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Feature: Polynomials and rational functions #469

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lounres merged 132 commits from feature/polynomials into dev 2022-07-28 18:04:06 +03:00
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6 changed files with 181 additions and 68 deletions
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39
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractPolynomial.kt
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@ -71,19 +71,19 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
* *
* The operation is equivalent to adding [other] copies of unit polynomial to [this]. * The operation is equivalent to adding [other] copies of unit polynomial to [this].
*/ */
public operator fun P.plus(other: Int): P = optimizedAddMultiplied(this, one, other) public operator fun P.plus(other: Int): P = addMultipliedBySquaring(this, one, other)
/** /**
* Returns difference between the polynomial and the integer represented as polynomial. * Returns difference between the polynomial and the integer represented as polynomial.
* *
* The operation is equivalent to subtraction [other] copies of unit polynomial from [this]. * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
*/ */
public operator fun P.minus(other: Int): P = optimizedAddMultiplied(this, one, -other) public operator fun P.minus(other: Int): P = addMultipliedBySquaring(this, one, -other)
/** /**
* Returns product of the polynomial and the integer represented as polynomial. * Returns product of the polynomial and the integer represented as polynomial.
* *
* The operation is equivalent to sum of [other] copies of [this]. * The operation is equivalent to sum of [other] copies of [this].
*/ */
public operator fun P.times(other: Int): P = optimizedMultiply(this, other) public operator fun P.times(other: Int): P = multiplyBySquaring(this, other)
// endregion // endregion
// region Integer-polynomial relation // region Integer-polynomial relation
@ -92,19 +92,19 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
* *
* The operation is equivalent to adding [this] copies of unit polynomial to [other]. * The operation is equivalent to adding [this] copies of unit polynomial to [other].
*/ */
public operator fun Int.plus(other: P): P = optimizedAddMultiplied(other, one, this) public operator fun Int.plus(other: P): P = addMultipliedBySquaring(other, one, this)
/** /**
* Returns difference between the integer represented as polynomial and the polynomial. * Returns difference between the integer represented as polynomial and the polynomial.
* *
* The operation is equivalent to subtraction [this] copies of unit polynomial from [other]. * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
*/ */
public operator fun Int.minus(other: P): P = optimizedAddMultiplied(-other, one, this) public operator fun Int.minus(other: P): P = addMultipliedBySquaring(-other, one, this)
/** /**
* Returns product of the integer represented as polynomial and the polynomial. * Returns product of the integer represented as polynomial and the polynomial.
* *
* The operation is equivalent to sum of [this] copies of [other]. * The operation is equivalent to sum of [this] copies of [other].
*/ */
public operator fun Int.times(other: P): P = optimizedMultiply(other, this) public operator fun Int.times(other: P): P = multiplyBySquaring(other, this)
// endregion // endregion
// region Constant-constant relation // region Constant-constant relation
@ -138,6 +138,12 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
@JvmName("constantTimes") @JvmName("constantTimes")
@JsName("constantTimes") @JsName("constantTimes")
public operator fun C.times(other: C): C public operator fun C.times(other: C): C
/**
* Raises [arg] to the integer power [exponent].
*/
@JvmName("constantPower")
@JsName("constantPower")
public fun power(arg: C, exponent: UInt) : C
/** /**
* Check if the instant is zero constant. * Check if the instant is zero constant.
@ -225,6 +231,10 @@ public interface AbstractPolynomialSpace<C, P: AbstractPolynomial<C>> : Ring<P>
* Returns product of the polynomials. * Returns product of the polynomials.
*/ */
public override operator fun P.times(other: P): P public override operator fun P.times(other: P): P
/**
* Raises [arg] to the integer power [exponent].
*/
public override fun power(arg: P, exponent: UInt) : P = exponentiationBySquaring(arg, exponent)
/** /**
* Check if the instant is zero polynomial. * Check if the instant is zero polynomial.
