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Move all functions to a static context, stopping unnecessary lookups.

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Danila Fedorin 2017-07-30 21:10:11 -07:00
parent 6b8d8497e2
commit 03eb669eb3
1 changed files with 223 additions and 216 deletions
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439
src/main/java/org/nwapw/abacus/plugin/StandardPlugin.java
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@ -16,6 +16,213 @@ import java.util.function.BiFunction;
*/ */
public class StandardPlugin extends Plugin { public class StandardPlugin extends Plugin {
public static final Operator OP_ADD = new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length >= 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface sum = params[0];
for(int i = 1; i < params.length; i++){
sum = sum.add(params[i]);
}
return sum;
}
});
public static final Operator OP_SUBTRACT = new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 2;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return params[0].subtract(params[1]);
}
});
public static final Operator OP_MULTIPLY = new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX,1, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length >= 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface product = params[0];
for(int i = 1; i < params.length; i++){
product = product.multiply(params[i]);
}
return product;
}
});
public static final Operator OP_DIVIDE = new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX,1, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length >= 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface product = params[0];
for(int i = 1; i < params.length; i++){
product = product.multiply(params[i]);
}
return product;
}
});
public static final Operator OP_CARET = new Operator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 2, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 2;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return FUNCTION_EXP.apply(FUNCTION_LN.apply(params[0]).multiply(params[1]));
}
});
public static final Operator OP_FACTORIAL = new Operator(OperatorAssociativity.RIGHT, OperatorType.UNARY_POSTFIX, 0, new Function() {
//private HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> storedList = new HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>>();
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
if(params[0].signum() == 0){
return (new NaiveNumber(1)).promoteTo(params[0].getClass());
}
NumberInterface factorial = params[0];
NumberInterface multiplier = params[0];
//It is necessary to later prevent calls of factorial on anything but non-negative integers.
while((multiplier = multiplier.subtract(NaiveNumber.ONE.promoteTo(multiplier.getClass()))).signum() == 1){
factorial = factorial.multiply(multiplier);
}
return factorial;
/*if(!storedList.containsKey(params[0].getClass())){
storedList.put(params[0].getClass(), new ArrayList<NumberInterface>());
storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
}*/
}
});
public static final Function FUNCTION_ABS = new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return params[0].multiply((new NaiveNumber(params[0].signum())).promoteTo(params[0].getClass()));
}
};
public static final Function FUNCTION_EXP = new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
boolean takeReciprocal = params[0].signum() == -1;
params[0] = FUNCTION_ABS.apply(params[0]);
NumberInterface sum = sumSeries(params[0], StandardPlugin::getExpSeriesTerm, getNTermsExp(getMaxError(params[0]), params[0]));
if(takeReciprocal){
sum = NaiveNumber.ONE.promoteTo(sum.getClass()).divide(sum);
}
return sum;
}
};
public static final Function FUNCTION_LN = new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface param = params[0];
int powersOf2 = 0;
while(FUNCTION_ABS.apply(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass()))).compareTo((new NaiveNumber(0.1)).promoteTo(param.getClass())) >= 0){
if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() == 1) {
param = param.divide(new NaiveNumber(2).promoteTo(param.getClass()));
powersOf2++;
if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
break;
//No infinite loop for you.
}
}
else {
param = param.multiply(new NaiveNumber(2).promoteTo(param.getClass()));
powersOf2--;
if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
break;
//No infinite loop for you.
}
}
}
return getLog2(param).multiply((new NaiveNumber(powersOf2)).promoteTo(param.getClass())).add(getLogPartialSum(param));
}
/**
* Returns the partial sum of the Taylor series for logx (around x=1).
* Automatically determines the number of terms needed based on the precision of x.
* @param x value at which the series is evaluated. 0 < x < 2. (x=2 is convergent but impractical.)
* @return the partial sum.
*/
private NumberInterface getLogPartialSum(NumberInterface x){
NumberInterface maxError = getMaxError(x);
x = x.subtract(NaiveNumber.ONE.promoteTo(x.getClass())); //Terms used are for log(x+1).
