Generador frecuencia (dds)

Como generar frecuencias analógicas usando dds (Direct Digital Sintesis)

Esta técnica consiste en usar el generador PWM del microcontrolador para ir generando los distintos muestreos (samples) de la onda, para hacer que la onda tenga mas o menos frecuencia aumentaremos o reduciremos el numero de muestreos de nuestra onda de referencia.

Esto es así ya que la velocidad de generación de muestreos está sujeta a la velocidad del ciclo del PWM (256 ciclos de reloj), y está velocidad no podemos cambiarla, por lo tanto para modificar la frecuencia cambiamos el numero de muestreos dentro de nuestra onda de referencia, lo que significa que si usamos todos los muestreos la onda será más grave (la onda tarda mas en generarse y por lo tanto menos frecuencia), y si usamos menos muestreos la onda será mas aguda (la onda tarda menos en generarse y por lo tanto más frecuencia).

La onda de referencia la tendremos almacenada en un array.

                                           /* Direct-digital synthesis */

// ------- Preamble -------- //
#include <avr/io.h>                        /* Defines pins, ports, etc */
#include <util/delay.h>                     /* Functions to waste time */
#include <avr/power.h>

#include "fullSine.h"

static inline void initTimer0(void) {
  TCCR0A |= (1 << COM0A1);                      /* PWM output on OCR0A */
  DDRD |= (1 << PD6);               /* enable output on pin */

  TCCR0A |= (1 << WGM00);                             /* Fast PWM mode */
  TCCR0A |= (1 << WGM01);                       /* Fast PWM mode, pt.2 */

  TCCR0B |= (1 << CS00);                    /* Clock with /1 prescaler */
}

int main(void) {

  uint16_t accumulator = 0;
  uint16_t accumulatorSteps = 921;                    /* approx 440 Hz */
  uint8_t waveStep;
  int8_t pwmValue;

  // -------- Inits --------- //

  clock_prescale_set(clock_div_1);                  /* CPU clock 8 MHz */
  initTimer0();

  // ------ Event loop ------ //
  while (1) {

    accumulator += accumulatorSteps;          /* advance accumulator */
    waveStep = accumulator >> 8;           /* which entry in lookup? */
    pwmValue = fullSine[waveStep];                 /* lookup voltage */

    loop_until_bit_is_set(TIFR0, TOV0);        /* wait for PWM cycle */
    OCR0A = 128 + pwmValue;                     /* set new PWM value */
    TIFR0 |= (1 << TOV0);                  /* reset PWM overflow bit */

  }                                                  /* End event loop */
  return 0;                            /* This line is never reached */
}

El accumulatorSteps define cuantos samples avanzamos en nuestra onda en cada uno de los ciclos del pwm, en este caso estamos usando una técnica de supersampling para el accumulatorSteps, básicamente usamos un valor de 2 bytes y al final del todo lo convertimos en un valor de 1 byte para que podamos tener mas resolución a la hora de indicar el accumulatorSteps, esto nos deja con que el valor mínimo de accumulatorSteps será 256 y el valor máximo 65535, despues de aplicar la reducción del supersampling esto nos dejará con un mínimo de 1 y un máximo de 255 que es el rango de muestreos (samples) que tiene nuestra onda.

La frecuencia más baja que podemos generar es indicando accumulatorSteps a 256, para hacer el calculo tenemos que tener en cuenta que el ciclo de la generación del PWM es de 256 ciclos de reloj, por lo tanto teniendo en cuenta que estamos usando un microcontrolador a 8 Mhz con un prescaler de 1, nos deja que cada ciclo son 0.125 microsegundos, cada ciclo PWM es 32 microsegundos (0.125 por 256 ciclos de reloj) y cada generación de onda es 8192 microsegundos (32 por 256 samples que hay en la onda), esto en frecuencia se traduce mas o menos en 122 Hz (1/0.008192).