@ -331,19 +341,19 @@ public interface AbstractPolynomialSpaceOverRing<C, P: AbstractPolynomial<C>, A:
* *
* The operation is equivalent to adding [other] copies of unit of underlying ring to [this]. * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
*/ */
public override operator fun C.plus(other: Int): C = ring { optimizedAddMultiplied(this@plus, one, other) } public override operator fun C.plus(other: Int): C = ring { addMultipliedBySquaring(this@plus, one, other) }
/** /**
* Returns difference between the constant and the integer represented as constant (member of underlying ring). * Returns difference between the constant and the integer represented as constant (member of underlying ring).
* *
* The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this]. * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
*/ */
public override operator fun C.minus(other: Int): C = ring { optimizedAddMultiplied(this@minus, one, -other) } public override operator fun C.minus(other: Int): C = ring { addMultipliedBySquaring(this@minus, one, -other) }
/** /**
* Returns product of the constant and the integer represented as constant (member of underlying ring). * Returns product of the constant and the integer represented as constant (member of underlying ring).
* *
* The operation is equivalent to sum of [other] copies of [this]. * The operation is equivalent to sum of [other] copies of [this].
*/ */
public override operator fun C.times(other: Int): C = ring { optimizedMultiply(this@times, other) } public override operator fun C.times(other: Int): C = ring { multiplyBySquaring(this@times, other) }
// endregion // endregion
// region Integer-constant relation // region Integer-constant relation
@ -352,19 +362,19 @@ public interface AbstractPolynomialSpaceOverRing<C, P: AbstractPolynomial<C>, A:
* *
* The operation is equivalent to adding [this] copies of unit of underlying ring to [other]. * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
*/ */
public override operator fun Int.plus(other: C): C = ring { optimizedAddMultiplied(other, one, this@plus) } public override operator fun Int.plus(other: C): C = ring { addMultipliedBySquaring(other, one, this@plus) }
/** /**
* Returns difference between the integer represented as constant (member of underlying ring) and the constant. * Returns difference between the integer represented as constant (member of underlying ring) and the constant.
* *
* The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other]. * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
*/ */
public override operator fun Int.minus(other: C): C = ring { optimizedAddMultiplied(-other, one, this@minus) } public override operator fun Int.minus(other: C): C = ring { addMultipliedBySquaring(-other, one, this@minus) }
/** /**
* Returns product of the integer represented as constant (member of underlying ring) and the constant. * Returns product of the integer represented as constant (member of underlying ring) and the constant.
* *
* The operation is equivalent to sum of [this] copies of [other]. * The operation is equivalent to sum of [this] copies of [other].
*/ */
public override operator fun Int.times(other: C): C = ring { optimizedMultiply(other, this@times) } public override operator fun Int.times(other: C): C = ring { multiplyBySquaring(other, this@times) }
// endregion // endregion
// region Constant-constant relation // region Constant-constant relation
@ -388,6 +398,11 @@ public interface AbstractPolynomialSpaceOverRing<C, P: AbstractPolynomial<C>, A:
*/ */
@JvmName("constantTimes") @JvmName("constantTimes")
public override operator fun C.times(other: C): C = ring { this@times * other } public override operator fun C.times(other: C): C = ring { this@times * other }
/**
* Raises [arg] to the integer power [exponent].
*/
@JvmName("constantPower")
override fun power(arg: C, exponent: UInt): C = ring { power(arg, exponent) }
/** /**
* Instance of zero constant (zero of the underlying ring). * Instance of zero constant (zero of the underlying ring).

52
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/AbstractRationalFunction.kt
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@ -120,19 +120,19 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
* *
* The operation is equivalent to adding [other] copies of unit polynomial to [this]. * The operation is equivalent to adding [other] copies of unit polynomial to [this].
*/ */
public operator fun R.plus(other: Int): R = optimizedAddMultiplied(this, one, other) public operator fun R.plus(other: Int): R = addMultipliedBySquaring(this, one, other)
/** /**
* Returns difference between the rational function and the integer represented as rational function. * Returns difference between the rational function and the integer represented as rational function.
