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Creating a power function in C# without using Math.Pow(x, y) [duplicate]

System.Numerics.BigInteger lets you multiply large integers together, but is there anything of the same type for floating point numbers? If not, is there a free library I can use?
//this but with floats
System.Numerics.BigInteger maxint = new BigInteger(int.MaxValue);
System.Numerics.BigInteger big = maxint * maxint * maxint;
System.Console.WriteLine(big);

Perhaps you're looking for BigRational? Microsoft released it under their BCL project on CodePlex. Not actually sure how or if it will fit your needs.
It keeps it as a rational number. You can get the a string with the decimal value either by casting or some multiplication.
var r = new BigRational(5000, 3768);
Console.WriteLine((decimal)r);
Console.WriteLine((double)r);
Or with a simple(ish) extension method like this:
public static class BigRationalExtensions
{
public static string ToDecimalString(this BigRational r, int precision)
{
var fraction = r.GetFractionPart();
// Case where the rational number is a whole number
if(fraction.Numerator == 0 && fraction.Denominator == 1)
{
return r.GetWholePart() + ".0";
}
var adjustedNumerator = (fraction.Numerator
* BigInteger.Pow(10, precision));
var decimalPlaces = adjustedNumerator / fraction.Denominator;
// Case where precision wasn't large enough.
if(decimalPlaces == 0)
{
return "0.0";
}
// Give it the capacity for around what we should need for
// the whole part and total precision
// (this is kinda sloppy, but does the trick)
var sb = new StringBuilder(precision + r.ToString().Length);
bool noMoreTrailingZeros = false;
for (int i = precision; i > 0; i--)
{
if(!noMoreTrailingZeros)
{
if ((decimalPlaces%10) == 0)
{
decimalPlaces = decimalPlaces/10;
continue;
}
noMoreTrailingZeros = true;
}
// Add the right most decimal to the string
sb.Insert(0, decimalPlaces%10);
decimalPlaces = decimalPlaces/10;
}
// Insert the whole part and decimal
sb.Insert(0, ".");
sb.Insert(0, r.GetWholePart());
return sb.ToString();
}
}
If it's out of the precision range of a decimal or double, they will be cast to their respective types with a value of 0.0. Also, casting to decimal, when the result is outside of its range, will cause an OverflowException to be thrown.
The extension method I wrote (which may not be the best way to calculate a fraction's decimal representation) will accurately convert it to a string, with unlimited precision. However, if the number is smaller than the precision requested, it will return 0.0, just like decimal or double would.

It should be considered what the implications would be if there were a BigFloat type.
BigFloat x = 1.0;
BigFloat y = 3.0;
BigFloat z = x / y;
The answer would be 0.333333333333333333333333333333333333333333333333333333 recurring. Forever. Infinite. Out of Memory Error.
It is easy to construct an infinite BigFloat.
However, if you are happy to stick to rational numbers, those express by the dividing one integer with another than you can use BigInteger to build a BigRational type that can provide arbitrary precision for representing any real number.
BigRational x = 1;
BigRational y = 3;
BigRational z = x / y;
This works and gives us this type:
You can just NuGet BigRational and you'll find many implementations, including once from Microsoft.

Double every time brings different values

It's my generating algorithm it's generating random double elements for the array which sum must be 1
public static double [] GenerateWithSumOfElementsIsOne(int elements)
{
double sum = 1;
double [] arr = new double [elements];
for (int i = 0; i < elements - 1; i++)
{
arr[i] = RandomHelper.GetRandomNumber(0, sum);
sum -= arr[i];
}
arr[elements - 1] = sum;
return arr;
}
And the method helper
public static double GetRandomNumber(double minimum, double maximum)
{
Random random = new Random();
return random.NextDouble() * (maximum - minimum) + minimum;
}
My test cases are:
[Test]
[TestCase(7)]
[TestCase(5)]
[TestCase(4)]
[TestCase(8)]
[TestCase(10)]
[TestCase(50)]
public void GenerateWithSumOfElementsIsOne(int num)
{
Assert.AreEqual(1, RandomArray.GenerateWithSumOfElementsIsOne(num).Sum());
}
And the thing is - when I'm testing it returns every time different value like this cases :
Expected: 1
But was: 0.99999999999999967d
Expected: 1
But was: 0.99999999999999989d
But in the next test, it passes sometimes all of them, sometimes not.
I know that troubles with rounding and ask for some help, dear experts :)

