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ExactRational

eqiora::kernel::pure_operator

Struct ExactRational 

pub struct ExactRational(/* private fields */);
Description

Exact reduced rational used by operator definitions and proofs.

Coefficients admit every finite binary64 value, including subnormals. Each numerator and denominator is limited to 8192 bits. Checked arithmetic rejects larger operands/results; executable arithmetic retains its original node order.

Implementations§

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impl ExactRational

Signature links:§ExactRational

pub fn from_binary64(value: f64) -> Option<ExactRational>

Signature links:from_binary64f64OptionExactRational

Represent every finite binary64 value exactly as a reduced dyadic rational. Signed zeros have the same canonical rational value; nonfinite values reject.

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impl ExactRational

Signature links:§ExactRational

pub fn new( numerator: i64, denominator: i64, ) -> Result<ExactRational, PureOperatorError>

Signature links:newi64i64ResultExactRationalPureOperatorError

Construct and reduce an exact ratio of signed integers.

§Errors

Rejects a zero denominator.

pub fn from_canonical_parts( numerator: &str, denominator: &str, ) -> Result<ExactRational, PureOperatorError>

Signature links:from_canonical_partsstrstrResultExactRationalPureOperatorError

Reconstruct reduced canonical decimal parts without leading zeros or +.

§Errors

Rejects noncanonical spelling, a nonpositive denominator, unreduced ratios, and operands outside the arithmetic work budget before normalization.

pub fn append_canonical_bytes(&self, bytes: &mut Vec<u8>)

Signature links:append_canonical_bytesVecu8

Encode the same length-prefixed signed numerator and positive denominator for every exact-calculus identity owner.

pub fn integer(value: i64) -> ExactRational

Signature links:integeri64ExactRational

Exact integer.

pub fn from_decimal_parts( coefficient: &str, exponent: i64, negative: bool, ) -> Result<ExactRational, PureOperatorError>

Signature links:from_decimal_partsstri64boolResultExactRationalPureOperatorError

Exact nonnegative decimal coefficient times a signed power of ten.

§Errors

Rejects malformed coefficients or input/result sizes outside the work budget.

pub fn to_i32_ratio(&self) -> Option<(i32, i32)>

Signature links:to_i32_ratioOptioni32i32

Checked conversion of both parts to signed 32-bit integers.

pub fn to_f64(&self) -> Result<f64, PureOperatorError>

Signature links:to_f64Resultf64PureOperatorError

Correctly rounded binary64 coefficient for executable lowering.

§Errors

Rejects overflow and rounding a nonzero exact coefficient to zero.

pub fn is_zero(&self) -> bool

Signature links:is_zerobool

Whether this value is exactly zero.

pub fn checked_neg(&self) -> Result<ExactRational, PureOperatorError>

Signature links:checked_negResultExactRationalPureOperatorError

Exact negation within the coefficient work budget.

pub fn checked_add( &self, other: ExactRational, ) -> Result<ExactRational, PureOperatorError>

Signature links:checked_addExactRationalResultExactRationalPureOperatorError

Exact sum within the coefficient work budget.

pub fn checked_mul( &self, other: ExactRational, ) -> Result<ExactRational, PureOperatorError>

Signature links:checked_mulExactRationalResultExactRationalPureOperatorError

Exact product within the coefficient work budget.

pub fn checked_div( &self, other: ExactRational, ) -> Result<ExactRational, PureOperatorError>

Signature links:checked_divExactRationalResultExactRationalPureOperatorError

Exact quotient within the coefficient work budget; rejects division by zero.

Trait Implementations§

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impl Clone for ExactRational

Signature links:§CloneExactRational
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fn clone(&self) -> ExactRational

Signature links:§cloneExactRational
Returns a duplicate of the value. Read more
1.0.0 (const: unstable) · Source§

fn clone_from(&mut self, source: &Self)

Signature links:unstableSource§clone_from
Performs copy-assignment from source. Read more
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impl Debug for ExactRational

Signature links:§DebugExactRational
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fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Signature links:§fmtFormatterResult()Error
Formats the value using the given formatter. Read more
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impl<'de> Deserialize<'de> for ExactRational

Signature links:§DeserializeExactRational
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fn deserialize<__D>( __deserializer: __D, ) -> Result<ExactRational, <__D as Deserializer<'de>>::Error>
where __D: Deserializer<'de>,

