var_dump((float)'79.10') returns me 79.09999999999999. I've tried a million ways to try and round this value up to the original 79.10 as a float (number_format, round), and I can't find a way to do it.
Is there any way I can get a float value of 79.10 from the original string?
No, because 0.1 (and, by extension, 79.1) is not actually representable as a float (assuming IEEE-754 single or double precision encoding). 0.1 in that encoding has an infinitely recurring fractional part:
1001 1001 1001 1001 ...
You'll either have to leave it as a string or accept the fact that the encoding scheme does not have infinite precision and work around it.
An example of the latter is to only output the numbers to a certain precision, such as two decimal digits, and to make sure that (in-)equality comparisons use either absolute or relative deltas to compare numbers.
When you're adding numbers, it takes quite a few operations for the imprecision effects to become visible at the hundredths level. It's quicker when multiplying but still takes a while.
While paxdiablo is right and working with floats does not have infinite precision, I've discovered that it is indeed possible to represent 79.10 as a float by first adjusting PHP's precision setting:
ini_set('precision', 15);
After that, var_dump((float)'79.10') correctly returns a float of 79.1. The different results that everyone is seeing on their own machines seems to be a result of everyone having different precision values set by default.
This is impossible as a float because it does not offer enough precision (see here for more information)
Now, in most languages you could cast it to a double... Unfortunately, in PHP, float and double use exactly the same underlying datatype so in order to get the value you want, you would have to recompile PHP.
Your best option would be to use something like the PHP BCMath module for arbitrary precision.
Related
I have read a bunch of questions and comments but haven't seen this mentioned, and since others may have the same question, I'm posting it here.
Considering floating point errors, is it ever possible to get a result one point higher than it should be from a ceil($a / $b) where the rest of $a / $b is 0?
If so, since I'm working with positive integers higher than 0, perhaps I should write my_ceil() where I check for $a % $b first and if it's not 0, add 0.1 to $a before calling the built-in function…
If what you appear to be asking is how to use floating points including their correct non-absolute errors in deciding a ceil outcome, the following should guide you:
1) http://www.php.net/manual/en/language.types.float.php
Rational numbers that are exactly representable as floating point
numbers in base 10, like 0.1 or 0.7, do not have an exact
representation as floating point numbers in base 2, which is used
internally, no matter the size of the mantissa. Hence, they cannot be
converted into their internal binary counterparts without a small loss
of precision. This can lead to confusing results: for example,
floor((0.1+0.7)*10) will usually return 7 instead of the expected 8,
since the internal representation will be something like
7.9999999999999991118....
So never trust floating number results to the last digit, and do not
compare floating point numbers directly for equality [my emphasis]. If higher
precision is necessary, the arbitrary precision math functions and gmp functions are available.
Read up
Arbitrary precision math functions : http://uk1.php.net/manual/en/ref.bc.php
And gmp : http://uk1.php.net/manual/en/ref.gmp.php
2) You are caring about floats (as the single input value) when using ceil($float) when ceil will only ever round up to the nearest integer so whatever the floating value is, is irrelevant. You may be considering using the round() function instead. which has it's own ways of dealing with the above floating point inaccuracy issue.
http://php.net/manual/en/function.round.php
To answer the original question of Considering floating point errors, is it ever possible to get a result one point higher than it should be from a ceil($a / $b) where the rest of $a / $b is 0? the answer is YES because of two points:
Float is potentially significantly inaccurate in base10 numbers, and,
You are using the wrong function to get the output you want to the precision you need. In this situation using multiple float numbers you want a function that have built in precision required, such as gmp or maths functions .
Looking at the ceil source code on github, it seems that it is dependent on your C library's ceil function.
Edit: To answer the question – YES, it (probably) can.
I guess this doesn't really have anything to do with ceil() but rather with if the division in question returns a float or integer type value.
According to http://php.net/manual/en/language.operators.arithmetic.php …
The division operator ("/") returns a float value unless the two operands are integers (or strings that get converted to integers) and the numbers are evenly divisible, in which case an integer value will be returned.
So using at least one float value could produce a ceil() "error", but I should be fine with two integers.
It's kind of a common knowledge that (most) floating point numbers are not stored precisely (when IEEE-754 format is used). So one shouldn't do this:
0.3 - 0.2 === 0.1; // very wrong
... as it will result in false, unless some specific arbitrary-precision type/class was used (BigDecimal in Java/Ruby, BCMath in PHP, Math::BigInt/Math::BigFloat in Perl, to name a few) instead.
