evm-maths

➗ Useful bigint math libraries to ease your journey through off-chain fixed-point arithmetics

Install

npm install evm-maths

yarn add evm-maths

---

Usage

Just import the module and you'll benefit from an augmented, and typed, BigInt class!

import "evm-maths";

const WAD = BigInt.pow10(18);

BigInt.from(1).wadMul(WAD); // 1
BigInt.from(WAD * 2n).rayMul(0.5e27); // WAD

If you choose to avoid prototype pollution, you can always import specific utilities:

import * as WadMath from "evm-maths/lib/wad";
import * as RayMath from "evm-maths/lib/ray";
import * as PercentMath from "evm-maths/lib/percent";

---

Book

• Scale-agnostic utilities
  • approxEqAbs
  • min
  • max
  • sum
  • format
  • toFloat
  • pow10
  • mulDiv
  • mulDivUp
  • mulDivDown
• Scale constants
  • WAD
  • RAY
  • PERCENT
  • HALF_WAD
  • HALF_RAY
  • HALF_PERCENT
• Wad-based utilities
  • wadMul
  • wadDiv
  • wadAdd
  • wadSub
  • wadAvg
  • wadPow
  • wadPowUp
  • wadPowDown
  • wadExpTaylorN
  • wadMulUp
  • wadMulDown
  • wadDivUp
  • wadDivDown
  • formatWad
  • toWadFloat
  • wadToPercent
  • wadToRay
  • wadToDecimals
• Ray-based utilities
  • rayMul
  • rayDiv
  • rayAdd
  • raySub
  • rayAvg
  • rayPow
  • rayPowUp
  • rayPowDown
  • rayExpTaylorN
  • rayMulUp
  • rayMulDown
  • rayDivUp
  • rayDivDown
  • formatRay
  • toRayFloat
  • rayToPercent
  • rayToWad
  • rayToDecimals
• Percent-based utilities
  • percentMul
  • percentDiv
  • percentAdd
  • percentSub
  • percentAvg
  • percentPow
  • percentPowUp
  • percentPowDown
  • percentExpTaylorN
  • percentMulUp
  • percentMulDown
  • percentDivUp
  • percentDivDown
  • formatPercent
  • toPercentFloat
  • percentToWad
  • percentToRay
  • percentToDecimals

---

Scale-agnostic utilities

approxEqAbs

Returns whether the BigNumber is approximately close to the given BigNumber, within the given tolerance

// only if you want to avoid BigNumber prototype pollution
import { approxEqAbs } from "evm-maths/lib/utils";

// Returns whether the BigNumber is approximately close to the given BigNumber, within the given tolerance: true
approxEqAbs(0, 1, "1");
BigNumber.approxEqAbs(0, 1, "1");
BigNumber.from(0).approxEqAbs(1, "1");

min

Returns the minimum between input BigNumberish, as a BigInt

// only if you want to avoid BigInt prototype pollution
import { min } from "evm-maths/lib/utils";

// Returns the minimum between input BigNumberish, as a BigInt: 0
min(0, 1, "2", ...);
BigInt.min(0, 1, "2", ...);
BigInt.from(0).min(1, "2", ...);

max

Returns the maximum between input BigNumberish, as a BigInt

// only if you want to avoid BigInt prototype pollution
import { max } from "evm-maths/lib/utils";

// Returns the maximum between input BigNumberish, as a BigInt: 2
max(0, 1, "2", ...);
BigInt.max(0, 1, "2", ...);
BigInt.from(0).max(1, "2", ...);

sum

Returns the sum of input BigNumberish array, as a BigInt

// only if you want to avoid BigInt prototype pollution
import { sum } from "evm-maths/lib/utils";

// Returns the sum of input BigNumberish array, as a BigInt: 3
sum([0, 1, "2"]);
BigInt.sum([0, 1, "2"]);
BigInt.from(0).sum([1, "2"]);

format

Returns a string representation of the BigInt's value, formatted according to:

• the input number of decimals the BigInt value holds (default: 0)
• the input number of digits expected after the unit, truncating the trailing digits if any (default: keep all digits after the decimal point)

// Returns a string representation of the BigInt's value: 0.01
BigInt.from(19).format(3, 2);

toFloat

Returns a float representation of the BigInt's value, parsed according to the input number of decimals the BigInt value holds (default: 0)

Note: parsing a too large value may result in parsing NaN (because the BigInt's value may still be too large to fit in a JS floating-point number)

