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Adic utilities seem to be too specific to be in a generic utilities c…
…lass. Moved it to padic.impl
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219 changes: 219 additions & 0 deletions
219
mihxil-algebra/src/main/java/org/meeuw/math/abstractalgebra/padic/impl/Utils.java
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| package org.meeuw.math.abstractalgebra.padic.impl; | ||
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| import java.util.*; | ||
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| import org.meeuw.math.DigitUtils; | ||
| import org.meeuw.math.text.TextUtils; | ||
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| import static java.lang.Byte.toUnsignedInt; | ||
| import static java.lang.System.arraycopy; | ||
| import static org.meeuw.math.DigitUtils.multiplyInverseDigitsWithCarry; | ||
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| public class Utils { | ||
| /** | ||
| * Long multiplication of adic numbers. With proper propagation of the repetitive part. | ||
| * @param base The base to interpret the digitis for | ||
| * @param multiplier | ||
| * @param multiplicand | ||
| */ | ||
| public static AdicDigits multiplyAdicDigits( | ||
| final int base, | ||
| final AdicDigits multiplier, | ||
| final AdicDigits multiplicand) { | ||
| int i = -1; | ||
| AdicDigits sum = null; | ||
| List<DigitUtils.MultiplierAndNewDigitAndCarry> list = null; // only relevant when repeating digits. | ||
| while(true) { | ||
| i++; | ||
| AdicDigits.ByteAndIndex multiplierDigit = multiplier.get(i).orElse(null); | ||
| if (multiplierDigit == null) { | ||
| return sum; | ||
| } | ||
| if (multiplierDigit.value != 0) { | ||
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| var shiftedMultiplicand = multiplicand.leftShift(i); | ||
| final AdicDigits summand = multiplyAdicDigits(base, | ||
| multiplierDigit.value, | ||
| shiftedMultiplicand | ||
| ); | ||
| if (sum == null) { | ||
| sum = summand; | ||
| } else { | ||
| sum = sumAdicDigits(base, sum, summand); | ||
| } | ||
| } | ||
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| if (multiplierDigit.repeating) { | ||
| AdicDigits.ByteAndIndex newDigit = sum.get(i).orElseThrow(() -> new IllegalStateException()); | ||
| if (list == null) { | ||
| list = new ArrayList<>(); | ||
| } | ||
| byte carry = sum.repetend[0]; | ||
| DigitUtils.MultiplierAndNewDigitAndCarry l = new DigitUtils.MultiplierAndNewDigitAndCarry(multiplierDigit.index, multiplierDigit.value, newDigit.value, carry); | ||
| int indexOf = list.indexOf(l); | ||
| if (indexOf >= 0) { | ||
| //if (i > 100) { | ||
| System.out.println(sum + "\nAlready saw " + l); | ||
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| // so we know the length of the repetitive bit. | ||
| byte[] repetitive = new byte[indexOf + 1]; | ||
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| arraycopy(sum.digits , sum.digits.length - repetitive.length, repetitive, 0, repetitive.length); | ||
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| // what remains are the normal digits. | ||
| int digitLength = sum.digits.length - repetitive.length; | ||
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| byte[] digits = new byte[digitLength]; | ||
| arraycopy(sum.digits, 0, digits, 0, digits.length); | ||
| return AdicDigits.create(repetitive, digits); | ||
| } else { | ||
| //System.out.println(i + " new " + l + " (" +sum + "->" + sum + ")"); | ||
| list.add(0, l); | ||
| } | ||
| } | ||
| } | ||
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| } | ||
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| public static AdicDigits sumAdicDigits(int base, AdicDigits... summands) { | ||
| return sumAdicDigits((byte) base, summands); | ||
| } | ||
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| /** | ||
| * Performs a sum of number of integers | ||
| * @param base The base of this number | ||
| */ | ||
| public static AdicDigits sumAdicDigits(byte base, AdicDigits... summands) { | ||
| byte[] result = new byte[100]; | ||
| int carry = 0; | ||
| int i = 0; | ||
| List<DigitUtils.CarryAndIndices> detecting = new ArrayList<>(); | ||
| while(true) { | ||
| int r = carry; | ||
| boolean detectRepetition = true; | ||
| boolean anyPresent = false; | ||
| for (AdicDigits summand : summands) { | ||
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| Optional<AdicDigits.ByteAndIndex> byteAndIndex = summand.get(i); | ||
| if (byteAndIndex.isPresent()) { | ||
| anyPresent = true; | ||
| detectRepetition &= byteAndIndex.get().repeating; | ||