Por lo tanto un accumulatorSteps de 256 nos generará una onda de 122Hz, si queremos obtener una frecuencia distinta solo tenemos que hacer una regla de 3 para obtener el accumulatorSteps, por ejemplo para 440Hz sería (440*256)/122, lo que nos daría un accumulatorSteps de unos 923.

FullSine

int8_t fullSine[256] = { 
	0, 3, 6, 9, 12, 15, 18, 21,
	24, 27, 30, 34, 37, 39, 42, 45,
	48, 51, 54, 57, 60, 62, 65, 68,
	70, 73, 75, 78, 80, 83, 85, 87,
	90, 92, 94, 96, 98, 100, 102, 104,
	106, 107, 109, 110, 112, 113, 115, 116,
	117, 118, 120, 121, 122, 122, 123, 124,
	125, 125, 126, 126, 126, 127, 127, 127,
	127, 127, 127, 127, 126, 126, 126, 125,
	125, 124, 123, 122, 122, 121, 120, 118,
	117, 116, 115, 113, 112, 110, 109, 107,
	106, 104, 102, 100, 98, 96, 94, 92,
	90, 87, 85, 83, 80, 78, 75, 73,
	70, 68, 65, 62, 60, 57, 54, 51,
	48, 45, 42, 39, 37, 34, 30, 27,
	24, 21, 18, 15, 12, 9, 6, 3,
	0, -4, -7, -10, -13, -16, -19, -22,
	-25, -28, -31, -35, -38, -40, -43, -46,
	-49, -52, -55, -58, -61, -63, -66, -69,
	-71, -74, -76, -79, -81, -84, -86, -88,
	-91, -93, -95, -97, -99, -101, -103, -105,
	-107, -108, -110, -111, -113, -114, -116, -117,
	-118, -119, -121, -122, -123, -123, -124, -125,
	-126, -126, -127, -127, -127, -128, -128, -128,
	-128, -128, -128, -128, -127, -127, -127, -126,
	-126, -125, -124, -123, -123, -122, -121, -119,
	-118, -117, -116, -114, -113, -111, -110, -108,
	-107, -105, -103, -101, -99, -97, -95, -93,
	-91, -88, -86, -84, -81, -79, -76, -74,
	-71, -69, -66, -63, -61, -58, -55, -52,
	-49, -46, -43, -40, -38, -35, -31, -28,
	-25, -22, -19, -16, -13, -10, -7, -4
};

FullTriangle

int8_t fullTriangle[256] = { 
	0, 1, 3, 5, 7, 9, 11, 13,
	15, 17, 19, 21, 23, 25, 27, 29,
	31, 33, 35, 37, 39, 41, 43, 45,
	47, 49, 51, 53, 55, 57, 59, 61,
	63, 65, 67, 69, 71, 73, 75, 77,
	79, 81, 83, 85, 87, 89, 91, 93,
	95, 97, 99, 101, 103, 105, 107, 109,
	111, 113, 115, 117, 119, 121, 123, 125,
	127, 125, 123, 121, 119, 117, 115, 113,
	111, 109, 107, 105, 103, 101, 99, 97,
	95, 93, 91, 89, 87, 85, 83, 81,
	79, 77, 75, 73, 71, 69, 67, 65,
	63, 61, 59, 57, 55, 53, 51, 49,
	47, 45, 43, 41, 39, 37, 35, 33,
	31, 29, 27, 25, 23, 21, 19, 17,
	15, 13, 11, 9, 7, 5, 3, 1,
	0, -2, -4, -6, -8, -10, -12, -14,
	-16, -18, -20, -22, -24, -26, -28, -30,
	-32, -34, -36, -38, -40, -42, -44, -46,
	-48, -50, -52, -54, -56, -58, -60, -62,
	-64, -66, -68, -70, -72, -74, -76, -78,
	-80, -82, -84, -86, -88, -90, -92, -94,
	-96, -98, -100, -102, -104, -106, -108, -110,
	-112, -114, -116, -118, -120, -122, -124, -126,
	-128, -126, -124, -122, -120, -118, -116, -114,
	-112, -110, -108, -106, -104, -102, -100, -98,
	-96, -94, -92, -90, -88, -86, -84, -82,
	-80, -78, -76, -74, -72, -70, -68, -66,
	-64, -62, -60, -58, -56, -54, -52, -50,
	-48, -46, -44, -42, -40, -38, -36, -34,
	-32, -30, -28, -26, -24, -22, -20, -18,
	-16, -14, -12, -10, -8, -6, -4, -2
};

