I have an integer which I want to convert to a string, but taking the last 3 numbers and showing only the first 2 of them as decimals,
something like this: 85893 => 85.89
or failing that: 469 => 0.46
I have thought about rounding it, formatting it with string, even regex, but I would like to know what is the most optimal way to do it, since it will be done in several iterations per second
[UPDATE]
The best performing option I found was: #juharr
(num / 1000M).ToString("F2");
thanks a lot
It would appear your are truncating towards zero rather than rounding to get to 1/100ths.
I might do something like this:
public static string FormatSpecial( this int n )
{
return Math.Round( ((decimal) n) / 1000 , 2 , MidpointRounding.ToZero ).ToString();
}
If that is insufficiently efficient, perhaps something like this:
public static string FormatSpecial( this int n )
{
int ddd = n / 1000 ; // integer portion
int ttt = n % 1000 ; // fractional portion (1/1000ths)
int hh = thousands / 10 ; // truncate thousandths to 1/100ths
string s = string.Format("{0}.{1:00}", ddd, hh );
}
Just 3 integer divisions, followed by conversion to string.
I would hope that the optimizer and the JIT would collapse the 1st 2 divisions into a single machine instruction: on most CPUs, the integer division op usually produces both a quotient and remainder as its result.
If that's still insufficiently efficient, then something like this to optimize the string formatting. Since we know that the max value of a 64-bit unsigned integer (ulong) is 18446744073709551615, the resulting formatted string will never exceed 25 characters in length. So...
public static string FormatSpecial( this int n )
{
const BUFL = 25 ;
const DECIMAL_POINT = BUFL - 4 ;
const MIN = BUFL - 5 ;
char[] buf = new char[BUFL] ;
int i = BUFL - 1 ;
do
{
if ( i == DECIMAL_POINT)
{
buf[i--] = '.';
}
char digit = '0' + ( n % 10 );
buf[i--] = digit ;
n /= 10 ;
} while ( n != 0 || i > MIN );
int len = BUFL - i - 1;
return new String( buf , i , len );
}
If you care about precision, you could just take your numbers and multiply by 0.001, then take a Substring of it so that it chops off the last digit, I did it this way because it looks like you don't want it rounding depending on the last digit in the thousandths place of the decimal,
EDIT: After doing more research I found that if using newer versions of .Net you could use a System.ReadOnlySpan<T> since this is a reference to the string it won't create a new copy, so instead of the commented out line using .Substring() it would be like:
int num = 469;
string number = (num * 0.001).ToString("0.000");
//Console.WriteLine(number.Substring(0, number.Length - 1));
Console.WriteLine(number.AsSpan(0, number.Length - 1));
reference - (String.Substring() seems to bottleneck this code):
If you don't care about precision:
int num = 469;
Console.WriteLine(Math.Round(num * 0.001, 2));
Related
I'm trying to get the last two digits of an int that is a minimum of 3 digits long. Here is my (rather sloppy) attempt:
char[] number = num.ToString().ToCharArray();
int firstnum;
int secondnum;
string strLastTwoDigits = "";
int intLastTwoDigits;
firstnum = number[number.ToString().Length - 1];
secondnum = number[number.ToString().Length - 2];
strLastTwoDigits = (firstnum.ToString() + secondnum.ToString());
intLastTwoDigits = int.Parse(strLastTwoDigits);
The num variable is the number I'm trying to get the last two digits of. I'm trying to turn them into strings and use the string functions to do it, probably not the way it's done. The logic to check whether it's 3 digits or more isn't included, I don't need help with that, just getting those last two digits.
Any ideas?
Do you need those two numbers as a String? Or do you plan to convert them back to a number.
Because if you want to have a number at the end, just use the modulo- operator %.
You can find an example on how to use it here: https://www.dotnetperls.com/modulo
Edit: to state the obvious: last2 = number % 100;
Just perform a modulo operation.
var intLastTwoDigits = num % 100;
You can use the modulo of that number, it should be something like
int lastTwoDigits = num % 100;
This function will divide num / 100and gives you the rest as integer.
