Hello Friends!
I am using this code with this formula for non blocking led:
float val = ( exp ( sin (i/2000.0PI10)) - 0.36787944)*108.0;
the val value is going from 0 to 255 and back, works everything well.. but in my case I need to change to - from 20 to 255 and back. Any idea how can I change this formula? For now I made it like this:
if(val < 20) val = 20;
but I can clearly see this freezing and it looks not so nice.
Thanks!
Suggest you just generate a 20-255 PWM wave form using a non-blocking TIMER.
The values must start at 20 and still only go up to 255.
So this means the values start at 20 which is done by a +20
and to not exceed 255 the values shall only go up to 255 -20 = 235
So this means you have to tweak the amplitude of the sinus-function
I haven't done something like this before.
My first try would be to reduce the 108.0 to a smaller value
I would do the tweaking by printing the value of variable "val" to the serial monitor
best regards Stefan
I have tried to change all values 108, 10, 2000, but it affects only the speed, but not the endpoints.
#define ledPin 11
byte index = 20;
int incDec = 1;
unsigned long breathe_delay = 4;
unsigned long breathe_time = 0;
//********************************************^************************************************
void setup()
{
Serial.begin(115200);
pinMode(ledPin, OUTPUT);
} //END of setup()
//********************************************^************************************************
void loop()
{
//**********************************
//is it time to change LED brightness ?
if (millis() - breathe_time >= breathe_delay)
{
//restart this TIMER
breathe_time = millis();
analogWrite(ledPin, index);
index = index + incDec;
if (index == 255)
{
incDec = -1;
}
else if (index == 20)
{
incDec = 1;
}
}
//**********************************
//other non-blocking code goes here
//**********************************
} //END of loop()
Thank you Larry for your code. The problem is it uses proportional to time brightness value. The code I have posted use S curve brightness value. It looks more natural.
Correct.
At the expense of using the math library. 
If you are trying to plot a sine wave, using floats and sine() will make it g;acier slow compared to tabling int values of sine * 10000 and fetching those values to scale with. So sine of 30 gives 5000 to use in calcs and divide by 10000 if you don't want the extra places but can take smaller units ( I could say 3.333V or I could say 3333mV and totally avoid the decimal point and dirt-in-sand IEEE floating-point 
).
Integers (like type long) lose places in round-off-division (get the remainder with the % operation if you want) so I go big to get extra places to lose, for meters to 3 places I may use micrometers (6 places) and lose 3 at the end and the label says "mm" or I crank out and print meters then print a dec pt then print the /1000 remainder but only the high 3 places and always be correct.
You should have room in flash for a big table, 1 quadrant worth can give sine and cosine (read in reverse order) in like 6 cycles, less than 1/2 a microsecond or spend 100's of cycles on a single float operation.
This method of looking up pre-calculated values is how 6502 computers were able to run any kind of flight sims at all!
To change the formula so that the val value goes from -20 to 255 and back, you can modify the formula as follows:
float val = (exp(sin(i/2000.0*PI*10)) - 0.36787944) * 127.5; // Adjust the scaling factor
val = val - 20; // Shift the range by -20
if (val < 0) val = 0; // Ensure the minimum value is 0
This modification scales the range from 0-255 to -20-255 and ensures that the value doesn't go below 0. This should give you the effect you need without freezing and with a smoother transition.
Does not work. Intuitively @StefanL38 notices that the range is 0 - 255, and that to make it occupy a smaller range would have to involve decreasing the 108.0 constant.
Did you run the code that you wrote? I did, it does not work, as we suspected.
This comes closer
val = (exp(sin(i/2000.0*PI*10)) - 0.36787944) * 99; // Adjust the scaling factor
val = val + 20; // Shift the range by 20
if (val < 20.0) val = 20.0; // Ensure the minimum value is 20.0
a7
In my understanding this is not what user @mastino2 wants
The lowest value shall be 20 and going up from there to 255
I coded a second function that does iterate a few periods
what is inside the sine-function determines frequency
this is
sin( i / 2000.0 * PI * 10)
so if you keep i / 2000.0 * PI * 10 the same the frequency stays the same
I defined constants for the numbers
#define div2000 2000.0
#define minus0_36 0.55 // 0.36787944
#define mult108 100.0 // 108
#define baseOffset 38 // 0
I did some modifications to
and finally landed at
float val = (exp ( sin( i / div2000 * PI * 10) ) - minus0_36) * mult108 + baseOffset;
which is
float val = (exp ( sin( i / 2000.0 * PI * 10) ) - 0.55) * 100.0 + 38.0;
The steepness of the S-curve is determined by the -0.55 and the * 100
If you use a table-calculation-software like LibreOffice-Calc
and display the data as a XY-diagramm you will see what parameter does what
So here is the complete code for the tweaking that I used
/*
NonBlockingBreathingLed 0.1
by Luca Soltoggio - 2015