// Returns a string representation of the BigInt's value: 0.01
BigInt.from(19).toFloat(3, 2);

pow10

Returns a 1 followed by the input number of zeros (10 raised to the power of the input)

// only if you want to avoid BigInt prototype pollution
import { pow10 } from "evm-maths/lib/utils";

// Returns a 1 followed by the input number of zeros: 100
pow10(2);
BigInt.pow10(2);

mulDiv

Performs a multiplication followed by a division, rounded half up

// only if you want to avoid BigInt prototype pollution
import { mulDivHalfUp } from "evm-maths/lib/utils";

// 1.0 (in wad) * 1 / 1 = 1.0 (in wad)
mulDivHalfUp(BigInt.WAD, 1, 1);
BigInt.WAD.mulDiv(1, 1);

mulDivUp

Performs a multiplication followed by a division, rounded up

// only if you want to avoid BigInt prototype pollution
import { mulDivUp } from "evm-maths/lib/utils";

// 0.999999999999999999 * 1 / WAD = 1.0 (in wad, rounded up)
mulDivUp(BigInt.WAD - 1n, 1, BigInt.WAD);
(BigInt.WAD - 1n).mulDivUp(1, BigInt.WAD);

mulDivDown

Performs a multiplication followed by a division, rounded down

// only if you want to avoid BigInt prototype pollution
import { mulDivDown } from "evm-maths/lib/utils";

// 1.000000000000000001 * 1 / WAD = 1.0 (in wad, rounded down)
mulDivDown(BigInt.WAD + 1n, 1, BigInt.WAD);
(BigInt.WAD + 1n).mulDivDown(1, BigInt.WAD);

---

Scale constants

WAD

Returns the common WAD unit, which is also known as ether in Solidity

Most commonly used as the ERC20 token unit

// only if you want to avoid BigInt prototype pollution
import { WAD } from "evm-maths/lib/constants";

// Returns a 1 followed by 18 zeros: 1000000000000000000
WAD;
BigInt.WAD;

RAY

Returns the common RAY unit, which is also known as 1e9 ether in Solidity

Most commonly used as Aave's index unit

// only if you want to avoid BigInt prototype pollution
import { RAY } from "evm-maths/lib/constants";

// Returns a 1 followed by 27 zeros: 1000000000000000000000000000
RAY;
BigInt.RAY;

PERCENT

Returns the common PERCENT unit, which is also known as 100% in basis points

Most commonly used as Aave's PERCENTAGE_FACTOR

// only if you want to avoid BigInt prototype pollution
import { PERCENT } from "evm-maths/lib/constants";

// Returns a 1 followed by 4 zeros: 10000
PERCENT;
BigInt.PERCENT;

HALF_WAD

Returns half of the common WAD unit, which is also known as 0.5 ether in Solidity

// only if you want to avoid BigInt prototype pollution
import { HALF_WAD } from "evm-maths/lib/constants";

// Returns a 1 followed by 18 zeros: 1000000000000000000
HALF_WAD;
BigInt.HALF_WAD;

HALF_RAY

Returns half of the common RAY unit, which is also known as 0.5e9 ether in Solidity

// only if you want to avoid BigInt prototype pollution
import { HALF_RAY } from "evm-maths/lib/constants";

// Returns a 1 followed by 27 zeros: 1000000000000000000000000000
HALF_RAY;
BigInt.HALF_RAY;

HALF_PERCENT

Returns the common PERCENT unit, which is also known as 50% in basis points

Most commonly used as Aave's HALF_PERCENTAGE_FACTOR

// only if you want to avoid BigInt prototype pollution
import { HALF_PERCENT } from "evm-maths/lib/constants";

// Returns a 1 followed by 4 zeros: 10000
HALF_PERCENT;
BigInt.HALF_PERCENT;

---

Wad-based utilities

wadMul

Returns the result of the wad-based multiplication (18 decimals precision), rounded half up

BigInt.WAD.wadMul(BigInt.WAD); // 1.0 * 1.0 = 1.0 (in wad)

wadDiv

Returns the result of the wad-based division (18 decimals precision), rounded half up

BigInt.WAD.wadDiv(BigInt.WAD); // 1.0 / 1.0 = 1.0 (in wad)

wadAdd

Returns the result of the addition of a BigNumberish and a wad-based percentage of it (18 decimals), rounded half up

