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32 changes: 32 additions & 0 deletions
32
exact-numbers/src/main/kotlin/xyz/lbres/exactnumbers/exactfraction/exactFractionHelpers.kt
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,32 @@ | ||
| package xyz.lbres.exactnumbers.exactfraction | ||
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| import xyz.lbres.kotlinutils.biginteger.ext.isNegative | ||
| import xyz.lbres.kotlinutils.biginteger.ext.isZero | ||
| import xyz.lbres.kotlinutils.biginteger.getGCD | ||
| import java.math.BigInteger | ||
|
|
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| /** | ||
| * Simplify numerator and denominator values to smallest values with same ratio, and move all negatives into numerator | ||
| * | ||
| * @param numerator [BigInteger]: numerator of fraction to simplify | ||
| * @param denominator [BigInteger]: denominator of fraction to simplify | ||
| * @return Pair<BigInteger, BigInteger>: pair where first value represents simplified numerator, and second value represents simplified denominator | ||
| */ | ||
| internal fun simplifyFraction(numerator: BigInteger, denominator: BigInteger): Pair<BigInteger, BigInteger> { | ||
| // set denominator to 1 when numerator is 0 | ||
| if (numerator.isZero()) { | ||
| return Pair(BigInteger.ZERO, BigInteger.ONE) | ||
| } | ||
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| // simplify using greatest common divisor | ||
| val gcd = getGCD(numerator, denominator) | ||
| val simplifiedNumerator = numerator / gcd | ||
| val simplifiedDenominator = denominator / gcd | ||
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| // move negatives to numerator | ||
| return if (denominator.isNegative()) { | ||
| Pair(-simplifiedNumerator, -simplifiedDenominator) | ||
| } else { | ||
| Pair(simplifiedNumerator, simplifiedDenominator) | ||
| } | ||
| } |
103 changes: 103 additions & 0 deletions
103
exact-numbers/src/main/kotlin/xyz/lbres/exactnumbers/exactfraction/exactFractionOperators.kt
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,103 @@ | ||
| package xyz.lbres.exactnumbers.exactfraction | ||
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| import java.math.BigInteger | ||
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| /** | ||
| * Add two ExactFractions | ||
| * | ||
| * @param ef1 [ExactFraction] | ||
| * @param ef2 [ExactFraction] | ||
| * @return [ExactFraction]: sum of [ef1] and [ef2] | ||
| */ | ||
| internal fun efAdd(ef1: ExactFraction, ef2: ExactFraction): ExactFraction { | ||
| if (ef1.denominator == ef2.denominator) { | ||
| val newNumerator = ef1.numerator + ef2.numerator | ||
| return ExactFraction(newNumerator, ef1.denominator) | ||
| } | ||
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| val newNumerator = ef1.numerator * ef2.denominator + ef2.numerator * ef1.denominator | ||
| val newDenominator = ef1.denominator * ef2.denominator | ||
| return ExactFraction(newNumerator, newDenominator) | ||
| } | ||
|
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| /** | ||
| * Multiply two ExactFractions | ||
| * | ||
| * @param ef1 [ExactFraction] | ||
| * @param ef2 [ExactFraction] | ||
| * @return [ExactFraction]: product of [ef1] and [ef2] | ||
| */ | ||
| internal fun efTimes(ef1: ExactFraction, ef2: ExactFraction): ExactFraction { | ||
| val newNumerator = ef1.numerator * ef2.numerator | ||
| val newDenominator = ef1.denominator * ef2.denominator | ||
| return ExactFraction(newNumerator, newDenominator) | ||
| } | ||
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| /** | ||
| * Apply exponent to an ExactFraction | ||
| * | ||
| * @param base [ExactFraction]: base of exponentiation | ||
| * @param exponent [ExactFraction]: exponent, must be a whole number | ||
| * @return [ExactFraction] | ||
| */ | ||
| internal fun efPow(base: ExactFraction, exponent: ExactFraction): ExactFraction { | ||
| // TODO | ||
| // if (!exponent.isWholeNumber()) { | ||
| if (exponent.denominator != BigInteger.ONE) { | ||
| throw ArithmeticException("Exponents must be whole numbers") | ||
| } | ||
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| when { | ||
| base == ExactFraction.ONE || exponent.isZero() -> return ExactFraction.ONE | ||
| base.isZero() -> return ExactFraction.ZERO | ||
| exponent == ExactFraction.ONE -> return base | ||
| } | ||
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| var powNumerator = BigInteger.ONE | ||
| var powDenominator = BigInteger.ONE | ||
| var remaining = exponent.numerator.abs() | ||
| val intMax = Int.MAX_VALUE | ||
|
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| try { | ||
| while (remaining > BigInteger.ZERO) { | ||
| if (remaining > intMax.toBigInteger()) { | ||
| powNumerator *= base.numerator.pow(intMax) | ||
| powDenominator *= base.denominator.pow(intMax) | ||
| remaining -= intMax.toBigInteger() | ||
| } else { | ||
| val exp = remaining.toInt() | ||
| powNumerator = base.numerator.pow(exp) | ||
| powDenominator = base.denominator.pow(exp) | ||
| remaining = BigInteger.ZERO | ||
| } | ||
| } | ||
| } catch (e: ArithmeticException) { | ||
| if (e.message == "BigInteger would overflow supported range") { | ||
| throw ExactFractionOverflowException() | ||
| } | ||
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| throw e | ||
| } | ||
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| return if (exponent.isNegative()) { | ||
| ExactFraction(powDenominator, powNumerator) | ||
| } else { | ||
| ExactFraction(powNumerator, powDenominator) | ||
| } | ||
| } | ||
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| /** | ||
| * Compare two ExactFractions | ||
| * | ||
| * @param ef1 [ExactFraction] | ||
| * @param ef2 [ExactFraction] | ||
| * @return [Int]: comparison of [ef1] to [ef2] | ||
| */ | ||
| internal fun efCompare(ef1: ExactFraction, ef2: ExactFraction): Int { | ||
| val difference = ef1 - ef2 | ||
| return when { | ||
| difference.isNegative() -> -1 | ||
| difference.isZero() -> 0 | ||
| else -> 1 | ||
| } | ||
| } |
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