https://en.wikipedia.org/wiki/Floating-point_arithmetic
In computing, floating-point arithmetic is arithmetic using formulaic
representation of real numbers as an approximation so as to support a
trade-off between range and precision. For this reason, floating-point
computation is often found in systems which include very small and
very large real numbers, which require fast processing times. A number
is, in general, represented approximately to a fixed number of
significant digits (the significand) and scaled using an exponent in
some fixed base; the base for the scaling is normally two, ten, or
sixteen.
In short, this is what floats do, they dont hold every single value and do approximate. If you would like more precision try using a Decimal instead, or adding tolerance by an epsilon (an upper bound on the relative error due to rounding in floating point arithmetic)
var ratio = a / b;
var diff = Math.Abs(ratio - 1);
return diff <= epsilon;

Round up errors are frequent in case of floating point types (like Single and Double), e.g. let's compute an easy sum:
// 0.1 + 0.1 + ... + 0.1 = ? (100 times). Is it 0.1 * 100 == 10? No!
Console.WriteLine((Enumerable.Range(1, 100).Sum(i => 0.1)).ToString("R"));
Outcome:
9.99999999999998
That's why when comparing floatinfg point values with == or != add tolerance:
// We have at least 8 correct digits
// i.e. the asbolute value of the (round up) error is less than tolerance
Assert.IsTrue(Math.Abs(RandomArray.GenerateWithSumOfElementsIsOne(num).Sum() - 1.0) < 1e-8);

'Grokkable' algorithm to understand exponentiation where the exponent is floating point

To clarify first:
2^3 = 8. That's equivalent to 2*2*2. Easy.
2^4 = 16. That's equivalent to 2*2*2*2. Also easy.
2^3.5 = 11.313708... Er, that's not so easy to grok.
Want I want is a simple algorithm which most clearly shows how 2^3.5 = 11.313708. It should preferably not use any functions apart from the basic addition, subtract, multiply, or divide operators.
The code certainly doesn't have to be fast, nor does it necessarily need to be short (though that would help). Don't worry, it can be approximate to a given user-specified accuracy (which should also be part of the algorithm). I'm hoping there will be a binary chop/search type thing going on, as that's pretty simple to grok.
So far I've found this, but the top answer is far from simple to understand on a conceptual level.
The more answers the merrier, so I can try to understand different ways of attacking the problem.
My language preference for the answer would be C#/C/C++/Java, or pseudocode for all I care.

Ok, let's implement pow(x, y) using only binary searches, addition and multiplication.
Driving y below 1
First, take this out of the way:
pow(x, y) == pow(x*x, y/2)
pow(x, y) == 1/pow(x, -y)
This is important to handle negative exponents and drive y below 1, where things start getting interesting. This reduces the problem to finding pow(x, y) where 0<y<1.
Implementing sqrt
In this answer I assume you know how to perform sqrt. I know sqrt(x) = x^(1/2), but it is easy to implement it just using a binary search to find y = sqrt(x) using y*y=x search function, e.g.:
#define EPS 1e-8
double sqrt2(double x) {
double a = 0, b = x>1 ? x : 1;
while(abs(a-b) > EPS) {
double y = (a+b)/2;
if (y*y > x) b = y; else a = y;
}
return a;
}
Finding the answer
The rationale is that every number below 1 can be approximated as a sum of fractions 1/2^x:
0.875 = 1/2 + 1/4 + 1/8
0.333333... = 1/4 + 1/16 + 1/64 + 1/256 + ...
If you find those fractions, you actually find that:
x^0.875 = x^(1/2+1/4+1/8) = x^(1/2) * x^(1/4) * x^(1/8)
That ultimately leads to
sqrt(x) * sqrt(sqrt(x)) * sqrt(sqrt(sqrt(x)))
So, implementation (in C++)
#define EPS 1e-8
double pow2(double x, double y){
if (x < 0 and abs(round(y)-y) < EPS) {
return pow2(-x, y) * ((int)round(y)%2==1 ? -1 : 1);
} else if (y < 0) {
return 1/pow2(x, -y);
} else if(y > 1) {
return pow2(x * x, y / 2);
} else {
double fraction = 1;
double result = 1;
while(y > EPS) {
if (y >= fraction) {
y -= fraction;
result *= x;
}
fraction /= 2;
x = sqrt2(x);
}
return result;
}
}

