Does .NET have a built-in method to calculate the ULP of a given double or float?
If not, what is the most efficient way to do so?
It seems the function is pretty trivial; this is based on the pseudocode in the accepted answer to the question linked by vulkanino:
double value = whatever;
long bits = BitConverter.DoubleToInt64Bits(value);
double nextValue = BitConverter.Int64BitsToDouble(bits + 1);
double result = nextValue - value;
For floats, you'd need to provide your own implementation of SingleToInt32Bits and Int32BitsToSingle, since BitConverter doesn't have those functions.
This page shows the special cases in the java implementation of the function; handling those should be fairly trivial, too.
phoog answer is good but has weaknesses with negative numbers, max_double, infinity and NaN.
phoog_ULP(positive x) --> a positive number. Good.
phoog_ULP(negative x) --> a negative number. I would expect positive number.
To fix this I recommend instead:
long bits = BitConverter.DoubleToInt64Bits(value) & 0x7FFFFFFFFFFFFFFFL;
Below are fringe cases that need resolution should you care...
phoog_ULP(x = +/- Max_double 1.797...e+308) returns an infinite result. (+1.996...e+292) expected.
phoog_ULP(x = +/- Infinity) results in a NaN. +Infinity expected.
phoog_ULP(x = +/- NaN) may unexpectedly change from a sNan to a qNaN. No change expected. One could argue either way on if the sign should become + in this case.
To solve these, I only see a short series of brutish if() tests to accommodate these, possible on the "bits" value for expediency. Example:
double ulpc(double value) {
long long bits = BitConverter::DoubleToInt64Bits(value);
if ((bits & 0x7FF0000000000000L) == 0x7FF0000000000000L) { // if x is not finite
if (bits & 0x000FFFFFFFFFFFFFL) { // if x is a NaN
return value; // I did not force the sign bit here with NaNs.
}
return BitConverter.Int64BitsToDouble(0x7FF0000000000000L); // Positive Infinity;
}
bits &= 0x7FFFFFFFFFFFFFFFL; // make positive
if (bits == 0x7FEFFFFFFFFFFFFFL) { // if x == max_double (notice the _E_)
return BitConverter.Int64BitsToDouble(bits) - BitConverter.Int64BitsToDouble(bits-1);
}
double nextValue = BitConverter.Int64BitsToDouble(bits + 1);
double result = nextValue - fabs(value);
return result;
}
Related
I have been looking at some way to determine the scale and precision of a decimal in C#, which led me to several SO questions, yet none of them seem to have correct answers, or have misleading titles (they really are about SQL server or some other databases, not C#), or any answers at all. The following post, I think, is the closest to what I'm after, but even this seems wrong:
Determine the decimal precision of an input number
First, there seems to be some confusion about the difference between scale and precision. Per Google (per MSDN):
Precision is the number of digits in a number. Scale is the number of digits to the right of the decimal point in a number.
With that being said, the number 12345.67890M would have a scale of 5 and a precision of 10. I have not discovered a single code example that would accurately calculate this in C#.
I want to make two helper methods, decimal.Scale(), and decimal.Precision(), such that the following unit test passes:
[TestMethod]
public void ScaleAndPrecisionTest()
{
//arrange
var number = 12345.67890M;
//act
var scale = number.Scale();
var precision = number.Precision();
//assert
Assert.IsTrue(precision == 10);
Assert.IsTrue(scale == 5);
}
but I have yet to find a snippet that will do this, though several people have suggested using decimal.GetBits(), and others have said, convert it to a string and parse it.
Converting it to a string and parsing it is, in my mind, an awful idea, even disregarding the localization issue with the decimal point. The math behind the GetBits() method, however, is like Greek to me.
Can anyone describe what the calculations would look like for determining scale and precision in a decimal value for C#?
