This C# code will calculate Pi to whatever length I specify. I want to be able to start at a given index without recalculating to that point. Precision is not a great concern as this is a puzzle project but I do need this code to reproduce the same results over and over. It works fine as is but I haven't been able to figure out how to modify for a starting point.
//Looking to pass BigInteger to specify a starting index for continuation of calculating Pi
public static BigInteger GetPi(int digits, int iterations)
{
return 16 * ArcTan1OverX(5, digits).ElementAt(iterations)
- 4 * ArcTan1OverX(239, digits).ElementAt(iterations);
}
public static IEnumerable<BigInteger> ArcTan1OverX(int x, int digits)
{
var mag = BigInteger.Pow(10, digits);
var sum = BigInteger.Zero;
bool sign = true;
for (int i = 1; true; i += 2)
{
var cur = mag / (BigInteger.Pow(x, i) * i);
if (sign)
{
sum += cur;
}
else
{
sum -= cur;
}
yield return sum;
sign = !sign;
}
}
You are using the Machin formula with the Taylor serie expansion for Arctan. It should give you about 1.4 digits of precision for each "cycle" (see here). You can't "shortcut" the calculation of the Taylor serie. You can speed-up a little the program removing the IEnumerable<BigInteger> part and simply returning the nth iteration (the yield instruction has a cost) and by changing the BigInteger.Pow with a fixed multiplication. But the calculation will still be made iteratively. There is no known way for calculating PI with a precision of n digits in O(1) time.
Note that there are algorithms (see the wiki) that converge in a smaller number of cycles, but I'm not sure if they converge in a smaller number of operations (their cycles are much more complex).
An optimized version of the code:
public static BigInteger GetPi2(int digits, int iterations)
{
return 16 * ArcTan1OverX2(5, digits, iterations)
- 4 * ArcTan1OverX2(239, digits, iterations);
}
public static BigInteger ArcTan1OverX2(int x, int digits, int iterations)
{
var mag = BigInteger.Pow(10, digits);
var sum = BigInteger.Zero;
bool sign = true;
int imax = 1 + (2 * iterations);
int xsquared = x * x;
BigInteger pow = x;
for (int i = 1; i <= imax; i += 2)
{
if (i != 1)
{
pow *= xsquared;
}
var cur = mag / (pow * i);
if (sign)
{
sum += cur;
}
else
{
sum -= cur;
}
sign = !sign;
}
return sum;
}
If I have a double (234.004223), etc., I would like to round this to x significant digits in C#.
So far I can only find ways to round to x decimal places, but this simply removes the precision if there are any 0s in the number.
For example, 0.086 to one decimal place becomes 0.1, but I would like it to stay at 0.08.
The framework doesn't have a built-in function to round (or truncate, as in your example) to a number of significant digits. One way you can do this, though, is to scale your number so that your first significant digit is right after the decimal point, round (or truncate), then scale back. The following code should do the trick:
static double RoundToSignificantDigits(this double d, int digits){
if(d == 0)
return 0;
double scale = Math.Pow(10, Math.Floor(Math.Log10(Math.Abs(d))) + 1);
return scale * Math.Round(d / scale, digits);
}
If, as in your example, you really want to truncate, then you want:
static double TruncateToSignificantDigits(this double d, int digits){
if(d == 0)
return 0;
double scale = Math.Pow(10, Math.Floor(Math.Log10(Math.Abs(d))) + 1 - digits);
return scale * Math.Truncate(d / scale);
}
I've been using pDaddy's sigfig function for a few months and found a bug in it. You cannot take the Log of a negative number, so if d is negative the results is NaN.
The following corrects the bug:
public static double SetSigFigs(double d, int digits)
{
if(d == 0)
return 0;
decimal scale = (decimal)Math.Pow(10, Math.Floor(Math.Log10(Math.Abs(d))) + 1);
return (double) (scale * Math.Round((decimal)d / scale, digits));
}
It sounds to me like you don't want to round to x decimal places at all - you want to round to x significant digits. So in your example, you want to round 0.086 to one significant digit, not one decimal place.
