sine function on 16-bit microcontroller - c

I need to generate a sine wave to fill a char table of size 1024. The word size on the microcontroller is 16-bit and floating-point operations are not available.
The sine wave itself will oscillate between the value of 0 to 255, with 127 being the center point.
Any ideas?


You only actually need to store one quarter of the sine wave -- you can lookup the other three quarters from the first quadrant. So you only need 256 bytes.
To generate the values on the micro controller, implement CORDIC. You can store one value, and generate the whole sine wave from that.


Create a precomputed array on your PC. You only have to create a fourth of the array if ROM (or equivalent, such as flash or code segment) space is at a premium, then mirror this part out to the other 768 bytes of the array.


Write a sin table generator in your favorite language using float.
Scale and round the results to desired ranges 1024/-127..+128 (you may do that right away).
From the table, generate a source file in ASM or C, what ever works better for you.
Make sure the generated table in marked "const" in C or make go to a approbiate section in ASM so it goes to FLASH rather than RAM.
Include the file in your project.
Now intsin(x)1 is:
int intsin(int x)
limit x // 0..360° or 2PI
scale to 1024
read table at x
return x
You can improve resolution by using the table for the first quadrant only. You can than use positive values only, too (0..255). Then your intsin(x) would need to determine the quadrant and mirror the first quadrant results.


