Fixed-point Module

Fixed-Point Data Types. More...

Classes
class	itpp::CFix
	Complex fixed-point data type. More...
class	itpp::CFixed< w, e, o, q >
	Templated complex fixed-point data type. More...
class	itpp::Fix
	Fixed-point data type. More...
class	itpp::Fix_Base
	Base class for fixed-point data types. More...
class	itpp::Fix_Factory
	Class factory for fixed-point data types Fix and CFix. More...
class	itpp::Fixed< w, e, o, q >
	Templated fixed-point data type. More...

Typedefs
typedef Vec< CFix >	itpp::cfixvec
	Typedef for complex fixed-point vector type.
typedef Mat< CFix >	itpp::cfixmat
	Typedef for complex fixed-point matrix type.
typedef Vec< Fix >	itpp::fixvec
	Typedef for fixed-point vector type.
typedef Mat< Fix >	itpp::fixmat
	Typedef for fixed-point matrix type.
typedef int64_t	itpp::fixrep
	Representation for fixed-point data types.

Enumerations
enum	itpp::e_mode { itpp::TC, itpp::US }
	Sign encoding modes (aligned with SystemC) More...
enum	itpp::o_mode {   itpp::SAT, itpp::SAT_ZERO, itpp::SAT_SYM, itpp::WRAP,   itpp::WRAP_SM }
	Overflow modes (aligned with SystemC) More...
enum	itpp::q_mode {   itpp::RND, itpp::RND_ZERO, itpp::RND_MIN_INF, itpp::RND_INF,   itpp::RND_CONV, itpp::RND_CONV_ODD, itpp::TRN, itpp::TRN_ZERO }
	Quantization modes (aligned with SystemC) More...
enum	itpp::output_mode { itpp::OUTPUT_FIX, itpp::OUTPUT_FIX_SHIFT, itpp::OUTPUT_FLOAT, itpp::OUTPUT_FLOAT_SHIFT }
	Output modes. More...

