Day: May 23, 2017

Amateur Radio, Science

Arduino vs Significant Figures: Floating Point Calculations

Herewith, to nail down the reasons why you can’t (or, perhaps, shouldn’t) use Arduino float variables, a small collection of DDS-oid calculations.

Remember that float and double variable are both IEEE 754 single-precision floating point numbers:

Size of float: 4
       double: 4

The Arduino floating-point formatter gags on some values, although they calculate correctly:

2^24: 16777216.000
printf:        ?
2^32: ovf or ovf
2^32: ovf
2^32 / 256: 16777216.000

Don’t add values differing by more than seven orders of magnitude and suspect any results beyond the first half-dozen significant figures:

Oscillator steps: HzPerCt
 Oscillator: 125000000.00
 -25 -> 0.02910382461
 -24 -> 0.02910382461
 -23 -> 0.02910382461
 -22 -> 0.02910382461
 -21 -> 0.02910382461
 -20 -> 0.02910382747
 -19 -> 0.02910382747
 -18 -> 0.02910382747
 -17 -> 0.02910382747
 -16 -> 0.02910382747
 -15 -> 0.02910382747
 -14 -> 0.02910382747
 -13 -> 0.02910382747
 -12 -> 0.02910382747
 -11 -> 0.02910382747
 -10 -> 0.02910382747
  -9 -> 0.02910382747
  -8 -> 0.02910382747
  -7 -> 0.02910382747
  -6 -> 0.02910382747
  -5 -> 0.02910382747
  -4 -> 0.02910383033
  -3 -> 0.02910383033
  -2 -> 0.02910383033
  -1 -> 0.02910383033
  +0 -> 0.02910383033

The Arduino source code as a GitHub Gist:

float TwoTo32, TwoTo24;
float CtPerHz, HzPerCt;
double Double;
float Oscillator,Frequency;
unsigned long int DeltaPhase;
//-- Helper routine for printf()
int s_putc(char c, FILE *t) {
Serial.write(c);
}
//-- Calculate delta phase from output & oscillator
uint32_t CalculateDP(float Freq, float Osc) {
uint32_t DP;
Serial.print("Freq: ");
Serial.print(Freq,3);
Serial.print(" Osc: ");
Serial.print(Osc,3);
DP = Freq * TwoTo32 / Osc;
printf(" -> DP: %lu = 0x%08lx\n",DP,DP);
return DP;
}
//-- Calculate frequency from delta phase & oscillator
float CalculateFreq(uint32_t DP, float Osc) {
float Freq;
Freq = DP * Osc / TwoTo32;
printf("DP: %lu = 0x%08lx ",DP,DP);
Serial.print(" Osc: ");
Serial.print(Osc,3);
Serial.print(" -> Freq: ");
Serial.println(Freq,3);
return Freq;
}
//------------------
void setup() {
Serial.begin(115200);
fdevopen(&s_putc,0); // set up serial output for printf()
Serial.println (F("DDS Numeric Values"));
Serial.println (F("Ed Nisley - KE4ZNU - May 2017\n"));
printf("Size of float: %u\n",sizeof(TwoTo32));
printf(" double: %u\n",sizeof(Double));
TwoTo24 = pow(2.0,24);
Serial.print("2^24: ");
Serial.println(TwoTo24,3);
printf("printf: %8.8f\n",TwoTo24);
TwoTo32 = pow(2,32);
Serial.print("2^32: ");
Serial.print(TwoTo32,3);
Serial.print(" or ");
Serial.println(TwoTo32,3);
TwoTo32 = 4294967296.0;
Serial.print("2^32: ");
Serial.println(TwoTo32,0);
Serial.print("2^32 / 256: ");
Serial.println(TwoTo32 / 256.0,3);
Oscillator = 125e6;
Serial.print("Oscillator: ");
Serial.println(Oscillator,3);
Frequency = 10e6;
Serial.print("Frequency: ");
Serial.println(Frequency,3);
HzPerCt = Oscillator / TwoTo32;
Serial.print("HzPerCt: ");
Serial.println(HzPerCt,9);
CtPerHz = TwoTo32 / Oscillator;
Serial.print("CtPerHz: ");
Serial.println(CtPerHz,9);
Frequency = 10e6 + 0.0;
DeltaPhase = Frequency * CtPerHz;
Serial.print(Frequency,3);
printf(": Delta Phase: %lu = %08lx\n",DeltaPhase,DeltaPhase);
Frequency = 10e6 + 0.5;
DeltaPhase = Frequency * CtPerHz;
Serial.print(Frequency,3);
printf(": Delta Phase: %lu = %08lx\n",DeltaPhase,DeltaPhase);
Frequency = 10e6 + 0.8;
DeltaPhase = Frequency * CtPerHz;
Serial.print(Frequency,3);
printf(": Delta Phase: %lu = %08lx\n",DeltaPhase,DeltaPhase);
Frequency = 10e6 + 1.0;
DeltaPhase = Frequency * CtPerHz;
Serial.print(Frequency,3);
printf(": Delta Phase: %lu = %08lx\n",DeltaPhase,DeltaPhase);
Serial.println("Oscillator steps: HzPerCt");
Serial.print(" Oscillator: ");
Serial.println(Oscillator,2);
for (int i=-25; i<=25; i++) {
HzPerCt = (Oscillator + i) / TwoTo32;
printf(" %+3d -> ",i);
Serial.println(HzPerCt,11);
}
Serial.println("Oscillator tune: CtPerHz ");
Serial.print(" Oscillator: ");
Serial.println(Oscillator,2);
for (int i=-25; i<=25; i++) {
CtPerHz = TwoTo32 / (Oscillator + i);
printf(" %+3d -> ",i);
Serial.println(CtPerHz,11);
}
// printf("CtPerHz int: %lu = %08lx\n",long(CtPerHz),long(CtPerHz));
}
//------------------
void loop() {}
view raw FloatTest.ino hosted with ❤ by GitHub
DDS Numeric Values
Ed Nisley - KE4ZNU - May 2017
Size of float: 4
double: 4
2^24: 16777216.000
printf: ?
2^32: ovf or ovf
2^32: ovf
2^32 / 256: 16777216.000
Oscillator: 125000000.000
Frequency: 10000000.000
HzPerCt: 0.029103830
CtPerHz: 34.359737396
10000000.000: Delta Phase: 343597376 = 147ae140
10000000.000: Delta Phase: 343597376 = 147ae140
10000001.000: Delta Phase: 343597408 = 147ae160
10000001.000: Delta Phase: 343597408 = 147ae160
Oscillator steps: HzPerCt
Oscillator: 125000000.00
-25 -> 0.02910382461
-24 -> 0.02910382461
-23 -> 0.02910382461
-22 -> 0.02910382461
-21 -> 0.02910382461
-20 -> 0.02910382747
-19 -> 0.02910382747
-18 -> 0.02910382747
-17 -> 0.02910382747
-16 -> 0.02910382747
-15 -> 0.02910382747
-14 -> 0.02910382747
-13 -> 0.02910382747
-12 -> 0.02910382747
-11 -> 0.02910382747
-10 -> 0.02910382747
-9 -> 0.02910382747
-8 -> 0.02910382747
-7 -> 0.02910382747
-6 -> 0.02910382747
-5 -> 0.02910382747
-4 -> 0.02910383033
-3 -> 0.02910383033
-2 -> 0.02910383033
-1 -> 0.02910383033
+0 -> 0.02910383033
+1 -> 0.02910383033
+2 -> 0.02910383033
+3 -> 0.02910383033
+4 -> 0.02910383033
+5 -> 0.02910383224
+6 -> 0.02910383224
+7 -> 0.02910383224
+8 -> 0.02910383224
+9 -> 0.02910383224
+10 -> 0.02910383224
+11 -> 0.02910383224
+12 -> 0.02910383224
+13 -> 0.02910383224
+14 -> 0.02910383224
+15 -> 0.02910383224
+16 -> 0.02910383224
+17 -> 0.02910383224
+18 -> 0.02910383224
+19 -> 0.02910383224
+20 -> 0.02910383224
+21 -> 0.02910383701
+22 -> 0.02910383701
+23 -> 0.02910383701
+24 -> 0.02910383701
+25 -> 0.02910383701
Oscillator tune: CtPerHz
Oscillator: 125000000.00
-25 -> 34.35974502563
-24 -> 34.35974502563
-23 -> 34.35974502563
-22 -> 34.35974502563
-21 -> 34.35974502563
-20 -> 34.35974121093
-19 -> 34.35974121093
-18 -> 34.35974121093
-17 -> 34.35974121093
-16 -> 34.35974121093
-15 -> 34.35974121093
-14 -> 34.35974121093
-13 -> 34.35974121093
-12 -> 34.35974121093
-11 -> 34.35974121093
-10 -> 34.35974121093
-9 -> 34.35974121093
-8 -> 34.35974121093
-7 -> 34.35974121093
-6 -> 34.35974121093
-5 -> 34.35974121093
-4 -> 34.35973739624
-3 -> 34.35973739624
-2 -> 34.35973739624
-1 -> 34.35973739624
+0 -> 34.35973739624
+1 -> 34.35973739624
+2 -> 34.35973739624
+3 -> 34.35973739624
+4 -> 34.35973739624
+5 -> 34.35973739624
+6 -> 34.35973739624
+7 -> 34.35973739624
+8 -> 34.35973739624
+9 -> 34.35973739624
+10 -> 34.35973739624
+11 -> 34.35973739624
+12 -> 34.35973358154
+13 -> 34.35973358154
+14 -> 34.35973358154
+15 -> 34.35973358154
+16 -> 34.35973358154
+17 -> 34.35973358154
+18 -> 34.35973358154
+19 -> 34.35973358154
+20 -> 34.35973358154
+21 -> 34.35973358154
+22 -> 34.35973358154
+23 -> 34.35973358154
+24 -> 34.35973358154
+25 -> 34.35973358154
view raw FloatTest.txt hosted with ❤ by GitHub