FullTri3

int8_t fullTri3[256] = { 
	0, 2, 4, 7, 9, 11, 13, 16,
	18, 20, 22, 24, 27, 29, 31, 33,
	35, 37, 38, 40, 42, 44, 46, 48,
	50, 52, 54, 56, 58, 60, 62, 64,
	66, 68, 70, 73, 75, 77, 80, 82,
	85, 87, 90, 92, 95, 97, 100, 102,
	105, 107, 109, 112, 114, 116, 118, 119,
	121, 122, 123, 125, 125, 126, 127, 127,
	127, 127, 127, 126, 125, 125, 123, 122,
	121, 119, 118, 116, 114, 112, 109, 107,
	105, 102, 100, 97, 95, 92, 90, 87,
	85, 82, 80, 77, 75, 73, 70, 68,
	66, 64, 62, 60, 58, 56, 54, 52,
	50, 48, 46, 44, 42, 40, 38, 37,
	35, 33, 31, 29, 27, 24, 22, 20,
	18, 16, 13, 11, 9, 7, 4, 2,
	0, -3, -5, -8, -10, -12, -14, -17,
	-19, -21, -23, -25, -28, -30, -32, -34,
	-36, -38, -39, -41, -43, -45, -47, -49,
	-51, -53, -55, -57, -59, -61, -63, -65,
	-67, -69, -71, -74, -76, -78, -81, -83,
	-86, -88, -91, -93, -96, -98, -101, -103,
	-106, -108, -110, -113, -115, -117, -119, -120,
	-122, -123, -124, -126, -126, -127, -128, -128,
	-128, -128, -128, -127, -126, -126, -124, -123,
	-122, -120, -119, -117, -115, -113, -110, -108,
	-106, -103, -101, -98, -96, -93, -91, -88,
	-86, -83, -81, -78, -76, -74, -71, -69,
	-67, -65, -63, -61, -59, -57, -55, -53,
	-51, -49, -47, -45, -43, -41, -39, -38,
	-36, -34, -32, -30, -28, -25, -23, -21,
	-19, -17, -14, -12, -10, -8, -5, -3
};

FullTri7

int8_t fullTri7[256] = { 
	0, 2, 4, 6, 8, 10, 12, 14,
	16, 18, 20, 22, 24, 26, 28, 30,
	32, 34, 36, 39, 41, 43, 45, 47,
	49, 51, 53, 55, 57, 59, 61, 63,
	65, 67, 69, 71, 73, 76, 78, 80,
	82, 84, 86, 88, 90, 92, 94, 96,
	97, 99, 101, 103, 106, 108, 110, 113,
	115, 118, 120, 122, 124, 125, 126, 127,
	127, 127, 126, 125, 124, 122, 120, 118,
	115, 113, 110, 108, 106, 103, 101, 99,
	97, 96, 94, 92, 90, 88, 86, 84,
	82, 80, 78, 76, 73, 71, 69, 67,
	65, 63, 61, 59, 57, 55, 53, 51,
	49, 47, 45, 43, 41, 39, 36, 34,
	32, 30, 28, 26, 24, 22, 20, 18,
	16, 14, 12, 10, 8, 6, 4, 2,
	0, -3, -5, -7, -9, -11, -13, -15,
	-17, -19, -21, -23, -25, -27, -29, -31,
	-33, -35, -37, -40, -42, -44, -46, -48,
	-50, -52, -54, -56, -58, -60, -62, -64,
	-66, -68, -70, -72, -74, -77, -79, -81,
	-83, -85, -87, -89, -91, -93, -95, -97,
	-98, -100, -102, -104, -107, -109, -111, -114,
	-116, -119, -121, -123, -125, -126, -127, -128,
	-128, -128, -127, -126, -125, -123, -121, -119,
	-116, -114, -111, -109, -107, -104, -102, -100,
	-98, -97, -95, -93, -91, -89, -87, -85,
	-83, -81, -79, -77, -74, -72, -70, -68,
	-66, -64, -62, -60, -58, -56, -54, -52,
	-50, -48, -46, -44, -42, -40, -37, -35,
	-33, -31, -29, -27, -25, -23, -21, -19,
	-17, -15, -13, -11, -9, -7, -5, -3
};