Functions
int	itpp::assert_shifts (const CFix &x, const CFix &y)
	Check that x.shift==y.shift OR x==0 OR y==0 and return the shift (for the non-zero argument)
int	itpp::assert_shifts (const CFix &x, const Fix &y)
	Check that x.shift==y.shift OR x==0 OR y==0 and return the shift (for the non-zero argument)
int	itpp::assert_shifts (const CFix &x, int y)
	Check that x.shift==0 OR x==0 OR y==0 and return x.shift.
std::istream &	itpp::operator>> (std::istream &is, CFix &x)
	Input bit representation and, optionally, the shift.
std::ostream &	itpp::operator<< (std::ostream &os, const CFix &x)
	Output bit representation and, optionally, the shift.
int	itpp::assert_shifts (const Fix &x, const Fix &y)
	Check that x.shift==y.shift OR x==0 OR y==0 and return the shift (for the non-zero argument)
int	itpp::assert_shifts (const Fix &x, int y)
	Check that x.shift==0 OR x==0 OR y==0 and return x.shift.
std::istream &	itpp::operator>> (std::istream &is, Fix &x)
	Input bit representation and, optionally, the shift.
std::ostream &	itpp::operator<< (std::ostream &os, const Fix &x)
	Output bit representation and, optionally, the shift.
std::ostream &	itpp::operator<< (std::ostream &os, const output_mode &o)
	Set output mode.
template<>
void	itpp::create_elements< Fix > (Fix *&ptr, const int n, const Factory &f)
	Create an n-length array of Fix using Fix_Factory f.
template<>
void	itpp::create_elements< CFix > (CFix *&ptr, const int n, const Factory &f)
	Create an n-length array of CFix using Fix_Factory f.
template<class T >
bool	itpp::is_fix (const T &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
template<>
bool	itpp::is_fix (const Fix &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
template<>
bool	itpp::is_fix (const fixvec &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
template<>
bool	itpp::is_fix (const fixmat &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
template<>
bool	itpp::is_fix (const CFix &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
template<class T >
bool	itpp::is_fix (const Array< T > &)
	Return true only if argument is of type Fix or CFix (or an Array/Vec/Mat of Fix or CFix)
void	itpp::set_fix (Fix &y, double x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	itpp::set_fix (Fix &y, double x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	itpp::set_fix (fixvec &y, const vec &x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	itpp::set_fix (fixvec &y, const vec &x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	itpp::set_fix (fixmat &y, const mat &x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	itpp::set_fix (fixmat &y, const mat &x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	itpp::set_fix (double &y, double x, int)
	Set y = x. Useful in templated code.
void	itpp::set_fix (double &y, double x, int, q_mode)
	Set y = x. Useful in templated code.
void	itpp::set_fix (vec &y, const vec &x, int)
	Set y = x. Useful in templated code.
void	itpp::set_fix (vec &y, const vec &x, int, q_mode)
	Set y = x. Useful in templated code.
void	itpp::set_fix (mat &y, const mat &x, int)
	Set y = x. Useful in templated code.
void	itpp::set_fix (mat &y, const mat &x, int, q_mode)
	Set y = x. Useful in templated code.
void	itpp::set_fix (CFix &y, std::complex< double > x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	itpp::set_fix (CFix &y, double real, double imag, int n)
	Set y = (real + i*imag) * pow2(n) using the quantization mode of y.
void	itpp::set_fix (CFix &y, std::complex< double > x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	itpp::set_fix (CFix &y, double real, double imag, int n, q_mode q)
	Set y = (real + i*imag) * pow2(n) using the specified quantization mode q.
void	itpp::set_fix (cfixvec &y, const cvec &x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	itpp::set_fix (cfixvec &y, const vec &real, const vec &imag, int n)
	Set y = (real + i*imag) * pow2(n) using the quantization mode of y.
void	itpp::set_fix (cfixvec &y, const cvec &x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	itpp::set_fix (cfixvec &y, const vec &real, const vec &imag, int n, q_mode q)
	Set y = (real + i*imag) * pow2(n) using the specified quantization mode q.
void	itpp::set_fix (cfixmat &y, const cmat &x, int n)
	Set y = x * pow2(n) using the quantization mode of y.