Yet I wonder why when one tries to print the result of this expression, 0.3 - 0.2, scripting languages (Perl and PHP) give 0.1, but "virtual-machine" ones (Java, JavaScript and Erlang) give something more similar to 0.09999999999999998 instead?
And why is it also inconsistent in Ruby? version 1.8.6 (codepad) gives 0.1, version 1.9.3 (ideone) gives 0.0999...
As for php, output is related to ini settings of precision:
ini_set('precision', 15);
print 0.3 - 0.2; // 0.1
ini_set('precision', 17);
print 0.3 - 0.2; //0.099999999999999978
This may be also cause for other languages
Floating-point numbers are printed differently because printing is done for different purposes, so different choices are made about how to do it.
Printing a floating-point number is a conversion operation: A value encoded in an internal format is converted to a decimal numeral. However, there are choices about the details of the conversion.
(A) If you are doing precise mathematics and want to see the actual value represented by the internal format, then the conversion must be exact: It must produce a decimal numeral that has exactly the same value as the input. (Each floating-point number represents exactly one number. A floating-point number, as defined in the IEEE 754 standard, does not represent an interval.) At times, this may require producing a very large number of digits.
(B) If you do not need the exact value but do need to convert back and forth between the internal format and decimal, then you need to convert it to a decimal numeral precisely (and accurately) enough to distinguish it from any other result. That is, you must produce enough digits that the result is different from what you would get by converting numbers that are adjacent in the internal format. This may require producing a large number of digits, but not so many as to be unmanageable.
(C) If you only want to give the reader a sense of the number, and do not need to produce the exact value in order for your application to function as desired, then you only need to produce as many digits as are needed for your particular application.
Which of these should a conversion do?
Different languages have different defaults because they were developed for different purposes, or because it was not expedient during development to do all the work necessary to produce exact results, or for various other reasons.
(A) requires careful code, and some languages or implementations of them do not provide, or do not guarantee to provide, this behavior.
(B) is required by Java, I believe. However, as we saw in a recent question, it can have some unexpected behavior. (65.12 is printed as “65.12” because the latter has enough digits to distinguish it from nearby values, but 65.12-2 is printed as “63.120000000000005” because there is another floating-point value between it and 63.12, so you need the extra digits to distinguish them.)
(C) is what some languages use by default. It is, in essence, wrong, since no single value for how many digits to print can be suitable for all applications. Indeed, we have seen over decades that it fosters continuing misconceptions about floating-point, largely by concealing the true values involved. It is, however, easy to implement, and hence is attractive to some implementors. Ideally, a language should by default print the correct value of a floating-point number. If fewer digits are to be displayed, the number of digits should be selected only by the application implementor, hopefully including consideration of the appropriate number of digits to produce the desire results.
Worse, some languages, in addition to not displaying the actual value or enough digits to distinguish it, do not even guarantee that the digits produced are correct in some sense (such as being the value you would get by rounding the exact value to the number of digits shown). When programming in an implementation that does not provide a guarantee about this behavior, you are not doing engineering.
PHP automatically rounds the number to an arbitrary precision.
Floating-point numbers in general aren't accurate (as you noted), and you should use the language-specific round() function if you need a comparison with only a few decimal places. Otherwise, take the absolute value of the equation, and test they are within a given range.
PHP Example from php.net:
$a = 1.23456789;
$b = 1.23456780;
$epsilon = 0.00001;
if(abs($a - $b) < $epsilon) {
echo "true";
}
As for the Ruby issue, they appear to be using different versions. Codepad uses 1.8.6, While Ideaone uses 1.9.3, but it's more likely related to a config somewhere.
If we want this property
every two different float has a different printed representation
Or an even stronger one useful for REPL
printed representation shall be re-interpreted unchanged
Then I see 3 solutions for printing a float/double with base 2 internal representation into base 10
print the EXACT representation.
print enough decimal digits (with proper rounding)
print the shortest decimal representation that can be reinterpreted unchanged
Since in base two, the float number is an_integer * 2^an_exponent, its base 10 exact representation has a finite number of digits.
Unfortunately, this can result in very long strings...
For example 1.0e-10 is represented exactly as 1.0000000000000000364321973154977415791655470655996396089904010295867919921875e-10
Solution 2 is easy, you use printf with 17 digits for IEEE-754 double...