12 May 2015
http://www.arduinoelettronica.com/
https://arduinoelectronics.wordpress.com/
http://minibianpi.wodpress.com/
Use a exp + sin function to recreate a
non-blocking breathing led effect
Released under GPL v.2 license
*/
#include <math.h>
#define ledPin 11
#define div2000 2000.0
#define minus0_36 0.55 // 0.36787944
#define mult108 100.0 // 108
#define baseOffset 38 // 0
/*
#define div2000 2000.0
#define minus0_36 0.36787944
#define mult108 108
#define baseOffset 0
*/
int i = 0;
int breathe_delay = 15; // delay between loops
unsigned long breathe_time = millis();
void setup() {
Serial.begin(115200);
OnenonBlockingBreath();
}
void loop() {
//nonBlockingBreath(); // call the nonblocking function
// yourOtherCodeHere();
}
void OnenonBlockingBreath() {
for (int i = 0; i < 1500; i++) {
//if ( (breathe_time + breathe_delay) < millis() ) {
breathe_time = millis();
//float val = (exp ( sin( i / 2000.0 * PI * 10) ) - 0.36787944) * 108.0;
float val = (exp ( sin( i / div2000 * PI * 10) ) - minus0_36) * mult108 + baseOffset;
Serial.print(i);
Serial.print(" ");
Serial.println(val);
//(exp ( sin(i / 2000.0 * PI * 10) ) - 0.36787944) * 108.0;
// this is the math function recreating the effect
analogWrite(ledPin, val); // PWM
//i = i + 1;
//}
}
}
void nonBlockingBreath() {
if ( (breathe_time + breathe_delay) < millis() ) {
breathe_time = millis();
float val = (exp ( sin( i / 2000.0 * PI * 10) ) - 0.36787944) * 108.0;
Serial.println(val);
//(exp ( sin(i / 2000.0 * PI * 10) ) - 0.36787944) * 108.0;
// this is the math function recreating the effect
analogWrite(ledPin, val); // PWM
i = i + 1;
}
}here is the comparising of the modificated and the original values
modificated original
1 84.58 1 69.98
2 86.19 2 71.72
3 87.82 3 73.48
4 89.48 4 75.27
5 91.16 5 77.08
6 92.87 6 78.93
7 94.60 7 80.80
8 96.35 8 82.69
9 98.13 9 84.61
10 99.93 10 86.56
11 101.76 11 88.53
12 103.61 12 90.53
13 105.48 13 92.55
14 107.38 14 94.60
15 109.29 15 96.67
16 111.23 16 98.76
17 113.20 17 100.88
18 115.18 18 103.02
19 117.18 19 105.19
20 119.21 20 107.37
21 121.25 21 109.58
22 123.32 22 111.81
23 125.40 23 114.06
24 127.50 24 116.33
25 129.62 25 118.62
26 131.76 26 120.93
27 133.91 27 123.25
28 136.08 28 125.59
29 138.26 29 127.95
30 140.46 30 130.32
31 142.67 31 132.71
32 144.89 32 135.11
33 147.13 33 137.52
34 149.37 34 139.95
35 151.62 35 142.38
36 153.89 36 144.83
37 156.16 37 147.28
38 158.43 38 149.74
39 160.71 39 152.20
40 163.00 40 154.67
41 165.29 41 157.14
42 167.58 42 159.61
43 169.87 43 162.09
44 172.16 44 164.56
45 174.45 45 167.03
46 176.73 46 169.50
47 179.01 47 171.96
48 181.29 48 174.42
49 183.55 49 176.87
50 185.81 50 179.31
51 188.06 51 181.73
52 190.29 52 184.15
53 192.52 53 186.55
54 194.72 54 188.93
55 196.91 55 191.30
56 199.09 56 193.64
57 201.24 57 195.97
58 203.37 58 198.27
59 205.48 59 200.55
60 207.57 60 202.80
61 209.63 61 205.03
62 211.66 62 207.23
63 213.67 63 209.39
64 215.64 64 211.52
65 217.58 65 213.62
66 219.49 66 215.68
67 221.36 67 217.70
68 223.20 68 219.69
69 225.00 69 221.63
70 226.76 70 223.53
71 228.48 71 225.38
72 230.15 72 227.19
73 231.78 73 228.95
74 233.37 74 230.66
75 234.90 75 232.33
76 236.39 76 233.93
77 237.83 77 235.49
78 239.22 78 236.99
79 240.56 79 238.43
80 241.84 80 239.82
81 243.07 81 241.15
82 244.25 82 242.42
83 245.36 83 243.62
84 246.42 84 244.76
85 247.42 85 245.84
86 248.36 86 246.86
87 249.24 87 247.81
88 250.06 88 248.69
89 250.81 89 249.50
90 251.50 90 250.25
91 252.13 91 250.93
92 252.69 92 251.54
93 253.19 93 252.08
94 253.62 94 252.54
95 253.99 95 252.94
96 254.29 96 253.26
97 254.53 97 253.52
98 254.69 98 253.70
99 254.79 99 253.81
100 254.83 100 253.84
101 254.79 101 253.81
102 254.69 102 253.70
103 254.53 103 253.52
104 254.29 104 253.26
105 253.99 105 252.94
106 253.62 106 252.54
107 253.19 107 252.08
108 252.69 108 251.54
109 252.13 109 250.93
110 251.50 110 250.25
111 250.81 111 249.50
112 250.06 112 248.69
113 249.24 113 247.81
114 248.36 114 246.86
115 247.42 115 245.84
116 246.42 116 244.76
117 245.36 117 243.62
118 244.25 118 242.42
119 243.07 119 241.15
120 241.84 120 239.82
121 240.56 121 238.43
122 239.22 122 236.99
123 237.83 123 235.49
124 236.39 124 233.93
125 234.90 125 232.33
126 233.37 126 230.66
127 231.78 127 228.95
128 230.15 128 227.19
129 228.48 129 225.38
130 226.76 130 223.53
131 225.00 131 221.63
132 223.20 132 219.69
133 221.36 133 217.70
134 219.49 134 215.68
135 217.58 135 213.62
136 215.64 136 211.52
137 213.67 137 209.39
138 211.66 138 207.23
139 209.63 139 205.03
140 207.57 140 202.80
141 205.48 141 200.55
142 203.37 142 198.27
143 201.24 143 195.97
144 199.09 144 193.64
145 196.91 145 191.30
146 194.72 146 188.93
147 192.52 147 186.55
148 190.29 148 184.15
149 188.06 149 181.73
150 185.81 150 179.31
151 183.55 151 176.87
152 181.29 152 174.42
153 179.01 153 171.96
154 176.73 154 169.50
155 174.45 155 167.03
156 172.16 156 164.56
157 169.87 157 162.09
158 167.58 158 159.61
159 165.29 159 157.14
160 163.00 160 154.67
161 160.71 161 152.20
162 158.43 162 149.74
163 156.16 163 147.28
164 153.89 164 144.83
165 151.62 165 142.38
166 149.37 166 139.95
167 147.13 167 137.52
168 144.89 168 135.11
169 142.67 169 132.71
170 140.46 170 130.32
171 138.26 171 127.95
172 136.08 172 125.59
173 133.91 173 123.25
