code-paul-creator · Nov 11, 2026
diff --git a/conversions/cmyk_to_rgb.py b/conversions/cmyk_to_rgb.py
@@ -0,0 +1,102 @@
+"""
+Convert a CMYK colour (percentages) back to RGB (0..255).
+
+This is the inverse of ``rgb_cmyk_conversion.rgb_to_cmyk``. CMYK values are
+percentages of paint, so each channel is in the range 0..100:
+
+    R = 255 * (1 - C/100) * (1 - K/100)
+    G = 255 * (1 - M/100) * (1 - K/100)
+    B = 255 * (1 - Y/100) * (1 - K/100)
+
+``rgb_to_cmyk`` rounds to whole percentages, so the conversion is lossy and a
+round trip rgb -> cmyk -> rgb can differ from the original by a few units per
+channel. Like the forward algorithm, this is the simple linear formula and not a
+colour-managed (ICC profile) conversion.
+
+Reference: https://www.rapidtables.com/convert/color/cmyk-to-rgb.html
+"""
+
+
+def cmyk_to_rgb(
+    c_input: int, m_input: int, y_input: int, k_input: int
+) -> tuple[int, int, int]:
+    """
+    Simple CMYK to RGB conversion. Takes percentages (0..100) of CMYK paint and
+    returns the RGB channels as integers in 0..255.
+
+    >>> cmyk_to_rgb(0, 0, 0, 0)  # white
+    (255, 255, 255)
+    >>> cmyk_to_rgb(0, 0, 0, 100)  # black
+    (0, 0, 0)
+    >>> cmyk_to_rgb(0, 0, 0, 50)  # gray
+    (128, 128, 128)
+    >>> cmyk_to_rgb(0, 100, 100, 0)  # red
+    (255, 0, 0)
+    >>> cmyk_to_rgb(100, 0, 100, 0)  # green
+    (0, 255, 0)
+    >>> cmyk_to_rgb(100, 100, 0, 0)  # blue
+    (0, 0, 255)
+
+    Floats are accepted as long as they are in range:
+
+    >>> cmyk_to_rgb(0.0, 50.0, 100.0, 0.0)
+    (255, 128, 0)
+
+    The inverse of rgb_to_cmyk, within rounding (+-1 per channel for these colours):
+
+    >>> from conversions.rgb_cmyk_conversion import rgb_to_cmyk
+    >>> cmyk_to_rgb(*rgb_to_cmyk(255, 0, 0))
+    (255, 0, 0)
+    >>> cmyk_to_rgb(*rgb_to_cmyk(0, 255, 0))
+    (0, 255, 0)
+    >>> cmyk_to_rgb(*rgb_to_cmyk(255, 255, 255))
+    (255, 255, 255)
+    >>> cmyk_to_rgb(*rgb_to_cmyk(0, 0, 0))
+    (0, 0, 0)
+    >>> cmyk_to_rgb(*rgb_to_cmyk(128, 128, 128))
+    (128, 128, 128)
+    >>> all(
+    ...     abs(a - b) <= 1
+    ...     for rgb in [(255, 0, 0), (0, 255, 0), (0, 0, 255), (128, 128, 128)]
+    ...     for a, b in zip(rgb, cmyk_to_rgb(*rgb_to_cmyk(*rgb)))
+    ... )
+    True
+
+    Invalid input raises ValueError:
+
+    >>> cmyk_to_rgb(0, 0, 0, "a")
+    Traceback (most recent call last):
+        ...
+    ValueError: Expected int or float, found (<class 'int'>, <class 'int'>, \
+<class 'int'>, <class 'str'>)
+    >>> cmyk_to_rgb(0, 0, 0, 101)
+    Traceback (most recent call last):
+        ...
+    ValueError: Expected a value in the range 0..100
+    >>> cmyk_to_rgb(-1, 0, 0, 0)
+    Traceback (most recent call last):
+        ...
+    ValueError: Expected a value in the range 0..100
+    """
+    inputs = (c_input, m_input, y_input, k_input)
+    if not all(isinstance(x, (int, float)) and not isinstance(x, bool) for x in inputs):
+        msg = f"Expected int or float, found {tuple(type(x) for x in inputs)}"
+        raise ValueError(msg)
+
+    if not all(0 <= x <= 100 for x in inputs):
+        raise ValueError("Expected a value in the range 0..100")
+
+    # changing range from 0..100 to 0..1
+    c, m, y, k = (x / 100 for x in inputs)
+
+    r = round(255 * (1 - c) * (1 - k))
+    g = round(255 * (1 - m) * (1 - k))
+    b = round(255 * (1 - y) * (1 - k))
+
+    return r, g, b
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()
diff --git a/work/R23-T052/VARIANT.md b/work/R23-T052/VARIANT.md
@@ -0,0 +1,50 @@
+# R23-T052: conversions/cmyk_to_rgb.py
+
+## What it does
+`cmyk_to_rgb(c, m, y, k)` is the inverse of `rgb_cmyk_conversion.rgb_to_cmyk`.
+Inputs are percentages of paint (0..100); output is `(r, g, b)` in 0..255:
+
+    R = 255 * (1 - C/100) * (1 - K/100)   (same for G with M, B with Y)
+
+It raises `ValueError` for non-numeric input or values outside 0..100.
+
+## How it differs from rgb_to_cmyk (time / space)
+| | rgb_to_cmyk | cmyk_to_rgb |
+|---|---|---|
+| Time | O(1) | O(1) |
+| Space | O(1) | O(1) |
+| Measured (20,000 random colours, avg per call) | ~0.70 us | ~1.87 us |
+
+Both are constant time and constant space. `cmyk_to_rgb` is slower per call
+only because of its generic validation (`all(isinstance(...))` and
+`all(0 <= x <= 100)` over a 4-tuple); the arithmetic itself is just 3 multiplications
+and 3 roundings. Timings are from one run on a cloud machine, so treat them as
+rough.
+
+## Why the round trip is not exact (rounding)
+`rgb_to_cmyk` rounds C, M, Y and K to **whole percentages**. That throws away
+information: 256 levels per RGB channel are squeezed into 101 levels per CMYK
+channel. Converting back cannot recover the lost detail, so rgb -> cmyk -> rgb
+can be off by a few units.
+
+Each CMYK value can be off by up to 0.5 percent, and R depends on two of them
+(C and K), so the worst case error is about 2 per channel. Measured over a
+grid of every 5th value per channel (140,608 colours):
+
+| max error per channel | colours |
+|---|---|
+| 0 | 27,214 |
+| 1 | 106,608 |
+| 2 | 6,786 |
+
+(A larger sample of every 3rd value, 636,056 colours, also had a maximum error
+of 2.) So "within +-1 per channel" holds for most colours and for the colours
+used in the doctests (red, green, blue, white, black and mid-gray), but not for
+every possible colour. The doctest checks the cases that do hold; this file
+documents the limit.
+
+## Checks run
+- `python3 scripts/validate_filenames.py` -> passed
+- `ruff check conversions/cmyk_to_rgb.py` -> all checks passed
+- `ruff format --check conversions/cmyk_to_rgb.py` -> already formatted
+- `python -m pytest --doctest-modules conversions/cmyk_to_rgb.py conversions/rgb_cmyk_conversion.py` -> passed