You just generate table on your PC and use it on your MCU. As somebody said you just need a quater period, but to answer your question fully, here are all 1024 chars:
for k := 0 to 1023 do
buffer[k] := (round(128+127*sin(2*pi*k/1024)));
128, 129, 130, 130, 131, 132, 133, 133, 134, 135, 136, 137, 137, 138, 139, 140, 140,
141, 142, 143, 144, 144, 145, 146, 147, 147, 148, 149, 150, 150, 151, 152, 153,
154, 154, 155, 156, 157, 157, 158, 159, 160, 160, 161, 162, 163, 163, 164, 165,
166, 166, 167, 168, 169, 169, 170, 171, 172, 172, 173, 174, 174, 175, 176, 177,
177, 178, 179, 179, 180, 181, 182, 182, 183, 184, 184, 185, 186, 186, 187, 188,
189, 189, 190, 191, 191, 192, 193, 193, 194, 195, 195, 196, 197, 197, 198, 199,
199, 200, 200, 201, 202, 202, 203, 204, 204, 205, 206, 206, 207, 207, 208, 209,
209, 210, 210, 211, 212, 212, 213, 213, 214, 214, 215, 216, 216, 217, 217, 218,
218, 219, 219, 220, 221, 221, 222, 222, 223, 223, 224, 224, 225, 225, 226, 226,
227, 227, 228, 228, 229, 229, 230, 230, 230, 231, 231, 232, 232, 233, 233, 234,
234, 234, 235, 235, 236, 236, 237, 237, 237, 238, 238, 239, 239, 239, 240, 240,
240, 241, 241, 241, 242, 242, 242, 243, 243, 243, 244, 244, 244, 245, 245, 245,
246, 246, 246, 246, 247, 247, 247, 248, 248, 248, 248, 249, 249, 249, 249, 250,
250, 250, 250, 250, 251, 251, 251, 251, 251, 252, 252, 252, 252, 252, 252, 253,
253, 253, 253, 253, 253, 253, 254, 254, 254, 254, 254, 254, 254, 254, 254, 254,
254, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255,
255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 255, 254, 254,
254, 254, 254, 254, 254, 254, 254, 254, 254, 253, 253, 253, 253, 253, 253, 253,
252, 252, 252, 252, 252, 252, 251, 251, 251, 251, 251, 250, 250, 250, 250, 250,
249, 249, 249, 249, 248, 248, 248, 248, 247, 247, 247, 246, 246, 246, 246, 245,
245, 245, 244, 244, 244, 243, 243, 243, 242, 242, 242, 241, 241, 241, 240, 240,
240, 239, 239, 239, 238, 238, 237, 237, 237, 236, 236, 235, 235, 234, 234, 234,
233, 233, 232, 232, 231, 231, 230, 230, 230, 229, 229, 228, 228, 227, 227, 226,
226, 225, 225, 224, 224, 223, 223, 222, 222, 221, 221, 220, 219, 219, 218, 218,
217, 217, 216, 216, 215, 214, 214, 213, 213, 212, 212, 211, 210, 210, 209, 209,
208, 207, 207, 206, 206, 205, 204, 204, 203, 202, 202, 201, 200, 200, 199, 199,
198, 197, 197, 196, 195, 195, 194, 193, 193, 192, 191, 191, 190, 189, 189, 188,
187, 186, 186, 185, 184, 184, 183, 182, 182, 181, 180, 179, 179, 178, 177, 177,
176, 175, 174, 174, 173, 172, 172, 171, 170, 169, 169, 168, 167, 166, 166, 165,
164, 163, 163, 162, 161, 160, 160, 159, 158, 157, 157, 156, 155, 154, 154, 153,
152, 151, 150, 150, 149, 148, 147, 147, 146, 145, 144, 144, 143, 142, 141, 140,
140, 139, 138, 137, 137, 136, 135, 134, 133, 133, 132, 131, 130, 130, 129, 128,
127, 126, 126, 125, 124, 123, 123, 122, 121, 120, 119, 119, 118, 117, 116, 116,
115, 114, 113, 112, 112, 111, 110, 109, 109, 108, 107, 106, 106, 105, 104, 103,
102, 102, 101, 100, 99, 99, 98, 97, 96, 96, 95, 94, 93, 93, 92, 91,
90, 90, 89, 88, 87, 87, 86, 85, 84, 84, 83, 82, 82, 81, 80, 79,
79, 78, 77, 77, 76, 75, 74, 74, 73, 72, 72, 71, 70, 70, 69, 68,
67, 67, 66, 65, 65, 64, 63, 63, 62, 61, 61, 60, 59, 59, 58, 57,
57, 56, 56, 55, 54, 54, 53, 52, 52, 51, 50, 50, 49, 49, 48, 47,
47, 46, 46, 45, 44, 44, 43, 43, 42, 42, 41, 40, 40, 39, 39, 38,
38, 37, 37, 36, 35, 35, 34, 34, 33, 33, 32, 32, 31, 31, 30, 30,
29, 29, 28, 28, 27, 27, 26, 26, 26, 25, 25, 24, 24, 23, 23, 22,
22, 22, 21, 21, 20, 20, 19, 19, 19, 18, 18, 17, 17, 17, 16, 16,
16, 15, 15, 15, 14, 14, 14, 13, 13, 13, 12, 12, 12, 11, 11, 11,
10, 10, 10, 10, 9, 9, 9, 8, 8, 8, 8, 7, 7, 7, 7, 6,
6, 6, 6, 6, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4, 3,
3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2,
2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3,
4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6,
7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11,
11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16,
16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 21, 21, 22, 22, 22,
23, 23, 24, 24, 25, 25, 26, 26, 26, 27, 27, 28, 28, 29, 29, 30,
30, 31, 31, 32, 32, 33, 33, 34, 34, 35, 35, 36, 37, 37, 38, 38,
39, 39, 40, 40, 41, 42, 42, 43, 43, 44, 44, 45, 46, 46, 47, 47,
48, 49, 49, 50, 50, 51, 52, 52, 53, 54, 54, 55, 56, 56, 57, 57,
58, 59, 59, 60, 61, 61, 62, 63, 63, 64, 65, 65, 66, 67, 67, 68,
69, 70, 70, 71, 72, 72, 73, 74, 74, 75, 76, 77, 77, 78, 79, 79,
80, 81, 82, 82, 83, 84, 84, 85, 86, 87, 87, 88, 89, 90, 90, 91,
92, 93, 93, 94, 95, 96, 96, 97, 98, 99, 99, 100, 101, 102, 102, 103,
104, 105, 106, 106, 107, 108, 109, 109, 110, 111, 112, 112, 113, 114, 115, 116,
116, 117, 118, 119, 119, 120, 121, 122, 123, 123, 124, 125, 126, 126, 127