BigInt.WAD.wadAdd(
  BigInt.HALF_WAD, // 50% in wad
); // 1.0 * (1.0 + 0.5) = 1.5 (in wad)

wadSub

Returns the result of the subtraction of a BigNumberish and a wad-based percentage of it (18 decimals), rounded half up

BigInt.WAD.wadSub(
  BigInt.HALF_WAD, // 50% in wad
); // 1.0 * (1.0 - 0.5) = 0.5 (in wad)

wadAvg

Returns the weighted average of 2 BigNumberishs, using a wad-based weight (18 decimals), rounded half up

BigInt.WAD.wadAvg(
  BigInt.WAD * 2n, // 2 WAD
  BigInt.HALF_WAD, // 50% in WAD
); // 1.0 * (1.0 - 0.5) + 2.0 * 0.5 = 1.5 (in wad)

wadPow

Returns the integer power of a BigInt, calculated using wad-based multiplications (18 decimals precision), rounded half up

BigInt.WAD *
  2n // 2 WAD
    .wadPow(2n); // 2.0 ** 2 = 4.0 (in wad)

wadPowUp

Returns the integer power of a BigInt, calculated using wad-based multiplications (4 decimals precision), rounded up

BigInt.PERCENT *
  2n // 200% in wad
    .wadPowUp(2n); // 2.0 ** 2 = 4.0 (in wad)

wadPowDown

Returns the integer power of a BigInt, calculated using wad-based multiplications (18 decimals precision), rounded down

BigInt.PERCENT *
  2n // 200% in wad
    .wadPowDown(2n); // 2.0 ** 2 = 4.0 (in wad)

wadExpTaylorN

Returns the N-th order Taylor polynomial approximation of the integer exp of a BigInt, calculated using wad-based multiplications (18 decimals precision), rounded down

BigInt.PERCENT.wadExpTaylorN(3n); // ~exp(1.0) ~= exp (in wad), using third-order Taylor polynomial

wadMulUp

Returns the result of the wad-based multiplication (18 decimals precision), rounded up

(BigInt.WAD - 1n).wadMulUp(BigInt.WAD - 1n); // 0.999999999999999999 * 0.999999999999999999 = 0.999999999999999999 (in wad, rounded up)

wadMulDown

Returns the result of the wad-based multiplication (18 decimals precision), rounded down

(BigInt.WAD - 1n).wadMulDown(BigInt.WAD - 1n); // 0.999999999999999999 * 0.999999999999999999 = 0.999999999999999998 (in wad, rounded down)

wadDivUp

Returns the result of the wad-based division (18 decimals precision), rounded up

BigInt.WAD.wadDivUp(BigInt.WAD - 1n); // 1.0 * 0.999999999999999999 = 1.000000000000000002 (in wad, rounded up)

wadDivDown

Returns the result of the wad-based division (18 decimals precision), rounded down

BigInt.WAD.wadDivDown(BigInt.WAD - 1n); // 1.0 * 0.999999999999999999 = 1.000000000000000001 (in wad, rounded down)

formatWad

Returns a string representation of the BigInt's value, formatted to 18 decimals and with the input number of digits expected after the unit, truncating the trailing digits if any (default: keep all digits after the decimal point)

BigInt.WAD.formatWad(3); // 1.000

toWadFloat

Returns a float representation of the BigInt's value, parsed as a wad-based number.

Note: parsing a too large value may result in parsing NaN (because the BigInt's value may still be too large to fit in a JS floating-point number)

BigInt.WAD.toWadFloat(); // 1.0

wadToPercent

Scales the wad-based BigInt down to the percent scale (losing 14 decimals)

BigInt.WAD.wadToPercent(); // 1 PERCENT

wadToRay

Scales the wad-based BigInt up to the ray scale (adding 9 decimals)

BigInt.WAD.wadToRay(); // 1 RAY

wadToDecimals

Scales the wad-based BigInt up or down to the given scale defined by its number of decimals

BigInt.WAD.wadToDecimals(27); // 1 RAY

---

Ray-based utilities

rayMul

Returns the result of the ray-based multiplication (27 decimals precision), rounded half up

BigInt.RAY.rayMul(BigInt.RAY); // 1.0 * 1.0 = 1.0 (in ray)

rayDiv

Returns the result of the ray-based division (27 decimals precision), rounded half up