174 131.76 174 120.93
175 129.62 175 118.62
176 127.50 176 116.33
177 125.40 177 114.06
178 123.32 178 111.81
179 121.25 179 109.58
180 119.21 180 107.37
181 117.18 181 105.19
182 115.18 182 103.02
183 113.20 183 100.88
184 111.23 184 98.76
185 109.29 185 96.67
186 107.38 186 94.60
187 105.48 187 92.55
188 103.61 188 90.53
189 101.76 189 88.53
190 99.93 190 86.56
191 98.13 191 84.61
192 96.35 192 82.69
193 94.60 193 80.79
194 92.87 194 78.93
195 91.16 195 77.08
196 89.48 196 75.27
197 87.82 197 73.48
198 86.19 198 71.72
199 84.58 199 69.98
200 83.00 200 68.27
201 81.44 201 66.59
202 79.91 202 64.93
203 78.40 203 63.30
204 76.91 204 61.70
205 75.45 205 60.12
206 74.02 206 58.57
207 72.61 207 57.04
208 71.22 208 55.55
209 69.86 209 54.08
210 68.52 210 52.63
211 67.20 211 51.21
212 65.91 212 49.81
213 64.65 213 48.45
214 63.40 214 47.10
215 62.18 215 45.78
216 60.98 216 44.49
217 59.81 217 43.22
218 58.65 218 41.98
219 57.52 219 40.76
220 56.42 220 39.56
221 55.33 221 38.39
222 54.27 222 37.24
223 53.22 223 36.11
224 52.20 224 35.01
225 51.20 225 33.93
226 50.22 226 32.87
227 49.26 227 31.83
228 48.33 228 30.82
229 47.41 229 29.83
230 46.51 230 28.86
231 45.63 231 27.91
232 44.77 232 26.98
233 43.93 233 26.07
234 43.11 234 25.18
235 42.30 235 24.32
236 41.52 236 23.47
237 40.75 237 22.64
238 40.00 238 21.83
239 39.27 239 21.04
240 38.56 240 20.27
241 37.86 241 19.52
242 37.18 242 18.78
243 36.51 243 18.06
244 35.87 244 17.36
245 35.23 245 16.68
246 34.62 246 16.02
247 34.02 247 15.37
248 33.43 248 14.74
249 32.86 249 14.12
250 32.31 250 13.52
251 31.77 251 12.94
252 31.24 252 12.37
253 30.73 253 11.82
254 30.23 254 11.28
255 29.75 255 10.76
256 29.28 256 10.25
257 28.82 257 9.76
258 28.38 258 9.28
259 27.95 259 8.81
260 27.53 260 8.36
261 27.12 261 7.92
262 26.73 262 7.50
263 26.35 263 7.09
264 25.98 264 6.69
265 25.63 265 6.31
266 25.28 266 5.94
267 24.95 267 5.58
268 24.63 268 5.23
269 24.32 269 4.90
270 24.02 270 4.58
271 23.74 271 4.27
272 23.46 272 3.97
273 23.20 273 3.68
274 22.94 274 3.41
275 22.70 275 3.14
276 22.46 276 2.89
277 22.24 277 2.65
278 22.03 278 2.42
279 21.83 279 2.20
280 21.63 280 1.99
281 21.45 281 1.80
282 21.28 282 1.61
283 21.12 283 1.43
284 20.96 284 1.27
285 20.82 285 1.11
286 20.68 286 0.97
287 20.56 287 0.83
288 20.45 288 0.71
289 20.34 289 0.60
290 20.24 290 0.49
291 20.16 291 0.40
292 20.08 292 0.31
293 20.01 293 0.24
294 19.95 294 0.18
295 19.90 295 0.12
296 19.86 296 0.08
297 19.83 297 0.04
298 19.81 298 0.02
299 19.79 299 0.00
300 19.79 300 0.00
301 19.79 301 0.00
302 19.81 302 0.02
303 19.83 303 0.04
304 19.86 304 0.08
305 19.90 305 0.12
306 19.95 306 0.18
307 20.01 307 0.24
308 20.08 308 0.31
309 20.16 309 0.40
310 20.24 310 0.49
311 20.34 311 0.60
312 20.45 312 0.71
313 20.56 313 0.83
314 20.68 314 0.97
315 20.82 315 1.11
316 20.96 316 1.27
317 21.12 317 1.43
318 21.28 318 1.61
319 21.45 319 1.80
320 21.63 320 1.99
321 21.83 321 2.20
322 22.03 322 2.42
323 22.24 323 2.65
324 22.46 324 2.89
325 22.70 325 3.14
326 22.94 326 3.41
327 23.20 327 3.68
328 23.46 328 3.97
329 23.74 329 4.27
330 24.02 330 4.58
331 24.32 331 4.90
332 24.63 332 5.23
333 24.95 333 5.58
334 25.28 334 5.94
335 25.63 335 6.31
336 25.98 336 6.69
337 26.35 337 7.09
338 26.73 338 7.50
339 27.12 339 7.92
340 27.53 340 8.36
341 27.95 341 8.81
342 28.38 342 9.28
343 28.82 343 9.76
344 29.28 344 10.25
345 29.75 345 10.76
346 30.23 346 11.28
347 30.73 347 11.82
348 31.24 348 12.37
349 31.77 349 12.94
350 32.31 350 13.52
351 32.86 351 14.12
352 33.43 352 14.74
353 34.02 353 15.37
354 34.62 354 16.02
355 35.23 355 16.68
356 35.87 356 17.36
357 36.51 357 18.06
358 37.18 358 18.78
359 37.86 359 19.52
360 38.56 360 20.27
361 39.27 361 21.04
362 40.00 362 21.83
363 40.75 363 22.64
364 41.52 364 23.47
365 42.30 365 24.32
366 43.11 366 25.18
367 43.93 367 26.07
368 44.77 368 26.98
369 45.63 369 27.91
370 46.51 370 28.86
371 47.41 371 29.83
372 48.33 372 30.82
373 49.26 373 31.83
374 50.22 374 32.87
375 51.20 375 33.93
376 52.20 376 35.01
377 53.22 377 36.11
378 54.27 378 37.24
379 55.33 379 38.39
380 56.42 380 39.56
381 57.52 381 40.76
382 58.65 382 41.98
383 59.81 383 43.22
384 60.98 384 44.49
385 62.18 385 45.78
386 63.40 386 47.10
387 64.65 387 48.45
388 65.91 388 49.81
389 67.20 389 51.21
390 68.52 390 52.63
391 69.86 391 54.08
392 71.22 392 55.55
393 72.61 393 57.04
394 74.02 394 58.57
395 75.45 395 60.12
396 76.91 396 61.70
397 78.40 397 63.30
398 79.91 398 64.93
399 81.44 399 66.59
400 83.00 400 68.27
401 84.58 401 69.98
402 86.19 402 71.72
403 87.82 403 73.48
404 89.48 404 75.27
405 91.16 405 77.08
406 92.87 406 78.93
407 94.60 407 80.80
408 96.35 408 82.69
409 98.13 409 84.61
410 99.93 410 86.56
411 101.76 411 88.53
412 103.61 412 90.53
413 105.48 413 92.55
414 107.38 414 94.60
415 109.29 415 96.67
416 111.23 416 98.76
417 113.20 417 100.88
418 115.18 418 103.02
419 117.18 419 105.19
420 119.21 420 107.37
421 121.25 421 109.58
422 123.32 422 111.81
423 125.40 423 114.06
424 127.50 424 116.33
425 129.62 425 118.62
426 131.76 426 120.93
427 133.91 427 123.25
428 136.08 428 125.59
429 138.26 429 127.95
430 140.46 430 130.32
431 142.67 431 132.71
432 144.89 432 135.11
433 147.13 433 137.52
434 149.37 434 139.95
435 151.62 435 142.38
436 153.89 436 144.83