If you need the last to digits as int, you could just use modulo:
int lasttwo = num % 100;
the modulo operator (%) will return you the remainder of the division of one integer is by another - in this case your number divided by 100 - the remainder will always be the last two digits
If you want to use strings for that, string.Substring method will help you
var numString = num.ToString();
var strLastTwoDigits = numString.Substring(numString.Length - 2, 2);
var intLastTwoDigits = int.Parse(strLastTwoDigits);
Another (and more simpler option) is to use remainder % operator for that
int intLastTwoDigits = num % 100;
You get a remainder of division into 100, because you need the 2 last digits
Lets say someone enter a four digit number 1234 in the console. How can you separate this number in to 1 2 3 4 using only division and the modulo operator?
public static void MathProblem()
{
Console.WriteLine("Type a four digit number:");
//Ex input: 1234
string inputNumber = Console.ReadLine();
// I'm guessing you first need to parse the
// string as an int in some way?
// And then assign it to some variable
// Now, for seperating the digits to be: 1 2 3 4,
// you can (and must) use both division (/), and the remainder (%).
// The first one will be simple, just dividing value with 1000, but
// how about the others? (Remember, % also need to be used at least
// once)
Console.Write("{0},{1},{2},{3}", value/1000, ?, ?, ?;
}
Any guidelines for making this possible for any given four digit input?
Since this seems like a homework problem, I'll simply explain the method in a few steps rather than giving you the code. Having parsed the input as an integer,
A number modulo 10 allows you to obtain its last digit.
Dividing (integer division) the number by 10 removes the last digit.
Repeat while the number is greater than 0.
int num = int.Parse(inputNumber);
Console.Write(string.Format("{0},{1},{2},{3}", (num/1000) % 100, (num/100) % 10, (num/10) % 10, num % 10));
OR
List<int> listOfInts = new List<int>();
while(num > 0)
{
listOfInts.Add(num % 10);
num = num / 10;
}
Console.Write("{0},{1},{2},{3}", listOfInts[3], listOfInts[2], listOfInts[1], listOfInts[0]);
No need to do this by division or modulo operators. Use LINQ. You can get an integer array using LINQ as below:
string inputNumber= "1234"
var intList = inputNumber.Select(digit => int.Parse(digit.ToString()));
Then, you can simply use it as you want like this:
Console.Write("{0},{1},{2},{3}", intList[0]/1000, intList[1], intList[2], intList[3]);
Or simply the way you wanted it using Division and Modulo Operator:
public int[] ParseIntString(int number)
{
List<int> digits= new List<int>();
while(number> 0)
{
digits.Add(number% 10);
number= number/ 10;
}
digits.Reverse();
return digits.ToArray();
}
I hope this helps you
int[] values;
Seperate(inputNumber, out values);
Console.Write("{0},{1},{2},{3}", values[0] / 1000, values[1], values[2], values[3]);
Console.ReadKey();
}
public static void Seperate(string numbers, out int[] values)
{
values = new int[numbers.Length];
for (int x = 0; x <= numbers.Length - 1; x++)
{
values[x] = int.Parse(numbers[x].ToString());
}
}
I just started a course in coding and had this as homework as well. I did it in excel first because I thought it was easier than running code over and over and it's more a math problem than a coding one.
Say the number is 4352.
The first digit is easy, it's the integer of the number / 1000 = 4.
Then you simply multilpy by 1000 to get 4000. Remove that and you get 352. The integer of that / 100 is 3.
Then you times that by 100 to get 300 and remove that and you get 52, the integer of that / 10 is 5. Multiply that by 10 and remove that and you're left with 2.
Just read that you must use % so I suggest getting the last number as a modular of 10
I already know when a fraction is repeating decimals. Here is the function.
public bool IsRepeatingDecimal
{
get
{
if (Numerator % Denominator == 0)
return false;
var primes = MathAlgorithms.Primes(Denominator);
foreach (int n in primes)
{
if (n != 2 && n != 5)
return true;
}
return false;
}
}
Now, I'm trying to get the repeated number. I'm checking this web site: http://en.wikipedia.org/wiki/Repeating_decimal
public decimal RepeatingDecimal()
{
if (!IsRepeatingDecimal) throw new InvalidOperationException("The fraction is not producing repeating decimals");
int digitsToTake;
switch (Denominator)
{
case 3:
case 9: digitsToTake = 1; break;
case 11: digitsToTake = 2; break;
case 13: digitsToTake = 6; break;
default: digitsToTake = Denominator - 1; break;
}
return MathExtensions.TruncateAt((decimal)Numerator / Denominator, digitsToTake);
}
But I really realized, that some numbers has a partial decimal finite and later infinite. For example: 1/28
Do you know a better way to do this? Or an Algorithm?
