问题
I'm looking to for a reasonably efficient way of determining if a floating point value (double) can be exactly represented by an integer data type (long, 64 bit).
My initial thought was to check the exponent to see if it was 0 (or more precisely 127). But that won't work because 2.0 would be e=1 m=1...
So basically, I am stuck. I have a feeling that I can do this with bit masks, but I'm just not getting my head around how to do that at this point.
So how can I check to see if a double is exactly representable as a long?
Thanks
回答1:
Here's one method that could work in most cases. I'm not sure if/how it will break if you give it NaN, INF, very large (overflow) numbers...
(Though I think they will all return false - not exactly representable.)
You could:
- Cast it to an integer.
- Cast it back to a floating-point.
- Compare with original value.
Something like this:
double val = ... ; // Value
if ((double)(long long)val == val){
// Exactly representable
}
floor() and ceil() are also fair game (though they may fail if the value overflows an integer):
floor(val) == val
ceil(val) == val
And here's a messy bit-mask solution:
This uses union type-punning and assumes IEEE double-precision. Union type-punning is only valid in C99 TR2 and later.
int representable(double x){
// Handle corner cases:
if (x == 0)
return 1;
// -2^63 is representable as a signed 64-bit integer, but +2^63 is not.
if (x == -9223372036854775808.)
return 1;
// Warning: Union type-punning is only valid in C99 TR2 or later.
union{
double f;
uint64_t i;
} val;
val.f = x;
uint64_t exp = val.i & 0x7ff0000000000000ull;
uint64_t man = val.i & 0x000fffffffffffffull;
man |= 0x0010000000000000ull; // Implicit leading 1-bit.
int shift = (exp >> 52) - 1075;
// Out of range
if (shift < -52 || shift > 10)
return 0;
// Test mantissa
if (shift < 0){
shift = -shift;
return ((man >> shift) << shift) == man;
}else{
return ((man << shift) >> shift) == man;
}
}
回答2:
I think I have found a way to clamp a double into an integer in a standard-conforming fashion (this is not really what the question is about, but it helps a lot). First, we need to see why the obvious code is not correct.
// INCORRECT CODE
uint64_t double_to_uint64 (double x)
{
if (x < 0.0) {
return 0;
}
if (x > UINT64_MAX) {
return UINT64_MAX;
}
return x;
}
The problem here is that in the second comparison, UINT64_MAX is being implicitly converted to double. The C standard does not specify exactly how this conversion works, only that it is to be rounded up or down to a representable value. This means that the second comparison may be false, even if should mathematically be true (which can happen when UINT64_MAX is rounded up, and 'x' is mathematically between UINT64_MAX and (double)UINT64_MAX). As such, the conversion of double to uint64_t can result in undefined behavior in that edge case.
Surprisingly, the solution is very simple. Consider that while UINT64_MAX may not be exactly representable in a double, UINT64_MAX+1, being a power of two (and not too large), certainly is. So, if we first round the input to an integer, the comparison x > UINT64_MAX is equivalent to x >= UINT64_MAX+1, except for possible overflow in the addition. We can fix the overflow by using ldexp instead of adding one to UINT64_MAX. That being said, the following code should be correct.
/* Input: a double 'x', which must not be NaN.
* Output: If 'x' is lesser than zero, then zero;
* otherwise, if 'x' is greater than UINT64_MAX, then UINT64_MAX;
* otherwise, 'x', rounded down to an integer.
*/
uint64_t double_to_uint64 (double x)
{
assert(!isnan(x));
double y = floor(x);
if (y < 0.0) {
return 0;
}
if (y >= ldexp(1.0, 64)) {
return UINT64_MAX;
}
return y;
}
Now, to back to your question: is x is exactly representable in an uint64_t? Only if it was neither rounded nor clamped.
/* Input: a double 'x', which must not be NaN.
* Output: If 'x' is exactly representable in an uint64_t,
* then 1, otherwise 0.
*/
int double_representable_in_uint64 (double x)
{
assert(!isnan(x));
return (floor(x) == x && x >= 0.0 && x < ldexp(1.0, 64));
}
The same algorithm can be used for integers of different size, and also for signed integers with a minor modification. The code that follows does some very basic tests of the uint32_t and uint64_t versions (only false positives can possibly be caught), but is also suitable for manual examination of the edge cases.
