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Implement RealDigits with apfloat.org data types
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.../matheclipse-core/src/main/java/org/matheclipse/core/numerics/utils/RealDigitsResult.java
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| Original file line number | Diff line number | Diff line change |
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| package org.matheclipse.core.numerics.utils; | ||
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| import java.io.EOFException; | ||
| import java.io.IOException; | ||
| import java.io.Writer; | ||
| import java.util.HashMap; | ||
| import java.util.Map; | ||
| import org.apfloat.Apfloat; | ||
| import org.apfloat.ApfloatMath; | ||
| import org.apfloat.Apint; | ||
| import org.apfloat.Aprational; | ||
| import org.apfloat.AprationalMath; | ||
| import org.matheclipse.core.expression.F; | ||
| import org.matheclipse.core.interfaces.IAST; | ||
| import org.matheclipse.core.interfaces.IASTAppendable; | ||
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| public class RealDigitsResult { | ||
| public static RealDigitsResult create(Apfloat a) { | ||
| return create(a, a.radix()); | ||
| } | ||
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| public static RealDigitsResult create(Apfloat a, int radix) { | ||
| return create(a, radix, Long.MIN_VALUE); | ||
| } | ||
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| public static RealDigitsResult create(Apfloat a, int radix, long length) { | ||
| RealDigitsResult rd = new RealDigitsResult(); | ||
| rd.digits(a, radix, length, Long.MIN_VALUE); | ||
| // System.out.println(rd.digitsList + " : " + rd.numberOfLeftDigits); | ||
| return rd; | ||
| } | ||
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| public static RealDigitsResult create(Apfloat a, int radix, long length, long startDigit) { | ||
| RealDigitsResult rd = new RealDigitsResult(); | ||
| rd.digits(a, radix, length, startDigit); | ||
| // System.out.println(rd.digitsList + " : " + rd.numberOfLeftDigits); | ||
| return rd; | ||
| } | ||
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| public static RealDigitsResult create(Aprational a) { | ||
| return create(a, a.radix()); | ||
| } | ||
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| public static RealDigitsResult create(Aprational a, int radix) { | ||
| RealDigitsResult rd = new RealDigitsResult(); | ||
| rd.digits(a, radix); | ||
| // System.out.println(rd.digitsList + " : " + rd.numberOfLeftDigits); | ||
| return rd; | ||
| } | ||
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| IASTAppendable digitsList; | ||
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| long numberOfLeftDigits; | ||
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| private RealDigitsResult() {} | ||
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| private void digits(Apfloat a, int radix, long length, long startDigit) { | ||
| a = a.toRadix(radix); | ||
| if (length == Long.MIN_VALUE) { | ||
| if (a.isZero()) { | ||
| length = 1; | ||
| } else if (a.precision() == Apfloat.INFINITE) { | ||
| length = Math.max(a.scale(), a.size()); | ||
| } else { | ||
| length = a.precision(); | ||
| } | ||
| } | ||
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| if (a.isZero()) { | ||
| if (length > Integer.MAX_VALUE) { | ||
| throw new RuntimeException("List size exceeded"); | ||
| } | ||
| digitsList = F.constantArray(F.C0, (int) length); | ||
| numberOfLeftDigits = startDigit == Long.MIN_VALUE ? 1 : startDigit + 1; | ||
| return; | ||
| } | ||
| long scale = a.scale(); | ||
| digitsList = F.ListAlloc(); | ||
| numberOfLeftDigits = scale; | ||
| if (startDigit != Long.MIN_VALUE) { | ||
| long adjust = scale - 1; | ||
| if (adjust < startDigit) { | ||
| // Pad beginning of list with zeros | ||
| long padLength = Math.min(length, startDigit - adjust); | ||
| if (padLength > Integer.MAX_VALUE) { | ||
| throw new RuntimeException("List size exceeded"); | ||
| } | ||
| IASTAppendable constantArray = F.constantArray(F.C0, (int) padLength); | ||
| digitsList.appendArgs(constantArray); | ||
| } else if (adjust > startDigit) { | ||
| // Truncate first significant digits | ||
| a = ApfloatMath.scale(a, -startDigit - 1); | ||
| a = a.frac(); | ||
| a = ApfloatMath.scale(a, startDigit + 1); | ||
| } | ||
| numberOfLeftDigits = startDigit + 1; | ||
| } | ||
| long size = a.size(); | ||
| final long lengthFinal = length; | ||
| Writer writer = new Writer() { | ||
| long writeSize; | ||
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| @Override | ||
| public void close() {} | ||