A very simple algorithm is this: implement long division. Record every intermediate division you do. As soon as you see a division identical to the one you've done before, you have what's being repeated.
Example: 7/13.
1. 13 goes into 7 0 times with remainder 7; bring down a 0.
2. 13 goes into 70 5 times with remainder 5; bring down a 0.
3. 13 goes into 50 3 times with remainder 11; bring down a 0.
4. 13 goes into 110 8 times with remainder 6; bring down a 0.
5. 13 goes into 60 4 times with remainder 8; bring down a 0.
6. 13 goes into 80 6 times with remainder 2; bring down a 0.
7. 13 goes into 20 1 time with remainder 7; bring down a 0.
8. We have already seen 13/70 on line 2; so lines 2-7 have the repeating part
The algorithm gives us 538461 as the repeating part. My calculator says 7/13 is 0.538461538. Looks right to me! All that remains are implementation details, or to find a better algorithm!
If you have a (positive) reduced fraction numerator / denominator, the decimal expansion of the fraction terminates if and only if denominator has no prime factor other than 2 or 5. If it has any other prime factor, the decimal expansion will be periodic. However, the cases where the denominator is divisible by at least one of 2 and 5 and where it isn't give rise to slightly different behaviour. We have three cases:
denominator = 2^a * 5^b, then the decimal expansion terminates max {a, b} digits after the decimal point.
denominator = 2^a * 5^b * m where m > 1 is not divisible by 2 or by 5, then the fractional part of the decimal expansions consists of two parts, the pre-period of length max {a, b} and the period, whose length is determined by m and independent of the numerator.
denominator > 1 is not divisible by 2 or by 5, then the decimal expansion is purely periodic, meaning the period starts immediately after the decimal point.
The treatment of cases 1. and 2. has a common part, let c = max {a, b}, then
numerator / denominator = (numerator * 2^(c-a) * 5^(c-b)) / (10^c * m)
where m = 1 for case 1. Note that one of the factors 2^(c-a) and 5^(c-b) with which we multiply the numerator is 1. Then you get the decimal expansion by expanding
(numerator * 2^(c-a) * 5^(c-b)) / m
and shifting the decimal point c places to the left. In the first case (m = 1) that part is trivial.
The treatment of cases 2. and 3. also has a common part, the calculation of a fraction
n / m
where n and m have no common prime factor (and m > 1). We can write n = q*m + r with 0 <= r < m (division with remainder, r = n % m), q is the integral part of the fraction and rather uninteresting.
Since the fraction was assumed reduced, we have r > 0, so we want to find the expansion of a fraction r / m where 0 < r < m and m is not divisible by 2 or by 5. As mentioned above, such an expansion is purely periodic, so finding the period means finding the complete expansion.
Let's go about finding the period heuristically. So let k be the length of the (shortest) period and p = d_1d1_2...d_k the period. So
r / m = 0.d_1d_2...d_kd_1d_2...d_kd_1...
= (d_1d_2...d_k)/(10^k) + (d_1d_2...d_k)/(10^(2k)) + (d_1d_2...d_k)/(10^(3k)) + ...
= p/(10^k) * (1 + 1/(10^k) + 1/(10^(2k)) + 1/(10^(3k)) + ...)
The last term is a geometric series, 1 + q + q^2 + q^3 + ... which, for |q| < 1 has the sum 1/(1-q).
In our case, 0 < q = 1/(10^k) < 1, so the sum is 1 / (1 - 1/(10^k)) = 10^k / (10^k-1). Thus we have seen that
r / m = p / (10^k-1)
Since r and m have no common factor, that means there is an s with 10^k - 1 = s*m and p = s*r. If we know k, the length of the period, we can simply find the digits of the period by calculating
p = ((10^k - 1)/m) * r
and padding with leading zeros until we have k digits. (Note: it is that simple only if k is sufficiently small or a big integer type is available. To calculate the period of for example 17/983 with standard fixed-width integer types, use long division as explained by #Patrick87.)
So it remains to find the length of the period. We can revert the reasoning above and find that if m divides 10^u - 1, then we can write
r / m = t/(10^u - 1) = t/(10^u) + t/(10^(2u)) + t/(10^(3u)) + ...