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Problem using PROGMEM with pointer to an int array

my arduino nano drives an LED Matrix. evrything works fine.
but my "outline path" ist too big for the SRAM, so i try to put it into PROGMEM.
Now reading values from this progmem array leads to totally wrong integers.
what am i doing wrong?
thx for helping!!
bye
andre
void progStarsWarp() {
const static PROGMEM int outlinePath[] = {30, 31, 29, 28, 27, 26, 36, 42, 43, 44, 45, 46, 25, 9, 8, 0, 1, 2, 4, 3, 16, 17, 56, 57, 91, 92, 101, 102, 111, 112, 121, 122, 162, 192, 193, 229, 230, 262, 263, 274, 275, 276, 277, 270, 269, 254, 239, 240, 241, 242, 243, 244, 253, 252, 251, 250, 249, 211, 210, 176, 177, 178, 179, 175, 161, 152, 151, 142, 141, 132, 131, 77, 72, 73, 74, 75, 76, 37, 31};
int *pointerOutlinePath;
FastLED.clear();
for (unsigned int i = 0; i < 79; i++) {
pointerOutlinePath = &outlinePath[i];
int test = pgm_read_word(pointerOutlinePath);
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FastLED on Arduino with int[] Array

I built a LED Matrix with ws2812b LEDs. It is driven by an arduino nano. I use the CLED lib in combination with FastLED. It works fine!
Now I have a very simple routine here that wont work although there is no error or warning.
The problem seems to be the array which is a path of LEDs I want to activate.
So what am I missing? When I activate this on the arduino it freezes. The getRandomColorValue() function simply returns a color value 0-255. that one works like a charm.
int outlinePath[] = {30, 31, 29, 28, 27, 26, 26, 42, 43, 44, 45, 46, 25, 9, 8, 0, 1, 2, 4, 3, 16, 17, 56, 57, 91, 92, 101, 102, 111, 112, 121, 122, 162, 192, 193, 229, 230, 262, 263, 274, 275, 276, 277, 270, 269, 254, 239, 240, 241, 242, 243, 244, 253, 252, 251, 250, 249, 211, 210, 176, 177, 178, 179, 175, 161, 152, 151, 142, 141, 132, 131, 77, 72, 73, 74, 75, 76, 37, 31};
FastLED.clear();
for (int i = 0; i < 70; i++) {
int test = outlinePath[i];
leds.m_LED[test] = CRGB(getRandomColorValue(), getRandomColorValue(), getRandomColorValue());
}
FastLED.show();
delay(1000);
And this one works very well:
void progFastBlingBling() {
FastLED.clear();
leds.m_LED[random(0, anz_LEDs)] = CRGB(getRandomColorValue(), getRandomColorValue(), getRandomColorValue());
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Convert from byte array to Image

