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added fixed-point CORDIC atan2

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Ahmet Inan 2019-02-13 02:36:39 +01:00
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7
README.md
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@ -56,6 +56,13 @@ The following [infinite impulse response](https://en.wikipedia.org/wiki/Infinite
[atan](https://en.wikipedia.org/wiki/Inverse_trigonometric_functions) and [atan2](https://en.wikipedia.org/wiki/Atan2).
### [cordic.hh](cordic.hh)
When working on a device where multiplication is expensive, the [CORDIC](https://en.wikipedia.org/wiki/CORDIC) comes in handy for computing [trigonometric functions](https://en.wikipedia.org/wiki/Trigonometric_functions).
The following implementations are a good (max 1 LSB error at full range) starting point for your own designs:
* [Fixed-point](https://en.wikipedia.org/wiki/Fixed-point_arithmetic) [atan2](https://en.wikipedia.org/wiki/Atan2) implementation
### [trigger.hh](trigger.hh)
Implemented are the following [trigger functions](https://en.wikipedia.org/wiki/Flip-flop_(electronics)):

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cordic.hh Normal file
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/*
CORDIC atan2 implementation
Copyright 2019 Ahmet Inan <inan@aicodix.de>
*/
#pragma once
/*
for ((i = 0; i < 16; ++i)) ; do
echo -n "int(0.5+FAC*"
echo "scale=100; a((1/2)^$i)/(4*a(1))" | bc -l | head -n1 | sed 's/\\/L),/'
done
*/
namespace DSP {
template <typename TYPE>
class CORDIC
{
static const int BYTES = sizeof(TYPE);
static const int BITS = 8 * BYTES;
static_assert(BITS <= 16, "LUT not big enough");
static const int FAC = BYTES << BITS;
static constexpr int LUT[16] = {
int(0.5+FAC*.2500000000000000000000000000000000000000000000000000000000000000000L),
int(0.5+FAC*.1475836176504332741754010762247405259511345238869178945999223128627L),
int(0.5+FAC*.0779791303773693254605128897731301351165246187810070349907614355625L),
int(0.5+FAC*.0395834241605655420108516713400380263836230512014484657091255843474L),
int(0.5+FAC*.0198685243055408390593598828581045592395809198311117360197658161834L),
int(0.5+FAC*.0099439478235892739286124987559949706675355099351305855673205197301L),
int(0.5+FAC*.0049731872789504128535623156837751800756022858309425918885230220925L),
int(0.5+FAC*.0024867453936697392949686323634656804594951905170750175789691381407L),
int(0.5+FAC*.0012433916687141004173529641246144055092826557912518235730426698546L),
int(0.5+FAC*.0006216982059233715959748655390818054931061630817558971376245115402L),
int(0.5+FAC*.0003108493994100203787468007466901774427133407538770647518959302312L),
int(0.5+FAC*.0001554247367611315255509951068712763232641191255978216125229683284L),
int(0.5+FAC*.0000777123730125834146038201984686638046103667177724187710747868218L),
int(0.5+FAC*.0000388561870852939914306938515989779351910341528053916759630446151L),
int(0.5+FAC*.0000194280936150222836580154085598088977275755448309525831225639103L),
int(0.5+FAC*.0000097140468165580528976715963565423783044063210250363625335628380L),
};
public:
static TYPE atan2(TYPE y, TYPE x)
{
int angle = 0;
int real = x << 1;
int imag = y << 1;
if (x < 0)
real = -real;
for (int i = 0; i < BITS; ++i) {
int re = real;
int im = imag;
if (imag < 0) {
angle -= LUT[i];
re -= imag >> i;
im += real >> i;
} else {
angle += LUT[i];
re += imag >> i;
im -= real >> i;
}
real = re; imag = im;
}
if (x < 0)
angle = FAC - angle;
return angle >> BYTES;
}
};
}

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tests/cordic_test.cc Normal file
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@ -0,0 +1,33 @@
/*
Test for the CORDIC atan2 function
Copyright 2019 Ahmet Inan <inan@aicodix.de>
*/
#include <cassert>
#include <iostream>
#include <cmath>
#include "unit_circle.hh"
#include "cordic.hh"
#include "const.hh"
template <typename TYPE>
void test()
{
const int N = 1 << (8*sizeof(TYPE));
for (int n = -N/2; n < N/2; ++n) {
TYPE x = nearbyint((N/2-1) * DSP::UnitCircle<double>::cos(n, N));
TYPE y = nearbyint((N/2-1) * DSP::UnitCircle<double>::sin(n, N));
TYPE a = DSP::CORDIC<TYPE>::atan2(y, x);
assert(abs(a-n) <= 1);
}
}
int main()
{
test<char>();
test<short>();
std::cerr << "CORDIC atan2 test passed!" << std::endl;
return 0;
}