This is how you get the scale using the GetBits() function:
decimal x = 12345.67890M;
int[] bits = decimal.GetBits(x);
byte scale = (byte) ((bits[3] >> 16) & 0x7F);
And the best way I can think of to get the precision is by removing the fraction point (i.e. use the Decimal Constructor to reconstruct the decimal number without the scale mentioned above) and then use the logarithm:
decimal x = 12345.67890M;
int[] bits = decimal.GetBits(x);
//We will use false for the sign (false = positive), because we don't care about it.
//We will use 0 for the last argument instead of bits[3] to eliminate the fraction point.
decimal xx = new Decimal(bits[0], bits[1], bits[2], false, 0);
int precision = (int)Math.Floor(Math.Log10((double)xx)) + 1;
Now we can put them into extensions:
public static class Extensions{
public static int GetScale(this decimal value){
if(value == 0)
return 0;
int[] bits = decimal.GetBits(value);
return (int) ((bits[3] >> 16) & 0x7F);
}
public static int GetPrecision(this decimal value){
if(value == 0)
return 0;
int[] bits = decimal.GetBits(value);
//We will use false for the sign (false = positive), because we don't care about it.
//We will use 0 for the last argument instead of bits[3] to eliminate the fraction point.
decimal d = new Decimal(bits[0], bits[1], bits[2], false, 0);
return (int)Math.Floor(Math.Log10((double)d)) + 1;
}
}
And here is a fiddle.
First of all, solve the "physical" problem: how you're gonna decide which digits are significant. The fact is, "precision" has no physical meaning unless you know or guess the absolute error.
Now, there are 2 fundamental ways to determine each digit (and thus, their number):
get+interpret the meaningful parts
calculate mathematically
The 2nd way can't detect trailing zeros in the fractional part (which may or may not be significant depending on your answer to the "physical" problem), so I won't cover it unless requested.
For the first one, in the Decimal's interface, I see 2 basic methods to get the parts: ToString() (a few overloads) and GetBits().
ToString(String, IFormatInfo) is actually a reliable way since you can define the format exactly.
E.g. use the F specifier and pass a culture-neutral NumberFormatInfo in which you have manually set all the fields that affect this particular format.
regarding the NumberDecimalDigits field: a test shows that it is the minimal number - so set it to 0 (the docs are unclear on this), - and trailing zeros are printed all right if there are any
The semantics of GetBits() result are documented clearly in its MSDN article (so laments like "it's Greek to me" won't do ;) ). Decompiling with ILSpy shows that it's actually a tuple of the object's raw data fields:
public static int[] GetBits(decimal d)
{
return new int[]
{
d.lo,
d.mid,
d.hi,
d.flags
};
}
And their semantics are:
|high|mid|low| - binary digits (96 bits), interpreted as an integer (=aligned to the right)
flags:
bits 16 to 23 - "the power of 10 to divide the integer number" (=number of fractional decimal digits)
(thus (flags>>16)&0xFF is the raw value of this field)
bit 31 - sign (doesn't concern us)
as you can see, this is very similar to IEEE 754 floats.
So, the number of fractional digits is the exponent value. The number of total digits is the number of digits in the decimal representation of the 96-bit integer.
Racil's answer gives you the value of the internal scale value of the decimal which is correct, although if the internal representation ever changes it'll be interesting.
In the current format the precision portion of decimal is fixed at 96 bits, which is between 28 and 29 decimal digits depending on the number. All .NET decimal values share this precision. Since this is constant there's no internal value you can use to determine it.
What you're apparently after though is the number of digits, which we can easily determine from the string representation. We can also get the scale at the same time or at least using the same method.
public struct DecimalInfo
{
public int Scale;
public int Length;
public override string ToString()
{
return string.Format("Scale={0}, Length={1}", Scale, Length);
}
}
public static class Extensions
{
public static DecimalInfo GetInfo(this decimal value)
{
string decStr = value.ToString().Replace("-", "");
int decpos = decStr.IndexOf(".");
int length = decStr.Length - (decpos < 0 ? 0 : 1);
int scale = decpos < 0 ? 0 : length - decpos;
return new DecimalInfo { Scale = scale, Length = length };
}
}
My scenario is that if
47/15= 3.13333
i want to convert it into 4, if the result has decimal i want to increase the result by 1, right now i am doing this like
float res = ((float)(62-15) / 15);
if (res.ToString().Contains("."))
