generate_gaussian
Produce a random number based on a Gaussian (normal) distribution between 0 and 1 using MCP Rand's utility for statistical modeling or simulation needs.
Instructions
Generate a random number following a Gaussian (normal) distribution between 0 and 1
Input Schema
TableJSON Schema
| Name | Required | Description | Default |
|---|---|---|---|
No arguments | |||
Implementation Reference
- The main handler function for the 'generate_gaussian' tool. It calls the internal generateGaussian() helper and returns the result as MCP tool content (text).
export const generateGaussianHandler = async ( _request: CallToolRequest ): Promise<CallToolResult> => { const gaussian = generateGaussian(); return { content: [ { type: 'text', text: gaussian.toString() } ] }; }; - Tool schema/specification defining name, description, and empty input schema for no parameters.
export const toolSpec = { name: 'generate_gaussian', description: 'Generate a random number following a Gaussian (normal) distribution between 0 and 1', inputSchema: { type: 'object' as const, properties: {} } }; - src/index.ts:21-21 (registration)Registers the generateGaussianHandler under the 'tools/call' method for the tool name 'generate_gaussian' in the MCP server.
registry.register('tools/call', 'generate_gaussian', generateGaussianHandler as Handler); - Core helper implementing Box-Muller transform with error function to generate Gaussian random number normalized to [0,1].
function generateGaussian(): number { let u1 = 0; let u2 = 0; // Avoid u1 being zero do { u1 = Math.random(); u2 = Math.random(); } while (u1 <= Number.EPSILON); const z0 = Math.sqrt(-2.0 * Math.log(u1)) * Math.cos(2.0 * Math.PI * u2); // Convert from standard normal distribution (mean 0, std dev 1) // to a value between 0 and 1 using the error function (erf) // We add 1 and divide by 2 to shift from [-1,1] to [0,1] const normalized = (erf(z0 / Math.SQRT2) + 1) / 2; // Clamp to [0,1] in case of floating point errors return Math.max(0, Math.min(1, normalized)); } - Approximation of the error function (erf) used in generateGaussian for normalizing the distribution.
// Abramowitz and Stegun approximation (maximum error: 1.5×10−7) function erf(x: number): number { const sign = Math.sign(x); x = Math.abs(x); const p = 0.3275911; const a1 = 0.254829592; const a2 = -0.284496736; const a3 = 1.421413741; const a4 = -1.453152027; const a5 = 1.061405429; const t = 1.0 / (1.0 + p * x); const poly = t * (a1 + t * (a2 + t * (a3 + t * (a4 + t * a5)))); return sign * (1 - poly * Math.exp(-x * x)); }