BigInt.RAY.rayDiv(BigInt.RAY); // 1.0 / 1.0 = 1.0 (in ray)

rayAdd

Returns the result of the addition of a BigNumberish and a ray-based percentage of it (27 decimals), rounded half up

BigInt.RAY.rayAdd(
  BigInt.HALF_RAY, // 50% in ray
); // 1.0 * (1.0 + 0.5) = 1.5 (in ray)

raySub

Returns the result of the subtraction of a BigNumberish and a ray-based percentage of it (27 decimals), rounded half up

BigInt.RAY.raySub(
  BigInt.HALF_RAY, // 50% in ray
); // 1.0 * (1.0 - 0.5) = 0.5 (in ray)

rayAvg

Returns the weighted average of 2 BigNumberishs, using a ray-based weight (27 decimals), rounded half up

BigInt.RAY.rayAvg(
  BigInt.RAY * 2n, // 2 RAY
  BigInt.HALF_RAY, // 50% in RAY
); // 1.0 * (1.0 - 0.5) + 2.0 * 0.5 = 1.5 (in ray)

rayPow

Returns the integer power of a BigInt, calculated using ray-based multiplications (27 decimals precision), rounded half up

(BigInt.RAY * 2n) // 2 RAY
  .rayPow(2n); // 2.0 ** 2 = 4.0 (in ray)

rayPowUp

Returns the integer power of a BigInt, calculated using ray-based multiplications (4 decimals precision), rounded up

BigInt.PERCENT *
  2n // 200% in ray
    .rayPowUp(2n); // 2.0 ** 2 = 4.0 (in ray)

rayPowDown

Returns the integer power of a BigInt, calculated using ray-based multiplications (27 decimals precision), rounded down

BigInt.PERCENT *
  2n // 200% in ray
    .rayPowDown(2n); // 2.0 ** 2 = 4.0 (in ray)

rayExpTaylorN

Returns the N-th order Taylor polynomial approximation of the integer exp of a BigInt, calculated using ray-based multiplications (27 decimals precision), rounded down

BigInt.PERCENT.rayExpTaylorN(3n); // ~exp(1.0) ~= exp (in ray), using third-order Taylor polynomial

rayMulUp

Returns the result of the ray-based multiplication (27 decimals precision), rounded up

(BigInt.RAY - 1n).rayMulUp(BigInt.RAY - 1n); // 0.999999999999999999999999999 * 0.999999999999999999999999999 = 0.999999999999999999999999999 (in ray, rounded up)

rayMulDown

Returns the result of the ray-based multiplication (27 decimals precision), rounded down

(BigInt.RAY - 1n).rayMulDown(BigInt.RAY - 1n); // 0.999999999999999999999999999 * 0.999999999999999999999999999 = 0.999999999999999999999999998 (in ray, rounded down)

rayDivUp

Returns the result of the ray-based division (27 decimals precision), rounded up

BigInt.RAY.rayDivUp(BigInt.RAY - 1n); // 1.0 * 0.999999999999999999999999999 = 1.000000000000000000000000002 (in ray, rounded up)

rayDivDown

Returns the result of the ray-based division (27 decimals precision), rounded down

BigInt.RAY.rayDivDown(BigInt.RAY - 1n); // 1.0 * 0.999999999999999999999999999 = 1.000000000000000000000000001 (in ray, rounded down)

formatRay

Returns a string representation of the BigInt's value, formatted to 27 decimals and with the input number of digits expected after the unit, truncating the trailing digits if any (default: keep all digits after the decimal point)

BigInt.RAY.formatRay(3); // 1.000

toRayFloat

Returns a float representation of the BigInt's value, parsed as a ray-based number.

Note: parsing a too large value may result in parsing NaN (because the BigInt's value may still be too large to fit in a JS floating-point number)

BigInt.RAY.toRayFloat(); // 1.0

rayToPercent

Scales the ray-based BigInt down to the percent scale (losing 23 decimals)

BigInt.RAY.rayToPercent(); // 1 PERCENT

rayToWad

Scales the ray-based BigInt down to the wad scale (losing 9 decimals)

BigInt.RAY.rayToWad(); // 1 WAD

rayToDecimals

Scales the ray-based BigInt up or down to the given scale defined by its number of decimals

BigInt.RAY.rayToDecimals(18); // 1 WAD

---

Percent-based utilities

percentMul

Returns the result of the percent-based multiplication (4 decimals precision), rounded half up