void	itpp::set_fix (cfixmat &y, const mat &real, const mat &imag, int n)
	Set y = (real + i*imag) * pow2(n) using the quantization mode of y.
void	itpp::set_fix (cfixmat &y, const cmat &x, int n, q_mode q)
	Set y = x * pow2(n) using the specified quantization mode q.
void	itpp::set_fix (cfixmat &y, const mat &real, const mat &imag, int n, q_mode q)
	Set y = (real + i*imag) * pow2(n) using the specified quantization mode q.
void	itpp::set_fix (std::complex< double > &y, const std::complex< double > &x, int)
	Set y = x. Useful in templated code.
void	itpp::set_fix (std::complex< double > &y, double real, double imag, int)
	Set y = real + i*imag. Useful in templated code.
void	itpp::set_fix (std::complex< double > &y, const std::complex< double > &x, int, q_mode)
	Set y = x. Useful in templated code.
void	itpp::set_fix (std::complex< double > &y, double real, double imag, int, q_mode)
	Set y = real + i*imag. Useful in templated code.
void	itpp::set_fix (cvec &y, const cvec &x, int)
	Set y = x. Useful in templated code.
void	itpp::set_fix (cvec &y, const vec &real, const vec &imag, int)
	Set y = real + i*imag. Useful in templated code.
void	itpp::set_fix (cvec &y, const cvec &x, int, q_mode)
	Set y = x. Useful in templated code.
void	itpp::set_fix (cvec &y, const vec &real, const vec &imag, int, q_mode)
	Set y = real + i*imag. Useful in templated code.
void	itpp::set_fix (cmat &y, const cmat &x, int)
	Set y = x. Useful in templated code.
void	itpp::set_fix (cmat &y, const mat &real, const mat &imag, int)
	Set y = real + i*imag. Useful in templated code.
void	itpp::set_fix (cmat &y, const cmat &x, int, q_mode)
	Set y = x. Useful in templated code.
void	itpp::set_fix (cmat &y, const mat &real, const mat &imag, int, q_mode)
	Set y = real + i*imag. Useful in templated code.
template<class T1 , class T2 >
void	itpp::set_fix (Array< T1 > &y, const Array< T2 > &x, int n)
	Call set_fix for each Array element.
template<class T1 , class T2 >
void	itpp::set_fix (Array< T1 > &y, const Array< T2 > &real, const Array< T2 > &imag, int n)
	Call set_fix for each Array element.
template<class T1 , class T2 >
void	itpp::set_fix (Array< T1 > &y, const Array< T2 > &x, int n, q_mode q)
	Call set_fix for each Array element.
template<class T1 , class T2 >
void	itpp::set_fix (Array< T1 > &y, const Array< T2 > &real, const Array< T2 > &imag, int n, q_mode q)
	Call set_fix for each Array element.
void	itpp::lshift_fix (Fix &y, int n)
	Left shift n bits.
void	itpp::rshift_fix (Fix &y, int n)
	Right shift n bits using the quantization mode of y.
void	itpp::rshift_fix (Fix &y, int n, q_mode q)
	Right shift n bits using the specified quantization mode q.
void	itpp::lshift_fix (fixvec &y, int n)
	Left shift n bits.
void	itpp::rshift_fix (fixvec &y, int n)
	Right shift n bits using the quantization mode of y.
void	itpp::rshift_fix (fixvec &y, int n, q_mode q)
	Right shift n bits using the specified quantization mode q.
void	itpp::lshift_fix (fixmat &y, int n)
	Left shift n bits.
void	itpp::rshift_fix (fixmat &y, int n)
	Right shift n bits using the quantization mode of y.
void	itpp::rshift_fix (fixmat &y, int n, q_mode q)
	Right shift n bits using the specified quantization mode q.
void	itpp::lshift_fix (double &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (double &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (double &, int, q_mode)
	Dummy function useful in templated code.
void	itpp::lshift_fix (vec &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (vec &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (vec &, int, q_mode)
	Dummy function useful in templated code.
void	itpp::lshift_fix (mat &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (mat &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (mat &, int, q_mode)
	Dummy function useful in templated code.
void	itpp::lshift_fix (CFix &y, int n)
	Left shift n bits.
void	itpp::rshift_fix (CFix &y, int n)
	Right shift n bits using the quantization mode of y.
void	itpp::rshift_fix (CFix &y, int n, q_mode q)
	Right shift n bits using the specified quantization mode q.
void	itpp::lshift_fix (std::complex< double > &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (std::complex< double > &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (std::complex< double > &, int, q_mode)
	Dummy function useful in templated code.