437 156.16 437 147.28
438 158.43 438 149.74
439 160.71 439 152.20
440 163.00 440 154.67
441 165.29 441 157.14
442 167.58 442 159.61
443 169.87 443 162.09
444 172.16 444 164.56
445 174.45 445 167.03
446 176.73 446 169.50
447 179.01 447 171.96
448 181.29 448 174.42
449 183.55 449 176.87
450 185.81 450 179.31
451 188.06 451 181.73
452 190.29 452 184.15
453 192.52 453 186.55
454 194.72 454 188.93
455 196.91 455 191.30
456 199.09 456 193.64
457 201.24 457 195.97
458 203.37 458 198.27
459 205.48 459 200.55
460 207.57 460 202.80
461 209.63 461 205.03
462 211.66 462 207.23
463 213.67 463 209.39
464 215.64 464 211.52
465 217.58 465 213.62
466 219.49 466 215.68
467 221.36 467 217.70
468 223.20 468 219.69
469 225.00 469 221.63
470 226.76 470 223.53
471 228.48 471 225.38
472 230.15 472 227.19
473 231.78 473 228.95
474 233.37 474 230.66
475 234.90 475 232.33
476 236.39 476 233.93
477 237.83 477 235.49
478 239.22 478 236.99
479 240.56 479 238.43
480 241.84 480 239.82
481 243.07 481 241.15
482 244.25 482 242.42
483 245.36 483 243.62
484 246.42 484 244.76
485 247.42 485 245.84
486 248.36 486 246.86
487 249.24 487 247.81
488 250.06 488 248.69
489 250.81 489 249.50
490 251.50 490 250.25
491 252.13 491 250.93
492 252.69 492 251.54
493 253.19 493 252.08
494 253.62 494 252.54
495 253.99 495 252.94
496 254.29 496 253.26
497 254.53 497 253.52
498 254.69 498 253.70
499 254.79 499 253.81
500 254.83 500 253.84
501 254.79 501 253.81
502 254.69 502 253.70
503 254.53 503 253.52
504 254.29 504 253.26
505 253.99 505 252.94
506 253.62 506 252.54
507 253.19 507 252.08
508 252.69 508 251.54
509 252.13 509 250.93
510 251.50 510 250.25
511 250.81 511 249.50
512 250.06 512 248.69
513 249.24 513 247.81
514 248.36 514 246.86
515 247.42 515 245.84
516 246.42 516 244.76
517 245.36 517 243.62
518 244.25 518 242.42
519 243.07 519 241.15
520 241.84 520 239.82
521 240.56 521 238.43
522 239.22 522 236.99
523 237.83 523 235.49
524 236.39 524 233.93
525 234.90 525 232.33
526 233.37 526 230.66
527 231.78 527 228.95
528 230.15 528 227.19
529 228.48 529 225.38
530 226.76 530 223.53
531 225.00 531 221.63
532 223.20 532 219.69
533 221.36 533 217.70
534 219.49 534 215.68
535 217.58 535 213.62
536 215.64 536 211.52
537 213.67 537 209.39
538 211.66 538 207.23
539 209.63 539 205.03
540 207.57 540 202.80
541 205.48 541 200.55
542 203.37 542 198.27
543 201.24 543 195.97
544 199.09 544 193.64
545 196.91 545 191.30
546 194.72 546 188.93
547 192.52 547 186.55
548 190.29 548 184.15
549 188.06 549 181.73
550 185.81 550 179.31
551 183.55 551 176.87
552 181.29 552 174.42
553 179.01 553 171.96
554 176.73 554 169.50
555 174.45 555 167.03
556 172.16 556 164.56
557 169.87 557 162.09
558 167.58 558 159.61
559 165.29 559 157.14
560 163.00 560 154.67
561 160.71 561 152.20
562 158.43 562 149.74
563 156.16 563 147.28
564 153.89 564 144.83
565 151.62 565 142.38
566 149.37 566 139.95
567 147.13 567 137.52
568 144.89 568 135.11
569 142.67 569 132.71
570 140.46 570 130.32
571 138.26 571 127.95
572 136.08 572 125.59
573 133.91 573 123.25
574 131.76 574 120.93
575 129.62 575 118.62
576 127.50 576 116.33
577 125.40 577 114.06
578 123.32 578 111.81
579 121.25 579 109.58
580 119.21 580 107.37
581 117.18 581 105.19
582 115.18 582 103.02
583 113.20 583 100.88
584 111.23 584 98.76
585 109.29 585 96.67
586 107.38 586 94.60
587 105.48 587 92.55
588 103.61 588 90.53
589 101.76 589 88.53
590 99.93 590 86.56
591 98.13 591 84.61
592 96.35 592 82.69
593 94.60 593 80.80
594 92.87 594 78.93
595 91.16 595 77.08
596 89.48 596 75.27
597 87.82 597 73.48
598 86.19 598 71.72
599 84.58 599 69.98
600 83.00 600 68.27
601 81.44 601 66.59
602 79.91 602 64.93
603 78.40 603 63.30
604 76.91 604 61.70
605 75.45 605 60.12
606 74.02 606 58.57
607 72.61 607 57.04
608 71.22 608 55.55
609 69.86 609 54.08
610 68.52 610 52.63
611 67.20 611 51.21
612 65.91 612 49.81
613 64.65 613 48.45
614 63.40 614 47.10
615 62.18 615 45.78
616 60.98 616 44.49
617 59.81 617 43.22
618 58.65 618 41.98
619 57.52 619 40.76
620 56.42 620 39.56
621 55.33 621 38.39
622 54.27 622 37.24
623 53.22 623 36.11
624 52.20 624 35.01
625 51.20 625 33.93
626 50.22 626 32.87
627 49.26 627 31.83
628 48.33 628 30.82
629 47.41 629 29.83
630 46.51 630 28.86
631 45.63 631 27.91
632 44.77 632 26.98
633 43.93 633 26.07
634 43.11 634 25.18
635 42.30 635 24.32
636 41.52 636 23.47
637 40.75 637 22.64
638 40.00 638 21.83
639 39.27 639 21.04
640 38.56 640 20.27
641 37.86 641 19.52
642 37.18 642 18.78
643 36.51 643 18.06
644 35.87 644 17.36
645 35.23 645 16.68
646 34.62 646 16.02
647 34.02 647 15.37
648 33.43 648 14.74
649 32.86 649 14.12
650 32.31 650 13.52
651 31.77 651 12.94
652 31.24 652 12.37
653 30.73 653 11.82
654 30.23 654 11.28
655 29.75 655 10.76
656 29.28 656 10.25
657 28.82 657 9.76
658 28.38 658 9.28
659 27.95 659 8.81
660 27.53 660 8.36
661 27.12 661 7.92
662 26.73 662 7.50
663 26.35 663 7.09
664 25.98 664 6.69
665 25.63 665 6.31
666 25.28 666 5.94
667 24.95 667 5.58
668 24.63 668 5.23
669 24.32 669 4.90
670 24.02 670 4.58
671 23.74 671 4.27
672 23.46 672 3.97
673 23.20 673 3.68
674 22.94 674 3.41
675 22.70 675 3.14
676 22.46 676 2.89
677 22.24 677 2.65
678 22.03 678 2.42
679 21.83 679 2.20
680 21.63 680 1.99
681 21.45 681 1.80
682 21.28 682 1.61
683 21.12 683 1.43
684 20.96 684 1.27
685 20.82 685 1.11