Deriving ideas from the other excellent posts, I came up with my own implementation. The answer is based on the idea that base^(exponent*accuracy) = answer^accuracy. Given that we know the base, exponent and accuracy variables beforehand, we can perform a search (binary chop or whatever) so that the equation can be balanced by finding answer. We want the exponent in both sides of the equation to be an integer (otherwise we're back to square one), so we can make accuracy any size we like, and then round it to the nearest integer afterwards.
I've given two ways of doing it. The first is very slow, and will often produce extremely high numbers which won't work with most languages. On the other hand, it doesn't use log, and is simpler conceptually.
public double powSimple(double a, double b)
{
int accuracy = 10;
bool negExponent = b < 0;
b = Math.Abs(b);
bool ansMoreThanA = (a>1 && b>1) || (a<1 && b<1); // Example 0.5^2=0.25 so answer is lower than A.
double accuracy2 = 1.0 + 1.0 / accuracy;
double total = a;
for (int i = 1; i < accuracy* b; i++) total = total*a;
double t = a;
while (true) {
double t2 = t;
for(int i = 1; i < accuracy; i++) t2 = t2 * t; // Not even a binary search. We just hunt forwards by a certain increment
if((ansMoreThanA && t2 > total) || (!ansMoreThanA && t2 < total)) break;
if (ansMoreThanA) t *= accuracy2; else t /= accuracy2;
}
if (negExponent) t = 1 / t;
return t;
}
This one below is a little more involved as it uses log(). But it is much quicker and doesn't suffer from the super-high number problems as above.
public double powSimple2(double a, double b)
{
int accuracy = 1000000;
bool negExponent= b<0;
b = Math.Abs(b);
double accuracy2 = 1.0 + 1.0 / accuracy;
bool ansMoreThanA = (a>1 && b>1) || (a<1 && b<1); // Example 0.5^2=0.25 so answer is lower than A.
double total = Math.Log(a) * accuracy * b;
double t = a;
while (true) {
double t2 = Math.Log(t) * accuracy;
if ((ansMoreThanA && t2 > total) || (!ansMoreThanA && t2 < total)) break;
if (ansMoreThanA) t *= accuracy2; else t /= accuracy2;
}
if (negExponent) t = 1 / t;
return t;
}

You can verify that 2^3.5 = 11.313708 very easily: check that 11.313708^2 = (2^3.5)^2 = 2^7 = 128
I think the easiest way to understand the computation you would actually do for this would be to refresh your understanding of logarithms - one starting point would be http://en.wikipedia.org/wiki/Logarithm#Exponentiation.
If you really want to compute non-integer powers with minimal technology one way to do that would be to express them as fractions with denominator a power of two and then take lots of square roots. E.g. x^3.75 = x^3 * x^(1/2) * x^(1/4) then x^(1/2) = sqrt(x), x^(1/4) = sqrt(sqrt(x)) and so on.
Here is another approach, based on the idea of verifying a guess. Given y, you want to find x such that x^(a/b) = y, where a and b are integers. This equation implies that x^a = y^b. You can calculate y^b, since you know both numbers. You know a, so you can - as you originally suspected - use binary chop or perhaps some numerically more efficient algorithm to solve x^a = y^b for x by simply guessing x, computing x^a for this guess, comparing it with y^b, and then iteratively improving the guess.
Example: suppose we wish to find 2^0.878 by this method. Then set a = 439, b = 500, so we wish to find 2^(439/500). If we set x=2^(439/500) we have x^500 = 2^439, so compute 2^439 and (by binary chop or otherwise) find x such that x^500 = 2^439.