FullTri15

int8_t fullTri15[256] = { 
	0, 2, 4, 6, 8, 10, 12, 14,
	16, 18, 20, 22, 24, 26, 28, 30,
	32, 34, 36, 38, 40, 42, 44, 46,
	48, 50, 52, 54, 56, 58, 60, 62,
	64, 66, 68, 70, 72, 74, 76, 78,
	80, 82, 84, 86, 88, 90, 92, 94,
	96, 98, 100, 102, 105, 107, 109, 111,
	112, 114, 116, 119, 121, 123, 125, 127,
	127, 127, 125, 123, 121, 119, 116, 114,
	112, 111, 109, 107, 105, 102, 100, 98,
	96, 94, 92, 90, 88, 86, 84, 82,
	80, 78, 76, 74, 72, 70, 68, 66,
	64, 62, 60, 58, 56, 54, 52, 50,
	48, 46, 44, 42, 40, 38, 36, 34,
	32, 30, 28, 26, 24, 22, 20, 18,
	16, 14, 12, 10, 8, 6, 4, 2,
	0, -3, -5, -7, -9, -11, -13, -15,
	-17, -19, -21, -23, -25, -27, -29, -31,
	-33, -35, -37, -39, -41, -43, -45, -47,
	-49, -51, -53, -55, -57, -59, -61, -63,
	-65, -67, -69, -71, -73, -75, -77, -79,
	-81, -83, -85, -87, -89, -91, -93, -95,
	-97, -99, -101, -103, -106, -108, -110, -112,
	-113, -115, -117, -120, -122, -124, -126, -128,
	-128, -128, -126, -124, -122, -120, -117, -115,
	-113, -112, -110, -108, -106, -103, -101, -99,
	-97, -95, -93, -91, -89, -87, -85, -83,
	-81, -79, -77, -75, -73, -71, -69, -67,
	-65, -63, -61, -59, -57, -55, -53, -51,
	-49, -47, -45, -43, -41, -39, -37, -35,
	-33, -31, -29, -27, -25, -23, -21, -19,
	-17, -15, -13, -11, -9, -7, -5, -3
};

