From 18a5a99887c670120d18519426514b4f0ef551e9 Mon Sep 17 00:00:00 2001 From: Arthur Drobot Date: Thu, 27 Jul 2017 13:04:41 -0700 Subject: [PATCH] Add natural log function. May not be terribly efficient currently, but it works and is usable. --- .../nwapw/abacus/plugin/StandardPlugin.java | 81 ++++++++++++++++++- 1 file changed, 78 insertions(+), 3 deletions(-) diff --git a/src/org/nwapw/abacus/plugin/StandardPlugin.java b/src/org/nwapw/abacus/plugin/StandardPlugin.java index 694fcda..5772762 100755 --- a/src/org/nwapw/abacus/plugin/StandardPlugin.java +++ b/src/org/nwapw/abacus/plugin/StandardPlugin.java @@ -126,6 +126,81 @@ public class StandardPlugin extends Plugin { 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; + } + }); } /** @@ -145,16 +220,16 @@ public class StandardPlugin extends Plugin { * @param x where the function is evaluated. * @return */ - private int getNTermsExp(NumberInterface maxError, NumberInterface x){ + private int getNTermsExp(NumberInterface maxError, NumberInterface x) { //We need n such that |x^(n+1)| <= (n+1)! * maxError //The variables LHS and RHS refer to the above inequality. int n = 0; x = this.getFunction("abs").apply(x); NumberInterface LHS = x, RHS = maxError; - while(LHS.compareTo(RHS) > 0){ + while (LHS.compareTo(RHS) > 0) { n++; LHS = LHS.multiply(x); - RHS = RHS.multiply(new NaiveNumber(n+1).promoteTo(RHS.getClass())); + RHS = RHS.multiply(new NaiveNumber(n + 1).promoteTo(RHS.getClass())); } return n; }