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CakeML
some interesting job openings in Sydney listed here
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august 2019 by nhaliday
Errors in Math Functions (The GNU C Library)
https://stackoverflow.com/questions/22259537/guaranteed-precision-of-sqrt-function-in-c-c
For C99, there are no specific requirements. But most implementations try to support Annex F: IEC 60559 floating-point arithmetic as good as possible. It says:

An implementation that defines __STDC_IEC_559__ shall conform to the specifications in this annex.

And:

The sqrt functions in <math.h> provide the IEC 60559 square root operation.

IEC 60559 (equivalent to IEEE 754) says about basic operations like sqrt:

Except for binary <-> decimal conversion, each of the operations shall be performed as if it first produced an intermediate result correct to infinite precision and with unbounded range, and then coerced this intermediate result to fit in the destination's format.

The final step consists of rounding according to several rounding modes but the result must always be the closest representable value in the target precision.

[ed.: The list of other such correctly rounded functions is included in the IEEE-754 standard (which I've put w/ the C1x and C++2x standard drafts) under section 9.2, and it mainly consists of stuff that can be expressed in terms of exponentials (exp, log, trig functions, powers) along w/ sqrt/hypot functions.

Fun fact: this question was asked by Yeputons who has a codeforces profile.]
https://stackoverflow.com/questions/20945815/math-precision-requirements-of-c-and-c-standard
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july 2019 by nhaliday
Factorization of polynomials over finite fields - Wikipedia
In mathematics and computer algebra the factorization of a polynomial consists of decomposing it into a product of irreducible factors. This decomposition is theoretically possible and is unique for polynomials with coefficients in any field, but rather strong restrictions on the field of the coefficients are needed to allow the computation of the factorization by means of an algorithm. In practice, algorithms have been designed only for polynomials with coefficients in a finite field, in the field of rationals or in a finitely generated field extension of one of them.

All factorization algorithms, including the case of multivariate polynomials over the rational numbers, reduce the problem to this case; see polynomial factorization. It is also used for various applications of finite fields, such as coding theory (cyclic redundancy codes and BCH codes), cryptography (public key cryptography by the means of elliptic curves), and computational number theory.

As the reduction of the factorization of multivariate polynomials to that of univariate polynomials does not have any specificity in the case of coefficients in a finite field, only polynomials with one variable are considered in this article.

...

In the algorithms that follow, the complexities are expressed in terms of number of arithmetic operations in Fq, using classical algorithms for the arithmetic of polynomials.

[ed.: Interesting choice...]

...

Factoring algorithms
Many algorithms for factoring polynomials over finite fields include the following three stages:

Square-free factorization
Distinct-degree factorization
Equal-degree factorization
An important exception is Berlekamp's algorithm, which combines stages 2 and 3.

Berlekamp's algorithm
Main article: Berlekamp's algorithm
The Berlekamp's algorithm is historically important as being the first factorization algorithm, which works well in practice. However, it contains a loop on the elements of the ground field, which implies that it is practicable only over small finite fields. For a fixed ground field, its time complexity is polynomial, but, for general ground fields, the complexity is exponential in the size of the ground field.

[ed.: This actually looks fairly implementable.]
wiki  reference  concept  algorithms  calculation  nibble  numerics  math  algebra  math.CA  fields  polynomials  levers  multiplicative  math.NT 
july 2019 by nhaliday
Chaospy - Toolbox for performing uncertainty quantification.
A library to perform uncertainty quantification on data an experiments written in python
code  uncertainty-quantification  science  numerics  python 
june 2019 by gyger
c++ - Constexpr Math Functions - Stack Overflow
Actually, because of old and annoying legacy, almost none of the math functions can be constexpr, since they all have the side-effect of setting errno on various error conditions, usually domain errors.
--
Note, gcc has implemented most of the math function as constexpr although the extension is non-conforming this should change. So definitely doable. – Shafik Yaghmour Jan 12 '15 at 20:2
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june 2019 by nhaliday

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