I'm trying to use the nfp() function in Processing to present my floats on screen with a certain number of decimal places. In the manual page for this function, it says that
There are two versions: one for formatting floats, and one for formatting ints.
However, when I'm trying to use the function with a float variable (and an int variable for the number of decimal points), I get the following error:
The function "nfp()" expects parameters like; "nfp(int,int)".
Am I missing something here? How can I access the float version of the function?
The nfp function formats numbers into strings and adds zeros to it.
This is done for integers always before the given number, which is why the function npf(int, int) requires only one more parameter for the digits.
The function nfp(float, int) does not work. The function requires for a float input two integers: nfp(float, int, int).
This is, since it needs to know, how many digits will be added before the dot (left) and how many should be added after the dot (right).
nfp(1.2, 1, 2) will lead to +1.20
nfp(1.2, 2, 1) will lead to +01.2
Not a big issue? NO! This is a perfect example to learn two things:
It is important that thrown Errors have to make clear what the problem really is about.
Documentation has to be clear about the usage of functions, especially, when they accept different variations of parameters.
If both are not considered well enough, when designing a framework, developers (like op in this case) get stuck on problems that could have been easily avoided.
Related
I am working on a C extension for Chicken Scheme and have everything in place but I am running into an issue with complex number types.
My code can only handle integers and when any math is done that involves say a square root my extension may end up having to handle complex number.
I just need to remove the decimal place and get whatever integer is close by. I am not worried about accuracy for this.
I have looked around and through the code but did not find anything.
Thanks!
Well, you can inspect the number type from the header tag. A complex number is a block object which has 2 slots; the real and imaginary part. Then, those numbers themselves can be ratnums, flonums, fixnums or bignums. You'll need to handle those situations as well if you want to do it all in C.
It's probably a lot easier to declare your C code as accepting an integer and do any conversion necessary in Scheme.
What is the correct scalar type to use in my protobuf definition file, if I want to transmit an arbitrary-precision decimal value?
I am using shopspring/decimal instead of a float64 in my Go code to prevent math errors. When writing my protobuf file with the intention of transmitting these values over gRPC, I could use:
double which translates to a float64
string which would certainly be precise in its own way but strikes me as clunky
Something like decimal from mgravell/protobuf-net?
Conventional wisdom has taught me to skirt floats in monetary applications, but I may be over-careful since it's a point of serialization.
If you really need arbitrary precision, I fear there is no correct answer right now. There is https://github.com/protocolbuffers/protobuf/issues/4406 open, but it does not seem to be very active. Without built-in support, you will really need to perform the serialization manually and then use either string or bytes to store the result. Which one to use between string and bytes likely depends on whether you need cross-platform/cross-library compatibility: if you need compatibility, use string and parse the decimal representation in the string using the appropriate arbitrary precision type in the reader; if you don't need it and you're going to read the data using the same cpu architecture and library you can probably just use the binary serialization provided by that library (MarshalBinary/UnmarshalBinary) and use bytes.
On the other hand, if you just need to send monetary values with an appropriate precision and do not need arbitrary precision, you can probably just use sint64/uint64 and use an appropriate unit (these are commonly called fixed-point numbers). To give an example, if you need to represent a monetary value in dollars with 4 decimal digits, your unit would be 1/10000th of a dollar so that e.g. the value 1 represents $0.0001, the value 19900 represents $1.99, -500000 represents $-50, and so on. With such a unit you can represent the range $-922,337,203,685,477.5808 to $922,337,203,685,477.5807 - that should likely be sufficient for most purposes. You will still need to perform the scaling manually, but it should be fairly trivial and portable. Given the range above, I would suggest using sint64 is preferable as it allows you also to represent negative values; uint64 should be considered only if you need the extra positive range and don't need negative values.
Alternatively, if you don't mind importing another package, you may want to take a look at https://github.com/googleapis/googleapis/blob/master/google/type/money.proto or https://github.com/googleapis/googleapis/blob/master/google/type/decimal.proto (that incidentally implement something very similar to the two models described above), and the related utility functions at https://pkg.go.dev/github.com/googleapis/go-type-adapters/adapters
As a side note, you are completely correct that you should almost never use floating point for monetary values.
I'm working from the template program given here:
https://www.gnu.org/software/gsl/manual/html_node/Trivial-example.html
The program as they give it compiles and runs perfectly, which is nice. What I would like to do is generalise this method to find the minimum of a function with an arbitrary number of parameters.
Some cursory reading suggests that the metric function (M1) is only used in certain diagnostic and printing situations and so can more or less be ignored. All that remains is then to define E1 and S1 appropriately. Unfortunately my knowledge of using pointers and void is incomplete, so I'm stuck trying to upgrade the configuration 'xp' to be an array of parameters, rather than a single double.