FullSquare3

int8_t fullSquare3[256] = { 
	0, 10, 20, 29, 39, 48, 57, 66,
	74, 82, 89, 96, 102, 107, 112, 116,
	119, 122, 124, 126, 127, 127, 127, 126,
	125, 124, 122, 121, 118, 116, 114, 111,
	109, 107, 104, 102, 100, 99, 97, 96,
	95, 95, 94, 94, 94, 95, 96, 97,
	98, 99, 101, 102, 104, 106, 108, 109,
	111, 112, 114, 115, 116, 117, 117, 118,
	118, 118, 117, 117, 116, 115, 114, 112,
	111, 109, 108, 106, 104, 102, 101, 99,
	98, 97, 96, 95, 94, 94, 94, 95,
	95, 96, 97, 99, 100, 102, 104, 107,
	109, 111, 114, 116, 118, 121, 122, 124,
	125, 126, 127, 127, 127, 126, 124, 122,
	119, 116, 112, 107, 102, 96, 89, 82,
	74, 66, 57, 48, 39, 29, 20, 10,
	0, -11, -21, -30, -40, -49, -58, -67,
	-75, -83, -90, -97, -103, -108, -113, -117,
	-120, -123, -125, -127, -128, -128, -128, -127,
	-126, -125, -123, -122, -119, -117, -115, -112,
	-110, -108, -105, -103, -101, -100, -98, -97,
	-96, -96, -95, -95, -95, -96, -97, -98,
	-99, -100, -102, -103, -105, -107, -109, -110,
	-112, -113, -115, -116, -117, -118, -118, -119,
	-119, -119, -118, -118, -117, -116, -115, -113,
	-112, -110, -109, -107, -105, -103, -102, -100,
	-99, -98, -97, -96, -95, -95, -95, -96,
	-96, -97, -98, -100, -101, -103, -105, -108,
	-110, -112, -115, -117, -119, -122, -123, -125,
	-126, -127, -128, -128, -128, -127, -125, -123,
	-120, -117, -113, -108, -103, -97, -90, -83,
	-75, -67, -58, -49, -40, -30, -21, -11
};

FullSquare7

int8_t fullSquare7[256] = { 
	-1, 23, 46, 66, 85, 100, 112, 120,
	125, 127, 126, 123, 119, 114, 109, 104,
	100, 98, 97, 97, 98, 101, 104, 107,
	110, 113, 114, 115, 115, 114, 112, 110,
	108, 106, 104, 102, 101, 101, 102, 103,
	105, 107, 109, 111, 112, 113, 113, 112,
	111, 110, 108, 106, 105, 103, 103, 103,
	103, 104, 105, 107, 108, 110, 111, 112,
	112, 112, 111, 110, 108, 107, 105, 104,
	103, 103, 103, 103, 105, 106, 108, 110,
	111, 112, 113, 113, 112, 111, 109, 107,
	105, 103, 102, 101, 101, 102, 104, 106,
	108, 110, 112, 114, 115, 115, 114, 113,
	110, 107, 104, 101, 98, 97, 97, 98,
	100, 104, 109, 114, 119, 123, 126, 127,
	125, 120, 112, 100, 85, 66, 46, 23,
	0, -24, -47, -67, -86, -101, -113, -121,
	-126, -128, -127, -124, -120, -115, -110, -105,
	-101, -99, -98, -98, -99, -102, -105, -108,
	-111, -114, -115, -116, -116, -115, -113, -111,
	-109, -107, -105, -103, -102, -102, -103, -104,
	-106, -108, -110, -112, -113, -114, -114, -113,
	-112, -111, -109, -107, -106, -104, -104, -104,
	-104, -105, -106, -108, -109, -111, -112, -113,
	-113, -113, -112, -111, -109, -108, -106, -105,
	-104, -104, -104, -104, -106, -107, -109, -111,
	-112, -113, -114, -114, -113, -112, -110, -108,
	-106, -104, -103, -102, -102, -103, -105, -107,
	-109, -111, -113, -115, -116, -116, -115, -114,
	-111, -108, -105, -102, -99, -98, -98, -99,
	-101, -105, -110, -115, -120, -124, -127, -128,
	-126, -121, -113, -101, -86, -67, -47, -24
};