Now, using a double and rounding to a number of significant digits is problematic to start with, due to the way doubles are stored. For instance, you could round 0.12 to something close to 0.1, but 0.1 isn't exactly representable as a double. Are you sure you shouldn't actually be using a decimal? Alternatively, is this actually for display purposes? If it's for display purposes, I suspect you should actually convert the double directly to a string with the relevant number of significant digits.
If you can answer those points, I can try to come up with some appropriate code. Awful as it sounds, converting to a number of significant digits as a string by converting the number to a "full" string and then finding the first significant digit (and then taking appropriate rounding action after that) may well be the best way to go.
If it is for display purposes (as you state in the comment to Jon Skeet's answer), you should use Gn format specifier. Where n is the number of significant digits - exactly what you are after.
Here is the the example of usage if you want 3 significant digits (printed output is in the comment of each line):
Console.WriteLine(1.2345e-10.ToString("G3"));//1.23E-10
Console.WriteLine(1.2345e-5.ToString("G3")); //1.23E-05
Console.WriteLine(1.2345e-4.ToString("G3")); //0.000123
Console.WriteLine(1.2345e-3.ToString("G3")); //0.00123
Console.WriteLine(1.2345e-2.ToString("G3")); //0.0123
Console.WriteLine(1.2345e-1.ToString("G3")); //0.123
Console.WriteLine(1.2345e2.ToString("G3")); //123
Console.WriteLine(1.2345e3.ToString("G3")); //1.23E+03
Console.WriteLine(1.2345e4.ToString("G3")); //1.23E+04
Console.WriteLine(1.2345e5.ToString("G3")); //1.23E+05
Console.WriteLine(1.2345e10.ToString("G3")); //1.23E+10
I found two bugs in the methods of P Daddy and Eric. This solves for example the precision error that was presented by Andrew Hancox in this Q&A. There was also a problem with round directions. 1050 with two significant figures isn't 1000.0, it's 1100.0. The rounding was fixed with MidpointRounding.AwayFromZero.
static void Main(string[] args) {
double x = RoundToSignificantDigits(1050, 2); // Old = 1000.0, New = 1100.0
double y = RoundToSignificantDigits(5084611353.0, 4); // Old = 5084999999.999999, New = 5085000000.0
double z = RoundToSignificantDigits(50.846, 4); // Old = 50.849999999999994, New = 50.85
}
static double RoundToSignificantDigits(double d, int digits) {
if (d == 0.0) {
return 0.0;
}
else {
double leftSideNumbers = Math.Floor(Math.Log10(Math.Abs(d))) + 1;
double scale = Math.Pow(10, leftSideNumbers);
double result = scale * Math.Round(d / scale, digits, MidpointRounding.AwayFromZero);
// Clean possible precision error.
if ((int)leftSideNumbers >= digits) {
return Math.Round(result, 0, MidpointRounding.AwayFromZero);
}
else {
return Math.Round(result, digits - (int)leftSideNumbers, MidpointRounding.AwayFromZero);
}
}
}
As Jon Skeet mentions: better handle this in the textual domain. As a rule: for display purposes, don't try to round / change your floating point values, it never quite works 100%. Display is a secondary concern and you should handle any special formatting requirements like these working with strings.
My solution below I implemented several years ago and has proven very reliable. It has been thoroughly tested and it performs quite well also. About 5 times longer in execution time than P Daddy / Eric's solution.
Examples of input + output given below in code.
using System;
using System.Text;
namespace KZ.SigDig
{
public static class SignificantDigits
{
public static string DecimalSeparator;
static SignificantDigits()
{
System.Globalization.CultureInfo ci = System.Threading.Thread.CurrentThread.CurrentCulture;
DecimalSeparator = ci.NumberFormat.NumberDecimalSeparator;
}
/// <summary>
/// Format a double to a given number of significant digits.
