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Numeric types

r[type.numeric]

Integer types

r[type.numeric.int]

r[type.numeric.int.unsigned] The unsigned integer types consist of:

Type Minimum Maximum
u8 0 28-1
u16 0 216-1
u32 0 232-1
u64 0 264-1
u128 0 2128-1

r[type.numeric.int.signed] The signed two's complement integer types consist of:

Type Minimum Maximum
i8 -(27) 27-1
i16 -(215) 215-1
i32 -(231) 231-1
i64 -(263) 263-1
i128 -(2127) 2127-1

Floating-point types

r[type.numeric.float]

The IEEE 754-2008 "binary32" and "binary64" floating-point types are f32 and f64, respectively.

Machine-dependent integer types

r[type.numeric.int.size]

r[type.numeric.int.size.usize] The usize type is an unsigned integer type with the same number of bits as the platform's pointer type. It can represent every memory address in the process.

r[type.numeric.int.size.isize] The isize type is a signed integer type with the same number of bits as the platform's pointer type. The theoretical upper bound on object and array size is the maximum isize value. This ensures that isize can be used to calculate differences between pointers into an object or array and can address every byte within an object along with one byte past the end.

r[type.numeric.int.size.minimum] usize and isize are at least 16-bits wide.

Note: Many pieces of Rust code may assume that pointers, usize, and isize are either 32-bit or 64-bit. As a consequence, 16-bit pointer support is limited and may require explicit care and acknowledgment from a library to support.

Representation

r[type.numeric.repr]

r[type.numeric.repr.integer] Each value of an integer type is a whole number. For unsigned types, this is a positive integer or 0. For signed types, this can either be a positive integer, negative integer, or 0.

r[type.numeric.repr.integer-width] The range of values an integer type can represent depends on its signedness and its width, in bits. The width of type uN or iN is N. The width of type usize or isize is the value of the target_pointer_width property.

Note

There are exactly 1<<N unique values of an integer type of width N. In particular, for an unsigned type, these values are in the range 0..(1<<N) and for a signed type, are in the range -(1<<(N-1))..(1<<(N-1)), using rust range syntax.

r[type.numeric.repr.unsigned] A value i of an unsigned integer type U is represented by a sequence of initialized bytes, where the mth successive byte according to the byte order of the platform is (i >> (m*8)) as u8, where m is between 0 and the size of U. None of the bytes produced by encoding an unsigned integer has a pointer fragment.

Note

The two primary byte orders are little endian, where the bytes are ordered from lowest memory address to highest, and big endian, where the bytes are ordered from highest memory address to lowest. The cfg predicate target_endian indicates the byte order

[!WARN] On little endian, the order of bytes used to decode an integer type is the same as the natural order of a u8 array - that is, the m value corresponds with the m index into a same-sized u8 array. On big endian, however, the order is the opposite of this order - that is, the m value corresponds with the size_of::<T>() - m index in that array.

r[type.numeric.repr.signed] A value i of a signed integer type with width N is represented the same as the corresponding value of the unsigned counterpart type which is congruent modulo 2^N.

Note

This encoding of signed integers is known as the 2s complement encoding.

r[type.numeric.repr.float-width] Each floating-point type has a width. The type fN has a width of N.

r[type.numeric.repr.float] A floating-point value is represented by the following decoding:

  • The byte sequence is decoded as the unsigned integer type with the same width as the floating-point type,
  • The resulting integer is decoded according to IEEE 754-2019 into the format used for the type.

r[type.numeric.repr.float-format] The IEEE 754-2019 binary32 format is used for f32, and the binary64 format is used for f64. The set of values for each floating-point type are determined by the respective format.