CanonicalForeignField
Extends
ForeignFieldWithMul
Constructors
new CanonicalForeignField(x)
new CanonicalForeignField(x:
| string
| number
| bigint
| Field3
| CanonicalForeignField): CanonicalForeignField
Parameters
• x:
| string
| number
| bigint
| Field3
| CanonicalForeignField
Returns
Overrides
ForeignFieldWithMul.constructor
Source
lib/provable/foreign-field.ts:514
Properties
type
type: "FullyReduced";
Source
lib/provable/foreign-field.ts:512
value
value: Field3;
The internal representation of a foreign field element, as a tuple of 3 limbs.
Inherited from
ForeignFieldWithMul.value
Source
lib/provable/foreign-field.ts:50
_Bigint
static _Bigint: undefined | {} = undefined;
Inherited from
ForeignFieldWithMul._Bigint
Source
lib/provable/foreign-field.ts:28
_modulus
static _modulus: undefined | bigint = undefined;
Inherited from
ForeignFieldWithMul._modulus
Source
lib/provable/foreign-field.ts:29
_provable
static _provable: undefined | ProvablePureExtended<CanonicalForeignField, bigint, string> = undefined;
Overrides
ForeignFieldWithMul._provable
Source
lib/provable/foreign-field.ts:518
_variants
static _variants: undefined | {
almostReduced: typeof AlmostForeignField;
canonical: typeof CanonicalForeignField;
unreduced: typeof UnreducedForeignField;
} = undefined;
Sibling classes that represent different ranges of field elements.
Inherited from
ForeignFieldWithMul._variants
Source
lib/provable/foreign-field.ts:59
Accessors
Constructor
get Constructor(): typeof ForeignField
Returns
typeof ForeignField
Source
lib/provable/foreign-field.ts:52
modulus
get modulus(): bigint
Returns
bigint
Source
lib/provable/foreign-field.ts:40
AlmostReduced
get static AlmostReduced(): typeof AlmostForeignField
Constructor for field elements that are "almost reduced", i.e. lie in the range [0, 2^ceil(log2(p))).
Returns
typeof AlmostForeignField
Source
lib/provable/foreign-field.ts:77
Bigint
get static Bigint(): {}
Returns
{}
Source
lib/provable/foreign-field.ts:32
Canonical
get static Canonical(): typeof CanonicalForeignField
Constructor for field elements that are fully reduced, i.e. lie in the range [0, p).
Returns
typeof CanonicalForeignField
Source
lib/provable/foreign-field.ts:84
Unreduced
get static Unreduced(): typeof UnreducedForeignField
Constructor for unreduced field elements.
Returns
typeof UnreducedForeignField
Source
lib/provable/foreign-field.ts:70
modulus
get static modulus(): bigint
Returns
bigint
Source
lib/provable/foreign-field.ts:36
provable
get static provable(): ProvablePureExtended<CanonicalForeignField, bigint, string>
Returns
ProvablePureExtended\<CanonicalForeignField, bigint, string>
Source
lib/provable/foreign-field.ts:521
sizeInBits
get static sizeInBits(): number
Returns
number
Source
lib/provable/foreign-field.ts:43
Methods
add()
add(y: number | bigint | ForeignField): UnreducedForeignField
Finite field addition
Parameters
• y: number | bigint | ForeignField
Returns
UnreducedForeignField
Inherited from
ForeignFieldWithMul.add
Example
x.add(2); // x + 2 mod p
Source
lib/provable/foreign-field.ts:208
assertAlmostReduced()
assertAlmostReduced(): AlmostForeignField
Assert that this field element lies in the range [0, 2^k), where k = ceil(log2(p)) and p is the foreign field modulus.
Returns the field element as a AlmostForeignField.
For a more efficient version of this for multiple field elements, see assertAlmostReduced.
Note: this does not ensure that the field elements is in the canonical range [0, p). To assert that stronger property, there is assertCanonical. You should typically use assertAlmostReduced though, because it is cheaper to prove and sufficient for ensuring validity of all our non-native field arithmetic methods.