= 0.t_1t_2...t_ut_1t_2...t_ut_1...
and r/m has a period of length u. So the length of the shortest period is the minimal positive u such that m divides 10^u - 1, or, put another way, the smallest positive u such that 10^u % m == 1.
We can find it in O(m) time with
u = 0;
a = 1;
do {
++u;
a = (10*a) % m;
while(a != 1);
Now, finding the length of the period that way is not more efficient than finding the digits and length of the period together with long division, and for small enough m that is the most efficient method.
int[] long_division(int numerator, int denominator) {
if (numerator < 1 || numerator >= denominator) throw new IllegalArgumentException("Bad call");
// now we know 0 < numerator < denominator
if (denominator % 2 == 0 || denominator % 5 == 0) throw new IllegalArgumentException("Bad denominator");
// now we know we get a purely periodic expansion
int[] digits = new int[denominator];
int k = 0, n = numerator;
do {
n *= 10;
digits[k++] = n / denominator;
n = n % denominator;
}while(n != numerator);
int[] period = new int[k];
for(n = 0; n < k; ++n) {
period[n] = digits[n];
}
return period;
}
That works as long as 10*(denominator - 1) doesn't overflow, of course int could be a 32-bit or 64-bit integer as needed.
But for large denominators, that is inefficient, one can find the period length and also the period faster by considering the prime factorisation of the denominator. Regarding the period length,
If the denominator is a prime power, m = p^k, the period length of r/m is a divisor of (p-1) * p^(k-1)
If a and b are coprime and m = a * b, the period length of r/m is the least common multiple of the period lengths of 1/a and 1/b.
Taken together, the period length of r/m is a divisor of λ(m), where λ is the Carmichael function.
So to find the period length of r/m, find the prime factorisation of m and for all prime power factors p^k, find the period of 1/(p^k) - equivalently, the multiplicative order of 10 modulo p^k, which is known to be a divisor of (p-1) * p^(k-1). Since such numbers haven't many divisors, that is quickly done.
Then find the least common multiple of all these.
For the period itself (the digits), if a big integer type is available and the period isn't too long, the formula
p = (10^k - 1)/m * r
is a quick way to compute it. If the period is too long or no big integer type is available, efficiently computing the digits is messier, and off the top of my head I don't remember how exactly that is done.
One way would be to repeat the way that you do long division by hand, and keep note of the remainder at each stage. When the remainder repeats, the rest of the process must repeat as well. E.g. the digits of 1.0/7 are 0.1 remainder 3 then 0.14 remainder 2 then 0.142 remainder 6 then 0.1428 remainder 4 then 0.14285 remainder 5 then 0.142857 remainder 1 which is the 1 that starts it off again amd so you get 0.1428571 remainder 3 and it repeats again from there.
The long division algorithm is pretty good, so I have nothing to add there.
But note that your algorithm IsRepeatingDecimal may not work and is inneficient.
It will not work if your fraction is not irreductible, that is if there exists an integer larger than 1 that divides both your numerator and your denominator. For example, if you feed 7/14 then your algorithm will return true when it should return false.
To reduce your fraction, find the gcd between both numerator and denominator and divide both by this gcd.
If you assume that the fraction is irreducible, then your test
if (Numerator % Denominator == 0)
can simply be replaced with
if (Denominator == 1)
But that is still unnecessary since if Denominator is 1, then your list 'primes' is going to be empty and your algorithm will return false anyway.
Finally, calling MathAlgorithms.Primes(Denominator) is going to be expensive for large numbers and can be avoided. Indeed, all you need to do is divide your denominator by 5 (respectively 2) untill it is no longer divisible by 5 (resp. 2). If the end result is 1, then return false, otherwise return true.
I came here expecting to be able to copy & paste the code to do this, but it didn't exist. So after reading #Patrick87's answer, I went ahead and coded it up. I spent some time testing it thoroughly and giving things a nice name. I thought I would leave it here so others don't have to waste their time.
Features:
If the decimal terminates, it handles that. It calculates the period and puts that in a separate variable called period, in case you want to know the length of the reptend.
