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ScalarField

Defined in: lib/provable/scalar-field.ts:12

ForeignField representing the scalar field of Pallas and the base field of Vesta

Extends

Constructors

new ScalarField()

new ScalarField(x: string | number | bigint | Field3 | ForeignField): ScalarField

Defined in: lib/provable/foreign-field.ts:91

Create a new ForeignField from a bigint, number, string or another ForeignField.

Parameters

x

string | number | bigint | Field3 | ForeignField

Returns

ScalarField

Example

let x = new ForeignField(5);

Note: Inputs must be range checked if they originate from a different field with a different modulus or if they are not constants.

  • When constructing from another ForeignField instance, ensure the modulus matches. If not, check the modulus using Gadgets.ForeignField.assertLessThan() and handle appropriately.
  • When constructing from a Field3 array, ensure all elements are valid Field elements and range checked.
  • Ensure constants are correctly reduced to the modulus of the field.

Inherited from

UnreducedForeignField.constructor

Properties

type

type: "Unreduced" | "AlmostReduced" | "FullyReduced" = 'Unreduced';

Defined in: lib/provable/foreign-field.ts:455

Inherited from

UnreducedForeignField.type


value

value: Field3;

Defined in: lib/provable/foreign-field.ts:39

The internal representation of a foreign field element, as a tuple of 3 limbs.

Inherited from

UnreducedForeignField.value


_Bigint

static _Bigint: undefined | {} = undefined;

Defined in: lib/provable/foreign-field.ts:17

Inherited from

UnreducedForeignField._Bigint


_modulus

static _modulus: undefined | bigint = undefined;

Defined in: lib/provable/foreign-field.ts:18

Inherited from

UnreducedForeignField._modulus


_provable

static _provable: 
| undefined
| ProvablePureExtended<UnreducedForeignField, bigint, string> = undefined;

Defined in: lib/provable/foreign-field.ts:457

Inherited from

UnreducedForeignField._provable


_variants

static _variants: 
| undefined
| {
almostReduced: typeof AlmostForeignField;
canonical: typeof CanonicalForeignField;
unreduced: typeof UnreducedForeignField;
} = undefined;

Defined in: lib/provable/foreign-field.ts:48

Sibling classes that represent different ranges of field elements.

Inherited from

UnreducedForeignField._variants

Accessors

Constructor

Get Signature

get Constructor(): typeof ForeignField

Defined in: lib/provable/foreign-field.ts:41

Returns

typeof ForeignField

Inherited from

UnreducedForeignField.Constructor


modulus

Get Signature

get modulus(): bigint

Defined in: lib/provable/foreign-field.ts:29

Returns

bigint

Inherited from

UnreducedForeignField.modulus


AlmostReduced

Get Signature

get static AlmostReduced(): typeof AlmostForeignField

Defined in: lib/provable/foreign-field.ts:66

Constructor for field elements that are "almost reduced", i.e. lie in the range [0, 2^ceil(log2(p))).

Returns

typeof AlmostForeignField

Inherited from

UnreducedForeignField.AlmostReduced


Bigint

Get Signature

get static Bigint(): {}

Defined in: lib/provable/foreign-field.ts:21

Returns
{}

Inherited from

UnreducedForeignField.Bigint


Canonical

Get Signature

get static Canonical(): typeof CanonicalForeignField

Defined in: lib/provable/foreign-field.ts:73

Constructor for field elements that are fully reduced, i.e. lie in the range [0, p).

Returns

typeof CanonicalForeignField

Inherited from

UnreducedForeignField.Canonical


modulus

Get Signature

get static modulus(): bigint

Defined in: lib/provable/foreign-field.ts:25

Returns

bigint

Inherited from

UnreducedForeignField.modulus


provable

Get Signature

get static provable(): ProvablePureExtended<UnreducedForeignField, bigint, string>

Defined in: lib/provable/foreign-field.ts:459

Provable<ForeignField>, see Provable

Returns

ProvablePureExtended<UnreducedForeignField, bigint, string>

Inherited from

UnreducedForeignField.provable


sizeInBits

Get Signature

get static sizeInBits(): number

Defined in: lib/provable/foreign-field.ts:32

Returns

number

Inherited from

UnreducedForeignField.sizeInBits


Unreduced

Get Signature

get static Unreduced(): typeof UnreducedForeignField

Defined in: lib/provable/foreign-field.ts:59

Constructor for unreduced field elements.

Returns

typeof UnreducedForeignField

Inherited from

UnreducedForeignField.Unreduced

Methods

add()

add(y: number | bigint | ForeignField): UnreducedForeignField

Defined in: lib/provable/foreign-field.ts:210

Finite field addition

Parameters

y

number | bigint | ForeignField

Returns

UnreducedForeignField

Example

x.add(2); // x + 2 mod p

Inherited from

UnreducedForeignField.add


assertAlmostReduced()

assertAlmostReduced(): AlmostForeignField

Defined in: lib/provable/foreign-field.ts:165

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

AlmostForeignField

Inherited from

UnreducedForeignField.assertAlmostReduced


assertCanonical()

assertCanonical(): CanonicalForeignField

Defined in: lib/provable/foreign-field.ts:196

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

CanonicalForeignField

Inherited from

UnreducedForeignField.assertCanonical


assertEquals()

Call Signature

assertEquals(y: number | bigint | CanonicalForeignField, message?: string): CanonicalForeignField

Defined in: lib/provable/foreign-field.ts:288

Assert equality with a ForeignField-like value

Parameters
y

number | bigint | CanonicalForeignField

message?