Drawback: it's not exact, nor the shortest! If you enter 0.1, you get
0.100000000000000006
Solution 3 is the best one for REPL languages, if you enter 0.1, it prints 0.1
Unfortunately it is not found in standard libraries (a shame).
At least, Scheme, Python and recent Squeak/Pharo Smalltalk do it right, I think Java too.
As for Javascript, base2 is being used internally for calculations.
> 0.2 + 0.4
0.6000000000000001
For that, Javascript can only deliver even numbers, if the resulting base2 number is not periodic.
0.6 is 0.10011 10011 10011 10011 ... in base2 (periodic), whereas 0.5 is not and therefore correctly printed.
It's kind of a common knowledge that (most) floating point numbers are not stored precisely (when IEEE-754 format is used). So one shouldn't do this:
0.3 - 0.2 === 0.1; // very wrong
... as it will result in false, unless some specific arbitrary-precision type/class was used (BigDecimal in Java/Ruby, BCMath in PHP, Math::BigInt/Math::BigFloat in Perl, to name a few) instead.
Yet I wonder why when one tries to print the result of this expression, 0.3 - 0.2, scripting languages (Perl and PHP) give 0.1, but "virtual-machine" ones (Java, JavaScript and Erlang) give something more similar to 0.09999999999999998 instead?
And why is it also inconsistent in Ruby? version 1.8.6 (codepad) gives 0.1, version 1.9.3 (ideone) gives 0.0999...
As for php, output is related to ini settings of precision:
ini_set('precision', 15);
print 0.3 - 0.2; // 0.1
ini_set('precision', 17);
print 0.3 - 0.2; //0.099999999999999978
This may be also cause for other languages
Floating-point numbers are printed differently because printing is done for different purposes, so different choices are made about how to do it.
Printing a floating-point number is a conversion operation: A value encoded in an internal format is converted to a decimal numeral. However, there are choices about the details of the conversion.
(A) If you are doing precise mathematics and want to see the actual value represented by the internal format, then the conversion must be exact: It must produce a decimal numeral that has exactly the same value as the input. (Each floating-point number represents exactly one number. A floating-point number, as defined in the IEEE 754 standard, does not represent an interval.) At times, this may require producing a very large number of digits.
(B) If you do not need the exact value but do need to convert back and forth between the internal format and decimal, then you need to convert it to a decimal numeral precisely (and accurately) enough to distinguish it from any other result. That is, you must produce enough digits that the result is different from what you would get by converting numbers that are adjacent in the internal format. This may require producing a large number of digits, but not so many as to be unmanageable.
(C) If you only want to give the reader a sense of the number, and do not need to produce the exact value in order for your application to function as desired, then you only need to produce as many digits as are needed for your particular application.
Which of these should a conversion do?
Different languages have different defaults because they were developed for different purposes, or because it was not expedient during development to do all the work necessary to produce exact results, or for various other reasons.
(A) requires careful code, and some languages or implementations of them do not provide, or do not guarantee to provide, this behavior.
(B) is required by Java, I believe. However, as we saw in a recent question, it can have some unexpected behavior. (65.12 is printed as “65.12” because the latter has enough digits to distinguish it from nearby values, but 65.12-2 is printed as “63.120000000000005” because there is another floating-point value between it and 63.12, so you need the extra digits to distinguish them.)
(C) is what some languages use by default. It is, in essence, wrong, since no single value for how many digits to print can be suitable for all applications. Indeed, we have seen over decades that it fosters continuing misconceptions about floating-point, largely by concealing the true values involved. It is, however, easy to implement, and hence is attractive to some implementors. Ideally, a language should by default print the correct value of a floating-point number. If fewer digits are to be displayed, the number of digits should be selected only by the application implementor, hopefully including consideration of the appropriate number of digits to produce the desire results.
Worse, some languages, in addition to not displaying the actual value or enough digits to distinguish it, do not even guarantee that the digits produced are correct in some sense (such as being the value you would get by rounding the exact value to the number of digits shown). When programming in an implementation that does not provide a guarantee about this behavior, you are not doing engineering.
PHP automatically rounds the number to an arbitrary precision.
Floating-point numbers in general aren't accurate (as you noted), and you should use the language-specific round() function if you need a comparison with only a few decimal places. Otherwise, take the absolute value of the equation, and test they are within a given range.
PHP Example from php.net:
$a = 1.23456789;
$b = 1.23456780;
$epsilon = 0.00001;
if(abs($a - $b) < $epsilon) {
echo "true";
}
As for the Ruby issue, they appear to be using different versions. Codepad uses 1.8.6, While Ideaone uses 1.9.3, but it's more likely related to a config somewhere.