686 20.68 686 0.97
687 20.56 687 0.83
688 20.45 688 0.71
689 20.34 689 0.60
690 20.24 690 0.49
691 20.16 691 0.40
692 20.08 692 0.31
693 20.01 693 0.24
694 19.95 694 0.18
695 19.90 695 0.12
696 19.86 696 0.08
697 19.83 697 0.04
698 19.81 698 0.02
699 19.79 699 0.00
700 19.79 700 0.00
701 19.79 701 0.00
702 19.81 702 0.02
703 19.83 703 0.04
704 19.86 704 0.08
705 19.90 705 0.12
706 19.95 706 0.18
707 20.01 707 0.24
708 20.08 708 0.31
709 20.16 709 0.40
710 20.24 710 0.49
711 20.34 711 0.60
712 20.45 712 0.71
713 20.56 713 0.83
714 20.68 714 0.97
715 20.82 715 1.11
716 20.96 716 1.27
717 21.12 717 1.43
718 21.28 718 1.61
719 21.45 719 1.80
720 21.63 720 1.99
721 21.83 721 2.20
722 22.03 722 2.42
723 22.24 723 2.65
724 22.46 724 2.89
725 22.70 725 3.14
726 22.94 726 3.41
727 23.20 727 3.68
728 23.46 728 3.97
729 23.74 729 4.27
730 24.02 730 4.58
731 24.32 731 4.90
732 24.63 732 5.23
733 24.95 733 5.58
734 25.28 734 5.94
735 25.63 735 6.31
736 25.98 736 6.69
737 26.35 737 7.09
738 26.73 738 7.50
739 27.12 739 7.92
740 27.53 740 8.36
741 27.95 741 8.81
742 28.38 742 9.28
743 28.82 743 9.76
744 29.28 744 10.25
745 29.75 745 10.76
746 30.23 746 11.28
747 30.73 747 11.82
748 31.24 748 12.37
749 31.77 749 12.94
750 32.31 750 13.52
751 32.86 751 14.12
752 33.43 752 14.74
753 34.02 753 15.37
754 34.62 754 16.02
755 35.23 755 16.68
756 35.87 756 17.36
757 36.51 757 18.06
758 37.18 758 18.78
759 37.86 759 19.52
760 38.56 760 20.27
761 39.27 761 21.04
762 40.00 762 21.83
763 40.75 763 22.64
764 41.52 764 23.47
765 42.30 765 24.32
766 43.11 766 25.18
767 43.93 767 26.07
768 44.77 768 26.98
769 45.63 769 27.91
770 46.51 770 28.86
771 47.41 771 29.83
772 48.33 772 30.82
773 49.26 773 31.83
774 50.22 774 32.87
775 51.20 775 33.93
776 52.20 776 35.01
777 53.22 777 36.11
778 54.27 778 37.24
779 55.33 779 38.39
780 56.42 780 39.56
781 57.52 781 40.76
782 58.65 782 41.98
783 59.81 783 43.22
784 60.98 784 44.49
785 62.18 785 45.78
786 63.40 786 47.10
787 64.65 787 48.45
788 65.91 788 49.81
789 67.20 789 51.21
790 68.52 790 52.63
791 69.86 791 54.08
792 71.22 792 55.55
793 72.61 793 57.04
794 74.02 794 58.57
795 75.45 795 60.12
796 76.91 796 61.70
797 78.40 797 63.30
798 79.91 798 64.93
799 81.44 799 66.59
800 83.00 800 68.27
801 84.58 801 69.98
802 86.19 802 71.72
803 87.82 803 73.48
804 89.48 804 75.27
805 91.16 805 77.08
806 92.87 806 78.93
807 94.60 807 80.79
808 96.35 808 82.69
809 98.13 809 84.61
810 99.93 810 86.56
811 101.76 811 88.53
812 103.61 812 90.53
813 105.48 813 92.55
814 107.38 814 94.60
815 109.29 815 96.67
816 111.23 816 98.76
817 113.20 817 100.88
818 115.18 818 103.02
819 117.18 819 105.19
820 119.21 820 107.37
821 121.25 821 109.58
822 123.32 822 111.81
823 125.40 823 114.06
824 127.50 824 116.33
825 129.62 825 118.62
826 131.76 826 120.93
827 133.91 827 123.25
828 136.08 828 125.59
829 138.26 829 127.95
830 140.46 830 130.32
831 142.67 831 132.71
832 144.89 832 135.11
833 147.13 833 137.52
834 149.37 834 139.95
835 151.62 835 142.38
836 153.89 836 144.83
837 156.16 837 147.28
838 158.43 838 149.74
839 160.71 839 152.20
840 163.00 840 154.67
841 165.29 841 157.14
842 167.58 842 159.61
843 169.87 843 162.09
844 172.16 844 164.56
845 174.45 845 167.03
846 176.73 846 169.50
847 179.01 847 171.96
848 181.29 848 174.42
849 183.55 849 176.87
850 185.81 850 179.31
851 188.06 851 181.73
852 190.29 852 184.15
853 192.52 853 186.55
854 194.72 854 188.93
855 196.91 855 191.30
856 199.09 856 193.64
857 201.24 857 195.97
858 203.37 858 198.27
859 205.48 859 200.55
860 207.57 860 202.80
861 209.63 861 205.03
862 211.66 862 207.23
863 213.67 863 209.39
864 215.64 864 211.52
865 217.58 865 213.62
866 219.49 866 215.68
867 221.36 867 217.70
868 223.20 868 219.69
869 225.00 869 221.63
870 226.76 870 223.53
871 228.48 871 225.38
872 230.15 872 227.19
873 231.78 873 228.95
874 233.37 874 230.66
875 234.90 875 232.33
876 236.39 876 233.93
877 237.83 877 235.49
878 239.22 878 236.99
879 240.56 879 238.43
880 241.84 880 239.82
881 243.07 881 241.15
882 244.25 882 242.42
883 245.36 883 243.62
884 246.42 884 244.76
885 247.42 885 245.84
886 248.36 886 246.86
887 249.24 887 247.81
888 250.06 888 248.69
889 250.81 889 249.50
890 251.50 890 250.25
891 252.13 891 250.93
892 252.69 892 251.54
893 253.19 893 252.08
894 253.62 894 252.54
895 253.99 895 252.94
896 254.29 896 253.26
897 254.53 897 253.52
898 254.69 898 253.70
899 254.79 899 253.81
900 254.83 900 253.84
901 254.79 901 253.81
902 254.69 902 253.70
903 254.53 903 253.52
904 254.29 904 253.26
905 253.99 905 252.94
906 253.62 906 252.54
907 253.19 907 252.08
908 252.69 908 251.54
909 252.13 909 250.93
910 251.50 910 250.25
911 250.81 911 249.50
912 250.06 912 248.69
913 249.24 913 247.81
914 248.36 914 246.86
915 247.42 915 245.84
916 246.42 916 244.76
917 245.36 917 243.62
918 244.25 918 242.42
919 243.07 919 241.15
920 241.84 920 239.82
921 240.56 921 238.43
922 239.22 922 236.99
923 237.83 923 235.49
924 236.39 924 233.93
925 234.90 925 232.33
926 233.37 926 230.66
927 231.78 927 228.95
928 230.15 928 227.19
929 228.48 929 225.38
930 226.76 930 223.53
931 225.00 931 221.63
932 223.20 932 219.69
933 221.36 933 217.70
934 219.49 934 215.68
935 217.58 935 213.62
936 215.64 936 211.52
937 213.67 937 209.39
938 211.66 938 207.23
