kernel/include/linux/fixp-arith.h

/* SPDX-License-Identifier: GPL-2.0-or-later */
#ifndef _FIXP_ARITH_H
#define _FIXP_ARITH_H

#include <linux/math64.h>

/*
 * Simplistic fixed-point arithmetics.
 * Hmm, I'm probably duplicating some code :(
 *
 * Copyright (c) 2002 Johann Deneux
 */

/*
 *
 * Should you need to contact me, the author, you can do so by
 * e-mail - mail your message to <johann.deneux@gmail.com>
 */

#include <linux/types.h>

static const s32 sin_table[] = {
	0x00000000, 0x023be165, 0x04779632, 0x06b2f1d2, 0x08edc7b6, 0x0b27eb5c,
	0x0d61304d, 0x0f996a26, 0x11d06c96, 0x14060b67, 0x163a1a7d, 0x186c6ddd,
	0x1a9cd9ac, 0x1ccb3236, 0x1ef74bf2, 0x2120fb82, 0x234815ba, 0x256c6f9e,
	0x278dde6e, 0x29ac379f, 0x2bc750e8, 0x2ddf003f, 0x2ff31bdd, 0x32037a44,
	0x340ff241, 0x36185aee, 0x381c8bb5, 0x3a1c5c56, 0x3c17a4e7, 0x3e0e3ddb,
	0x3fffffff, 0x41ecc483, 0x43d464fa, 0x45b6bb5d, 0x4793a20f, 0x496af3e1,
	0x4b3c8c11, 0x4d084650, 0x4ecdfec6, 0x508d9210, 0x5246dd48, 0x53f9be04,
	0x55a6125a, 0x574bb8e5, 0x58ea90c2, 0x5a827999, 0x5c135399, 0x5d9cff82,
	0x5f1f5ea0, 0x609a52d1, 0x620dbe8a, 0x637984d3, 0x64dd894f, 0x6639b039,
	0x678dde6d, 0x68d9f963, 0x6a1de735, 0x6b598ea1, 0x6c8cd70a, 0x6db7a879,
	0x6ed9eba0, 0x6ff389de, 0x71046d3c, 0x720c8074, 0x730baeec, 0x7401e4bf,
	0x74ef0ebb, 0x75d31a5f, 0x76adf5e5, 0x777f903b, 0x7847d908, 0x7906c0af,
	0x79bc384c, 0x7a6831b8, 0x7b0a9f8c, 0x7ba3751c, 0x7c32a67c, 0x7cb82884,
	0x7d33f0c8, 0x7da5f5a3, 0x7e0e2e31, 0x7e6c924f, 0x7ec11aa3, 0x7f0bc095,
	0x7f4c7e52, 0x7f834ecf, 0x7fb02dc4, 0x7fd317b3, 0x7fec09e1, 0x7ffb025e,
	0x7fffffff
};

/**
 * __fixp_sin32() returns the sin of an angle in degrees
 *
 * @degrees: angle, in degrees, from 0 to 360.
 *
 * The returned value ranges from -0x7fffffff to +0x7fffffff.
 */
static inline s32 __fixp_sin32(int degrees)
{
	s32 ret;
	bool negative = false;

	if (degrees > 180) {
		negative = true;
		degrees -= 180;
	}
	if (degrees > 90)
		degrees = 180 - degrees;

	ret = sin_table[degrees];

	return negative ? -ret : ret;
}

/**
 * fixp_sin32() returns the sin of an angle in degrees
 *
 * @degrees: angle, in degrees. The angle can be positive or negative
 *
 * The returned value ranges from -0x7fffffff to +0x7fffffff.
 */
static inline s32 fixp_sin32(int degrees)
{
	degrees = (degrees % 360 + 360) % 360;

	return __fixp_sin32(degrees);
}

/* cos(x) = sin(x + 90 degrees) */
#define fixp_cos32(v) fixp_sin32((v) + 90)

/*
 * 16 bits variants
 *
 * The returned value ranges from -0x7fff to 0x7fff
 */

#define fixp_sin16(v) (fixp_sin32(v) >> 16)
#define fixp_cos16(v) (fixp_cos32(v) >> 16)

/**
 * fixp_sin32_rad() - calculates the sin of an angle in radians
 *
 * @radians: angle, in radians
 * @twopi: value to be used for 2*pi
 *
 * Provides a variant for the cases where just 360
 * values is not enough. This function uses linear
 * interpolation to a wider range of values given by
 * twopi var.
 *
 * Experimental tests gave a maximum difference of
 * 0.000038 between the value calculated by sin() and
 * the one produced by this function, when twopi is
 * equal to 360000. That seems to be enough precision
 * for practical purposes.
 *
 * Please notice that two high numbers for twopi could cause
 * overflows, so the routine will not allow values of twopi
 * bigger than 1^18.
 */
static inline s32 fixp_sin32_rad(u32 radians, u32 twopi)
{
	int degrees;
	s32 v1, v2, dx, dy;
	s64 tmp;

	/*
	 * Avoid too large values for twopi, as we don't want overflows.
	 */
	BUG_ON(twopi > 1 << 18);

	degrees = (radians * 360) / twopi;
	tmp = radians - (degrees * twopi) / 360;

	degrees = (degrees % 360 + 360) % 360;
	v1 = __fixp_sin32(degrees);

	v2 = fixp_sin32(degrees + 1);

	dx = twopi / 360;
	dy = v2 - v1;

	tmp *= dy;

	return v1 +  div_s64(tmp, dx);
}

/* cos(x) = sin(x + pi/2 radians) */

#define fixp_cos32_rad(rad, twopi)	\
	fixp_sin32_rad(rad + twopi / 4, twopi)

/**
 * fixp_linear_interpolate() - interpolates a value from two known points
 *
 * @x0: x value of point 0
 * @y0: y value of point 0
 * @x1: x value of point 1
 * @y1: y value of point 1
 * @x: the linear interpolant
 */
static inline int fixp_linear_interpolate(int x0, int y0, int x1, int y1, int x)
{
	if (y0 == y1 || x == x0)
		return y0;
	if (x1 == x0 || x == x1)
		return y1;

	return y0 + ((y1 - y0) * (x - x0) / (x1 - x0));
}

#endif