Template:Ceil

This template produces an expression for the value of a given expression, rounded up to an integer. If the value is in the range of integer-type numbers, the resulting expression is of type integer.

Thus, when applying #expr, if the value is in the range of integer-type numbers the exact result is produced. The reason for not applying #expr in this template is:

• for integer-type numbers: in subsequent use in another expression the value would be rounded to float
• for floats: they would be rounded to 14 digits

Examples:

• {{ceil|123.45}} → floor((123.45))
• {{ceil|10/7}} → floor((10/7))
• {{ceil|123.45e20}} → (123.45e20)

Advantage compared with the function ceil:

• for integer-type numbers with an absolute value between 2^53 and 2^63 the function rounds to float (not necessarily upward), while the template gives the integer-type expression for the exact result