/// </summary>
/// <example>
/// 0.086 -> "0.09" (digits = 1)
/// 0.00030908 -> "0.00031" (digits = 2)
/// 1239451.0 -> "1240000" (digits = 3)
/// 5084611353.0 -> "5085000000" (digits = 4)
/// 0.00000000000000000846113537656557 -> "0.00000000000000000846114" (digits = 6)
/// 50.8437 -> "50.84" (digits = 4)
/// 50.846 -> "50.85" (digits = 4)
/// 990.0 -> "1000" (digits = 1)
/// -5488.0 -> "-5000" (digits = 1)
/// -990.0 -> "-1000" (digits = 1)
/// 0.0000789 -> "0.000079" (digits = 2)
/// </example>
public static string Format(double number, int digits, bool showTrailingZeros = true, bool alwaysShowDecimalSeparator = false)
{
if (Double.IsNaN(number) ||
Double.IsInfinity(number))
{
return number.ToString();
}
string sSign = "";
string sBefore = "0"; // Before the decimal separator
string sAfter = ""; // After the decimal separator
if (number != 0d)
{
if (digits < 1)
{
throw new ArgumentException("The digits parameter must be greater than zero.");
}
if (number < 0d)
{
sSign = "-";
number = Math.Abs(number);
}
// Use scientific formatting as an intermediate step
string sFormatString = "{0:" + new String('#', digits) + "E0}";
string sScientific = String.Format(sFormatString, number);
string sSignificand = sScientific.Substring(0, digits);
int exponent = Int32.Parse(sScientific.Substring(digits + 1));
// (the significand now already contains the requested number of digits with no decimal separator in it)
StringBuilder sFractionalBreakup = new StringBuilder(sSignificand);
if (!showTrailingZeros)
{
while (sFractionalBreakup[sFractionalBreakup.Length - 1] == '0')
{
sFractionalBreakup.Length--;
exponent++;
}
}
// Place decimal separator (insert zeros if necessary)
int separatorPosition = 0;
if ((sFractionalBreakup.Length + exponent) < 1)
{
sFractionalBreakup.Insert(0, "0", 1 - sFractionalBreakup.Length - exponent);
separatorPosition = 1;
}
else if (exponent > 0)
{
sFractionalBreakup.Append('0', exponent);
separatorPosition = sFractionalBreakup.Length;
}
else
{
separatorPosition = sFractionalBreakup.Length + exponent;
}
sBefore = sFractionalBreakup.ToString();
if (separatorPosition < sBefore.Length)
{
sAfter = sBefore.Substring(separatorPosition);
sBefore = sBefore.Remove(separatorPosition);
}
}
string sReturnValue = sSign + sBefore;
if (sAfter == "")
{
if (alwaysShowDecimalSeparator)
{
sReturnValue += DecimalSeparator + "0";
}
}
else
{
sReturnValue += DecimalSeparator + sAfter;
}
return sReturnValue;
}
}
}
Math.Round() on doubles is flawed (see Notes to Callers in its documentation). The later step of multiplying the rounded number back up by its decimal exponent will introduce further floating point errors in the trailing digits. Using another Round() as #Rowanto does won't reliably help and suffers from other problems. However if you're willing to go via decimal then Math.Round() is reliable, as is multiplying and dividing by powers of 10:
static ClassName()
{
powersOf10 = new decimal[28 + 1 + 28];
powersOf10[28] = 1;
decimal pup = 1, pdown = 1;
for (int i = 1; i < 29; i++) {
pup *= 10;
powersOf10[i + 28] = pup;
pdown /= 10;
powersOf10[28 - i] = pdown;
}
}
/// <summary>Powers of 10 indexed by power+28. These are all the powers
/// of 10 that can be represented using decimal.</summary>
static decimal[] powersOf10;
static double RoundToSignificantDigits(double v, int digits)
{
if (v == 0.0 || Double.IsNaN(v) || Double.IsInfinity(v)) {
return v;
} else {
int decimal_exponent = (int)Math.Floor(Math.Log10(Math.Abs(v))) + 1;
if (decimal_exponent < -28 + digits || decimal_exponent > 28 - digits) {
// Decimals won't help outside their range of representation.
// Insert flawed Double solutions here if you like.
return v;
} else {
decimal d = (decimal)v;
decimal scale = powersOf10[decimal_exponent + 28];
return (double)(scale * Math.Round(d / scale, digits, MidpointRounding.AwayFromZero));
}
}
}
I agree with the spirit of Jon's assessment:
Awful as it sounds, converting to a number of significant digits as a string by converting the number to a "full" string and then finding the first significant digit (and then taking appropriate rounding action after that) may well be the best way to go.
