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Abacus
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Merge branch 'sig-fig'

This commit is contained in:
Arthur Drobot 2017-08-08 09:46:46 -07:00
parent 12710c625b f8b3559cec
commit b6e4c6d2ea
5 changed files with 48 additions and 30 deletions
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4
src/main/java/org/nwapw/abacus/number/NaiveNumber.java
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@ -128,5 +128,9 @@ public class NaiveNumber extends NumberInterface {
return Double.toString(Math.round(value * shiftBy) / shiftBy);
}
@Override
public NumberInterface getMaxError(){
return new NaiveNumber(Math.pow(10, -18));
}
}

7
src/main/java/org/nwapw/abacus/number/NumberInterface.java
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@ -255,4 +255,11 @@ public abstract class NumberInterface {
return promoteToInternal(toClass);
}
/**
* Returns the smallest error this instance can tolerate depending
* on its precision and value.
* @return the smallest error that should be permitted in calculations.
*/
public abstract NumberInterface getMaxError();
}

29
src/main/java/org/nwapw/abacus/number/PreciseNumber.java
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@ -1,7 +1,7 @@
package org.nwapw.abacus.number;
import java.math.BigDecimal;
import java.math.RoundingMode;
import java.math.MathContext;
/**
* A number that uses a BigDecimal to store its value,
@ -22,6 +22,21 @@ public class PreciseNumber extends NumberInterface {
*/
public static final PreciseNumber TEN = new PreciseNumber(BigDecimal.TEN);
/**
* The number of extra significant figures kept in calculations before rounding for output.
*/
private static int numExtraInternalSigFigs = 15;
/**
* MathContext that is used when rounding a number prior to output.
*/
private static MathContext outputContext = new MathContext(50);
/**
* MathContext that is actually used in calculations.
*/
private static MathContext internalContext = new MathContext(outputContext.getPrecision()+numExtraInternalSigFigs);
/**
* The value of the PreciseNumber.
*/
@ -48,7 +63,7 @@ public class PreciseNumber extends NumberInterface {
@Override
public int getMaxPrecision() {
return 65;
return internalContext.getPrecision();
}
@Override
@ -58,7 +73,7 @@ public class PreciseNumber extends NumberInterface {
@Override
public NumberInterface divideInternal(NumberInterface divisor) {
return new PreciseNumber(value.divide(((PreciseNumber) divisor).value, this.getMaxPrecision(), RoundingMode.HALF_UP));
return new PreciseNumber(value.divide(((PreciseNumber) divisor).value, internalContext));
}
@Override
@ -147,7 +162,11 @@ public class PreciseNumber extends NumberInterface {
@Override
public String toString() {
BigDecimal rounded = value.setScale(getMaxPrecision() - 15, RoundingMode.HALF_UP);
return rounded.stripTrailingZeros().toPlainString();
return value.round(outputContext).toString();
}
@Override
public NumberInterface getMaxError(){
return new PreciseNumber(value.ulp()).multiplyInternal(TEN.intPowInternal(value.precision()-internalContext.getPrecision()));
}
}