In my naivete tried moving from
double x = *((double *) xp);
to
double x = (*((double *) xp))[0];
where appropriate, but obviously that didn't work. I'm sure I'm missing something stupid, so any hints would be nice! I will obviously be defining my own E1 output function which will take these N parameters and return a number.
The underlying algorithm, gsl_siman_solve() from the link provided, is generalized to work with any data type. This is why the ubiquitous xp parameter is always being cast to a double pointer before use. It should be straightforward to use any struct or array or array of arrays instead of simply doubles provided all the callbacks are coded properly.
The problem is that gsl_siman_solve() only seems to support a scalar double step size, initial guess, and 'uniform' value (from gsl_rng_uniform()), so you would need to map scalar double values into what are naturally multidimensional quantities. This can be done, but it is messy and not very flexible. In your case, the mapping would be done in S1().
This is akin to mapping the digits of a decimal number into a multidimensional space: the ones digit represents the X axis, the tens digit represents the Y axis, and the hundreds digit represents the Z axis, for example. By incrementing an integer, one can walk the entire 3D space from (0, 0, 0) to (9, 9, 9). You don't have to use integers and powers of 10, and the components don't even have to have the same range, but there is an inherent limit in the range of each component of the packed value. You would actually do this in reverse: taking a scalar double and unpacking it into multiple quantities.
Lastly, your code double x = (*((double *) xp))[0]; won't work because you are attempting to dereference a double as an array, not a pointer to a double, which would be OK. In other words, it's that first * that is the problem.
double r = 11.631;
double theta = 21.4;
In the debugger, these are shown as 11.631000000000000 and 21.399999618530273.
How can I avoid this?
These accuracy problems are due to the internal representation of floating point numbers and there's not much you can do to avoid it.
By the way, printing these values at run-time often still leads to the correct results, at least using modern C++ compilers. For most operations, this isn't much of an issue.
I liked Joel's explanation, which deals with a similar binary floating point precision issue in Excel 2007:
See how there's a lot of 0110 0110 0110 there at the end? That's because 0.1 has no exact representation in binary... it's a repeating binary number. It's sort of like how 1/3 has no representation in decimal. 1/3 is 0.33333333 and you have to keep writing 3's forever. If you lose patience, you get something inexact.
So you can imagine how, in decimal, if you tried to do 3*1/3, and you didn't have time to write 3's forever, the result you would get would be 0.99999999, not 1, and people would get angry with you for being wrong.
If you have a value like:
double theta = 21.4;
And you want to do:
if (theta == 21.4)
{
}
You have to be a bit clever, you will need to check if the value of theta is really close to 21.4, but not necessarily that value.
if (fabs(theta - 21.4) <= 1e-6)
{
}
This is partly platform-specific - and we don't know what platform you're using.
It's also partly a case of knowing what you actually want to see. The debugger is showing you - to some extent, anyway - the precise value stored in your variable. In my article on binary floating point numbers in .NET, there's a C# class which lets you see the absolutely exact number stored in a double. The online version isn't working at the moment - I'll try to put one up on another site.
Given that the debugger sees the "actual" value, it's got to make a judgement call about what to display - it could show you the value rounded to a few decimal places, or a more precise value. Some debuggers do a better job than others at reading developers' minds, but it's a fundamental problem with binary floating point numbers.
Use the fixed-point decimal type if you want stability at the limits of precision. There are overheads, and you must explicitly cast if you wish to convert to floating point. If you do convert to floating point you will reintroduce the instabilities that seem to bother you.
Alternately you can get over it and learn to work with the limited precision of floating point arithmetic. For example you can use rounding to make values converge, or you can use epsilon comparisons to describe a tolerance. "Epsilon" is a constant you set up that defines a tolerance. For example, you may choose to regard two values as being equal if they are within 0.0001 of each other.
It occurs to me that you could use operator overloading to make epsilon comparisons transparent. That would be very cool.
For mantissa-exponent representations EPSILON must be computed to remain within the representable precision. For a number N, Epsilon = N / 10E+14
System.Double.Epsilon is the smallest representable positive value for the Double type. It is too small for our purpose. Read Microsoft's advice on equality testing
I've come across this before (on my blog) - I think the surprise tends to be that the 'irrational' numbers are different.
By 'irrational' here I'm just referring to the fact that they can't be accurately represented in this format. Real irrational numbers (like π - pi) can't be accurately represented at all.
Most people are familiar with 1/3 not working in decimal: 0.3333333333333...