I have data of length 498, and I want to convert it to an image. The data (byte array) is:
ba = [4, 41, 80, 3, 41, 130, 134, 225, 196, 184, 63, 255, 137, 50, 182, 95, 3, 86, 250, 7, 218, 114, 246, 93, 132, 101, 56, 224, 233, 234, 185, 149, 132, 245, 245, 239, 1, 171, 245, 214, 66, 198, 133, 254, 18, 19, 247, 92, 72, 151, 118, 152, 21, 131, 248, 128, 74, 103, 172, 72, 37, 163, 233, 146, 196, 54, 244, 15, 85, 91, 229, 89, 195, 22, 64, 200, 73, 131, 246, 215, 133, 166, 137, 237, 85, 27, 246, 85, 68, 70, 122, 208, 134, 179, 246, 77, 199, 119, 246, 184, 145, 147, 247, 73, 143, 217, 240, 152, 149, 3, 56, 8, 183, 58, 13, 10, 181, 131, 248, 29, 80, 8, 1, 1, 217, 131, 248, 32, 11, 248, 250, 232, 245, 99, 245, 83, 196, 22, 192, 183, 21, 156, 246, 60, 74, 104, 106, 209, 14, 212, 233, 155, 195, 248, 247, 231, 21, 236, 245, 66, 136, 87, 102, 201, 33, 92, 233, 149, 1, 200, 185, 224, 50, 100, 248, 31, 8, 184, 120, 7, 62, 20, 247, 52, 9, 136, 108, 201, 62, 4, 248, 33, 11, 185, 116, 239, 105, 156, 246, 179, 78, 40, 203, 45, 121, 204, 248, 156, 196, 117, 77, 215, 138, 20, 247, 175, 77, 57, 203, 221, 149, 156, 213, 40, 28, 186, 108, 36, 182, 252, 248, 145, 7, 185, 139, 200, 210, 180, 248, 142, 199, 167, 139, 200, 209, 252, 233, 140, 70, 248, 197, 208, 233, 12, 246, 155, 140, 105, 151, 168, 9, 213, 246, 143, 8, 152, 215, 200, 26, 29, 233, 130, 132, 249, 71, 233, 38, 37, 248, 134, 7, 199, 5, 217, 73, 69, 248, 128, 197, 214, 3, 225, 133, 93, 247, 126, 131, 215, 1, 225, 158, 237, 247, 4, 65, 7, 194, 39, 73, 28, 117, 86, 133, 198, 255, 127, 121, 165, 117, 121, 194, 24, 126, 250, 161, 45, 121, 125, 128, 246, 193, 248, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 249, 99, 35, 114, 51, 162, 86, 36, 33, 70, 65, 51, 69, 116, 52, 70, 70, 50, 83, 34, 54, 83, 49, 63, 67, 34, 50, 85, 109, 48, 245, 50, 98, 134, 49, 101, 1, 63, 95, 66, 101, 19, 51, 35, 55, 52, 113, 100, 82, 86, 18, 35, 114, 49, 20, 134, 67, 20, 115, 246, 36, 49, 68, 53, 19, 65, 33, 69, 52, 38, 65, 115, 19, 21, 53, 83, 68, 82, 50, 68, 113, 51, 67, 65, 47, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 211, 203]
I tried using
Image.frombuffer('L', (498), ba, 'raw', 'L', 0, 1)
But, this gave an error saying 'size must be a tuple', I tried giving (498,0) and (0,498), this gave no error, but while saving the image there was an error as 'SystemError: tile cannot extend outside image'.

You can try fromarray function
import numpy as np
image = Image.fromarray(np.array(ba).reshape(498,1))

appIdentityService.signForApp (Java) and app_identity.sign_blob (Python) results are different

