To pack your 4000 bits of data in the first place, write a C or Python program that runs on a host computer and writes out array definitions that you can cut and paste into a sketch.

To pack your 4000 bits of data in the first place, write a C or Python program that runs on a host computer and writes out array definitions that you can cut and paste into a sketch. Here's an example (in Python) that packs bits into bytes:

data = [1,1,0,0,0,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0,0,0,0,0,1,1,0,0,1,0,0,0,0,0,1,0,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,1,1,1,0,0,1,1,1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0,1,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,1]

first = 1; byt = 0
for i, b in enumerate(data):
  if i%8==0:
    if first:
       print 'const uint8_t fnums[] PROGMEM {',
       first = 0
    else:
       print '{},'.format(byt),
       byt = 0
  byt = (byt<<1) | b        # add bit into byte being built

print byt<<(8-i%8), '};'

Here is what the program produces:

const uint8_t fnums[] PROGMEM { 197, 43, 32, 200, 47, 197, 30, 119, 153, 37, 180, 117, 48, 218, 214, 212, 170, 262 };

If you want that code to instead pack bits into 16-bit words, change 8 to 16 in four places. Note, the code stores bits in the “bit 0 as MSb and bit 7 as LSb” order mentioned in Ignacio's answer. Thus, data[0] is stored in the high bit of fnums[0], data[8] is stored in the high bit of fnums[1] , and so forth.

As noted in Ignacio's answer, you can pack your bits of data into bytes and access them via pgm_read_byte() calls. If you prefer to pack the bits into larger units, you can use word and dword access functions, as listed in AVR pgmspace.h documentation. The _near and _far suffixes denote 16 or 32 bit pointers, respectively; for an Uno with its 32K flash memory, _near is always suitable. See PROGMEM documentation at arduino.cc for further discussion.

Here's an example program that accesses and prints data from program memory in 16-bit chunks:

void setup() {
  Serial.begin(115200);         // initialize serial port
}
int k=0;
const uint16_t fnums[] PROGMEM {191, 272, 353, 434, 515, 646, 767, 888};
void loop() {
  uint16_t b = pgm_read_word_near(fnums+k);
  Serial.print(k);  Serial.print(" ");
  Serial.print(b);  Serial.println();
  k = (k+1)%8;
  delay(1000);
}

To pack your 4000 bits of data in the first place, write a C or Python program that runs on a host computer and writes out array definitions that you can cut and paste into a sketch.

As noted in Ignacio's answer, you can pack your bits of data into bytes and access them via pgm_read_byte() calls. If (for coding convenience, not for efficiency) you prefer to pack the bits into larger units, you can use word and dword access functions, as listed in AVR pgmspace.h documentation. The _near and _far suffixes denote 16 or 32 bit pointers, respectively; for an Uno with its 32K flash memory, _near is always suitable. See PROGMEM documentation at arduino.cc for further discussion.

Here's an example program that accesses and prints data from program memory in 16-bit chunks:

void setup() {
  Serial.begin(115200);         // initialize serial port
}
int k=0;
const uint16_t fnums[] PROGMEM {191, 272, 353, 434, 515, 646, 767, 888};
void loop() {
  uint16_t b = pgm_read_word_near(fnums+k);
  Serial.print(k);  Serial.print(" ");
  Serial.print(b);  Serial.println();
  k = (k+1)%8;
  delay(1000);
}

To pack your 4000 bits of data in the first place, write a C or Python program that runs on a host computer and writes out array definitions that you can cut and paste into a sketch.