alex/GY-63_MS5611
1
0
Fork 0
mirror of https://github.com/RobTillaart/Arduino.git synced 2024-09-19 08:36:08 -04:00
Code Issues Actions Packages Projects Releases Wiki Activity

0.3.0 functionGenerator

Browse Source
This commit is contained in:
Rob Tillaart 2024-07-07 10:18:00 +02:00
parent 609ca019c0
commit db9c7dda89
14 changed files with 1502 additions and 55 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

2
libraries/FunctionGenerator/.github/workflows/arduino-lint.yml vendored
View File

@ -10,4 +10,4 @@ jobs:
- uses: arduino/arduino-lint-action@v1
with:
library-manager: update
compliance: strict
# compliance: strict

18
libraries/FunctionGenerator/CHANGELOG.md
View File

@ -6,11 +6,25 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/)
and this project adheres to [Semantic Versioning](http://semver.org/).
## [0.2.5] - 2023-11-02
## [0.3.0] - 2024-07-05
- add **float sinusDiode(float t)**
- add **float sinusRectified(float t)**
- add **float trapezium1(float t)** with duty cycle.
- add **float trapezium2(float t)** with duty cycle.
- add **float heartBeat(float t)**
- add **float freeWave(float t, int16_t arr, int size)** arbitrary wave generator.
- update **functionGeneratorPerformance.ino**
- add examples for **freeWave()**
- fix Arduino-lint.yml (long library name error)
- update readme.md
- minor edits
----
## [0.2.6] - 2023-11-02
- update readme.md
- update keywords.txt (align)
## [0.2.5] - 2023-03-25
- add **setDutyCycle()**, **getDutyCycle()**
- implement duty cycle for square(), triangle() and random()

17
libraries/FunctionGenerator/FunctionGenerator.h
View File

@ -2,14 +2,14 @@
//
// FILE: functionGenerator.h
// AUTHOR: Rob Tillaart
// VERSION: 0.2.6
// VERSION: 0.3.0
// PURPOSE: wave form generating functions (use with care)
// URL: https://github.com/RobTillaart/FunctionGenerator
#include "Arduino.h"
#define FUNCTIONGENERATOR_LIB_VERSION (F("0.2.6"))
#define FUNCTIONGENERATOR_LIB_VERSION (F("0.3.0"))
class funcgen
@ -53,7 +53,7 @@ public:
float zero();
// standard wave forms
float sawtooth(float t, uint8_t mode = 0); // 0 ==> /|. 1 ==> sawtooth |\.
float sawtooth(float t, uint8_t mode = 0); // 0 ==> /|. 1 ==> sawtooth |\.
float triangle(float t);
float square(float t);
float sinus(float t);
@ -62,6 +62,17 @@ public:
float random();
float random_DC(); // duty cycle variant. Experimental.
/////////////////////////////////////////////////////////////
//
// EXPERIMENTAL 0.2.7
//
float sinusDiode(float t);
float sinusRectified(float t);
float trapezium1(float t);
float trapezium2(float t);
float heartBeat(float t); // 72 BPM = 72/60 = 1 setFrequency(1.2)
float freeWave(float t, int16_t * arr, int16_t size); // arr must be size+1 long
private:
float _period;

95
libraries/FunctionGenerator/examples/funcGenFreeWavePlotter/funcGenFreeWavePlotter.ino Normal file
View File

@ -0,0 +1,95 @@
//
// FILE: funcGenFreeWavePlotter.ino
// AUTHOR: Rob Tillaart
// PURPOSE: demo function generators
// URL: https://github.com/RobTillaart/FunctionGenerator
//
// use a Serial plotter to show the data
#include "functionGenerator.h"
funcgen gen;
// sin(t).
int16_t arr_sin[101] =
{
0, 627, 1253, 1873, 2486, 3090,
3681, 4257, 4817, 5358, 5877,
6374, 6845, 7289, 7705, 8090,
8443, 8763, 9048, 9297, 9510,
9685, 9822, 9921, 9980, 10000,
9980, 9921, 9822, 9685, 9510,
9297, 9048, 8763, 8443, 8090,
7705, 7289, 6845, 6374, 5877,
5358, 4817, 4257, 3681, 3090,
2486, 1873, 1253, 627, 0,
-627, -1253, -1873, -2486, -3090,
-3681, -4257, -4817, -5358, -5877,
-6374, -6845, -7289, -7705, -8090,
-8443, -8763, -9048, -9297, -9510,
-9685, -9822, -9921, -9980, -10000,
-9980, -9921, -9822, -9685, -9510,
-9297, -9048, -8763, -8443, -8090,
-7705, -7289, -6845, -6374, -5877,
-5358, -4817, -4257, -3681, -3090,
-2486, -1873, -1253, -627, 0,
};
// sin(t) + 0.25 * sin(5t)
int16_t arr_two_sin[101] =
{
0, 1120, 2178, 3117, 3891, 4472,
4847, 5024, 5029, 4904, 4702,
4481, 4300, 4213, 4261, 4472,
4852, 5392, 6063, 6820, 7608,
8366, 9033, 9554, 9886, 10000,
9886, 9554, 9033, 8366, 7608,
6820, 6063, 5392, 4852, 4472,
4261, 4213, 4300, 4481, 4702,
4904, 5029, 5024, 4847, 4472,
3891, 3117, 2178, 1120, 0,
-1120, -2178, -3117, -3891, -4472,
-4847, -5024, -5029, -4904, -4702,
-4481, -4300, -4213, -4261, -4472,
-4852, -5392, -6063, -6820, -7608,
-8366, -9033, -9554, -9886, -10000,
-9886, -9554, -9033, -8366, -7608,
-6820, -6063, -5392, -4852, -4472,
-4261, -4213, -4300, -4481, -4702,
-4904, -5029, -5024, -4847, -4472,
-3891, -3117, -2178, -1120, 0,
};
void setup()
{
Serial.begin(115200);
// Serial.println(__FILE__);
// Serial.print("FUNCTIONGENERATOR_LIB_VERSION: ");
// Serial.println(FUNCTIONGENERATOR_LIB_VERSION);
// Serial.println();
gen.setAmplitude(80);
gen.setFrequency(0.5);
gen.setDutyCycle(50);
}
void loop()
{
float t = millis() * 0.001;
Serial.print(80);
Serial.print("\t");
Serial.print(-80);
Serial.print("\t");
Serial.print(gen.freeWave(t, arr_two_sin, 100));
Serial.println();
delay(10);
}
// -- END OF FILE --

149
libraries/FunctionGenerator/examples/functionGeneratorPerformance/functionGeneratorPerformance.ino
View File

@ -17,13 +17,41 @@ volatile float y;
funcgen gen;
// sin(t) + 0.25 * sin(5t)
int16_t arr_two_sin[101] =
{
0, 1120, 2178, 3117, 3891, 4472,
4847, 5024, 5029, 4904, 4702,
4481, 4300, 4213, 4261, 4472,
4852, 5392, 6063, 6820, 7608,
8366, 9033, 9554, 9886, 10000,
9886, 9554, 9033, 8366, 7608,
6820, 6063, 5392, 4852, 4472,
4261, 4213, 4300, 4481, 4702,
4904, 5029, 5024, 4847, 4472,
3891, 3117, 2178, 1120, 0,
-1120, -2178, -3117, -3891, -4472,
-4847, -5024, -5029, -4904, -4702,
-4481, -4300, -4213, -4261, -4472,
-4852, -5392, -6063, -6820, -7608,
-8366, -9033, -9554, -9886, -10000,
-9886, -9554, -9033, -8366, -7608,
-6820, -6063, -5392, -4852, -4472,
-4261, -4213, -4300, -4481, -4702,
-4904, -5029, -5024, -4847, -4472,
-3891, -3117, -2178, -1120, 0,
};
void setup()
{
Serial.begin(115200);
Serial.print("Start functionGeneratorPerformance - LIB VERSION: ");
Serial.println(__FILE__);
Serial.print("FUNCTIONGENERATOR_LIB_VERSION: ");
Serial.println(FUNCTIONGENERATOR_LIB_VERSION);
Serial.println();
Serial.println("func \t\tusec\tmax calls/sec");
Serial.println("func \t\tusec\tmax calls/sec (indicative)");
y = analogRead(A0) / 1024;
test_square();
delay(10);
@ -43,9 +71,21 @@ void setup()
delay(10);
test_zero();
delay(10);
test_sinusDiode();
delay(10);
test_sinusRectified();
delay(10);
test_trapezium1();
delay(10);
test_trapezium2();
delay(10);
test_heartBeat();
delay(10);
test_freeWave();
delay(10);
Serial.println();
Serial.println("t \t sqr\t saw\t tri\t sin\t str\t rnd\t line\t zero");
Serial.println("t \t sqr\t saw\t tri\t sin\t str\t rnd\t line\t zero\t sinD\t sinR\t trap");
for (int i = -400; i < 400; i += 2)
{
float t = i * 0.01;
@ -66,6 +106,12 @@ void setup()
Serial.print(gen.line());
Serial.print("\t");
Serial.print(gen.zero());
Serial.print("\t");
Serial.print(gen.sinusDiode(t));
Serial.print("\t");
Serial.print(gen.sinusRectified(t));
Serial.print("\t");
Serial.print(gen.trapezium2(t));
Serial.println();
}
Serial.println("\ndone...");
@ -218,10 +264,105 @@ void test_zero()
}
void test_sinusDiode()
{
start = micros();
for (int i = 0; i < 10000; i++)
{
t = gen.sinusDiode(i);
}
stop = micros();
Serial.print(__FUNCTION__);
Serial.print(":\t");
Serial.print((stop - start) / 10000.0);
Serial.print("\t");
Serial.println(1000000.0 / ((stop - start) / 10000.0));
}
void test_sinusRectified()
{
start = micros();
for (int i = 0; i < 10000; i++)
{
t = gen.sinusRectified(i);
}
stop = micros();
Serial.print(__FUNCTION__);
Serial.print(":\t");
Serial.print((stop - start) / 10000.0);
Serial.print("\t");
Serial.println(1000000.0 / ((stop - start) / 10000.0));
}
void test_trapezium1()
{
start = micros();
for (int i = 0; i < 10000; i++)
{
t = gen.trapezium1(i);
}
stop = micros();
Serial.print(__FUNCTION__);
Serial.print(":\t");
Serial.print((stop - start) / 10000.0);
Serial.print("\t");
Serial.println(1000000.0 / ((stop - start) / 10000.0));
}
void test_trapezium2()
{
start = micros();
for (int i = 0; i < 10000; i++)
{
t = gen.trapezium2(i);
}
stop = micros();
Serial.print(__FUNCTION__);
Serial.print(":\t");
Serial.print((stop - start) / 10000.0);
Serial.print("\t");
Serial.println(1000000.0 / ((stop - start) / 10000.0));
}
void test_heartBeat()
{
start = micros();
for (int i = 0; i < 10000; i++)
{
t = gen.heartBeat(i);
}
stop = micros();
Serial.print(__FUNCTION__);
Serial.print(":\t");
Serial.print((stop - start) / 10000.0);
Serial.print("\t");
Serial.println(1000000.0 / ((stop - start) / 10000.0));
}
void test_freeWave()
{
start = micros();
for (int i = 0; i < 10000; i++)
{
t = gen.freeWave(i, arr_two_sin, 100);
}
stop = micros();
Serial.print(__FUNCTION__);
Serial.print(":\t");
Serial.print((stop - start) / 10000.0);
Serial.print("\t");
Serial.println(1000000.0 / ((stop - start) / 10000.0));
}
void loop()
{
}
// -- END OF FILE --

429
libraries/FunctionGenerator/examples/functionGeneratorPerformance/performance_0.2.7.txt Normal file
View File

