fixp-arith.h

  1/* SPDX-License-Identifier: GPL-2.0-or-later */
  2#ifndef _FIXP_ARITH_H
  3#define _FIXP_ARITH_H
  4
  5#include <linux/bug.h>
  6#include <linux/math64.h>
  7
  8/*
  9 * Simplistic fixed-point arithmetics.
 10 * Hmm, I'm probably duplicating some code :(
 11 *
 12 * Copyright (c) 2002 Johann Deneux
 13 */
 14
 15/*
 16 *
 17 * Should you need to contact me, the author, you can do so by
 18 * e-mail - mail your message to <johann.deneux@gmail.com>
 19 */
 20
 21#include <linux/types.h>
 22
 23static const s32 sin_table[] = {
 24	0x00000000, 0x023be165, 0x04779632, 0x06b2f1d2, 0x08edc7b6, 0x0b27eb5c,
 25	0x0d61304d, 0x0f996a26, 0x11d06c96, 0x14060b67, 0x163a1a7d, 0x186c6ddd,
 26	0x1a9cd9ac, 0x1ccb3236, 0x1ef74bf2, 0x2120fb82, 0x234815ba, 0x256c6f9e,
 27	0x278dde6e, 0x29ac379f, 0x2bc750e8, 0x2ddf003f, 0x2ff31bdd, 0x32037a44,
 28	0x340ff241, 0x36185aee, 0x381c8bb5, 0x3a1c5c56, 0x3c17a4e7, 0x3e0e3ddb,
 29	0x3fffffff, 0x41ecc483, 0x43d464fa, 0x45b6bb5d, 0x4793a20f, 0x496af3e1,
 30	0x4b3c8c11, 0x4d084650, 0x4ecdfec6, 0x508d9210, 0x5246dd48, 0x53f9be04,
 31	0x55a6125a, 0x574bb8e5, 0x58ea90c2, 0x5a827999, 0x5c135399, 0x5d9cff82,
 32	0x5f1f5ea0, 0x609a52d1, 0x620dbe8a, 0x637984d3, 0x64dd894f, 0x6639b039,
 33	0x678dde6d, 0x68d9f963, 0x6a1de735, 0x6b598ea1, 0x6c8cd70a, 0x6db7a879,
 34	0x6ed9eba0, 0x6ff389de, 0x71046d3c, 0x720c8074, 0x730baeec, 0x7401e4bf,
 35	0x74ef0ebb, 0x75d31a5f, 0x76adf5e5, 0x777f903b, 0x7847d908, 0x7906c0af,
 36	0x79bc384c, 0x7a6831b8, 0x7b0a9f8c, 0x7ba3751c, 0x7c32a67c, 0x7cb82884,
 37	0x7d33f0c8, 0x7da5f5a3, 0x7e0e2e31, 0x7e6c924f, 0x7ec11aa3, 0x7f0bc095,
 38	0x7f4c7e52, 0x7f834ecf, 0x7fb02dc4, 0x7fd317b3, 0x7fec09e1, 0x7ffb025e,
 39	0x7fffffff
 40};
 41
 42/**
 43 * __fixp_sin32() returns the sin of an angle in degrees
 44 *
 45 * @degrees: angle, in degrees, from 0 to 360.
 46 *
 47 * The returned value ranges from -0x7fffffff to +0x7fffffff.
 48 */
 49static inline s32 __fixp_sin32(int degrees)
 50{
 51	s32 ret;
 52	bool negative = false;
 53
 54	if (degrees > 180) {
 55		negative = true;
 56		degrees -= 180;
 57	}
 58	if (degrees > 90)
 59		degrees = 180 - degrees;
 60
 61	ret = sin_table[degrees];
 62
 63	return negative ? -ret : ret;
 64}
 65
 66/**
 67 * fixp_sin32() returns the sin of an angle in degrees
 68 *
 69 * @degrees: angle, in degrees. The angle can be positive or negative
 70 *
 71 * The returned value ranges from -0x7fffffff to +0x7fffffff.
 72 */
 73static inline s32 fixp_sin32(int degrees)
 74{
 75	degrees = (degrees % 360 + 360) % 360;
 76
 77	return __fixp_sin32(degrees);
 78}
 79
 80/* cos(x) = sin(x + 90 degrees) */
 81#define fixp_cos32(v) fixp_sin32((v) + 90)
 82
 83/*
 84 * 16 bits variants
 85 *
 86 * The returned value ranges from -0x7fff to 0x7fff
 87 */
 88
 89#define fixp_sin16(v) (fixp_sin32(v) >> 16)
 90#define fixp_cos16(v) (fixp_cos32(v) >> 16)
 91
 92/**
 93 * fixp_sin32_rad() - calculates the sin of an angle in radians
 94 *
 95 * @radians: angle, in radians
 96 * @twopi: value to be used for 2*pi
 97 *
 98 * Provides a variant for the cases where just 360
 99 * values is not enough. This function uses linear
100 * interpolation to a wider range of values given by
101 * twopi var.
102 *
103 * Experimental tests gave a maximum difference of
104 * 0.000038 between the value calculated by sin() and
105 * the one produced by this function, when twopi is
106 * equal to 360000. That seems to be enough precision
107 * for practical purposes.
108 *
109 * Please notice that two high numbers for twopi could cause
110 * overflows, so the routine will not allow values of twopi
111 * bigger than 1^18.
112 */
113static inline s32 fixp_sin32_rad(u32 radians, u32 twopi)
114{
115	int degrees;
116	s32 v1, v2, dx, dy;
117	s64 tmp;
118
119	/*
120	 * Avoid too large values for twopi, as we don't want overflows.
121	 */
122	BUG_ON(twopi > 1 << 18);
123
124	degrees = (radians * 360) / twopi;
125	tmp = radians - (degrees * twopi) / 360;
126
127	degrees = (degrees % 360 + 360) % 360;
128	v1 = __fixp_sin32(degrees);
129
130	v2 = fixp_sin32(degrees + 1);
131
132	dx = twopi / 360;
133	dy = v2 - v1;
134
135	tmp *= dy;
136
137	return v1 +  div_s64(tmp, dx);
138}
139
140/* cos(x) = sin(x + pi/2 radians) */
141
142#define fixp_cos32_rad(rad, twopi)	\
143	fixp_sin32_rad(rad + twopi / 4, twopi)
144
145/**
146 * fixp_linear_interpolate() - interpolates a value from two known points
147 *
148 * @x0: x value of point 0
149 * @y0: y value of point 0
150 * @x1: x value of point 1
151 * @y1: y value of point 1
152 * @x: the linear interpolant
153 */
154static inline int fixp_linear_interpolate(int x0, int y0, int x1, int y1, int x)
155{
156	if (y0 == y1 || x == x0)
157		return y0;
158	if (x1 == x0 || x == x1)
159		return y1;
160
161	return y0 + ((y1 - y0) * (x - x0) / (x1 - x0));
162}
163
164#endif