153 lines
5.2 KiB
C++
153 lines
5.2 KiB
C++
/*
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* fxpt_atan2.c
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*
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* Copyright (C) 2012, Xo Wang
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*
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* Hacked up to be a bit more ARM-friendly by:
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* Copyright (C) 2013 Jared Boone, ShareBrained Technology, Inc.
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy of
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* this software and associated documentation files (the "Software"), to deal in
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* the Software without restriction, including without limitation the rights to
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* use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
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* of the Software, and to permit persons to whom the Software is furnished to do
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* so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in all
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* copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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* SOFTWARE.
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*
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*/
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#include <math.h>
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#include <stdint.h>
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#include <stdlib.h>
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/**
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* Convert floating point to Q15 (1.0.15 fixed point) format.
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*
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* @param d floating-point value within range -1 to (1 - (2**-15)), inclusive
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* @return Q15 value representing d; same range
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*/
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/*
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static inline int16_t q15_from_double(const double d) {
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return lrint(d * 32768);
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}
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*/
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/**
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* Negative absolute value. Used to avoid undefined behavior for most negative
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* integer (see C99 standard 7.20.6.1.2 and footnote 265 for the description of
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* abs/labs/llabs behavior).
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*
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* @param i 16-bit signed integer
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* @return negative absolute value of i; defined for all values of i
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*/
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/*
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static inline int16_t s16_nabs(const int16_t j) {
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#if (((int16_t)-1) >> 1) == ((int16_t)-1)
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// signed right shift sign-extends (arithmetic)
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const int16_t negSign = ~(j >> 15); // splat sign bit into all 16 and complement
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// if j is positive (negSign is -1), xor will invert j and sub will add 1
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// otherwise j is unchanged
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return (j ^ negSign) - negSign;
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#else
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return (j < 0 ? j : -j);
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#endif
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}
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*/
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/**
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* Q15 (1.0.15 fixed point) multiplication. Various common rounding modes are in
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* the function definition for reference (and preference).
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*
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* @param j 16-bit signed integer representing -1 to (1 - (2**-15)), inclusive
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* @param k same format as j
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* @return product of j and k, in same format
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*/
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static inline int16_t q15_mul(const int16_t j, const int16_t k) {
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const int32_t intermediate = j * k;
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#if 0 // don't round
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return intermediate >> 15;
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#elif 0 // biased rounding
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return (intermediate + 0x4000) >> 15;
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#else // unbiased rounding
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return (intermediate + ((intermediate & 0x7FFF) == 0x4000 ? 0 : 0x4000)) >> 15;
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#endif
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}
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/**
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* Q15 (1.0.15 fixed point) division (non-saturating). Be careful when using
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* this function, as it does not behave well when the result is out-of-range.
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*
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* Value is not defined if numerator is greater than or equal to denominator.
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*
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* @param numer 16-bit signed integer representing -1 to (1 - (2**-15))
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* @param denom same format as numer; must be greater than numerator
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* @return numer / denom in same format as numer and denom
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*/
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static inline int16_t q15_div(const int16_t numer, const int16_t denom) {
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return (static_cast<int32_t>(numer) << 15) / denom;
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}
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/**
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* 16-bit fixed point four-quadrant arctangent. Given some Cartesian vector
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* (x, y), find the angle subtended by the vector and the positive x-axis.
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*
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* The value returned is in units of 1/65536ths of one turn. This allows the use
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* of the full 16-bit unsigned range to represent a turn. e.g. 0x0000 is 0
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* radians, 0x8000 is pi radians, and 0xFFFF is (65535 / 32768) * pi radians.
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*
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* Because the magnitude of the input vector does not change the angle it
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* represents, the inputs can be in any signed 16-bit fixed-point format.
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*
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* @param y y-coordinate in signed 16-bit
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* @param x x-coordinate in signed 16-bit
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* @return angle in (val / 32768) * pi radian increments from 0x0000 to 0xFFFF
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*/
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static inline int16_t nabs(const int16_t j) {
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//return -abs(x);
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return (j < 0 ? j : -j);
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}
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int16_t fxpt_atan2(const int16_t y, const int16_t x) {
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static const int16_t k1 = 2847;
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static const int16_t k2 = 11039;
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if (x == y) { // x/y or y/x would return -1 since 1 isn't representable
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if (y > 0) { // 1/8
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return 8192;
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} else if (y < 0) { // 5/8
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return 40960;
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} else { // x = y = 0
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return 0;
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}
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}
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const int16_t nabs_y = nabs(y);
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const int16_t nabs_x = nabs(x);
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if (nabs_x < nabs_y) { // octants 1, 4, 5, 8
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const int16_t y_over_x = q15_div(y, x);
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const int16_t correction = q15_mul(k1, nabs(y_over_x));
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const int16_t unrotated = q15_mul(k2 + correction, y_over_x);
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if (x > 0) { // octants 1, 8
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return unrotated;
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} else { // octants 4, 5
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return 32768 + unrotated;
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}
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} else { // octants 2, 3, 6, 7
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const int16_t x_over_y = q15_div(x, y);
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const int16_t correction = q15_mul(k1, nabs(x_over_y));
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const int16_t unrotated = q15_mul(k2 + correction, x_over_y);
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if (y > 0) { // octants 2, 3
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return 16384 - unrotated;
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} else { // octants 6, 7
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return 49152 - unrotated;
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}
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}
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}
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