Limitations:
It will fail if the transient + reptend is longer than can be represented by a System.Decimal.
public static string FormatDecimalExpansion(RationalNumber value)
{
RationalNumber currentValue = value;
string decimalString = value.ToDecimal().ToString();
int currentIndex = decimalString.IndexOf('.');
Dictionary<RationalNumber, int> dict = new Dictionary<RationalNumber, int>();
while (!dict.ContainsKey(currentValue))
{
dict.Add(currentValue, currentIndex);
int rem = currentValue.Numerator % currentValue.Denominator;
int carry = rem * 10;
if (rem == 0) // Terminating decimal
{
return decimalString;
}
currentValue = new RationalNumber(carry, currentValue.Denominator);
currentIndex++;
}
int startIndex = dict[currentValue];
int endIndex = currentIndex;
int period = (endIndex - startIndex); // The period is the length of the reptend
if (endIndex >= decimalString.Length)
{
throw new ArgumentOutOfRangeException(nameof(value),
"The value supplied has a decimal expansion that is longer" +
$" than can be represented by value of type {nameof(System.Decimal)}.");
}
string transient = decimalString.Substring(0, startIndex);
string reptend = decimalString.Substring(startIndex, period);
return transient + $"({reptend})";
}
And for good measure, I will include my RationalNumber class.
Note: It inherits from IEquatable so that it works correctly with the dictionary:
public struct RationalNumber : IEquatable<RationalNumber>
{
public int Numerator;
public int Denominator;
public RationalNumber(int numerator, int denominator)
{
Numerator = numerator;
Denominator = denominator;
}
public decimal ToDecimal()
{
return Decimal.Divide(Numerator, Denominator);
}
public bool Equals(RationalNumber other)
{
return (Numerator == other.Numerator && Denominator == other.Denominator);
}
public override int GetHashCode()
{
return new Tuple<int, int>(Numerator, Denominator).GetHashCode();
}
public override string ToString()
{
return $"{Numerator}/{Denominator}";
}
}
Enjoy!
I have a problem and cant find a solution. I have numbers (decimal) like 85.12343 or 100 or 1.123324. I want to format this in a way that the result is always 13 chars long including the separator.
100 --> 100.000000000
1.123324 --> 1.12332400000
I tried with toString, but failed. How could I do this?
Thanks :)
int digits = 13;
decimal d = 100433.2414242241214M;
int positive = Decimal.Truncate(d).ToString().Length;
int decimals = digits - positive - 1; //-1 for the dot
if (decimals < 0)
decimals = 0;
string dec = d.ToString("f" + decimals);
It will not remove digits from the whole part, only the fraction, when needed.
I'd go with Kobi's answer, unless it's possible you could have more than 13 digits to start with, in which case you might need to do something like this (warning: I have not even attempted to make this efficient; surely there are ways it could be optimized if necessary):
public static string ToTrimmedString(this decimal value, int numDigits)
{
// First figure out how many decimal places are to the left
// of the decimal point.
int digitsToLeft = 0;
// This should be safe since you said all inputs will be <= 100M anyway.
int temp = decimal.ToInt32(Math.Truncate(value));
while (temp > 0)
{
++digitsToLeft;
temp /= 10;
}
// Then simply display however many decimal places remain "available,"
// taking the value to the left of the decimal point and the decimal point
// itself into account. (If negative numbers are a possibility, you'd want
// to subtract another digit for negative values to allow for the '-' sign.)
return value.ToString("#." + new string('0', numDigits - digitsToLeft - 1));
}
Example inputs/output:
Input Output
---------------------------------------
100 100.000000000
1.232487 1.23248700000
1.3290435309439872321 1.32904353094
100.320148109932888473 100.320148110
0.000383849080819849081 .000383849081
0.0 .000000000000
Quick 'n' dirty:
return (value.ToString("0.#") + "0000000000000").Substring(0, 13);
string formatted = original.ToString("0.000000000000").Remove(13);
Besides simply padding the string you can do some more elaborate math to determine the number of digits:
String FormatField(Int32 fieldWidth, Decimal value) {
var integerPartDigits =
value != Decimal.Zero ? (int) Math.Log10((Double) value) + 1 : 1;
var fractionalPartDigits = Math.Max(0, fieldWidth - integerPartDigits - 1);
return value.ToString("F" + fractionalPartDigits);
}
Note that if the value is negative or has an integer part with one less digit than the field width you will not get the desired result. However, you can modify the code to accommodate these cases based on exactly how you want to format and align these numbers.