{
string digit=res.ToString().Substring(0, res.ToString().IndexOf('.'));
int incrementDigit=Convert.ToInt16(k) + 1;
}
I want to know is there any shortcut way or built in function in c# so that i can do this fast without implementing string functions.
Thanks a lot.
Do you mean you want to perform integer division, but always rounding up? I suspect you want:
public static int DivideByFifteenRoundingUp(int value) {
return (value + 14) / 15;
}
This avoids using floating point arithmetic at all - it just allows any value which isn't an exact multiple of 15 to be rounded up, due to the way that integer arithmetic truncates towards zero.
Note that this does not work for negative input - for example, if you passed in -15 this would return 0. you could fix this with:
public static int DivideByFifteenRoundingUp(int value) {
return value < 0 ? value / 15 : (value + 14) / 15;
}
Use Math.Ceiling Quoting MSDN:
Returns the smallest integral value that is greater than or equal to
the specified decimal number.
You are looking for Math.Ceiling().
Convert the value you have to a Decimal or Double and the result of that method is what you need. Like:
double number = ((double)(62-15) / (double)15);
double result = Math.Ceiling(number);
Note the fact that I cast 15 to a double, so I avoid integer division. That is most likely not what you want here.
Another way of doing what you ask is to add 0.5 to every number, then floor it (truncate the decimal places). I'm afraid I don't have access to a C# compiler right now to confirm the exact function calls!
NB: But as others have confirmed, I would think the Math.Ceiling function best communicates to others what you intend.
Something like:
float res = ((float)(62-15) / 15);
int incrementDigit = (int)Math.Ceiling(res);
or
int incrementDigit = (int)(res + 0.5f);
I am doing a calculation which frequently involves values like 3.47493E+17298. This is way beyond what a double can handle, and I don't need extra precision, just extra range of exponents, so I created my own little struct in C#.
My struct uses a long for significand and sign, and an int for exponent, so I effectively have:
1 sign bit
32 exponent bits (regular 2's complement exponent)
63 significand bits
I am curious what steps could be made to make my multiplication routine more efficient. I am running an enormous number of multiplications of these extended range values, and it is pretty fast, but I was looking for hints as to making it faster.
My multiplication routine:
public static BigFloat Multiply(BigFloat left, BigFloat right)
{
long shsign1;
long shsign2;
if (left.significand == 0)
{
return bigZero;
}
if (right.significand == 0)
{
return bigZero;
}
shsign1 = left.significand;
shsign2 = right.significand;
// scaling down significand to prevent overflow multiply
// s1 and s2 indicate how much the left and right
// significands need shifting.
// The multLimit is a long constant indicating the
// max value I want either significand to be
int s1 = qshift(shsign1, multLimit);
int s2 = qshift(shsign2, multLimit);
shsign1 >>= s1;
shsign2 >>= s2;
BigFloat r;
r.significand = shsign1 * shsign2;
r.exponent = left.exponent + right.exponent + s1 + s2;
return r;
}
And the qshift:
It just finds out how much to shift the val to make it smaller in absolute value than the limit.
public static int qshift(long val, long limit)
{
long q = val;
long c = limit;
long nc = -limit;
int counter = 0;
while (q > c || q < nc)
{
q >>= 1;
counter++;
}
return counter;
}
Here is a completely different idea...
Use the hardware's floating-point machinery, but augment it with your own integer exponents. Put another way, make BigFloat.significand be a floating-point number instead of an integer.