I need to sign JWT using Google Cloud appIdentity.
I tried using python agent and it is working. But the Java client gives signature error.
So I run test code to get signature of same input from Java and Python. It returns different result.
python code
import array
from google.appengine.api import app_identity
header_and_payload = "test"
(key_name, signature) = app_identity.sign_blob(header_and_payload)
print array.array('B', signature)
java code
import com.google.appengine.api.appidentity.AppIdentityService;
import com.google.appengine.api.appidentity.AppIdentityServiceFactory;
headerAndPayload = "test";
AppIdentityService appIdentityService = AppIdentityServiceFactory.getAppIdentityService();
AppIdentityService.SigningResult signingResult = appIdentityService.signForApp(headerAndPayload.getBytes());
System.out.println(Arrays.toString(signingResult.getSignature()));
Python output
[205, 130, 214, 28, 19, 7, 233, 69, 92, 161, 8, 160, 36, 162, 149, 125, 5, 100, 8, 219, 244, 235, 188, 126, 118, 45, 176, 63, 61, 88, 91, 151, 151, 114, 228, 31, 85, 209, 117, 134, 66, 120, 13, 159, 10, 155, 70, 16, 110, 56, 212, 79, 165, 40, 222, 46, 26, 74, 182, 80, 223, 57, 244, 44, 224, 122, 230, 184, 114, 236, 158, 204, 145, 152, 133, 131, 115, 43, 224, 132, 219, 232, 186, 237, 82, 86, 243, 194, 155, 127, 26, 227, 19, 165, 142, 216, 238, 163, 99, 251, 41, 191, 164, 206, 85, 239, 64, 133, 41, 49, 120, 235, 120, 226, 96, 224, 105, 68, 81, 186, 184, 65, 233, 129, 211, 231, 211, 135, 15, 88, 35, 20, 217, 95, 56, 215, 134, 71, 210, 28, 43, 22, 231, 69, 134, 116, 227, 161, 202, 94, 54, 222, 132, 158, 108, 45, 73, 68, 240, 90, 59, 139, 222, 118, 6, 82, 162, 198, 143, 7, 233, 148, 233, 232, 101, 135, 182, 71, 148, 136, 246, 168, 5, 28, 94, 11, 10, 78, 147, 4, 200, 36, 79, 244, 117, 223, 114, 33, 2, 206, 13, 66, 204, 201, 102, 147, 237, 83, 83, 17, 221, 16, 136, 206, 115, 141, 32, 149, 131, 136, 183, 96, 51, 31, 212, 174, 245, 120, 18, 120, 191, 174, 90, 111, 122, 136, 96, 152, 81, 8, 72, 52, 33, 46, 227, 241, 41, 77, 40, 176, 97, 189, 195, 197, 202, 71]
java output
[10, -64, 92, 105, 15, 35, -32, -101, 47, 111, -1, -72, 110, 105, -77, -117, 23, 69, 113, -49, -14, -104, 110, 78, 84, -78, 30, 26, 38, -43, 36, 112, 33, -10, -5, -63, -11, 47, -53, -116, -71, 2, -64, -16, 36, 122, 45, 79, 3, 49, -7, 120, -10, 125, 92, 43, -43, -34, 100, 75, -54, -36, 5, 106, -128, 106, -120, 36, 59, -31, -2, 100, 79, 65, -118, -50, -83, 11, -19, -28, -80, -125, -8, 59, -94, -125, 91, -104, -96, -12, 14, 31, -108, 61, 12, 6, 90, -6, -24, -47, -57, 55, -64, -50, 41, 26, -46, -81, -124, 122, 82, -120, 31, 19, 85, -7, -17, 40, -18, -118, -64, 114, -76, -60, 116, -12, -16, 12, -91, 55, -57, -61, 108, 88, -13, 80, -38, 100, 121, -11, -20, -5, -105, 20, 87, 60, -125, 33, -11, 111, -115, -69, 24, 0, -113, -24, 49, 21, -27, 96, 27, 12, 72, 50, 12, 15, -61, -40, -52, -76, -63, 29, -99, 114, 88, 41, 111, 9, 127, 96, -123, 58, 92, -91, 17, 114, -11, -105, -79, -110, -100, -35, 16, 103, 27, -21, -50, 7, -28, 117, 119, -124, -127, -115, -116, 86, 74, 57, -46, 114, 102, -18, -73, 97, 10, -113, 119, -1, -68, -18, -16, -119, 49, -120, 104, 121, 113, -82, -42, -119, -81, 95, -114, 16, -11, -58, 36, -24, 58, -50, 101, -117, -55, -101, -19, 62, -53, 30, -59, 106, 37, 98, 102, 75, -9, 91]
What is the issue in Java code? Thank you.

In the line:
print array.array('B', signature)
you are using the option 'B' for unsigned char according to the docs. If you use the option 'b' (for signed char) like in
print array.array('b', signature)
you will get the same results for both the Java and the python versions.
I performed tests with the sample codes for Python and Java. In the Python example I set the message variable to the same value as in Java:
message = "abcdefg"
and added this line:
self.response.write('Signature Array: {}\n'.format(array.array('b', signature)))
Hope this helps.

building an array from several ranges

I want to build an array out of several ranges. The following works:
array_of_ranges = (70..89).to_a + (184..193).to_a + (224..233).to_a + (296..304).to_a + (336..345).to_a
=> [70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 296, 297, 298, 299, 300, 301, 302, 303, 304, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345]
and it's certainly much nicer than typing in a bunch of numbers - but I suspect there's a nicer, cleaner way to do this. Any ideas?

You can use the splat operator to do this quite cleanly:
[*70..89, *184..193, *224..233, *296..304, *336..345]
Result:
[70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 296, 297, 298, 299, 300, 301, 302, 303, 304, 336, 337, 338, 339, 340, 341, 342, 343, 344, 345]

def arrays_from *ranges
ranges.map do |r|
r.to_a
end.flatten
end
or
def arrays_from *ranges
ranges.map( &:to_a ).flatten
end
arrays_from 70..89, 184..193, 224..233
=> [70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233]

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