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Date: Mon, 01 Dec 2008 12:48:52 +0000

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Message-Id: <E1L78Cq-0008Jq-I9@farnsworth.w3.org>

Date: Mon, 01 Dec 2008 12:48:52 +0000

To: public-qt-comments@w3.org

Message-Id: <E1L78Cq-0008Jq-I9@farnsworth.w3.org>

http://www.w3.org/Bugs/Public/show_bug.cgi?id=6240 --- Comment #2 from Michael Kay <mike@saxonica.com> 2008-12-01 12:48:52 --- Proposal: define a 2-argument version of fn:round, where the second argument is used to indicate the required precision in the same way as fn:round-half-to-even. The two functions round() and round-half-to-even() should then be the same except for the way that they round values that are half-way between two multiples of 10^-p. Currently round-half-to-even always casts the argument to a decimal; this would be inappropriate for fn:round because it could introduce errors for large doubles that can't be so converted. So the proposal is to state (in line with format-number()) that the conversion to decimal must not lose precision. Proposed text for the two functions is therefore shown below, with differences tagged as appropriate. <rh2e> fn:round-half-to-even($arg as numeric?) as numeric? fn:round-half-to-even($arg as numeric?, $precision as xs:integer) as numeric? </rhte> <round> fn:round($arg as numeric?) as numeric? fn:round($arg as numeric?, $precision as xs:integer) as numeric? </round> Summary: The value returned is the nearest (that is, numerically closest) value to $arg that is a multiple of ten to the power of minus $precision. If two such values are equally near (e.g. if the fractional part in $arg is exactly .500...), the function returns <rh2e>the one whose least significant digit is even</rh2e><round>the one that is closest to positive infinity</round>. If the type of $arg is one of the four numeric types xs:float, xs:double, xs:decimal or xs:integer the type of the result is the same as the type of $arg. If the type of $arg is a type derived from one of the numeric types, the result is an instance of the base numeric type. The first signature of this function produces the same result as the second signature with $precision=0. For arguments of type xs:float and xs:double, if the argument is NaN, positive or negative zero, or positive or negative infinity, then the result is the same as the argument. In other cases, the argument is cast to xs:decimal using an implementation of xs:decimal that imposes no limits on the number of digits that can be represented. The function is applied to this xs:decimal value, and the resulting xs:decimal is cast back to xs:float or xs:double as appropriate to form the function result. If the resulting xs:decimal value is zero, then positive or negative zero is returned according to the sign of the original argument. If $arg is of type xs:float or xs:double, rounding occurs on the value of the mantissa computed with exponent = 0. For detailed type semantics, see Section 7.2.3 The fn:abs, fn:ceiling, fn:floor, fn:round, and fn:round-half-to-even functionsFS Note: This function is typically used with a non-zero $precision in financial applications where the argument is of type xs:decimal. For arguments of type xs:float and xs:double the results may be counterintuitive. For example, consider <rh2e>round-half-to-even(xs:float(150.0150), 2)</rh2e><round>[some similar example]</round>. <rh2e>The implementation will convert the argument to the xs:decimal 150.014999389... which will then be rounded to the xs:decimal 150.01 which will be converted back to the xs:float whose exact value is 150.0099945068... whereas round-half-to-even(xs:decimal(150.0150), 2) will result in the xs:decimal whose exact value is 150.02.</rh2e><round>[some similar example]</round> Note: fn:round() and fn:round-half-to-even() produce the same result in all cases except when the argument is exactly midway between two multiples of 10 to the power of -$precision. <round>Other ways of rounding midway values can be achieved as follows. Towards negative infinity: -fn:round(-$x)). Away from zero: fn:round(fn:abs($x))*fn:compare($x,0). Towards zero: fn:abs(fn:round(-$x))*-fn:compare($x,0)</round> -- Configure bugmail: http://www.w3.org/Bugs/Public/userprefs.cgi?tab=email ------- You are receiving this mail because: ------- You are the QA contact for the bug.Received on Monday, 1 December 2008 12:49:02 UTC

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