BigInt.PERCENT.percentMul(BigInt.PERCENT); // 1.0 * 1.0 = 1.0 (in percent)

percentDiv

Returns the result of the percent-based division (4 decimals precision), rounded half up

BigInt.PERCENT.percentDiv(BigInt.PERCENT); // 1.0 / 1.0 = 1.0 (in percent)

percentAdd

Returns the result of the addition of a BigNumberish and a percent-based percentage of it (4 decimals), rounded half up

BigInt.PERCENT.percentAdd(
  BigInt.HALF_PERCENT, // 50% in percent
); // 1.0 * (1.0 + 0.5) = 1.5 (in percent)

percentSub

Returns the result of the subtraction of a BigNumberish and a percent-based percentage of it (4 decimals), rounded half up

BigInt.PERCENT.percentSub(
  BigInt.HALF_PERCENT, // 50% in percent
); // 1.0 * (1.0 - 0.5) = 0.5 (in percent)

percentAvg

Returns the weighted average of 2 BigNumberishs, using a percent-based weight (4 decimals), rounded half up

BigInt.PERCENT.percentAvg(
  BigInt.PERCENT * 2n, // 200% in percent
  BigInt.HALF_PERCENT, // 50% in percent
); // 1.0 * (1.0 - 0.5) + 2.0 * 0.5 = 1.5 (in percent)

percentPow

Returns the integer power of a BigInt, calculated using percent-based multiplications (4 decimals precision), rounded half up

BigInt.PERCENT *
  2n // 200% in percent
    .percentPow(2n); // 2.0 ** 2 = 4.0 (in percent)

percentPowUp

Returns the integer power of a BigInt, calculated using percent-based multiplications (4 decimals precision), rounded up

BigInt.PERCENT *
  2n // 200% in percent
    .percentPowUp(2n); // 2.0 ** 2 = 4.0 (in percent)

percentPowDown

Returns the integer power of a BigInt, calculated using percent-based multiplications (4 decimals precision), rounded down

BigInt.PERCENT *
  2n // 200% in percent
    .percentPowDown(2n); // 2.0 ** 2 = 4.0 (in percent)

percentExpTaylorN

Returns the N-th order Taylor polynomial approximation of the integer exp of a BigInt, calculated using percent-based multiplications (4 decimals precision), rounded down

BigInt.PERCENT.percentExpTaylorN(3n); // ~exp(1.0) ~= exp (in percent), using third-order Taylor polynomial

percentMulUp

Returns the result of the percent-based multiplication (4 decimals precision), rounded up

(BigInt.PERCENT - 1n).percentMulUp(BigInt.PERCENT - 1n); // 0.9999 * 0.9999 = 0.9999 (in percent, rounded up)

percentMulDown

Returns the result of the percent-based multiplication (4 decimals precision), rounded down

(BigInt.PERCENT - 1n).percentMulDown(BigInt.PERCENT - 1n); // 0.9999 * 0.9999 = 0.9998 (in percent, rounded down)

percentDivUp

Returns the result of the percent-based division (4 decimals precision), rounded up

BigInt.PERCENT.percentDivUp(BigInt.PERCENT - 1n); // 1.0 * 0.9999 = 1.0002 (in percent, rounded up)

percentDivDown

Returns the result of the percent-based division (4 decimals precision), rounded down

BigInt.PERCENT.percentDivDown(BigInt.PERCENT - 1n); // 1.0 * 0.9999 = 1.0001 (in percent, rounded down)

formatPercent

Returns a string representation of the BigInt's value, formatted to 4 decimals and with the input number of digits expected after the unit, truncating the trailing digits if any (default: keep all digits after the decimal point)

BigInt.PERCENT.formatPercent(3); // 1.000

toPercentFloat

Returns a float representation of the BigInt's value, parsed as a percent-based number.

Note: parsing a too large value may result in parsing NaN (because the BigInt's value may still be too large to fit in a JS floating-point number)

BigInt.PERCENT.toPercentFloat(); // 1.0

percentToWad

Scales the percent-based BigInt up to the wad scale (adding 14 decimals)

BigInt.PERCENT.percentToWad(); // 1 WAD

percentToRay

Scales the percent-based BigInt up to the ray scale (adding 23 decimals)

BigInt.PERCENT.percentToRay(); // 1 RAY

percentToDecimals

Scales the percent-based BigInt up or down to the given scale defined by its number of decimals

BigInt.RAY.percentToDecimals(27); // 1 RAY