Then you can use ldexp and frexp to keep the actual exponent on the float equal to zero. These should be single machine instructions.
So BigFloat multiply becomes:
r.significand = left.significand * right.significand
r.exponent = left.exponent + right.exponent
tmp = (actual exponent of r.significand from frexp)
r.exponent += tmp
(use ldexp to subtract tmp from actual exponent of r.significand)
Unfortunately,the last two steps require frexp and ldexp, which searches suggest are not available in C#. So you might have to write this bit in C.
...
Or, actually...
Use floating-point numbers for the significands, but just keep them normalized between 1 and 2. So again, use floats for the significands, and multiply like this:
r.significand = left.significand * right.significand;
r.exponent = left.exponent + right.exponent;
if (r.significand >= 2) {
r.significand /= 2;
r.exponent += 1;
}
assert (r.significand >= 1 && r.significand < 2); // for debugging...
This should work as long as you maintain the invariant mentioned in the assert(). (Because if x is between 1 and 2 and y is between 1 and 2 then x*y is between 1 and 4, so the normalization step is just has to check for when the significand product is between 2 and 4.)
You will also need to normalize the results of additions etc., but I suspect you are already doing that.
Although you will need to special-case zero after all :-).
[edit, to flesh out the frexp version]
BigFloat BigFloat::normalize(BigFloat b)
{
double temp = b.significand;
double tempexp = b.exponent;
double temp2, tempexp2;
temp2 = frexp(temp, &tempexp2);
// Need to test temp2 for infinity and NaN here
tempexp += tempexp2;
if (tempexp < MIN_EXP)
// underflow!
if (tempexp > MAX_EXP)
// overflow!
BigFloat r;
r.exponent = tempexp;
r.significand = temp2;
}
In other words, I would suggest factoring this out as a "normalize" routine, since presumably you want to use it following additions, subtractions, multiplications, and divisions.
And then there are all the corner cases to worry about...
You probably want to handle underflow by returning zero. Overflow depends on your tastes; should either be an error or +-infinity. Finally, if the result of frexp() is infinity or NaN, the value of tempexp2 is undefined, so you might want to check those cases, too.
I am not much of a C# programmer, but here are some general ideas.
First, are there any profiling tools for C#? If so, start with those...
The time is very likely being spent in your qshift() function; in particular, the loop. Mispredicted branches are nasty.
I would rewrite it as:
long q = abs(val);
int x = q/nc;
(find next power of 2 bigger than x)
For that last step, see this question and answer.
Then instead of shifting by qshift, just divide by this power of 2. (Does C# have "find first set" (aka. ffs)? If so, you can use it to get the shift count from the power of 2; it should be one instruction.)
Definitely inline this sequence if the compiler will not do it for you.
Also, I would ditch the special cases for zero, unless you are multiplying by zero a lot. Linear code good; conditionals bad.
If you're sure there won't be an overflow, you can use an unchecked block.
That will remove the overflow checks, and give you a bit more performance.
I'm running NUnit tests to evaluate some known test data and calculated results. The numbers are floating point doubles so I don't expect them to be exactly equal, but I'm not sure how to treat them as equal for a given precision.
In NUnit we can compare with a fixed tolerance:
double expected = 0.389842845321551d;
double actual = 0.38984284532155145d; // really comes from a data import
Expect(actual, EqualTo(expected).Within(0.000000000000001));
and that works fine for numbers below zero, but as the numbers grow the tolerance really needs to be changed so we always care about the same number of digits of precision.
Specifically, this test fails:
double expected = 1.95346834136148d;
double actual = 1.9534683413614817d; // really comes from a data import
Expect(actual, EqualTo(expected).Within(0.000000000000001));
and of course larger numbers fail with tolerance..
double expected = 1632.4587642911599d;
double actual = 1632.4587642911633d; // really comes from a data import
Expect(actual, EqualTo(expected).Within(0.000000000000001));
What's the correct way to evaluate two floating point numbers are equal with a given precision? Is there a built-in way to do this in NUnit?