NumberInterface currentTerm = x, sum = x;
int n = 1;
while(FUNCTION_ABS.apply(currentTerm).compareTo(maxError) > 0){
n++;
currentTerm = currentTerm.multiply(x).multiply((new NaiveNumber(n-1)).promoteTo(x.getClass())).divide((new NaiveNumber(n)).promoteTo(x.getClass())).negate();
sum = sum.add(currentTerm);
}
return sum;
}
/**
* Returns natural log of 2 to the required precision of the class of number.
* @param number a number of the same type as the return type. (Used for precision.)
* @return the value of log(2) with the appropriate precision.
*/
private NumberInterface getLog2(NumberInterface number){
NumberInterface maxError = getMaxError(number);
//NumberInterface errorBound = (new NaiveNumber(1)).promoteTo(number.getClass());
//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.
//a is also an error bound.
NumberInterface a = (new NaiveNumber(1)).promoteTo(number.getClass()), b = a, c = a;
NumberInterface sum = NaiveNumber.ZERO.promoteTo(number.getClass());
int n = 0;
while(a.compareTo(maxError) >= 1){
n++;
a = a.divide((new NaiveNumber(3)).promoteTo(number.getClass()));
b = b.divide((new NaiveNumber(4)).promoteTo(number.getClass()));
c = NaiveNumber.ONE.promoteTo(number.getClass()).divide((new NaiveNumber(n)).promoteTo(number.getClass()));
sum = sum.add(a.add(b).multiply(c));
}
return sum;
}
};
public static final Function FUNCTION_SQRT = new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return OP_CARET.getFunction().apply(params[0], ((new NaiveNumber(0.5)).promoteTo(params[0].getClass())));
}
};
public StandardPlugin(PluginManager manager) { public StandardPlugin(PluginManager manager) {
super(manager); super(manager);
} }
@ -25,217 +232,17 @@ public class StandardPlugin extends Plugin {
registerNumber("naive", NaiveNumber.class); registerNumber("naive", NaiveNumber.class);
registerNumber("precise", PreciseNumber.class); registerNumber("precise", PreciseNumber.class);
registerOperator("+", new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0, new Function() { registerOperator("+", OP_ADD);
@Override registerOperator("-", OP_SUBTRACT);
protected boolean matchesParams(NumberInterface[] params) { registerOperator("*", OP_MULTIPLY);
return params.length >= 1; registerOperator("/", OP_DIVIDE);
} registerOperator("^", OP_CARET);
registerOperator("!", OP_FACTORIAL);
@Override registerFunction("abs", FUNCTION_ABS);
protected NumberInterface applyInternal(NumberInterface[] params) { registerFunction("exp", FUNCTION_EXP);
NumberInterface sum = params[0]; registerFunction("ln", FUNCTION_LN);
for(int i = 1; i < params.length; i++){ registerFunction("sqrt",FUNCTION_SQRT);
sum = sum.add(params[i]);
}
return sum;
}
}));
registerOperator("-", new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX, 0, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 2;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return params[0].subtract(params[1]);
}
}));
registerOperator("*", new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX,1, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length >= 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface product = params[0];
for(int i = 1; i < params.length; i++){
product = product.multiply(params[i]);
}
return product;
}
}));
registerOperator("/", new Operator(OperatorAssociativity.LEFT, OperatorType.BINARY_INFIX,1, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 2;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return params[0].divide(params[1]);
}
}));
registerOperator("^", new Operator(OperatorAssociativity.RIGHT, OperatorType.BINARY_INFIX, 2, new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 2;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return StandardPlugin.this.getFunction("exp").apply(StandardPlugin.this.getFunction("ln").apply(params[0]).multiply(params[1]));
}
}));
registerOperator("!", new Operator(OperatorAssociativity.RIGHT, OperatorType.UNARY_POSTFIX, 0, new Function() {
//private HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>> storedList = new HashMap<Class<? extends NumberInterface>, ArrayList<NumberInterface>>();
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
if(params[0].signum() == 0){
return (new NaiveNumber(1)).promoteTo(params[0].getClass());
}
NumberInterface factorial = params[0];
NumberInterface multiplier = params[0];
//It is necessary to later prevent calls of factorial on anything but non-negative integers.
