Representability

June 7, 2023

We’ve learned about types, type identity, and type assignability. But you may recall a bit of a discussion about some of the esoteric features of constants in Go. Namely, they can be untyped, and they don’t overflow. So how do we know if a constant can be represented faithfully by a particular type?

We finally have the answer, in all its detailed glory:

Representability

A constant x is representable by a value of type T, where T is not a type parameter, if one of the following conditions applies:

  • x is in the set of values determined by T.
  • T is a floating-point type and x can be rounded to T’s precision without overflow. Rounding uses IEEE 754 round-to-even rules but with an IEEE negative zero further simplified to an unsigned zero. Note that constant values never result in an IEEE negative zero, NaN, or infinity.
  • T is a complex type, and x’s components real(x) and imag(x) are representable by values of T’s component type (float32 or float64).

If T is a type parameter, x is representable by a value of type T if x is representable by a value of each type in T’s type set.

x                   T           x is representable by a value of T because

'a'                 byte        97 is in the set of byte values
97                  rune        rune is an alias for int32, and 97 is in the set of 32-bit integers
"foo"               string      "foo" is in the set of string values
1024                int16       1024 is in the set of 16-bit integers
42.0                byte        42 is in the set of unsigned 8-bit integers
1e10                uint64      10000000000 is in the set of unsigned 64-bit integers
2.718281828459045   float32     2.718281828459045 rounds to 2.7182817 which is in the set of float32 values
-1e-1000            float64     -1e-1000 rounds to IEEE -0.0 which is further simplified to 0.0
0i                  int         0 is an integer value
(42 + 0i)           float32     42.0 (with zero imaginary part) is in the set of float32 values
x                   T           x is not representable by a value of T because

0                   bool        0 is not in the set of boolean values
'a'                 string      'a' is a rune, it is not in the set of string values
1024                byte        1024 is not in the set of unsigned 8-bit integers
-1                  uint16      -1 is not in the set of unsigned 16-bit integers
1.1                 int         1.1 is not an integer value
42i                 float32     (0 + 42i) is not in the set of float32 values
1e1000              float64     1e1000 overflows to IEEE +Inf after rounding

Quotes from The Go Programming Language Specification Version of December 15, 2022


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