FullSquare15

int8_t fullSquare15[256] = { 
	-1, 49, 90, 116, 127, 125, 115, 105,
	98, 98, 103, 109, 114, 115, 113, 108,
	104, 102, 104, 107, 110, 112, 112, 110,
	107, 104, 104, 106, 109, 111, 111, 110,
	108, 106, 105, 105, 107, 109, 111, 111,
	109, 107, 106, 105, 106, 108, 110, 110,
	110, 108, 106, 106, 106, 107, 109, 110,
	110, 109, 107, 106, 106, 107, 108, 110,
	110, 110, 108, 107, 106, 106, 107, 109,
	110, 110, 109, 107, 106, 106, 106, 108,
	110, 110, 110, 108, 106, 105, 106, 107,
	109, 111, 111, 109, 107, 105, 105, 106,
	108, 110, 111, 111, 109, 106, 104, 104,
	107, 110, 112, 112, 110, 107, 104, 102,
	104, 108, 113, 115, 114, 109, 103, 98,
	98, 105, 115, 125, 127, 116, 90, 49,
	0, -50, -91, -117, -128, -126, -116, -106,
	-99, -99, -104, -110, -115, -116, -114, -109,
	-105, -103, -105, -108, -111, -113, -113, -111,
	-108, -105, -105, -107, -110, -112, -112, -111,
	-109, -107, -106, -106, -108, -110, -112, -112,
	-110, -108, -107, -106, -107, -109, -111, -111,
	-111, -109, -107, -107, -107, -108, -110, -111,
	-111, -110, -108, -107, -107, -108, -109, -111,
	-111, -111, -109, -108, -107, -107, -108, -110,
	-111, -111, -110, -108, -107, -107, -107, -109,
	-111, -111, -111, -109, -107, -106, -107, -108,
	-110, -112, -112, -110, -108, -106, -106, -107,
	-109, -111, -112, -112, -110, -107, -105, -105,
	-108, -111, -113, -113, -111, -108, -105, -103,
	-105, -109, -114, -116, -115, -110, -104, -99,
	-99, -106, -116, -126, -128, -117, -91, -50
};

FullSaw3

int8_t fullSaw3[256] = { 
	0, 2, 4, 6, 8, 10, 12, 14,
	16, 18, 20, 22, 23, 25, 27, 28,
	29, 31, 32, 33, 34, 35, 35, 36,
	37, 37, 38, 38, 38, 38, 39, 39,
	39, 39, 39, 38, 38, 38, 38, 38,
	38, 38, 38, 38, 38, 38, 38, 38,
	39, 39, 40, 40, 41, 42, 43, 44,
	45, 46, 47, 49, 51, 52, 54, 56,
	58, 61, 63, 65, 68, 70, 73, 76,
	79, 81, 84, 87, 90, 93, 96, 98,
	101, 104, 106, 109, 111, 114, 116, 118,
	120, 121, 123, 124, 125, 126, 126, 127,
	127, 127, 126, 126, 125, 124, 122, 120,
	118, 116, 113, 110, 107, 104, 100, 96,
	92, 87, 83, 78, 72, 67, 62, 56,
	50, 44, 38, 32, 25, 19, 12, 6,
	0, -7, -13, -20, -26, -33, -39, -45,
	-51, -57, -63, -68, -73, -79, -84, -88,
	-93, -97, -101, -105, -108, -111, -114, -117,
	-119, -121, -123, -125, -126, -127, -127, -128,
	-128, -128, -127, -127, -126, -125, -124, -122,
	-121, -119, -117, -115, -112, -110, -107, -105,
	-102, -99, -97, -94, -91, -88, -85, -82,
	-80, -77, -74, -71, -69, -66, -64, -62,
	-59, -57, -55, -53, -52, -50, -48, -47,
	-46, -45, -44, -43, -42, -41, -41, -40,
	-40, -39, -39, -39, -39, -39, -39, -39,
	-39, -39, -39, -39, -39, -39, -40, -40,
	-40, -40, -40, -39, -39, -39, -39, -38,
	-38, -37, -36, -36, -35, -34, -33, -32,
	-30, -29, -28, -26, -24, -23, -21, -19,
	-17, -15, -13, -11, -9, -7, -5, -3
};