* *
* The operation is equivalent to subtraction [other] copies of unit polynomial from [this]. * The operation is equivalent to subtraction [other] copies of unit polynomial from [this].
*/ */
public operator fun R.minus(other: Int): R = optimizedAddMultiplied(this, one, -other) public operator fun R.minus(other: Int): R = addMultipliedBySquaring(this, one, -other)
/** /**
* Returns product of the rational function and the integer represented as rational function. * Returns product of the rational function and the integer represented as rational function.
* *
* The operation is equivalent to sum of [other] copies of [this]. * The operation is equivalent to sum of [other] copies of [this].
*/ */
public operator fun R.times(other: Int): R = optimizedMultiply(this, other) public operator fun R.times(other: Int): R = multiplyBySquaring(this, other)
// endregion // endregion
// region Integer-Rational relation // region Integer-Rational relation
@ -141,19 +141,19 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
* *
* The operation is equivalent to adding [this] copies of unit polynomial to [other]. * The operation is equivalent to adding [this] copies of unit polynomial to [other].
*/ */
public operator fun Int.plus(other: R): R = optimizedAddMultiplied(other, one, this) public operator fun Int.plus(other: R): R = addMultipliedBySquaring(other, one, this)
/** /**
* Returns difference between the integer represented as rational function and the rational function. * Returns difference between the integer represented as rational function and the rational function.
* *
* The operation is equivalent to subtraction [this] copies of unit polynomial from [other]. * The operation is equivalent to subtraction [this] copies of unit polynomial from [other].
*/ */
public operator fun Int.minus(other: R): R = optimizedAddMultiplied(-other, one, this) public operator fun Int.minus(other: R): R = addMultipliedBySquaring(-other, one, this)
/** /**
* Returns product of the integer represented as rational function and the rational function. * Returns product of the integer represented as rational function and the rational function.
* *
* The operation is equivalent to sum of [this] copies of [other]. * The operation is equivalent to sum of [this] copies of [other].
*/ */
public operator fun Int.times(other: R): R = optimizedMultiply(other, this) public operator fun Int.times(other: R): R = multiplyBySquaring(other, this)
// endregion // endregion
// region Constant-constant relation // region Constant-constant relation
@ -187,6 +187,12 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
@JvmName("constantTimes") @JvmName("constantTimes")
@JsName("constantTimes") @JsName("constantTimes")
public operator fun C.times(other: C): C public operator fun C.times(other: C): C
/**
* Raises [arg] to the integer power [exponent].
*/
@JvmName("constantPower")
@JsName("constantPower")
public fun power(arg: C, exponent: UInt) : C
/** /**
* Check if the instant is zero constant. * Check if the instant is zero constant.
@ -274,6 +280,10 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
* Returns product of the polynomials. * Returns product of the polynomials.
*/ */
public operator fun P.times(other: P): P public operator fun P.times(other: P): P
/**
* Raises [arg] to the integer power [exponent].
*/
public fun power(arg: P, exponent: UInt) : P
/** /**
* Check if the instant is zero polynomial. * Check if the instant is zero polynomial.
@ -400,6 +410,10 @@ public interface AbstractRationalFunctionalSpace<C, P: AbstractPolynomial<C>, R:
* Returns product of the rational functions. * Returns product of the rational functions.
*/ */
public override operator fun R.times(other: R): R public override operator fun R.times(other: R): R
/**
* Raises [arg] to the integer power [exponent].
*/
public override fun power(arg: R, exponent: UInt) : R = exponentiationBySquaring(arg, exponent)
/** /**
* Check if the instant is zero rational function. * Check if the instant is zero rational function.
@ -536,19 +550,19 @@ public interface AbstractRationalFunctionalSpaceOverRing<C, P: AbstractPolynomia
* *
* The operation is equivalent to adding [other] copies of unit of underlying ring to [this]. * The operation is equivalent to adding [other] copies of unit of underlying ring to [this].