#include <inttypes.h>
#include <math.h>
#include <limits.h>
#include <assert.h>
#include <stdio.h>
uint32_t double_to_uint32 (double x)
{
assert(!isnan(x));
double y = floor(x);
if (y < 0.0) {
return 0;
}
if (y >= ldexp(1.0, 32)) {
return UINT32_MAX;
}
return y;
}
uint64_t double_to_uint64 (double x)
{
assert(!isnan(x));
double y = floor(x);
if (y < 0.0) {
return 0;
}
if (y >= ldexp(1.0, 64)) {
return UINT64_MAX;
}
return y;
}
int double_representable_in_uint32 (double x)
{
assert(!isnan(x));
return (floor(x) == x && x >= 0.0 && x < ldexp(1.0, 32));
}
int double_representable_in_uint64 (double x)
{
assert(!isnan(x));
return (floor(x) == x && x >= 0.0 && x < ldexp(1.0, 64));
}
int main ()
{
{
printf("Testing 32-bit\n");
for (double x = 4294967295.999990; x < 4294967296.000017; x = nextafter(x, INFINITY)) {
uint32_t y = double_to_uint32(x);
int representable = double_representable_in_uint32(x);
printf("%f -> %" PRIu32 " representable=%d\n", x, y, representable);
assert(!representable || (double)(uint32_t)x == x);
}
}
{
printf("Testing 64-bit\n");
double x = ldexp(1.0, 64) - 40000.0;
for (double x = 18446744073709510656.0; x < 18446744073709629440.0; x = nextafter(x, INFINITY)) {
uint64_t y = double_to_uint64(x);
int representable = double_representable_in_uint64(x);
printf("%f -> %" PRIu64 " representable=%d\n", x, y, representable);
assert(!representable || (double)(uint64_t)x == x);
}
}
}
回答3:
You can use the modf function to split a float into the integer and fraction parts. modf is in the standard C library.
#include <math.h>
#include <limits.h>
double val = ...
double i;
long l;
/* check if fractional part is 0 */
if (modf(val, &i) == 0.0) {
/* val is an integer. check if it can be stored in a long */
if (val >= LONG_MIN && val <= LONG_MAX) {
/* can be exactly represented by a long */
l = val;
}
}
回答4:
How to check if float can be exactly represented as an integer ?
I'm looking to for a reasonably efficient way of determining if a floating point value
doublecan be exactly represented by an integer data typelong, 64 bit.
Range (LONG_MIN, LONG_MAX) and fraction (frexp()) tests needed. Also need to watch out for not-a-numbers.
The usual idea is to test like (double)(long)x == x, but to avoid its direct usage. (long)x, when x is out of range, is undefined behavior (UB).
The valid range of conversion for (long)x is LONG_MIN - 1 < x < LONG_MAX + 1 as code discards any fractional part of x during the conversion. So code needs to test, using FP math, if x is in range.
#include <limits.h>
#include <stdbool.h>
#define DBL_LONG_MAXP1 (2.0*(LONG_MAX/2+1))
#define DBL_LONG_MINM1 (2.0*(LONG_MIN/2-1))
bool double_to_long_exact_possible(double x) {
if (x < DBL_LONG_MAXP1) {
double whole_number_part;
if (frexp(x, &whole_number_part) != 0.0) {
return false; // Fractional part exist.
}
#if -LONG_MAX == LONG_MIN
// rare non-2's complement machine
return x > DBL_LONG_MINM1;
#else
return x - LONG_MIN > -1.0;
#endif
}
return false; // Too large or NaN
}
回答5:
Any IEEE floating-point double or float value with a magnitude at or above 2^52 or 2^23 will be whole number. Adding 2^52 or 2^23 to a positive number whose magnitude is less than that will cause it to be rounded to a whole number. Subtracting the value that was added will yield a whole number which will equal the original iff the original was a whole number. Note that this algorithm will fail with some numbers larger than 2^52, but it isn't needed for numbers that big.
回答6:
Could you use the modulus operator to check if the double is divisible by one... or am I completely misunderstanding the question?
double val = ... ; // Value
if(val % 1 == 0) {
// Val is evenly divisible by 1 and is therefore a whole number
}
来源：https://stackoverflow.com/questions/8905246/how-to-check-if-float-can-be-exactly-represented-as-an-integer