string

Returns

CanonicalForeignField

Examples
x.assertEquals(0, "x is zero");

Since asserting equality can also serve as a range check, this method returns x with the appropriate type:

let xChecked = x.assertEquals(1, "x is 1");
xChecked satisfies CanonicalForeignField;
Inherited from

UnreducedForeignField.assertEquals

Call Signature

assertEquals(y: AlmostForeignField, message?: string): AlmostForeignField

Defined in: lib/provable/foreign-field.ts:289

Assert equality with a ForeignField-like value

Parameters
y

AlmostForeignField

message?

string

Returns

AlmostForeignField

Examples
x.assertEquals(0, "x is zero");

Since asserting equality can also serve as a range check, this method returns x with the appropriate type:

let xChecked = x.assertEquals(1, "x is 1");
xChecked satisfies CanonicalForeignField;
Inherited from

UnreducedForeignField.assertEquals

Call Signature

assertEquals(y: ForeignField, message?: string): ForeignField

Defined in: lib/provable/foreign-field.ts:290

Assert equality with a ForeignField-like value

Parameters
y

ForeignField

message?

string

Returns

ForeignField

Examples
x.assertEquals(0, "x is zero");

Since asserting equality can also serve as a range check, this method returns x with the appropriate type:

let xChecked = x.assertEquals(1, "x is 1");
xChecked satisfies CanonicalForeignField;
Inherited from

UnreducedForeignField.assertEquals


assertLessThan()

assertLessThan(c: number | bigint, message?: string): void

Defined in: lib/provable/foreign-field.ts:325

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

Example

x.assertLessThan(10);

Inherited from

UnreducedForeignField.assertLessThan


neg()

neg(): AlmostForeignField

Defined in: lib/provable/foreign-field.ts:221

Finite field negation

Returns

AlmostForeignField

Example

x.neg(); // -x mod p = p - x

Inherited from

UnreducedForeignField.neg


sub()

sub(y: number | bigint | ForeignField): UnreducedForeignField

Defined in: lib/provable/foreign-field.ts:236

Finite field subtraction

Parameters

y

number | bigint | ForeignField

Returns

UnreducedForeignField

Example

x.sub(1); // x - 1 mod p

Inherited from

UnreducedForeignField.sub


toBigInt()

toBigInt(): bigint

Defined in: lib/provable/foreign-field.ts:148

Convert this field element to a bigint.

Returns

bigint

Inherited from

UnreducedForeignField.toBigInt


toBits()

toBits(length?: number): Bool[]

Defined in: lib/provable/foreign-field.ts:344

Unpack a field element to its bits, as a Bool[] array.

This method is provable!

Parameters

length?

number

Returns

Bool[]

Inherited from

UnreducedForeignField.toBits


toFields()

toFields(): Field[]

Defined in: lib/provable/foreign-field.ts:392

Instance version of Provable<ForeignField>.toFields, see Provable.toFields

Returns

Field[]

Inherited from

UnreducedForeignField.toFields


toScalar()

toScalar(): Scalar

Defined in: lib/provable/scalar-field.ts:16

Provable method to convert a ScalarField into a Scalar

Returns

Scalar


assertAlmostReduced()

static assertAlmostReduced<T>(...xs: T): [...{ [i in string | number | symbol]: AlmostForeignField }[]]

Defined in: lib/provable/foreign-field.ts:179

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

UnreducedForeignField.assertAlmostReduced


check()

static check(x: ForeignField): void

Defined in: lib/provable/foreign-field.ts:464

Parameters

x

ForeignField

Returns

void

Inherited from

UnreducedForeignField.check


from()

Call Signature

static from(x: string | number | bigint): CanonicalForeignField

Defined in: lib/provable/foreign-field.ts:114

Coerce the input to a ForeignField.

Parameters
x

string | number | bigint

Returns

CanonicalForeignField

Inherited from

UnreducedForeignField.from

Call Signature

static from(x: string | number | bigint | ForeignField): ForeignField

Defined in: lib/provable/foreign-field.ts:115

Coerce the input to a ForeignField.

Parameters
x

string | number | bigint | ForeignField

Returns

ForeignField

Inherited from

UnreducedForeignField.from


fromBits()

static fromBits(bits: Bool[]): AlmostForeignField

Defined in: lib/provable/foreign-field.ts:374

Create a field element from its bits, as a Bool[] array.

This method is provable!

Parameters

bits

Bool[]

Returns

AlmostForeignField

Inherited from

UnreducedForeignField.fromBits


fromScalar()

static fromScalar(s: Scalar): ScalarField

Defined in: lib/provable/scalar-field.ts:32

Converts this Scalar into a ScalarField

Parameters

s

Scalar

Returns

ScalarField


random()

static random(): CanonicalForeignField

Defined in: lib/provable/foreign-field.ts:385

Returns

CanonicalForeignField

Inherited from

UnreducedForeignField.random


sum()

static sum(xs: (number | bigint | ForeignField)[], operations: (-1 | 1)[]): UnreducedForeignField

Defined in: lib/provable/foreign-field.ts:261

Sum (or difference) of multiple finite field elements.

Parameters

xs

(number | bigint | ForeignField)[]

operations

(-1 | 1)[]

Returns

UnreducedForeignField

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.

Inherited from

UnreducedForeignField.sum


toScalar()

static toScalar(field: ForeignField): Scalar

Defined in: lib/provable/scalar-field.ts:20

Parameters

field

ForeignField

Returns

Scalar