*/ */
public override operator fun C.plus(other: Int): C = ring { optimizedAddMultiplied(this@plus, one, other) } public override operator fun C.plus(other: Int): C = ring { addMultipliedBySquaring(this@plus, one, other) }
/** /**
* Returns difference between the constant and the integer represented as constant (member of underlying ring). * Returns difference between the constant and the integer represented as constant (member of underlying ring).
* *
* The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this]. * The operation is equivalent to subtraction [other] copies of unit of underlying ring from [this].
*/ */
public override operator fun C.minus(other: Int): C = ring { optimizedAddMultiplied(this@minus, one, -other) } public override operator fun C.minus(other: Int): C = ring { addMultipliedBySquaring(this@minus, one, -other) }
/** /**
* Returns product of the constant and the integer represented as constant (member of underlying ring). * Returns product of the constant and the integer represented as constant (member of underlying ring).
* *
* The operation is equivalent to sum of [other] copies of [this]. * The operation is equivalent to sum of [other] copies of [this].
*/ */
public override operator fun C.times(other: Int): C = ring { optimizedMultiply(this@times, other) } public override operator fun C.times(other: Int): C = ring { multiplyBySquaring(this@times, other) }
// endregion // endregion
// region Integer-constant relation // region Integer-constant relation
@ -557,19 +571,19 @@ public interface AbstractRationalFunctionalSpaceOverRing<C, P: AbstractPolynomia
* *
* The operation is equivalent to adding [this] copies of unit of underlying ring to [other]. * The operation is equivalent to adding [this] copies of unit of underlying ring to [other].
*/ */
public override operator fun Int.plus(other: C): C = ring { optimizedAddMultiplied(other, one, this@plus) } public override operator fun Int.plus(other: C): C = ring { addMultipliedBySquaring(other, one, this@plus) }
/** /**
* Returns difference between the integer represented as constant (member of underlying ring) and the constant. * Returns difference between the integer represented as constant (member of underlying ring) and the constant.
* *
* The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other]. * The operation is equivalent to subtraction [this] copies of unit of underlying ring from [other].
*/ */
public override operator fun Int.minus(other: C): C = ring { optimizedAddMultiplied(-other, one, this@minus) } public override operator fun Int.minus(other: C): C = ring { addMultipliedBySquaring(-other, one, this@minus) }
/** /**
* Returns product of the integer represented as constant (member of underlying ring) and the constant. * Returns product of the integer represented as constant (member of underlying ring) and the constant.
* *
* The operation is equivalent to sum of [this] copies of [other]. * The operation is equivalent to sum of [this] copies of [other].
*/ */
public override operator fun Int.times(other: C): C = ring { optimizedMultiply(other, this@times) } public override operator fun Int.times(other: C): C = ring { multiplyBySquaring(other, this@times) }
// endregion // endregion
// region Constant-constant relation // region Constant-constant relation
@ -598,6 +612,11 @@ public interface AbstractRationalFunctionalSpaceOverRing<C, P: AbstractPolynomia
*/ */
@JvmName("constantTimes") @JvmName("constantTimes")
public override operator fun C.times(other: C): C = ring { this@times * other } public override operator fun C.times(other: C): C = ring { this@times * other }
/**
* Raises [arg] to the integer power [exponent].
*/
@JvmName("constantPower")
public override fun power(arg: C, exponent: UInt) : C = ring { power(arg, exponent) }
/** /**
* Instance of zero constant (zero of the underlying ring). * Instance of zero constant (zero of the underlying ring).
@ -740,6 +759,11 @@ public interface AbstractRationalFunctionalSpaceOverPolynomialSpace<
*/ */
@JvmName("constantTimes") @JvmName("constantTimes")
public override operator fun C.times(other: C): C = polynomialRing { this@times * other } public override operator fun C.times(other: C): C = polynomialRing { this@times * other }
/**
* Raises [arg] to the integer power [exponent].
*/
@JvmName("constantPower")
public override fun power(arg: C, exponent: UInt) : C = polynomialRing { power(arg, exponent) }
/** /**
* Check if the instant is zero constant. * Check if the instant is zero constant.
