add gamma module

src/groovylight/gamma.py

@@ -0,0 +1,52 @@
+# Gamma correction by adjusting the display OE/Expose timings.
+
+
+# Most gamma correction is done on the values being displayed.
+# i.e gammacorrect (RGB) -> RGB (adjusted). However this adds
+# a complex look-up step which adds complexity and cycles.
+# There is a simpler solution which uses some properties of the
+# gamma function as well as the fact that we are manually doing
+# color depth using BCM/PWM.
+#
+# Consider the default BCM timing layout:
+# MSB  MSB-1  MSB-2  MSB-3
+# P*8    P*4    P*2   P
+# that is, we have a baseline display, measured in clocks/us/whatever
+# and then the next most significant bit is displayed for twice that,
+# four times that, and so on.
+# But, we can adjust the individual bit timings to adjust the brightness
+# curve as we see fit. This has numerous advantages:
+# 1. It's free, we don't have to do any math on the board, just adjusting
+#    an existing process.
+# 2. We can go more granular that n-bits of color. This means that the gamma
+#    curve will be effective and accurate regardless of the color depth.
+#
+# This file contains code to generate these timing adjustments and 
+# control/quantify them.
+
+from math import pow
+
+
+
+def _gammavec(vals: [float], g: float) -> [float]:
+    return [pow(x,g) for x in vals]
+
+def _nbit_scale(f, nbits:int) -> [float]:
+    """Computes the equivalent linear value for each bit of n_bits.
+    That is, the list contains scalar values that are doubling as they progress,
+    [ x, 2x, 4x ] such that the sum(list) = 7x = f
+    """
+    base = float(f) / (pow(2.0, nbits) - 1.0)
+    return [base * pow(2.0, x) for x in range(nbits)]
+
+
+def gamma_timings(gamma:float = 2.2, nbits:int = 8, max_clocks: int = 4096):
+    """Computes the clock cycle timings for a given gamma correction.
+    """
+    linear_values = _nbit_scale(1.0, nbits)
+    gamma_values = _gammavec(linear_values, gamma)
+
+    bclk_ratio = max_clocks / gamma_values[-1]
+    result = [round(bclk_ratio * x) for x in gamma_values]
+    return result
+