Sorin Petcu (8/8/2008)

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Again, other guy who make wrong suppositions. Theoretical, from math point of view, "SQRT cannot receive a negative number as an input", but here, we are talking about computer universe. Please, lay down the theory and read carrefully the documentation (BOL). On the other side, FLOAT has negative values, also.

Books Online
Returns the square root of the given expression.
Syntax

SQRT ( float_expression )

Arguments
float_expression
An expression whose type can be implicitly converted to float.

Return Value
float

Approximate-number data types for use with floating point numeric data. Floating point data is approximate; therefore, not all values in the data type range can be represented exactly.

Note:
The SQL-92 synonym for real is float(24).



Data type Range Storage
float
- 1.79E+308 to -2.23E-308, 0 and 2.23E-308 to 1.79E+308
Depends on the value of n

real
- 3.40E + 38 to -1.18E - 38, 0 and 1.18E - 38 to 3.40E + 38
4 Bytes


Transact-SQL Syntax Conventions

mtassin (8/8/2008)

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This is nothing to do with theory. Read Books Online about the float data type and tell me where it supports complex numbers. The return data type of SQRT is a float, a float data type cannot contain an imaginary or a complex number.

The Square Root of -1 is i, which is an imaginary/complex number. It cannot be returned as a float data type because it is out of the domain of the float data type.

It's right there in BOL.




And here is the BOL entry for the float data type.


Where is i listed as an allowed value for a float data type? If the SQRT function returns a float value, the return value has to be within the allowed values for it. The value of SQRT(-1) is outside of the allowed returnable values for the function.

This isn't theory... this is fact.

As a much simpler approach, take a calculator and try to take the SQRT of -1... if you have a really neato calculator you'll get a complex number back, if you don't you'll get an error.

http://en.wikipedia.org/wiki/Imaginary_number

Sorin Petcu (8/8/2008)

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The Square Root of -1 is i, which is an imaginary/complex number."
The computer didn't know nothing about complex numbers. You assume that SQRT function, which is written by a computer programmer, should return i for -1 argument. Why? you wrong here. I could write my SQRT function how my muscles want. It is about programming and not about theory. Negative numbers are represented in computer different way by the way you know from theory. So, please don't mix the math theory with what is inside a computer.

SELECT -1 * -1

mtassin (8/8/2008)

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We're not talking about negative numbers, negative numbers are just the input to a function, we're talking about the output of the function.

The Square Root of a Negative number (the output of the function) is represented in mathematics as an imaginary (pure) or complex (mixed a +bi) number.

The SQRT function used by SQL server returns a float. The Float data type is not able to contain a complex number. Thus the return data type of the SQRT of -1 is out of the domain of the float data type and we get an error message. How the function determines this (either it actually tries to calculate it and gets an error after attempting to find this value, or if it throws the error as soon as it sees the negative I don't know.. and frankly, I don't care).

Sorin Petcu (8/8/2008)

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[quote]
I think you don't understand or you don't want to understand.
Let me see: how it is represented the number -5 in computer? as binar form as 1111111111111111111111111111111111111111111111111111111111111011 and this number would be reconverted as 18446744073709551611 in decimal format.
So, SQRT(-5) would be what? guess what:
select SQRT(18446744073709551611) = 4294967296
So we are talking only about numbers and not math theory. You said forth and forth about complex numbers. Wrong! Why you want to receive a complex number from a function built in a programming language? Why you want all the time that float number can't be asimilated as complex number? It is nothing to do with complex numbers in a programming language or an engine like sql server. Complex numbers are in math theory. So wake up!

select convert(binary,-5)

select convert(int,0x0000000000000000000000000000000000000000000000000000FFFFFFFB)

select convert(int,convert(binary,-5))

mtassin (8/8/2008)
The Square Root of -1 is i, which is an imaginary/complex number. It cannot be returned as a float data type because it is out of the domain of the float data type.