SQLEngineering

SQLEngineering includes:

• Cylindrical and Spherical Bessel / Neumann functions
• Laguerre, Legendre, Hermite polynomials and Spherical Harmonics
• Elliptical integrals
• Error functions
• Exponential integrals
• Complex numbers implemented as a new SQL type including 53 different arithmetic, trigonometric and hyperbolic functions
• Number base conversions between decimal, hexadecimal, binary, octal and base64
• Unit conversions for 190+ different units of measure (including distance, velocity, acceleration, area, volume, mass, density, pressure, flow, energy, power, time, temperature, flux, angle etc)

Beyond Excel
A few of the functions available in SQLEngineering (e.g. some of the base and unit conversions) are numerically faithful equivalents of similar functions found in Microsoft Excel, but offer a much broader range of functionality. These - and the many additional functions that have no analogue in Excel - use the innate power and ability of SQL Server to rapidly crunch through huge volumes of data - giving you an analytical capability that completely blows away anything you could do with spreadsheets.

Native Look and Feel
All TotallySQL Transact-SQL extensions are implemented using familiar programming objects within SQL (scalar and table-valued functions, aggregate functions, user-defined types, stored procedures) , keeping the syntax clean and making them as fast and easy to use as the built-in native functions such as SUM, AVG etc.

Outstanding Performance and Numerical Accuracy
The algorithms behind the SQLEngineering functions use industry-proven, best-in-class techniques devised by some of the world's leading numerical computing experts to maximise performance and accuracy even for fairly extreme input values. Careful heuristics and edge-case checks through the code ensure that problems caused by the limitations of floating-point arithmetic on digital computers (such as cancellation errors) are kept to an absolute mininum, and a broad range of special-purpose, high-performance numerical computing approaches are used in place of the slow, expensive computations that would result from 'naive' implementations of the underlying mathematics.

SQLEngineering Features

• Cylindrical & spherical Bessel / Neumann functions
• Elliptical integrals in Carlson symmetric and Legendre forms
• Legendre, Laguerre & Hermite polynomials & spherical harmonics
• Error function, its complement and their inverses
• Exponential integrals Number base conversions between decimal, hexadecimal, octal, binary and base64
• Unit conversions to / from 196 different units with support for metric prefixes kilo, mega etc
• Complex number type that can be stored in tables & local variables
• Complex number constructors for Cartesian (real, imag) & polar (magnitude, phase) inputs
• Cartesian (real, imaginary) & polar (magnitude, phase) component accessor functions 
• Full set of trigonometric functions & inverses for complex numbers, returning complex results
• Full set of hyperbolic functions & inverses for complex numbers, returning complex results
• Addition, subtraction, multiplication & division for both complex / complex & complex / real 
• Logs of complex numbers to base e, base 10 & to any complex, real or imaginary base Exponents of complex numbers & powers to any complex, real or imaginary power
• Conjugate, negation & comparison of complex numbers