939 209.63 939 205.03
940 207.57 940 202.80
941 205.48 941 200.55
942 203.37 942 198.27
943 201.24 943 195.97
944 199.09 944 193.64
945 196.91 945 191.30
946 194.72 946 188.93
947 192.52 947 186.55
948 190.29 948 184.15
949 188.06 949 181.73
950 185.81 950 179.31
951 183.55 951 176.87
952 181.29 952 174.42
953 179.01 953 171.96
954 176.73 954 169.50
955 174.45 955 167.03
956 172.16 956 164.56
957 169.87 957 162.09
958 167.58 958 159.61
959 165.29 959 157.14
960 163.00 960 154.67
961 160.71 961 152.20
962 158.43 962 149.74
963 156.16 963 147.28
964 153.89 964 144.83
965 151.62 965 142.38
966 149.37 966 139.95
967 147.13 967 137.52
968 144.89 968 135.11
969 142.67 969 132.71
970 140.46 970 130.32
971 138.26 971 127.95
972 136.08 972 125.59
973 133.91 973 123.25
974 131.76 974 120.93
975 129.62 975 118.62
976 127.50 976 116.33
977 125.40 977 114.06
978 123.32 978 111.81
979 121.25 979 109.58
980 119.21 980 107.37
981 117.18 981 105.19
982 115.18 982 103.02
983 113.20 983 100.88
984 111.23 984 98.76
985 109.29 985 96.67
986 107.38 986 94.60
987 105.48 987 92.55
988 103.61 988 90.53
989 101.76 989 88.53
990 99.93 990 86.56
991 98.13 991 84.61
992 96.35 992 82.69
993 94.60 993 80.80
994 92.87 994 78.93
995 91.16 995 77.08
996 89.48 996 75.27
997 87.82 997 73.48
998 86.19 998 71.72
999 84.58 999 69.98
1000 83.00 1000 68.27
1001 81.44 1001 66.59
1002 79.91 1002 64.93
1003 78.40 1003 63.30
1004 76.91 1004 61.70
1005 75.45 1005 60.12
1006 74.02 1006 58.57
1007 72.61 1007 57.04
1008 71.22 1008 55.55
1009 69.86 1009 54.08
1010 68.52 1010 52.63
1011 67.20 1011 51.21
1012 65.91 1012 49.81
1013 64.65 1013 48.45
1014 63.40 1014 47.10
1015 62.18 1015 45.78
1016 60.98 1016 44.49
1017 59.81 1017 43.22
1018 58.65 1018 41.98
1019 57.52 1019 40.76
1020 56.42 1020 39.56
1021 55.33 1021 38.39
1022 54.27 1022 37.24
1023 53.22 1023 36.11
1024 52.20 1024 35.01
1025 51.20 1025 33.93
1026 50.22 1026 32.87
1027 49.26 1027 31.83
1028 48.33 1028 30.82
1029 47.41 1029 29.83
1030 46.51 1030 28.86
1031 45.63 1031 27.91
1032 44.77 1032 26.98
1033 43.93 1033 26.07
1034 43.11 1034 25.18
1035 42.30 1035 24.32
1036 41.52 1036 23.47
1037 40.75 1037 22.64
1038 40.00 1038 21.83
1039 39.27 1039 21.04
1040 38.56 1040 20.27
1041 37.86 1041 19.52
1042 37.18 1042 18.78
1043 36.51 1043 18.06
1044 35.87 1044 17.36
1045 35.23 1045 16.68
1046 34.62 1046 16.02
1047 34.02 1047 15.37
1048 33.43 1048 14.74
1049 32.86 1049 14.12
1050 32.31 1050 13.52
1051 31.77 1051 12.94
1052 31.24 1052 12.37
1053 30.73 1053 11.82
1054 30.23 1054 11.28
1055 29.75 1055 10.76
1056 29.28 1056 10.25
1057 28.82 1057 9.76
1058 28.38 1058 9.28
1059 27.95 1059 8.81
1060 27.53 1060 8.36
1061 27.12 1061 7.92
1062 26.73 1062 7.50
1063 26.35 1063 7.09
1064 25.98 1064 6.69
1065 25.63 1065 6.31
1066 25.28 1066 5.94
1067 24.95 1067 5.58
1068 24.63 1068 5.23
1069 24.32 1069 4.90
1070 24.02 1070 4.58
1071 23.74 1071 4.27
1072 23.46 1072 3.97
1073 23.20 1073 3.68
1074 22.94 1074 3.41
1075 22.70 1075 3.14
1076 22.46 1076 2.89
1077 22.24 1077 2.65
1078 22.03 1078 2.42
1079 21.83 1079 2.20
1080 21.63 1080 1.99
1081 21.45 1081 1.80
1082 21.28 1082 1.61
1083 21.12 1083 1.43
1084 20.96 1084 1.27
1085 20.82 1085 1.11
1086 20.68 1086 0.97
1087 20.56 1087 0.83
1088 20.45 1088 0.71
1089 20.34 1089 0.60
1090 20.24 1090 0.49
1091 20.16 1091 0.40
1092 20.08 1092 0.31
1093 20.01 1093 0.24
1094 19.95 1094 0.18
1095 19.90 1095 0.12
1096 19.86 1096 0.08
1097 19.83 1097 0.04
1098 19.81 1098 0.02
1099 19.79 1099 0.00
1100 19.79 1100 0.00
1101 19.79 1101 0.00
1102 19.81 1102 0.02
1103 19.83 1103 0.04
1104 19.86 1104 0.08
1105 19.90 1105 0.12
1106 19.95 1106 0.18
1107 20.01 1107 0.24
1108 20.08 1108 0.31
1109 20.16 1109 0.40
1110 20.24 1110 0.49
1111 20.34 1111 0.60
1112 20.45 1112 0.71
1113 20.56 1113 0.83
1114 20.68 1114 0.97
1115 20.82 1115 1.11
1116 20.96 1116 1.27
1117 21.12 1117 1.43
1118 21.28 1118 1.61
1119 21.45 1119 1.80
1120 21.63 1120 1.99
1121 21.83 1121 2.20
1122 22.03 1122 2.42
1123 22.24 1123 2.65
1124 22.46 1124 2.89
1125 22.70 1125 3.14
1126 22.94 1126 3.41
1127 23.20 1127 3.68
1128 23.46 1128 3.97
1129 23.74 1129 4.27
1130 24.02 1130 4.58
1131 24.32 1131 4.90
1132 24.63 1132 5.23
1133 24.95 1133 5.58
1134 25.28 1134 5.94
1135 25.63 1135 6.31
1136 25.98 1136 6.69
1137 26.35 1137 7.09
1138 26.73 1138 7.50
1139 27.12 1139 7.92
1140 27.53 1140 8.36
1141 27.95 1141 8.81
1142 28.38 1142 9.28
1143 28.82 1143 9.76
1144 29.28 1144 10.25
1145 29.75 1145 10.76
1146 30.23 1146 11.28
1147 30.73 1147 11.82
1148 31.24 1148 12.37
1149 31.77 1149 12.94
1150 32.31 1150 13.52
1151 32.86 1151 14.12
1152 33.43 1152 14.74
1153 34.02 1153 15.37
1154 34.62 1154 16.02
1155 35.23 1155 16.68
1156 35.87 1156 17.36
1157 36.51 1157 18.06
1158 37.18 1158 18.78
1159 37.86 1159 19.52
1160 38.56 1160 20.27
1161 39.27 1161 21.04
1162 40.00 1162 21.83
1163 40.75 1163 22.64
1164 41.52 1164 23.47
1165 42.30 1165 24.32
1166 43.11 1166 25.18
1167 43.93 1167 26.07
1168 44.77 1168 26.98
1169 45.63 1169 27.91
1170 46.51 1170 28.86
1171 47.41 1171 29.83
1172 48.33 1172 30.82
1173 49.26 1173 31.83
1174 50.22 1174 32.87
1175 51.20 1175 33.93
1176 52.20 1176 35.01
1177 53.22 1177 36.11
1178 54.27 1178 37.24
1179 55.33 1179 38.39
1180 56.42 1180 39.56
1181 57.52 1181 40.76
