From f8d78938143807e006d0f8bf9b7069db1615a25e Mon Sep 17 00:00:00 2001
From: "Quentin Dauprat, PhD" <heziode@protonmail.com>
Date: Mon, 1 Dec 2025 12:09:31 +0100
Subject: [PATCH] spark_math 0.1.0 (via `alr publish`) (#1692)

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+name = "spark_math"
+description = "Formally verified mathematical library in SPARK"
+version = "0.1.0"
+
+authors = ["Heziode"]
+maintainers = ["Heziode <heziode@protonmail.com>"]
+maintainers-logins = ["heziode"]
+licenses = "Apache-2.0 WITH LLVM-exception"
+website = ""
+tags = ["spark", "verification", "math", "sqrt", "fixed-point"]
+
+long-description = """
+# Spark_Math
+
+[![License](https://img.shields.io/badge/license-Apache--2.0%20WITH%20LLVM--exception-blue.svg)](LICENSE)
+[![SPARK](https://img.shields.io/badge/SPARK-Gold-gold.svg)](https://www.adacore.com/about-spark)
+
+A formally verified mathematical library written in SPARK/Ada, providing common mathematical functions for both integer and fixed-point types with compile-time proof of correctness.
+
+## Features
+
+### Integer Math (`Spark_Math.Integer`)
+
+| Function | Description | Complexity |
+|----------|-------------|------------|
+| `Sqrt` | Integer square root (floor of sqrt N) | O(log N) |
+| `Power` | Exponentiation with overflow protection | O(Exp) |
+| `GCD` | Greatest common divisor (Euclidean algorithm) | O(log min(A,B)) |
+| `Max` | Maximum of two values | O(1) |
+| `Min` | Minimum of two values | O(1) |
+
+### Fixed-Point Math (`Spark_Math.Fixed`)
+
+| Function | Description | Complexity |
+|----------|-------------|------------|
+| `Sqrt` | Square root approximation (within `'Small`) | O(log(N/Small)) |
+| `Max` | Maximum of two values | O(1) |
+| `Min` | Minimum of two values | O(1) |
+
+## Roadmap
+
+The goal is to provide SPARK-verified equivalents of `Ada.Numerics.Generic_Elementary_Functions` for fixed-point and integer types.
+
+### Planned Functions
+
+| Category | Functions | Status |
+|----------|-----------|--------|
+| **Basic** | `Sqrt` | Implemented |
+| **Exponential** | `Log`, `Log(Base)`, `Exp`, `**` | Planned |
+| **Trigonometric** | `Sin`, `Cos`, `Tan`, `Cot` | Planned |
+| **Inverse Trig** | `Arcsin`, `Arccos`, `Arctan`, `Arccot` | Planned |
+| **Hyperbolic** | `Sinh`, `Cosh`, `Tanh`, `Coth` | Planned |
+| **Inverse Hyperbolic** | `Arcsinh`, `Arccosh`, `Arctanh`, `Arccoth` | Planned |
+
+### Implementation Notes
+
+Unlike floating-point implementations, fixed-point math requires:
+
+- **CORDIC algorithms** for trigonometric functions (no FPU dependency)
+- **Polynomial approximations** with bounded error analysis
+- **Range reduction** techniques proven correct in SPARK
+- **Cycle parameter support** for degree/radian flexibility
+
+Contributions for any of these functions are welcome!
+
+## Usage
+
+### Integer Math Example
+
+```ada
+with Spark_Math.Integer;
+
+procedure Example is
+   --  Instantiate for your integer type
+   package My_Math is new Spark_Math.Integer (Integer);
+   
+   Result : Integer;
+begin
+   --  Square root (floor)
+   Result := My_Math.Sqrt (17);      --  Returns 4
+   
+   --  Exponentiation
+   Result := My_Math.Power (2, 10);  --  Returns 1024
+   
+   --  Greatest common divisor
+   Result := My_Math.GCD (48, 18);   --  Returns 6
+   
+   --  Max and Min
+   Result := My_Math.Max (5, 3);     --  Returns 5
+   Result := My_Math.Min (5, 3);     --  Returns 3
+end Example;
+```
+
+### Fixed-Point Math Example
+
+```ada
+with Spark_Math.Fixed;
+
+procedure Example is
+   --  Define your fixed-point type
+   type Voltage is delta 0.001 range 0.0 .. 100.0;
+   
+   --  Instantiate for your type
+   package Voltage_Math is new Spark_Math.Fixed (Voltage);
+   
+   Result : Voltage;
+begin
+   --  Square root (approximation within 'Small)
+   Result := Voltage_Math.Sqrt (4.0);   --  Returns ~= 2.0
+   Result := Voltage_Math.Sqrt (2.0);   --  Returns ~= 1.414
+   
+   --  Max and Min
+   Result := Voltage_Math.Max (3.5, 2.1);  --  Returns 3.5
+   Result := Voltage_Math.Min (3.5, 2.1);  --  Returns 2.1
+end Example;
+```
+
+## SPARK Verification
+
+This library is designed for formal verification with SPARK. All functions include:
+
+- **Preconditions** (`Pre`): Specify valid input constraints
+- **Postconditions** (`Post`): Guarantee output properties
+- **Loop invariants**: Enable proof of loop correctness
+- **No runtime exceptions**: All potential issues are caught at proof time
+
+### Verification Status
+
+SPARK defines five proof levels:
+
+| Level | Description |
+|-------|-------------|
+| **Stone** | Valid SPARK code |
+| **Bronze** | Initialization and correct data flow |
+| **Silver** | Absence of run-time errors (AoRTE) |
+| **Gold** | Proof of key integrity properties |
+| **Platinum** | Full functional proof of requirements |
+
+| Package | Level |
+|---------|-------|
+| `Spark_Math.Numerics_Core` | Gold |
+| `Spark_Math.Integer` | Gold |
+| `Spark_Math.Fixed` | Gold |
+
+## Contributing
+
+Contributions are welcome!
+
+## License
+
+This project is licensed under the Apache-2.0 WITH LLVM-exception license. See [LICENSE](LICENSE) for details.
+
+"""
+[origin]
+commit = "8939f758a129b2dc44094de32e373f2243b9c6f7"
+url = "git+https://github.com/adarium-labs/spark_math.git"
+