Most of it comes down to being able to invert the power operation.
In other words, the basic idea is that (for example) N2 should be basically the "opposite" of N1/2 so that if you do something like:
M = N2
L = M1/2
Then the result you get in L should be the same as the original value in N (ignoring any rounding and such).
Mathematically, that means that N1/2 is the same as sqrt(N), N1/3 is the cube root of N, and so on.
The next step after that would be something like N3/2. This is pretty much the same idea: the denominator is a root, and the numerator is a power, so N3/2 is the square root of the cube of N (or the cube of the square root of N--works out the same).
With decimals, we're just expressing a fraction in a slightly different form, so something like N3.14 can be viewed as N314/100--the hundredth root of N raised to the power 314.
As far as how you compute these: there are quite a few different ways, depending heavily on the compromise you prefer between complexity (chip area, if you're implementing it in hardware) and speed. The obvious way is to use a logarithm: AB = Log-1(Log(A)*B).
For a more restricted set of inputs, such as just finding the square root of N, you can often do better than that extremely general method though. For example, the binary reducing method is quite fast--implemented in software, it's still about the same speed as Intel's FSQRT instruction.

As stated in the comments, its not clear if you want a mathematical description of how fractional powers work, or an algorithm to calculate fractional powers.
I will assume the latter.
For almost all functions (like y = 2^x) there is a means of approximating the function using a thing called the Taylor Series http://en.wikipedia.org/wiki/Taylor_series. This approximates any reasonably behaved function as a polynomial, and polynomials can be calculated using only multiplication, division, addition and subtraction (all of which the CPU can do directly). If you calculate the Taylor series for y = 2^x and plug in x = 3.5 you will get 11.313...
This almost certainly not how exponentiation is actually done on your computer. There are many algorithms which run faster for different inputs. For example, if you calculate 2^3.5 using the Taylor series, then you would have to look at many terms to calculate it with any accuracy. However, the Taylor series will converge much faster for x = 0.5 than for x = 3.5. So one obvious improvement is to calculate 2^3.5 as 2^3 * 2^0.5, as 2^3 is easy to calculate directly. Modern exponentiation algorithms will use many, many tricks to speed up processing - but the principle is still much the same, approximate the exponentiation function as some infinite sum, and calculate as many terms as you need to get the accuracy that is required.

double and rounding is very hard, but this is crazy

double a = 135.24; // a is set to 135.24000000000001 actually
double b = Math.Round(a, 0); // set to 135.0
double c = Math.Round(a, 1); // set to 135.19999999999999
double d = Math.Round(a, 2); // set to 135.24000000000001
double e = Math.Round(a, 3); // set to 135.24000000000001
double f = Math.Round(a, 4); // set to 135.24000000000001
double g = Math.Round(a, 5); // set to 135.24000000000001
double h = Math.Round(a, 10); // set to 135.24000000000001
double i = Math.Round(a, 14); // set to 135.24000000000001
double j = Math.Round(a, 2
, MidpointRounding.AwayFromZero ); // set to 135.24000000000001
double k = Math.Round(a, 2
, MidpointRounding.ToEven ); // set to 135.24000000000001
Sooooo, this means that 135.24 cannot be represented with a double, right?