void	itpp::lshift_fix (cvec &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (cvec &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (cvec &, int, q_mode)
	Dummy function useful in templated code.
void	itpp::lshift_fix (cmat &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (cmat &, int)
	Dummy function useful in templated code.
void	itpp::rshift_fix (cmat &, int, q_mode)
	Dummy function useful in templated code.
template<class T >
void	itpp::lshift_fix (Array< T > &y, int n)
	Call lshift_fix for each Array element.
template<class T >
void	itpp::rshift_fix (Array< T > &y, int n)
	Call rshift_fix for each Array element.
template<class T >
void	itpp::rshift_fix (Array< T > &y, int n, q_mode q)
	Call rshift_fix for each Array element.
void	itpp::assert_fixshift (double, int)
	If x is a fixed-point variable, assert that x has the specified shift value, otherwise do nothing.
void	itpp::assert_fixshift (const std::complex< double > &, int)
	If x is a fixed-point variable, assert that x has the specified shift value, otherwise do nothing.
void	itpp::assert_fixshift (const Fix &x, int shift)
	If x is a fixed-point variable, assert that x has the specified shift value, otherwise do nothing.
void	itpp::assert_fixshift (const CFix &x, int shift)
	If x is a fixed-point variable, assert that x has the specified shift value, otherwise do nothing.
vec	itpp::to_vec (const fixvec &v)
	Converts a fixvec to vec.
cvec	itpp::to_cvec (const cfixvec &v)
	Converts a cfixvec to cvec.
mat	itpp::to_mat (const fixmat &m)
	Converts a fixmat to mat.
cmat	itpp::to_cmat (const cfixmat &m)
	Converts a cfixmat to cmat.
template<class T >
T	itpp::to (double x)
	Convert double to T.
template<class T >
T	itpp::to (const Fix &x)
	Convert Fix to T.
template<class T >
T	itpp::to (const std::complex< double > &x)
	Convert std::complex<double> to T.
template<class T >
T	itpp::to (const CFix &x)
	Convert CFix to T.
template<class T >
T	itpp::to (double real, double imag)
	Convert double (real and imaginary parts) to T.
template<class T >
T	itpp::to (const Fix &real, const Fix &imag)
	Convert Fix (real and imaginary parts) to T.
template<class T , class U >
Vec< T >	itpp::to (const Vec< U > &x)
	Convert Vec<U> to Vec<T>
template<>
vec	itpp::to< double > (const vec &x)
	Convert vec to vec.
template<>
cvec	itpp::to< std::complex< double > > (const cvec &x)
	Convert cvec to cvec.
template<>
fixvec	itpp::to< Fix > (const fixvec &x)
	Convert fixvec to fixvec.
template<>
cfixvec	itpp::to< CFix > (const cfixvec &x)
	Convert cfixvec to cfixvec.
template<class T , class U >
Vec< T >	itpp::to (const Vec< U > &real, const Vec< U > &imag)
	Convert Vec<U> (real and imaginary parts) to Vec<T>
template<class T , class U >
Mat< T >	itpp::to (const Mat< U > &x)
	Convert Mat<U> to Mat<T>
template<>
mat	itpp::to< double > (const mat &x)
	Convert mat to mat.
template<>
cmat	itpp::to< std::complex< double > > (const cmat &x)
	Convert cmat to cmat.
template<>
fixmat	itpp::to< Fix > (const fixmat &x)
	Convert fixmat to fixmat.
template<>
cfixmat	itpp::to< CFix > (const cfixmat &x)
	Convert cfixmat to cfixmat.
template<class T , class U >
Mat< T >	itpp::to (const Mat< U > &real, const Mat< U > &imag)
	Convert Mat<U> (real and imaginary parts) to Mat<T>
template<class T , class U >
Array< typename ConvertU2T< T, U >::result >	itpp::to (const Array< U > &x)
	Convert Array<U>, where U can be an Array/Vec/Mat, to a corresponding Array with T elements.
template<class T , class U >
Array< typename ConvertU2T< T, U >::result >	itpp::to (const Array< U > &real, const Array< U > &imag)
	Convert Array<U> (real and imaginary parts), where U can be an Array/Vec/Mat, to a corresponding Array with T elements.
double	itpp::unfix (const Fix &x)
	Convert Fix to double by multiplying the bit representation with pow2(-shift)
std::complex< double >	itpp::unfix (const CFix &x)
	Convert CFix to std::complex<double> by multiplying the bit representation with pow2(-shift)
vec	itpp::unfix (const fixvec &x)
	Convert fixvec to vec by multiplying the bit representations with pow2(-shift)
mat	itpp::unfix (const fixmat &x)
	Convert fixmat to mat by multiplying the bit representations with pow2(-shift)
double	itpp::unfix (double x)
	Convert double to double i.e. do nothing.
std::complex< double >	itpp::unfix (const std::complex< double > &x)
