Numeric and Math Functions

The numeric family covers abs(), ceiling(), floor(), round() and round-half-to-even() (banker's rounding), the aggregates sum(), avg(), min() and max(), and formatting with format-number() (decimal pictures) and format-integer() (words, Roman numerals, ordinals). math:pi(), math:sqrt(), math:pow(), math:exp(), math:log(), math:log10() and the trigonometric functions sit in the math: namespace and work in xs:double. On untyped prices, the type of the input decides the type of the answer:

xp 'sum(//price)' 'sum(//price ! xs:decimal(.))' 'avg(//price ! xs:decimal(.))' \
   'round(2.5), round(-2.5)' 'round-half-to-even(2.5)' 'round(8452, -2)' \
   'format-number(sum(//price ! xs:decimal(.)), "$#,##0.00")' \
   'format-integer(57, "I")' 'math:sqrt(2)'

sum(//price)                           => 1.3474e2
sum(//price ! xs:decimal(.))           => 134.74
avg(//price ! xs:decimal(.))           => 22.45666666666666666667
round(2.5), round(-2.5)                => 3 -2
round-half-to-even(2.5)                => 2
round(8452, -2)                        => 8500
format-number(sum(//price ! xs:decimal(.)), "$#,##0.00") => "$134.74"
format-integer(57, "I")                => "LVII"
math:sqrt(2)                           => 1.4142135623730951e0

Untyped values are summed as doubles; cast to xs:decimal first and the arithmetic is exact, the rule for money in every pipeline. round() rounds halves toward positive infinity (so -2.5 becomes -2), while round-half-to-even() avoids the upward bias that matters when you round thousands of line items. A negative precision rounds to tens or hundreds. Older reference tables get some of these wrong (a negative -8500 here, or format-integer() for decimal pictures), so test on Saxon 726,956 before you trust a table.

Numeric Functions

Values courtesy of http://www.w3.org/TR/2014/REC-xpath-functions-30-20140408/#func-number 189 .

round(1.125, 2)

1.13

Math Functions

math:sqrt(1.0e6)

1.0e3