Returns
Inherited from
ForeignFieldWithMul.assertAlmostReduced
Source
lib/provable/foreign-field.ts:163
assertCanonical()
assertCanonical(): CanonicalForeignField
Assert that this field element is fully reduced, i.e. lies in the range [0, p), where p is the foreign field modulus.
Returns the field element as a CanonicalForeignField.
Returns
Inherited from
ForeignFieldWithMul.assertCanonical
Source
lib/provable/foreign-field.ts:194
assertEquals()
assertEquals(y, message)
assertEquals(y: number | bigint | CanonicalForeignField, message?: string): CanonicalForeignField
Assert equality with a ForeignField-like value
Parameters
• y: number | bigint | CanonicalForeignField
• message?: string
Returns
Inherited from
ForeignFieldWithMul.assertEquals
Example
x.assertEquals(0, "x is zero");
Since asserting equality can also serve as a range check,
this method returns x with the appropriate type:
Example
let xChecked = x.assertEquals(1, "x is 1");
xChecked satisfies CanonicalForeignField;
Source
lib/provable/foreign-field.ts:286
assertEquals(y, message)
assertEquals(y: AlmostForeignField, message?: string): AlmostForeignField
Parameters
• y: AlmostForeignField
• message?: string
Returns
Inherited from
ForeignFieldWithMul.assertEquals
Source
lib/provable/foreign-field.ts:290
assertEquals(y, message)
assertEquals(y: ForeignField, message?: string): ForeignField
Parameters
• y: ForeignField
• message?: string
Returns
Inherited from
ForeignFieldWithMul.assertEquals
Source
lib/provable/foreign-field.ts:291
assertLessThan()
assertLessThan(c: number | bigint, message?: string): void
Assert that this field element is less than a constant c: x < c.
The constant must satisfy 0 <= c < 2^264, otherwise an error is thrown.
Parameters
• c: number | bigint
• message?: string
Returns
void
Inherited from
ForeignFieldWithMul.assertLessThan
Example
x.assertLessThan(10);
Source
lib/provable/foreign-field.ts:333
div()
div(y: number | bigint | AlmostForeignField): AlmostForeignField
Division in the finite field, i.e. x*y^(-1) mod p where y^(-1) is the finite field inverse.
Parameters
• y: number | bigint | AlmostForeignField
Returns
Inherited from
ForeignFieldWithMul.div
Example
let z = x.div(y); // x/y mod p
z.mul(y).assertEquals(x);
Source
lib/provable/foreign-field.ts:446
equals()
equals(y: number | bigint | CanonicalForeignField): Bool
Check equality with a ForeignField-like value.
Parameters
• y: number | bigint | CanonicalForeignField
Returns
Example
let isEqual = x.equals(y);
Note: This method only exists on canonical fields; on unreduced fields, it would be easy to misuse, because not being exactly equal does not imply being unequal modulo p.
Source
lib/provable/foreign-field.ts:551
inv()
inv(): AlmostForeignField
Multiplicative inverse in the finite field
Returns
Inherited from
ForeignFieldWithMul.inv
Example
let z = x.inv(); // 1/x mod p
z.mul(x).assertEquals(1);
Source
lib/provable/foreign-field.ts:432
isConstant()
isConstant(): boolean
Checks whether this field element is a constant.
See FieldVar to understand constants vs variables.
Returns
boolean
Inherited from
ForeignFieldWithMul.isConstant
Source
lib/provable/foreign-field.ts:126
mul()
mul(y: number | bigint | AlmostForeignField): UnreducedForeignField
Finite field multiplication
Parameters
• y: number | bigint | AlmostForeignField
Returns
UnreducedForeignField
Inherited from
ForeignFieldWithMul.mul
Example
x.mul(y); // x*y mod p
Source
lib/provable/foreign-field.ts:418
neg()
neg(): AlmostForeignField
Finite field negation
Returns
Inherited from
ForeignFieldWithMul.neg
Example
x.neg(); // -x mod p = p - x
Source
lib/provable/foreign-field.ts:219
sub()
sub(y: number | bigint | ForeignField): UnreducedForeignField
Finite field subtraction
Parameters
• y: number | bigint | ForeignField
Returns
UnreducedForeignField
Inherited from
ForeignFieldWithMul.sub
Example
x.sub(1); // x - 1 mod p
Source
lib/provable/foreign-field.ts:234
toBigInt()
toBigInt(): bigint
Convert this field element to a bigint.
