Preprocessor math errors?

I'm working on some code to read the supply battery's voltage level from an analog input pin. Vin supplies input to a voltage divider circuit, which is then connected to an analog input of the MCU. I am using preprocessor definitions rather than constants because I would like to keep static memory use to a minimum, though out of desperation I did try a version of my code using constants with the same results.

Here is a simple test sketch which illustrates the problems I am experiencing:

#include "WProgram.h"

#define BATT_R1    220000.0
#define BATT_R2    100000.0

#define BATT_VOUT  5.0 * 1000000.0
#define BATT_VIN   BATT_VOUT / (BATT_R2 / (BATT_R1 + BATT_R2))

#define BATT_STEPS  1024.0
#define BATT_STEP   BATT_VIN / BATT_STEPS

#define BATT_ADJUST  100000.0 / BATT_STEP

void setup()
{
   Serial.begin(9600);
   
   Serial.println("---- Begin ----");
   
   Serial.print("BATT_R1: ");
   Serial.println(BATT_R1);
   
   Serial.print("BATT_R2: ");
   Serial.println(BATT_R2);
   
   Serial.print("BATT_VOUT: ");
   Serial.println(BATT_VOUT);
   
   Serial.print("BATT_VIN: ");
   Serial.println(BATT_VIN);
   
   Serial.print("BATT_STEPS: ");
   Serial.println(BATT_STEPS);
   
   Serial.print("BATT_STEP: ");
   Serial.println(BATT_STEP);
   
   Serial.print("BATT_ADJUST: ");
   Serial.println(BATT_ADJUST);
   
   Serial.println("---- End ----");
}

void loop()
{
}

And the output from that sketch:

---- Begin ----
BATT_R1: 220000.00
BATT_R2: 100000.00
BATT_VOUT: 5000000.00
BATT_VIN: 16000000.00
BATT_STEPS: 1024.00
BATT_STEP: 15625.00
BATT_ADJUST: 62500000.00
---- End ----

The portion that is calculated incorrectly is the BATT_ADJUST definition. The value should be 6.4. Also notice that all my definitions supply numbers in floating point values. More of the calculations are skewed when I provide integral values. I have tried casting these values to type float or unsigned long and the results are exactly the same. I also find this very strange since, even casting to an integral value, the println() method still displays BATT_ADJUST as if it were a floating point value, defaulting to 2 decimal places. I'm fairly certain that the Arduino is being reprogrammed since it responds appropriately when I reprogram it with additional calls to the print method, or with an entirely different sketch.

I am using an official Arduino Mega 2560. I write most of the code in Vim, but am programming the board with Arduino software version 0022 under Mac OS X 10.6. In case you are wondering, I am aware that the Arduino software must reload the sketch if any code has been altered outside the ide.

Any assistance would be greatly appreciated.

Order of operations agrees with the complier:

100000.0 / 5.0 * 1000000.0 / (100000.0 / (220000.0 + 100000.0)) / 1024.0

100000.0 / 5.0 * 1000000.0 / ( 100000.0 / 320000.0 ) / 1024. 0

20000 * 1000000.0 / ( 100000.0 / 320000.0 ) / 1024. 0

20000000000 / (.3125) / 1024.0

64000000000 / 1024 62500000

I just expanded the macros out, I get what the complier does... Keep in mind the complier just does a simple text substitution for the #define macros. It doesn't "calculate" BATT_VIN and then replace "BATT_VIN" with a calculated value. Instead, anywhere "BATT_VIN" is used, it is replaced with "BATT_VOUT / (BATT_R2 / (BATT_R1 + BATT_R2))". So work with your last Macro and go backwards.

Enclose all your intermediate defines in parens to enforce the order of operations you want.

Order of operations agrees with the complier

Well, this is embarrassing. I'd been plugging the intermediate steps into my calculator separately and coming up with the answers I needed. Of course, not thinking that this method of computation is the same as placing parenthesis around each separate calculation. Funny how the most obvious errors are sometimes the hardest to spot.

I changed my defines so that everything that does a calculation is in parenthesis which has fixed the problem. I thank you folks for your assistance. Much appreciated! :)

Does your sketch size really change when you use #define instead of float? By how much?