@ -827,6 +851,10 @@ public interface AbstractRationalFunctionalSpaceOverPolynomialSpace<
* Returns product of the polynomials. * Returns product of the polynomials.
*/ */
public override operator fun P.times(other: P): P = polynomialRing { this@times * other } public override operator fun P.times(other: P): P = polynomialRing { this@times * other }
/**
* Raises [arg] to the integer power [exponent].
*/
public override fun power(arg: P, exponent: UInt) : P = polynomialRing { power(arg, exponent) }
/** /**
* Check if the instant is zero polynomial. * Check if the instant is zero polynomial.

124
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/algebraicStub.kt
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@ -5,53 +5,54 @@
package space.kscience.kmath.functions package space.kscience.kmath.functions
import space.kscience.kmath.operations.Group import space.kscience.kmath.operations.*
// TODO: All of this should be moved to algebraic structures' place for utilities // TODO: All of this should be moved to algebraic structures' place for utilities
// TODO: Move receiver to context receiver // TODO: Move receiver to context receiver
/** /**
* Multiplication of element and integer. * Returns product of [arg] and integer [multiplier].
* *
* @receiver the multiplicand. * @param arg the multiplicand.
* @param other the multiplier. * @param multiplier the integer multiplier.
* @return the difference. * @return product of the multiplicand [arg] and the multiplier [multiplier].
* @author Gleb Minaev * @author Gleb Minaev
*/ */
internal fun <C> Group<C>.optimizedMultiply(arg: C, other: Int): C = internal fun <C> Group<C>.multiplyBySquaring(arg: C, multiplier: Int): C =
if (other >= 0) optimizedMultiply(arg, other.toUInt()) if (multiplier >= 0) multiplyBySquaring(arg, multiplier.toUInt())
else optimizedMultiply(arg, (-other).toUInt()) else multiplyBySquaring(-arg, (-multiplier).toUInt())
// TODO: Move receiver to context receiver // TODO: Move receiver to context receiver
/** /**
* Adds product of [arg] and [multiplier] to [base]. * Adds product of [arg] and [multiplier] to [base].
* *
* @receiver the algebra to provide multiplication.
* @param base the augend. * @param base the augend.
* @param arg the multiplicand. * @param arg the multiplicand.
* @param multiplier the multiplier. * @param multiplier the integer multiplier.
* @return sum of the augend [base] and product of the multiplicand [arg] and the multiplier [multiplier]. * @return sum of the augend [base] and product of the multiplicand [arg] and the multiplier [multiplier].
* @author Gleb Minaev * @author Gleb Minaev
*/ */
internal fun <C> Group<C>.optimizedAddMultiplied(base: C, arg: C, multiplier: Int): C = internal fun <C> GroupOps<C>.addMultipliedBySquaring(base: C, arg: C, multiplier: Int): C =
if (multiplier >= 0) optimizedAddMultiplied(base, arg, multiplier.toUInt()) if (multiplier >= 0) addMultipliedBySquaring(base, arg, multiplier.toUInt())
else optimizedAddMultiplied(base, arg, (-multiplier).toUInt()) else addMultipliedBySquaring(base, -arg, (-multiplier).toUInt())
// TODO: Move receiver to context receiver // TODO: Move receiver to context receiver
/** /**
* Multiplication of element and integer. * Returns product of [arg] and integer [multiplier].
* *
* @receiver the multiplicand. * This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring)
* @param other the multiplier. *
* @return the difference. * @param arg the multiplicand.
* @param multiplier the integer multiplier.
* @return product of the multiplicand [arg] and the multiplier [multiplier].