What about
string newString;
if (original.ToString().Length >= 13)
{
newString = original.ToString().Substring(13);
}
else
{
newString = original.ToString().PadRight(13, '0');
}
int noofdecimal=3;
double value=1567.9800
value.ToString("#." + new string('0', noofdecimal));
//Result=1567.980
.NET Framework 3.5.
I'm trying to calculate the average of some pretty large numbers.
For instance:
using System;
using System.Linq;
class Program
{
static void Main(string[] args)
{
var items = new long[]
{
long.MaxValue - 100,
long.MaxValue - 200,
long.MaxValue - 300
};
try
{
var avg = items.Average();
Console.WriteLine(avg);
}
catch (OverflowException ex)
{
Console.WriteLine("can't calculate that!");
}
Console.ReadLine();
}
}
Obviously, the mathematical result is 9223372036854775607 (long.MaxValue - 200), but I get an exception there. This is because the implementation (on my machine) to the Average extension method, as inspected by .NET Reflector is:
public static double Average(this IEnumerable<long> source)
{
if (source == null)
{
throw Error.ArgumentNull("source");
}
long num = 0L;
long num2 = 0L;
foreach (long num3 in source)
{
num += num3;
num2 += 1L;
}
if (num2 <= 0L)
{
throw Error.NoElements();
}
return (((double) num) / ((double) num2));
}
I know I can use a BigInt library (yes, I know that it is included in .NET Framework 4.0, but I'm tied to 3.5).
But I still wonder if there's a pretty straight forward implementation of calculating the average of integers without an external library. Do you happen to know about such implementation?
Thanks!!
UPDATE:
The previous example, of three large integers, was just an example to illustrate the overflow issue. The question is about calculating an average of any set of numbers which might sum to a large number that exceeds the type's max value. Sorry about this confusion. I also changed the question's title to avoid additional confusion.
Thanks all!!
This answer used to suggest storing the quotient and remainder (mod count) separately. That solution is less space-efficient and more code-complex.
In order to accurately compute the average, you must keep track of the total. There is no way around this, unless you're willing to sacrifice accuracy. You can try to store the total in fancy ways, but ultimately you must be tracking it if the algorithm is correct.
For single-pass algorithms, this is easy to prove. Suppose you can't reconstruct the total of all preceding items, given the algorithm's entire state after processing those items. But wait, we can simulate the algorithm then receiving a series of 0 items until we finish off the sequence. Then we can multiply the result by the count and get the total. Contradiction. Therefore a single-pass algorithm must be tracking the total in some sense.
Therefore the simplest correct algorithm will just sum up the items and divide by the count. All you have to do is pick an integer type with enough space to store the total. Using a BigInteger guarantees no issues, so I suggest using that.
var total = BigInteger.Zero
var count = 0
for i in values
count += 1
total += i
return total / (double)count //warning: possible loss of accuracy, maybe return a Rational instead?
If you're just looking for an arithmetic mean, you can perform the calculation like this:
public static double Mean(this IEnumerable<long> source)
{
if (source == null)
{
throw Error.ArgumentNull("source");
}
double count = (double)source.Count();
double mean = 0D;
foreach(long x in source)
{
mean += (double)x/count;
}
return mean;
}
Edit:
In response to comments, there definitely is a loss of precision this way, due to performing numerous divisions and additions. For the values indicated by the question, this should not be a problem, but it should be a consideration.
You may try the following approach:
let number of elements is N, and numbers are arr[0], .., arr[N-1].
You need to define 2 variables:
mean and remainder.
initially mean = 0, remainder = 0.
at step i you need to change mean and remainder in the following way:
mean += arr[i] / N;
remainder += arr[i] % N;
mean += remainder / N;
remainder %= N;
after N steps you will get correct answer in mean variable and remainder / N will be fractional part of the answer (I am not sure you need it, but anyway)
If you know approximately what the average will be (or, at least, that all pairs of numbers will have a max difference < long.MaxValue), you can calculate the average difference from that value instead. I take an example with low numbers, but it works equally well with large ones.
// Let's say numbers cannot exceed 40.