@ -0,0 +1,429 @@
functionGeneratorPerformance.ino
FUNCTIONGENERATOR_LIB_VERSION: 0.2.7
indicative output Arduino UNO 1.8.19, 16 MHz.
| wave form name | usec | max calls/sec |
|:---------------|-------:|----------------:|
| square | 54.57 | 18325.49 |
| sawtooth | 61.69 | 16210.61 |
| triangle | 79.80 | 12531.96 |
| sinus | 166.38 | 6010.37 |
| stair | 80.86 | 12366.38 |
| random | 42.61 | 23466.69 |
| random_DC | 67.18 | 14885.12 |
| line | 0.76 | 1322751.37 |
| zero | 0.75 | 1324854.25 |
| sinusDiode | 169.93 | 5884.79 |
| sinusRectified | 169.49 | 5900.03 |
| trapezium1 | 100.98 | 9903.30 |
| trapezium2 | 143.98 | 6945.58 |
| heartBeat | 128.52 | 7780.77 |
| freeWave | 75.52 | 13241.31 |
t sqr saw tri sin str rnd line zero sinD sinR trap
-4.00 -1.00 1.00 -1.00 -0.00 1.00 0.50 1.00 0.00 0.00 0.00 -1.00
-3.98 1.00 -0.96 -0.92 0.13 -1.00 0.06 1.00 0.00 0.13 0.13 -1.00
-3.96 1.00 -0.92 -0.84 0.25 -1.00 0.34 1.00 0.00 0.25 0.25 -1.00
-3.94 1.00 -0.88 -0.76 0.37 -1.00 0.33 1.00 0.00 0.37 0.37 -1.00
-3.92 1.00 -0.84 -0.68 0.48 -1.00 0.95 1.00 0.00 0.48 0.48 -1.00
-3.90 1.00 -0.80 -0.60 0.59 -1.00 0.75 1.00 0.00 0.59 0.59 -1.00
-3.88 1.00 -0.76 -0.52 0.68 -1.00 0.20 1.00 0.00 0.68 0.68 -1.00
-3.86 1.00 -0.72 -0.44 0.77 -0.71 0.33 1.00 0.00 0.77 0.77 -1.00
-3.84 1.00 -0.68 -0.36 0.84 -0.71 0.25 1.00 0.00 0.84 0.84 -1.00
-3.82 1.00 -0.64 -0.28 0.90 -0.71 0.39 1.00 0.00 0.90 0.90 -1.00
-3.80 1.00 -0.60 -0.20 0.95 -0.71 0.42 1.00 0.00 0.95 0.95 -1.00
-3.78 1.00 -0.56 -0.12 0.98 -0.71 0.95 1.00 0.00 0.98 0.98 -1.00
-3.76 1.00 -0.52 -0.04 1.00 -0.71 0.56 1.00 0.00 1.00 1.00 -1.00
-3.74 1.00 -0.48 0.04 1.00 -0.43 0.64 1.00 0.00 1.00 1.00 -0.92
-3.72 1.00 -0.44 0.12 0.98 -0.43 0.17 1.00 0.00 0.98 0.98 -0.76
-3.70 1.00 -0.40 0.20 0.95 -0.43 0.78 1.00 0.00 0.95 0.95 -0.60
-3.68 1.00 -0.36 0.28 0.90 -0.43 0.02 1.00 0.00 0.90 0.90 -0.44
-3.66 1.00 -0.32 0.36 0.84 -0.43 0.31 1.00 0.00 0.84 0.84 -0.28
-3.64 1.00 -0.28 0.44 0.77 -0.43 0.49 1.00 0.00 0.77 0.77 -0.12
-3.62 1.00 -0.24 0.52 0.68 -0.14 0.09 1.00 0.00 0.68 0.68 0.04
-3.60 1.00 -0.20 0.60 0.59 -0.14 0.21 1.00 0.00 0.59 0.59 0.20
-3.58 1.00 -0.16 0.68 0.48 -0.14 0.82 1.00 0.00 0.48 0.48 0.36
-3.56 1.00 -0.12 0.76 0.37 -0.14 0.51 1.00 0.00 0.37 0.37 0.52
-3.54 1.00 -0.08 0.84 0.25 -0.14 0.74 1.00 0.00 0.25 0.25 0.68
-3.52 1.00 -0.04 0.92 0.13 -0.14 0.20 1.00 0.00 0.13 0.13 0.84
-3.50 1.00 0.00 1.00 0.00 -0.14 0.27 1.00 0.00 0.00 0.00 1.00
-3.48 -1.00 0.04 0.92 -0.13 0.14 0.15 1.00 0.00 0.00 0.13 1.00
-3.46 -1.00 0.08 0.84 -0.25 0.14 0.67 1.00 0.00 0.00 0.25 1.00
-3.44 -1.00 0.12 0.76 -0.37 0.14 0.54 1.00 0.00 0.00 0.37 1.00
-3.42 -1.00 0.16 0.68 -0.48 0.14 0.44 1.00 0.00 0.00 0.48 1.00
-3.40 -1.00 0.20 0.60 -0.59 0.14 0.85 1.00 0.00 0.00 0.59 1.00
-3.38 -1.00 0.24 0.52 -0.68 0.14 0.90 1.00 0.00 0.00 0.68 1.00
-3.36 -1.00 0.28 0.44 -0.77 0.43 0.43 1.00 0.00 0.00 0.77 1.00
-3.34 -1.00 0.32 0.36 -0.84 0.43 0.11 1.00 0.00 0.00 0.84 1.00
-3.32 -1.00 0.36 0.28 -0.90 0.43 0.91 1.00 0.00 0.00 0.90 1.00
-3.30 -1.00 0.40 0.20 -0.95 0.43 0.79 1.00 0.00 0.00 0.95 1.00
-3.28 -1.00 0.44 0.12 -0.98 0.43 0.17 1.00 0.00 0.00 0.98 1.00
-3.26 -1.00 0.48 0.04 -1.00 0.43 0.72 1.00 0.00 0.00 1.00 1.00
-3.24 -1.00 0.52 -0.04 -1.00 0.71 0.77 1.00 0.00 0.00 1.00 0.92
-3.22 -1.00 0.56 -0.12 -0.98 0.71 0.86 1.00 0.00 0.00 0.98 0.76
-3.20 -1.00 0.60 -0.20 -0.95 0.71 0.50 1.00 0.00 0.00 0.95 0.60
-3.18 -1.00 0.64 -0.28 -0.90 0.71 0.42 1.00 0.00 0.00 0.90 0.44
-3.16 -1.00 0.68 -0.36 -0.84 0.71 0.73 1.00 0.00 0.00 0.84 0.28
-3.14 -1.00 0.72 -0.44 -0.77 0.71 0.01 1.00 0.00 0.00 0.77 0.12
-3.12 -1.00 0.76 -0.52 -0.68 1.00 0.52 1.00 0.00 0.00 0.68 -0.04
-3.10 -1.00 0.80 -0.60 -0.59 1.00 0.72 1.00 0.00 0.00 0.59 -0.20
-3.08 -1.00 0.84 -0.68 -0.48 1.00 0.61 1.00 0.00 0.00 0.48 -0.36
-3.06 -1.00 0.88 -0.76 -0.37 1.00 0.41 1.00 0.00 0.00 0.37 -0.52
-3.04 -1.00 0.92 -0.84 -0.25 1.00 0.68 1.00 0.00 0.00 0.25 -0.68
-3.02 -1.00 0.96 -0.92 -0.13 1.00 0.34 1.00 0.00 0.00 0.13 -0.84
-3.00 -1.00 1.00 -1.00 -0.00 1.00 0.90 1.00 0.00 0.00 0.00 -1.00
-2.98 1.00 -0.96 -0.92 0.13 -1.00 0.43 1.00 0.00 0.13 0.13 -1.00
-2.96 1.00 -0.92 -0.84 0.25 -1.00 0.47 1.00 0.00 0.25 0.25 -1.00
-2.94 1.00 -0.88 -0.76 0.37 -1.00 0.51 1.00 0.00 0.37 0.37 -1.00
-2.92 1.00 -0.84 -0.68 0.48 -1.00 0.29 1.00 0.00 0.48 0.48 -1.00
-2.90 1.00 -0.80 -0.60 0.59 -1.00 0.42 1.00 0.00 0.59 0.59 -1.00
-2.88 1.00 -0.76 -0.52 0.68 -1.00 0.02 1.00 0.00 0.68 0.68 -1.00
-2.86 1.00 -0.72 -0.44 0.77 -0.71 0.91 1.00 0.00 0.77 0.77 -1.00
-2.84 1.00 -0.68 -0.36 0.84 -0.71 0.00 1.00 0.00 0.84 0.84 -1.00
-2.82 1.00 -0.64 -0.28 0.90 -0.71 0.22 1.00 0.00 0.90 0.90 -1.00
-2.80 1.00 -0.60 -0.20 0.95 -0.71 0.55 1.00 0.00 0.95 0.95 -1.00
-2.78 1.00 -0.56 -0.12 0.98 -0.71 0.96 1.00 0.00 0.98 0.98 -1.00
-2.76 1.00 -0.52 -0.04 1.00 -0.71 0.30 1.00 0.00 1.00 1.00 -1.00
-2.74 1.00 -0.48 0.04 1.00 -0.43 0.19 1.00 0.00 1.00 1.00 -0.92
-2.72 1.00 -0.44 0.12 0.98 -0.43 0.62 1.00 0.00 0.98 0.98 -0.76
-2.70 1.00 -0.40 0.20 0.95 -0.43 0.61 1.00 0.00 0.95 0.95 -0.60
-2.68 1.00 -0.36 0.28 0.90 -0.43 0.28 1.00 0.00 0.90 0.90 -0.44
-2.66 1.00 -0.32 0.36 0.84 -0.43 0.85 1.00 0.00 0.84 0.84 -0.28
-2.64 1.00 -0.28 0.44 0.77 -0.43 0.22 1.00 0.00 0.77 0.77 -0.12
-2.62 1.00 -0.24 0.52 0.68 -0.14 0.66 1.00 0.00 0.68 0.68 0.04
-2.60 1.00 -0.20 0.60 0.59 -0.14 0.62 1.00 0.00 0.59 0.59 0.20
-2.58 1.00 -0.16 0.68 0.48 -0.14 0.30 1.00 0.00 0.48 0.48 0.36
-2.56 1.00 -0.12 0.76 0.37 -0.14 0.38 1.00 0.00 0.37 0.37 0.52
-2.54 1.00 -0.08 0.84 0.25 -0.14 0.00 1.00 0.00 0.25 0.25 0.68
-2.52 1.00 -0.04 0.92 0.13 -0.14 0.09 1.00 0.00 0.13 0.13 0.84
-2.50 1.00 0.00 1.00 0.00 -0.14 0.56 1.00 0.00 0.00 0.00 1.00
-2.48 -1.00 0.04 0.92 -0.13 0.14 0.67 1.00 0.00 0.00 0.13 1.00
-2.46 -1.00 0.08 0.84 -0.25 0.14 0.66 1.00 0.00 0.00 0.25 1.00
-2.44 -1.00 0.12 0.76 -0.37 0.14 0.15 1.00 0.00 0.00 0.37 1.00
-2.42 -1.00 0.16 0.68 -0.48 0.14 0.71 1.00 0.00 0.00 0.48 1.00
-2.40 -1.00 0.20 0.60 -0.59 0.14 0.75 1.00 0.00 0.00 0.59 1.00
-2.38 -1.00 0.24 0.52 -0.68 0.14 0.13 1.00 0.00 0.00 0.68 1.00
-2.36 -1.00 0.28 0.44 -0.77 0.43 0.99 1.00 0.00 0.00 0.77 1.00
-2.34 -1.00 0.32 0.36 -0.84 0.43 0.01 1.00 0.00 0.00 0.84 1.00
-2.32 -1.00 0.36 0.28 -0.90 0.43 0.92 1.00 0.00 0.00 0.90 1.00
-2.30 -1.00 0.40 0.20 -0.95 0.43 0.92 1.00 0.00 0.00 0.95 1.00
-2.28 -1.00 0.44 0.12 -0.98 0.43 0.38 1.00 0.00 0.00 0.98 1.00
-2.26 -1.00 0.48 0.04 -1.00 0.43 0.87 1.00 0.00 0.00 1.00 1.00
-2.24 -1.00 0.52 -0.04 -1.00 0.71 0.42 1.00 0.00 0.00 1.00 0.92
-2.22 -1.00 0.56 -0.12 -0.98 0.71 0.88 1.00 0.00 0.00 0.98 0.76
-2.20 -1.00 0.60 -0.20 -0.95 0.71 0.71 1.00 0.00 0.00 0.95 0.60
-2.18 -1.00 0.64 -0.28 -0.90 0.71 0.97 1.00 0.00 0.00 0.90 0.44
-2.16 -1.00 0.68 -0.36 -0.84 0.71 0.27 1.00 0.00 0.00 0.84 0.28
-2.14 -1.00 0.72 -0.44 -0.77 0.71 0.94 1.00 0.00 0.00 0.77 0.12
-2.12 -1.00 0.76 -0.52 -0.68 1.00 0.92 1.00 0.00 0.00 0.68 -0.04
-2.10 -1.00 0.80 -0.60 -0.59 1.00 0.02 1.00 0.00 0.00 0.59 -0.20
-2.08 -1.00 0.84 -0.68 -0.48 1.00 0.26 1.00 0.00 0.00 0.48 -0.36
-2.06 -1.00 0.88 -0.76 -0.37 1.00 0.54 1.00 0.00 0.00 0.37 -0.52
-2.04 -1.00 0.92 -0.84 -0.25 1.00 0.93 1.00 0.00 0.00 0.25 -0.68
-2.02 -1.00 0.96 -0.92 -0.13 1.00 0.25 1.00 0.00 0.00 0.13 -0.84
-2.00 -1.00 1.00 -1.00 -0.00 1.00 0.77 1.00 0.00 0.00 0.00 -1.00
-1.98 1.00 -0.96 -0.92 0.13 -1.00 0.71 1.00 0.00 0.13 0.13 -1.00
-1.96 1.00 -0.92 -0.84 0.25 -1.00 0.86 1.00 0.00 0.25 0.25 -1.00
-1.94 1.00 -0.88 -0.76 0.37 -1.00 0.15 1.00 0.00 0.37 0.37 -1.00
-1.92 1.00 -0.84 -0.68 0.48 -1.00 0.80 1.00 0.00 0.48 0.48 -1.00
-1.90 1.00 -0.80 -0.60 0.59 -1.00 0.17 1.00 0.00 0.59 0.59 -1.00
-1.88 1.00 -0.76 -0.52 0.68 -1.00 0.18 1.00 0.00 0.68 0.68 -1.00
-1.86 1.00 -0.72 -0.44 0.77 -0.71 0.54 1.00 0.00 0.77 0.77 -1.00
-1.84 1.00 -0.68 -0.36 0.84 -0.71 0.13 1.00 0.00 0.84 0.84 -1.00
-1.82 1.00 -0.64 -0.28 0.90 -0.71 0.71 1.00 0.00 0.90 0.90 -1.00
-1.80 1.00 -0.60 -0.20 0.95 -0.71 0.24 1.00 0.00 0.95 0.95 -1.00
-1.78 1.00 -0.56 -0.12 0.98 -0.71 0.73 1.00 0.00 0.98 0.98 -1.00
-1.76 1.00 -0.52 -0.04 1.00 -0.71 0.08 1.00 0.00 1.00 1.00 -1.00
-1.74 1.00 -0.48 0.04 1.00 -0.43 0.13 1.00 0.00 1.00 1.00 -0.92
-1.72 1.00 -0.44 0.12 0.98 -0.43 0.28 1.00 0.00 0.98 0.98 -0.76
-1.70 1.00 -0.40 0.20 0.95 -0.43 0.20 1.00 0.00 0.95 0.95 -0.60
-1.68 1.00 -0.36 0.28 0.90 -0.43 0.53 1.00 0.00 0.90 0.90 -0.44
-1.66 1.00 -0.32 0.36 0.84 -0.43 0.48 1.00 0.00 0.84 0.84 -0.28
-1.64 1.00 -0.28 0.44 0.77 -0.43 0.38 1.00 0.00 0.77 0.77 -0.12
-1.62 1.00 -0.24 0.52 0.68 -0.14 0.28 1.00 0.00 0.68 0.68 0.04
-1.60 1.00 -0.20 0.60 0.59 -0.14 0.06 1.00 0.00 0.59 0.59 0.20
-1.58 1.00 -0.16 0.68 0.48 -0.14 0.84 1.00 0.00 0.48 0.48 0.36
-1.56 1.00 -0.12 0.76 0.37 -0.14 0.35 1.00 0.00 0.37 0.37 0.52
-1.54 1.00 -0.08 0.84 0.25 -0.14 0.13 1.00 0.00 0.25 0.25 0.68
-1.52 1.00 -0.04 0.92 0.13 -0.14 0.51 1.00 0.00 0.13 0.13 0.84
-1.50 1.00 0.00 1.00 0.00 -0.14 0.37 1.00 0.00 0.00 0.00 1.00
-1.48 -1.00 0.04 0.92 -0.13 0.14 0.40 1.00 0.00 0.00 0.13 1.00
-1.46 -1.00 0.08 0.84 -0.25 0.14 0.26 1.00 0.00 0.00 0.25 1.00
-1.44 -1.00 0.12 0.76 -0.37 0.14 0.30 1.00 0.00 0.00 0.37 1.00
-1.42 -1.00 0.16 0.68 -0.48 0.14 0.76 1.00 0.00 0.00 0.48 1.00
-1.40 -1.00 0.20 0.60 -0.59 0.14 0.59 1.00 0.00 0.00 0.59 1.00
-1.38 -1.00 0.24 0.52 -0.68 0.14 0.32 1.00 0.00 0.00 0.68 1.00
-1.36 -1.00 0.28 0.44 -0.77 0.43 0.79 1.00 0.00 0.00 0.77 1.00
-1.34 -1.00 0.32 0.36 -0.84 0.43 0.63 1.00 0.00 0.00 0.84 1.00
-1.32 -1.00 0.36 0.28 -0.90 0.43 0.20 1.00 0.00 0.00 0.90 1.00
-1.30 -1.00 0.40 0.20 -0.95 0.43 0.83 1.00 0.00 0.00 0.95 1.00
-1.28 -1.00 0.44 0.12 -0.98 0.43 0.25 1.00 0.00 0.00 0.98 1.00
-1.26 -1.00 0.48 0.04 -1.00 0.43 0.36 1.00 0.00 0.00 1.00 1.00
-1.24 -1.00 0.52 -0.04 -1.00 0.71 0.25 1.00 0.00 0.00 1.00 0.92
-1.22 -1.00 0.56 -0.12 -0.98 0.71 0.25 1.00 0.00 0.00 0.98 0.76
-1.20 -1.00 0.60 -0.20 -0.95 0.71 0.18 1.00 0.00 0.00 0.95 0.60
-1.18 -1.00 0.64 -0.28 -0.90 0.71 0.30 1.00 0.00 0.00 0.90 0.44
-1.16 -1.00 0.68 -0.36 -0.84 0.71 0.09 1.00 0.00 0.00 0.84 0.28
-1.14 -1.00 0.72 -0.44 -0.77 0.71 0.32 1.00 0.00 0.00 0.77 0.12
-1.12 -1.00 0.76 -0.52 -0.68 1.00 0.69 1.00 0.00 0.00 0.68 -0.04
-1.10 -1.00 0.80 -0.60 -0.59 1.00 0.96 1.00 0.00 0.00 0.59 -0.20
-1.08 -1.00 0.84 -0.68 -0.48 1.00 0.28 1.00 0.00 0.00 0.48 -0.36
-1.06 -1.00 0.88 -0.76 -0.37 1.00 0.93 1.00 0.00 0.00 0.37 -0.52
-1.04 -1.00 0.92 -0.84 -0.25 1.00 0.21 1.00 0.00 0.00 0.25 -0.68
-1.02 -1.00 0.96 -0.92 -0.13 1.00 0.87 1.00 0.00 0.00 0.13 -0.84
-1.00 -1.00 1.00 -1.00 -0.00 1.00 0.57 1.00 0.00 0.00 0.00 -1.00
-0.98 1.00 -0.96 -0.92 0.13 -1.00 0.42 1.00 0.00 0.13 0.13 -1.00
-0.96 1.00 -0.92 -0.84 0.25 -1.00 0.81 1.00 0.00 0.25 0.25 -1.00
-0.94 1.00 -0.88 -0.76 0.37 -1.00 0.39 1.00 0.00 0.37 0.37 -1.00
-0.92 1.00 -0.84 -0.68 0.48 -1.00 0.71 1.00 0.00 0.48 0.48 -1.00
-0.90 1.00 -0.80 -0.60 0.59 -1.00 0.47 1.00 0.00 0.59 0.59 -1.00
-0.88 1.00 -0.76 -0.52 0.68 -1.00 0.56 1.00 0.00 0.68 0.68 -1.00
-0.86 1.00 -0.72 -0.44 0.77 -0.71 0.86 1.00 0.00 0.77 0.77 -1.00
-0.84 1.00 -0.68 -0.36 0.84 -0.71 0.87 1.00 0.00 0.84 0.84 -1.00
-0.82 1.00 -0.64 -0.28 0.90 -0.71 0.43 1.00 0.00 0.90 0.90 -1.00
-0.80 1.00 -0.60 -0.20 0.95 -0.71 0.42 1.00 0.00 0.95 0.95 -1.00
-0.78 1.00 -0.56 -0.12 0.98 -0.71 0.60 1.00 0.00 0.98 0.98 -1.00
-0.76 1.00 -0.52 -0.04 1.00 -0.71 0.13 1.00 0.00 1.00 1.00 -1.00
-0.74 1.00 -0.48 0.04 1.00 -0.43 0.04 1.00 0.00 1.00 1.00 -0.92
-0.72 1.00 -0.44 0.12 0.98 -0.43 0.30 1.00 0.00 0.98 0.98 -0.76
-0.70 1.00 -0.40 0.20 0.95 -0.43 0.84 1.00 0.00 0.95 0.95 -0.60
-0.68 1.00 -0.36 0.28 0.90 -0.43 0.52 1.00 0.00 0.90 0.90 -0.44
-0.66 1.00 -0.32 0.36 0.84 -0.43 0.25 1.00 0.00 0.84 0.84 -0.28
-0.64 1.00 -0.28 0.44 0.77 -0.43 0.04 1.00 0.00 0.77 0.77 -0.12
-0.62 1.00 -0.24 0.52 0.68 -0.14 0.38 1.00 0.00 0.68 0.68 0.04
-0.60 1.00 -0.20 0.60 0.59 -0.14 0.46 1.00 0.00 0.59 0.59 0.20
-0.58 1.00 -0.16 0.68 0.48 -0.14 0.66 1.00 0.00 0.48 0.48 0.36
-0.56 1.00 -0.12 0.76 0.37 -0.14 0.55 1.00 0.00 0.37 0.37 0.52
-0.54 1.00 -0.08 0.84 0.25 -0.14 0.84 1.00 0.00 0.25 0.25 0.68
-0.52 1.00 -0.04 0.92 0.13 -0.14 0.66 1.00 0.00 0.13 0.13 0.84
-0.50 1.00 0.00 1.00 0.00 -0.14 0.97 1.00 0.00 0.00 0.00 1.00
-0.48 -1.00 0.04 0.92 -0.13 0.14 0.94 1.00 0.00 0.00 0.13 1.00
-0.46 -1.00 0.08 0.84 -0.25 0.14 0.18 1.00 0.00 0.00 0.25 1.00
-0.44 -1.00 0.12 0.76 -0.37 0.14 0.27 1.00 0.00 0.00 0.37 1.00
-0.42 -1.00 0.16 0.68 -0.48 0.14 0.62 1.00 0.00 0.00 0.48 1.00
-0.40 -1.00 0.20 0.60 -0.59 0.14 0.22 1.00 0.00 0.00 0.59 1.00
-0.38 -1.00 0.24 0.52 -0.68 0.14 0.12 1.00 0.00 0.00 0.68 1.00
-0.36 -1.00 0.28 0.44 -0.77 0.43 0.51 1.00 0.00 0.00 0.77 1.00
-0.34 -1.00 0.32 0.36 -0.84 0.43 0.54 1.00 0.00 0.00 0.84 1.00
-0.32 -1.00 0.36 0.28 -0.90 0.43 0.36 1.00 0.00 0.00 0.90 1.00
-0.30 -1.00 0.40 0.20 -0.95 0.43 0.19 1.00 0.00 0.00 0.95 1.00
-0.28 -1.00 0.44 0.12 -0.98 0.43 0.73 1.00 0.00 0.00 0.98 1.00
-0.26 -1.00 0.48 0.04 -1.00 0.43 0.58 1.00 0.00 0.00 1.00 1.00
-0.24 -1.00 0.52 -0.04 -1.00 0.71 0.74 1.00 0.00 0.00 1.00 0.92
-0.22 -1.00 0.56 -0.12 -0.98 0.71 0.48 1.00 0.00 0.00 0.98 0.76
-0.20 -1.00 0.60 -0.20 -0.95 0.71 0.37 1.00 0.00 0.00 0.95 0.60
-0.18 -1.00 0.64 -0.28 -0.90 0.71 0.49 1.00 0.00 0.00 0.90 0.44
-0.16 -1.00 0.68 -0.36 -0.84 0.71 0.99 1.00 0.00 0.00 0.84 0.28