From msdn:
By default, a Double value contains 15 decimal digits of precision, although a maximum of 17 digits is maintained internally.
Let's assume 15, then.
So, we could say that we want the tolerance to be to the same degree.
How many precise figures do we have after the decimal point? We need to know the distance of the most significant digit from the decimal point, right? The magnitude. We can get this with a Log10.
Then we need to divide 1 by 10 ^ precision to get a value around the precision we want.
Now, you'll need to do more test cases than I have, but this seems to work:
double expected = 1632.4587642911599d;
double actual = 1632.4587642911633d; // really comes from a data import
// Log10(100) = 2, so to get the manitude we add 1.
int magnitude = 1 + (expected == 0.0 ? -1 : Convert.ToInt32(Math.Floor(Math.Log10(expected))));
int precision = 15 - magnitude ;
double tolerance = 1.0 / Math.Pow(10, precision);
Assert.That(actual, Is.EqualTo(expected).Within(tolerance));
It's late - there could be a gotcha in here. I tested it against your three sets of test data and each passed. Changing pricision to be 16 - magnitude caused the test to fail. Setting it to 14 - magnitude obviously caused it to pass as the tolerance was greater.
This is what I came up with for The Floating-Point Guide (Java code, but should translate easily, and comes with a test suite, which you really really need):
public static boolean nearlyEqual(float a, float b, float epsilon)
{
final float absA = Math.abs(a);
final float absB = Math.abs(b);
final float diff = Math.abs(a - b);
if (a * b == 0) { // a or b or both are zero
// relative error is not meaningful here
return diff < (epsilon * epsilon);
} else { // use relative error
return diff / (absA + absB) < epsilon;
}
}
The really tricky question is what to do when one of the numbers to compare is zero. The best answer may be that such a comparison should always consider the domain meaning of the numbers being compared rather than trying to be universal.
How about converting the items each to string and comparing the strings?
string test1 = String.Format("{0:0.0##}", expected);
string test2 = String.Format("{0:0.0##}", actual);
Assert.AreEqual(test1, test2);
Assert.That(x, Is.EqualTo(y).Within(10).Percent);
is a decent option (changes it to a relative comparison, where x is required to be within 10% of y). You may want to add extra handling for 0, as otherwise you'll get an exact comparison in that case.
Update:
Another good option is
Assert.That(x, Is.EqualTo(y).Within(1).Ulps);
where Ulps means units in the last place. See https://docs.nunit.org/articles/nunit/writing-tests/constraints/EqualConstraint.html#comparing-floating-point-values.
I don't know if there's a built-in way to do it with nunit, but I would suggest multiplying each float by the 10x the precision you're seeking, storing the results as longs, and comparing the two longs to each other.
For example:
double expected = 1632.4587642911599d;
double actual = 1632.4587642911633d;
//for a precision of 4
long lActual = (long) 10000 * actual;
long lExpected = (long) 10000 * expected;
if(lActual == lExpected) { // Do comparison
// Perform desired actions
}
This is a quick idea, but how about shifting them down till they are below zero? Should be something like num/(10^ceil(log10(num))) . . . not to sure about how well it would work, but its an idea.
1632.4587642911599 / (10^ceil(log10(1632.4587642911599))) = 0.16324587642911599
How about:
const double significantFigures = 10;
Assert.AreEqual(Actual / Expected, 1.0, 1.0 / Math.Pow(10, significantFigures));
The difference between the two values should be less than either value divided by the precision.
Assert.Less(Math.Abs(firstValue - secondValue), firstValue / Math.Pow(10, precision));
open FsUnit
actual |> should (equalWithin errorMargin) expected
This code works (C# 3)
double d;
if(d == (double)(int)d) ...;
Is there a better way to do this?