* @author Gleb Minaev * @author Gleb Minaev
*/ */
internal tailrec fun <C> Group<C>.optimizedMultiply(arg: C, other: UInt): C = internal tailrec fun <C> Group<C>.multiplyBySquaring(arg: C, multiplier: UInt): C =
when { when {
other == 0u -> zero multiplier == 0u -> zero
other == 1u -> arg multiplier == 1u -> arg
other % 2u == 0u -> optimizedMultiply(arg + arg, other / 2u) multiplier and 1u == 0u -> multiplyBySquaring(arg + arg, multiplier shr 1)
other % 2u == 1u -> optimizedAddMultiplied(arg, arg + arg, other / 2u) multiplier and 1u == 1u -> addMultipliedBySquaring(arg, arg + arg, multiplier shr 1)
else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1") else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1")
} }
@ -59,18 +60,87 @@ internal tailrec fun <C> Group<C>.optimizedMultiply(arg: C, other: UInt): C =
/** /**
* Adds product of [arg] and [multiplier] to [base]. * Adds product of [arg] and [multiplier] to [base].
* *
* @receiver the algebra to provide multiplication. * This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring)
*
* @param base the augend. * @param base the augend.
* @param arg the multiplicand. * @param arg the multiplicand.
* @param multiplier the multiplier. * @param multiplier the integer multiplier.
* @return sum of the augend [base] and product of the multiplicand [arg] and the multiplier [multiplier]. * @return sum of the augend [base] and product of the multiplicand [arg] and the multiplier [multiplier].
* @author Gleb Minaev * @author Gleb Minaev
*/ */
internal tailrec fun <C> Group<C>.optimizedAddMultiplied(base: C, arg: C, multiplier: UInt): C = internal tailrec fun <C> GroupOps<C>.addMultipliedBySquaring(base: C, arg: C, multiplier: UInt): C =
when { when {
multiplier == 0u -> base multiplier == 0u -> base
multiplier == 1u -> base + arg multiplier == 1u -> base + arg
multiplier % 2u == 0u -> optimizedAddMultiplied(base, arg + arg, multiplier / 2u) multiplier and 1u == 0u -> addMultipliedBySquaring(base, arg + arg, multiplier shr 1)
multiplier % 2u == 1u -> optimizedAddMultiplied(base + arg, arg + arg, multiplier / 2u) multiplier and 1u == 1u -> addMultipliedBySquaring(base + arg, arg + arg, multiplier shr 1)
else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1")
}
// TODO: Move receiver to context receiver
/**
* Raises [arg] to the integer power [exponent].
*
* @param arg the base of the power.
* @param exponent the exponent of the power.
* @return [arg] raised to the power [exponent].
* @author Gleb Minaev
*/
internal fun <C> Field<C>.exponentiationBySquaring(arg: C, exponent: Int): C =
if (exponent >= 0) exponentiationBySquaring(arg, exponent.toUInt())
else exponentiationBySquaring(one / arg, (-exponent).toUInt())
// TODO: Move receiver to context receiver
/**
* Multiplies [base] and [arg] raised to the integer power [exponent].
*
* @param base the multiplicand.
* @param arg the base of the power.
* @param exponent the exponent of the power.
* @return product of [base] and [arg] raised to the power [exponent].
* @author Gleb Minaev
*/
internal fun <C> Field<C>.multiplyExponentiationBySquaring(base: C, arg: C, exponent: Int): C =
if (exponent >= 0) multiplyExponentiationBySquaring(base, arg, exponent.toUInt())
else multiplyExponentiationBySquaring(base, one / arg, (-exponent).toUInt())
// TODO: Move receiver to context receiver
/**
* Raises [arg] to the integer power [exponent].
*
* This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring)
*
* @param arg the base of the power.
* @param exponent the exponent of the power.
* @return [arg] raised to the power [exponent].
* @author Gleb Minaev
*/
internal tailrec fun <C> Ring<C>.exponentiationBySquaring(arg: C, exponent: UInt): C =
when {
exponent == 0u -> zero
exponent == 1u -> arg
exponent and 1u == 0u -> exponentiationBySquaring(arg * arg, exponent shr 1)
exponent and 1u == 1u -> multiplyExponentiationBySquaring(arg, arg * arg, exponent shr 1)
else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1")
}
// TODO: Move receiver to context receiver
/**
* Multiplies [base] and [arg] raised to the integer power [exponent].