Signature links:§deserializeResultExactRationalDeserializerErrorDeserializer
Deserialize this value from the given Serde deserializer. Read more
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impl Hash for ExactRational

Signature links:§HashExactRational
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fn hash<__H>(&self, state: &mut __H)
where __H: Hasher,

Signature links:§hash&mut __HHasher
Feeds this value into the given Hasher. Read more
1.3.0 · Source§

fn hash_slice<H>(data: &[Self], state: &mut H)
where H: Hasher, Self: Sized,

Signature links:Source§hash_slice&mut HHasherSized
Feeds a slice of this type into the given Hasher. Read more
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impl Ord for ExactRational

Signature links:§OrdExactRational
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fn cmp(&self, other: &ExactRational) -> Ordering

Signature links:§cmpExactRationalOrdering
This method returns an Ordering between self and other. Read more
1.21.0 (const: unstable) · Source§

fn max(self, other: Self) -> Self
where Self: Sized,

Signature links:unstableSource§maxSized
Compares and returns the maximum of two values. Read more
1.21.0 (const: unstable) · Source§

fn min(self, other: Self) -> Self
where Self: Sized,

Signature links:unstableSource§minSized
Compares and returns the minimum of two values. Read more
1.50.0 (const: unstable) · Source§

fn clamp(self, min: Self, max: Self) -> Self
where Self: Sized,

Signature links:unstableSource§clampSized
Restrict a value to a certain interval. Read more
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impl PartialEq for ExactRational

Signature links:§PartialEqExactRational
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fn eq(&self, other: &ExactRational) -> bool

Signature links:§eqExactRationalbool
Tests for self and other values to be equal, and is used by ==.
1.0.0 (const: unstable) · Source§

fn ne(&self, other: &Rhs) -> bool

Signature links:unstableSource§ne&Rhsbool
Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl PartialOrd for ExactRational

Signature links:§PartialOrdExactRational
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fn partial_cmp(&self, other: &ExactRational) -> Option<Ordering>

Signature links:§partial_cmpExactRationalOptionOrdering
This method returns an ordering between self and other values if one exists. Read more
1.0.0 (const: unstable) · Source§

fn lt(&self, other: &Rhs) -> bool

Signature links:unstableSource§lt&Rhsbool
Tests less than (for self and other) and is used by the < operator. Read more
1.0.0 (const: unstable) · Source§

fn le(&self, other: &Rhs) -> bool

Signature links:unstableSource§le&Rhsbool
Tests less than or equal to (for self and other) and is used by the <= operator. Read more
1.0.0 (const: unstable) · Source§

fn gt(&self, other: &Rhs) -> bool

Signature links:unstableSource§gt&Rhsbool
Tests greater than (for self and other) and is used by the > operator. Read more
1.0.0 (const: unstable) · Source§

fn ge(&self, other: &Rhs) -> bool

Signature links:unstableSource§ge&Rhsbool
Tests greater than or equal to (for self and other) and is used by the >= operator. Read more
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impl Serialize for ExactRational

Signature links:§SerializeExactRational
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fn serialize<__S>( &self, __serializer: __S, ) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error>
where __S: Serializer,

Signature links:§serializeResultSerializerOkSerializerErrorSerializer
Serialize this value into the given Serde serializer. Read more
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impl TryFrom<CanonicalRational> for ExactRational

Signature links:§TryFromExactRational
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type Error = PureOperatorError

Signature links:§ErrorPureOperatorError
The type returned in the event of a conversion error.
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fn try_from( value: CanonicalRational, ) -> Result<ExactRational, <ExactRational as TryFrom<CanonicalRational>>::Error>

Signature links:§try_fromResultExactRationalExactRationalTryFromError
Performs the conversion.
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impl TryFrom<Ratio<BigInt>> for ExactRational

Signature links:§TryFromRatioBigIntExactRational
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fn try_from( value: Ratio<BigInt>, ) -> Result<ExactRational, <ExactRational as TryFrom<Ratio<BigInt>>>::Error>

Signature links:§try_fromRatioBigIntResultExactRationalExactRationalTryFromRatioBigIntError

Admit an existing exact ratio through the same canonical work bound.

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type Error = PureOperatorError

Signature links:§ErrorPureOperatorError
The type returned in the event of a conversion error.
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impl Eq for ExactRational

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impl StructuralPartialEq for ExactRational

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