-0.14 -1.00 0.72 -0.44 -0.77 0.71 0.38 1.00 0.00 0.00 0.77 0.12
-0.12 -1.00 0.76 -0.52 -0.68 1.00 0.16 1.00 0.00 0.00 0.68 -0.04
-0.10 -1.00 0.80 -0.60 -0.59 1.00 0.20 1.00 0.00 0.00 0.59 -0.20
-0.08 -1.00 0.84 -0.68 -0.48 1.00 0.36 1.00 0.00 0.00 0.48 -0.36
-0.06 -1.00 0.88 -0.76 -0.37 1.00 0.93 1.00 0.00 0.00 0.37 -0.52
-0.04 -1.00 0.92 -0.84 -0.25 1.00 0.31 1.00 0.00 0.00 0.25 -0.68
-0.02 -1.00 0.96 -0.92 -0.13 1.00 0.71 1.00 0.00 0.00 0.13 -0.84
0.00 1.00 -1.00 -1.00 0.00 -1.00 0.35 1.00 0.00 0.00 0.00 -1.00
0.02 1.00 -0.96 -0.92 0.13 -1.00 0.58 1.00 0.00 0.13 0.13 -0.84
0.04 1.00 -0.92 -0.84 0.25 -1.00 0.38 1.00 0.00 0.25 0.25 -0.68
0.06 1.00 -0.88 -0.76 0.37 -1.00 0.45 1.00 0.00 0.37 0.37 -0.52
0.08 1.00 -0.84 -0.68 0.48 -1.00 0.96 1.00 0.00 0.48 0.48 -0.36
0.10 1.00 -0.80 -0.60 0.59 -1.00 0.00 1.00 0.00 0.59 0.59 -0.20
0.12 1.00 -0.76 -0.52 0.68 -1.00 0.59 1.00 0.00 0.68 0.68 -0.04
0.14 1.00 -0.72 -0.44 0.77 -0.71 0.09 1.00 0.00 0.77 0.77 0.12
0.16 1.00 -0.68 -0.36 0.84 -0.71 0.93 1.00 0.00 0.84 0.84 0.28
0.18 1.00 -0.64 -0.28 0.90 -0.71 0.17 1.00 0.00 0.90 0.90 0.44
0.20 1.00 -0.60 -0.20 0.95 -0.71 0.32 1.00 0.00 0.95 0.95 0.60
0.22 1.00 -0.56 -0.12 0.98 -0.71 0.18 1.00 0.00 0.98 0.98 0.76
0.24 1.00 -0.52 -0.04 1.00 -0.71 0.87 1.00 0.00 1.00 1.00 0.92
0.26 1.00 -0.48 0.04 1.00 -0.43 0.67 1.00 0.00 1.00 1.00 1.00
0.28 1.00 -0.44 0.12 0.98 -0.43 0.22 1.00 0.00 0.98 0.98 1.00
0.30 1.00 -0.40 0.20 0.95 -0.43 0.83 1.00 0.00 0.95 0.95 1.00
0.32 1.00 -0.36 0.28 0.90 -0.43 0.65 1.00 0.00 0.90 0.90 1.00
0.34 1.00 -0.32 0.36 0.84 -0.43 0.32 1.00 0.00 0.84 0.84 1.00
0.36 1.00 -0.28 0.44 0.77 -0.43 0.30 1.00 0.00 0.77 0.77 1.00
0.38 1.00 -0.24 0.52 0.68 -0.14 0.90 1.00 0.00 0.68 0.68 1.00
0.40 1.00 -0.20 0.60 0.59 -0.14 0.86 1.00 0.00 0.59 0.59 1.00
0.42 1.00 -0.16 0.68 0.48 -0.14 0.30 1.00 0.00 0.48 0.48 1.00
0.44 1.00 -0.12 0.76 0.37 -0.14 0.68 1.00 0.00 0.37 0.37 1.00
0.46 1.00 -0.08 0.84 0.25 -0.14 0.06 1.00 0.00 0.25 0.25 1.00
0.48 1.00 -0.04 0.92 0.13 -0.14 0.27 1.00 0.00 0.13 0.13 1.00
0.50 -1.00 0.00 1.00 -0.00 0.14 0.00 1.00 0.00 0.00 0.00 1.00
0.52 -1.00 0.04 0.92 -0.13 0.14 0.62 1.00 0.00 0.00 0.13 0.84
0.54 -1.00 0.08 0.84 -0.25 0.14 0.18 1.00 0.00 0.00 0.25 0.68
0.56 -1.00 0.12 0.76 -0.37 0.14 0.13 1.00 0.00 0.00 0.37 0.52
0.58 -1.00 0.16 0.68 -0.48 0.14 0.96 1.00 0.00 0.00 0.48 0.36
0.60 -1.00 0.20 0.60 -0.59 0.14 0.83 1.00 0.00 0.00 0.59 0.20
0.62 -1.00 0.24 0.52 -0.68 0.14 0.11 1.00 0.00 0.00 0.68 0.04
0.64 -1.00 0.28 0.44 -0.77 0.43 0.56 1.00 0.00 0.00 0.77 -0.12
0.66 -1.00 0.32 0.36 -0.84 0.43 0.44 1.00 0.00 0.00 0.84 -0.28
0.68 -1.00 0.36 0.28 -0.90 0.43 0.05 1.00 0.00 0.00 0.90 -0.44
0.70 -1.00 0.40 0.20 -0.95 0.43 0.35 1.00 0.00 0.00 0.95 -0.60
0.72 -1.00 0.44 0.12 -0.98 0.43 0.82 1.00 0.00 0.00 0.98 -0.76
0.74 -1.00 0.48 0.04 -1.00 0.43 0.71 1.00 0.00 0.00 1.00 -0.92
0.76 -1.00 0.52 -0.04 -1.00 0.71 0.26 1.00 0.00 0.00 1.00 -1.00
0.78 -1.00 0.56 -0.12 -0.98 0.71 0.79 1.00 0.00 0.00 0.98 -1.00
0.80 -1.00 0.60 -0.20 -0.95 0.71 0.63 1.00 0.00 0.00 0.95 -1.00
0.82 -1.00 0.64 -0.28 -0.90 0.71 0.54 1.00 0.00 0.00 0.90 -1.00
0.84 -1.00 0.68 -0.36 -0.84 0.71 0.34 1.00 0.00 0.00 0.84 -1.00
0.86 -1.00 0.72 -0.44 -0.77 0.71 0.59 1.00 0.00 0.00 0.77 -1.00
0.88 -1.00 0.76 -0.52 -0.68 1.00 0.43 1.00 0.00 0.00 0.68 -1.00
0.90 -1.00 0.80 -0.60 -0.59 1.00 0.24 1.00 0.00 0.00 0.59 -1.00
0.92 -1.00 0.84 -0.68 -0.48 1.00 0.94 1.00 0.00 0.00 0.48 -1.00
0.94 -1.00 0.88 -0.76 -0.37 1.00 0.54 1.00 0.00 0.00 0.37 -1.00
0.96 -1.00 0.92 -0.84 -0.25 1.00 0.77 1.00 0.00 0.00 0.25 -1.00
0.98 -1.00 0.96 -0.92 -0.13 1.00 0.43 1.00 0.00 0.00 0.13 -1.00
1.00 1.00 -1.00 -1.00 0.00 -1.00 0.16 1.00 0.00 0.00 0.00 -1.00
1.02 1.00 -0.96 -0.92 0.13 -1.00 0.44 1.00 0.00 0.13 0.13 -0.84
1.04 1.00 -0.92 -0.84 0.25 -1.00 0.76 1.00 0.00 0.25 0.25 -0.68
1.06 1.00 -0.88 -0.76 0.37 -1.00 0.54 1.00 0.00 0.37 0.37 -0.52
1.08 1.00 -0.84 -0.68 0.48 -1.00 0.52 1.00 0.00 0.48 0.48 -0.36
1.10 1.00 -0.80 -0.60 0.59 -1.00 0.56 1.00 0.00 0.59 0.59 -0.20
1.12 1.00 -0.76 -0.52 0.68 -1.00 0.25 1.00 0.00 0.68 0.68 -0.04
1.14 1.00 -0.72 -0.44 0.77 -0.71 0.80 1.00 0.00 0.77 0.77 0.12
1.16 1.00 -0.68 -0.36 0.84 -0.71 0.02 1.00 0.00 0.84 0.84 0.28
1.18 1.00 -0.64 -0.28 0.90 -0.71 0.85 1.00 0.00 0.90 0.90 0.44
1.20 1.00 -0.60 -0.20 0.95 -0.71 0.13 1.00 0.00 0.95 0.95 0.60
1.22 1.00 -0.56 -0.12 0.98 -0.71 0.05 1.00 0.00 0.98 0.98 0.76
1.24 1.00 -0.52 -0.04 1.00 -0.71 0.93 1.00 0.00 1.00 1.00 0.92
1.26 1.00 -0.48 0.04 1.00 -0.43 0.97 1.00 0.00 1.00 1.00 1.00
1.28 1.00 -0.44 0.12 0.98 -0.43 0.34 1.00 0.00 0.98 0.98 1.00
1.30 1.00 -0.40 0.20 0.95 -0.43 0.57 1.00 0.00 0.95 0.95 1.00
1.32 1.00 -0.36 0.28 0.90 -0.43 0.60 1.00 0.00 0.90 0.90 1.00
1.34 1.00 -0.32 0.36 0.84 -0.43 0.91 1.00 0.00 0.84 0.84 1.00
1.36 1.00 -0.28 0.44 0.77 -0.43 0.96 1.00 0.00 0.77 0.77 1.00
1.38 1.00 -0.24 0.52 0.68 -0.14 0.25 1.00 0.00 0.68 0.68 1.00
1.40 1.00 -0.20 0.60 0.59 -0.14 0.56 1.00 0.00 0.59 0.59 1.00
1.42 1.00 -0.16 0.68 0.48 -0.14 0.06 1.00 0.00 0.48 0.48 1.00
1.44 1.00 -0.12 0.76 0.37 -0.14 0.75 1.00 0.00 0.37 0.37 1.00
1.46 1.00 -0.08 0.84 0.25 -0.14 0.14 1.00 0.00 0.25 0.25 1.00
1.48 1.00 -0.04 0.92 0.13 -0.14 0.92 1.00 0.00 0.13 0.13 1.00
1.50 -1.00 0.00 1.00 -0.00 0.14 0.35 1.00 0.00 0.00 0.00 1.00
1.52 -1.00 0.04 0.92 -0.13 0.14 0.32 1.00 0.00 0.00 0.13 0.84
1.54 -1.00 0.08 0.84 -0.25 0.14 0.50 1.00 0.00 0.00 0.25 0.68
1.56 -1.00 0.12 0.76 -0.37 0.14 0.97 1.00 0.00 0.00 0.37 0.52
1.58 -1.00 0.16 0.68 -0.48 0.14 0.28 1.00 0.00 0.00 0.48 0.36
1.60 -1.00 0.20 0.60 -0.59 0.14 0.43 1.00 0.00 0.00 0.59 0.20
1.62 -1.00 0.24 0.52 -0.68 0.14 0.42 1.00 0.00 0.00 0.68 0.04
1.64 -1.00 0.28 0.44 -0.77 0.43 0.87 1.00 0.00 0.00 0.77 -0.12
1.66 -1.00 0.32 0.36 -0.84 0.43 0.20 1.00 0.00 0.00 0.84 -0.28
1.68 -1.00 0.36 0.28 -0.90 0.43 0.51 1.00 0.00 0.00 0.90 -0.44
1.70 -1.00 0.40 0.20 -0.95 0.43 0.34 1.00 0.00 0.00 0.95 -0.60
1.72 -1.00 0.44 0.12 -0.98 0.43 0.26 1.00 0.00 0.00 0.98 -0.76
1.74 -1.00 0.48 0.04 -1.00 0.43 0.04 1.00 0.00 0.00 1.00 -0.92
1.76 -1.00 0.52 -0.04 -1.00 0.71 0.04 1.00 0.00 0.00 1.00 -1.00
1.78 -1.00 0.56 -0.12 -0.98 0.71 0.60 1.00 0.00 0.00 0.98 -1.00
1.80 -1.00 0.60 -0.20 -0.95 0.71 0.82 1.00 0.00 0.00 0.95 -1.00
1.82 -1.00 0.64 -0.28 -0.90 0.71 0.23 1.00 0.00 0.00 0.90 -1.00
1.84 -1.00 0.68 -0.36 -0.84 0.71 0.93 1.00 0.00 0.00 0.84 -1.00
1.86 -1.00 0.72 -0.44 -0.77 0.71 0.31 1.00 0.00 0.00 0.77 -1.00
1.88 -1.00 0.76 -0.52 -0.68 1.00 0.50 1.00 0.00 0.00 0.68 -1.00
1.90 -1.00 0.80 -0.60 -0.59 1.00 0.08 1.00 0.00 0.00 0.59 -1.00
1.92 -1.00 0.84 -0.68 -0.48 1.00 0.47 1.00 0.00 0.00 0.48 -1.00
1.94 -1.00 0.88 -0.76 -0.37 1.00 0.30 1.00 0.00 0.00 0.37 -1.00
1.96 -1.00 0.92 -0.84 -0.25 1.00 0.63 1.00 0.00 0.00 0.25 -1.00
1.98 -1.00 0.96 -0.92 -0.13 1.00 0.59 1.00 0.00 0.00 0.13 -1.00
2.00 1.00 -1.00 -1.00 0.00 -1.00 0.36 1.00 0.00 0.00 0.00 -1.00
2.02 1.00 -0.96 -0.92 0.13 -1.00 0.53 1.00 0.00 0.13 0.13 -0.84
2.04 1.00 -0.92 -0.84 0.25 -1.00 0.87 1.00 0.00 0.25 0.25 -0.68
2.06 1.00 -0.88 -0.76 0.37 -1.00 0.18 1.00 0.00 0.37 0.37 -0.52
2.08 1.00 -0.84 -0.68 0.48 -1.00 0.24 1.00 0.00 0.48 0.48 -0.36
2.10 1.00 -0.80 -0.60 0.59 -1.00 0.27 1.00 0.00 0.59 0.59 -0.20
2.12 1.00 -0.76 -0.52 0.68 -1.00 0.31 1.00 0.00 0.68 0.68 -0.04
2.14 1.00 -0.72 -0.44 0.77 -0.71 0.06 1.00 0.00 0.77 0.77 0.12
2.16 1.00 -0.68 -0.36 0.84 -0.71 0.64 1.00 0.00 0.84 0.84 0.28
2.18 1.00 -0.64 -0.28 0.90 -0.71 0.30 1.00 0.00 0.90 0.90 0.44
2.20 1.00 -0.60 -0.20 0.95 -0.71 0.75 1.00 0.00 0.95 0.95 0.60
2.22 1.00 -0.56 -0.12 0.98 -0.71 0.87 1.00 0.00 0.98 0.98 0.76
2.24 1.00 -0.52 -0.04 1.00 -0.71 0.96 1.00 0.00 1.00 1.00 0.92
2.26 1.00 -0.48 0.04 1.00 -0.43 0.48 1.00 0.00 1.00 1.00 1.00
2.28 1.00 -0.44 0.12 0.98 -0.43 0.54 1.00 0.00 0.98 0.98 1.00
2.30 1.00 -0.40 0.20 0.95 -0.43 0.20 1.00 0.00 0.95 0.95 1.00
2.32 1.00 -0.36 0.28 0.90 -0.43 0.64 1.00 0.00 0.90 0.90 1.00
2.34 1.00 -0.32 0.36 0.84 -0.43 0.72 1.00 0.00 0.84 0.84 1.00
2.36 1.00 -0.28 0.44 0.77 -0.43 0.07 1.00 0.00 0.77 0.77 1.00
2.38 1.00 -0.24 0.52 0.68 -0.14 0.38 1.00 0.00 0.68 0.68 1.00
2.40 1.00 -0.20 0.60 0.59 -0.14 0.51 1.00 0.00 0.59 0.59 1.00
2.42 1.00 -0.16 0.68 0.48 -0.14 0.47 1.00 0.00 0.48 0.48 1.00
2.44 1.00 -0.12 0.76 0.37 -0.14 0.93 1.00 0.00 0.37 0.37 1.00
2.46 1.00 -0.08 0.84 0.25 -0.14 0.13 1.00 0.00 0.25 0.25 1.00
2.48 1.00 -0.04 0.92 0.13 -0.14 0.80 1.00 0.00 0.13 0.13 1.00
2.50 -1.00 0.00 1.00 -0.00 0.14 0.10 1.00 0.00 0.00 0.00 1.00
2.52 -1.00 0.04 0.92 -0.13 0.14 0.61 1.00 0.00 0.00 0.13 0.84
2.54 -1.00 0.08 0.84 -0.25 0.14 0.26 1.00 0.00 0.00 0.25 0.68
2.56 -1.00 0.12 0.76 -0.37 0.14 0.40 1.00 0.00 0.00 0.37 0.52
2.58 -1.00 0.16 0.68 -0.48 0.14 0.90 1.00 0.00 0.00 0.48 0.36
2.60 -1.00 0.20 0.60 -0.59 0.14 0.77 1.00 0.00 0.00 0.59 0.20
2.62 -1.00 0.24 0.52 -0.68 0.14 0.20 1.00 0.00 0.00 0.68 0.04
2.64 -1.00 0.28 0.44 -0.77 0.43 0.54 1.00 0.00 0.00 0.77 -0.12
2.66 -1.00 0.32 0.36 -0.84 0.43 0.88 1.00 0.00 0.00 0.84 -0.28
2.68 -1.00 0.36 0.28 -0.90 0.43 1.00 1.00 0.00 0.00 0.90 -0.44
2.70 -1.00 0.40 0.20 -0.95 0.43 0.38 1.00 0.00 0.00 0.95 -0.60
2.72 -1.00 0.44 0.12 -0.98 0.43 0.82 1.00 0.00 0.00 0.98 -0.76
2.74 -1.00 0.48 0.04 -1.00 0.43 0.92 1.00 0.00 0.00 1.00 -0.92
2.76 -1.00 0.52 -0.04 -1.00 0.71 0.88 1.00 0.00 0.00 1.00 -1.00
2.78 -1.00 0.56 -0.12 -0.98 0.71 0.90 1.00 0.00 0.00 0.98 -1.00
2.80 -1.00 0.60 -0.20 -0.95 0.71 0.48 1.00 0.00 0.00 0.95 -1.00
2.82 -1.00 0.64 -0.28 -0.90 0.71 0.57 1.00 0.00 0.00 0.90 -1.00
2.84 -1.00 0.68 -0.36 -0.84 0.71 0.60 1.00 0.00 0.00 0.84 -1.00
2.86 -1.00 0.72 -0.44 -0.77 0.71 0.49 1.00 0.00 0.00 0.77 -1.00
2.88 -1.00 0.76 -0.52 -0.68 1.00 0.60 1.00 0.00 0.00 0.68 -1.00
2.90 -1.00 0.80 -0.60 -0.59 1.00 0.79 1.00 0.00 0.00 0.59 -1.00
2.92 -1.00 0.84 -0.68 -0.48 1.00 0.35 1.00 0.00 0.00 0.48 -1.00
2.94 -1.00 0.88 -0.76 -0.37 1.00 0.39 1.00 0.00 0.00 0.37 -1.00
2.96 -1.00 0.92 -0.84 -0.25 1.00 0.85 1.00 0.00 0.00 0.25 -1.00
2.98 -1.00 0.96 -0.92 -0.13 1.00 0.84 1.00 0.00 0.00 0.13 -1.00
3.00 1.00 -1.00 -1.00 0.00 -1.00 0.30 1.00 0.00 0.00 0.00 -1.00
3.02 1.00 -0.96 -0.92 0.13 -1.00 0.76 1.00 0.00 0.13 0.13 -0.84
3.04 1.00 -0.92 -0.84 0.25 -1.00 0.07 1.00 0.00 0.25 0.25 -0.68
3.06 1.00 -0.88 -0.76 0.37 -1.00 0.09 1.00 0.00 0.37 0.37 -0.52
3.08 1.00 -0.84 -0.68 0.48 -1.00 0.22 1.00 0.00 0.48 0.48 -0.36
3.10 1.00 -0.80 -0.60 0.59 -1.00 0.86 1.00 0.00 0.59 0.59 -0.20
3.12 1.00 -0.76 -0.52 0.68 -1.00 0.04 1.00 0.00 0.68 0.68 -0.04
3.14 1.00 -0.72 -0.44 0.77 -0.71 0.80 1.00 0.00 0.77 0.77 0.12
3.16 1.00 -0.68 -0.36 0.84 -0.71 0.83 1.00 0.00 0.84 0.84 0.28
3.18 1.00 -0.64 -0.28 0.90 -0.71 0.23 1.00 0.00 0.90 0.90 0.44
3.20 1.00 -0.60 -0.20 0.95 -0.71 0.49 1.00 0.00 0.95 0.95 0.60
3.22 1.00 -0.56 -0.12 0.98 -0.71 0.77 1.00 0.00 0.98 0.98 0.76
3.24 1.00 -0.52 -0.04 1.00 -0.71 0.78 1.00 0.00 1.00 1.00 0.92
3.26 1.00 -0.48 0.04 1.00 -0.43 0.35 1.00 0.00 1.00 1.00 1.00
3.28 1.00 -0.44 0.12 0.98 -0.43 0.99 1.00 0.00 0.98 0.98 1.00
3.30 1.00 -0.40 0.20 0.95 -0.43 0.14 1.00 0.00 0.95 0.95 1.00
3.32 1.00 -0.36 0.28 0.90 -0.43 0.05 1.00 0.00 0.90 0.90 1.00
3.34 1.00 -0.32 0.36 0.84 -0.43 0.70 1.00 0.00 0.84 0.84 1.00
3.36 1.00 -0.28 0.44 0.77 -0.43 0.82 1.00 0.00 0.77 0.77 1.00
3.38 1.00 -0.24 0.52 0.68 -0.14 0.62 1.00 0.00 0.68 0.68 1.00
3.40 1.00 -0.20 0.60 0.59 -0.14 0.01 1.00 0.00 0.59 0.59 1.00
3.42 1.00 -0.16 0.68 0.48 -0.14 0.69 1.00 0.00 0.48 0.48 1.00
3.44 1.00 -0.12 0.76 0.37 -0.14 0.19 1.00 0.00 0.37 0.37 1.00
3.46 1.00 -0.08 0.84 0.25 -0.14 0.39 1.00 0.00 0.25 0.25 1.00
3.48 1.00 -0.04 0.92 0.13 -0.14 0.39 1.00 0.00 0.13 0.13 1.00
3.50 -1.00 0.00 1.00 -0.00 0.14 0.46 1.00 0.00 0.00 0.00 1.00
3.52 -1.00 0.04 0.92 -0.13 0.14 0.75 1.00 0.00 0.00 0.13 0.84
3.54 -1.00 0.08 0.84 -0.25 0.14 0.21 1.00 0.00 0.00 0.25 0.68
3.56 -1.00 0.12 0.76 -0.37 0.14 0.85 1.00 0.00 0.00 0.37 0.52
3.58 -1.00 0.16 0.68 -0.48 0.14 0.92 1.00 0.00 0.00 0.48 0.36
3.60 -1.00 0.20 0.60 -0.59 0.14 0.78 1.00 0.00 0.00 0.59 0.20
3.62 -1.00 0.24 0.52 -0.68 0.14 0.41 1.00 0.00 0.00 0.68 0.04
3.64 -1.00 0.28 0.44 -0.77 0.43 0.90 1.00 0.00 0.00 0.77 -0.12
3.66 -1.00 0.32 0.36 -0.84 0.43 0.71 1.00 0.00 0.00 0.84 -0.28
3.68 -1.00 0.36 0.28 -0.90 0.43 0.94 1.00 0.00 0.00 0.90 -0.44
3.70 -1.00 0.40 0.20 -0.95 0.43 0.92 1.00 0.00 0.00 0.95 -0.60
3.72 -1.00 0.44 0.12 -0.98 0.43 0.91 1.00 0.00 0.00 0.98 -0.76
3.74 -1.00 0.48 0.04 -1.00 0.43 0.79 1.00 0.00 0.00 1.00 -0.92
3.76 -1.00 0.52 -0.04 -1.00 0.71 0.64 1.00 0.00 0.00 1.00 -1.00
3.78 -1.00 0.56 -0.12 -0.98 0.71 0.08 1.00 0.00 0.00 0.98 -1.00
3.80 -1.00 0.60 -0.20 -0.95 0.71 0.49 1.00 0.00 0.00 0.95 -1.00
3.82 -1.00 0.64 -0.28 -0.90 0.71 0.50 1.00 0.00 0.00 0.90 -1.00
3.84 -1.00 0.68 -0.36 -0.84 0.71 0.86 1.00 0.00 0.00 0.84 -1.00
3.86 -1.00 0.72 -0.44 -0.77 0.71 0.61 1.00 0.00 0.00 0.77 -1.00
3.88 -1.00 0.76 -0.52 -0.68 1.00 0.42 1.00 0.00 0.00 0.68 -1.00
3.90 -1.00 0.80 -0.60 -0.59 1.00 0.25 1.00 0.00 0.00 0.59 -1.00
3.92 -1.00 0.84 -0.68 -0.48 1.00 0.06 1.00 0.00 0.00 0.48 -1.00
3.94 -1.00 0.88 -0.76 -0.37 1.00 0.97 1.00 0.00 0.00 0.37 -1.00
3.96 -1.00 0.92 -0.84 -0.25 1.00 0.81 1.00 0.00 0.00 0.25 -1.00
3.98 -1.00 0.96 -0.92 -0.13 1.00 0.57 1.00 0.00 0.00 0.13 -1.00
done...