1182 58.65 1182 41.98
1183 59.81 1183 43.22
1184 60.98 1184 44.49
1185 62.18 1185 45.78
1186 63.40 1186 47.10
1187 64.65 1187 48.45
1188 65.91 1188 49.81
1189 67.20 1189 51.21
1190 68.52 1190 52.63
1191 69.86 1191 54.08
1192 71.22 1192 55.55
1193 72.61 1193 57.04
1194 74.02 1194 58.57
1195 75.45 1195 60.12
1196 76.91 1196 61.70
1197 78.40 1197 63.30
1198 79.91 1198 64.93
1199 81.44 1199 66.59
1200 83.00 1200 68.27
1201 84.58 1201 69.98
1202 86.19 1202 71.72
1203 87.82 1203 73.48
1204 89.48 1204 75.27
1205 91.16 1205 77.08
1206 92.87 1206 78.93
1207 94.60 1207 80.80
1208 96.35 1208 82.69
1209 98.13 1209 84.61
1210 99.93 1210 86.56
1211 101.76 1211 88.53
1212 103.61 1212 90.53
1213 105.48 1213 92.55
1214 107.38 1214 94.60
1215 109.29 1215 96.67
1216 111.23 1216 98.76
1217 113.20 1217 100.88
1218 115.18 1218 103.02
1219 117.18 1219 105.19
1220 119.21 1220 107.37
1221 121.25 1221 109.58
1222 123.32 1222 111.81
1223 125.40 1223 114.06
1224 127.50 1224 116.33
1225 129.62 1225 118.62
1226 131.76 1226 120.93
1227 133.91 1227 123.25
1228 136.08 1228 125.59
1229 138.26 1229 127.95
1230 140.46 1230 130.32
1231 142.67 1231 132.71
1232 144.89 1232 135.11
1233 147.13 1233 137.52
1234 149.37 1234 139.95
1235 151.62 1235 142.38
1236 153.89 1236 144.83
1237 156.16 1237 147.28
1238 158.43 1238 149.74
1239 160.71 1239 152.20
1240 163.00 1240 154.67
1241 165.29 1241 157.14
1242 167.58 1242 159.61
1243 169.87 1243 162.09
1244 172.16 1244 164.56
1245 174.45 1245 167.03
1246 176.73 1246 169.50
1247 179.01 1247 171.96
1248 181.29 1248 174.42
1249 183.55 1249 176.87
1250 185.81 1250 179.31
1251 188.06 1251 181.73
1252 190.29 1252 184.15
1253 192.52 1253 186.55
1254 194.72 1254 188.93
1255 196.91 1255 191.30
1256 199.09 1256 193.64
1257 201.24 1257 195.97
1258 203.37 1258 198.27
1259 205.48 1259 200.55
1260 207.57 1260 202.80
1261 209.63 1261 205.03
1262 211.66 1262 207.23
1263 213.67 1263 209.39
1264 215.64 1264 211.52
1265 217.58 1265 213.62
1266 219.49 1266 215.68
1267 221.36 1267 217.70
1268 223.20 1268 219.69
1269 225.00 1269 221.63
1270 226.76 1270 223.53
1271 228.48 1271 225.38
1272 230.15 1272 227.19
1273 231.78 1273 228.95
1274 233.37 1274 230.66
1275 234.90 1275 232.33
1276 236.39 1276 233.93
1277 237.83 1277 235.49
1278 239.22 1278 236.99
1279 240.56 1279 238.43
1280 241.84 1280 239.82
1281 243.07 1281 241.15
1282 244.25 1282 242.41
1283 245.36 1283 243.62
1284 246.42 1284 244.76
1285 247.42 1285 245.84
1286 248.36 1286 246.86
1287 249.24 1287 247.81
1288 250.06 1288 248.69
1289 250.81 1289 249.50
1290 251.50 1290 250.25
1291 252.13 1291 250.93
1292 252.69 1292 251.54
1293 253.19 1293 252.08
1294 253.62 1294 252.54
1295 253.99 1295 252.94
1296 254.29 1296 253.26
1297 254.53 1297 253.52
1298 254.69 1298 253.70
1299 254.79 1299 253.81
1300 254.83 1300 253.84
1301 254.79 1301 253.81
1302 254.69 1302 253.70
1303 254.53 1303 253.52
1304 254.29 1304 253.26
1305 253.99 1305 252.94
1306 253.62 1306 252.54
1307 253.19 1307 252.08
1308 252.69 1308 251.54
1309 252.13 1309 250.93
1310 251.50 1310 250.25
1311 250.81 1311 249.50
1312 250.06 1312 248.69
1313 249.24 1313 247.81
1314 248.36 1314 246.86
1315 247.42 1315 245.84
1316 246.42 1316 244.76
1317 245.36 1317 243.62
1318 244.25 1318 242.42
1319 243.07 1319 241.15
1320 241.84 1320 239.82
1321 240.56 1321 238.43
1322 239.22 1322 236.99
1323 237.83 1323 235.49
1324 236.39 1324 233.93
1325 234.90 1325 232.33
1326 233.37 1326 230.66
1327 231.78 1327 228.95
1328 230.15 1328 227.19
1329 228.48 1329 225.38
1330 226.76 1330 223.53
1331 225.00 1331 221.63
1332 223.20 1332 219.69
1333 221.36 1333 217.70
1334 219.49 1334 215.68
1335 217.58 1335 213.62
1336 215.64 1336 211.52
1337 213.67 1337 209.39
1338 211.66 1338 207.23
1339 209.63 1339 205.03
1340 207.57 1340 202.80
1341 205.48 1341 200.55
1342 203.37 1342 198.27
1343 201.24 1343 195.97
1344 199.09 1344 193.64
1345 196.91 1345 191.30
1346 194.72 1346 188.93
1347 192.52 1347 186.55
1348 190.29 1348 184.15
1349 188.06 1349 181.73
1350 185.81 1350 179.31
1351 183.55 1351 176.87
1352 181.29 1352 174.42
1353 179.01 1353 171.96
1354 176.73 1354 169.50
1355 174.45 1355 167.03
1356 172.16 1356 164.56
1357 169.87 1357 162.09
1358 167.58 1358 159.61
1359 165.29 1359 157.14
1360 163.00 1360 154.67
1361 160.71 1361 152.20
1362 158.43 1362 149.74
1363 156.16 1363 147.28
1364 153.89 1364 144.83
1365 151.62 1365 142.38
1366 149.37 1366 139.95
1367 147.13 1367 137.52
1368 144.89 1368 135.11
1369 142.67 1369 132.71
1370 140.46 1370 130.32
1371 138.26 1371 127.95
1372 136.08 1372 125.59
1373 133.91 1373 123.25
1374 131.76 1374 120.93
1375 129.62 1375 118.62
1376 127.50 1376 116.33
1377 125.40 1377 114.06
1378 123.32 1378 111.81
1379 121.25 1379 109.58
1380 119.21 1380 107.37
1381 117.18 1381 105.19
1382 115.18 1382 103.02
1383 113.20 1383 100.88
1384 111.23 1384 98.76
1385 109.29 1385 96.67
1386 107.38 1386 94.60
1387 105.48 1387 92.55
1388 103.61 1388 90.53
1389 101.76 1389 88.53
1390 99.93 1390 86.56
1391 98.13 1391 84.61
1392 96.35 1392 82.69
1393 94.60 1393 80.79
1394 92.87 1394 78.93
1395 91.16 1395 77.08
1396 89.48 1396 75.27
1397 87.82 1397 73.48
1398 86.19 1398 71.72
1399 84.58 1399 69.98
1400 83.00 1400 68.27
1401 81.44 1401 66.59
1402 79.91 1402 64.93
1403 78.40 1403 63.30
1404 76.91 1404 61.70