	Convert std::complex<double> to std::complex<double> i.e. do nothing.
vec	itpp::unfix (const vec &x)
	Convert vec to vec i.e. do nothing.
cvec	itpp::unfix (const cvec &x)
	Convert cvec to cvec i.e. do nothing.
mat	itpp::unfix (const mat &x)
	Convert mat to mat i.e. do nothing.
cmat	itpp::unfix (const cmat &x)
	Convert cmat to cmat i.e. do nothing.
template<class T >
Array< typename Convert< T > ::to_double >	itpp::unfix (const Array< T > &x)
	Convert floating- or fixed-point Array to floating-point Array.
Fix	itpp::abs (const Fix &x)
	Absolute value.
Fix	itpp::real (const CFix &x)
	Real part of complex value.
Fix	itpp::imag (const CFix &x)
	Imaginary part of complex value.
CFix	itpp::conj (const CFix &x)
	Conjugate of complex value.
Fix	itpp::operator+ (const Fix &x, const Fix &y)
	Fix + Fix.
Fix	itpp::operator- (const Fix &x, const Fix &y)
	Fix - Fix.
Fix	itpp::operator* (const Fix &x, const Fix &y)
	Fix * Fix.
Fix	itpp::operator/ (const Fix &x, const Fix &y)
	Fix / Fix using quantization mode TRN.
Fix	itpp::operator+ (const Fix &x, const int y)
	Fix + int.
Fix	itpp::operator- (const Fix &x, const int y)
	Fix - int.
Fix	itpp::operator* (const Fix &x, const int y)
	Fix * int.
Fix	itpp::operator/ (const Fix &x, const int y)
	Fix / int using quantization mode TRN.
Fix	itpp::operator+ (const int x, const Fix &y)
	int + Fix
Fix	itpp::operator- (const int x, const Fix &y)
	int - Fix
Fix	itpp::operator* (const int x, const Fix &y)
	int * Fix
Fix	itpp::operator/ (const int x, const Fix &y)
	int / Fix using quantization mode TRN
fixvec	itpp::operator+ (const fixvec &v, const int s)
	fixvec + int
fixvec	itpp::operator+ (const int s, const fixvec &v)
	int + fixvec
fixvec	itpp::operator- (const fixvec &v, const int s)
	fixvec - int
fixvec	itpp::operator- (const int s, const fixvec &v)
	int - fixvec
fixvec	itpp::operator* (const fixvec &v, const int s)
	fixvec * int
fixvec	itpp::operator* (const int s, const fixvec &v)
	int * fixvec
fixvec	itpp::operator/ (const fixvec &v, const int s)
	fixvec / int using quantization mode TRN
fixmat	itpp::operator+ (const fixmat &v, const int s)
	fixmat + int
fixmat	itpp::operator+ (const int s, const fixmat &v)
	int + fixmat
fixmat	itpp::operator- (const fixmat &v, const int s)
	fixmat - int
fixmat	itpp::operator- (const int s, const fixmat &v)
	int - fixmat
fixmat	itpp::operator* (const fixmat &v, const int s)
	fixmat * int
fixmat	itpp::operator* (const int s, const fixmat &v)
	int * fixmat
fixmat	itpp::operator/ (const fixmat &v, const int s)
	fixmat / int using quantization mode TRN
fixvec	itpp::operator+ (const fixvec &a, const ivec &b)
	fixvec + ivec
fixvec	itpp::operator+ (const ivec &a, const fixvec &b)
	ivec + fixvec
fixvec	itpp::operator- (const fixvec &a, const ivec &b)
	fixvec - ivec
fixvec	itpp::operator- (const ivec &a, const fixvec &b)
	ivec - fixvec
Fix	itpp::operator* (const fixvec &a, const ivec &b)
	fixvec * ivec
Fix	itpp::operator* (const ivec &a, const fixvec &b)
	ivec * fixvec
fixmat	itpp::operator+ (const fixmat &a, const imat &b)
	fixmat + imat
fixmat	itpp::operator+ (const imat &a, const fixmat &b)
	imat + fixmat
fixmat	itpp::operator- (const fixmat &a, const imat &b)
	fixmat - imat
fixmat	itpp::operator- (const imat &a, const fixmat &b)
	imat - fixmat
fixmat	itpp::operator* (const fixmat &a, const imat &b)
	fixmat * imat
fixmat	itpp::operator* (const imat &a, const fixmat &b)
	imat * fixmat
CFix	itpp::operator+ (const CFix &x, const CFix &y)
	CFix + CFix.
CFix	itpp::operator- (const CFix &x, const CFix &y)
	CFix - CFix.
CFix	itpp::operator* (const CFix &x, const CFix &y)
	CFix * CFix.
CFix	itpp::operator/ (const CFix &x, const CFix &y)
	CFix / CFix using quantization mode TRN.
CFix	itpp::operator+ (const CFix &x, const Fix &y)
	CFix + Fix.
CFix	itpp::operator- (const CFix &x, const Fix &y)
	CFix - Fix.
CFix	itpp::operator* (const CFix &x, const Fix &y)
	CFix * Fix.
CFix	itpp::operator/ (const CFix &x, const Fix &y)
	CFix / Fix using quantization mode TRN.
CFix	itpp::operator+ (const Fix &x, const CFix &y)
	Fix + CFix.
CFix	itpp::operator- (const Fix &x, const CFix &y)
	Fix - CFix.
CFix	itpp::operator* (const Fix &x, const CFix &y)
	Fix * CFix.
CFix	itpp::operator/ (const Fix &x, const CFix &y)
	Fix / CFix using quantization mode TRN.
CFix	itpp::operator+ (const CFix &x, const int y)