*
* This is implementation of variation of [exponentiation by squaring](https://en.wikipedia.org/wiki/Exponentiation_by_squaring)
*
* @param base the multiplicand.
* @param arg the base of the power.
* @param exponent the exponent of the power.
* @return product of [base] and [arg] raised to the power [exponent].
* @author Gleb Minaev
*/
internal tailrec fun <C> RingOps<C>.multiplyExponentiationBySquaring(base: C, arg: C, exponent: UInt): C =
when {
exponent == 0u -> base
exponent == 1u -> base + arg
exponent and 1u == 0u -> multiplyExponentiationBySquaring(base, arg * arg, exponent shr 1)
exponent and 1u == 1u -> multiplyExponentiationBySquaring(base * arg, arg * arg, exponent shr 1)
else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1") else -> error("Error in multiplication group instant by unsigned integer: got reminder by division by 2 different from 0 and 1")
} }

16
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/labeledPolynomialUtil.kt
View File

@ -351,7 +351,7 @@ public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
} }
} }
}, },
optimizedMultiply(c, degs[variable]!!) multiplyBySquaring(c, degs[variable]!!)
) )
} }
} }
@ -382,7 +382,7 @@ public fun <C, A : Ring<C>> LabeledPolynomial<C>.derivativeWithRespectTo(
} }
} }
}, },
cleanedVariables.fold(c) { acc, variable -> optimizedMultiply(acc, degs[variable]!!) } cleanedVariables.fold(c) { acc, variable -> multiplyBySquaring(acc, degs[variable]!!) }
) )
} }
} }
@ -415,7 +415,7 @@ public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
}, },
degs[variable]!!.let { deg -> degs[variable]!!.let { deg ->
(deg downTo deg - order + 1u) (deg downTo deg - order + 1u)
.fold(c) { acc, ord -> optimizedMultiply(acc, ord) } .fold(c) { acc, ord -> multiplyBySquaring(acc, ord) }
} }
) )
} }
@ -451,7 +451,7 @@ public fun <C, A : Ring<C>> LabeledPolynomial<C>.nthDerivativeWithRespectTo(
filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) -> filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
degs[index]!!.let { deg -> degs[index]!!.let { deg ->
(deg downTo deg - order + 1u) (deg downTo deg - order + 1u)
.fold(acc1) { acc2, ord -> optimizedMultiply(acc2, ord) } .fold(acc1) { acc2, ord -> multiplyBySquaring(acc2, ord) }
} }
} }
) )
@ -478,7 +478,7 @@ public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
} }
put( put(
newDegs, newDegs,
c / optimizedMultiply(one, newDegs[variable]!!) c / multiplyBySquaring(one, newDegs[variable]!!)