| r += byteAndIndex.get().value; | ||
| } | ||
| } | ||
| if (! anyPresent) { | ||
| break; | ||
| } | ||
| result = DigitUtils.ensureCapacity(i, result); | ||
| result[i] = (byte) (r % base); | ||
| i++; | ||
| if (detectRepetition) { | ||
| DigitUtils.CarryAndIndices check = new DigitUtils.CarryAndIndices( | ||
| carry, | ||
| AdicDigits.getIndexes(i, summands) | ||
| ); | ||
| int indexOf = detecting.indexOf(check); | ||
| if (indexOf == -1) { | ||
| detecting.add(check); | ||
| } else { | ||
| i--; | ||
| while(indexOf-- > 0) { | ||
| detecting.remove(0); | ||
| } | ||
| break; | ||
| } | ||
| } | ||
| carry = r / base; | ||
| } | ||
| byte[] digits = new byte[i - detecting.size()]; | ||
| byte[] repetitive = new byte[detecting.size()]; | ||
| arraycopy(result, 0, digits, 0, digits.length); | ||
| arraycopy(result, i - detecting.size(), repetitive, 0, repetitive.length); | ||
| if (repetitive.length == 0) { | ||
| repetitive = AdicDigits.NOT_REPETITIVE; | ||
| } | ||
| return new AdicDigits(repetitive, digits); | ||
| } | ||
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| /** | ||
| * Multiply an {@link AdicDigits} with exactly one digit. | ||
| * @param multiplier The multiplier digit | ||
| * @param multiplicand The multiplicand {@link AdicDigits} | ||
| */ | ||
| public static AdicDigits multiplyAdicDigits( | ||
| final int base, | ||
| final byte multiplier, | ||
| final AdicDigits multiplicand) { | ||
| final byte[] resultDigits = multiplyInverseDigitsWithCarry(base, multiplier, multiplicand.digits); | ||
| final int originalCarry = toUnsignedInt(resultDigits[resultDigits.length - 1]); | ||
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| if (multiplicand.repetend.length == 0 || Arrays.equals(multiplicand.repetend, AdicDigits.NOT_REPETITIVE)) { | ||
| return AdicDigits.create( | ||
| AdicDigits.NOT_REPETITIVE, | ||
| resultDigits); | ||
| } | ||
| int carry = originalCarry; | ||
| int digiti = toUnsignedInt(multiplier); | ||
| List<DigitUtils.CarryAndIndex> carries = new ArrayList<>(); | ||
| List<Byte> moreDigits = new ArrayList<>(); | ||
| int i = 0; | ||
| byte[] repetitive; | ||
| while(true) { | ||
| int index = i % multiplicand.repetend.length; | ||
| DigitUtils.CarryAndIndex carryAndIndex = new DigitUtils.CarryAndIndex(carry, index); | ||
| int indexOf = carries.indexOf(carryAndIndex); | ||
| if (indexOf == -1) { | ||
| carries.add(carryAndIndex); | ||
| int ri = carry + digiti * toUnsignedInt(multiplicand.repetend[index]); | ||
| byte b = (byte) (ri % base); | ||
| moreDigits.add(Byte.valueOf(b)); | ||
| carry = ri / base; | ||
| i++; | ||
| } else { | ||
| repetitive = new byte[moreDigits.size() - indexOf]; | ||
| for (int j= 0; j < repetitive.length; j++) { | ||
| repetitive[j] = moreDigits.remove(indexOf);; | ||
| } | ||
| break; | ||
| } | ||
| } | ||
| int numberOfOriginalDigits = Math.max(0, resultDigits.length - 1); | ||
| int numberOfDigits = Math.max(0, moreDigits.size() + numberOfOriginalDigits); | ||
| byte[] digits = new byte[numberOfDigits]; | ||
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| arraycopy(resultDigits, 0, digits, 0, numberOfDigits); | ||
| for (int j = 0; j < moreDigits.size(); j++) { | ||
| digits[numberOfOriginalDigits + j] = moreDigits.get(j); | ||
| } | ||
| return AdicDigits.create(repetitive, digits); | ||
| } | ||
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| public static String adicToString(int base, AdicDigits digits) { | ||
| return adicToString((byte) base, digits); | ||
| } | ||
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| public static String adicToString(byte base, AdicDigits digits) { | ||
| return digits.toString() + TextUtils.subscript(base); | ||
| } | ||
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| public static AdicDigits negate(byte base, AdicDigits negated) { | ||
| byte[] negatedDigits = new byte[negated.digits.length]; | ||
| byte[] negatedRepetend = new byte[negated.repetend.length]; | ||
| byte carry = 0; | ||
| for (int i = 0 ; i < negated.digits.length; i++) { | ||
| negatedDigits[i] = (byte) (base - negated.digits[i] - carry); | ||
| carry = 1; | ||
| } | ||
| for (int i = 0 ; i < negated.repetend.length; i++) { | ||
| negatedRepetend[i] = (byte) (base - negated.repetend[i] - carry); | ||
| carry = 1; | ||
| } | ||
| return AdicDigits.create(negatedRepetend, negatedDigits); | ||
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| } | ||
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| } |
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