I needed significant-digit rounding for approximate and non-performance-critical computational purposes, and the format-parse round-trip through "G" format is good enough:
public static double RoundToSignificantDigits(this double value, int numberOfSignificantDigits)
{
return double.Parse(value.ToString("G" + numberOfSignificantDigits));
}
This question is similiar to the one you're asking:
Formatting numbers with significant figures in C#
Thus you could do the following:
double Input2 = 234.004223;
string Result2 = Math.Floor(Input2) + Convert.ToDouble(String.Format("{0:G1}", Input2 - Math.Floor(Input2))).ToString("R6");
Rounded to 1 significant digit.
Let inputNumber be input that needs to be converted with significantDigitsRequired after decimal point, then significantDigitsResult is the answer to the following pseudo code.
integerPortion = Math.truncate(**inputNumber**)
decimalPortion = myNumber-IntegerPortion
if( decimalPortion <> 0 )
{
significantDigitsStartFrom = Math.Ceil(-log10(decimalPortion))
scaleRequiredForTruncation= Math.Pow(10,significantDigitsStartFrom-1+**significantDigitsRequired**)
**siginficantDigitsResult** = integerPortion + ( Math.Truncate (decimalPortion*scaleRequiredForTruncation))/scaleRequiredForTruncation
}
else
{
**siginficantDigitsResult** = integerPortion
}
Tested on .NET 6.0
In my opinion, the rounded results are inconsistent due to the defects of the framework and the error of the floating point. Therefore, be careful about use.
decimal.Parse(doubleValue.ToString("E"), NumberStyles.Float);
example:
using System.Diagnostics;
using System.Globalization;
List<double> doubleList = new();
doubleList.Add( 0.012345);
doubleList.Add( 0.12345 );
doubleList.Add( 1.2345 );
doubleList.Add( 12.345 );
doubleList.Add( 123.45 );
doubleList.Add( 1234.5 );
doubleList.Add(12345 );
doubleList.Add(10 );
doubleList.Add( 0 );
doubleList.Add( 1 );
doubleList.Add(-1 );
doubleList.Add( 0.1);
Debug.WriteLine("");
foreach (var item in doubleList)
{
Debug.WriteLine(decimal.Parse(item.ToString("E2"), NumberStyles.Float));
// 0.0123
// 0.123
// 1.23
// 12.3
// 123
// 1230
// 12300
// 10.0
// 0.00
// 1.00
// -1.00
// 0.100
}
Debug.WriteLine("");
foreach (var item in doubleList)
{
Debug.WriteLine(decimal.Parse(item.ToString("E3"), NumberStyles.Float));
// 0.01235
// 0.1235
// 1.234
// 12.35
// 123.5
// 1234
// 12340
// 10.00
// 0.000
// 1.000
// -1.000
// 0.1000
}
As pointed out by #Oliver Bock is that Math.Round() on doubles is flawed (see Notes to Callers in its documentation). The later step of multiplying the rounded number back up by its decimal exponent will introduce further floating point errors in the trailing digits. Generally, any multiplication by or division by a power of ten gives a non-exact result, since floating-point is typically represented in binary, not in decimal.
Using the following function will avoid floating point errors in the trailing digits:
static double RoundToSignificantDigits(double d, int digits)
{
if (d == 0.0 || Double.IsNaN(d) || Double.IsInfinity(d))
{
return d;
}
// Compute shift of the decimal point.
int shift = digits - 1 - (int)Math.Floor(Math.Log10(Math.Abs(d)));
// Return if rounding to the same or higher precision.
int decimalPlaces = 0;
for (long pow = 1; Math.Floor(d * pow) != (d * pow); pow *= 10) decimalPlaces++;
if (shift >= decimalPlaces)
return d;
// Round to sf-1 fractional digits of normalized mantissa x.dddd
double scale = Math.Pow(10, Math.Abs(shift));
return shift > 0 ?