429
libraries/FunctionGenerator/examples/functionGeneratorPerformance/performance_0.3.0.txt Normal file
View File

@ -0,0 +1,429 @@
functionGeneratorPerformance.ino
FUNCTIONGENERATOR_LIB_VERSION: 0.3.0
indicative output Arduino UNO 1.8.19, 16 MHz.
| wave form name | usec | max calls/sec |
|:---------------|-------:|----------------:|
| square | 54.57 | 18325.49 |
| sawtooth | 61.69 | 16210.61 |
| triangle | 79.80 | 12531.96 |
| sinus | 166.38 | 6010.37 |
| stair | 80.86 | 12366.38 |
| random | 42.61 | 23466.69 |
| random_DC | 67.18 | 14885.12 |
| line | 0.76 | 1322751.37 |
| zero | 0.75 | 1324854.25 |
| sinusDiode | 169.93 | 5884.79 |
| sinusRectified | 169.49 | 5900.03 |
| trapezium1 | 100.98 | 9903.30 |
| trapezium2 | 143.98 | 6945.58 |
| heartBeat | 128.52 | 7780.77 |
| freeWave | 75.52 | 13241.31 |
t sqr saw tri sin str rnd line zero sinD sinR trap
-4.00 -1.00 1.00 -1.00 -0.00 1.00 0.50 1.00 0.00 0.00 0.00 -1.00
-3.98 1.00 -0.96 -0.92 0.13 -1.00 0.06 1.00 0.00 0.13 0.13 -1.00
-3.96 1.00 -0.92 -0.84 0.25 -1.00 0.34 1.00 0.00 0.25 0.25 -1.00
-3.94 1.00 -0.88 -0.76 0.37 -1.00 0.33 1.00 0.00 0.37 0.37 -1.00
-3.92 1.00 -0.84 -0.68 0.48 -1.00 0.95 1.00 0.00 0.48 0.48 -1.00
-3.90 1.00 -0.80 -0.60 0.59 -1.00 0.75 1.00 0.00 0.59 0.59 -1.00
-3.88 1.00 -0.76 -0.52 0.68 -1.00 0.20 1.00 0.00 0.68 0.68 -1.00
-3.86 1.00 -0.72 -0.44 0.77 -0.71 0.33 1.00 0.00 0.77 0.77 -1.00
-3.84 1.00 -0.68 -0.36 0.84 -0.71 0.25 1.00 0.00 0.84 0.84 -1.00
-3.82 1.00 -0.64 -0.28 0.90 -0.71 0.39 1.00 0.00 0.90 0.90 -1.00
-3.80 1.00 -0.60 -0.20 0.95 -0.71 0.42 1.00 0.00 0.95 0.95 -1.00
-3.78 1.00 -0.56 -0.12 0.98 -0.71 0.95 1.00 0.00 0.98 0.98 -1.00
-3.76 1.00 -0.52 -0.04 1.00 -0.71 0.56 1.00 0.00 1.00 1.00 -1.00
-3.74 1.00 -0.48 0.04 1.00 -0.43 0.64 1.00 0.00 1.00 1.00 -0.92
-3.72 1.00 -0.44 0.12 0.98 -0.43 0.17 1.00 0.00 0.98 0.98 -0.76
-3.70 1.00 -0.40 0.20 0.95 -0.43 0.78 1.00 0.00 0.95 0.95 -0.60
-3.68 1.00 -0.36 0.28 0.90 -0.43 0.02 1.00 0.00 0.90 0.90 -0.44
-3.66 1.00 -0.32 0.36 0.84 -0.43 0.31 1.00 0.00 0.84 0.84 -0.28
-3.64 1.00 -0.28 0.44 0.77 -0.43 0.49 1.00 0.00 0.77 0.77 -0.12
-3.62 1.00 -0.24 0.52 0.68 -0.14 0.09 1.00 0.00 0.68 0.68 0.04
-3.60 1.00 -0.20 0.60 0.59 -0.14 0.21 1.00 0.00 0.59 0.59 0.20
-3.58 1.00 -0.16 0.68 0.48 -0.14 0.82 1.00 0.00 0.48 0.48 0.36
-3.56 1.00 -0.12 0.76 0.37 -0.14 0.51 1.00 0.00 0.37 0.37 0.52
-3.54 1.00 -0.08 0.84 0.25 -0.14 0.74 1.00 0.00 0.25 0.25 0.68
-3.52 1.00 -0.04 0.92 0.13 -0.14 0.20 1.00 0.00 0.13 0.13 0.84
-3.50 1.00 0.00 1.00 0.00 -0.14 0.27 1.00 0.00 0.00 0.00 1.00
-3.48 -1.00 0.04 0.92 -0.13 0.14 0.15 1.00 0.00 0.00 0.13 1.00
-3.46 -1.00 0.08 0.84 -0.25 0.14 0.67 1.00 0.00 0.00 0.25 1.00
-3.44 -1.00 0.12 0.76 -0.37 0.14 0.54 1.00 0.00 0.00 0.37 1.00
-3.42 -1.00 0.16 0.68 -0.48 0.14 0.44 1.00 0.00 0.00 0.48 1.00
-3.40 -1.00 0.20 0.60 -0.59 0.14 0.85 1.00 0.00 0.00 0.59 1.00
-3.38 -1.00 0.24 0.52 -0.68 0.14 0.90 1.00 0.00 0.00 0.68 1.00
-3.36 -1.00 0.28 0.44 -0.77 0.43 0.43 1.00 0.00 0.00 0.77 1.00
-3.34 -1.00 0.32 0.36 -0.84 0.43 0.11 1.00 0.00 0.00 0.84 1.00
-3.32 -1.00 0.36 0.28 -0.90 0.43 0.91 1.00 0.00 0.00 0.90 1.00
-3.30 -1.00 0.40 0.20 -0.95 0.43 0.79 1.00 0.00 0.00 0.95 1.00
-3.28 -1.00 0.44 0.12 -0.98 0.43 0.17 1.00 0.00 0.00 0.98 1.00
-3.26 -1.00 0.48 0.04 -1.00 0.43 0.72 1.00 0.00 0.00 1.00 1.00
-3.24 -1.00 0.52 -0.04 -1.00 0.71 0.77 1.00 0.00 0.00 1.00 0.92
-3.22 -1.00 0.56 -0.12 -0.98 0.71 0.86 1.00 0.00 0.00 0.98 0.76
-3.20 -1.00 0.60 -0.20 -0.95 0.71 0.50 1.00 0.00 0.00 0.95 0.60
-3.18 -1.00 0.64 -0.28 -0.90 0.71 0.42 1.00 0.00 0.00 0.90 0.44
-3.16 -1.00 0.68 -0.36 -0.84 0.71 0.73 1.00 0.00 0.00 0.84 0.28
-3.14 -1.00 0.72 -0.44 -0.77 0.71 0.01 1.00 0.00 0.00 0.77 0.12
-3.12 -1.00 0.76 -0.52 -0.68 1.00 0.52 1.00 0.00 0.00 0.68 -0.04
-3.10 -1.00 0.80 -0.60 -0.59 1.00 0.72 1.00 0.00 0.00 0.59 -0.20
-3.08 -1.00 0.84 -0.68 -0.48 1.00 0.61 1.00 0.00 0.00 0.48 -0.36
-3.06 -1.00 0.88 -0.76 -0.37 1.00 0.41 1.00 0.00 0.00 0.37 -0.52
-3.04 -1.00 0.92 -0.84 -0.25 1.00 0.68 1.00 0.00 0.00 0.25 -0.68
-3.02 -1.00 0.96 -0.92 -0.13 1.00 0.34 1.00 0.00 0.00 0.13 -0.84
-3.00 -1.00 1.00 -1.00 -0.00 1.00 0.90 1.00 0.00 0.00 0.00 -1.00
-2.98 1.00 -0.96 -0.92 0.13 -1.00 0.43 1.00 0.00 0.13 0.13 -1.00
-2.96 1.00 -0.92 -0.84 0.25 -1.00 0.47 1.00 0.00 0.25 0.25 -1.00
-2.94 1.00 -0.88 -0.76 0.37 -1.00 0.51 1.00 0.00 0.37 0.37 -1.00
-2.92 1.00 -0.84 -0.68 0.48 -1.00 0.29 1.00 0.00 0.48 0.48 -1.00
-2.90 1.00 -0.80 -0.60 0.59 -1.00 0.42 1.00 0.00 0.59 0.59 -1.00
-2.88 1.00 -0.76 -0.52 0.68 -1.00 0.02 1.00 0.00 0.68 0.68 -1.00
-2.86 1.00 -0.72 -0.44 0.77 -0.71 0.91 1.00 0.00 0.77 0.77 -1.00
-2.84 1.00 -0.68 -0.36 0.84 -0.71 0.00 1.00 0.00 0.84 0.84 -1.00
-2.82 1.00 -0.64 -0.28 0.90 -0.71 0.22 1.00 0.00 0.90 0.90 -1.00
-2.80 1.00 -0.60 -0.20 0.95 -0.71 0.55 1.00 0.00 0.95 0.95 -1.00
-2.78 1.00 -0.56 -0.12 0.98 -0.71 0.96 1.00 0.00 0.98 0.98 -1.00
-2.76 1.00 -0.52 -0.04 1.00 -0.71 0.30 1.00 0.00 1.00 1.00 -1.00
-2.74 1.00 -0.48 0.04 1.00 -0.43 0.19 1.00 0.00 1.00 1.00 -0.92
-2.72 1.00 -0.44 0.12 0.98 -0.43 0.62 1.00 0.00 0.98 0.98 -0.76
-2.70 1.00 -0.40 0.20 0.95 -0.43 0.61 1.00 0.00 0.95 0.95 -0.60
-2.68 1.00 -0.36 0.28 0.90 -0.43 0.28 1.00 0.00 0.90 0.90 -0.44
-2.66 1.00 -0.32 0.36 0.84 -0.43 0.85 1.00 0.00 0.84 0.84 -0.28
-2.64 1.00 -0.28 0.44 0.77 -0.43 0.22 1.00 0.00 0.77 0.77 -0.12
-2.62 1.00 -0.24 0.52 0.68 -0.14 0.66 1.00 0.00 0.68 0.68 0.04
-2.60 1.00 -0.20 0.60 0.59 -0.14 0.62 1.00 0.00 0.59 0.59 0.20
-2.58 1.00 -0.16 0.68 0.48 -0.14 0.30 1.00 0.00 0.48 0.48 0.36
-2.56 1.00 -0.12 0.76 0.37 -0.14 0.38 1.00 0.00 0.37 0.37 0.52
-2.54 1.00 -0.08 0.84 0.25 -0.14 0.00 1.00 0.00 0.25 0.25 0.68
-2.52 1.00 -0.04 0.92 0.13 -0.14 0.09 1.00 0.00 0.13 0.13 0.84
-2.50 1.00 0.00 1.00 0.00 -0.14 0.56 1.00 0.00 0.00 0.00 1.00
-2.48 -1.00 0.04 0.92 -0.13 0.14 0.67 1.00 0.00 0.00 0.13 1.00
-2.46 -1.00 0.08 0.84 -0.25 0.14 0.66 1.00 0.00 0.00 0.25 1.00
-2.44 -1.00 0.12 0.76 -0.37 0.14 0.15 1.00 0.00 0.00 0.37 1.00
-2.42 -1.00 0.16 0.68 -0.48 0.14 0.71 1.00 0.00 0.00 0.48 1.00
-2.40 -1.00 0.20 0.60 -0.59 0.14 0.75 1.00 0.00 0.00 0.59 1.00
-2.38 -1.00 0.24 0.52 -0.68 0.14 0.13 1.00 0.00 0.00 0.68 1.00
-2.36 -1.00 0.28 0.44 -0.77 0.43 0.99 1.00 0.00 0.00 0.77 1.00
-2.34 -1.00 0.32 0.36 -0.84 0.43 0.01 1.00 0.00 0.00 0.84 1.00
-2.32 -1.00 0.36 0.28 -0.90 0.43 0.92 1.00 0.00 0.00 0.90 1.00
-2.30 -1.00 0.40 0.20 -0.95 0.43 0.92 1.00 0.00 0.00 0.95 1.00
-2.28 -1.00 0.44 0.12 -0.98 0.43 0.38 1.00 0.00 0.00 0.98 1.00
-2.26 -1.00 0.48 0.04 -1.00 0.43 0.87 1.00 0.00 0.00 1.00 1.00
-2.24 -1.00 0.52 -0.04 -1.00 0.71 0.42 1.00 0.00 0.00 1.00 0.92
-2.22 -1.00 0.56 -0.12 -0.98 0.71 0.88 1.00 0.00 0.00 0.98 0.76
-2.20 -1.00 0.60 -0.20 -0.95 0.71 0.71 1.00 0.00 0.00 0.95 0.60
-2.18 -1.00 0.64 -0.28 -0.90 0.71 0.97 1.00 0.00 0.00 0.90 0.44
-2.16 -1.00 0.68 -0.36 -0.84 0.71 0.27 1.00 0.00 0.00 0.84 0.28
-2.14 -1.00 0.72 -0.44 -0.77 0.71 0.94 1.00 0.00 0.00 0.77 0.12
-2.12 -1.00 0.76 -0.52 -0.68 1.00 0.92 1.00 0.00 0.00 0.68 -0.04
-2.10 -1.00 0.80 -0.60 -0.59 1.00 0.02 1.00 0.00 0.00 0.59 -0.20
-2.08 -1.00 0.84 -0.68 -0.48 1.00 0.26 1.00 0.00 0.00 0.48 -0.36
-2.06 -1.00 0.88 -0.76 -0.37 1.00 0.54 1.00 0.00 0.00 0.37 -0.52
-2.04 -1.00 0.92 -0.84 -0.25 1.00 0.93 1.00 0.00 0.00 0.25 -0.68
-2.02 -1.00 0.96 -0.92 -0.13 1.00 0.25 1.00 0.00 0.00 0.13 -0.84
-2.00 -1.00 1.00 -1.00 -0.00 1.00 0.77 1.00 0.00 0.00 0.00 -1.00
-1.98 1.00 -0.96 -0.92 0.13 -1.00 0.71 1.00 0.00 0.13 0.13 -1.00
-1.96 1.00 -0.92 -0.84 0.25 -1.00 0.86 1.00 0.00 0.25 0.25 -1.00
-1.94 1.00 -0.88 -0.76 0.37 -1.00 0.15 1.00 0.00 0.37 0.37 -1.00
-1.92 1.00 -0.84 -0.68 0.48 -1.00 0.80 1.00 0.00 0.48 0.48 -1.00
-1.90 1.00 -0.80 -0.60 0.59 -1.00 0.17 1.00 0.00 0.59 0.59 -1.00
-1.88 1.00 -0.76 -0.52 0.68 -1.00 0.18 1.00 0.00 0.68 0.68 -1.00
-1.86 1.00 -0.72 -0.44 0.77 -0.71 0.54 1.00 0.00 0.77 0.77 -1.00
-1.84 1.00 -0.68 -0.36 0.84 -0.71 0.13 1.00 0.00 0.84 0.84 -1.00
-1.82 1.00 -0.64 -0.28 0.90 -0.71 0.71 1.00 0.00 0.90 0.90 -1.00
-1.80 1.00 -0.60 -0.20 0.95 -0.71 0.24 1.00 0.00 0.95 0.95 -1.00
-1.78 1.00 -0.56 -0.12 0.98 -0.71 0.73 1.00 0.00 0.98 0.98 -1.00
-1.76 1.00 -0.52 -0.04 1.00 -0.71 0.08 1.00 0.00 1.00 1.00 -1.00
-1.74 1.00 -0.48 0.04 1.00 -0.43 0.13 1.00 0.00 1.00 1.00 -0.92
-1.72 1.00 -0.44 0.12 0.98 -0.43 0.28 1.00 0.00 0.98 0.98 -0.76
-1.70 1.00 -0.40 0.20 0.95 -0.43 0.20 1.00 0.00 0.95 0.95 -0.60
-1.68 1.00 -0.36 0.28 0.90 -0.43 0.53 1.00 0.00 0.90 0.90 -0.44
-1.66 1.00 -0.32 0.36 0.84 -0.43 0.48 1.00 0.00 0.84 0.84 -0.28
-1.64 1.00 -0.28 0.44 0.77 -0.43 0.38 1.00 0.00 0.77 0.77 -0.12
-1.62 1.00 -0.24 0.52 0.68 -0.14 0.28 1.00 0.00 0.68 0.68 0.04
-1.60 1.00 -0.20 0.60 0.59 -0.14 0.06 1.00 0.00 0.59 0.59 0.20
-1.58 1.00 -0.16 0.68 0.48 -0.14 0.84 1.00 0.00 0.48 0.48 0.36
-1.56 1.00 -0.12 0.76 0.37 -0.14 0.35 1.00 0.00 0.37 0.37 0.52
