Best way of checking if a floating point is an integer
Some other options to consider (different compilers / libraries may produce different intrinsic sequences for these tests and be faster/slower):
bool is_int(float f) { return floor(f) == f; }
This is in addition to the tests for overflow you have...
If you are looking to really optimize, you could try the following (works for positive floats, not thoroughly tested): This assumes IEEE 32-bit floats, which are not mandated by the C++ standard AFAIK.
bool is_int(float f)
{
const float nf = f + float(1 << 23);
const float bf = nf - float(1 << 23);
return f == bf;
}
Conclusion:
The answer is use std::trunc(f) == f the time difference is insignificant when comparing all these methods. Even if the specific IEEE unwinding code we write in the example below is technically twice is fast we are only talking about 1 nano second faster.
The maintenance costs in the long run though would be significantly higher. So use a solution that is easier to read and understand by the maintainer is better.
Time in microseconds to complete 12,000,000 operations on a random set of numbers:
- IEEE breakdown: 18
std::trunc(f) == f32std::floor(val) - val == 035((uint64_t)f) - f) == 0.038std::fmod(val, 1.0) == 087
The Working out of the conclusion.
A floating point number is two parts:
mantissa: The data part of the value.
exponent: a power to multiply it by.
such that:
value = mantissa * (2^exponent)
So the exponent is basically how many binary digits we are going to shift the "binary point" down the mantissa. A positive value shifts it right a negative value shifts it left. If all the digits to the right of the binary point are zero then we have an integer.
If we assume IEEE 754
We should note that this representation the value is normalized so that the most significant bit in the mantissa is shifted to be 1. Since this bit is always set it is not actually stored (the processor knows its there and compensates accordingly).
So:
If the exponent < 0 then you definitely do not have an integer as it can only be representing a fractional value. If the exponent >= <Number of bits In Mantissa> then there is definately no fractual part and it is an integer (though you may not be able to hold it in an int).
Otherwise we have to do some work. if the exponent >= 0 && exponent < <Number of bits In Mantissa> then you may be representing an integer if the mantissa is all zero in the bottom half (defined below).
Additional as part of the normalization 127 is added to the exponent (so that there are no negative values stored in the 8 bit exponent field).
#include <limits>
#include <iostream>
#include <cmath>
/*
* Bit 31 Sign
* Bits 30-23 Exponent
* Bits 22-00 Mantissa
*/
bool is_IEEE754_32BitFloat_AnInt(float val)
{
// Put the value in an int so we can do bitwise operations.
int valAsInt = *reinterpret_cast<int*>(&val);
// Remember to subtract 127 from the exponent (to get real value)
int exponent = ((valAsInt >> 23) & 0xFF) - 127;
int bitsInFraction = 23 - exponent;
int mask = exponent < 0
? 0x7FFFFFFF
: exponent > 23
? 0x00
: (1 << bitsInFraction) - 1;
return !(valAsInt & mask);
}
/*
* Bit 63 Sign
* Bits 62-52 Exponent
* Bits 51-00 Mantissa
*/
bool is_IEEE754_64BitFloat_AnInt(double val)
{
// Put the value in an long long so we can do bitwise operations.
