// SPDX-License-Identifier: MIT
// Generated by EML-lang Solidity backend
// Source module: catenary
// Source file:   /home/monogate/monogate/forge/examples/catenary.eml
// Functions:     1 (1 @verify-annotated)
// Constants:     2
// Transcendental stubs: cosh -- override in a derived contract (see PRBMath SD59x18)
// WARNING: 1 fractional Real literal(s) were rounded to int256 (e.g. 0.6108 -> 1).
// For fixed-point semantics, scale your EML constants
// by WAD (1e18) and override the transcendental stubs
// with PRBMath SD59x18 in a derived contract.

pragma solidity ^0.8.20;

contract Catenary {
    int256 constant H_MIN = 1;
    int256 constant H_MAX = 20;

    /// @notice Formal proof: catenary_within_envelope (MachLib). Compiled from EML-lang.
    /// @dev Pfaffian profile: chain_order=2, cost_class=p2-d5-w2-c0, drift_risk=MEDIUM.
    /// @dev Gas estimate: ~7,300 gas (PRBMath SD59x18 overrides assumed; run forge gas-bench for the canonical signal).
    /// @param scale scale (int256)
    /// @param curv curv (int256)
    /// @param x x (int256)
    /// @dev ensures: (result >= H_MIN)
    /// @dev ensures: (result <= H_MAX)
    function catenary(int256 scale, int256 curv, int256 x) external pure returns (int256) {
        require(((scale < 0 ? -scale : scale) <= 5), "catenary: refinement violated on scale: ((scale < 0 ? -scale : scale) <= 5)");
        require(((curv < 0 ? -curv : curv) <= 0 /* 0.5 rounded; see header re fixed-point */), "catenary: refinement violated on curv: ((curv < 0 ? -curv : curv) <= 0 /* 0.5 rounded; see header...");
        require(((x < 0 ? -x : x) <= 4), "catenary: refinement violated on x: ((x < 0 ? -x : x) <= 4)");
        int256 raw = (scale * _cosh((curv * x)));
        return _clamp(raw, H_MIN, H_MAX);
    }

    /// @dev clamp helper -- min(max(x, lo), hi).
    function _clamp(int256 x, int256 lo, int256 hi) internal pure returns (int256) {
        if (x < lo) return lo;
        if (x > hi) return hi;
        return x;
    }

    /// @dev cosh stub — override with a fixed-point implementation.
    function _cosh(int256 x) internal pure virtual returns (int256) {
        x; // silence unused-param warning
        revert("_cosh: stub — override in a derived contract (see PRBMath SD59x18.cosh)");
    }

}