gpio: Add support for binary_first base3 number system

This patch adds support for an alternative ternary number system in
which group of GPIOs can be interpreted. In this system, the digit
combinations that would form a binary number (i.e. that contain no 'Z'
state) are used to represent the lower values in the way they're used in
the normal binary system, and all the combinations that do contain a 'Z'
are used to represent values above those. We can use this for boards
that originally get strapped with binary board IDs but eventually
require more revisions than that representation allows. We can switch
their code to binary_first base3 and all old revisions with already
produced boards will still get read as the correct numbers.

Credit for the algorithm idea goes to Haran Talmon.

BRANCH=None
BUG=None
TEST=Stubbed out the actual GPIO reading and simulated all combinations
of 4 ternary digits for both number systems.

Change-Id: Ib5127656455f97f890ce2999ba5ac5f58a20cf93
Signed-off-by: Julius Werner <jwerner@chromium.org>
Reviewed-on: https://review.coreboot.org/14116
Tested-by: build bot (Jenkins)
Reviewed-by: David Hendricks <dhendrix@chromium.org>
Reviewed-by: Aaron Durbin <adurbin@chromium.org>

src/include/gpio.h

@@ -29,6 +29,7 @@ void gpio_input_pulldown(gpio_t gpio);
 void gpio_input_pullup(gpio_t gpio);
 void gpio_input(gpio_t gpio);
 void gpio_output(gpio_t gpio, int value);
+int _gpio_base3_value(gpio_t gpio[], int num_gpio, int binary_first);
 
 /*
  * Read the value presented by the set of GPIOs, when each pin is interpreted
@@ -48,6 +49,39 @@ int gpio_base2_value(gpio_t gpio[], int num_gpio);
  * gpio[]: pin positions to read. gpio[0] is less significant than gpio[1].
  * num_gpio: number of pins to read.
  */
-int gpio_base3_value(gpio_t gpio[], int num_gpio);
+static inline int gpio_base3_value(gpio_t gpio[], int num_gpio)
+{
+	return _gpio_base3_value(gpio, num_gpio, 0);
+}
+
+/*
+ * Read the value presented by the set of GPIOs, when each pin is interpreted
+ * as a base-3 digit (LOW = 0, HIGH = 1, Z/floating = 2) in a non-standard
+ * ternary number system where the first 2^n natural numbers are represented
+ * as they would be in a binary system (without any Z digits), and the following
+ * 3^n-2^n numbers use the remaining ternary representations in the normal
+ * ternary system order (skipping the values that were already used up).
+ * This is useful for boards which initially used a binary board ID and later
+ * decided to switch to tri-state after some revisions have already been built.
+ * Example: For num_gpio = 2 we get the following representation:
+ *
+ *   Number      X1     X0
+ *     0          0      0
+ *     1          0      1
+ *     2          1      0
+ *     3          1      1	// Start counting ternaries back at 0 after this
+ *     4          0      2	// Skipping 00 and 01 which are already used up
+ *     5          1      2	// Skipping 10 and 11 which are already used up
+ *     6          2      0
+ *     7          2      1
+ *     8          2      2
+ *
+ * gpio[]: pin positions to read. gpio[0] is less significant than gpio[1].
+ * num_gpio: number of pins to read.
+ */
+static inline int gpio_binary_first_base3_value(gpio_t gpio[], int num_gpio)
+{
+	return _gpio_base3_value(gpio, num_gpio, 1);
+}
 
 #endif /* __SRC_INCLUDE_GPIO_H__ */

src/lib/gpio.c

@@ -35,7 +35,7 @@ int gpio_base2_value(gpio_t gpio[], int num_gpio)
 	return result;
 }
 
-int gpio_base3_value(gpio_t gpio[], int num_gpio)
+int _gpio_base3_value(gpio_t gpio[], int num_gpio, int binary_first)
 {
 	/*
 	 * GPIOs which are tied to stronger external pull up or pull down
@@ -50,6 +50,8 @@ int gpio_base3_value(gpio_t gpio[], int num_gpio)
 	int temp;
 	int index;
 	int result = 0;
+	int has_z = 0;
+	int binary_below = 0;
 	char value[32];
 	assert(num_gpio <= 32);
 
@@ -85,8 +87,51 @@ int gpio_base3_value(gpio_t gpio[], int num_gpio)
 		temp |= ((value[index] ^ temp) << 1);
 		printk(BIOS_DEBUG, "%c ", tristate_char[temp]);
 		result = (result * 3) + temp;
+
+		/*
+		 * For binary_first we keep track of the normal ternary result
+		 * and whether we found any pin that was a Z. We also determine
+		 * the amount of numbers that can be represented with only
+		 * binary digits (no Z) whose value in the normal ternary system
+		 * is lower than the one we are parsing. Counting from the left,
+		 * we add 2^i for any '1' digit to account for the binary
+		 * numbers whose values would be below it if all following
+		 * digits we parsed would be '0'. As soon as we find a '2' digit
+		 * we can total the remaining binary numbers below as 2^(i+1)
+		 * because we know that all binary representations counting only
+		 * this and following digits must have values below our number
+		 * (since 1xxx is always smaller than 2xxx).
+		 *
+		 * Example: 1 0 2 1 (counting from the left / most significant)
+		 * '1' at 3^3: Add 2^3 = 8 to account for binaries 0000-0111
+		 * '0' at 3^2: Ignore (not all binaries 1000-1100 are below us)
+		 * '2' at 3^1: Add 2^(1+1) = 4 to account for binaries 1000-1011
+		 * Stop adding for lower digits (3^0), all already accounted
+		 * now. We know that there can be no binary numbers 1020-102X.
+		 */
+		if (binary_first && !has_z) {
+			switch(temp) {
+			case 0:	/* Ignore '0' digits. */
+				break;
+			case 1:	/* Account for binaries 0 to 2^index - 1. */
+				binary_below += 1 << index;
+				break;
+			case 2:	/* Account for binaries 0 to 2^(index+1) - 1. */
+				binary_below += 1 << (index + 1);
+				has_z = 1;
 			}
-	printk(BIOS_DEBUG, "= %d\n", result);
+		}
+	}
+
+	if (binary_first) {
+		if (has_z)
+			result = result + (1 << num_gpio) - binary_below;
+		else /* binary_below is normal binary system value if !has_z. */
+			result = binary_below;
+	}
+
+	printk(BIOS_DEBUG, "= %d (%s base3 number system)\n", result,
+	       binary_first ? "binary_first" : "standard");
 
 	/* Disable pull up / pull down to conserve power */
 	for (index = 0; index < num_gpio; ++index)