-1.54 1.00 -0.08 0.84 0.25 -0.14 0.13 1.00 0.00 0.25 0.25 0.68
-1.52 1.00 -0.04 0.92 0.13 -0.14 0.51 1.00 0.00 0.13 0.13 0.84
-1.50 1.00 0.00 1.00 0.00 -0.14 0.37 1.00 0.00 0.00 0.00 1.00
-1.48 -1.00 0.04 0.92 -0.13 0.14 0.40 1.00 0.00 0.00 0.13 1.00
-1.46 -1.00 0.08 0.84 -0.25 0.14 0.26 1.00 0.00 0.00 0.25 1.00
-1.44 -1.00 0.12 0.76 -0.37 0.14 0.30 1.00 0.00 0.00 0.37 1.00
-1.42 -1.00 0.16 0.68 -0.48 0.14 0.76 1.00 0.00 0.00 0.48 1.00
-1.40 -1.00 0.20 0.60 -0.59 0.14 0.59 1.00 0.00 0.00 0.59 1.00
-1.38 -1.00 0.24 0.52 -0.68 0.14 0.32 1.00 0.00 0.00 0.68 1.00
-1.36 -1.00 0.28 0.44 -0.77 0.43 0.79 1.00 0.00 0.00 0.77 1.00
-1.34 -1.00 0.32 0.36 -0.84 0.43 0.63 1.00 0.00 0.00 0.84 1.00
-1.32 -1.00 0.36 0.28 -0.90 0.43 0.20 1.00 0.00 0.00 0.90 1.00
-1.30 -1.00 0.40 0.20 -0.95 0.43 0.83 1.00 0.00 0.00 0.95 1.00
-1.28 -1.00 0.44 0.12 -0.98 0.43 0.25 1.00 0.00 0.00 0.98 1.00
-1.26 -1.00 0.48 0.04 -1.00 0.43 0.36 1.00 0.00 0.00 1.00 1.00
-1.24 -1.00 0.52 -0.04 -1.00 0.71 0.25 1.00 0.00 0.00 1.00 0.92
-1.22 -1.00 0.56 -0.12 -0.98 0.71 0.25 1.00 0.00 0.00 0.98 0.76
-1.20 -1.00 0.60 -0.20 -0.95 0.71 0.18 1.00 0.00 0.00 0.95 0.60
-1.18 -1.00 0.64 -0.28 -0.90 0.71 0.30 1.00 0.00 0.00 0.90 0.44
-1.16 -1.00 0.68 -0.36 -0.84 0.71 0.09 1.00 0.00 0.00 0.84 0.28
-1.14 -1.00 0.72 -0.44 -0.77 0.71 0.32 1.00 0.00 0.00 0.77 0.12
-1.12 -1.00 0.76 -0.52 -0.68 1.00 0.69 1.00 0.00 0.00 0.68 -0.04
-1.10 -1.00 0.80 -0.60 -0.59 1.00 0.96 1.00 0.00 0.00 0.59 -0.20
-1.08 -1.00 0.84 -0.68 -0.48 1.00 0.28 1.00 0.00 0.00 0.48 -0.36
-1.06 -1.00 0.88 -0.76 -0.37 1.00 0.93 1.00 0.00 0.00 0.37 -0.52
-1.04 -1.00 0.92 -0.84 -0.25 1.00 0.21 1.00 0.00 0.00 0.25 -0.68
-1.02 -1.00 0.96 -0.92 -0.13 1.00 0.87 1.00 0.00 0.00 0.13 -0.84
-1.00 -1.00 1.00 -1.00 -0.00 1.00 0.57 1.00 0.00 0.00 0.00 -1.00
-0.98 1.00 -0.96 -0.92 0.13 -1.00 0.42 1.00 0.00 0.13 0.13 -1.00
-0.96 1.00 -0.92 -0.84 0.25 -1.00 0.81 1.00 0.00 0.25 0.25 -1.00
-0.94 1.00 -0.88 -0.76 0.37 -1.00 0.39 1.00 0.00 0.37 0.37 -1.00
-0.92 1.00 -0.84 -0.68 0.48 -1.00 0.71 1.00 0.00 0.48 0.48 -1.00
-0.90 1.00 -0.80 -0.60 0.59 -1.00 0.47 1.00 0.00 0.59 0.59 -1.00
-0.88 1.00 -0.76 -0.52 0.68 -1.00 0.56 1.00 0.00 0.68 0.68 -1.00
-0.86 1.00 -0.72 -0.44 0.77 -0.71 0.86 1.00 0.00 0.77 0.77 -1.00
-0.84 1.00 -0.68 -0.36 0.84 -0.71 0.87 1.00 0.00 0.84 0.84 -1.00
-0.82 1.00 -0.64 -0.28 0.90 -0.71 0.43 1.00 0.00 0.90 0.90 -1.00
-0.80 1.00 -0.60 -0.20 0.95 -0.71 0.42 1.00 0.00 0.95 0.95 -1.00
-0.78 1.00 -0.56 -0.12 0.98 -0.71 0.60 1.00 0.00 0.98 0.98 -1.00
-0.76 1.00 -0.52 -0.04 1.00 -0.71 0.13 1.00 0.00 1.00 1.00 -1.00
-0.74 1.00 -0.48 0.04 1.00 -0.43 0.04 1.00 0.00 1.00 1.00 -0.92
-0.72 1.00 -0.44 0.12 0.98 -0.43 0.30 1.00 0.00 0.98 0.98 -0.76
-0.70 1.00 -0.40 0.20 0.95 -0.43 0.84 1.00 0.00 0.95 0.95 -0.60
-0.68 1.00 -0.36 0.28 0.90 -0.43 0.52 1.00 0.00 0.90 0.90 -0.44
-0.66 1.00 -0.32 0.36 0.84 -0.43 0.25 1.00 0.00 0.84 0.84 -0.28
-0.64 1.00 -0.28 0.44 0.77 -0.43 0.04 1.00 0.00 0.77 0.77 -0.12
-0.62 1.00 -0.24 0.52 0.68 -0.14 0.38 1.00 0.00 0.68 0.68 0.04
-0.60 1.00 -0.20 0.60 0.59 -0.14 0.46 1.00 0.00 0.59 0.59 0.20
-0.58 1.00 -0.16 0.68 0.48 -0.14 0.66 1.00 0.00 0.48 0.48 0.36
-0.56 1.00 -0.12 0.76 0.37 -0.14 0.55 1.00 0.00 0.37 0.37 0.52
-0.54 1.00 -0.08 0.84 0.25 -0.14 0.84 1.00 0.00 0.25 0.25 0.68
-0.52 1.00 -0.04 0.92 0.13 -0.14 0.66 1.00 0.00 0.13 0.13 0.84
-0.50 1.00 0.00 1.00 0.00 -0.14 0.97 1.00 0.00 0.00 0.00 1.00
-0.48 -1.00 0.04 0.92 -0.13 0.14 0.94 1.00 0.00 0.00 0.13 1.00
-0.46 -1.00 0.08 0.84 -0.25 0.14 0.18 1.00 0.00 0.00 0.25 1.00
-0.44 -1.00 0.12 0.76 -0.37 0.14 0.27 1.00 0.00 0.00 0.37 1.00
-0.42 -1.00 0.16 0.68 -0.48 0.14 0.62 1.00 0.00 0.00 0.48 1.00
-0.40 -1.00 0.20 0.60 -0.59 0.14 0.22 1.00 0.00 0.00 0.59 1.00
-0.38 -1.00 0.24 0.52 -0.68 0.14 0.12 1.00 0.00 0.00 0.68 1.00
-0.36 -1.00 0.28 0.44 -0.77 0.43 0.51 1.00 0.00 0.00 0.77 1.00
-0.34 -1.00 0.32 0.36 -0.84 0.43 0.54 1.00 0.00 0.00 0.84 1.00
-0.32 -1.00 0.36 0.28 -0.90 0.43 0.36 1.00 0.00 0.00 0.90 1.00
-0.30 -1.00 0.40 0.20 -0.95 0.43 0.19 1.00 0.00 0.00 0.95 1.00
-0.28 -1.00 0.44 0.12 -0.98 0.43 0.73 1.00 0.00 0.00 0.98 1.00
-0.26 -1.00 0.48 0.04 -1.00 0.43 0.58 1.00 0.00 0.00 1.00 1.00
-0.24 -1.00 0.52 -0.04 -1.00 0.71 0.74 1.00 0.00 0.00 1.00 0.92
-0.22 -1.00 0.56 -0.12 -0.98 0.71 0.48 1.00 0.00 0.00 0.98 0.76
-0.20 -1.00 0.60 -0.20 -0.95 0.71 0.37 1.00 0.00 0.00 0.95 0.60
-0.18 -1.00 0.64 -0.28 -0.90 0.71 0.49 1.00 0.00 0.00 0.90 0.44
-0.16 -1.00 0.68 -0.36 -0.84 0.71 0.99 1.00 0.00 0.00 0.84 0.28
-0.14 -1.00 0.72 -0.44 -0.77 0.71 0.38 1.00 0.00 0.00 0.77 0.12
-0.12 -1.00 0.76 -0.52 -0.68 1.00 0.16 1.00 0.00 0.00 0.68 -0.04
-0.10 -1.00 0.80 -0.60 -0.59 1.00 0.20 1.00 0.00 0.00 0.59 -0.20
-0.08 -1.00 0.84 -0.68 -0.48 1.00 0.36 1.00 0.00 0.00 0.48 -0.36
-0.06 -1.00 0.88 -0.76 -0.37 1.00 0.93 1.00 0.00 0.00 0.37 -0.52
-0.04 -1.00 0.92 -0.84 -0.25 1.00 0.31 1.00 0.00 0.00 0.25 -0.68
-0.02 -1.00 0.96 -0.92 -0.13 1.00 0.71 1.00 0.00 0.00 0.13 -0.84
0.00 1.00 -1.00 -1.00 0.00 -1.00 0.35 1.00 0.00 0.00 0.00 -1.00
0.02 1.00 -0.96 -0.92 0.13 -1.00 0.58 1.00 0.00 0.13 0.13 -0.84
0.04 1.00 -0.92 -0.84 0.25 -1.00 0.38 1.00 0.00 0.25 0.25 -0.68
0.06 1.00 -0.88 -0.76 0.37 -1.00 0.45 1.00 0.00 0.37 0.37 -0.52
0.08 1.00 -0.84 -0.68 0.48 -1.00 0.96 1.00 0.00 0.48 0.48 -0.36
0.10 1.00 -0.80 -0.60 0.59 -1.00 0.00 1.00 0.00 0.59 0.59 -0.20
0.12 1.00 -0.76 -0.52 0.68 -1.00 0.59 1.00 0.00 0.68 0.68 -0.04
0.14 1.00 -0.72 -0.44 0.77 -0.71 0.09 1.00 0.00 0.77 0.77 0.12
0.16 1.00 -0.68 -0.36 0.84 -0.71 0.93 1.00 0.00 0.84 0.84 0.28
0.18 1.00 -0.64 -0.28 0.90 -0.71 0.17 1.00 0.00 0.90 0.90 0.44
0.20 1.00 -0.60 -0.20 0.95 -0.71 0.32 1.00 0.00 0.95 0.95 0.60
0.22 1.00 -0.56 -0.12 0.98 -0.71 0.18 1.00 0.00 0.98 0.98 0.76
0.24 1.00 -0.52 -0.04 1.00 -0.71 0.87 1.00 0.00 1.00 1.00 0.92
0.26 1.00 -0.48 0.04 1.00 -0.43 0.67 1.00 0.00 1.00 1.00 1.00
0.28 1.00 -0.44 0.12 0.98 -0.43 0.22 1.00 0.00 0.98 0.98 1.00
0.30 1.00 -0.40 0.20 0.95 -0.43 0.83 1.00 0.00 0.95 0.95 1.00
0.32 1.00 -0.36 0.28 0.90 -0.43 0.65 1.00 0.00 0.90 0.90 1.00
0.34 1.00 -0.32 0.36 0.84 -0.43 0.32 1.00 0.00 0.84 0.84 1.00
0.36 1.00 -0.28 0.44 0.77 -0.43 0.30 1.00 0.00 0.77 0.77 1.00
0.38 1.00 -0.24 0.52 0.68 -0.14 0.90 1.00 0.00 0.68 0.68 1.00
0.40 1.00 -0.20 0.60 0.59 -0.14 0.86 1.00 0.00 0.59 0.59 1.00
0.42 1.00 -0.16 0.68 0.48 -0.14 0.30 1.00 0.00 0.48 0.48 1.00
0.44 1.00 -0.12 0.76 0.37 -0.14 0.68 1.00 0.00 0.37 0.37 1.00
0.46 1.00 -0.08 0.84 0.25 -0.14 0.06 1.00 0.00 0.25 0.25 1.00
0.48 1.00 -0.04 0.92 0.13 -0.14 0.27 1.00 0.00 0.13 0.13 1.00
0.50 -1.00 0.00 1.00 -0.00 0.14 0.00 1.00 0.00 0.00 0.00 1.00
0.52 -1.00 0.04 0.92 -0.13 0.14 0.62 1.00 0.00 0.00 0.13 0.84
0.54 -1.00 0.08 0.84 -0.25 0.14 0.18 1.00 0.00 0.00 0.25 0.68
0.56 -1.00 0.12 0.76 -0.37 0.14 0.13 1.00 0.00 0.00 0.37 0.52
0.58 -1.00 0.16 0.68 -0.48 0.14 0.96 1.00 0.00 0.00 0.48 0.36
0.60 -1.00 0.20 0.60 -0.59 0.14 0.83 1.00 0.00 0.00 0.59 0.20
0.62 -1.00 0.24 0.52 -0.68 0.14 0.11 1.00 0.00 0.00 0.68 0.04
0.64 -1.00 0.28 0.44 -0.77 0.43 0.56 1.00 0.00 0.00 0.77 -0.12
0.66 -1.00 0.32 0.36 -0.84 0.43 0.44 1.00 0.00 0.00 0.84 -0.28
0.68 -1.00 0.36 0.28 -0.90 0.43 0.05 1.00 0.00 0.00 0.90 -0.44
0.70 -1.00 0.40 0.20 -0.95 0.43 0.35 1.00 0.00 0.00 0.95 -0.60
0.72 -1.00 0.44 0.12 -0.98 0.43 0.82 1.00 0.00 0.00 0.98 -0.76
0.74 -1.00 0.48 0.04 -1.00 0.43 0.71 1.00 0.00 0.00 1.00 -0.92
0.76 -1.00 0.52 -0.04 -1.00 0.71 0.26 1.00 0.00 0.00 1.00 -1.00
0.78 -1.00 0.56 -0.12 -0.98 0.71 0.79 1.00 0.00 0.00 0.98 -1.00
0.80 -1.00 0.60 -0.20 -0.95 0.71 0.63 1.00 0.00 0.00 0.95 -1.00
0.82 -1.00 0.64 -0.28 -0.90 0.71 0.54 1.00 0.00 0.00 0.90 -1.00
0.84 -1.00 0.68 -0.36 -0.84 0.71 0.34 1.00 0.00 0.00 0.84 -1.00
0.86 -1.00 0.72 -0.44 -0.77 0.71 0.59 1.00 0.00 0.00 0.77 -1.00
0.88 -1.00 0.76 -0.52 -0.68 1.00 0.43 1.00 0.00 0.00 0.68 -1.00
0.90 -1.00 0.80 -0.60 -0.59 1.00 0.24 1.00 0.00 0.00 0.59 -1.00
0.92 -1.00 0.84 -0.68 -0.48 1.00 0.94 1.00 0.00 0.00 0.48 -1.00
0.94 -1.00 0.88 -0.76 -0.37 1.00 0.54 1.00 0.00 0.00 0.37 -1.00
0.96 -1.00 0.92 -0.84 -0.25 1.00 0.77 1.00 0.00 0.00 0.25 -1.00
0.98 -1.00 0.96 -0.92 -0.13 1.00 0.43 1.00 0.00 0.00 0.13 -1.00
1.00 1.00 -1.00 -1.00 0.00 -1.00 0.16 1.00 0.00 0.00 0.00 -1.00
1.02 1.00 -0.96 -0.92 0.13 -1.00 0.44 1.00 0.00 0.13 0.13 -0.84
1.04 1.00 -0.92 -0.84 0.25 -1.00 0.76 1.00 0.00 0.25 0.25 -0.68
1.06 1.00 -0.88 -0.76 0.37 -1.00 0.54 1.00 0.00 0.37 0.37 -0.52
1.08 1.00 -0.84 -0.68 0.48 -1.00 0.52 1.00 0.00 0.48 0.48 -0.36
1.10 1.00 -0.80 -0.60 0.59 -1.00 0.56 1.00 0.00 0.59 0.59 -0.20
1.12 1.00 -0.76 -0.52 0.68 -1.00 0.25 1.00 0.00 0.68 0.68 -0.04
1.14 1.00 -0.72 -0.44 0.77 -0.71 0.80 1.00 0.00 0.77 0.77 0.12
1.16 1.00 -0.68 -0.36 0.84 -0.71 0.02 1.00 0.00 0.84 0.84 0.28
1.18 1.00 -0.64 -0.28 0.90 -0.71 0.85 1.00 0.00 0.90 0.90 0.44
1.20 1.00 -0.60 -0.20 0.95 -0.71 0.13 1.00 0.00 0.95 0.95 0.60