uint64_t valAsInt = *reinterpret_cast<uint64_t*>(&val);
// Remember to subtract 1023 from the exponent (to get real value)
int exponent = ((valAsInt >> 52) & 0x7FF) - 1023;
int bitsInFraction = 52 - exponent;
uint64_t mask = exponent < 0
? 0x7FFFFFFFFFFFFFFFLL
: exponent > 52
? 0x00
: (1LL << bitsInFraction) - 1;
return !(valAsInt & mask);
}
bool is_Trunc_32BitFloat_AnInt(float val)
{
return (std::trunc(val) - val == 0.0F);
}
bool is_Trunc_64BitFloat_AnInt(double val)
{
return (std::trunc(val) - val == 0.0);
}
bool is_IntCast_64BitFloat_AnInt(double val)
{
return (uint64_t(val) - val == 0.0);
}
template<typename T, bool isIEEE = std::numeric_limits<T>::is_iec559>
bool isInt(T f);
template<>
bool isInt<float, true>(float f) {return is_IEEE754_32BitFloat_AnInt(f);}
template<>
bool isInt<double, true>(double f) {return is_IEEE754_64BitFloat_AnInt(f);}
template<>
bool isInt<float, false>(float f) {return is_Trunc_64BitFloat_AnInt(f);}
template<>
bool isInt<double, false>(double f) {return is_Trunc_64BitFloat_AnInt(f);}
int main()
{
double x = 16;
std::cout << x << "=> " << isInt(x) << "\n";
x = 16.4;
std::cout << x << "=> " << isInt(x) << "\n";
x = 123.0;
std::cout << x << "=> " << isInt(x) << "\n";
x = 0.0;
std::cout << x << "=> " << isInt(x) << "\n";
x = 2.0;
std::cout << x << "=> " << isInt(x) << "\n";
x = 4.0;
std::cout << x << "=> " << isInt(x) << "\n";
x = 5.0;
std::cout << x << "=> " << isInt(x) << "\n";
x = 1.0;
std::cout << x << "=> " << isInt(x) << "\n";
}
Results:
> ./a.out
16=> 1
16.4=> 0
123=> 1
0=> 1
2=> 1
4=> 1
5=> 1
1=> 1
Running Some Timing tests.
Test data was generated like this:
(for a in {1..3000000};do echo $RANDOM.$RANDOM;done ) > test.data
(for a in {1..3000000};do echo $RANDOM;done ) >> test.data
(for a in {1..3000000};do echo $RANDOM$RANDOM0000;done ) >> test.data
(for a in {1..3000000};do echo 0.$RANDOM;done ) >> test.data
Modified main() to run tests:
int main()
{
// ORIGINAL CODE still here.
// Added this trivial speed test.
std::ifstream testData("test.data"); // Generated a million random numbers
std::vector<double> test{std::istream_iterator<double>(testData), std::istream_iterator<double>()};
std::cout << "Data Size: " << test.size() << "\n";
int count1 = 0;
int count2 = 0;
int count3 = 0;
auto start = std::chrono::system_clock::now();
for(auto const& v: test)
{ count1 += is_IEEE754_64BitFloat_AnInt(v);
}
auto p1 = std::chrono::system_clock::now();
for(auto const& v: test)
{ count2 += is_Trunc_64BitFloat_AnInt(v);
}
auto p2 = std::chrono::system_clock::now();
for(auto const& v: test)
{ count3 += is_IntCast_64BitFloat_AnInt(v);
}
auto end = std::chrono::system_clock::now();
std::cout << "IEEE " << count1 << " Time: " << std::chrono::duration_cast<std::chrono::milliseconds>(p1 - start).count() << "\n";
std::cout << "Trunc " << count2 << " Time: " << std::chrono::duration_cast<std::chrono::milliseconds>(p2 - p1).count() << "\n";
std::cout << "Int Cast " << count3 << " Time: " << std::chrono::duration_cast<std::chrono::milliseconds>(end - p2).count() << "\n"; }
The tests show:
> ./a.out
16=> 1
16.4=> 0
123=> 1
0=> 1
2=> 1
4=> 1
5=> 1
1=> 1
Data Size: 12000000
IEEE 6000199 Time: 18
Trunc 6000199 Time: 32
Int Cast 6000199 Time: 38
The IEEE code (in this simple test) seem to beat the truncate method and generate the same result. BUT the amount of time is insignificant. Over 12 million calls we saw a difference in 14 milliseconds.
This test is good:
if ( f >= std::numeric_limits<T>::min()
&& f <= std::numeric_limits<T>::max()
&& f == (T)f))
These tests are incomplete:
using std::fmod to extract the remainder and test equality to 0.
using std::remainder and test equality to 0.
They both fail to check that the conversion to T is defined. Float-to-integral conversions that overflow the integral type result in undefined behaviour, which is even worse than roundoff.
