Refactor fixed-point data types to a single parameterized type

Co-authored-by: Gemini CLI <gemini-cli@google.com>

Author: mkitti

data-types/binary_fixed_point/README.md

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+# Binary Fixed-Point Data Type
+
+A parameterized data type for binary fixed-point numbers.
+
+**Status:** proposal
+
+## Data type name
+
+`binary_fixed_point`
+
+## Configuration
+
+This data type represents a binary fixed-point number based on an underlying integer type.
+It is defined by a base integer type, the number of fractional bits, and the number of integer bits.
+
+- **`base_data_type`**: The underlying integer data type. Must be one of `uint8`, `uint16`, `uint32`, `uint64`, `int8`, `int16`, `int32`, `int64`.
+- **`fractional_bits`**: The number of bits representing the fractional part.
+- **`integer_bits`**: The number of bits representing the integer part.
+
+## Interpretation
+
+The value is interpreted as:
+$$ v = i \times 2^{-f} $$
+where $i$ is the integer value stored in the `base_data_type` and $f$ is `fractional_bits`.
+
+- If `base_data_type` is signed, $i$ is a signed integer.
+- If `base_data_type` is unsigned, $i$ is an unsigned integer.
+
+## Q Notation
+
+Fixed-point numbers are commonly described using "Q notation", often written as `Qn.m`. To avoid ambiguity, we define the relationship between the `Qn.m` notation and this data type's parameters as follows:
+
+- **`n`** (the first number) corresponds to **`integer_bits`**.
+- **`m`** (the second number) corresponds to **`fractional_bits`**.
+
+### Relationship to Base Data Type
+
+The choice of `base_data_type` (bit width $W$) limits the possible values for `integer_bits` and `fractional_bits`.
+
+- **Signed Types (`int*`)**:
+  The underlying type must accommodate the sign bit, integer bits, and fractional bits.
+  $$ W \ge 1 + \text{integer\_bits} (n) + \text{fractional\_bits} (m) $$
+  *Example:* `Q1.14` (1 integer, 14 fractional) requires $1 + 1 + 14 = 16$ bits, fitting into `int16`.
+
+- **Unsigned Types (`uint*`)**:
+  The underlying type must accommodate the integer bits and fractional bits. Unsigned fixed-point is sometimes denoted as `UQn.m`.
+  $$ W \ge \text{integer\_bits} (n) + \text{fractional\_bits} (m) $$
+  *Example:* `UQ8.8` (8 integer, 8 fractional) requires $8 + 8 = 16$ bits, fitting into `uint16`.
+
+## Fill value representation
+
+The `fill_value` SHOULD be represented as a JSON number with the value to be represented.
+To represent the underlying integer bits exactly, the `fill_value` MAY be provided as a hexadecimal string representing the underlying integer (e.g., `"0x0000"`).
+
+## Examples
+
+| Configuration | Q Notation | Description | Range (approx) |
+|---|---|---|---|
+| `{"base_data_type": "int16", "fractional_bits": 15, "integer_bits": 0}` | Q0.15 | Signed 16-bit, 15 fractional bits | -1.0 to 0.99997 |
+| `{"base_data_type": "uint16", "fractional_bits": 8, "integer_bits": 8}` | UQ8.8 | Unsigned 16-bit, 8 fractional bits | 0.0 to 255.996 |
+| `{"base_data_type": "int32", "fractional_bits": 16, "integer_bits": 15}` | Q15.16 | Signed 32-bit, 16 fractional bits | -32768.0 to 32767.99998 |
+
+## See also
+
+- [FixedPointNumbers.jl](https://github.com/JuliaMath/FixedPointNumbers.jl) (Note: roughly corresponds to `Fixed{T, f}`)
+- [Rust `fixed` crate](https://crates.io/crates/fixed)
+
+## Current maintainers
+
+- Mark Kittisopikul (@mkitti), Howard Hughes Medical Institute

data-types/binary_fixed_point/schema.json

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+{
+  "$schema": "https://json-schema.org/draft/2020-12/schema",
+  "type": "object",
+  "properties": {
+    "name": {
+      "const": "binary_fixed_point"
+    },
+    "configuration": {
+      "type": "object",
+      "properties": {
+        "base_data_type": {
+          "enum": [
+            "uint8",
+            "uint16",
+            "uint32",
+            "uint64",
+            "int8",
+            "int16",
+            "int32",
+            "int64"
+          ]
+        },
+        "fractional_bits": {
+          "type": "integer",
+          "minimum": 0
+        },
+        "integer_bits": {
+          "type": "integer",
+          "minimum": 0
+        }
+      },
+      "required": [
+        "base_data_type",
+        "fractional_bits",
+        "integer_bits"
+      ],
+      "additionalProperties": false
+    }
+  },
+  "required": [
+    "name",
+    "configuration"
+  ],
+  "additionalProperties": false
+}