Returns
bigint
Inherited from
ForeignFieldWithMul.toBigInt
Source
lib/provable/foreign-field.ts:146
toBits()
toBits(length?: number): Bool[]
Unpack a field element to its bits, as a Bool[] array.
This method is provable!
Parameters
• length?: number
Returns
Bool[]
Inherited from
ForeignFieldWithMul.toBits
Source
lib/provable/foreign-field.ts:352
toConstant()
toConstant(): ForeignField
Convert this field element to a constant.
See FieldVar to understand constants vs variables.
Warning: This function is only useful in Provable.witness or Provable.asProver blocks, that is, in situations where the prover computes a value outside provable code.
Returns
Inherited from
ForeignFieldWithMul.toConstant
Source
lib/provable/foreign-field.ts:138
toFields()
toFields(): Field[]
Instance version of Provable<ForeignField>.toFields, see Provable.toFields
Returns
Field[]
Inherited from
ForeignFieldWithMul.toFields
Source
lib/provable/foreign-field.ts:391
assertAlmostReduced()
static assertAlmostReduced<T>(...xs: T): [...{ [i in string | number | symbol]: AlmostForeignField }[]]
Assert that one or more field elements lie in the range [0, 2^k), where k = ceil(log2(p)) and p is the foreign field modulus.
This is most efficient than when checking a multiple of 3 field elements at once.
Type parameters
• T extends Tuple\<ForeignField>
Parameters
• ...xs: T
Returns
[...{ [i in string | number | symbol]: AlmostForeignField }[]]
Inherited from
ForeignFieldWithMul.assertAlmostReduced
Source
lib/provable/foreign-field.ts:177
check()
static check(x: ForeignField): void
Parameters
• x: ForeignField
Returns
void
Overrides
ForeignFieldWithMul.check
Source
lib/provable/foreign-field.ts:526
from()
from(x)
static from(x: string | number | bigint): CanonicalForeignField
Coerce the input to a ForeignField.
Parameters
• x: string | number | bigint
Returns
Inherited from
ForeignFieldWithMul.from
Source
lib/provable/foreign-field.ts:114
from(x)
static from(x: string | number | bigint | ForeignField): ForeignField
Parameters
• x: string | number | bigint | ForeignField
Returns
Inherited from
ForeignFieldWithMul.from
Source
lib/provable/foreign-field.ts:115
fromBits()
static fromBits(bits: Bool[]): AlmostForeignField
Create a field element from its bits, as a Bool[] array.
This method is provable!
Parameters
• bits: Bool[]
Returns
Inherited from
ForeignFieldWithMul.fromBits
Source
lib/provable/foreign-field.ts:373
random()
static random(): CanonicalForeignField
Returns
Inherited from
ForeignFieldWithMul.random
Source
lib/provable/foreign-field.ts:384
sum()
static sum(xs: (number | bigint | ForeignField)[], operations: (-1 | 1)[]): UnreducedForeignField
Sum (or difference) of multiple finite field elements.
Parameters
• xs: (number | bigint | ForeignField)[]
• operations: (-1 | 1)[]
Returns
UnreducedForeignField
Inherited from
ForeignFieldWithMul.sum
Example
let z = ForeignField.sum([3, 2, 1], [-1, 1]); // 3 - 2 + 1
z.assertEquals(2);
This method expects a list of ForeignField-like values, x0,...,xn,
and a list of "operations" op1,...,opn where every op is 1 or -1 (plus or minus),
and returns
x0 + op1*x1 + ... + opn*xn
where the sum is computed in finite field arithmetic.
Important: For more than two summands, this is significantly more efficient than chaining calls to ForeignField.add and ForeignField.sub.
Source
lib/provable/foreign-field.ts:259
unsafeFrom()
static unsafeFrom(x: ForeignField): CanonicalForeignField
Coerce the input to a CanonicalForeignField without additional assertions.
Warning: Only use if you know what you're doing.
Parameters
• x: ForeignField