Overview
In my recent work on the Theoretica project, I tackled an issue related to test coverage for bitwise operations. You can find my pull request here: #88  Add comprehensive test cases for bitwise operations in bit_op.h
. The project lacked thorough tests for the library, so my goal was to add detailed test cases to ensure these functions operate as expected.
The Issue
The issue focused on validating the bitwise operations in bit_op.h
. The file contains functions for multiplying two 64bit integers, bit mixing, bit rotation, and bitreverse swapping. The existing tests in the repository didn’t cover these, so there was a need for targeted tests to verify the accuracy and functionality of these operations.
Preparation and Setup
Setting up the environment for testing Theoretica was straightforward, as I only needed to clone the repository and configure the Chebyshev testing framework. Since the project already included setup instructions, it didn’t take long to get things running. However, I had to familiarize myself with the prec
module within Chebyshev, which manages test precision, error handling, and estimation options.
Learning and Research
Before I could start writing test cases, I had to understand the specific functions in bit_op.h
:

mul_uint128
: This function multiplies two 64bit integers and stores the result in two 64bit variables, providing a 128bit product. 
mix_mum
: A bitmixing function that computes a 128bit product and returns the XOR of its high and low bits. 
bit_rotate
: Rotates the bits of an unsigned integer by a specified number of positions. 
swap_bit_reverse
: Swaps elements in a vector based on bitreversed indices.
Additionally, I researched how std::function
is used in Chebyshev to manage various test configurations. I explored how the prec::estimate
and prec::equals
functions work, as they are the core of the testing framework in this project. prec::estimate
evaluates the accuracy of function approximations over intervals, while prec::equals
checks exact matches, which is particularly useful for bitwise operations.
Explanation of the Code
Here’s a breakdown of how each test works:

mul_uint128
Test:
uint64_t a = 0xFFFFFFFFFFFFFFFF;
uint64_t b = 0x2;
uint64_t c_low, c_high;
theoretica::mul_uint128(a, b, c_low, c_high);
prec::equals("th::mul_uint128 (c_low)", c_low, 0xFFFFFFFFFFFFFFFE);
prec::equals("th::mul_uint128 (c_high)", c_high, 0x1);
This test multiplies two max 64bit integers and checks if the results are split correctly across c_low
and c_high
.

mix_mum
Test:
uint64_t a = 0x12345678ABCDEF00;
uint64_t b = 0x0FEDCBA987654321;
uint64_t result = theoretica::mix_mum(a, b);
prec::equals("th::mix_mum nonzero result", result != 0, true);
The test ensures the mix_mum
function produces a nonzero result by checking if the XOR operation on the product’s high and low bits yields a valid outcome.

bit_rotate
Test:
uint64_t x = 0x12345678ABCDEF00;
unsigned int i = 8;
uint64_t rotated = theoretica::bit_rotate(x, i);
prec::equals("th::bit_rotate (64bit)", rotated, 0x345678ABCDEF0012);
This checks that bit_rotate
shifts bits correctly, returning the expected result after rotation.

swap_bit_reverse
Test:
std::vector<uint8_t> vec = {1, 2, 3, 4};
theoretica::swap_bit_reverse(vec, 2);
std::vector<uint8_t> expected = {1, 3, 2, 4};
prec::equals("th::swap_bit_reverse", vec == expected, true);
It validates that elements in a vector are correctly swapped based on bitreversed indices.
Challenges and Interactions
One challenge was ensuring I correctly understood the prec
module for this project. Specifically, I found it tricky to grasp how prec::estimate
works with continuous functions and whether it would apply to discrete bitwise operations. After some research and experimentation, I concluded that prec::equals
was better suited for these exact comparisons.
I reached out to the project maintainers for feedback on my approach. They confirmed that using prec::equals
for deterministic checks was the right path. Their guidance helped me confirm that I was on the right track before proceeding with further test cases.
Conclusion
This initial work focused on bitwise operations, but I plan to continue adding test cases for other functions within Theoretica. It was a valuable experience learning how to work within a large project’s testing framework, and I appreciated the maintainers' feedback. For anyone tackling similar issues, I recommend thoroughly understanding the testing framework before jumping into the code.
Pull Request: Add comprehensive test cases for bitwise operations in bit_op.h
By sharing my approach, code, and insights, I hope this post provides a helpful look into how I contributed to the Theoretica project and my future plans for testing enhancements.
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