Description
$DECIMAL returns a number converted to the InterSystems decimal format, which corresponds to the FLOAT SQL data type. This is the inverse of the operation performed by the $DOUBLE function.
The num value can be specified as a number or a numeric string. If the num value is outside of the range of values that can be converted to an InterSystems decimal format number, $DECIMAL generates a <MAXNUMBER> error.
$DECIMAL returns a numeric value in canonical form.
Rounding
Specifying $DECIMAL(num,n) where n is between 1 and 38 (inclusive) returns a canonical numeric string with no more than n significant digits. When num is an ObjectScript decimal format number, it returns at most 19 significant decimal digits. When num is an IEEE Binary, the input can have at least 767 significant decimal digits, although $DECIMAL(num,n) will not display more than 38 significant digits.
Note that a canonical numeric string will not have leading zeroes before the decimal point or trailing zeroes after the decimal point.
Although $DECIMAL(num,n) never displays more than 38 significant digits, the $FNUMBER function can be used to display more significant digits on an IEEE Binary value. The $DOUBLE function will only look at the first 38 significant digits when given a string with a long sequence of significant digits.
Rounding is done as follows:
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If n is not specified and num has more than 19 significant digits, $DECIMAL rounds the number and returns an InterSystems decimal format number with either 18 or 19 significant digits. $DECIMAL always rounds to the greater absolute value. There is an exception when the value to be converted to ObjectScript decimal format falls between the range of 18-digit precision and 19-digit precision. In this case, the result is the larger 18 digit value. The following example shows a number with 20 significant digits which $DECIMAL(num) rounds to 19 significant digits:
USER>w $DOUBLE(12345678901234567890123456789)
12345678901234568227000000000
USER>w $DECIMAL($DOUBLE(12345678901234567890123456789))
12345678901234568230000000000
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If n is a positive integer, rounding is done using the IEEE rounding standard. $DECIMAL returns a decimal format number as a numeric string in canonical form. If num has more than 38 significant digits (and n=38) $DECIMAL rounds the fractional portion of the number at the 38th digit and represents all of the following num digits with zeros.
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If n=0, $DECIMAL returns a decimal format number as a numeric string in canonical form as follows:
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If n=0 and the decimal format value corresponding to num is 20 digits or less, $DECIMAL returns that value.
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If n=0 and the decimal format value corresponding to num is more than 20 digits, special rounding (not IEEE rounding) is performed, as follows: The decimal string value is truncated to 20 significant digits. If the 20th digit is not a "5" or "0" then that truncated number with 20 significant digits is the result. If the 20th digit is a "5" or "0", the 20th digit is replaced with a "6" or "1" respectively, and that 20 digit numeric string is the result. This special rounding prevents “double rounding” errors if the result is later rounded to less than 20 digits. This is shown in the following example:
USER>WRITE $DECIMAL($DOUBLE(123456789012345678901234567),20)
123456789012345678150000000
USER>WRITE $DECIMAL($DOUBLE(123456789012345678901234567),0)
123456789012345678160000000
Examples
The following example demonstrates that $DECIMAL has no effect when applied to a fractional number that is already in InterSystems IRIS format:
SET x=$DECIMAL($ZPI)
SET y=$ZPI
IF x=y { WRITE !,"Identical:"
WRITE !,"IRIS $DECIMAL: ",x
WRITE !,"Native IRIS: ",y }
ELSE { WRITE !,"Different:"
WRITE !,"IRIS $DECIMAL: ",x
WRITE !,"Native IRIS: ",y }
The following example returns the value of pi as a $DOUBLE value and as a standard InterSystems IRIS numeric value. This example shows that equality operations should not be attempted between $DOUBLE and standard InterSystems IRIS numbers, and that equivalence cannot be restored by using $DECIMAL to convert IEEE back to InterSystems IRIS:
SET x=$DECIMAL($ZPI)
SET y=$DOUBLE($ZPI)
SET z=$DECIMAL(y)
IF x=y { WRITE !,"IRIS & IEEE Same" }
ELSEIF x=z { WRITE !,"IRIS & IEEE-to-IRIS same" }
ELSE { WRITE !,"All three different"
WRITE !,"IRIS decimal: ",x
WRITE !,"IEEE float: ",y
WRITE !,"IEEE to IRIS: ",z }
The following example returns the $DECIMAL conversion of pi as a $DOUBLE value. These conversions are rounded by different n argument values:
SET x=$DOUBLE($ZPI)
WRITE !,$DECIMAL(x)
/* returns 3.141592653589793116 (19 digits) */
WRITE !,$DECIMAL(x,1)
/* returns 3 */
WRITE !,$DECIMAL(x,8)
/* returns 3.1415927 (note rounding) */
WRITE !,$DECIMAL(x,12)
/* returns 3.14159265359 (note rounding) */
WRITE !,$DECIMAL(x,18)
/* returns 3.14159265358979312 */
WRITE !,$DECIMAL(x,19)
/* returns 3.141592653589793116 (19 digits) */
WRITE !,$DECIMAL(x,20)
/* returns 3.141592653589793116 (19 digits) */
WRITE !,$DECIMAL(x,21)
/* returns 3.141592653589793116 (19 digits) */
WRITE !,$DECIMAL(x,0)
/* returns 3.1415926535897931159 (20 digits) */
