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Re: ACTION-2146: Update definition of power()

From: Steven Pemberton <steven.pemberton@cwi.nl>
Date: Wed, 13 Dec 2017 13:57:51 +0100
To: public-xformsusers@w3.org, "XForms Users Community Group Issue Tracker" <sysbot+tracker@w3.org>
Message-ID: <op.za6rmpvssmjzpq@steven-xps>
For power(x, y), we say:

"Raises the first argument to the power of the second argument, returning  
the result. Both arguments may be fractional and negative. If the  
calculation does not result in a real number, then NaN is returned."

and the problem is with the meaning of "if the calculation does not result  
in a real number"

XPath functions says:
https://www.w3.org/TR/xpath-functions/#func-math-pow

pow($x, $y)

"If $y is an instance of xs:integer, the result is $x raised to the power  
of $y as defined in the [IEEE 754-2008] specification of the pown function  
applied to a 64-bit binary floating point value and an integer.

Otherwise $y is converted to an xs:double by numeric promotion, and the  
result is the value of $x raised to the power of $y as defined in the  
[IEEE 754-2008] specification of the pow function applied to two 64-bit  
binary floating point values."

IEEE 754 says:

"For the pown function (integral exponents only):
pown(x, 0) is 1 for any x (even a zero, quiet NaN, or infinity)
pown(±0, n) is ±∞ and signals the divideByZero exception for odd integral  
n<0
pown(±0, n) is +∞ and signals the divideByZero exception for even integral  
n<0
pown(±0, n) is +0 for even integral n>0
pown(±0, n) is ±0 for odd integral n>0.

For the pow function (integral exponents get special treatment):
pow(x, ±0) is 1 for any x (even a zero, quiet NaN, or infinity)
pow(±0, y) is ±∞ and signals the divideByZero exception for y an odd  
integer <0
pow(±0, −∞) is +∞ with no exception
pow(±0, +∞) is +0 with no exception
pow(±0, y) is +∞ and signals the divideByZero exception for finite y<0 and  
not an odd integer
pow(±0, y) is ±0 for finite y>0 an odd integer
pow(±0, y) is +0 for finite y>0 and not an odd integer
pow(−1, ±∞) is 1 with no exception
pow(+1, y) is 1 for any y (even a quiet NaN)
pow(x, y) signals the invalid operation exception for finite x<0 and  
finite non-integer y"

So I propose for our text:

"Raises the first argument to the power of the second argument, returning  
the result. The value of power(0,0) is 1.

Both arguments may be fractional and negative, however,
  power(0, y) = NaN for negative y
  power(x, y) = NaN for negative x and non integer y.
"

Steven
Received on Wednesday, 13 December 2017 12:58:19 UTC

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