Converting the base of a given B-complement number: Given the digits x of a B-complemnt number to base oldB, the function computes (dVal,y) where dVal is a BigInteger that denotes the value of the given number in decimal and y are the digits of the B-complement representation of that number to the new radix newB.

Converting the base of a given radix-B number: Given the digits x of a radix-B number to base oldB, the function computes (dVal,y) where dVal is a BigInteger that denotes the value of the radix-B number in decimal and y are the digits of that number to the new radix newB.

convert a complement number to an integer (if possible)

convolution of two vectors x and y (which is the result of the Fourier transform of x and y if these are doubled in size by padding zeros to the higher indices)

Decode an array of given RNS numbers rnsNums for the RNS base primes, i.e., primes are the relatively prime numbers that form the RNS base, and the function computes for every rnsNums[j] a value X[j] such that rnsNums[j][i] = X[j] mod prime[i] for all i.

ExtEuclid implements the extended Euclidean algorithm (see also Lemma of Bézout): For given integers a and b, it computes numbers u,v,g such that u*a + v*b = g = gcd(a,b).

to be called from the web page as the online teaching tool

Generate the (inverse) 2^p x 2^p Fourier matrix in the ring ZF[2^{2^n}+1]. Note that w = 2^{2^{n+1-p}} is a principal (2^p)-th root of unity and that w^{-1} = 2^{2^{n+1}-2^{n+1-p}} is its multiplicative inverse (for w=2, we would use p=n+1).

Convert a given floating point representation (without hidden bits) given as triple (s,e,m) where s is the sign, e the exponent and m the mantissa (exponent and mantissa were given as radix-B numbers). The result is the corresponding floating point number.

convert an integer to a radix number of given base

convert an integer to a radix number of given base

This function implements a restoring division for B-complement numbers. In case argument doPrint is true, it will print the calculation to stream ostr, otherwise, it just returns the quotient q and remainder r as (q,r).

This function implements a carry-ripple adder that can be configured via input isBC to work with B-complement or radix-B numbers in that it applies functions alpha/beta to the most significant digits or not. It is required that the operands have the same number of digits (you may use functions ZeroEqualize and SignEqualize to achieve this). The output is a pair of B-complement or radix-B numbers (c,s) where c and s holds the carry and sum digits, respectively.

This function implements a multiplier array that can be configured via input isBC to work with B-complement or radix-B numbers in that may apply functions alpha/beta to the most significant digits. The output is a pair of B-complement or radix-B numbers (pp,cp,p) where pp holds the partial products, cp are the carry digits for computing rowise additions, and p is the final product, respectively.

This function implements a multiplier array using carry-save addition that can be configured via input isBC to work with B-complement or radix-B numbers in that may apply functions alpha/beta to the most significant digits. The output is a pair of B-complement or radix-B numbers (pp,cp,cr,p) where pp holds the partial products, cp are the carry digits for computing rowise additions, cr are the carry bits for the final additiona, and p is the final product, respectively.

This function is a carry-ripple subtraction that can be configured via input isBC to work with B-complement or radix-B numbers in that it applies functions alpha/beta to the most significant digits or not. It is required that the operands have the same number of digits (you may use functions ZeroEqualize and SignEqualize to achieve this). The output is a pair of B-complement or radix-B numbers (c,s) where c and s holds the carry and sum digits, respectively.

Compute multiplicative inverse b which satisfies (a*b) mod p = 1 for a given number a and a number p such that gcd(a,p) = 1. This is done by (ExtEuclid a p) which yields numbers (x,y,g) such that a*x+p*y = gcd(a,p) = 1 holds, thus a*x mod p = 1

This function implements a restoring division for radix-B numbers. In case argument doPrint is true, it will print the calculation to stream ostr, otherwise, it just returns the quotient q and remainder r as (q,r).

negative wrapped convolution of two vectors x and y

parsing numbers: a number is expected as "<[C;F;3;2]>16" where instead semicola also comma are allowed, and in case of a base less than 35, the digits 0..9 A..Z may be directly concatenated. One may even use "<...>" and "[...]" instead of "<[...]>" for the digit list.

positive wrapped convolution of two vectors x and y (which is the result of the Fourier transform of x and y)

print a matrix over numbers ZF[2^{2^n}+1] (like the Fourier matrix)

main function to be called by the radix-B and B-complement number tool

main function to be called by the RadixBaseConverterTool

convert a radix number to an integer (if possible)

main function to be called by the residue number tool

reduction of radix-B multiplication to a multiplication in ZF[2^{2*l}+1]

main function to be called by the SchoenhageStrassen tool

demonstration of SchoenhageStrassen multiplication in ZF[2^{2*l}+1]

given numbers x and y, extend the shorter one by B-1 to give them the same length

extend B-complement number x by n digits

remove redundant digits from a B-complement number

compute a slow Fourier transform (just a matrix multiplication)

Given radix-B numbers x and y, this function computes several floating point representations of number x/y where additionally the sign is determined by input isNegative. The floating point numbers will all have mDigits digits for the mantissa and eDigits digits for the exponent, and both are given in base B also. The result is a list of pairs of the form (mode,f) where f is an optional triple (sign,mantissa,exponent) where mode is one of the following rounding modes:

• roundToZero
• roundToMinusInfty
• roundToPlusInfty
• roundToNearestZero
• roundToNearestMinusInfty
• roundToNearestPlusInfty
• roundToNearestEven

Clearly, the triple (sign,mantissa,exponent) denotes the representation of the floating point number in radix B with mDigits for the mantissa, and eDigits for the exponent (with bias).

given numbers x and y, extend the shorter one by zeros to give them the same length

extend radix-B number x by n digits

remove redundant digits from a radix-B number

converting number x given to base B to a string; for bases less than 36, notation without semicola and commata is preferred for the digit list

This function prints a carry-ripple adder as a SVG graphics. Input printVars is used to control whether variables like "x[2]" are printed or whether their values are printed in the svg graphics.

This function prints a carry-ripple multiplier array as a SVG figure. Input printVars is used to control whether variables like "x[2]" are printed or whether their values are printed in the svg graphics.

This function prints a carry-save multiplier array as a SVG figure. Input printVars is used to control whether variables like "x[2]" are printed or whether their values are printed in the svg graphics.

This function prints a carry-ripple adder as a SVG figure. Input printVars is used to control whether variables like "x[2]" are printed or whether their values are printed in the svg graphics.