lib: add generic polynomial calculation

Some temperature and voltage sensors use a polynomial to convert between
raw data points and actual temperature or voltage. The polynomial is
usually the result of a curve fitting of the diode characteristic.

The BT1 PVT hwmon driver already uses such a polynonmial calculation
which is rather generic. Move it to lib/ so other drivers can reuse it.

Signed-off-by: Michael Walle <[e-mail]>
Reviewed-by: Guenter Roeck <[e-mail]>
Link: https://lore.kernel.org/r/[e-mail]
Signed-off-by: Guenter Roeck <[e-mail]>

include/linux/polynomial.h

···
+/* SPDX-License-Identifier: GPL-2.0-only */
+/*
+ * Copyright (C) 2020 BAIKAL ELECTRONICS, JSC
+ */
+
+#ifndef _POLYNOMIAL_H
+#define _POLYNOMIAL_H
+
+/*
+ * struct polynomial_term - one term descriptor of a polynomial
+ * @deg: degree of the term.
+ * @coef: multiplication factor of the term.
+ * @divider: distributed divider per each degree.
+ * @divider_leftover: divider leftover, which couldn't be redistributed.
+ */
+struct polynomial_term {
+	unsigned int deg;
+	long coef;
+	long divider;
+	long divider_leftover;
+};
+
+/*
+ * struct polynomial - a polynomial descriptor
+ * @total_divider: total data divider.
+ * @terms: polynomial terms, last term must have degree of 0
+ */
+struct polynomial {
+	long total_divider;
+	struct polynomial_term terms[];
+};
+
+long polynomial_calc(const struct polynomial *poly, long data);
+
+#endif

lib/Kconfig

···
 
 config ASN1_ENCODER
        tristate
+
+config POLYNOMIAL
+       tristate

lib/Makefile

···
 obj-$(CONFIG_STMP_DEVICE) += stmp_device.o
 obj-$(CONFIG_IRQ_POLL) += irq_poll.o
 
+obj-$(CONFIG_POLYNOMIAL) += polynomial.o
+
 # stackdepot.c should not be instrumented or call instrumented functions.
 # Prevent the compiler from calling builtins like memcmp() or bcmp() from this
 # file.

lib/polynomial.c

···
+// SPDX-License-Identifier: GPL-2.0-only
+/*
+ * Generic polynomial calculation using integer coefficients.
+ *
+ * Copyright (C) 2020 BAIKAL ELECTRONICS, JSC
+ *
+ * Authors:
+ *   Maxim Kaurkin <[e-mail]>
+ *   Serge Semin <[e-mail]>
+ *
+ */
+
+#include <linux/kernel.h>
+#include <linux/module.h>
+#include <linux/polynomial.h>
+
+/*
+ * Originally this was part of drivers/hwmon/bt1-pvt.c.
+ * There the following conversion is used and should serve as an example here:
+ *
+ * The original translation formulae of the temperature (in degrees of Celsius)
+ * to PVT data and vice-versa are following:
+ *
+ * N = 1.8322e-8*(T^4) + 2.343e-5*(T^3) + 8.7018e-3*(T^2) + 3.9269*(T^1) +
+ *     1.7204e2
+ * T = -1.6743e-11*(N^4) + 8.1542e-8*(N^3) + -1.8201e-4*(N^2) +
+ *     3.1020e-1*(N^1) - 4.838e1
+ *
+ * where T = [-48.380, 147.438]C and N = [0, 1023].
+ *
+ * They must be accordingly altered to be suitable for the integer arithmetics.
+ * The technique is called 'factor redistribution', which just makes sure the
+ * multiplications and divisions are made so to have a result of the operations
+ * within the integer numbers limit. In addition we need to translate the
+ * formulae to accept millidegrees of Celsius. Here what they look like after
+ * the alterations:
+ *
+ * N = (18322e-20*(T^4) + 2343e-13*(T^3) + 87018e-9*(T^2) + 39269e-3*T +
+ *     17204e2) / 1e4
+ * T = -16743e-12*(D^4) + 81542e-9*(D^3) - 182010e-6*(D^2) + 310200e-3*D -
+ *     48380
+ * where T = [-48380, 147438] mC and N = [0, 1023].
+ *
+ * static const struct polynomial poly_temp_to_N = {
+ *         .total_divider = 10000,
+ *         .terms = {
+ *                 {4, 18322, 10000, 10000},
+ *                 {3, 2343, 10000, 10},
+ *                 {2, 87018, 10000, 10},
+ *                 {1, 39269, 1000, 1},
+ *                 {0, 1720400, 1, 1}
+ *         }
+ * };
+ *
+ * static const struct polynomial poly_N_to_temp = {
+ *         .total_divider = 1,
+ *         .terms = {
+ *                 {4, -16743, 1000, 1},
+ *                 {3, 81542, 1000, 1},
+ *                 {2, -182010, 1000, 1},
+ *                 {1, 310200, 1000, 1},
+ *                 {0, -48380, 1, 1}
+ *         }
+ * };
+ */
+
+/**
+ * polynomial_calc - calculate a polynomial using integer arithmetic
+ *
+ * @poly: pointer to the descriptor of the polynomial
+ * @data: input value of the polynimal
+ *
+ * Calculate the result of a polynomial using only integer arithmetic. For
+ * this to work without too much loss of precision the coefficients has to
+ * be altered. This is called factor redistribution.
+ *
+ * Returns the result of the polynomial calculation.
+ */
+long polynomial_calc(const struct polynomial *poly, long data)
+{
+	const struct polynomial_term *term = poly->terms;
+	long total_divider = poly->total_divider ?: 1;
+	long tmp, ret = 0;
+	int deg;
+
+	/*
+	 * Here is the polynomial calculation function, which performs the
+	 * redistributed terms calculations. It's pretty straightforward.
+	 * We walk over each degree term up to the free one, and perform
+	 * the redistributed multiplication of the term coefficient, its
+	 * divider (as for the rationale fraction representation), data
+	 * power and the rational fraction divider leftover. Then all of
+	 * this is collected in a total sum variable, which value is
+	 * normalized by the total divider before being returned.
+	 */
+	do {
+		tmp = term->coef;
+		for (deg = 0; deg < term->deg; ++deg)
+			tmp = mult_frac(tmp, data, term->divider);
+		ret += tmp / term->divider_leftover;
+	} while ((term++)->deg);
+
+	return ret / total_divider;
+}
+EXPORT_SYMBOL_GPL(polynomial_calc);
+
+MODULE_DESCRIPTION("Generic polynomial calculations");
+MODULE_LICENSE("GPL");