Update README

Author: youknowone

README.md

@@ -1,30 +1,150 @@
 pymath
 ======
 
-A binary representation compatible Rust implementation of Python's math library.
+**0 ULP (bit-exact) compatibility with CPython's math and cmath modules.**
+
+Every function produces identical results to Python at the binary representation level - not just "close enough", but exactly the same bits.
 
 ## Overview
 
-`pymath` is a line-by-line port of the CPython math library to Rust. This library aims to provide mathematical functions that produce identical results to Python's standard math library at the bit level.
+`pymath` is a strict port of CPython's math library to Rust. Each function has been carefully translated from CPython's C implementation, preserving the same algorithms, constants, and corner case handling.
 
-## Implementation
+## Implemented Functions
 
-Each function has been carefully translated from CPython's C implementation to Rust, preserving the same algorithms, constants, and corner case handling. The code maintains the same numerical properties, but in Rust!
+### math
 
-## Module Structure
+- [x] `ceil`
+- [x] `copysign`
+- [x] `fabs`
+- [x] `floor`
+- [x] `fmod`
+- [x] `frexp`
+- [x] `isclose`
+- [x] `isfinite`
+- [x] `isinf`
+- [x] `isnan`
+- [x] `ldexp`
+- [x] `modf`
+- [x] `nextafter`
+- [x] `remainder`
+- [x] `trunc`
+- [x] `ulp`
+- [x] `cbrt`
+- [x] `exp`
+- [x] `exp2`
+- [x] `expm1`
+- [x] `log`
+- [x] `log10`
+- [x] `log1p`
+- [x] `log2`
+- [x] `pow`
+- [x] `sqrt`
+- [x] `acos`
+- [x] `acosh`
+- [x] `asin`
+- [x] `asinh`
+- [x] `atan`
+- [x] `atan2`
+- [x] `atanh`
+- [x] `cos`
+- [x] `cosh`
+- [x] `sin`
+- [x] `sinh`
+- [x] `tan`
+- [x] `tanh`
+- [x] `erf`
+- [x] `erfc`
+- [x] `gamma`
+- [x] `lgamma`
+- [x] `dist`
+- [x] `fsum`
+- [x] `hypot`
+- [x] `prod`
+- [x] `sumprod`
+- [x] `degrees`
+- [x] `radians`
+- [x] `pi`
+- [x] `e`
+- [x] `tau`
+- [x] `inf`
+- [x] `nan`
 
-- `pymath::math` - Real number math functions (Python's `math` module)
-- `pymath::cmath` - Complex number functions (Python's `cmath` module, requires `complex` feature)
-- `pymath::m` - Direct libm bindings
+### math.integer (requires `num-bigint` or `malachite-bigint` feature)
+
+- [x] `comb`
+- [x] `factorial`
+- [x] `gcd`
+- [x] `isqrt`
+- [x] `lcm`
+- [x] `perm`
+
+### cmath (requires `complex` feature)
+
+- [x] `abs`
+- [x] `isclose`
+- [x] `isfinite`
+- [x] `isinf`
+- [x] `isnan`
+- [x] `phase`
+- [x] `polar`
+- [x] `rect`
+- [x] `exp`
+- [x] `log`
+- [x] `log10`
+- [x] `sqrt`
+- [x] `acos`
+- [x] `acosh`
+- [x] `asin`
+- [x] `asinh`
+- [x] `atan`
+- [x] `atanh`
+- [x] `cos`
+- [x] `cosh`
+- [x] `sin`
+- [x] `sinh`
+- [x] `tan`
+- [x] `tanh`
 
 ## Usage
 
 ```rust
-use pymath::math::{gamma, lgamma};
+use pymath::math::{sqrt, gamma, lgamma};
 
 fn main() {
-    // Get the same results as Python's math.gamma and math.lgamma
+    let sqrt_result = sqrt(2.0).unwrap();
     let gamma_result = gamma(4.5).unwrap();
     let lgamma_result = lgamma(4.5).unwrap();
 }
 ```
+
+### Bit-exact verification
+
+```python
+# Python 3.14
+>>> import math
+>>> math.gamma(0.5).hex()
+'0x1.c5bf891b4ef6ap+0'
+```
+
+```rust
+// Rust - identical bits
+assert_eq!(
+    pymath::math::gamma(0.5).unwrap().to_bits(),
+    0x3ffc5bf891b4ef6a
+);
+```
+
+*Bit representation may vary across platforms, but CPython and pymath built on the same environment will always produce identical results.*
+
+## Features
+
+- `complex` (default) - Enable cmath module for complex number functions
+- `num-bigint` - Enable integer functions using num-bigint
+- `malachite-bigint` - Enable integer functions using malachite-bigint
+- `mul_add` - Use hardware FMA for bit-exact macOS compatibility
+
+## Module Structure
+
+- `pymath::math` - Real number math functions (Python's `math` module)
+- `pymath::cmath` - Complex number functions (Python's `cmath` module)
+- `pymath::m` - Direct libm bindings