I have picked two random double numbers:
double a = 7918.52;
double b = 5000.00;
I would expect to get 2918.52 from a - b.
Well, it gives me a result of 2918.5200000000004, which seems odd.
print(a - b); // -> 2918.5200000000004
But if I change double a to 7918.54, I will get the expected result of 2918.54.
Can someone explain to me why some double values result in unexpected rounding issues and others do not?
The reason for this is floating-point arithmetic and the fact that Dart uses the IEEE 754 standard as far as I am concerned.
This happens for all languages that use floating-point arithmetic. You can read through similar questions regarding other programming languages.
General question about floating-point arithmetic in modern programming languages.
creativecreatorormaybenot is right, this is issue comes from the Dart language itself.
The best solution I came up with was to manually round it to the precision you expect :
double substract(double a, double b, int precision) {
return (a - b).precision(precision);
}
double precision(int fractionDigits) {
num mod = pow(10.0, fractionDigits);
return ((this * mod).round().toDouble() / mod);
}
A simple solution would be:
depending on how many decimals you expect (lets assume 2, you can make it more generic...)
((a * 100).toInt() - (b * 100)).toInt() / 100.
Related
MQL4 documentation states that the value limits for double type variables is:
"Minimal Positive Value" = 2.2250738585072014e-308
"Maximum Value" = 1.7976931348623158e+308
See https://docs.mql4.com/basis/types/double
Why does StringToDouble() alter the value converted?
Am I doing one thing while expecting a different result?
void OnStart() {
string s1 = "5554535251504900090807060504030201";
double d1 = StringToDouble(s1);
string s2 = DoubleToString(d1);
Print("s2<",s2,">");
printf("%099.8f",d1);
Print("s1<",s1,">");
return;<br>
}
Here's what I get when I run that code:
s1<5554535251504900090807060504030201>
d1<000000000000000000000000000000000000000000000000000000005554535251504899684469244159852544.00000000>
s2<5554535251504899684469244159852544>
5554535251504900090807060504030201 amounts to5.55454E+33.
Obviously, that doesn't even come remotely close to the 1.7976931348623158e+308 limit.
What am I missing here?
Q : "What am I missing here?"
The documented facts.
MQL4 uses no more than 4-bytes to store int.
MQL4 uses no more than 8-bytes to store double.
IEEE-754 standard defines the rest - how many bits from those 64 are reserved for: exponent ( -308, 0, +308 )
sign ( +, - ) and
the rest, for normalised form of the mantissa : 0.???????...????
Argument, that an actual number is far from either "edge" of < DBL_MIN, DBL_MAX > does explain nothing about the shallow-ness of the exact number reduced-precision representation ( see DBL_EPSILON ~ 2E-16 or DBL_DIG ~ 15-significant digits, or DBL_MANT_DIG ~ 53-bits, left from a 64-bit ( 8-Byte ) storage-cell for mantissa ).
There are many numbers, that simply cannot be stored exactly, using IEEE-754 floating point number representation.
Tons of literature explain this, so feel free to dig deeper, or may use another tools, that rely on infinite-(unlimited)-precision number representation, should your use-case requires that.
Is there an easier way of comparing two floats in the metal shading language?
I'm currently multiplying by 1000 then converting to an int to get an integer comparison.
int r = (int)(color.r * 1000);
int checkColorR = (int)(50.0/255.0 * 1000);
if (r == checkColorR) ...
I'm after something like: Mathf.Approximately in Unity
A common technique is to compare the absolute difference to some desired precision:
if (fabs(color.r - 50.0/255.0) < 1.0/1000.0) ...
You can, of course, define a function for this rather than repeating it all over the place.
Your current technique is bad because it does integer truncation. The two values could be very close, but on either side of an integer, and they would compare as not equal because one would be truncated to the integer below. For example, 4.9999 and 5.0001.
I have trouble with integer division in Dart as it gives me error: 'Breaking on exception: type 'double' is not a subtype of type 'int' of 'c'.'
Here's the following code:
int a = 500;
int b = 250;
int c;
c = a / b; // <-- Gives warning in Dart Editor, and throws an error in runtime.
As you see, I was expecting that the result should be 2, or say, even if division of 'a' or 'b' would have a result of a float/double value, it should be converted directly to integer value, instead of throwing error like that.
I have a workaround by using .round()/.ceil()/.floor(), but this won't suffice as in my program, this little operation is critical as it is called thousands of times in one game update (or you can say in requestAnimationFrame).
I have not found any other solution to this yet, any idea? Thanks.
Dart version: 1.0.0_r30798
That is because Dart uses double to represent all numbers in dart2js. You can get interesting results, if you play with that:
Code:
int a = 1;
a is int;
a is double;
Result:
true
true
Actually, it is recommended to use type num when it comes to numbers, unless you have strong reasons to make it int (in for loop, for example). If you want to keep using int, use truncating division like this:
int a = 500;
int b = 250;
int c;
c = a ~/ b;
Otherwise, I would recommend to utilize num type.