Math.Round(d * scale, MidpointRounding.AwayFromZero) / scale :
Math.Round(d / scale, MidpointRounding.AwayFromZero) * scale;
}
However if you're willing to go via decimal then Math.Round() is reliable, as is multiplying and dividing by powers of 10:
static double RoundToSignificantDigits(double d, int digits)
{
if (d == 0.0 || Double.IsNaN(d) || Double.IsInfinity(d))
{
return d;
}
decimal scale = (decimal)Math.Pow(10, Math.Floor(Math.Log10(Math.Abs(d))) + 1);
return (double)(scale * Math.Round((decimal)d / scale, digits, MidpointRounding.AwayFromZero));
}
Console.WriteLine("{0:G17}", RoundToSignificantDigits(5.015 * 100, 15)); // 501.5
for me, this one works pretty fine and is also valid for negative numbers:
public static double RoundToSignificantDigits(double number, int digits)
{
int sign = Math.Sign(number);
if (sign < 0)
number *= -1;
if (number == 0)
return 0;
double scale = Math.Pow(10, Math.Floor(Math.Log10(Math.Abs(number))) + 1);
return sign * scale * Math.Round(number / scale, digits);
}
My solution may be helpful in some cases, I use it to display crypto prices which vary greatly in magnitude - it always gives me a specified number of significant figures but unlike ToString("G[number of digits]") it doesn't show small values in scientific notation (don't know a way to avoid this with ToString(), if there is then please let me know!)
const int MIN_SIG_FIGS = 6; //will be one more for < 0
int numZeros = (int)Math.Floor(Math.Log10(Math.Abs(price))); //get number of zeros before first digit, will be negative for price > 0
int decPlaces = numZeros < MIN_SIG_FIGS
? MIN_SIG_FIGS - numZeros < 0
? 0
: MIN_SIG_FIGS - numZeros
: 0; //dec. places: set to MIN_SIG_FIGS + number of zeros, unless numZeros greater than sig figs then no decimal places
return price.ToString($"F{decPlaces}");
Here's a version inspired by Peter Mortensen that adds a couple of safeguards for edge cases such as value being NaN, Inf or very small:
public static double RoundToSignificantDigits(this double value, int digits)
{
if (double.IsNaN(value) || double.IsInfinity(value))
return value;
if (value == 0.0)
return 0.0;
double leftSideNumbers = Math.Floor(Math.Log10(Math.Abs(value))) + 1;
int places = digits - (int)leftSideNumbers;
if (places > 15)
return 0.0;
double scale = Math.Pow(10, leftSideNumbers);
double result = scale * Math.Round(value / scale, digits, MidpointRounding.AwayFromZero);
if (places < 0)
places = 0;
return Math.Round(result, places, MidpointRounding.AwayFromZero);
}
I just did:
int integer1 = Math.Round(double you want to round,
significant figures you want to round to)
Here is something I did in C++
/*
I had this same problem I was writing a design sheet and
the standard values were rounded. So not to give my
values an advantage in a later comparison I need the
number rounded, so I wrote this bit of code.
It will round any double to a given number of significant
figures. But I have a limited range written into the
subroutine. This is to save time as my numbers were not
very large or very small. But you can easily change that
to the full double range, but it will take more time.
Ross Mckinstray
rmckinstray01#gmail.com
*/
#include <iostream>
#include <fstream>
#include <string>
#include <math.h>
#include <cmath>
#include <iomanip>
#using namespace std;
double round_off(double input, int places) {
double roundA;
double range = pow(10, 10); // This limits the range of the rounder to 10/10^10 - 10*10^10 if you want more change range;
for (double j = 10/range; j< 10*range;) {
if (input >= j && input < j*10){
double figures = pow(10, places)/10;
roundA = roundf(input/(j/figures))*(j/figures);
}
j = j*10;
}
cout << "\n in sub after loop";
if (input <= 10/(10*10) && input >= 10*10) {
roundA = input;
cout << "\nDID NOT ROUND change range";
}
return roundA;
}
int main() {
double number, sig_fig;
do {
cout << "\nEnter number ";
cin >> number;
cout << "\nEnter sig_fig ";
cin >> sig_fig;
double output = round_off(number, sig_fig);
cout << setprecision(10);
cout << "\n I= " << number;
cout << "\n r= " <<output;
cout << "\nEnter 0 as number to exit loop";
}
while (number != 0);
return 0;
}
Hopefully I did not change anything formatting it.