) )
} }
} }
@ -505,7 +505,7 @@ public fun <C, A : Field<C>> LabeledPolynomial<C>.antiderivativeWithRespectTo(
} }
put( put(
newDegs, newDegs,
cleanedVariables.fold(c) { acc, variable -> acc / optimizedMultiply(one, newDegs[variable]!!) } cleanedVariables.fold(c) { acc, variable -> acc / multiplyBySquaring(one, newDegs[variable]!!) }
) )
} }
} }
@ -534,7 +534,7 @@ public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo
newDegs, newDegs,
newDegs[variable]!!.let { deg -> newDegs[variable]!!.let { deg ->
(deg downTo deg - order + 1u) (deg downTo deg - order + 1u)
.fold(c) { acc, ord -> acc / optimizedMultiply(one, ord) } .fold(c) { acc, ord -> acc / multiplyBySquaring(one, ord) }
} }
) )
} }
@ -565,7 +565,7 @@ public fun <C, A : Field<C>> LabeledPolynomial<C>.nthAntiderivativeWithRespectTo
filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) -> filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
newDegs[index]!!.let { deg -> newDegs[index]!!.let { deg ->
(deg downTo deg - order + 1u) (deg downTo deg - order + 1u)
.fold(acc1) { acc2, ord -> acc2 / optimizedMultiply(one, ord) } .fold(acc1) { acc2, ord -> acc2 / multiplyBySquaring(one, ord) }
} }
} }
) )

16
kmath-functions/src/commonMain/kotlin/space/kscience/kmath/functions/numberedPolynomialUtil.kt
View File

@ -393,7 +393,7 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
else -> return@forEach else -> return@forEach
} }
}.cleanUp(), }.cleanUp(),
optimizedMultiply(c, degs[variable]) multiplyBySquaring(c, degs[variable])
) )
} }
} }
@ -424,7 +424,7 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.derivativeWithRespectTo(
else -> return@forEach else -> return@forEach
} }
}.cleanUp(), }.cleanUp(),
cleanedVariables.fold(c) { acc, variable -> optimizedMultiply(acc, degs[variable]) } cleanedVariables.fold(c) { acc, variable -> multiplyBySquaring(acc, degs[variable]) }
) )
} }
} }
@ -456,7 +456,7 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
}.cleanUp(), }.cleanUp(),
degs[variable].let { deg -> degs[variable].let { deg ->
(deg downTo deg - order + 1u) (deg downTo deg - order + 1u)
.fold(c) { acc, ord -> optimizedMultiply(acc, ord) } .fold(c) { acc, ord -> multiplyBySquaring(acc, ord) }
} }
) )
} }
@ -489,7 +489,7 @@ public fun <C, A : Ring<C>> NumberedPolynomial<C>.nthDerivativeWithRespectTo(
filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) -> filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
degs[index].let { deg -> degs[index].let { deg ->
(deg downTo deg - order + 1u) (deg downTo deg - order + 1u)
.fold(acc1) { acc2, ord -> optimizedMultiply(acc2, ord) } .fold(acc1) { acc2, ord -> multiplyBySquaring(acc2, ord) }
} }
} }
) )
@ -512,7 +512,7 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
.forEach { (degs, c) -> .forEach { (degs, c) ->
put( put(
List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + 1u }, List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + 1u },
c / optimizedMultiply(one, degs[variable]) c / multiplyBySquaring(one, degs[variable])
) )
} }
} }
@ -536,7 +536,7 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.antiderivativeWithRespectTo(
.forEach { (degs, c) -> .forEach { (degs, c) ->
put( put(
List(max(maxRespectedVariable + 1, degs.size)) { if (it !in variables) degs[it] else degs[it] + 1u }, List(max(maxRespectedVariable + 1, degs.size)) { if (it !in variables) degs[it] else degs[it] + 1u },
cleanedVariables.fold(c) { acc, variable -> acc / optimizedMultiply(one, degs[variable]) } cleanedVariables.fold(c) { acc, variable -> acc / multiplyBySquaring(one, degs[variable]) }
) )
} }
} }
@ -561,7 +561,7 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectT
List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + order }, List(max(variable + 1, degs.size)) { if (it != variable) degs[it] else degs[it] + order },
degs[variable].let { deg -> degs[variable].let { deg ->
(deg downTo deg - order + 1u) (deg downTo deg - order + 1u)
.fold(c) { acc, ord -> acc / optimizedMultiply(one, ord) } .fold(c) { acc, ord -> acc / multiplyBySquaring(one, ord) }
} }
) )
} }
@ -589,7 +589,7 @@ public fun <C, A : Field<C>> NumberedPolynomial<C>.nthAntiderivativeWithRespectT
filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) -> filteredVariablesAndOrders.entries.fold(c) { acc1, (index, order) ->
degs[index].let { deg -> degs[index].let { deg ->
(deg downTo deg - order + 1u) (deg downTo deg - order + 1u)
.fold(acc1) { acc2, ord -> acc2 / optimizedMultiply(one, ord) } .fold(acc1) { acc2, ord -> acc2 / multiplyBySquaring(one, ord) }
} }
} }
) )