An IEEE754 64-bit double can represent any 32-bit integer, simply because it has 53-odd^(a) bits available for precision and the 32-bit integer only needs, well, 32 :-)

It would be plausible for a (non IEEE754 double precision) 64-bit floating point number to have less than 32 bits of precision. That would allow truly huge numbers (due to the exponent) but at the cost of precision.

The bottom line is that, provided there are more bits of precision in the mantissa of the floating point number than there are in the integer (and enough bits in the exponent to scale it), then it can be represented without loss of precision.

^(a) Technically, the 53rd bit of precision is an implied 1 at the start of the sequence so the amount of "variablity" may only be 52 bits. Whether it's 52 or 53, it's still enough bits to represent every 32-bit integer.

xs:double and xs:float are defined by IEEE rules. See

3.3.5 double

The ·value space· of double contains the non-zero numbers m × 2e , where m is an integer whose absolute value is less than 253, and e is an integer between −1074 and 971, inclusive.

By contrast, the limits for xs:integer and xs:decimal are implementation-defined.

Section 3.3.3: [Definition:] decimal represents a subset of the real numbers, which can be represented by decimal numerals. The ·value space· of decimal is the set of numbers that can be obtained by dividing an integer by a non-negative power of ten, i.e., expressible as i / 10n where i and n are integers and n ≥ 0.

Section 5.4: All ·minimally conforming· processors must support decimal values whose absolute value can be expressed as i / 10^k, where i and k are nonnegative integers such that i < 1016 and k ≤ 16 (i.e., those expressible with sixteen total digits).

The minimum ranges you can rely on are:

• short int and int: -32,767 to 32,767
• unsigned short int and unsigned int: 0 to 65,535
• long int: -2,147,483,647 to 2,147,483,647
• unsigned long int: 0 to 4,294,967,295

This means that no, long int cannot be relied upon to store any 10-digit number. However, a larger type, long long int, was introduced to C in C99 and C++ in C++11 (this type is also often supported as an extension by compilers built for older standards that did not include it). The minimum range for this type, if your compiler supports it, is:

• long long int: -9,223,372,036,854,775,807 to 9,223,372,036,854,775,807
• unsigned long long int: 0 to 18,446,744,073,709,551,615

So that type will be big enough (again, if you have it available).

A note for those who believe I've made a mistake with these lower bounds: the C requirements for the ranges are written to allow for ones' complement or sign-magnitude integer representations, where the lowest representable value and the highest representable value differ only in sign. It is also allowed to have a two's complement representation where the value with sign bit 1 and all value bits 0 is a trap representation rather than a legal value. In other words, int is not required to be able to represent the value -32,768.