class Rational
{
private int Denominator, Numerator;
public Rational(int numerator = 0, int denominator = 1)
{
Numerator = numerator;
Denominator = denominator;
}
public override string ToString()
{
return string.Format("Fraction: {0} / {1}", Numerator, Denominator);
}
public void IncreaseBy(Rational other)
{
Numerator = other.Numerator + Numerator;
Denominator = other.Denominator + Denominator;
}
public void DecreaseBy(Rational other)
{
Numerator = Numerator - other.Numerator;
Denominator = Denominator - other.Denominator;
}
}
This class is a simple one. It is suppose to add or substract a denominator and numerator in my main.
This is in the main, bother under the same namespace
It is suppose to ask the user for the denominator and numerator 4 times. and add them both by 3
class Program
{
static void Main(string[] args)
{
int i = 0;
Console.WriteLine("Print 4 rational numbers.\n");
do
{
Console.Write("Choose a numberator: ");
int myNumerator = Convert.ToInt32(Console.ReadLine());
Console.Write("Choose a denominator: ");
int myDenominator = Convert.ToInt32(Console.ReadLine());
Rational original = new Rational(myNumerator, myDenominator);
original.IncreaseBy(3, 3);
Console.WriteLine(original);
i++;
} while (i < 4);
}
The IncreaseBy method takes one argument, you are giving it two. You need to give it one Rational, so...
original.IncreaseBy(new Rational(3, 3));
I'm trying to add two vulgar fractions together by finding the lowest common denominator and then adding. However, my code isn't behaving as expected, and is outputting two very high negative numbers. When I change the second fraction to 3/15 it outputs 0/0.
Here is my main program code:
class Program
{
static void Main(string[] args)
{
Fraction n = new Fraction(2, 4);
Fraction z = new Fraction(3, 12);
Fraction sum = n.Add(z, n);
int num = sum.Numerator;
int den = sum.Denominator;
Console.WriteLine("{0}/{1}", num, den);
Console.ReadKey(true);
}
}
Here is my Fraction class code:
internal class Fraction
{
public Fraction(int numerator, int denominator)
{
Numerator = numerator;
Denominator = denominator;
}
public int Numerator { get; private set; }
public int Denominator { get; private set; }
public Fraction Add(Fraction fraction2, Fraction fraction8)
{
int lcd = GetLCD(fraction8, fraction2);
int x = lcd/fraction8.Denominator;
int n = lcd/fraction2.Denominator;
int f2num = fraction2.Numerator*n;
int f8num = fraction8.Numerator*x;
int t = fraction2.Numerator;
Fraction Fraction3 = new Fraction(f2num+f8num,lcd);
return Fraction3;
}
public int GetLCD(Fraction b, Fraction c)
{
int i = b.Denominator;
int j = c.Denominator;
while (true)
{
if (i == j)
{
return i;
}
j = j + j;
i = i + i;
}
}
}
It didn't make sense to have GetLCD, Add & Subtract methods in the class. So, I moved it out of the class and made them static methods.
