math: interpolation: linear interpolation

Add linear interpolation function that respects floating point rounding
rules (away from zero).

Signed-off-by: Jordan Yates <jordan@embeint.com>

include/zephyr/math/interpolation.h

@@ -0,0 +1,75 @@
+/*
+ * Copyright (c) 2024 Embeint Inc
+ *
+ * SPDX-License-Identifier: Apache-2.0
+ */
+
+#ifndef ZEPHYR_INCLUDE_ZEPHYR_MATH_INTERPOLATION_H_
+#define ZEPHYR_INCLUDE_ZEPHYR_MATH_INTERPOLATION_H_
+
+#include <stdint.h>
+#include <math.h>
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/**
+ * @file
+ * @brief Provide linear interpolation functions
+ */
+
+/**
+ * @brief Perform a linear interpolation across an arbitrary curve
+ *
+ * @note Result rounding occurs away from 0, e.g:
+ *       1.5 -> 2, -5.5 -> -6
+ *
+ * @param x_axis Ascending list of X co-ordinates for @a y_axis data points
+ * @param y_axis Y co-ordinates for each X data point
+ * @param len Length of the @a x_axis and @a y_axis arrays
+ * @param x X co-ordinate to lookup
+ *
+ * @retval y_axis[0] if x < x_axis[0]
+ * @retval y_axis[len - 1] if x > x_axis[len - 1]
+ * @retval int32_t Linear interpolation between the two nearest @a y_axis values.
+ */
+static inline int32_t linear_interpolate(const int32_t *x_axis, const int32_t *y_axis, uint8_t len,
+					 int32_t x)
+{
+	float rise, run, slope;
+	int32_t x_shifted;
+	uint8_t idx_low = 0;
+
+	/* Handle out of bounds values */
+	if (x <= x_axis[0]) {
+		return y_axis[0];
+	} else if (x >= x_axis[len - 1]) {
+		return y_axis[len - 1];
+	}
+
+	/* Find the lower x axis bucket */
+	while (x >= x_axis[idx_low + 1]) {
+		idx_low++;
+	}
+
+	/* Shift input to origin */
+	x_shifted = x - x_axis[idx_low];
+	if (x_shifted == 0) {
+		return y_axis[idx_low];
+	}
+
+	/* Local slope */
+	rise = y_axis[idx_low + 1] - y_axis[idx_low];
+	run = x_axis[idx_low + 1] - x_axis[idx_low];
+	slope = rise / run;
+
+	/* Apply slope, undo origin shift and round */
+	return roundf(y_axis[idx_low] + (slope * x_shifted));
+}
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* ZEPHYR_INCLUDE_ZEPHYR_MATH_INTERPOLATION_H_ */