List<int> numbers = new List<int>() { 31 28 24 32 36 29 }; // Average: 30
List<int> diffs = new List<int>();
// This can probably be done more effectively in linq, but to show the idea:
foreach(int number in numbers.Skip(1))
{
diffs.Add(numbers.First()-number);
}
// diffs now contains { -3 -6 1 5 -2 }
var avgDiff = diffs.Sum() / diffs.Count(); // the average is -1
// To get the average value, just add the average diff to the first value:
var totalAverage = numbers.First()+avgDiff;
You can of course implement this in some way that makes it easier to reuse, for example as an extension method to IEnumerable<long>.
Here is how I would do if given this problem. First let's define very simple RationalNumber class, which contains two properties - Dividend and Divisor and an operator for adding two complex numbers. Here is how it looks:
public sealed class RationalNumber
{
public RationalNumber()
{
this.Divisor = 1;
}
public static RationalNumberoperator +( RationalNumberc1, RationalNumber c2 )
{
RationalNumber result = new RationalNumber();
Int64 nDividend = ( c1.Dividend * c2.Divisor ) + ( c2.Dividend * c1.Divisor );
Int64 nDivisor = c1.Divisor * c2.Divisor;
Int64 nReminder = nDividend % nDivisor;
if ( nReminder == 0 )
{
// The number is whole
result.Dividend = nDividend / nDivisor;
}
else
{
Int64 nGreatestCommonDivisor = FindGreatestCommonDivisor( nDividend, nDivisor );
if ( nGreatestCommonDivisor != 0 )
{
nDividend = nDividend / nGreatestCommonDivisor;
nDivisor = nDivisor / nGreatestCommonDivisor;
}
result.Dividend = nDividend;
result.Divisor = nDivisor;
}
return result;
}
private static Int64 FindGreatestCommonDivisor( Int64 a, Int64 b)
{
Int64 nRemainder;
while ( b != 0 )
{
nRemainder = a% b;
a = b;
b = nRemainder;
}
return a;
}
// a / b = a is devidend, b is devisor
public Int64 Dividend { get; set; }
public Int64 Divisor { get; set; }
}
Second part is really easy. Let's say we have an array of numbers. Their average is estimated by Sum(Numbers)/Length(Numbers), which is the same as Number[ 0 ] / Length + Number[ 1 ] / Length + ... + Number[ n ] / Length. For to be able to calculate this we will represent each Number[ i ] / Length as a whole number and a rational part ( reminder ). Here is how it looks:
Int64[] aValues = new Int64[] { long.MaxValue - 100, long.MaxValue - 200, long.MaxValue - 300 };
List<RationalNumber> list = new List<RationalNumber>();
Int64 nAverage = 0;
for ( Int32 i = 0; i < aValues.Length; ++i )
{
Int64 nReminder = aValues[ i ] % aValues.Length;
Int64 nWhole = aValues[ i ] / aValues.Length;
nAverage += nWhole;
if ( nReminder != 0 )
{
list.Add( new RationalNumber() { Dividend = nReminder, Divisor = aValues.Length } );
}
}
RationalNumber rationalTotal = new RationalNumber();
foreach ( var rational in list )
{
rationalTotal += rational;
}
nAverage = nAverage + ( rationalTotal.Dividend / rationalTotal.Divisor );
At the end we have a list of rational numbers, and a whole number which we sum together and get the average of the sequence without an overflow. Same approach can be taken for any type without an overflow for it, and there is no lost of precision.
EDIT:
Why this works:
Define: A set of numbers.
if Average( A ) = SUM( A ) / LEN( A ) =>
Average( A ) = A[ 0 ] / LEN( A ) + A[ 1 ] / LEN( A ) + A[ 2 ] / LEN( A ) + ..... + A[ N ] / LEN( 2 ) =>
if we define An to be a number that satisfies this: An = X + ( Y / LEN( A ) ), which is essentially so because if you divide A by B we get X with a reminder a rational number ( Y / B ).
=> so
Average( A ) = A1 + A2 + A3 + ... + AN = X1 + X2 + X3 + X4 + ... + Reminder1 + Reminder2 + ...;
Sum the whole parts, and sum the reminders by keeping them in rational number form. In the end we get one whole number and one rational, which summed together gives Average( A ). Depending on what precision you'd like, you apply this only to the rational number at the end.
Simple answer with LINQ...
var data = new[] { int.MaxValue, int.MaxValue, int.MaxValue };
var mean = (int)data.Select(d => (double)d / data.Count()).Sum();
Depending on the size of the set fo data you may want to force data .ToList() or .ToArray() before your process this method so it can't requery count on each pass. (Or you can call it before the .Select(..).Sum().)
