SQLMath

SQLMath Includes

• 17 additional trigonometric and hyperbolic functions that complement the 8 built-in trigonometric functions in T-SQL.
• 12 advanced rounding, truncation and modular arithmetic functions.
• A comprehensive implementation of matrices as SQL types and of matrix (and vector) arithmetic including 20 matrix-based functions and operations.
• 7 table-valued numerical series generators including arithmetic, geometric and harmonic series, alternating harmonic series, the p-series, prime numbers up to 263, and the Fibonacci sequence.
• 28 other general functions covering areas such as prime numbers, factorials, greatest common divisors, least common multiples, summation of series, and logs, powers, exponents and roots.

Beyond Excel
Among these functions are numerically faithful equivalents of mathematical functions found in Microsoft Excel and similar packages, but also many others which - combined with the innate power and ability of SQL Server to rapidly crunch through huge volumes of data - gives 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 statistics functions such as SIN, LOG etc.

Outstanding Performance and Numerical Accuracy
The algorithms behind the SQLMath 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.

Multi-Valued Aggregates - even in SQL2005
Several of the SQLMath functions (for example most of the summations) are in the form of aggregate functions that take multiple input values. This works fine for SQL2008 but is commonly supposed to be impossible in SQL2005 - since you can supply only one input parameter to an aggregate function. TotallySQL have, however, devised a very simple but smart way of doing this in SQL2005 using SQLTuples: you simply combine the input parameters (of any type) into a SQLTuples object on-the-fly as part of the function call. Only a very minor syntax change is needed and there is no measurable performance penalty even when used with truly enormous data sets.

SQLMath Features

• Number sequences: arithmetic, geometric, harmonic, alternating harmonic, p-series & Fibonacci
• Modular multiplication and modular powers of very large integers, quotients
• Rounding to specified multiples, decimal places & significant figures
• Factorial, double factorial, rising & falling factorials, log of factorial, binomial / multinomial coefficients
• Return nth prime, next prime, nth next prime, table of prime numbers, test of primeness
• Summations: sum (x.y), sum(x2), sum (x2-y2), sum((x-y)2), sum(x2+y2), sum(aix(n+im))
• Greatest common divisor & least common multiple of 2 numbers or of an entire dataset
• Cube root & hypotenuse (suitable for difficult values of x)
• Accurate computation of ex-1, ln(x+1) & sqrt(x+1) for small x, and of xy-1 for x near 1 or small y
• Trigonometric functions SEC & CSC and inverse functions ACOT, ACSC, ASEC
• Hyperbolic functions COSH, SINH, TANH, SECH, CSCH, COTH and inverses ACOSH, ASINH etc
• Conversion of numbers up to 9,999,999 into Roman numerals
• Matrix type: n x m matrices that can be stored in tables & local variables
• Aggregate constructor (table to matrix) & table-valued serializer (matrix to table) for matrices
• Add, subtract, multiply & compare matrices.Swap rows & columns, scale matrix, scale row, scale column, transpose, clone matrix
• Read and set individual matrix elements, return row & column counts
• Find determinant, inverse and reduced-row echelon form for matrices