bertini::multiprecision Namespace Reference

Typedefs
using	complex = bertini::complex_mp
	Shorthand for the multiprecision complex type within this namespace.

Functions
void	RandomRealAssign (complex &a, unsigned num_digits)
	Assign to a random real number , to current default precision.
complex	RandomReal ()
	Produce a random real number , to current default precision.
complex	RandomReal (unsigned num_digits)
	Produce a random real number , to specified precision.
complex	rand ()
	Produce a random complex number, to default precision.
complex	rand_unit ()
	Produce a random unit complex number, to default precision.
complex	RandomUnit ()
	Produce a random unit-modulus complex number, to default precision.
complex	rand_bounded_modulus ()
	Produce a random complex number whose modulus is pulled toward 1, to default precision.
complex	RandomComplexBoundedModulus ()
	Produce a random complex number whose modulus is pulled toward 1 (away from 0 and infinity), at default precision.
void	RandomComplexBoundedModulusAssign (complex &a, unsigned num_digits)
	Assign to a a random complex number whose modulus is pulled toward 1, at the given precision.
complex	RandomComplexBoundedModulus (unsigned num_digits)
	Produce a random complex number whose modulus is pulled toward 1, at the given precision.
complex	rand_real_bounded_modulus ()
	Produce a random REAL number whose modulus is pulled toward 1, to default precision.
complex	RandomRealBoundedModulus ()
	Produce a random REAL number (imaginary part 0) whose modulus is pulled toward 1, at default precision.
void	RandomRealBoundedModulusAssign (complex &a, unsigned num_digits)
	Assign to a a random REAL number (imaginary part 0) whose modulus is pulled toward 1, at the given precision.
complex	RandomRealBoundedModulus (unsigned num_digits)
	Produce a random REAL number (imaginary part 0) whose modulus is pulled toward 1, at the given precision.
void	rand_assign (complex &a, unsigned num_digits)
	Assign a random complex number to a, at the given precision.
void	RandomComplexAssign (complex &a, unsigned num_digits)
	Assign a random complex number to a, at the given precision.
complex	RandomComplex (unsigned num_digits)
	Produce a random complex number, at the given precision.
void	RandomUnitAssign (complex &a, unsigned num_digits)
	Assign a random unit-modulus complex number to a, at the given precision.
complex	RandomUnit (unsigned num_digits)
	Produce a random unit-modulus complex number, at the given precision.
template<unsigned int length_in_digits>
real_mp	RandomMp ()
	Produce a random number with at length_in_digits non-zero digits.

Typedef Documentation

complex

using bertini::multiprecision::complex = bertini::complex_mp

Shorthand for the multiprecision complex type within this namespace.

Function Documentation

rand()

complex bertini::multiprecision::rand ( )

inline

Produce a random complex number, to default precision.

rand_assign()

void bertini::multiprecision::rand_assign ( complex & a, unsigned num_digits )

inline

Assign a random complex number to a, at the given precision.

rand_bounded_modulus()

complex bertini::multiprecision::rand_bounded_modulus ( )

inline

Produce a random complex number whose modulus is pulled toward 1, to default precision.

Draw a box-uniform complex z (real, imag each in [-1,1]) and divide by sqrt(|z|), so the result has modulus sqrt(|z|): bounded away from both 0 and infinity, but NOT collapsed onto the unit circle (that would be z/abs(z) – see rand_unit). This is how Bertini 1 generates linear-form coefficients, and it avoids the heavy-tailed scaling of a ratio-of-integers draw (RandomRat: numerator/denominator each uniform, so the modulus has fat log-tails).

rand_real_bounded_modulus()

complex bertini::multiprecision::rand_real_bounded_modulus ( )

inline

Produce a random REAL number whose modulus is pulled toward 1, to default precision.

The real-line analog of rand_bounded_modulus: draw x box-uniform in [-1,1] (imaginary part 0) and divide by sqrt(|x|), giving sign(x)*sqrt(|x|) – bounded away from both 0 and infinity, the same Bertini-1 recipe the (complex) start-system and patch coefficients use, but kept REAL so a real patch does not complexify a real path.

rand_unit()

complex bertini::multiprecision::rand_unit ( )

inline

Produce a random unit complex number, to default precision.

RandomComplex()

complex bertini::multiprecision::RandomComplex ( unsigned num_digits )

inline

Produce a random complex number, at the given precision.

RandomComplexAssign()

void bertini::multiprecision::RandomComplexAssign ( complex & a, unsigned num_digits )

inline

Assign a random complex number to a, at the given precision.

RandomComplexBoundedModulus() [1/2]

complex bertini::multiprecision::RandomComplexBoundedModulus ( )

inline

Produce a random complex number whose modulus is pulled toward 1 (away from 0 and infinity), at default precision.

RandomComplexBoundedModulus() [2/2]

complex bertini::multiprecision::RandomComplexBoundedModulus ( unsigned num_digits )

inline

Produce a random complex number whose modulus is pulled toward 1, at the given precision.

RandomComplexBoundedModulusAssign()

void bertini::multiprecision::RandomComplexBoundedModulusAssign ( complex & a, unsigned num_digits )

inline

Assign to a a random complex number whose modulus is pulled toward 1, at the given precision.

RandomMp()

template<unsigned int length_in_digits>

real_mp bertini::RandomMp

(

)

Produce a random number with at length_in_digits non-zero digits.

Template Parameters

length_in_digits

The length of the desired random number

RandomReal() [1/2]

complex bertini::multiprecision::RandomReal ( )

inline

Produce a random real number , to current default precision.

RandomReal() [2/2]

complex bertini::multiprecision::RandomReal ( unsigned num_digits )

inline

Produce a random real number , to specified precision.

RandomRealAssign()

void bertini::multiprecision::RandomRealAssign ( complex & a, unsigned num_digits )

inline

Assign to a random real number , to current default precision.

RandomRealBoundedModulus() [1/2]

complex bertini::multiprecision::RandomRealBoundedModulus ( )

inline

Produce a random REAL number (imaginary part 0) whose modulus is pulled toward 1, at default precision.

RandomRealBoundedModulus() [2/2]

complex bertini::multiprecision::RandomRealBoundedModulus ( unsigned num_digits )

inline

Produce a random REAL number (imaginary part 0) whose modulus is pulled toward 1, at the given precision.

RandomRealBoundedModulusAssign()

void bertini::multiprecision::RandomRealBoundedModulusAssign ( complex & a, unsigned num_digits )

inline

Assign to a a random REAL number (imaginary part 0) whose modulus is pulled toward 1, at the given precision.

RandomUnit() [1/2]

complex bertini::multiprecision::RandomUnit ( )

inline

Produce a random unit-modulus complex number, to default precision.

RandomUnit() [2/2]

complex bertini::multiprecision::RandomUnit ( unsigned num_digits )

inline

Produce a random unit-modulus complex number, at the given precision.

RandomUnitAssign()

void bertini::multiprecision::RandomUnitAssign ( complex & a, unsigned num_digits )

inline

Assign a random unit-modulus complex number to a, at the given precision.