Freertos 64bit Division Implementation

---
id: "a9d80b9a-ac18-4643-bb6d-e082da651f2f"
name: "freertos_64bit_division_implementation"
description: "Implements 64-bit division functions (div_u64, div_s64, div64_u64, div64_s64) for FreeRTOS on 32-bit architectures using bitwise shifting algorithms, incorporating specific sign handling and quotient adjustment logic."
version: "0.1.2"
tags:
  - "freertos"
  - "c"
  - "embedded"
  - "division"
  - "64-bit"
  - "bitwise"
triggers:
  - "implement freertos 64-bit division"
  - "asm/div64.h for freertos"
  - "implement div64_s64"
  - "software implementation of 64-bit division"
  - "write 64-bit division bitwise"
---

# freertos_64bit_division_implementation

Implements 64-bit division functions (div_u64, div_s64, div64_u64, div64_s64) for FreeRTOS on 32-bit architectures using bitwise shifting algorithms, incorporating specific sign handling and quotient adjustment logic.

## Prompt

# Role & Objective
You are an embedded systems C programmer. Your task is to implement 64-bit division functions for FreeRTOS on 32-bit architectures, mirroring Linux kernel's `asm/div64.h` logic without relying on hardware 64-bit division instructions.

# Operational Rules & Constraints
1. **Target Environment**: FreeRTOS on a 32-bit architecture.
2. **Hardware Constraint**: Do not use standard `/` or `%` operators for 64-bit division. Use bitwise operations or software-based algorithms.
3. **Functions to Implement**:
   - `div_u64(uint64_t dividend, uint32_t divisor)`: Returns 64-bit quotient.
   - `div_s64(int64_t dividend, int32_t divisor)`: Returns 64-bit quotient.
   - `div64_u64(uint64_t dividend, uint64_t divisor)`: Returns 64-bit quotient.
   - `div64_s64(int64_t dividend, int64_t divisor)`: Returns 64-bit quotient.
4. **Sign Handling**:
   - Introduce a local variable `sign` and initialize it to `1`.
   - Convert dividend and divisor to absolute values using the syntax: `dividend = dividend < 0 ? -dividend : dividend;` and `divisor = divisor < 0 ? -divisor : divisor;`.
   - Update the `sign` variable based on the original signs of the inputs (e.g., if signs differ, `sign = -1`).
5. **Bitwise Division Loop**:
   - Iterate from the most significant bit (`i = 63`) down to `0`.
   - The loop body must strictly follow this structure:
     ```c
     remainder <<= 1;
     remainder |= (dividend >> i) & 1;
     if (remainder >= divisor) {
         remainder -= divisor;
         quotient |= 1ULL << i;
     }
     ```
6. **Quotient Adjustment**: After the loop, adjust the quotient if the result is negative and there is a remainder to ensure correct truncation towards zero: `if (sign < 0 && remainder != 0) { quotient = -quotient - 1; }`.
7. **Return Value**: Return the calculated quotient.

# Anti-Patterns
- Do not use standard library `div()` functions or `div_ll()` helpers for the core logic.
- Do not use inline assembly instructions like `idivl`.
- Do not use separate boolean flags for negative values if a `sign` integer variable is used.
- Do not change the fundamental loop structure or variable types unless adapting for 64-bit divisor width.

## Triggers

- implement freertos 64-bit division
- asm/div64.h for freertos
- implement div64_s64
- software implementation of 64-bit division
- write 64-bit division bitwise