31
src/main/java/org/nwapw/abacus/plugin/StandardPlugin.java
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@ -188,7 +188,7 @@ public class StandardPlugin extends Plugin {
*/
private NumberInterface getLogPartialSum(NumberInterface x) {
NumberInterface maxError = getMaxError(x);
NumberInterface maxError = x.getMaxError();
x = x.subtract(NaiveNumber.ONE.promoteTo(x.getClass())); //Terms used are for log(x+1).
NumberInterface currentNumerator = x, currentTerm = x, sum = x;
int n = 1;
@ -207,7 +207,7 @@ public class StandardPlugin extends Plugin {
* @return the value of log(2) with the appropriate precision.
*/
private NumberInterface getLog2(NumberInterface number) {
NumberInterface maxError = getMaxError(number);
NumberInterface maxError = number.getMaxError();
//NumberInterface errorBound = fromInt(number.getClass(), 1);
//We'll use the series \sigma_{n >= 1) ((1/3^n + 1/4^n) * 1/n)
//In the following, a=1/3^n, b=1/4^n, c = 1/n.
@ -301,16 +301,11 @@ public class StandardPlugin extends Plugin {
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface maxError = getMaxError(params[0]);
NumberInterface maxError = params[0].getMaxError();
int n = 0;
if (params[0].signum() <= 0) {
NumberInterface currentTerm = NaiveNumber.ONE.promoteTo(params[0].getClass()), sum = currentTerm;
while (FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0) {
n++;
currentTerm = currentTerm.multiply(params[0]).divide((new NaiveNumber(n)).promoteTo(params[0].getClass()));
sum = sum.add(currentTerm);
}
return sum;
if (params[0].signum() < 0) {
NumberInterface[] negatedParams = {params[0].negate()};
return fromInt(params[0].getClass(), 1).divide(applyInternal(negatedParams));
} else {
//We need n such that x^(n+1) * 3^ceil(x) <= maxError * (n+1)!.
//right and left refer to lhs and rhs in the above inequality.
@ -352,7 +347,7 @@ public class StandardPlugin extends Plugin {
return NaiveNumber.ONE.promoteTo(params[1].getClass());
//Detect integer bases:
if(params[0].fractionalPart().compareTo(fromInt(params[0].getClass(), 0)) == 0
&& FUNCTION_ABS.apply(params[0]).compareTo(fromInt(params[0].getClass(), Integer.MAX_VALUE)) < 0
&& FUNCTION_ABS.apply(params[1]).compareTo(fromInt(params[0].getClass(), Integer.MAX_VALUE)) < 0
&& FUNCTION_ABS.apply(params[1]).compareTo(fromInt(params[1].getClass(), 1)) >= 0){
NumberInterface[] newParams = {params[0], params[1].fractionalPart()};
return params[0].intPow(params[1].floor().intValue()).multiply(applyInternal(newParams));
@ -476,16 +471,6 @@ public class StandardPlugin extends Plugin {
return sum;
}
/**
* Returns the maximum error based on the precision of the class of number.
*
* @param number Any instance of the NumberInterface in question (should return an appropriate precision).
* @return the maximum error.
*/
private static NumberInterface getMaxError(NumberInterface number) {
return fromInt(number.getClass(), 10).intPow(-number.getMaxPrecision());
}
/**
* A factorial function that uses memoization for each number class; it efficiently
* computes factorials of non-negative integers.
@ -517,7 +502,7 @@ public class StandardPlugin extends Plugin {
*/
private static NumberInterface sinTaylor(NumberInterface x) {
NumberInterface power = x, multiplier = x.multiply(x).negate(), currentTerm = x, sum = x;
NumberInterface maxError = getMaxError(x);
NumberInterface maxError = x.getMaxError();
int n = 1;
do {
n += 2;

7
src/test/java/org/nwapw/abacus/tests/CalculationTests.java Normal file → Executable file
View File

@ -88,8 +88,8 @@ public class CalculationTests {
public void testExp(){
testOutput("exp0", "exp(0)", "1");
testOutput("exp1", "exp(1)", "2.718281828459045235360287471352662497757247");
testOutput("exp300", "exp(300)", "19424263952412559365842088360176992193662086");
testOutput("exp300", "exp(300)", "19424263952412559365842088360176992193662086");
testOutput("exp300", "exp(300)", "1.9424263952412559365842088360176992193662086");
testOutput("exp(-500)", "exp((500)`)", "7.1245764067412855315491573771227552469277568");
}
@Test
@ -99,6 +99,9 @@ public class CalculationTests {
testOutput("2^1", "(2^1)", "2");
testOutput("2^-1", "(2^(1)`)", "0.5");
testOutput("2^50", "(2^50)", "112589990684262");
testOutput("7^(-sqrt2*17)", "(7^((sqrt(2)*17))`)", "4.81354609155297814551845300063563");
testEvalError("0^0", "(0^0)");
testEvalError("(-13)^.9999", "((13)`^0.9999)");
}
}