What is the difference between intXX_t and int_fastXX_t?

Gnu libc defines {int,uint}_fast{16,32}_t as 64-bit when compiling for 64-bit CPUs and 32-bit otherwise. Operations on 64-bit integers are faster on Intel and AMD 64-bit x86 CPUs than the same operations on 32-bit integers.

In the C99 Standard, 7.18.1.3 Fastest minimum-width integer types.

(7.18.1.3p1) "Each of the following types designates an integer type that is usually fastest225) to operate with among all integer types that have at least the specified width."

225) "The designated type is not guaranteed to be fastest for all purposes; if the implementation has no clear grounds for choosing one type over another, it will simply pick some integer type satisfying the signedness and width requirements."

and

(7.18.1.3p2) "The typedef name int_fastN_t designates the fastest signed integer type with a width of at least N. The typedef name uint_fastN_t designates the fastest unsigned integer type with a width of at least N."

The types int_fastN_t and uint_fastN_t are counterparts to the exact-width integer types intN_t and uintN_t. The implementation guarantees that they take at least N bits, but the implementation can take more bits if it can perform optimization using larger types; it just guarantees they take at least N bits.

For example, on a 32-bit machine, uint_fast16_t could be defined as an unsigned int rather than as an unsigned short because working with types of machine word size would be more efficent.

Another reason of their existence is the exact-width integer types are optional in C but the fastest minimum-width integer types and the minimum-width integer types (int_leastN_t and uint_leastN_t) are required.