FullSaw7

int8_t fullSaw7[256] = { 
	0, 1, 3, 5, 7, 8, 10, 11,
	12, 13, 14, 15, 15, 15, 15, 16,
	16, 16, 16, 16, 16, 16, 16, 17,
	17, 18, 19, 20, 21, 23, 24, 26,
	28, 30, 32, 34, 36, 38, 39, 41,
	43, 44, 45, 46, 47, 47, 48, 48,
	48, 48, 48, 48, 48, 47, 47, 47,
	47, 47, 48, 49, 50, 51, 52, 54,
	55, 57, 60, 62, 64, 66, 69, 71,
	73, 75, 77, 79, 80, 81, 82, 82,
	82, 82, 82, 81, 80, 80, 79, 78,
	77, 76, 75, 75, 75, 76, 76, 78,
	79, 81, 84, 87, 90, 94, 98, 102,
	106, 110, 114, 117, 121, 123, 125, 127,
	127, 127, 125, 122, 119, 114, 108, 101,
	93, 84, 74, 63, 51, 39, 26, 13,
	0, -14, -27, -40, -52, -64, -75, -85,
	-94, -102, -109, -115, -120, -123, -126, -128,
	-128, -128, -126, -124, -122, -118, -115, -111,
	-107, -103, -99, -95, -91, -88, -85, -82,
	-80, -79, -77, -77, -76, -76, -76, -77,
	-78, -79, -80, -81, -81, -82, -83, -83,
	-83, -83, -83, -82, -81, -80, -78, -76,
	-74, -72, -70, -67, -65, -63, -61, -58,
	-56, -55, -53, -52, -51, -50, -49, -48,
	-48, -48, -48, -48, -49, -49, -49, -49,
	-49, -49, -49, -48, -48, -47, -46, -45,
	-44, -42, -40, -39, -37, -35, -33, -31,
	-29, -27, -25, -24, -22, -21, -20, -19,
	-18, -18, -17, -17, -17, -17, -17, -17,
	-17, -17, -16, -16, -16, -16, -15, -14,
	-13, -12, -11, -9, -8, -6, -4, -2
};

FullSaw15

int8_t fullSaw15[256] = { 
	0, 1, 3, 4, 5, 6, 7, 7,
	7, 7, 7, 7, 8, 9, 10, 12,
	13, 15, 17, 18, 20, 21, 21, 22,
	22, 22, 22, 22, 22, 23, 24, 25,
	27, 29, 31, 33, 34, 35, 36, 36,
	36, 36, 36, 36, 36, 37, 38, 39,
	41, 43, 45, 47, 48, 50, 51, 51,
	51, 51, 51, 51, 51, 51, 52, 53,
	54, 56, 58, 61, 63, 64, 66, 66,
	67, 66, 66, 65, 65, 65, 65, 66,
	68, 70, 72, 75, 77, 79, 81, 82,
	82, 82, 81, 80, 79, 78, 78, 78,
	80, 82, 85, 88, 92, 95, 97, 99,
	100, 99, 98, 95, 93, 90, 88, 88,
	89, 91, 96, 101, 108, 115, 121, 125,
	127, 125, 119, 108, 93, 74, 51, 26,
	0, -27, -52, -75, -94, -109, -120, -126,
	-128, -126, -122, -116, -109, -102, -97, -92,
	-90, -89, -89, -91, -94, -96, -99, -100,
	-101, -100, -98, -96, -93, -89, -86, -83,
	-81, -79, -79, -79, -80, -81, -82, -83,
	-83, -83, -82, -80, -78, -76, -73, -71,
	-69, -67, -66, -66, -66, -66, -67, -67,
	-68, -67, -67, -65, -64, -62, -59, -57,
	-55, -54, -53, -52, -52, -52, -52, -52,
	-52, -52, -52, -51, -49, -48, -46, -44,
	-42, -40, -39, -38, -37, -37, -37, -37,
	-37, -37, -37, -36, -35, -34, -32, -30,
	-28, -26, -25, -24, -23, -23, -23, -23,
	-23, -23, -22, -22, -21, -19, -18, -16,
	-14, -13, -11, -10, -9, -8, -8, -8,
	-8, -8, -8, -7, -6, -5, -4, -2
};

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