# Welcome

DeFiMath is a high-performance, open-source Solidity library designed for Ethereum smart contracts. It provides optimized, gas-efficient implementations of core DeFi primitives and mathematical utilities—built with precision and performance in mind.

### Why DefiMath?

* **DeFi primitives**: core building blocks tailored for advanced financial protocols like options, futures, and other derivatives.
* **Gas optimized**: carefully engineered for minimal gas usage without compromising precision.
* **High-precision math**: accurate fixed-point and integer operations essential for financial calculations.

### Get Started

Check out our [GitHub Repository](https://github.com/MerkleBlue/defimath) to explore the code and contribute.

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### What's inside?

DeFiMath implements advanced math and derivatives functions in Solidity. The following tables provide overview of derivatives and math functions you can use:

<table><thead><tr><th width="93.18359375">Function</th><th width="379.453125">Description</th><th>Gas</th><th>Avg relative error</th></tr></thead><tbody><tr><td>call</td><td>European call option pricing</td><td>3203</td><td>5.6e-12</td></tr><tr><td>put</td><td>European put option pricing</td><td>3229</td><td>5.4e-12</td></tr><tr><td>delta</td><td>Call and put option price sensitivity to underlying change</td><td>2033</td><td>6.9e-15</td></tr><tr><td>gamma</td><td>Option price sensitivity to delta change</td><td>1707</td><td>9.1e-17</td></tr><tr><td>theta</td><td>Option price sensitivity to time change</td><td>3823</td><td>3.7e-14</td></tr><tr><td>vega</td><td>Call and put option price sensitivity to volatility change</td><td>1680</td><td>4.8e-14</td></tr><tr><td></td><td></td><td></td><td></td></tr></tbody></table>

<table><thead><tr><th width="93.44921875">Function</th><th width="379.453125">Description</th><th>Gas</th><th>Avg relative error</th></tr></thead><tbody><tr><td>exp</td><td>Exponential function</td><td>359</td><td>5.1e-12</td></tr><tr><td>ln</td><td>Natural logarithm</td><td>608</td><td>1.5e-12</td></tr><tr><td>log2</td><td>Logarithm with base 2</td><td>681</td><td>1.5e-12</td></tr><tr><td>log10</td><td>Logarithm with base 10</td><td>681</td><td>1.4e-12</td></tr><tr><td>sqrt</td><td>Square root function</td><td>383</td><td>2.8e-14</td></tr><tr><td>cdf</td><td>Standard normal cumulative distribution function</td><td>799</td><td>4.6e-13</td></tr><tr><td>erf</td><td>Error function</td><td>773</td><td>7.4e-13</td></tr></tbody></table>