while((multiplier = multiplier.subtract(NaiveNumber.ONE.promoteTo(multiplier.getClass()))).signum() == 1){
factorial = factorial.multiply(multiplier);
}
return factorial;
/*if(!storedList.containsKey(params[0].getClass())){
storedList.put(params[0].getClass(), new ArrayList<NumberInterface>());
storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
storedList.get(params[0].getClass()).add(NaiveNumber.ONE.promoteTo(params[0].getClass()));
}*/
}
}));
registerFunction("abs", new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return params[0].multiply((new NaiveNumber(params[0].signum())).promoteTo(params[0].getClass()));
}
});
registerFunction("exp", new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
boolean takeReciprocal = params[0].signum() == -1;
params[0] = StandardPlugin.this.getFunction("abs").apply(params[0]);
NumberInterface sum = sumSeries(params[0], StandardPlugin.this::getExpSeriesTerm, getNTermsExp(getMaxError(params[0]), params[0]));
if(takeReciprocal){
sum = NaiveNumber.ONE.promoteTo(sum.getClass()).divide(sum);
}
return sum;
}
});
registerFunction("ln", new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
NumberInterface param = params[0];
int powersOf2 = 0;
while(StandardPlugin.this.getFunction("abs").apply(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass()))).compareTo((new NaiveNumber(0.1)).promoteTo(param.getClass())) >= 0){
if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() == 1) {
param = param.divide(new NaiveNumber(2).promoteTo(param.getClass()));
powersOf2++;
if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
break;
//No infinite loop for you.
}
}
else {
param = param.multiply(new NaiveNumber(2).promoteTo(param.getClass()));
powersOf2--;
if(param.subtract(NaiveNumber.ONE.promoteTo(param.getClass())).signum() != 1) {
break;
//No infinite loop for you.
}
}
}
return getLog2(param).multiply((new NaiveNumber(powersOf2)).promoteTo(param.getClass())).add(getLogPartialSum(param));
}
/**
* Returns the partial sum of the Taylor series for logx (around x=1).
* Automatically determines the number of terms needed based on the precision of x.
* @param x value at which the series is evaluated. 0 < x < 2. (x=2 is convergent but impractical.)
* @return the partial sum.
*/
private NumberInterface getLogPartialSum(NumberInterface x){
NumberInterface maxError = StandardPlugin.this.getMaxError(x);
x = x.subtract(NaiveNumber.ONE.promoteTo(x.getClass())); //Terms used are for log(x+1).
NumberInterface currentTerm = x, sum = x;
int n = 1;
while(StandardPlugin.this.getFunction("abs").apply(currentTerm).compareTo(maxError) > 0){
n++;
currentTerm = currentTerm.multiply(x).multiply((new NaiveNumber(n-1)).promoteTo(x.getClass())).divide((new NaiveNumber(n)).promoteTo(x.getClass())).negate();
sum = sum.add(currentTerm);
}
return sum;
}
/**
* Returns natural log of 2 to the required precision of the class of number.
* @param number a number of the same type as the return type. (Used for precision.)
* @return the value of log(2) with the appropriate precision.
*/
private NumberInterface getLog2(NumberInterface number){
NumberInterface maxError = StandardPlugin.this.getMaxError(number);
//NumberInterface errorBound = (new NaiveNumber(1)).promoteTo(number.getClass());
//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.
//a is also an error bound.
