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:
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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() {} |
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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 |