The odd thing is that 1.1 doesn't work in floats. People expect decimal values to work in floating point numbers because of how they think of them:
1.1 is 11 x 10^-1
When actually they're in base-2
1.1 is 154811237190861 x 2^-47
You can't avoid it, you just have to get used to the fact that some floats are 'irrational', in the same way that 1/3 is.
One way you can avoid this is to use a library that uses an alternative method of representing decimal numbers, such as BCD
If you are using Java and you need accuracy, use the BigDecimal class for floating point calculations. It is slower but safer.
Seems to me that 21.399999618530273 is the single precision (float) representation of 21.4. Looks like the debugger is casting down from double to float somewhere.
You cant avoid this as you're using floating point numbers with fixed quantity of bytes. There's simply no isomorphism possible between real numbers and its limited notation.
But most of the time you can simply ignore it. 21.4==21.4 would still be true because it is still the same numbers with the same error. But 21.4f==21.4 may not be true because the error for float and double are different.
If you need fixed precision, perhaps you should try fixed point numbers. Or even integers. I for example often use int(1000*x) for passing to debug pager.
Dangers of computer arithmetic
If it bothers you, you can customize the way some values are displayed during debug. Use it with care :-)
Enhancing Debugging with the Debugger Display Attributes
Refer to General Decimal Arithmetic
Also take note when comparing floats, see this answer for more information.
According to the javadoc
"If at least one of the operands to a numerical operator is of type double, then the
operation is carried out using 64-bit floating-point arithmetic, and the result of the
numerical operator is a value of type double. If the other operand is not a double, it is
first widened (§5.1.5) to type double by numeric promotion (§5.6)."
Here is the Source
As I tried to debug, I found that : just as I type in
Dim value As Double
value = 0.90000
then hit enter, and it automatically converts to 0.9
Shouldn't it keep the precision in double in visual basic?
For my calculation, I absolutely need to show the precision
If precision is required then the Currency data type is what you want to use.
There are at least two representations of your value in play. One is the value you see on the screen -- a string -- and one is the internal representation -- a binary value. In dealing with fractional values, the two are often not equivalent and where they aren't, it's because they can't be.
If you stick with doubles, VB will maintain 53 bits of mantissa throughout your calculations, no matter how they might appear when printed. If you transition through the string domain, say by saving to a file or DB and later retrieving, it often has to leave some of that precision behind. It's inevitable, because the interface between the two domains is not perfect. Some values that can be exactly represented as strings (or Decimals, that is, powers of ten) can't be exactly represented as fractional powers of 2.
This has nothing to do with VB, it's the nature of floating point. The best you can do is control where the rounding occurs. For this purpose your friend is the Format function, which controls how a value appears in string form.
? Format$(0.9, "0.00000") will show you an example.
You are getting what you see on the screen confused with what bits are being set in the Double to make that number.
VB is simply being "helpful", and simply knocking off excess zeros. But for all intents and purposes,
0.9
is identical to
0.90000
If you don't believe me, try doing this comparison:
Debug.Print CDbl("0.9") = CDbl("0.90000")
As has already been said, displayed precision can be shown using the Format$() function, e.g.
Debug.Print Format$(0.9, "0.00000")
No, it shouldn't keep the precision. Binary floating point values don't retain this information... and it would be somewhat odd to do so, given that you're expressing the value in one base even though it's being represented in another.
I don't know whether VB6 has a decimal floating point type, but that's probably what you want - or a fixed point decimal type, perhaps. Certainly in .NET, System.Decimal has retained extra 0s from .NET 1.1 onwards. If this doesn't help you, you could think about remembering two integers - e.g. "90000" and "100000" in this case, so that the value you're representing is one integer divided by another, with the associated level of precision.
EDIT: I thought that Currency may be what you want, but according to this article, that's fixed at 4 decimal places, and you're trying to retain 5. You could potentially just multiply by 10, if you always want 5 decimal places - but it's an awkward thing to remember to do everywhere... and you'd have to work out how to format it appropriately. It would also always be 4 decimal places, I suspect, even if you'd specified fewer - so if you want "0.300" to be different to "0.3000" then Currency may not be appropriate. I'm entirely basing this on articles online though...
You can also enter the value as 0.9# instead. This helps avoid implicit coercion within an expression that may truncate the precision you expect. In most cases the compiler won't require this hint though because floating point literals default to Double (indeed, the IDE typically deletes the # symbol unless the value was an integer, e.g. 9#).
Contrast the results of these:
MsgBox TypeName(0.9)
MsgBox TypeName(0.9!)
MsgBox TypeName(0.9#)