GeezerVison

The two conditions "v would overflow when cast to 'type'" and "type_MIN <= v <= type_MAX" are not equivalent. Which one do you want to test here?

For example, assuming a 32-bit int type: type_MAX would be 2147483647. If v = 2147483647.5 (which is exactly representable in IEEE 754 binary64 floating-point), then it satisfies the first condition - it doesn't overflow when cast to int - but not the second.

Sorry, but this isn't right.

For a 32-bit signed integer type, this condition becomes:

-2147483647.9999998 <= v <= 2147483646.9999998

but what we actually want is:

-2147483649.0 < v < 2147483648.0

or if we want to use <= and express the limits in terms of doubles:

-2147483648.9999995 <= v <= 2147483647.9999998

For a 64-bit signed integer type, this condition becomes:

-9223372036854774784.0 <= v <= 9223372036854774784.0

but the actual limits we need are

-9223372036854775808.0 <= v <= 9223372036854774784.0

Suggested alternative approach: given a double v that we want to safely convert to an int (say), first use modf to extract the fractional part fv and the integer part iv of v (both fv and iv are still doubles at this point). We can just ignore the fractional part fv: it doesn't affect whether we can safely cast to int or not. Now for iv, check whether it satisfies (double)INT_MIN <= iv and iv < -(double)INT_MIN. Note that INT_MIN is (always in practice, even though not guaranteed by the standard) the negation of a power of two, so the conversion to double doesn't change the value and we're effectively checking whether iv lies in the half-open interval [INT_MIN, -INT_MIN). Since iv is an integer, that's equivalent to checking whether iv lies in the closed interval [INT_MIN, -INT_MIN-1]. But making all our usual assumptions about integer representation (two's complement, no trap representation, no padding bits, etc.), -INT_MIN-1 is the same as INT_MAX, so we're effectively checking that the integer part of v is representable as an int, which is exactly what we want to be checking.

Similarly for long, long long, etc.