1.22 1.00 -0.56 -0.12 0.98 -0.71 0.05 1.00 0.00 0.98 0.98 0.76
1.24 1.00 -0.52 -0.04 1.00 -0.71 0.93 1.00 0.00 1.00 1.00 0.92
1.26 1.00 -0.48 0.04 1.00 -0.43 0.97 1.00 0.00 1.00 1.00 1.00
1.28 1.00 -0.44 0.12 0.98 -0.43 0.34 1.00 0.00 0.98 0.98 1.00
1.30 1.00 -0.40 0.20 0.95 -0.43 0.57 1.00 0.00 0.95 0.95 1.00
1.32 1.00 -0.36 0.28 0.90 -0.43 0.60 1.00 0.00 0.90 0.90 1.00
1.34 1.00 -0.32 0.36 0.84 -0.43 0.91 1.00 0.00 0.84 0.84 1.00
1.36 1.00 -0.28 0.44 0.77 -0.43 0.96 1.00 0.00 0.77 0.77 1.00
1.38 1.00 -0.24 0.52 0.68 -0.14 0.25 1.00 0.00 0.68 0.68 1.00
1.40 1.00 -0.20 0.60 0.59 -0.14 0.56 1.00 0.00 0.59 0.59 1.00
1.42 1.00 -0.16 0.68 0.48 -0.14 0.06 1.00 0.00 0.48 0.48 1.00
1.44 1.00 -0.12 0.76 0.37 -0.14 0.75 1.00 0.00 0.37 0.37 1.00
1.46 1.00 -0.08 0.84 0.25 -0.14 0.14 1.00 0.00 0.25 0.25 1.00
1.48 1.00 -0.04 0.92 0.13 -0.14 0.92 1.00 0.00 0.13 0.13 1.00
1.50 -1.00 0.00 1.00 -0.00 0.14 0.35 1.00 0.00 0.00 0.00 1.00
1.52 -1.00 0.04 0.92 -0.13 0.14 0.32 1.00 0.00 0.00 0.13 0.84
1.54 -1.00 0.08 0.84 -0.25 0.14 0.50 1.00 0.00 0.00 0.25 0.68
1.56 -1.00 0.12 0.76 -0.37 0.14 0.97 1.00 0.00 0.00 0.37 0.52
1.58 -1.00 0.16 0.68 -0.48 0.14 0.28 1.00 0.00 0.00 0.48 0.36
1.60 -1.00 0.20 0.60 -0.59 0.14 0.43 1.00 0.00 0.00 0.59 0.20
1.62 -1.00 0.24 0.52 -0.68 0.14 0.42 1.00 0.00 0.00 0.68 0.04
1.64 -1.00 0.28 0.44 -0.77 0.43 0.87 1.00 0.00 0.00 0.77 -0.12
1.66 -1.00 0.32 0.36 -0.84 0.43 0.20 1.00 0.00 0.00 0.84 -0.28
1.68 -1.00 0.36 0.28 -0.90 0.43 0.51 1.00 0.00 0.00 0.90 -0.44
1.70 -1.00 0.40 0.20 -0.95 0.43 0.34 1.00 0.00 0.00 0.95 -0.60
1.72 -1.00 0.44 0.12 -0.98 0.43 0.26 1.00 0.00 0.00 0.98 -0.76
1.74 -1.00 0.48 0.04 -1.00 0.43 0.04 1.00 0.00 0.00 1.00 -0.92
1.76 -1.00 0.52 -0.04 -1.00 0.71 0.04 1.00 0.00 0.00 1.00 -1.00
1.78 -1.00 0.56 -0.12 -0.98 0.71 0.60 1.00 0.00 0.00 0.98 -1.00
1.80 -1.00 0.60 -0.20 -0.95 0.71 0.82 1.00 0.00 0.00 0.95 -1.00
1.82 -1.00 0.64 -0.28 -0.90 0.71 0.23 1.00 0.00 0.00 0.90 -1.00
1.84 -1.00 0.68 -0.36 -0.84 0.71 0.93 1.00 0.00 0.00 0.84 -1.00
1.86 -1.00 0.72 -0.44 -0.77 0.71 0.31 1.00 0.00 0.00 0.77 -1.00
1.88 -1.00 0.76 -0.52 -0.68 1.00 0.50 1.00 0.00 0.00 0.68 -1.00
1.90 -1.00 0.80 -0.60 -0.59 1.00 0.08 1.00 0.00 0.00 0.59 -1.00
1.92 -1.00 0.84 -0.68 -0.48 1.00 0.47 1.00 0.00 0.00 0.48 -1.00
1.94 -1.00 0.88 -0.76 -0.37 1.00 0.30 1.00 0.00 0.00 0.37 -1.00
1.96 -1.00 0.92 -0.84 -0.25 1.00 0.63 1.00 0.00 0.00 0.25 -1.00
1.98 -1.00 0.96 -0.92 -0.13 1.00 0.59 1.00 0.00 0.00 0.13 -1.00
2.00 1.00 -1.00 -1.00 0.00 -1.00 0.36 1.00 0.00 0.00 0.00 -1.00
2.02 1.00 -0.96 -0.92 0.13 -1.00 0.53 1.00 0.00 0.13 0.13 -0.84
2.04 1.00 -0.92 -0.84 0.25 -1.00 0.87 1.00 0.00 0.25 0.25 -0.68
2.06 1.00 -0.88 -0.76 0.37 -1.00 0.18 1.00 0.00 0.37 0.37 -0.52
2.08 1.00 -0.84 -0.68 0.48 -1.00 0.24 1.00 0.00 0.48 0.48 -0.36
2.10 1.00 -0.80 -0.60 0.59 -1.00 0.27 1.00 0.00 0.59 0.59 -0.20
2.12 1.00 -0.76 -0.52 0.68 -1.00 0.31 1.00 0.00 0.68 0.68 -0.04
2.14 1.00 -0.72 -0.44 0.77 -0.71 0.06 1.00 0.00 0.77 0.77 0.12
2.16 1.00 -0.68 -0.36 0.84 -0.71 0.64 1.00 0.00 0.84 0.84 0.28
2.18 1.00 -0.64 -0.28 0.90 -0.71 0.30 1.00 0.00 0.90 0.90 0.44
2.20 1.00 -0.60 -0.20 0.95 -0.71 0.75 1.00 0.00 0.95 0.95 0.60
2.22 1.00 -0.56 -0.12 0.98 -0.71 0.87 1.00 0.00 0.98 0.98 0.76
2.24 1.00 -0.52 -0.04 1.00 -0.71 0.96 1.00 0.00 1.00 1.00 0.92
2.26 1.00 -0.48 0.04 1.00 -0.43 0.48 1.00 0.00 1.00 1.00 1.00
2.28 1.00 -0.44 0.12 0.98 -0.43 0.54 1.00 0.00 0.98 0.98 1.00
2.30 1.00 -0.40 0.20 0.95 -0.43 0.20 1.00 0.00 0.95 0.95 1.00
2.32 1.00 -0.36 0.28 0.90 -0.43 0.64 1.00 0.00 0.90 0.90 1.00
2.34 1.00 -0.32 0.36 0.84 -0.43 0.72 1.00 0.00 0.84 0.84 1.00
2.36 1.00 -0.28 0.44 0.77 -0.43 0.07 1.00 0.00 0.77 0.77 1.00
2.38 1.00 -0.24 0.52 0.68 -0.14 0.38 1.00 0.00 0.68 0.68 1.00
2.40 1.00 -0.20 0.60 0.59 -0.14 0.51 1.00 0.00 0.59 0.59 1.00
2.42 1.00 -0.16 0.68 0.48 -0.14 0.47 1.00 0.00 0.48 0.48 1.00
2.44 1.00 -0.12 0.76 0.37 -0.14 0.93 1.00 0.00 0.37 0.37 1.00
2.46 1.00 -0.08 0.84 0.25 -0.14 0.13 1.00 0.00 0.25 0.25 1.00
2.48 1.00 -0.04 0.92 0.13 -0.14 0.80 1.00 0.00 0.13 0.13 1.00
2.50 -1.00 0.00 1.00 -0.00 0.14 0.10 1.00 0.00 0.00 0.00 1.00
2.52 -1.00 0.04 0.92 -0.13 0.14 0.61 1.00 0.00 0.00 0.13 0.84
2.54 -1.00 0.08 0.84 -0.25 0.14 0.26 1.00 0.00 0.00 0.25 0.68
2.56 -1.00 0.12 0.76 -0.37 0.14 0.40 1.00 0.00 0.00 0.37 0.52
2.58 -1.00 0.16 0.68 -0.48 0.14 0.90 1.00 0.00 0.00 0.48 0.36
2.60 -1.00 0.20 0.60 -0.59 0.14 0.77 1.00 0.00 0.00 0.59 0.20
2.62 -1.00 0.24 0.52 -0.68 0.14 0.20 1.00 0.00 0.00 0.68 0.04
2.64 -1.00 0.28 0.44 -0.77 0.43 0.54 1.00 0.00 0.00 0.77 -0.12
2.66 -1.00 0.32 0.36 -0.84 0.43 0.88 1.00 0.00 0.00 0.84 -0.28
2.68 -1.00 0.36 0.28 -0.90 0.43 1.00 1.00 0.00 0.00 0.90 -0.44
2.70 -1.00 0.40 0.20 -0.95 0.43 0.38 1.00 0.00 0.00 0.95 -0.60
2.72 -1.00 0.44 0.12 -0.98 0.43 0.82 1.00 0.00 0.00 0.98 -0.76
2.74 -1.00 0.48 0.04 -1.00 0.43 0.92 1.00 0.00 0.00 1.00 -0.92
2.76 -1.00 0.52 -0.04 -1.00 0.71 0.88 1.00 0.00 0.00 1.00 -1.00
2.78 -1.00 0.56 -0.12 -0.98 0.71 0.90 1.00 0.00 0.00 0.98 -1.00
2.80 -1.00 0.60 -0.20 -0.95 0.71 0.48 1.00 0.00 0.00 0.95 -1.00
2.82 -1.00 0.64 -0.28 -0.90 0.71 0.57 1.00 0.00 0.00 0.90 -1.00
2.84 -1.00 0.68 -0.36 -0.84 0.71 0.60 1.00 0.00 0.00 0.84 -1.00
2.86 -1.00 0.72 -0.44 -0.77 0.71 0.49 1.00 0.00 0.00 0.77 -1.00
2.88 -1.00 0.76 -0.52 -0.68 1.00 0.60 1.00 0.00 0.00 0.68 -1.00
2.90 -1.00 0.80 -0.60 -0.59 1.00 0.79 1.00 0.00 0.00 0.59 -1.00
2.92 -1.00 0.84 -0.68 -0.48 1.00 0.35 1.00 0.00 0.00 0.48 -1.00
2.94 -1.00 0.88 -0.76 -0.37 1.00 0.39 1.00 0.00 0.00 0.37 -1.00
2.96 -1.00 0.92 -0.84 -0.25 1.00 0.85 1.00 0.00 0.00 0.25 -1.00
2.98 -1.00 0.96 -0.92 -0.13 1.00 0.84 1.00 0.00 0.00 0.13 -1.00
3.00 1.00 -1.00 -1.00 0.00 -1.00 0.30 1.00 0.00 0.00 0.00 -1.00
3.02 1.00 -0.96 -0.92 0.13 -1.00 0.76 1.00 0.00 0.13 0.13 -0.84
3.04 1.00 -0.92 -0.84 0.25 -1.00 0.07 1.00 0.00 0.25 0.25 -0.68
3.06 1.00 -0.88 -0.76 0.37 -1.00 0.09 1.00 0.00 0.37 0.37 -0.52
3.08 1.00 -0.84 -0.68 0.48 -1.00 0.22 1.00 0.00 0.48 0.48 -0.36
3.10 1.00 -0.80 -0.60 0.59 -1.00 0.86 1.00 0.00 0.59 0.59 -0.20
3.12 1.00 -0.76 -0.52 0.68 -1.00 0.04 1.00 0.00 0.68 0.68 -0.04
3.14 1.00 -0.72 -0.44 0.77 -0.71 0.80 1.00 0.00 0.77 0.77 0.12
3.16 1.00 -0.68 -0.36 0.84 -0.71 0.83 1.00 0.00 0.84 0.84 0.28
3.18 1.00 -0.64 -0.28 0.90 -0.71 0.23 1.00 0.00 0.90 0.90 0.44
3.20 1.00 -0.60 -0.20 0.95 -0.71 0.49 1.00 0.00 0.95 0.95 0.60
3.22 1.00 -0.56 -0.12 0.98 -0.71 0.77 1.00 0.00 0.98 0.98 0.76
3.24 1.00 -0.52 -0.04 1.00 -0.71 0.78 1.00 0.00 1.00 1.00 0.92
3.26 1.00 -0.48 0.04 1.00 -0.43 0.35 1.00 0.00 1.00 1.00 1.00
3.28 1.00 -0.44 0.12 0.98 -0.43 0.99 1.00 0.00 0.98 0.98 1.00
3.30 1.00 -0.40 0.20 0.95 -0.43 0.14 1.00 0.00 0.95 0.95 1.00
3.32 1.00 -0.36 0.28 0.90 -0.43 0.05 1.00 0.00 0.90 0.90 1.00
3.34 1.00 -0.32 0.36 0.84 -0.43 0.70 1.00 0.00 0.84 0.84 1.00
3.36 1.00 -0.28 0.44 0.77 -0.43 0.82 1.00 0.00 0.77 0.77 1.00
3.38 1.00 -0.24 0.52 0.68 -0.14 0.62 1.00 0.00 0.68 0.68 1.00
3.40 1.00 -0.20 0.60 0.59 -0.14 0.01 1.00 0.00 0.59 0.59 1.00
3.42 1.00 -0.16 0.68 0.48 -0.14 0.69 1.00 0.00 0.48 0.48 1.00
3.44 1.00 -0.12 0.76 0.37 -0.14 0.19 1.00 0.00 0.37 0.37 1.00
3.46 1.00 -0.08 0.84 0.25 -0.14 0.39 1.00 0.00 0.25 0.25 1.00
3.48 1.00 -0.04 0.92 0.13 -0.14 0.39 1.00 0.00 0.13 0.13 1.00
3.50 -1.00 0.00 1.00 -0.00 0.14 0.46 1.00 0.00 0.00 0.00 1.00
3.52 -1.00 0.04 0.92 -0.13 0.14 0.75 1.00 0.00 0.00 0.13 0.84
3.54 -1.00 0.08 0.84 -0.25 0.14 0.21 1.00 0.00 0.00 0.25 0.68
3.56 -1.00 0.12 0.76 -0.37 0.14 0.85 1.00 0.00 0.00 0.37 0.52
3.58 -1.00 0.16 0.68 -0.48 0.14 0.92 1.00 0.00 0.00 0.48 0.36
3.60 -1.00 0.20 0.60 -0.59 0.14 0.78 1.00 0.00 0.00 0.59 0.20
3.62 -1.00 0.24 0.52 -0.68 0.14 0.41 1.00 0.00 0.00 0.68 0.04
3.64 -1.00 0.28 0.44 -0.77 0.43 0.90 1.00 0.00 0.00 0.77 -0.12
3.66 -1.00 0.32 0.36 -0.84 0.43 0.71 1.00 0.00 0.00 0.84 -0.28
3.68 -1.00 0.36 0.28 -0.90 0.43 0.94 1.00 0.00 0.00 0.90 -0.44
3.70 -1.00 0.40 0.20 -0.95 0.43 0.92 1.00 0.00 0.00 0.95 -0.60
3.72 -1.00 0.44 0.12 -0.98 0.43 0.91 1.00 0.00 0.00 0.98 -0.76
3.74 -1.00 0.48 0.04 -1.00 0.43 0.79 1.00 0.00 0.00 1.00 -0.92
3.76 -1.00 0.52 -0.04 -1.00 0.71 0.64 1.00 0.00 0.00 1.00 -1.00
3.78 -1.00 0.56 -0.12 -0.98 0.71 0.08 1.00 0.00 0.00 0.98 -1.00
3.80 -1.00 0.60 -0.20 -0.95 0.71 0.49 1.00 0.00 0.00 0.95 -1.00
3.82 -1.00 0.64 -0.28 -0.90 0.71 0.50 1.00 0.00 0.00 0.90 -1.00
3.84 -1.00 0.68 -0.36 -0.84 0.71 0.86 1.00 0.00 0.00 0.84 -1.00
3.86 -1.00 0.72 -0.44 -0.77 0.71 0.61 1.00 0.00 0.00 0.77 -1.00
3.88 -1.00 0.76 -0.52 -0.68 1.00 0.42 1.00 0.00 0.00 0.68 -1.00
3.90 -1.00 0.80 -0.60 -0.59 1.00 0.25 1.00 0.00 0.00 0.59 -1.00
3.92 -1.00 0.84 -0.68 -0.48 1.00 0.06 1.00 0.00 0.00 0.48 -1.00
3.94 -1.00 0.88 -0.76 -0.37 1.00 0.97 1.00 0.00 0.00 0.37 -1.00
3.96 -1.00 0.92 -0.84 -0.25 1.00 0.81 1.00 0.00 0.00 0.25 -1.00
3.98 -1.00 0.96 -0.92 -0.13 1.00 0.57 1.00 0.00 0.00 0.13 -1.00
done...