Integer division is
c = a ~/ b;
you could also use
c = (a / b).floor();
c = (a / b).ceil();
if you want to define how fractions should be handled.
Short Answer
Use c = a ~/ b.
Long Answer
According to the docs, int are numbers without a decimal point, while double are numbers with a decimal point.
Both double and int are subtypes of num.
When two integers are divided using the / operator, the result is evaluated into a double. And the c variable was initialized as an integer. There are at least two things you can do:
Use c = a ~/ b.
The ~/ operator returns an int.
Use var c;. This creates a dynamic variable that can be assigned to any type, including a double and int and String etc.
Truncating division operator
You can use the truncating division operator ~/ to get an integer result from a division operation:
4 ~/ 2; // 2 (int)
Division operator
The regular division operator / will always return a double value at runtime (see the docs):
for (var i = 4; i == 4; i = 3) {
i / 2; // 2 (double)
}
Runtime versus compile time
You might have noticed that I wrote a loop for the second example (for the regular division operator) instead of 4 / 2.
The reason for this is the following:
When an expression can be evaluated at compile time, it will be simplified at that stage and also be typed accordingly. The compiler would simply convert 4 / 2 to 2 at compile time, which is then obviously an int. The loop prevents the compiler from evaluating the expression.
As long as your division happens at runtime (i.e. with variables that cannot be predicted at compile time), the return types of the / (double) and ~/ (int) operators will be the types you will see for your expressions at runtime.
See this fun example for further reference.
Conclusion
Generally speaking, the regular division operator / always returns a double value and truncate divide can be used to get an int result instead.
Compiler optimization might, however, cause some funky results :)
NSLog(#"CEIL %f",ceil(2/3));
should return 1. However, it shows:
CEIL 0.000000
Why and how to fix that problem? I use ceil([myNSArray count]/3) and it returns 0 when array count is 2.
The same rules as C apply: 2 and 3 are ints, so 2/3 is an integer divide. Integer division truncates so 2/3 produces the integer 0. That integer 0 will then be cast to a double precision float for the call to ceil, but ceil(0) is 0.
Changing the code to:
NSLog(#"CEIL %f",ceil(2.0/3.0));
Will display the result you're expecting. Adding the decimal point causes the constants to be recognised as double precision floating point numbers (and 2.0f is how you'd type a single precision floating point number).
Maudicus' solution works because (float)2/3 casts the integer 2 to a float and C's promotion rules mean that it'll promote the denominator to floating point in order to divide a floating point number by an integer, giving a floating point result.
So, your current statement ceil([myNSArray count]/3) should be changed to either:
([myNSArray count] + 2)/3 // no floating point involved
Or:
ceil((float)[myNSArray count]/3) // arguably more explicit
2/3 evaluates to 0 unless you cast it to a float.
So, you have to be careful with your values being turned to int's before you want.
float decValue = (float) 2/3;
NSLog(#"CEIL %f",ceil(decValue));
==>
CEIL 1.000000
For you array example
float decValue = (float) [myNSArray count]/3;
NSLog(#"CEIL %f",ceil(decValue));
It probably evaluates 2 and 3 as integers (as they are, obviously), evaluates the result (which is 0), and then converts it to float or double (which is also 0.00000). The easiest way to fix it is to type either 2.0f/3, 2/3.0f, or 2.0f/3.0f, (or without "f" if you wish, whatever you like more ;) ).
Hope it helps
I've been participating in a programming contest and one of the problems' input data included a fractional number in a decimal format: 0.75 is one example.
Parsing that into Double is trivial (I can use read for that), but the loss of precision is painful. One needs to be very careful with Double comparisons (I wasn't), which seems redundant since one has Rational data type in Haskell.
When trying to use that, I've discovered that to read a Rational one has to provide a string in the following format: numerator % denominator, which I, obviously, do not have.
So, the question is:
What is the easiest way to parse a decimal representation of a fraction into Rational?
The number of external dependencies should be taken into consideration too, since I can't install additional libraries into the online judge.
The function you want is Numeric.readFloat:
Numeric Data.Ratio> fst . head $ readFloat "0.75" :: Rational
3 % 4
How about the following (GHCi session):
> :m + Data.Ratio
> approxRational (read "0.1" :: Double) 0.01
1 % 10
Of course you have to pick your epsilon appropriately.
Perhaps you'd get extra points in the contest for implementing it yourself:
import Data.Ratio ( (%) )
readRational :: String -> Rational
readRational input = read intPart % 1 + read fracPart % (10 ^ length fracPart)
where (intPart, fromDot) = span (/='.') input
fracPart = if null fromDot then "0" else tail fromDot