将浮点数分解为其整数部分和小数部分

Question

I am implementing a fractional delay line algorithm. One of the tasks involved is the decomposition of a floating-point value into its integral and fractional part. I know there are a lot of posts about this topic on SO and I probably read most of them. However I haven't found one post that deals with the specifics of this scenario.

• The algorithm must be using 64-bit floating-point values.

• Input floating-point values are guaranteed to always be positive. (delay times cannot be negative)

• The output integer part has to be represented by an integer datatype.

• The integer datatype must have enough bits so that the double-to-integer conversion occurs without the risk of overflowing.

• Issues resulting from floating-point values lacking an exact internal representation must be avoided. (ie 9223372036854775809.0 might be internally represented as 9223372036854775808.9999998 and when cast to integer it erroneously becomes 9223372036854775808)

• The implementation should work regardless of rounding mode or compiler optimization settings.

So I wrote a function:

 double my_modf(double x, int64_t *intPartOut);

As you can see its signature is similar to the modf() function in the C standard library.

The first implementation I came up with is:

double my_modf(double x, int64_t *intPartOut)
{
    double y;
    double fracPart = modf(x, &y);
    *intPartOut = (int64_t)y;
    return fracPart;
}

I have also been experimenting with this implementation which - at least on my machine - runs faster than the previous, however I doubt its robustness.

double my_modf(double x, int64_t *intPartOut)
{
    int64_t y = (int64_t)x;
    *intPartOut = y;
    return x - y;
}

...and this is my latest attempt:

double my_modf(double x, int64_t *intPartOut)
{
    *intPartOut = llround(x);
    return x - floor(x);
}

I can't make up my mind as to which implementation would be best to use, or if there are other implementations that I haven't considered that would better accomplish the following goals. I am looking for the (1) most robust and (2) most efficient implementation to decompose a floating-point number into its integral and fractional part, keeping into consideration the list of points mentioned above.

Answer 1

Updated answer after reading your comment below.

If you are already sure the values are within [0, 2^63-1] then a simple cast will be faster than llround() since this function may also check for overflow (on my system, the manual page states so, however the C standard does not require it).

On my machine for example (x86-64 Nehalem) casting is a single instruction ( cvttsd2si ) and llround() is obviously more than one.

Am I guaranteed to get the right result with a simple cast (truncation) or is it safer to round?

Depends on what you mean with "right". If the value in the double can be correctly represented by an int64_t , then sure you're going to get exactly the same value. However, if the value cannot be precisely represented by the double then truncation is automatically performed when casting. If you want to round the value in a different way that's another story and you'll have to use one of ceil() , floor() or round() .

If you also are sure that no values will be +/- Infinity or NaN (and in that case you can use -Ofast ), then your second implementation should be the fastest if you want truncation, while the third should be the fastest if you want to floor() the value.

Answer 2

Given that the maximum value of the integer part of the floating-point input x is 2 ⁶³ −1 and that x is non-negative, then both:

double my_modf(double x, int64_t *intPartOut)
{
    double y;
    double fracPart = modf(x, &y);
    *intPartOut = y;
    return fracPart;
}

and:

double my_modf(double x, int64_t *intPartOut)
{
    int64_t y = x;
    *intPartOut = y;
    return x - y;
}

will correctly return the integer part in intPartOut and the fractional part in the return value regardless of rounding mode.

GCC 9.2 for x86_64 does a better job optimizing the latter version , and so does Apple Clang 11.0.0.

llround will not return the integer part as desired because it rounds to the nearest integer rather than truncating.

Issues about x containing errors cannot be resolved with the information provided in the question. The routines shown above have no error; they return exactly the integer and fractional parts of their input.