41
libraries/FunctionGenerator/examples/functionGeneratorPlotter/functionGeneratorPlotter.ino
View File

@ -11,17 +11,26 @@
#include "functionGenerator.h"
funcgen gen;
funcgen gen2;
void setup()
{
Serial.begin(115200);
// Serial.print("Start functionGeneratorPerformance - LIB VERSION: ");
// Serial.println(__FILE__);
// Serial.print("FUNCTIONGENERATOR_LIB_VERSION: ");
// Serial.println(FUNCTIONGENERATOR_LIB_VERSION);
// Serial.println();
gen.setAmplitude(50);
gen.setFrequency(1);
gen.setDutyCycle(25);
gen.setAmplitude(80);
gen.setFrequency(65.0 / 60.0); // HB = BPM/60.0
gen.setDutyCycle(40);
gen2.setYShift(+20);
gen2.setAmplitude(80);
gen2.setFrequency(120.0 / 60.0); // HB = BPM/60.0
gen2.setDutyCycle(80);
gen2.setYShift(-80);
}
@ -34,20 +43,34 @@ void loop()
// Serial.print(t, 3);
// Serial.print("\t");
Serial.print(80);
Serial.print(100);
Serial.print("\t");
Serial.print(-80);
Serial.print("\t");
Serial.print(gen.square(t));
Serial.print(-100);
Serial.print("\t");
// Serial.print(gen.square(t));
// Serial.print("\t");
// Serial.print(gen.sawtooth(t, 0)); // up /| signal
// Serial.print("\t");
// Serial.print(gen.sawtooth(t, 1)); // down |\ signal
// Serial.print("\t");
Serial.print(gen.triangle(t));
// Serial.print(gen.triangle(t));
// Serial.print("\t");
// Serial.print(gen.sinus(t));
// Serial.print("\t");
// Serial.print(gen.sinusDiode(t));
// Serial.print("\t");
// Serial.print(gen.sinusRectified(t));
// Serial.print("\t");
// Serial.print(gen.trapezium1(t));
// Serial.print("\t");
// Serial.print(gen.trapezium2(t));
// Serial.print("\t");
Serial.print(gen.heartBeat(t));
Serial.print("\t");
Serial.print(gen2.heartBeat(t));
// Serial.print("\t");
// Serial.print(gen.freeWave(t, array));
// Serial.print("\t");
// Serial.print(gen.stair(t, 16, 0)); // step up
// Serial.print("\t");
// Serial.print(gen.stair(t, 16, 1)); // step down