1405 75.45 1405 60.12
1406 74.02 1406 58.57
1407 72.61 1407 57.04
1408 71.22 1408 55.55
1409 69.86 1409 54.08
1410 68.52 1410 52.63
1411 67.20 1411 51.21
1412 65.91 1412 49.81
1413 64.64 1413 48.45
1414 63.40 1414 47.10
1415 62.18 1415 45.78
1416 60.98 1416 44.49
1417 59.81 1417 43.22
1418 58.65 1418 41.98
1419 57.52 1419 40.76
1420 56.42 1420 39.56
1421 55.33 1421 38.39
1422 54.27 1422 37.24
1423 53.22 1423 36.11
1424 52.20 1424 35.01
1425 51.20 1425 33.93
1426 50.22 1426 32.87
1427 49.26 1427 31.83
1428 48.33 1428 30.82
1429 47.41 1429 29.83
1430 46.51 1430 28.86
1431 45.63 1431 27.91
1432 44.77 1432 26.98
1433 43.93 1433 26.07
1434 43.11 1434 25.18
1435 42.30 1435 24.32
1436 41.52 1436 23.47
1437 40.75 1437 22.64
1438 40.00 1438 21.83
1439 39.27 1439 21.04
1440 38.56 1440 20.27
1441 37.86 1441 19.52
1442 37.18 1442 18.78
1443 36.51 1443 18.06
1444 35.87 1444 17.36
1445 35.23 1445 16.68
1446 34.62 1446 16.02
1447 34.02 1447 15.37
1448 33.43 1448 14.74
1449 32.86 1449 14.12
1450 32.31 1450 13.52
1451 31.77 1451 12.94
1452 31.24 1452 12.37
1453 30.73 1453 11.82
1454 30.23 1454 11.28
1455 29.75 1455 10.76
1456 29.28 1456 10.25
1457 28.82 1457 9.76
1458 28.38 1458 9.28
1459 27.95 1459 8.81
1460 27.53 1460 8.36
1461 27.12 1461 7.92
1462 26.73 1462 7.50
1463 26.35 1463 7.09
1464 25.98 1464 6.69
1465 25.63 1465 6.31
1466 25.28 1466 5.94
1467 24.95 1467 5.58
1468 24.63 1468 5.23
1469 24.32 1469 4.90
1470 24.02 1470 4.58
1471 23.74 1471 4.27
1472 23.46 1472 3.97
1473 23.20 1473 3.68
1474 22.94 1474 3.41
1475 22.70 1475 3.14
1476 22.46 1476 2.89
1477 22.24 1477 2.65
1478 22.03 1478 2.42
1479 21.83 1479 2.20
1480 21.63 1480 1.99
1481 21.45 1481 1.80
1482 21.28 1482 1.61
1483 21.12 1483 1.43
1484 20.96 1484 1.27
1485 20.82 1485 1.11
1486 20.68 1486 0.97
1487 20.56 1487 0.83
1488 20.45 1488 0.71
1489 20.34 1489 0.60
1490 20.24 1490 0.49
1491 20.16 1491 0.40
1492 20.08 1492 0.31
1493 20.01 1493 0.24
1494 19.95 1494 0.18
1495 19.90 1495 0.12
1496 19.86 1496 0.08
1497 19.83 1497 0.04
1498 19.81 1498 0.02
1499 19.79 1499 0.00
If you compare minimum and maximum they occur at the same numbers but the values are reduced to 20 - 254
best regards Stefan
That looks a lot like it will take longer than an analog read even if you weren't using float math.
Why i say TABLE is that the trig functions and exp are done through series calculations that eat cycles by the hundreds but there are 16000 cycles per ms so you won't notice but close timing will.
Yup. But for what ever reason, @mastino2 is OK with that. So as long as he's gone down the float, trig, exp road, just keep going, per Churchill 
So, simply take the result of the original function, scale it by 235.0 / 255.0 and add 20.
A fine example of a solution that is not optimized for microcontrollers.
Compute a table in Excel/LibreOfficeCalc/Whatever, and drop it in a LUT. Each value is only an 8-bit unsigned integer.
Your update rate should be determined by the rate at which you wish to 'breathe'. If 10 breaths per minute is the target, and you store 600 values, you'll update at 10 mS. If you decide to 'breathe' at 100 breaths per minute, you update at 1mS. Extrapolate those to the desired ends, and cut or increase your data as necessary.
If your data contains a lot of points consecutively at the min value, consider making the min value a keyword, which is always followed by a count.
Consider, with a key value of 0:
0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,3,2,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0
vs
0,17,1,2,3,2,1,0,25
In this case, a 50-sample run is compressed to 9 bytes.
Your limitation will be the number of values you can store, sure, but at least it won't be computation-constipated.
Just an alternative viewpoint, from a micro-dinosaur. All presumes a constant update rate, of course, though that could also be finessed with a flag value if necessary.
As pointed out, @mastino2 hasn't complained about the speed or appearance of the current solution. Are you suggesting he solve a problem that he doesn't have?
Nope, just pointing out there are alternatives. Sorry to offend, @gfvalvo.
was chosen because it is exp(-1.0).
As the entire sin curve runs from -1 to 1, so the exp will go from 0.3678 to 2.7183, thus informing the scaling factor if you are aiming for 235 (255 - 20) range, and the offset of 20 if it is indeed to go from 20 to 255.
This is very good, the constant is very close to 100. I would in all cases use some constraint on the floating point number to integer code. The AI code had suggested gurading against go below 20, you could add not going over 255, although neither happens in the first few seconds of the equation with 100 as the scale factor.
val = (exp(sin(i/2000.0*PI*10)) - 0.36787944) * 100; // Adjust the scaling factor
val = val + 20; // Shift the range by -20
HTH
a7
You need to adjust the calculated value.
Do you think this would work?
float val = ( exp ( sin (i/2000.0PI10)) - 0.36787944)*108.0;
val = 20 + val * ( (255-20) / 255.0); // do NOT ommit the decimal point
He has a problem in generating values that might be easier to solve on a PC, but maybe the idea of doing that is outside of the OP's box.
I think the questioner should take another look at the basics of trigonometry.