	CFix + int.
CFix	itpp::operator- (const CFix &x, const int y)
	CFix - int.
CFix	itpp::operator* (const CFix &x, const int y)
	CFix * int.
CFix	itpp::operator/ (const CFix &x, const int y)
	CFix / int using quantization mode TRN.
CFix	itpp::operator+ (const int x, const CFix &y)
	int + CFix
CFix	itpp::operator- (const int x, const CFix &y)
	int - CFix
CFix	itpp::operator* (const int x, const CFix &y)
	int * CFix
CFix	itpp::operator/ (const int x, const CFix &y)
	int / CFix using quantization mode TRN
cfixvec	itpp::operator+ (const fixvec &v, const CFix &s)
	fixvec + CFix
cfixvec	itpp::operator+ (const CFix &s, const fixvec &v)
	CFix + fixvec.
cfixvec	itpp::operator- (const fixvec &v, const CFix &s)
	fixvec - CFix
cfixvec	itpp::operator- (const CFix &s, const fixvec &v)
	CFix - fixvec.
cfixvec	itpp::operator* (const fixvec &v, const CFix &s)
	fixvec * CFix
cfixvec	itpp::operator* (const CFix &s, const fixvec &v)
	CFix * fixvec.
cfixvec	itpp::operator/ (const fixvec &v, const CFix &s)
	fixvec / CFix using quantization mode TRN
cfixmat	itpp::operator+ (const fixmat &m, const CFix &s)
	fixmat + CFix
cfixmat	itpp::operator+ (const CFix &s, const fixmat &m)
	CFix + fixmat.
cfixmat	itpp::operator- (const fixmat &m, const CFix &s)
	fixmat - CFix
cfixmat	itpp::operator- (const CFix &s, const fixmat &m)
	CFix - fixmat.
cfixmat	itpp::operator* (const fixmat &m, const CFix &s)
	fixmat * CFix
cfixmat	itpp::operator* (const CFix &s, const fixmat &m)
	CFix * fixmat.
cfixmat	itpp::operator/ (const fixmat &m, const CFix &s)
	fixmat / CFix using quantization mode TRN
cfixvec	itpp::operator+ (const ivec &v, const CFix &s)
	ivec + CFix
cfixvec	itpp::operator+ (const CFix &s, const ivec &v)
	CFix + ivec.
cfixvec	itpp::operator- (const ivec &v, const CFix &s)
	ivec - CFix
cfixvec	itpp::operator- (const CFix &s, const ivec &v)
	CFix - ivec.
cfixvec	itpp::operator* (const ivec &v, const CFix &s)
	ivec * CFix
cfixvec	itpp::operator* (const CFix &s, const ivec &v)
	CFix * ivec.
cfixvec	itpp::operator/ (const ivec &v, const CFix &s)
	ivec / CFix using quantization mode TRN
cfixmat	itpp::operator+ (const imat &m, const CFix &s)
	imat + CFix
cfixmat	itpp::operator+ (const CFix &s, const imat &m)
	CFix + imat.
cfixmat	itpp::operator- (const imat &m, const CFix &s)
	imat - CFix
cfixmat	itpp::operator- (const CFix &s, const imat &m)
	CFix - imat.
cfixmat	itpp::operator* (const imat &m, const CFix &s)
	imat * CFix
cfixmat	itpp::operator* (const CFix &s, const imat &m)
	CFix * imat.
cfixmat	itpp::operator/ (const imat &m, const CFix &s)
	imat / CFix using quantization mode TRN
cfixvec	itpp::operator+ (const cfixvec &v, const Fix &s)
	cfixvec + Fix
cfixvec	itpp::operator+ (const Fix &s, const cfixvec &v)
	Fix + cfixvec.
cfixvec	itpp::operator- (const cfixvec &v, const Fix &s)
	cfixvec - Fix
cfixvec	itpp::operator- (const Fix &s, const cfixvec &v)
	Fix - cfixvec.
cfixvec	itpp::operator* (const cfixvec &v, const Fix &s)
	cfixvec * Fix
cfixvec	itpp::operator* (const Fix &s, const cfixvec &v)
	Fix * cfixvec.
cfixvec	itpp::operator/ (const cfixvec &v, const Fix &s)
	cfixvec / Fix using quantization mode TRN
cfixmat	itpp::operator+ (const cfixmat &m, const Fix &s)
	cfixmat + Fix
cfixmat	itpp::operator+ (const Fix &s, const cfixmat &m)
	Fix + cfixmat.
cfixmat	itpp::operator- (const cfixmat &m, const Fix &s)
	cfixmat - Fix
cfixmat	itpp::operator- (const Fix &s, const cfixmat &m)
	Fix - cfixmat.
cfixmat	itpp::operator* (const cfixmat &m, const Fix &s)
	cfixmat * Fix
cfixmat	itpp::operator* (const Fix &s, const cfixmat &m)
	Fix * cfixmat.
cfixmat	itpp::operator/ (const cfixmat &m, const Fix &s)
	cfixmat / Fix using quantization mode TRN
cfixvec	itpp::operator+ (const cfixvec &a, const fixvec &b)
	cfixvec + fixvec
cfixvec	itpp::operator- (const cfixvec &a, const fixvec &b)
	cfixvec - fixvec
CFix	itpp::operator* (const cfixvec &a, const fixvec &b)
	cfixvec * fixvec
cfixmat	itpp::operator+ (const cfixmat &a, const fixmat &b)
	cfixmat + fixmat
cfixmat	itpp::operator- (const cfixmat &a, const fixmat &b)
	cfixmat - fixmat
cfixmat	itpp::operator* (const cfixmat &a, const fixmat &b)
	cfixmat * fixmat
void	itpp::Vec< Num_T >::set (const char *str)
	Set the vector equal to the values in the str string.
void	itpp::Mat< Num_T >::set (const char *str)
	Set matrix equal to values in the string str.