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| @Override | ||
| public void flush() {} | ||
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| @Override | ||
| public void write(char[] cbuf, int off, int len) throws IOException { | ||
| for (int i = 0; i < len; i++) { | ||
| if (digitsList.argSize() >= lengthFinal || writeSize >= size) { | ||
| throw new EOFException(); | ||
| } | ||
| char c = cbuf[i + off]; | ||
| if (c != '.' && c != '-') { | ||
| digitsList.append(Character.digit(c, radix)); | ||
| writeSize++; | ||
| } | ||
| } | ||
| } | ||
| }; | ||
| try { | ||
| a.writeTo(writer); | ||
| } catch (EOFException e) { | ||
| // Indication that we got the desired number of digits written | ||
| } catch (IOException e) { | ||
| throw new RuntimeException("Error writing digits", e); | ||
| } | ||
| long precision = a.precision(); | ||
| if (length > digitsList.argSize() && precision > digitsList.argSize()) { | ||
| // Pad with trailing zeros as long as we have precision | ||
| long padLength = Math.min(length, precision) - digitsList.argSize(); | ||
| if (padLength > Integer.MAX_VALUE) { | ||
| throw new RuntimeException("List size exceeded"); | ||
| } | ||
| IASTAppendable constantArray = F.constantArray(F.C0, (int) padLength); | ||
| digitsList.appendArgs(constantArray); | ||
| } | ||
| if (length > digitsList.argSize()) { | ||
| // Pad the remaining requested length with nulls as no significant digits exist | ||
| long padLength = length - digitsList.argSize(); | ||
| if (padLength > Integer.MAX_VALUE) { | ||
| throw new RuntimeException("List size exceeded"); | ||
| } | ||
| IASTAppendable constantArray = F.constantArray(F.C0, (int) padLength); | ||
| digitsList.appendArgs(constantArray); | ||
| } | ||
| } | ||
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| /** | ||
| * Create a list of digits for a rational number. The list will contain the integer part and the | ||
| * repeating part of the decimal expansion of the rational number. | ||
| * <p> | ||
| * <a href="https://en.wikipedia.org/wiki/Repeating_decimal">Wikipedia - Repeating decimal</a> | ||
| * | ||
| * @param a | ||
| * @param radix | ||
| */ | ||
| private void digits(Aprational a, int radix) { | ||
| a = AprationalMath.abs(a.toRadix(radix)); | ||
| if (a.isZero()) { | ||
| digitsList = F.ListAlloc(2); | ||
| digitsList.append(F.CListC0); | ||
| numberOfLeftDigits = 1; | ||
| return; | ||
| } | ||
| Apint b = new Apint(radix, radix); | ||
| Apint i = a.truncate(); | ||
| Aprational r = a.frac(); | ||
| Apint p = r.numerator(); | ||
| Apint q = r.denominator(); | ||
| IASTAppendable s = F.ListAlloc(); | ||
| int pos = 1; | ||
| int start = -1; | ||
| Map<Apint, Integer> occurs = new HashMap<>(); | ||
| while (!occurs.containsKey(p)) { | ||
| occurs.put(p, pos); | ||
| Apint bp = b.multiply(p); | ||
| Apint z = bp.divide((Aprational) q).floor(); | ||
| p = bp.subtract(z.multiply(q)); | ||
| if (p.isZero()) { | ||
| if (!z.isZero()) { | ||
| s.append(z.intValue()); | ||
| } | ||
| if (!i.isZero()) { | ||
| RealDigitsResult realDigits = create((Apfloat) i); | ||
| IAST dList = realDigits.getDigitsList(); | ||
| for (int j = 1; j < dList.size(); j++) { | ||
| s.append(j, dList.get(j)); | ||
| } | ||
| } else { | ||
| s = s.subList(start, s.size()); | ||
| } | ||
| digitsList = s; | ||
| numberOfLeftDigits = a.scale(); | ||
| return; | ||
| } | ||
| s.append(z.intValue()); | ||
| if (start < 0 && !z.isZero()) { | ||
| start = pos; | ||
| } | ||
| pos++; | ||
| } | ||
| IASTAppendable initial = s.subList(1, occurs.get(p)); | ||
| IASTAppendable repetend = s.subList(occurs.get(p), pos); | ||
| if (!i.isZero()) { | ||
| RealDigitsResult realDigits = create((Apfloat) i); | ||
| IAST dList = realDigits.getDigitsList(); | ||
| for (int j = 1; j < dList.size(); j++) { | ||
| initial.append(j, dList.get(j)); | ||
| } | ||
| } else { | ||
| initial = initial.subList(Math.min(initial.size(), start), initial.size()); | ||
| // Move leading zeros to the end in case there is no integer part | ||
| while (repetend.get(1).isZero()) { | ||
| repetend.remove(1); | ||
| repetend.append(F.C0); | ||
| } | ||
| } | ||
| digitsList = F.ListAlloc(2); | ||
| digitsList.appendArgs(initial); | ||
| digitsList.append(repetend); | ||
| numberOfLeftDigits = a.scale(); | ||
| } | ||
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| public IASTAppendable getDigitsList() { | ||
| return digitsList; | ||
| } | ||
|
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| public long getNumberOfLeftDigits() { | ||
| return numberOfLeftDigits; | ||
| } | ||
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| } |