Yes, 135.24 cannot be represented by double since double uses binary exponential notation.
That is: 135.24 can be represented exponentially in base of 2 as 1.0565625 * 128 = ( 1 + 1/32 + 1/64 + 1/128 + 1/1024 + ... ) * (2**7).
The representation cannot be done exactly, because 13524 does not divide by 5. Let's look:
135.24 = 13524/(10**2)
representation is finite <=> exist whole x and n satisfying 135.24 = x/(2**n)
135.24 = x/(2**n)
13524 / (10**2) = x / (2**n)
13524 * (2**n) = (10**2) * x
13524 * (2**n) = 2*2*5*5 * x
there is no "5" on the left side, so it cannot be done
(known as the Fundamental Theorem of Arithmetic)
In general, finite binary representation is exact only if there is sufficient number of "fives" in prime factorization of the decimal number.
Now the fun part:
double delta = 0.5;
while( 1 + delta > 1 )
delta /= 2;
Console.WriteLine( delta );
Precision of double is different near 1, different near 0, and different for some big numbers. Some binary representation examples on Wikipedia: Double precision floating point format
But the most important thing is that internal processor floating-point stack may have much better precision than 8 bytes (double). If number does not have to be transferred to RAM and stripped down to 8 bytes we can get a really nice precision.
Testing something like this on different processors (AMD, Intel), languages (C, C++, C#, Java) or compiler optimization levels can give results can be around 1e-16, 1e-20, or even 1e-320
Take a look at CIL / assembler / jasmin code to see exactly what is going on (eg: for C++ g++ -S test.cpp creates test.s file with assembler code in it)

That is generally a problem with floating point numbers. If you need an exact representation of numbers (e.g. for billing, ...) then you should use Decimal.
Try following piece of code and you will see that you do not have the output 0, 0.1, 0.2, ... 1.0.
for(double i = 0; i <= 1.0; i += 0.001)
{
Console.WriteLine(i);
}

Try using decimal instead. Floating points are not very precise (thus some numbers can't be represented) :)

Yes, it cannot. This is why there's another nonintegra datatype called decimal. It takes different amount of memory and has different min/max numerical ranges than double, and is NOT bit-convertible*) to double, but in turn it can held numbers precisely without any distortions.
*) That is, you cannot i.e. copy it as bytes and push to C++ code. However, you can still cast it to double and back. Just mind that the cast will NOT be precise, as double cannot hold some numbers that decimal can, and vice versa

You can see the definition.The Round function defined as-
public static double Round(double value, int digits, MidpointRounding mode)
{
if (digits < 0 || digits > 15)
throw new ArgumentOutOfRangeException("digits", Environment.GetResourceString("ArgumentOutOfRange_RoundingDigits"));
if (mode >= MidpointRounding.ToEven && mode <= MidpointRounding.AwayFromZero)
return Math.InternalRound(value, digits, mode);
throw new ArgumentException(Environment.GetResourceString("Argument_InvalidEnumValue", (object) mode, (object) "MidpointRounding"), "mode");
}
private static unsafe double InternalRound(double value, int digits, MidpointRounding mode)
{
if (Math.Abs(value) < Math.doubleRoundLimit)
{
double num1 = Math.roundPower10Double[digits];
value *= num1;
if (mode == MidpointRounding.AwayFromZero)
{
double num2 = Math.SplitFractionDouble(&value);
if (Math.Abs(num2) >= 0.5)
value += (double) Math.Sign(num2);
}
else
value = Math.Round(value);
value /= num1;
}
return value;
}

Truncate number of digit of double value in C#

How can i truncate the leading digit of double value in C#,I have tried Math.Round(doublevalue,2) but not giving the require result. and i didn't find any other method in Math class.
For example i have value 12.123456789 and i only need 12.12.

EDIT: It's been pointed out that these approaches round the value instead of truncating. It's hard to genuinely truncate a double value because it's not really in the right base... but truncating a decimal value is more feasible.
You should use an appropriate format string, either custom or standard, e.g.
string x = d.ToString("0.00");
or
string x = d.ToString("F2");
It's worth being aware that a double value itself doesn't "know" how many decimal places it has. It's only when you convert it to a string that it really makes sense to do so. Using Math.Round will get the closest double value to x.xx00000 (if you see what I mean) but it almost certainly won't be the exact value x.xx00000 due to the way binary floating point types work.
If you need this for anything other than string formatting, you should consider using decimal instead. What does the value actually represent?
I have articles on binary floating point and decimal floating point in .NET which you may find useful.