Variables
const int	itpp::MAX_WORDLEN = 64
	Max word length.
const uint64_t	itpp::UINT64_POW2 [64]
	Table for fast multiplication or division by 2^n.
const double	itpp::DOUBLE_POW2 [128]
	Table for fast multiplication by 2^(n-64)

Detailed Description

Fixed-Point Data Types.

Author

Johan Bergman

Contents

• Introduction
• Fix_Base
  • Shift factor
  • Word length
  • Sign encoding mode
  • Overflow mode
  • Quantization mode
  • Statistics object pointer
  • Output mode
• Fix and Fixed
• CFix and CFixed
• Fix_Factory
• Operators and methods
  • Initialization and assignment
  • Addition and subtraction
  • Multiplication and division
  • Bit-shifting
  • Conversion
  • Get data members
  • Input and output
• Functions
  • Function is_fix
  • Function set_fix
  • Functions lshift_fix and rshift_fix
  • Function assert_fixshift
  • Function unfix
  • Function to<T>
  • Other functions

Introduction

How to include the support for fixed-point data types in your program:

#include <itpp/itbase.h>
#include <itpp/itfixed.h>

using namespace itpp;

Fixed-point data types in IT++:

• itpp::Fix (real-valued, restrictions specified as constructor arguments)
• itpp::Fixed (real-valued, restrictions specified as template arguments)
• itpp::CFix (complex-valued, restrictions specified as constructor arguments)
• itpp::CFixed (complex-valued, restrictions specified as template arguments)

These classes have a common base class called Fix_Base; see inheritance diagram in the itpp::Fix_Base documentation. The following data members are inherited from Fix_Base:

• Shift factor
• Word length
• Sign encoding mode
• Overflow mode
• Quantization mode
• Statistics object pointer
• Output mode

The term "fixed-point restrictions" refers to all these data members except for the shift factor, which is considered to be part of the "fixed-point number". The shift factor has some resemblance to a binary point. The value of the shift factor is set in initializations and assignments and it is modified by multiplications, divisions and bit-shifting operations. The shift factor is used for checking that both terms have been shifted the same amount in additions and subtractions. Also, it is used to "un-shift" the data when a fixed-point number is converted to floating point.

