# Value ± Error rounding

I have a problem that I am trying to solve. Can anyone help me please?

I have as an input a value and its error (uncertainty). I want to create a string that is the Value ± Error but with appropriate rounding on both numbers. By appropriate rounding, I mean 2 significant figures in the error value.

I have written the following function that does mostly does this, but has some exceptions to which I am struggling to find a simple resolution.

Function/S FormatValueError(vVal,vErr)
variable vVal
variable vErr
// Return string containing value ± error rounded to 2 sf on error
// or "" if there was a problem
string sValErr = ""
string sVal,sErr
variable vPower
do
if( numType(vVal) == 2) //NaN
break // return empty string
endif
if( (numType(vErr) == 2) || (vErr == 0) ) // NaN or zero
sprintf sValErr, "%g", vVal // just return vVal
break
endif
// Find power 10 of Error
variable vErrPower = floor( log( abs(vErr) ) )
vErrPower -= 1 // go to 2 sf
// Find power 10 of Value
variable vValPower = floor( log( abs(vVal) ) )
if( vValPower < vErrPower ) // catch value less than error
vPower = vValPower - 1 //round to 2 sf in Value
else
vPower = vErrPower // round to 2 sf in Error
endif
// Now do the rounding
vVal=sign(vVal) * (10 ^ vPower) * round( abs(vVal) * (10 ^ (-vPower) ) )
sprintf sVal,"%g",vVal
vErr=sign(vErr) * (10 ^ vPower) * round( abs(vErr) * (10 ^ (-vPower) ) )
sErr=num2str(vErr)
sprintf sErr,"%g",vErr
// assemble the result
sValErr = sVal
if( strLen(sErr) > 0)
sValErr += " ± " + sErr
endif
break
while(1)
return sValErr
End

For example:
print FormatValueError(123.456,7.123456)
gives 123.5 ± 7.1 (correct)

print FormatValueError(1.008,0.111)
gives 1.01 ± 0.11 (correct)

print FormatValueError(1.0008,0.111)
gives 1 ± 0.11 (no - I would like to get 1.00 ± 0.11)

print FormatValueError(123.456E-4,1.345678E-5)
gives 0.012346 ± 1.3e-05 (no - I would like 0.012346 ± 0.000013 or 1234.6e-5 ± 1.3e-5)

Is there a cunning way of achieving the last two results without doing a heavy handed look for each type of number format and deal with each foreseeable situation bit by bit?

Thank you,
Kurt
KurtB wrote:

Is there a cunning way of achieving the last two results without doing a heavy handed look for each type of number format and deal with each foreseeable situation bit by bit?

Try `printf` and `sprintf`.