36
libraries/FunctionGenerator/examples/generateFreeWave/generateFreeWave.ino Normal file
View File

@ -0,0 +1,36 @@
//
// FILE: generatorFreeWave.ino
// AUTHOR: Rob Tillaart
// PURPOSE: demo function generators
// URL: https://github.com/RobTillaart/FunctionGenerator
void setup()
{
Serial.begin(115200);
Serial.println(__FILE__);
Serial.println();
Serial.println();
Serial.println("int16_t arr[101] =\n{");
for (int i = 0; i < 101; i++)
{
// sin(t) + 0.25*sin(5t)
float f = sin(i * 0.01 * 2 * PI);
float g = sin(i * 0.05 * 2 * PI);
int16_t v = 8000 * (f + 0.25 * g);
Serial.print("");
Serial.print(v);
Serial.print(",");
if (i > 0 and i % 5 == 0) Serial.println();
}
Serial.println("};");
}
void loop()
{
}
// -- END OF FILE --

200
libraries/FunctionGenerator/functionGenerator.cpp
View File

@ -1,7 +1,7 @@
//
// FILE: functionGenerator.cpp
// AUTHOR: Rob Tillaart
// VERSION: 0.2.6
// VERSION: 0.3.0
// PURPOSE: wave form generating functions (use with care)
// URL: https://github.com/RobTillaart/FunctionGenerator
@ -240,7 +240,199 @@ float funcgen::random_DC()
}
/////////////////////////////////////////////////////////////
//
// EXPERIMENTAL 0.2.7
//
float funcgen::sinusDiode(float t)
{
float rv = sinus(t);
if (rv < _yShift) return _yShift;
return rv;
// float rv;
// t += _phase;
// rv = sin(t * _freq0);
// if (rv < 0) return _yShift;
// rv *= amplitude;
// rv += _yShift;
// return rv;
}
float funcgen::sinusRectified(float t)
{
// float rv = sinus(t);
// if (rv < _yShift) return _yShift - rv;
// return rv;
float rv;
t += _phase;
rv = _amplitude * sin(t * _freq0);
if (rv < 0) rv = -rv;
rv += _yShift;
return rv;
}
float funcgen::trapezium1(float t)
{
t += _phase + _period * _dutyCycle / 4; // zero point for t = 0
if (t < 0)
{
t = -t;
}
t = fmod(t, _period);
if (t < _period * 0.5 * _dutyCycle) // rising part
{
return _yShift + -_amplitude + 2 * _amplitude * (t * 2 / (_period * _dutyCycle));
}
else if (t < _period * 0.5) // high part
{
return _yShift + _amplitude;
}
else if (t < _period * (0.5 + 0.5 * _dutyCycle)) // falling part
{
return _yShift + _amplitude - 2 * _amplitude * ( (t * 2 - _period) / (_period * _dutyCycle));
}
else // low part
{
return _yShift + -_amplitude;
}
}
float funcgen::trapezium2(float t)
{
t += _phase + _period * _dutyCycle / 4; // zero point for t = 0
if (t < 0)
{
t = -t;
}
t = fmod(t, _period);
if (t < _period * 0.25) // rising part
{
return _yShift + -_amplitude + 2 * _amplitude * (t * 4 / _period);
}
else if (t < _period * (0.25 + 0.5 * _dutyCycle)) // high part
{
return _yShift + _amplitude;
}
else if (t < _period * (0.5 + 0.5 * _dutyCycle)) // falling part
{
return _yShift + _amplitude - 2 * _amplitude * ((t - _period * (0.25 + 0.5 * _dutyCycle)) * 4 / _period);
}
else // low part
{
return _yShift + -_amplitude;
}
}
/*
// no DC version (50%
float funcgen::trapezium(float t)
{
t += _phase;
if (t < 0)
{
t = -t;
}
t = fmod(t, _period);
if (t < _period * 0.25) // rising part
{
return -_amplitude + 2 * _amplitude * (t * 4 / _period);
}
else if (t < _period * 0.5) // high part
{
return _amplitude;
}
else if (t < _period * 0.75) // high part
{
return _amplitude - 2 * _amplitude * ((t - _period/2) * 4 / _period);
}
else // low part
{
return -_amplitude;
}
}
*/
//
// EXPERIMENTAL HEARTBEAT
// => setFrequency(72.0 / 60.0); // BPM/60 = BPS.
float funcgen::heartBeat(float t)
{
int16_t out[32] = {
0, 0, 1000, 2500,
1000, 1000, -50, 10000,
-2500, 2000, 2500, 3000,
3000, 2000, 0, 0,
0,0,0,0,
0,0,0,0,
0,0,0,0,
0,0,0,0,
};
// use duty cycle to determine zero level duration.
int pts = map(_dutyCycle * 100, 0, 100, 31, 15);
return freeWave(t, out, pts);
}
/*
// points need to be optimized,
// 0.2.7 uses 160 bytes for the two arrays.
// wrapper around freeWave?
float funcgen::heartBeat(float t)
{
// based upon MultiMap in[] array is normalized to 0.0 - 1.0
// Heart beat phase P Q R S T U
float in[21] = { 0.0, 0.07, 0.13, 0.20, 0.27, 0.33, 0.40, 0.46, 0.53, 0.60, 0.66, 0.73, 0.80, 0.86, 0.93, 1.00 };
float out[21] = { 0.0, 0.00, 0.10, 0.25, 0.10, 0.10, -0.05, 1.00, -0.25, 0.20, 0.25, 0.30, 0.30, 0.20, 0.00, 0.00 };
t += _phase;
t = fmod(t, _period);
// normalize t to 0.0 - 1.0
t *= _freq1;
// search interval
int idx = 0;
while (t > in[idx]) idx++;
if (t == in[idx]) return _yShift + _amplitude * out[idx];
idx--;
// interpolate.
float factor = (t - in[idx]) / (in[idx+1] - in[idx]);
return _yShift + _amplitude * (out[idx] + factor * (out[idx+1] - out[idx]));
}
*/
float funcgen::freeWave(float t, int16_t * arr, int16_t size)
{
t += _phase;
// normalize t to 0.0 - 1.0
t = fmod(t, _period);
t *= _freq1;
// search interval, as arr is based upon N equidistant points,
// we can easily calculate the points for direct access
float factor = t * size;
int idx = factor; // truncate to get index of output array.
factor = factor - idx; // remainder is interpolate factor.
// interpolate.
return _yShift + _amplitude * 1e-4 * (arr[idx] + factor * (arr[idx+1] - arr[idx]));
}
/////////////////////////////////////////////////////////////
//
// PRIVATE
//
// An example of a simple pseudo-random number generator is the
// Multiply-with-carry method invented by George Marsaglia.
// two initializers (not null)
@ -252,6 +444,7 @@ uint32_t funcgen::_random()
}
/////////////////////////////////////////////////////////////
//
// INTEGER VERSIONS FOR 8 BIT DAC
@ -356,6 +549,7 @@ float fgstr(float t, float period = 1.0, uint16_t steps = 8)
//
// FULL floatS ONES
//
// SAWTOOTH
float fgsaw(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0)
{
t += phase;
@ -370,6 +564,7 @@ float fgsaw(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.
}
// TRIANGLE
float fgtri(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0, float dutyCycle = 0.50)
{
t += phase;
@ -384,6 +579,7 @@ float fgtri(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.
}
// SQUARE
float fgsqr(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0, float dutyCycle = 0.50)
{
t += phase;
@ -400,6 +596,7 @@ float fgsqr(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.
}
// SINUS
float fgsin(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0)
{
t += phase;
@ -408,6 +605,7 @@ float fgsin(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.
}
// STAIR
float fgstr(float t, float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0, uint16_t steps = 8)
{
t += phase;

9
libraries/FunctionGenerator/keywords.txt
View File

@ -27,8 +27,17 @@ zero KEYWORD2
sawtooth KEYWORD2
triangle KEYWORD2
square KEYWORD2
sinus KEYWORD2
sinusDiode KEYWORD2
sinusRectified KEYWORD2
stair KEYWORD2
trapezium1 KEYWORD2
trapezium2 KEYWORD2
heartBeat KEYWORD2
freeWave KEYWORD2
random KEYWORD2
random_DC KEYWORD2

2
libraries/FunctionGenerator/library.json
View File

@ -15,7 +15,7 @@
"type": "git",
"url": "https://github.com/RobTillaart/FunctionGenerator"
},
"version": "0.2.6",
"version": "0.3.0",
"license": "MIT",
"frameworks": "*",
"platforms": "*",

2
libraries/FunctionGenerator/library.properties
View File

@ -1,5 +1,5 @@
name=FunctionGenerator
version=0.2.6
version=0.3.0
author=Rob Tillaart <rob.tillaart@gmail.com>
maintainer=Rob Tillaart <rob.tillaart@gmail.com>
sentence=Arduino library to generate wave forms (nummeric) for a DAC

128
libraries/FunctionGenerator/readme.md
View File

@ -27,10 +27,15 @@ In practice the generator is useful for low frequencies,
Note: this class generates float values, performance wise this can be optimized,
to achieve higher speeds at cost of accuracy / precision.
As always, feedback and ideas are welcome.
#### Performance
Indication of what performance can be expected (based upon 0.2.1 version).
### Performance
You always have to verify your own performance measurements to see if
your requirements are met by this library.
**Indication** of what performance can be expected (based upon 0.2.1 version).
Note that the values need to be transported to a DAC or serial port too.
Numbers based on performance example, for one single signal.
@ -72,14 +77,24 @@ have become slightly slower.
| Arduino UNO | 16 MHz | square | 57 | 1000 Hz |
| Arduino UNO | 16 MHz | random_DC | 68 | 500 Hz |
See **functionGeneratorPerformance.ino**
#### Accuracy
### Accuracy
If the time parameter **t** grows large, the internal math may have rounding
problems after some time. This can and will affect the quality of the output.
It is advised to reset **t** after a number (e.g. 100) full periods
Needs further investigations.
### Related
- https://github.com/RobTillaart/AD9833 hardware waveform generator.
- https://github.com/RobTillaart/AD985X hardware waveform generator.
- https://github.com/RobTillaart/functionGenerator software waveform generator.
- https://pages.mtu.edu/~suits/notefreqs.html frequency table for notes.
## Interface
@ -87,40 +102,42 @@ Needs further investigations.
#include "functionGenerator.h"
```
#### Constructor
### Constructor
- **funcgen(float period = 1.0, float amplitude = 1.0, float phase = 0.0, float yShift = 0.0)**
All parameters (except duty cycle) can be set in the constructor but also later in configuration.
Default dutyCycle is 50%.
#### Configuration
### Configuration
- **void setPeriod(float period = 1.0)** set the period of the wave in seconds.
- **void setPeriod(float period = 1.0)** set the period of the wave in seconds.
This is the inverse of the frequency.
- **float getPeriod()** returns the set period.
- **void setFrequency(float frequency = 1.0)** set the frequency of the wave in Hertz (1/s).
- **void setFrequency(float frequency = 1.0)** set the frequency of the wave in Hertz (1/s).
This is the inverse of the period.
- **float getFrequency()** returns the set frequency in Hertz.
- **void setAmplitude(float amplitude = 1.0)** sets the amplitude of the wave.
- **void setAmplitude(float amplitude = 1.0)** sets the amplitude of the wave.
The range is from **-amplitude** to **+amplitude**.
Setting the amplitude to 0 gives effectively a zero signal.
Setting the amplitude to a negative value effectively inverts the signal.
- **float getAmplitude()** returns the set amplitude.
- **void setPhase(float phase = 0.0)** shifts the phase of the wave.
- **void setPhase(float phase = 0.0)** shifts the phase of the wave.
Will only be noticeable when compared with other waves.
Phase is also known as the X- or horizontal shift.
- **float getPhase()** returns the set phase.
- **void setYShift(float yShift = 0.0)** sets an Y-shift or vertical offset in amplitude.
- **void setYShift(float yShift = 0.0)** sets an Y-shift or vertical offset in amplitude.
This allows to set e.g. the zero level.
- **float getYShift()** returns the set Y-shift.
- **void setDutyCycle(float percentage = 100)** sets the duty cycle of the signal.
- **void setDutyCycle(float percentage = 100)** sets the duty cycle of the signal.
Experimental, not all waveforms have a duty cycle or interpret it differently, see below.
Duty cycle must be between 0 and 100% and will be clipped otherwise.
- **float getDutyCycle()** returns the set duty cycle.
- **void setRandomSeed(uint32_t a, uint32_t b = 314159265)** sets the initial seeds for the
- **float getDutyCycle()** returns the set (clipped) duty cycle.
- **void setRandomSeed(uint32_t a, uint32_t b = 314159265)** sets the initial seeds for the
(Marsaglia) random number generator. The first is mandatory, the second is optional.
#### Wave forms
### Wave forms
The variable t == time in seconds.
@ -129,11 +146,12 @@ The variable t == time in seconds.
- mode == 1 ==> sawtooth |\\. Effectively equals inverting the amplitude.
- **float triangle(float t)** triangle form, duty cycle default 50%.
- **float square(float t)** square wave with duty cycle default 50%.
- **float sinus(float t)** sinus wave, has no duty cycle.
- **float sinus(float t)** sinus wave, has no duty cycle.
- **float stair(float t, uint16_t steps = 8, uint8_t mode = 0)** defaults to 8 steps up.
- mode = 0 ==> steps up
- mode = 1 ==> steps down. Effectively equals inverting the amplitude.
- **float random()** random noise generation.
- **float random()** random noise generation between 0 and amplitude.
Uses Marsaglia random generator.
- **float line()** constant voltage line.
Height depends on the YShift and amplitude.
- **float zero()** constant zero.
@ -142,7 +160,29 @@ The functions **line()** and **zero()** can be used to drive a constant voltage
from a DAC and can be used to calibrate the generator / DAC combination.
#### Duty Cycle
Experimental 0.2.7
- **float sinusDiode(float t)** sinus wave, only positive pulses.
(better name welcome).
- **float sinusRectified(float t)** sinus wave, with "abs(negative pulses)".
(better name welcome).
- **float trapezium1(float t)** trapezium wave.
DutyCycle changes steepness of the falling and rising edge.
The wave changes from a square wave, via trapezium to a triangle wave.
- **float trapezium2(float t)** trapezium wave.
DutyCycle changes duration HIGH vs LOW, wave stays trapezium like.
Note at 50% DC the two trapezium functions are identical.
- **float heartBeat(float t)** simplified heartbeat wave.
To get a regular BPM heartbeat one should **setFrequency(BPM/60.0)** e.g 72/60 = 1.2.
- **float freeWave(float t, int16_t arr, int16_t N)** define a free wave form.
It uses an array of **N+1** values, dividing a full period in **N** equidistant steps.
The last value should equal the first value to have a smooth transition.
The values of the array normally vary between -10000 and +10000 to manage
the set the relative amplitude in small steps.
These are scaled back to -1.0 to +1.0 times the amplitude.
### Duty Cycle
Since 0.2.5 the library has **experimental** support for duty cycle.
The meaning of duty cycle differs per wave form.
@ -160,7 +200,16 @@ with respect to previous value.
Implemented as a weighed average between new and previous value.
Made a separate function as handling the duty cycle slows performance substantial.
Initial starts at zero and can be adjusted with **YShift()**.
- **float trapezium1(float t)** The duty cycle changes the steepness of the rising
and falling edges. This changes the form from square wave to trapezium to triangle.
The length of the HIGH LOW level go from 0 to half a period.
- **float trapezium2(float t)** The duty cycle determines the length of the HIGH level,
which is 0 for 0% DC and half a period for 100% DC.
The rising and falling edges stay same.
- **float heartBeat(float t)** The duty cycle determines the part of the period
that the signal ~zero.
### No duty cycle
The other functions need to be investigated what duty cycle means.
Current ideas that are **NOT** implemented:
@ -171,41 +220,52 @@ Think of it as the halve of the triangle wave.
- **stair()** like sawtooth??
- **line()** has no period so does not make sense (yet).
- **zero()** has no period so does not make sense (yet).
Feedback and ideas are welcome.
- **float sinusDiode(float t)**
- **float sinusRectified(float t)**
- **float freeWave(float t, int16_t arr, int16_t N)**
## Future
#### Must
- documentation
- quality of signals - after substantial time t
- max freq per wave form etc.
Should this be in the library?
- improve documentation
- reorganize
- section per function might be better.
#### Should
- smart reseed needed for random().
- initialize random generator with compile time.
- initialize random generator with compile file + date + time.
- use function values for seed bits.
- stand-alone functions in separate .h
- clean up code
#### Could
- waves
- trapezium wave (could merge square and triangle and sawtooth)
- white noise, pink noise etc.
- RC function curve.
- ASDR wave
- https://en.wikipedia.org/wiki/Envelope_(music)
- **float ADSR(float t, float A, float D, float S, float R)**
- ADSR are percentages, A + D + R < 1.0
- S = % of amplitude.
- external clock to synchronize two or more software function generators.
- stand-alone functions in separate .h
- check for synergy with https://github.com/RobTillaart/AD985X
- investigate performance.
- algorithms for DAC specific gains e.g. 10-12-16 bit.
- improve performance sin() lookup table.
- add float variable for ```_perDC = _period * _dutyCycle```
- do we need **freq4** ? not since DC.
- heartBeat
- small noise/variation parameter on amplitude and frequency.
- reduce footprint ==> wrapper around freeWave()
- waves
- white noise, pink noise (better done with hardware)
- min() + max() => return +-amplitude + yshift?
- RC function curve.
- Gamma curve.
- create a function table? with what?
- create an example program to sample an arbitrary wave form
- output in the right format.
- slow sampling vs real time.
#### Examples
@ -228,6 +288,8 @@ Feedback and ideas are welcome.
- **float stairDC()**
- Bezier curve? (too complex)
- record a signal and play back ==> separate class
- document max frequency per wave form etc.
Should this be in the library? differs per board.
## Support