➗ Useful bigint math libraries to ease the journey through off-chain fixed-point arithmetics
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> ➗ Useful bigint math libraries to ease your journey through off-chain fixed-point arithmetics
``bash`
npm install evm-maths
`bash`
yarn add evm-maths
---
Just import the module and you'll benefit from an augmented, and typed, BigInt class!
`typescript
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:
`typescript`
import * as WadMath from "evm-maths/lib/wad";
import * as RayMath from "evm-maths/lib/ray";
import * as PercentMath from "evm-maths/lib/percent";
---
- 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
---
#### approxEqAbs
Returns whether the BigNumber is approximately close to the given BigNumber, within the given tolerance
`typescript
// 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
`typescript
// 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
`typescript
// 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
`typescript
// 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)
`typescript`
// 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)
`typescript`
// 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)
`typescript
// 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
`typescript
// 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
`typescript
// 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
`typescript
// 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);
`
---
#### WAD
Returns the common WAD unit, which is also known as ether in Solidity
_Most commonly used as the ERC20 token unit_
`typescript
// 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_
`typescript
// 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_
`typescript
// 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
`typescript
// 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
`typescript
// 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_
`typescript
// 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;
`
---
#### wadMul
Returns the result of the wad-based multiplication (18 decimals precision), rounded half up
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
(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
`typescript`
(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
`typescript`
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
`typescript`
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)
`typescript`
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)
`typescript`
BigInt.WAD.toWadFloat(); // 1.0
#### wadToPercent
Scales the wad-based BigInt down to the percent scale (losing 14 decimals)
`typescript`
BigInt.WAD.wadToPercent(); // 1 PERCENT
#### wadToRay
Scales the wad-based BigInt up to the ray scale (adding 9 decimals)
`typescript`
BigInt.WAD.wadToRay(); // 1 RAY
#### wadToDecimals
Scales the wad-based BigInt up or down to the given scale defined by its number of decimals
`typescript`
BigInt.WAD.wadToDecimals(27); // 1 RAY
---
#### rayMul
Returns the result of the ray-based multiplication (27 decimals precision), rounded half up
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
(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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
(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
`typescript`
(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
`typescript`
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
`typescript`
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)
`typescript`
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)
`typescript`
BigInt.RAY.toRayFloat(); // 1.0
#### rayToPercent
Scales the ray-based BigInt down to the percent scale (losing 23 decimals)
`typescript`
BigInt.RAY.rayToPercent(); // 1 PERCENT
#### rayToWad
Scales the ray-based BigInt down to the wad scale (losing 9 decimals)
`typescript`
BigInt.RAY.rayToWad(); // 1 WAD
#### rayToDecimals
Scales the ray-based BigInt up or down to the given scale defined by its number of decimals
`typescript`
BigInt.RAY.rayToDecimals(18); // 1 WAD
---
#### percentMul
Returns the result of the percent-based multiplication (4 decimals precision), rounded half up
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
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
`typescript`
(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
`typescript`
(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
`typescript`
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
`typescript`
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)
`typescript`
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)
`typescript`
BigInt.PERCENT.toPercentFloat(); // 1.0
#### percentToWad
Scales the percent-based BigInt up to the wad scale (adding 14 decimals)
`typescript`
BigInt.PERCENT.percentToWad(); // 1 WAD
#### percentToRay
Scales the percent-based BigInt up to the ray scale (adding 23 decimals)
`typescript`
BigInt.PERCENT.percentToRay(); // 1 RAY
#### percentToDecimals
Scales the percent-based BigInt up or down to the given scale defined by its number of decimals
`typescript``
BigInt.RAY.percentToDecimals(27); // 1 RAY
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