Your GetLCD function doesn't get LCD correctly. This will give you the required result.(I didn't bother to make the Subtract method working, you can follow the below code & make it work yourself)
PS: I didn't change all of your variable names & I would recommend you to make them as meaningful as possible. n,z,x,y,b,c are not good variable names
static void Main(string[] args)
{
Fraction n = new Fraction(2, 4);
Fraction z = new Fraction(3, 12);
Fraction sum = Add(z, n);
int x = sum.Numerator;
int y = sum.Denominator;
Console.WriteLine("{0}/{1}", x, y);
Console.ReadKey(true);
}
public static Fraction Add(Fraction fraction2, Fraction fraction8)
{
int lcd = GetLCD(fraction8, fraction2);
int multiplier = 0;
if (fraction2.Denominator < lcd)
{
multiplier = lcd / fraction2.Denominator;
fraction2.Numerator = multiplier * (fraction2.Numerator);
fraction2.Denominator = multiplier * (fraction2.Denominator);
}
else
{
multiplier = lcd / fraction8.Denominator;
fraction8.Numerator = multiplier * (fraction8.Numerator);
fraction8.Denominator = multiplier * (fraction8.Denominator);
}
Fraction Fraction3 = new Fraction(fraction2.Numerator + fraction8.Numerator, lcd);
return Fraction3;
}
public static int GetLCD(Fraction b, Fraction c)
{
int i = b.Denominator;
int j = c.Denominator;
int greater = 0;
int lesser = 0;
if (i > j)
{
greater = i; lesser = j;
}
else if (i < j)
{
greater = j; lesser = i;
}
else
{
return i;
}
for (int iterator = 1; iterator <= lesser; iterator++)
{
if ((greater * iterator) % lesser == 0)
{
return iterator * greater;
}
}
return 0;
}
internal class Fraction
{
public Fraction(int numerator, int denominator)
{
Numerator = numerator;
Denominator = denominator;
}
public int Numerator { get; set; }
public int Denominator { get; set; }
}
Personally, I think your first mistake is trying to calculate the Lowest Common Denominator instead of just finding the simplest common denominator. Finding the LCD is a great stratgety for humans working this out on paper because of pattern recognition: we can recognize LCDs quickly; but calculating the LCD, and then converting the fractions to it is significantly more steps for a computer that must perform every step every time (and is not able to recognize patterns). Plus, once you add the two fractions after transforming them to their LCD it isn't even guaranteed to be a reduced result. I'm assuming that the reduced result is required, as is usually expected with fractional arithmetic. And because it seems useful, I put the reduction directly into the constructor code:
internal class Fraction
{
public Fraction(int numerator, int denominator, bool reduce = false)
{
if (!reduce)
{
Numerator = numerator;
Denominator = denominator;
}
else
{
var GCD = GreatestCommonDivisor(numerator, denominator);
Numerator = numerator / GCD;
Denominator = denominator / GCD;
}
}
public int Numerator { get; private set; }
public int Denominator { get; private set; }
public static Fraction Add(Fraction first, Fraction second)
{
return Combine(first, second, false);
}
public static Fraction Subtract(Fraction first, Fraction second)
{
return Combine(first, second, true);
}
private static Fraction Combine(Fraction first, Fraction second, bool isSubtract)
{
var newDenominator = first.Denominator * second.Denominator;
var newFirst = first.Numerator * second.Denominator;
var newSecond = first.Denominator * second.Denominator;
if (isSubtract)
{
newSecond = newSecond * -1;
}
return new Fraction(newFirst + newSecond, newDenominator, true);
}
private static int GreatestCommonDivisor(int a, int b)
{
return b == 0 ? a : GreatestCommonDivisor(b, a % b);
}
}
Edit: stole Greatest Common Divisor code from this answer
From http://msdn.microsoft.com/en-us/library/system.math.pow.aspx
int value = 2;
for (int power = 0; power <= 32; power++)
Console.WriteLine("{0}^{1} = {2:N0}",
value, power, (long) Math.Pow(value, power));
Math.Pow takes doubles as arguments, yet here we are passing in ints.
Question: Is there any danger of floating point rounding errors if there is an implicit conversion to double happening?
If yes, it is better to use something like:
public static int IntPow(int x, uint pow)
{
int ret = 1;
while (pow != 0)
{
if ((pow & 1) == 1)
ret *= x;
x *= x;
pow >>= 1;
}
return ret;
}
In your special case, when you are calculating 2 to the power x, you can use a simple left shift. This would simplify your code to:
public static int TwoPowX(int power)
{
return (1<<power);
}
No, there's no possibility of rounding error caused by the conversion to double. double can exactly represent all integers which fall in the domain of the power function.
Yes, there is an implicit conversion to double happening, and yes there is a possibility of floating point rounding errors as a result.
As to whether it's worth using the alternate method you propose, that's specific to the application. Is a floating point rounding error entirely unacceptable? Will you be using numbers that fit within int32 (it doesn't take a whole lot for powers to overflow)?
public static int IntPow(int number, uint power)
{
int result = 1;
for (int i = 0; i < power; i++)
{
result *= number;
}
return result;
}
for readability!