If we want this property
every two different float has a different printed representation
Or an even stronger one useful for REPL
printed representation shall be re-interpreted unchanged
Then I see 3 solutions for printing a float/double with base 2 internal representation into base 10
print the EXACT representation.
print enough decimal digits (with proper rounding)
print the shortest decimal representation that can be reinterpreted unchanged
Since in base two, the float number is an_integer * 2^an_exponent, its base 10 exact representation has a finite number of digits.
Unfortunately, this can result in very long strings...
For example 1.0e-10 is represented exactly as 1.0000000000000000364321973154977415791655470655996396089904010295867919921875e-10
Solution 2 is easy, you use printf with 17 digits for IEEE-754 double...
Drawback: it's not exact, nor the shortest! If you enter 0.1, you get
0.100000000000000006
Solution 3 is the best one for REPL languages, if you enter 0.1, it prints 0.1
Unfortunately it is not found in standard libraries (a shame).
At least, Scheme, Python and recent Squeak/Pharo Smalltalk do it right, I think Java too.
As for Javascript, base2 is being used internally for calculations.
> 0.2 + 0.4
0.6000000000000001
For that, Javascript can only deliver even numbers, if the resulting base2 number is not periodic.
0.6 is 0.10011 10011 10011 10011 ... in base2 (periodic), whereas 0.5 is not and therefore correctly printed.
When I print this number in php 137582392964679 I get this as the output 1.37582392965E+14
All I am doing is a simple
print 137582392964679;
Anyone know why it's doing this? It's as if it's converting to an exponential number automatically. Someone said it's because I'm on a 32 bit machine. If that's the case how can I get around this problem?
Thanks
Check the const PHP_INT_MAX. You're likely over the max, which is typically around 2 billion for a 32bit system.
The maximum number you can store in a signed integer on a 32-bit machine is 2147483647. You can store numbers larger than this in a float but you risk losing some precision.
If that's the case how can I get around this problem?
You probably want to use a big number library. Try GMP:
$sum = gmp_add("123456789012345", "76543210987655");
echo gmp_strval($sum) . "\n";
Result:
200000000000000
Another alternative you could use is BC Math.
If you don't need to do any calculations with these numbers, but just store tham correctly, then store them as strings rather than integers.
I am on a 64 bit machine and it does the same thing. You might want to try using: print number_format(137582392964679);
That number is too big to fit into a 32-bit integer, so yes, it is converting to a floating point type automatically. How to get around it depends on the requirements of your system. If you aren't going to do any arithmetic then just store it as a string. If precision isn't overly important then you could leave it as a float and format it using printf. If precision is important and you can upgrade to 64-bit that should fix it, if you can't upgrade and you need an integer then you could look into using the BC Math PHP extension.
The manual clearly says:
If PHP encounters a number beyond the
bounds of the integer type, it will
be interpreted as a float instead.
Also your number cannot be represented accurately because of inherent floating point limitations, hence it is being approximated.
I have a method that returns a float like 1.234567890.I want to test that it really does so. However, it seems that this returned float has different precision on different platforms so how do I assert that the returned value is 1.23456789? If I just do:
$this->assertEqual(1.23456789, $float);
Then that might fail on some platforms where there is not enough precision.
So far it hasn't been mentioned that assertEquals supports comparing floats by offering a delta to specifiy precision:
$this->assertEquals(1.23456789, $float, '', 0.0001);
Thanks to #Antoine87 for pointing out: since phpunit 7.5 you should use assertEqualsWithDelta():
$this->assertEqualsWithDelta(1.23456789, $float, 0.0001);
As an update to #bernhard-wagner answer, you should now use assertEqualsWithDelta() since phpunit 7.5.
$this->assertEqualsWithDelta(1.23456789, $float, 0.0001);
In general, it's a bad idea to test built-in floats for equality. Because of accuracy problems of floating point representation, the results of two different calculations may be perfectly equal mathematically, but different when you compare them at your PHP runtime.
Solution 1: compare how far apart they are. Say, if the absolute difference is less than 0.000001, you treat the values as equal.
Solution 2: use arbitrary precision mathematics, which supports numbers of any size and precision, represented as strings.
For greater accuracy you may consider using BCMath.
Alternatively of using bcmath() you can also set the default precision, like this:
ini_set('precision', 14);