I would recommend avoiding std::fmod for another reason. This code:
int isinteger(double d) {
return std::numeric_limits<int>::min() <= d
&& d <= std::numeric_limits<int>::max()
&& std::fmod(d, 1.0) == 0;
}
compiles (gcc version 4.9.1 20140903 (prerelease) (GCC) on x86_64 Arch Linux using -g -O3 -std=gnu++0x) to this:
0000000000400800 <_Z9isintegerd>:
400800: 66 0f 2e 05 10 01 00 ucomisd 0x110(%rip),%xmm0 # 400918 <_IO_stdin_used+0x18>
400807: 00
400808: 72 56 jb 400860 <_Z9isintegerd+0x60>
40080a: f2 0f 10 0d 0e 01 00 movsd 0x10e(%rip),%xmm1 # 400920 <_IO_stdin_used+0x20>
400811: 00
400812: 66 0f 2e c8 ucomisd %xmm0,%xmm1
400816: 72 48 jb 400860 <_Z9isintegerd+0x60>
400818: 48 83 ec 18 sub $0x18,%rsp
40081c: d9 e8 fld1
40081e: f2 0f 11 04 24 movsd %xmm0,(%rsp)
400823: dd 04 24 fldl (%rsp)
400826: d9 f8 fprem
400828: df e0 fnstsw %ax
40082a: f6 c4 04 test $0x4,%ah
40082d: 75 f7 jne 400826 <_Z9isintegerd+0x26>
40082f: dd d9 fstp %st(1)
400831: dd 5c 24 08 fstpl 0x8(%rsp)
400835: f2 0f 10 4c 24 08 movsd 0x8(%rsp),%xmm1
40083b: 66 0f 2e c9 ucomisd %xmm1,%xmm1
40083f: 7a 22 jp 400863 <_Z9isintegerd+0x63>
400841: 66 0f ef c0 pxor %xmm0,%xmm0
400845: 31 c0 xor %eax,%eax
400847: ba 00 00 00 00 mov $0x0,%edx
40084c: 66 0f 2e c8 ucomisd %xmm0,%xmm1
400850: 0f 9b c0 setnp %al
400853: 0f 45 c2 cmovne %edx,%eax
400856: 48 83 c4 18 add $0x18,%rsp
40085a: c3 retq
40085b: 0f 1f 44 00 00 nopl 0x0(%rax,%rax,1)
400860: 31 c0 xor %eax,%eax
400862: c3 retq
400863: f2 0f 10 0d bd 00 00 movsd 0xbd(%rip),%xmm1 # 400928 <_IO_stdin_used+0x28>
40086a: 00
40086b: e8 20 fd ff ff callq 400590 <fmod@plt>
400870: 66 0f 28 c8 movapd %xmm0,%xmm1
400874: eb cb jmp 400841 <_Z9isintegerd+0x41>
400876: 66 2e 0f 1f 84 00 00 nopw %cs:0x0(%rax,%rax,1)
40087d: 00 00 00
The first five instructions implement the range check against std::numeric_limits<int>::min() and std::numeric_limits<int>::max(). The rest is the fmod test, accounting for all the misbehaviour of a single invocation of the fprem instruction (400828..40082d) and some case where a NaN somehow arose.
You get similar code by using remainder.
Use std::fmod(f, 1.0) == 0.0 where f is either a float, double, or long double. If you're worried about spurious effects of unwanted floating point promotions when using floats, then use either 1.0f or the more comprehensive
std::fmod(f, static_cast<decltype(f)>(1.0)) == 0.0
which will force, obviously at compile time, the correct overload to be called. The return value of std::fmod(f, ...) will be in the range [0, 1) and it's perfectly safe to compare to 0.0 to complete your integer check.
If it turns out that f is an integer, then make sure it's within the permitted range of your chosen type before attempting a cast: else you risk invoking undefined behaviour. I see that you're already familiar with std::numeric_limits which can help you here.
My reservations against using std::remainder are possibly (i) my being a Luddite and (ii) it not being available in some compilers partially implementing the C++11 standard, such as MSVC12. I don't like solutions involving casts since the notation hides that reasonably expensive operation and you need to check in advance for safety. If you must adopt your first choice, at least replace the C-style cast with static_cast<T>(f);