Module exact 

The exact real types in the interpreter’s value model: real algebraic numbers, computable reals, the program’s infinitesimal and the hyperreals it generates, infinite integers, ordinals, and the values a supertask leaves.

How they mix with the numeric tower and with each other is decided once, in logicaffeine_base::tower, generic over a value model; this module is where RuntimeValue joins it, so the tree-walker and the VM compute exactly what a compiled program computes.

Structs

Branch

One branch of a residue-dependent value, compared by value.

HyperValue

A hyperreal value with the infinitesimal it is written in.

NaturalValue

An infinite integer with the infinitesimal whose reciprocal generates it.

Scale

An infinitesimal of the program: the name it was declared under, what is known about the residues of its reciprocal, the infinite natural ⌈1/dt⌉, and where it stands among the others.

Enums

HyperForm

A hyperreal’s representations: an exact rational function of dt; a real algebraic Puiseux series that is none, a root of one (crate::puiseux); the germ a flow leaves, known by its series in dt; or a value of several ordered infinitesimals (Multi). A Puiseux series compares and hashes by its value, a germ by its canonical encoding.

Op

The arithmetic operators the exact types take.

Rel

The relational operators the exact types answer.

Rounding

How an integer part rounds: down, up, or to the nearest integer with ties away from zero (the tower’s round).

Functions

apply_limit

Resolve a residue-dependent value under a limit rule.

arith

Apply op when either operand is an exact type; None when neither is.

depends_from_parts

A residue-dependent value rebuilt from its scale, modulus and per-class values.

display

How an exact value prints.

exact_bytes

An algebraic number, computable real or ordinal as its kind and canonical bytes.

from_algebraic

The canonical runtime value of an algebraic number: a rational is an Int/BigInt/Rational.

from_depends

The canonical runtime value of a residue-dependent value.

from_exact_bytes

The value exact_bytes wrote; None for a forged or non-canonical encoding.

from_exact_real

The canonical runtime value of a computable real: an algebraic one is an algebraic number.

from_germ

The canonical runtime value of a germ.

from_hyper

The canonical runtime value of a hyperreal.

from_natural

The canonical runtime value of an infinite integer.

from_ordinal

A finite ordinal is a natural number.

from_scaled_bytes

The value scaled_bytes wrote; None for a forged or non-canonical encoding.

generator_of

The infinite natural ⌈1/dt⌉ generated by an infinitesimal value.

germ_of

A number as a germ, or None.

integer_part

The integer part of an exact value under mode; None when v is not one.

is_exact_value

True for a value of one of the exact types.

is_infinitesimal

x ≈ 0: zero or an infinitesimal.

is_limited

Bounded by a standard number.

limit_rule

A limit rule by its English name.

new_infinitesimal

The program’s infinitesimal, its reciprocal’s residues modulo modulus limited to allowed.

new_ordered_infinitesimal

An infinitesimal declared much smaller than larger and much larger than smaller, each an infinitesimal or nothing.

not

not lifted over residue branches and through provisional values; None for any other value.

provisional

A provisional answer: the current guess after steps cases with revisions changes.

relation

Apply rel when either operand is an exact type; None when neither is.

scale_from_parts

The scale scale_parts wrote.

scale_parts

The infinitesimal’s name and its reciprocal’s residue facts.

scaled_bytes

A hyperreal, infinite integer or germ as its kind, scale and canonical bytes.

standard_part

The standard part of a limited value.

structurally_equal

Structural equality for collections and hashing; None when neither value is exact.

undecided_branch

Why a value cannot decide a branch, or None.

Type Aliases

DependsValue

A runtime value that depends on the residue of ⌈1/dt⌉.