What have you tried? It works as expected for me:
double original = 12.123456789;
double truncated = Math.Truncate(original * 100) / 100;
Console.WriteLine(truncated); // displays 12.12

double original = 12.123456789;
double truncated = Truncate(original, 2);
Console.WriteLine(truncated.ToString());
// or
// Console.WriteLine(truncated.ToString("0.00"));
// or
// Console.WriteLine(Truncate(original, 2).ToString("0.00"));
public static double Truncate(double value, int precision)
{
return Math.Truncate(value * Math.Pow(10, precision)) / Math.Pow(10, precision);
}

How about:
double num = 12.12890;
double truncatedNum = ((int)(num * 100))/100.00;

This could work (although not tested):
public double RoundDown(this double value, int digits)
{
int factor = Math.Pow(10,digits);
return Math.Truncate(value * factor) / factor;
}
Then you simply use it like this:
double rounded = number.RoundDown(2);

This code....
double x = 12.123456789;
Console.WriteLine(x);
x = Math.Round(x, 2);
Console.WriteLine(x);
Returns this....
12.123456789
12.12
What is your desired result that is different?
If you want to keep the value as a double, and just strip of any digits after the second decimal place and not actually round the number then you can simply subtract 0.005 from your number so that round will then work. For example.
double x = 98.7654321;
Console.WriteLine(x);
double y = Math.Round(x - 0.005, 2);
Console.WriteLine(y);
Produces this...
98.7654321
98.76

There are a lot of answers using Math.Truncate(double).
However, the approach using Math.Truncate(double) can lead to incorrect results.
For instance, it will return 5.01 truncating 5.02, because multiplying of double values doesn't work precisely and 5.02*100=501.99999999999994
If you really need this precision, consider, converting to Decimal before truncating.
public static double Truncate(double value, int precision)
{
decimal power = (decimal)Math.Pow(10, precision);
return (double)(Math.Truncate((decimal)value * power) / power);
}
Still, this approach is ~10 times slower.

I'm sure there's something more .netty out there but why not just:-
double truncVal = Math.Truncate(val * 100) / 100;
double remainder = val-truncVal;

If you are looking to have two points after the decimal without rounding the number, the following should work
string doubleString = doublevalue.ToString("0.0000"); //To ensure we have a sufficiently lengthed string to avoid index issues
Console.Writeline(doubleString
.Substring(0, (doubleString.IndexOf(".") +1) +2));
The second parameter of substring is the count, and IndexOf returns to zero-based index, so we have to add one to that before we add the 2 decimal values.
This answer is assuming that the value should NOT be rounded

For vb.net use this extension:
Imports System.Runtime.CompilerServices
Module DoubleExtensions
<Extension()>
Public Function Truncate(dValue As Double, digits As Integer)
Dim factor As Integer
factor = Math.Pow(10, digits)
Return Math.Truncate(dValue * factor) / factor
End Function
End Module

I use a little formatting class that I put together which can add gaps and all sorts.
Here is one of the methods that takes in a decimal and return different amounts of decimal places based on the decimal display setting in the app
public decimal DisplayDecimalFormatting(decimal input, bool valueIsWeightElseMoney)
{
string inputString = input.ToString();
if (valueIsWeightElseMoney)
{
int appDisplayDecimalCount = Program.SettingsGlobal.DisplayDecimalPlacesCount;
if (appDisplayDecimalCount == 3)//0.000
{
inputString = String.Format("{0:#,##0.##0}", input, displayCulture);
}
else if (appDisplayDecimalCount == 2)//0.00
{
inputString = String.Format("{0:#,##0.#0}", input, displayCulture);
}
else if (appDisplayDecimalCount == 1)//0.0
{
inputString = String.Format("{0:#,##0.0}", input, displayCulture);
}
else//appDisplayDecimalCount 0 //0
{
inputString = String.Format("{0:#,##0}", input, displayCulture);
}
}
else
{
inputString = String.Format("{0:#,##0.#0}", input, displayCulture);
}
//Check if worked and return if worked, else return 0
bool itWorked = false;
decimal returnDec = 0.00m;
itWorked = decimal.TryParse(inputString, out returnDec);
if (itWorked)
{
return returnDec;
}
else
{
return 0.00m;
}
}

object number = 12.123345534;
string.Format({"0:00"},number.ToString());