If you know in advance that all your numbers are going to be 'big' (in the sense of 'much nearer long.MaxValue than zero), you can calculate the average of their distance from long.MaxValue, then the average of the numbers is long.MaxValue less that.
However, this approach will fail if (m)any of the numbers are far from long.MaxValue, so it's horses for courses...
I guess there has to be a compromise somewhere or the other. If the numbers are really getting so large then few digits of lower orders (say lower 5 digits) might not affect the result as much.
Another issue is where you don't really know the size of the dataset coming in, especially in stream/real time cases. Here I don't see any solution other then the
(previousAverage*oldCount + newValue) / (oldCount <- oldCount+1)
Here's a suggestion:
*LargestDataTypePossible* currentAverage;
*SomeSuitableDatatypeSupportingRationalValues* newValue;
*int* count;
addToCurrentAverage(value){
newValue = value/100000;
count = count + 1;
currentAverage = (currentAverage * (count-1) + newValue) / count;
}
getCurrentAverage(){
return currentAverage * 100000;
}
Averaging numbers of a specific numeric type in a safe way while also only using that numeric type is actually possible, although I would advise using the help of BigInteger in a practical implementation. I created a project for Safe Numeric Calculations that has a small structure (Int32WithBoundedRollover) which can sum up to 2^32 int32s without any overflow (the structure internally uses two int32 fields to do this, so no larger data types are used).
Once you have this sum you then need to calculate sum/total to get the average, which you can do (although I wouldn't recommend it) by creating and then incrementing by total another instance of Int32WithBoundedRollover. After each increment you can compare it to the sum until you find out the integer part of the average. From there you can peel off the remainder and calculate the fractional part. There are likely some clever tricks to make this more efficient, but this basic strategy would certainly work without needing to resort to a bigger data type.
That being said, the current implementation isn't build for this (for instance there is no comparison operator on Int32WithBoundedRollover, although it wouldn't be too hard to add). The reason is that it is just much simpler to use BigInteger at the end to do the calculation. Performance wise this doesn't matter too much for large averages since it will only be done once, and it is just too clean and easy to understand to worry about coming up with something clever (at least so far...).
As far as your original question which was concerned with the long data type, the Int32WithBoundedRollover could be converted to a LongWithBoundedRollover by just swapping int32 references for long references and it should work just the same. For Int32s I did notice a pretty big difference in performance (in case that is of interest). Compared to the BigInteger only method the method that I produced is around 80% faster for the large (as in total number of data points) samples that I was testing (the code for this is included in the unit tests for the Int32WithBoundedRollover class). This is likely mostly due to the difference between the int32 operations being done in hardware instead of software as the BigInteger operations are.
How about BigInteger in Visual J#.
If you're willing to sacrifice precision, you could do something like:
long num2 = 0L;
foreach (long num3 in source)
{
num2 += 1L;
}
if (num2 <= 0L)
{
throw Error.NoElements();
}
double average = 0;
foreach (long num3 in source)
{
average += (double)num3 / (double)num2;
}
return average;
Perhaps you can reduce every item by calculating average of adjusted values and then multiply it by the number of elements in collection. However, you'll find a bit different number of of operations on floating point.
var items = new long[] { long.MaxValue - 100, long.MaxValue - 200, long.MaxValue - 300 };
var avg = items.Average(i => i / items.Count()) * items.Count();
You could keep a rolling average which you update once for each large number.
Use the IntX library on CodePlex.
NextAverage = CurrentAverage + (NewValue - CurrentAverage) / (CurrentObservations + 1)
Here is my version of an extension method that can help with this.
public static long Average(this IEnumerable<long> longs)
{
long mean = 0;
long count = longs.Count();
foreach (var val in longs)
{
mean += val / count;
}
return mean;
}
Let Avg(n) be the average in first n number, and data[n] is the nth number.
Avg(n)=(double)(n-1)/(double)n*Avg(n-1)+(double)data[n]/(double)n
Can avoid value overflow however loss precision when n is very large.
For two positive numbers (or two negative numbers) , I found a very elegant solution from here.
where an average computation of (a+b)/2 can be replaced with a+((b-a)/2.