NumberInterface a = (new NaiveNumber(1)).promoteTo(number.getClass()), b = a, c = a;
NumberInterface sum = NaiveNumber.ZERO.promoteTo(number.getClass());
int n = 0;
while(a.compareTo(maxError) >= 1){
n++;
a = a.divide((new NaiveNumber(3)).promoteTo(number.getClass()));
b = b.divide((new NaiveNumber(4)).promoteTo(number.getClass()));
c = NaiveNumber.ONE.promoteTo(number.getClass()).divide((new NaiveNumber(n)).promoteTo(number.getClass()));
sum = sum.add(a.add(b).multiply(c));
}
return sum;
}
});
registerFunction("sqrt", new Function() {
@Override
protected boolean matchesParams(NumberInterface[] params) {
return params.length == 1;
}
@Override
protected NumberInterface applyInternal(NumberInterface[] params) {
return StandardPlugin.this.getOperator("^").getFunction().apply(params[0], ((new NaiveNumber(0.5)).promoteTo(params[0].getClass())));
}
});
} }
@Override @Override
@ -249,8 +256,8 @@ public class StandardPlugin extends Plugin {
* @param x the real number at which the series is evaluated. * @param x the real number at which the series is evaluated.
* @return the nth term of the series. * @return the nth term of the series.
*/ */
private NumberInterface getExpSeriesTerm(int n, NumberInterface x){ private static NumberInterface getExpSeriesTerm(int n, NumberInterface x){
return x.intPow(n).divide(this.getOperator("!").getFunction().apply((new NaiveNumber(n)).promoteTo(x.getClass()))); return x.intPow(n).divide(OP_FACTORIAL.getFunction().apply((new NaiveNumber(n)).promoteTo(x.getClass())));
} }
/** /**
@ -260,11 +267,11 @@ public class StandardPlugin extends Plugin {
* @param x where the function is evaluated. * @param x where the function is evaluated.
* @return the number of terms needed to evaluated the exponential function. * @return the number of terms needed to evaluated the exponential function.
*/ */
private int getNTermsExp(NumberInterface maxError, NumberInterface x) { private static int getNTermsExp(NumberInterface maxError, NumberInterface x) {
//We need n such that |x^(n+1)| <= (n+1)! * maxError //We need n such that |x^(n+1)| <= (n+1)! * maxError
//The variables LHS and RHS refer to the above inequality. //The variables LHS and RHS refer to the above inequality.
int n = 0; int n = 0;
x = this.getFunction("abs").apply(x); x = FUNCTION_ABS.apply(x);
NumberInterface LHS = x, RHS = maxError; NumberInterface LHS = x, RHS = maxError;
while (LHS.compareTo(RHS) > 0) { while (LHS.compareTo(RHS) > 0) {
n++; n++;
@ -282,7 +289,7 @@ public class StandardPlugin extends Plugin {
* @param n the number of terms in the partial sum. * @param n the number of terms in the partial sum.
* @return the value of the partial sum that has the same class as x. * @return the value of the partial sum that has the same class as x.
*/ */
private NumberInterface sumSeries(NumberInterface x, BiFunction<Integer, NumberInterface, NumberInterface> nthTermFunction, int n){ private static NumberInterface sumSeries(NumberInterface x, BiFunction<Integer, NumberInterface, NumberInterface> nthTermFunction, int n){
NumberInterface sum = NaiveNumber.ZERO.promoteTo(x.getClass()); NumberInterface sum = NaiveNumber.ZERO.promoteTo(x.getClass());
for(int i = 0; i <= n; i++){ for(int i = 0; i <= n; i++){
sum = sum.add(nthTermFunction.apply(i, x)); sum = sum.add(nthTermFunction.apply(i, x));
@ -295,7 +302,7 @@ public class StandardPlugin extends Plugin {
* @param number Any instance of the NumberInterface in question (should return an appropriate precision). * @param number Any instance of the NumberInterface in question (should return an appropriate precision).
* @return the maximum error. * @return the maximum error.
*/ */
private NumberInterface getMaxError(NumberInterface number){ private static NumberInterface getMaxError(NumberInterface number){
return (new NaiveNumber(10)).promoteTo(number.getClass()).intPow(-number.getMaxPrecision()); return (new NaiveNumber(10)).promoteTo(number.getClass()).intPow(-number.getMaxPrecision());
} }