GNU Compiler Collection (GCC) Internals: Overview of poly_int

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### 10.1 Overview of `poly_int`

We define indeterminates x1, …, xn whose values are only known at runtime and use polynomials of the form:

    c0 + c1 * x1 + … + cn * xn

to represent a size or offset whose value might depend on some of these indeterminates. The coefficients c0, …, cn are always known at compile time, with the c0 term being the “constant” part that does not depend on any runtime value.

GCC uses the `poly_int` class to represent these coefficients. The class has two template parameters: the first specifies the number of coefficients (n + 1) and the second specifies the type of the coefficients. For example, ‘`poly_int<2, unsigned short>`’ represents a polynomial with two coefficients (and thus one indeterminate), with each coefficient having type `unsigned short`. When n is 0, the class degenerates to a single compile-time constant c0.

The number of coefficients needed for compilation is a fixed property of each target and is specified by the configuration macro `NUM_POLY_INT_COEFFS`. The default value is 1, since most targets do not have such runtime invariants. Targets that need a different value should `#define` the macro in their `cpu-modes.def` file. See Back End.

`poly_int` makes the simplifying requirement that each indeterminate must be a nonnegative integer. An indeterminate value of 0 should usually represent the minimum possible runtime value, with c0 specifying the value in that case.

For example, when targetting the Arm SVE ISA, the single indeterminate represents the number of 128-bit blocks in a vector beyond the minimum length of 128 bits. Thus the number of 64-bit doublewords in a vector is 2 + 2 * x1. If an aggregate has a single SVE vector and 16 additional bytes, its total size is 32 + 16 * x1 bytes.

The header file `poly-int-types.h` provides typedefs for the most common forms of `poly_int`, all having `NUM_POLY_INT_COEFFS` coefficients:

`poly_uint16`

  a ‘`poly_int`’ with `unsigned short` coefficients.

`poly_int64`

  a ‘`poly_int`’ with `HOST_WIDE_INT` coefficients.

`poly_uint64`

  a ‘`poly_int`’ with `unsigned HOST_WIDE_INT` coefficients.

`poly_offset_int`

  a ‘`poly_int`’ with `offset_int` coefficients.

`poly_wide_int`

  a ‘`poly_int`’ with `wide_int` coefficients.

`poly_widest_int`

  a ‘`poly_int`’ with `widest_int` coefficients.

Since the main purpose of `poly_int` is to represent sizes and offsets, the last two typedefs are only rarely used.

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