while with double

[perca]

Hi,
I have problems with the following code:


double LOW,HIGH,VALUE,STEP;
cout<<"Lower limit?\n";
cin>>LOW;
cout<<"Higher limit?\n";
cin>>HIGH;
STEP=0.1;
//first loop:
VALUE=LOW;
while (VALUE<HIGH+STEP)
{
cout<<"\t"<<VALUE;
VALUE=VALUE+STEP;
}
cout<<"\n";
//second loop:
VALUE=LOW;
while (!(VALUE>HIGH))
{
cout<<"\t"<<VALUE;
VALUE=VALUE+STEP;
}
cout<<"\n";


For instance:
If "LOW" is set to 0.7 and "HIGH" to 1.1, the first loop gives 0.7 up to 1.2 while the second loop works (0.7 to 1.1).
If "LOW" is set to 0.8 and "HIGH" to 1.2, the second loop gives 0.8 up to 1.1 while the second loop works (0.8 to 1.2).
Why is this?

[perca]

Oopps! Should read:


For instance:
If "LOW" is set to 0.7 and "HIGH" to 1.1, the first loop gives 0.7 up to 1.2 while the second loop works (0.7 to 1.1).
If "LOW" is set to 0.8 and "HIGH" to 1.2, the second loop gives 0.8 up to 1.1 while the FIRST loop works (0.8 to 1.2).
Why is this?

[Banfa]

This is due to what is called rounding errors. Floating point numbers do not hold an exact value but an approximation. When you do arithmatic on them then what you get is an approximate result. For instance given your first example

If "LOW" is set to 0.7 and "HIGH" to 1.1, the first loop gives 0.7 up to 1.2 while the second loop works (0.7 to 1.1).

it appears in the first loop that the condition

VALUE < HIGH+STEP is going wrong since when value = 1.2 (and is output)

1.2 < 1.1 + 0.1

appears to have been true when human logic would make it false.

The problem is that value is the result of many fp calculations, it may not be 1.2 but

1.19999999999999

This displays as 1.2 but when compared with 1.2 is actually lower.

The answer is not to use floating point numbers as loop control variables. having got the input parameters calculate the number of steps you wish to take and use an integer variable to control your loopand take that many steps.

Of course within the calculation of the number of steps you will have to take account of the fact that there may be a rounding error.

[perca]

Ok, that's what I was afraid of. Thanks anyway!

This is due to what is called rounding errors. Floating point numbers do not hold an exact value but an approximation. When you do arithmatic on them then what you get is an approximate result. For instance given your first example

If "LOW" is set to 0.7 and "HIGH" to 1.1, the first loop gives 0.7 up to 1.2 while the second loop works (0.7 to 1.1).

it appears in the first loop that the condition

VALUE < HIGH+STEP is going wrong since when value = 1.2 (and is output)

1.2 < 1.1 + 0.1

appears to have been true when human logic would make it false.

The problem is that value is the result of many fp calculations, it may not be 1.2 but

1.19999999999999

This displays as 1.2 but when compared with 1.2 is actually lower.

The answer is not to use floating point numbers as loop control variables. having got the input parameters calculate the number of steps you wish to take and use an integer variable to control your loopand take that many steps.

Of course within the calculation of the number of steps you will have to take account of the fact that there may be a rounding error.