Double subtract

Question

Hello,
Can you explain me what's wrong with the following code and the result I get?
Thank you for your help
Dom
// the code
import java.math.*;
public class SubtractMaxDouble{
static double r=0D;
public static final void main(String[] args){
System.out.println("Double.MAX_VALUE="+Double.MAX_VALUE);
r=Double.MAX_VALUE-1D;
if (r==Double.MAX_VALUE){System.out.println("BAD "+Double.MAX_VALUE+"-1="+r);}else{System.out.println("OK r="+r);}
System.out.println("MaxDouble= "+new BigDecimal(Double.MAX_VALUE).toString());
System.out.println("Diff = "+new BigDecimal(Double.MAX_VALUE-1D).toString());
// the output I get
Double.MAX_VALUE=1.7976931348623157E308
BAD 1.7976931348623157E308-1=1.7976931348623157E308
MaxDouble= 179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368
Diff = 179769313486231570814527423731704356798070567525844996598917476803157260780028538760589558632766878171540458953514382464234321326889464182768467546703537516986049910576551282076245490090389328944075868508455133942304583236903222948165808559332123348274797826204144723168738177180919299881250404026184124858368

Answer 1

Thanks for this answer, Danperkins.
I'm clearly a newbye with computer mathematics but also with american language...
Sig figs, dude. Sig figs.Sig figs, Google says Significant figures
I'm here to learn a maximum (Double.MAX_VALUE ?). Some "jargon" doesn't sound for me (I'm a french reader, I apologize). Can you explain me the meaning of "dude"? A cool nickname I hope!
About your explanation, I agree there is a big difference beetween the digits used to represent a "real" number (my human reading)
and the way they are represented inside the computer (using IEEE754). I perfectly understand that the continuum of real numbers cannot be represented.
So now the question is "what is the double X value that is enougth to obtain 1.7976931348623157E308-X=1.7976931348623156E308?"
X=1.7976931348623157E308-1.7976931348623156E308
I obtain X=1.9958403095347198E292
I'm really sorry but I have some difficulties to "agree" with such a huge X that means
All the "real" numbers from "1.7976931348623157E308-X+1" to "Double.MAX_VALUE" are represented by the internal IEE754 double 1.7976931348623157E308
that also means that for each Y in [Double.MIN_VALUE .. X-Double.MIN_VALUE] the answer to Double.MAX_VALUE-Y will be Double.MAX_VALUE
Where I'm wrong? And if I'm right "You know what Georges?" I'm not happy!
Dom
To satisfy your curiosity about adding the following class
import java.math.*;
public class AddMinDouble{
static double r=0D;
public static final void main(String[] args){
System.out.println("Double.MIN_VALUE="+Double.MIN_VALUE);
r=Double.MIN_VALUE+1D;
if (r==Double.MIN_VALUE){System.out.println("BAD "+Double.MIN_VALUE+"+1="+r);}else{System.out.println("OK r="+r);}
System.out.println("MinDouble= "+new BigDecimal(Double.MIN_VALUE).toString());
System.out.println("Add = "+new BigDecimal(Double.MIN_VALUE+1D).toString());
r=1.7976931348623157E-300+1D;// your value+1
if (r==1.7976931348623157E-300){System.out.println("BAD r=1.7976931348623157E-300");}else{System.out.println("OK r="+r);}
output
Double.MIN_VALUE=4.9E-324
OK r=1.0
MinDouble= 0.0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
31903114045278458171678489821036887186360569987307230500063874091535649843873124733972731696151400317153853980741262385655911710
389733598993664809941164205702637090279242767544565229087538682506419718265533447265625
Add = 1
OK r=1.0