Groovy & JSR223 Scripting

Generate Groovy scripts for the following JSR223 use cases in JMeter:

1. PreProcessor: Generate HMAC-SHA256 signature for request signing
   - Inputs: request body (${requestBody}), secret key (${apiSecret})
   - Output: JMeter variable ${signature}

2. PostProcessor: Parse nested JSON and extract a list of IDs into separate variables
   - Input: Response body with array $.items[*].id
   - Output: ${itemId_1}, ${itemId_2}, ... ${itemId_N} and ${itemId_count}

3. PreProcessor: Log request details to a custom file per test run
   - Include: timestamp, thread name, sampler label, iteration count

Include error handling and use JMeter API (vars, props, log) correctly.

I need to make a secondary HTTP call inside a JSR223 Groovy script (not as a separate JMeter sampler) to:
- GET [URL] to fetch a lookup value
- Store the result in a JMeter variable ${lookupValue}

Generate the Groovy script using:
1. JMeter's built-in HTTP client (org.apache.http)
2. Java's HttpURLConnection
3. Groovy's built-in HTTP support

Show all three approaches and recommend the best one for JMeter performance.