimal places. | ||
| str = strings.TrimRight(str, "0") | ||
| // Count the number of characters after the decimal point to determine the scale. | ||
| return int32(len(str) - dotIndex - 1) | ||
| } | ||
| return 0 // Return 0 if there is no fractional part. | ||
| } |
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