For extraneous reasons I want to avoid the double cast so; what nice ways exist other than this? (even if they aren't as good)
Note: Several people pointed out the (important) point that == is often problematic regrading floating point. In this cases I expect values in the range of 0 to a few hundred and they are supposed to be integers (non ints are errors) so if those points "shouldn't" be an issue for me.
d == Math.Floor(d)
does the same thing in other words.
NB: Hopefully you're aware that you have to be very careful when doing this kind of thing; floats/doubles will very easily accumulate miniscule errors that make exact comparisons (like this one) fail for no obvious reason.
This would work I think:
if (d % 1 == 0) {
//...
}
If your double is the result of another calculation, you probably want something like:
d == Math.Floor(d + 0.00001);
That way, if there's been a slight rounding error, it'll still match.
I cannot answer the C#-specific part of the question, but I must point out you are probably missing a generic problem with floating point numbers.
Generally, integerness is not well defined on floats. For the same reason that equality is not well defined on floats. Floating point calculations normally include both rounding and representation errors.
For example, 1.1 + 0.6 != 1.7.
Yup, that's just the way floating point numbers work.
Here, 1.1 + 0.6 - 1.7 == 2.2204460492503131e-16.
Strictly speaking, the closest thing to equality comparison you can do with floats is comparing them up to a chosen precision.
If this is not sufficient, you must work with a decimal number representation, with a floating point number representation with built-in error range, or with symbolic computations.
A simple test such as 'x == floor(x)' is mathematically assured to work correctly, for any fixed-precision FP number.
All legal fixed-precision FP encodings represent distinct real numbers, and so for every integer x, there is at most one fixed-precision FP encoding that matches it exactly.
Therefore, for every integer x that CAN be represented in such way, we have x == floor(x) necessarily, since floor(x) by definition returns the largest FP number y such that y <= x and y represents an integer; so floor(x) must return x.
If you are just going to convert it, Mike F / Khoth's answer is good, but doesn't quite answer your question. If you are going to actually test, and it's actually important, I recommend you implement something that includes a margin of error.
For instance, if you are considering money and you want to test for even dollar amounts, you might say (following Khoth's pattern):
if( Math.abs(d - Math.Floor(d + 0.001)) < 0.001)
In other words, take the absolute value of the difference of the value and it's integer representation and ensure that it's small.
You don't need the extra (double) in there. This works:
if (d == (int)d) {
//...
}
Use Math.Truncate()
This will let you choose what precision you're looking for, plus or minus half a tick, to account for floating point drift. The comparison is integral also which is nice.
static void Main(string[] args)
{
const int precision = 10000;
foreach (var d in new[] { 2, 2.9, 2.001, 1.999, 1.99999999, 2.00000001 })
{
if ((int) (d*precision + .5)%precision == 0)
{
Console.WriteLine("{0} is an int", d);
}
}
}
and the output is
2 is an int
1.99999999 is an int
2.00000001 is an int
Something like this
double d = 4.0;
int i = 4;
bool equal = d.CompareTo(i) == 0; // true
Could you use this
bool IsInt(double x)
{
try
{
int y = Int16.Parse(x.ToString());
return true;
}
catch
{
return false;
}
}
To handle the precision of the double...
Math.Abs(d - Math.Floor(d)) <= double.Epsilon
Consider the following case where a value less then double.Epsilon fails to compare as zero.
// number of possible rounds
const int rounds = 1;
// precision causes rounding up to double.Epsilon
double d = double.Epsilon*.75;
// due to the rounding this comparison fails
Console.WriteLine(d == Math.Floor(d));
// this comparison succeeds by accounting for the rounding
Console.WriteLine(Math.Abs(d - Math.Floor(d)) <= rounds*double.Epsilon);
// The difference is double.Epsilon, 4.940656458412465E-324
Console.WriteLine(Math.Abs(d - Math.Floor(d)).ToString("E15"));