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//! Branch Prediction Hints
//!
//! > *"Praedicere est praevidere."*
//! > — To predict is to foresee.
//!
//! This module provides branch prediction hints for performance-critical code paths.
//!
//! # Implementation
//!
//! With the `nightly` cargo feature enabled (requires a nightly toolchain),
//! these functions delegate to [`core::hint::likely`]/[`core::hint::unlikely`],
//! which map directly to LLVM's `@llvm.expect` intrinsics for optimal codegen.
//! Per hashbrown benchmarks, this provides 10-15% improvement in hot paths.
//! On stable Rust (the default) they are identity functions — semantics are
//! identical either way; only codegen quality changes.
//!
//! # Usage
//!
//! ```rust
//! use ordofp_core::hints::{likely, unlikely};
//!
//! # fn fast_path() {}
//! # fn slow_path() {}
//! # fn handle_error() {}
//! # let condition = true;
//! # let error_condition = false;
//! if likely(condition) {
//! // Hot path - compiler will optimize for this case
//! fast_path();
//! } else {
//! // Cold path
//! slow_path();
//! }
//!
//! if unlikely(error_condition) {
//! // Error handling - compiler knows this is rare
//! handle_error();
//! }
//! ```
//!
//! # Latin Etymology
//!
//! *Verisimilis* = likely (from *verus* "true" + *similis* "similar")
//! *Improbabilis* = unlikely (from *in-* "not" + *probabilis* "probable")
/// Hint that a condition is likely to be true.
///
/// Use this in `if` conditions when the true branch is the hot path.
/// Uses the stabilized `core::hint::likely` for optimal LLVM codegen.
///
/// # Example
///
/// ```rust
/// use ordofp_core::hints::likely;
///
/// # fn process(_x: i32) {}
/// # fn handle_negative(_x: i32) {}
/// # let x = 10;
/// if likely(x > 0) {
/// // This is the common case
/// process(x);
/// } else {
/// // This rarely happens
/// handle_negative(x);
/// }
/// ```
pub const
/// Hint that a condition is unlikely to be true.
///
/// Use this in `if` conditions when the true branch is the cold path
/// (error handling, edge cases, etc.).
/// Uses the stabilized `core::hint::unlikely` for optimal LLVM codegen.
///
/// # Example
///
/// ```rust
/// use ordofp_core::hints::unlikely;
///
/// fn handle_error(result: Result<i32, String>) -> String {
/// result.unwrap_err()
/// }
///
/// fn process(result: Result<i32, String>) -> Result<(), String> {
/// if unlikely(result.is_err()) {
/// // Error handling - this rarely happens
/// return Err(handle_error(result));
/// }
/// // Happy path continues
/// Ok(())
/// }
///
/// assert!(process(Ok(1)).is_ok());
/// assert!(process(Err("oops".to_string())).is_err());
/// ```
pub const
/// Hint that a condition is extremely likely (>99% probability).
///
/// Stronger hint than `likely` - use sparingly for truly invariant conditions.
pub const
/// Hint that a condition represents an error that should never happen.
///
/// This is semantically equivalent to `unlikely` but documents intent better.
pub const
/// Mark a function as cold (rarely called).
///
/// This is a helper for documenting cold paths. Functions marked `#[cold]`
/// will be optimized for size rather than speed and placed in cold code sections.
///
/// Usage:
/// ```rust
/// use ordofp_core::cold_path;
///
/// #[cold]
/// fn handle_rare_error() {
/// // Cold path: optimized for size, placed out of line by the compiler.
/// }
///
/// let result = cold_path!({
/// handle_rare_error();
/// 42
/// });
/// assert_eq!(result, 42);
/// ```
///
/// This macro doesn't change behavior but serves as documentation.
/// The actual `#[cold]` attribute should be applied to the function.
/// Execute code on the hot path (likely to be executed).
///
/// This is semantically a no-op but documents the hot path and ensures
/// the code is inlined aggressively.
// =============================================================================
// Wide Arithmetic Helpers
// =============================================================================
// Const-stable multi-precision building blocks; each lowers to the same
// add-with-carry / widening-multiply codegen as the corresponding intrinsic.
/// Add two u64 values with carry propagation.
///
/// Returns (low, carry) representing the full-width sum `a + b + carry_in`.
///
/// # Example
///
/// ```rust
/// use ordofp_core::hints::wide_add_u64;
///
/// let (low, carry) = wide_add_u64(u64::MAX, 1, false);
/// assert_eq!(low, 0);
/// assert!(carry);
/// ```
pub const
/// Multiply two u64 values producing a 128-bit result.
///
/// Implemented via `u128` multiplication (which lowers to the same
/// mulx/umulh codegen as the nightly `widening_mul` intrinsic).
/// Returns (low, high) representing the full 128-bit product.
///
/// # Example
///
/// ```rust
/// use ordofp_core::hints::wide_mul_u64;
///
/// let (low, high) = wide_mul_u64(u64::MAX, 2);
/// // u64::MAX * 2 = 2^65 - 2 = (high: 1, low: u64::MAX - 1)
/// assert_eq!(high, 1);
/// assert_eq!(low, u64::MAX - 1);
/// ```
pub const
/// Multiply-accumulate for multi-precision arithmetic.
///
/// Computes `a * b + c` with full precision (no overflow).
/// Implemented via `u128` accumulation (equivalent codegen to the nightly
/// `carrying_mul` intrinsic, without depending on its signature).
///
/// # Example
///
/// ```rust
/// use ordofp_core::hints::wide_mul_add_u64;
///
/// // u64::MAX * u64::MAX + u64::MAX = u64::MAX * (u64::MAX + 1) = u64::MAX << 64
/// let (low, high) = wide_mul_add_u64(u64::MAX, u64::MAX, u64::MAX);
/// assert_eq!(low, 0);
/// assert_eq!(high, u64::MAX);
/// ```
pub const
/// Strict addition that panics on overflow (release mode safe).
///
/// Panics on overflow regardless of build profile. Use this when overflow
/// is a logic error.
///
/// # Panics
///
/// Panics if `a + b` would overflow.
pub const
/// Strict multiplication that panics on overflow (release mode safe).
///
/// Panics on overflow regardless of build profile. Use this when overflow
/// is a logic error.
///
/// # Panics
///
/// Panics if `a * b` would overflow.
pub const