Arduino vs. Significant Figures: BigNumber Library

The BigNumber library wraps the bc arbitrary precision calculator into a set of Arduino routines that seem like a reasonable basis for DDS calculations requiring more than the half-dozen digits of a floating point number or the limited range of scaled fixed point numbers tucked into an long int.

Treating programming as an experimental science produces some Arduino source code and its output as a GitHub Gist:

// BigNumber exercise
#include "BigNumber.h"
//-- Helper routine for printf()
int s_putc(char c, FILE *t) {
Serial.write(c);
}
void setup ()
{
Serial.begin (115200);
fdevopen(&s_putc,0); // set up serial output for printf()
Serial.println ("BigNumber exercise");
Serial.println ("Ed Nisley - KE4ZNU - April 2017");
#define WHOLES 10
#define FRACTS 10
printf("Fraction digits: %d\n",FRACTS);
BigNumber::begin (FRACTS);
char *pBigNumber;
#define BUFFLEN (WHOLES + FRACTS)
char NumString[BUFFLEN];
BigNumber Tenth = "0.1"; // useful constants
BigNumber Half = "0.5";
BigNumber One = 1;
BigNumber Two = 2;
BigNumber ThirtyTwoBits = Two.pow(32);
Serial.println(ThirtyTwoBits);
BigNumber Oscillator = "125000000";
Serial.println(Oscillator);
BigNumber HertzPerCount;
HertzPerCount = Oscillator / ThirtyTwoBits;
Serial.println(HertzPerCount);
BigNumber CountPerHertz;
CountPerHertz = ThirtyTwoBits / Oscillator;
Serial.println(CountPerHertz);
BigNumber TestFreq = "60000";
Serial.println(TestFreq);
BigNumber DeltaPhi;
DeltaPhi = TestFreq * CountPerHertz;
Serial.println(DeltaPhi);
long DeltaPhiL;
DeltaPhiL = DeltaPhi;
printf("Long: %ld\n",DeltaPhiL);
Serial.println("0.1 Hz increment …");
Serial.println(TestFreq + Tenth);
DeltaPhi = (TestFreq + Tenth) * CountPerHertz;
Serial.println(DeltaPhi);
TestFreq = DeltaPhi * HertzPerCount;
Serial.println(TestFreq);
Serial.println("Rounding DeltaPhi up …");
DeltaPhi += Half;
Serial.println(DeltaPhi);
TestFreq = DeltaPhi * HertzPerCount;
Serial.println(TestFreq);
pBigNumber = DeltaPhi.toString();
printf("String: %04x → %s\n",pBigNumber,pBigNumber);
free(pBigNumber);
DeltaPhiL = DeltaPhi;
printf("Unsigned: %ld\n",DeltaPhiL);
pBigNumber = "59999.9";
TestFreq = pBigNumber;
Serial.println(TestFreq);
DeltaPhi = TestFreq * CountPerHertz;
Serial.println(DeltaPhi);
Serial.println("Rounding DeltaPhi up …");
DeltaPhi = TestFreq * CountPerHertz + Half;
Serial.println(DeltaPhi);
DeltaPhiL = DeltaPhi;
int rc = snprintf(NumString,BUFFLEN,"%ld",DeltaPhiL);
if (rc > 0 && rc < BUFFLEN) {
printf("String length: %d\n",rc);
}
else {
printf("Whoops: %d for %ld\n",rc,DeltaPhiL);
strncpy(NumString,"123456789",sizeof(NumString));
NumString[BUFFLEN-1] = 0;
printf(" forced: %s\n",NumString);
}
printf("Back from string [%s]\n",NumString);
DeltaPhi = NumString;
Serial.println(DeltaPhi);
TestFreq = DeltaPhi * HertzPerCount;
Serial.println(TestFreq);
}
void loop () {
}
view raw BigNumTest.ino hosted with ❤ by GitHub
BigNumber exercise
Ed Nisley - KE4ZNU - April 2017
Fraction digits: 10
4294967296
125000000
0.0291038304
34.3597383680
60000
2061584.3020800000
Long: 2061584
0.1 Hz increment …
60000.1000000000
2061587.7380538368
60000.0998830384
Rounding DeltaPhi up …
2061588.2380538368
60000.1144349536
String: 045e → 2061588.2380538368
Unsigned: 2061588
59999.9
2061580.8661061632
Rounding DeltaPhi up …
2061581.3661061632
String length: 7
Back from string [2061581]
2061581
59999.9037798624
view raw BigNumTest.txt hosted with ❤ by GitHub

All that happened incrementally, as you might expect, with the intent of seeing how it works, rather than actually doing anything.

Some musings, in no particular order:

The library soaks up quite a hunk of program space:

Sketch uses 13304 bytes (43%) of program storage space. Maximum is 30720 bytes.

I think you could cut that back a little by eliminating unused bc routines, like square root / exponential / modulus.

That test code also blots up quite a bit of RAM:

Global variables use 508 bytes (24%) of dynamic memory, leaving 1540 bytes for local variables. Maximum is 2048 bytes.

All the BigNumber variables live inside the setup() function (or whatever it’s called in Arduino-speak), so they count as local variables. They’re four bytes each, excluding the dynamically allocated storage for the actual numbers at roughly a byte per digit. With 10 decimal places for all numbers, plus (maybe) an average of half a dozen integer digits, those ten BigNumbers soak up 200 = 10 × (4 + 16) bytes of precious RAM.

You can load a BigNumber from an int (not a long) or a string, then export the results to a long or a string. Given that controlling a DDS frequency with a knob involves mostly adding and subtracting a specific step size, strings would probably work fine, using snprintf() to jam the string equivalent of a long into a BigNumber as needed.

You must have about ten decimal places to hold enough significant figures in the HertzPerCount and CountPerHertz values. The library scale factor evidently forces all the numbers to have at least that many digits, with the decimal point stuck in front of them during string output conversions.

The biggest integers happen in the Oscillator and ThirtyTwoBits values, with 9 and 10 digits, respectively.

It looks useful, although I’m uncomfortable with the program space required. I have no way to estimate the program space for a simpleminded DDS controller, other than knowing it’ll be more than I estimate.

While poking around, however, I discovered the Arduino compiler does provide (limited) support for long long int variables. Given a 64 bit unit for simple arithmetic operations, a simpler implementation of fixed point numbers may be do-able: 32 bits for the integer and fraction should suffice! More on that shortly.