Names of classes and enums have been aligned with the fixed-point data types in SystemC to some extent, but the fixed-point data types in IT++ and SystemC are quite different. In fact, the fixed-point data types in IT++ probably correspond better to the variable-precision integer types in SystemC (with one important difference: the fixed-point numbers in IT++ remember the amount of bit-shifting that has been applied to them, so that they can be converted back to "floating-point magnitude" easily if this is desired). The reason for this design choice in IT++ is to make the fixed-point simulations as fast as possible. If necessary, the core parts in itbase.h (e.g. Array, Vec and Mat) should be able to use some other data type than the ones presented here, assuming that a proper itpp::Factory is created for the data type, just like itpp::Fix_Factory has been created for these data types.

Sometimes the documentation for the IT++ fixed-point data types states that a function is "useful in templated code". This means that the function facilitates writing templated code where the template argument is meant to be either a floating-point type (double or complex<double>) or a fixed-point type (Fix or CFix), i.e. code which is supposed to support both floating-point and fixed-point simulations. For example, the operator >>= is defined for Fix and CFix, but not for double and complex<double>, so it might be a better idea to use the function rshift_fix which is defined for Fix and CFix as well as double and complex<double>.

For an example program, take a look at tests/fix_test.cpp.

Fix_Base

Shift factor

Supported shift factors: -64 ... +63 bit-shifts. 0 is default.

An IT++ fixed-point number consists of a bit representation and a shift factor. The shift factor is a member of Fix_Base, while the bit representation is a member of the inherited class (Fix or CFix). The shift factor indicates the number of bit-shifts that have been performed on the data. A positive shift factor means that the data has been left-shifted while a negative shift factor means that the data has been right-shifted. For information about how the shift factor is affected by different operators, see section Operators and methods.

Word length

Supported word lengths: 1 ... 64 bits. 64 is default.

Warning

Fix, Fixed, CFix and CFixed always use signed 64-bit integers to represent the fixed-point data. Therefore it is not recommended to declare variables with 64 bits and sign encoding mode US.

Sign encoding mode

Supported sign encoding modes (itpp::e_mode):

• TC (Two's complement)
• US (Unsigned)

TC is default.

Warning

Fix, Fixed, CFix and CFixed always use signed 64-bit integers to represent the fixed-point data. Therefore it is not recommended to declare variables with 64 bits and sign encoding mode US.

Overflow mode

Supported overflow modes (itpp::o_mode):

• SAT (Saturation)
• WRAP (Wrap-around)

WRAP is default.

Note

Fix, Fixed, CFix and CFixed apply this restriction during initialization and assignments only.

Quantization mode

Supported quantization modes (itpp::q_mode), with definitions borrowed from SystemC (see SystemC documentation for further details):

• RND (Rounding to plus infinity): Add the most significant deleted bit to the remaining bits.
• RND_ZERO (Rounding to zero): If the most significant deleted bit is 1, and either the sign bit or at least one other deleted bit is 1, add 1 to the remaining bits.
• RND_MIN_INF (Rounding to minus infinity): If the most significant deleted bit is 1, and at least one other deleted bit is 1, add 1 to the remaining bits.
• RND_INF (Rounding to infinity): If the most significant deleted bit is 1, and either the inverted value of the sign bit or at least one other deleted bit is 1, add 1 to the remaining bits.
• RND_CONV (Convergent rounding with half-way value rounded to even value): If the most significant deleted bit is 1, and either the least significant of the remaining bits or at least one other deleted bit is 1, add 1 to the remaining bits.
• RND_CONV_ODD (Convergent rounding with half-way value rounded to odd value): If the most significant deleted bit is 1, and either the least significant of the remaining bits is 0 or at least one other deleted bit is 1, add 1 to the remaining bits (not defined in SystemC).
• TRN (Truncation): Just copy the remaining bits.
• TRN_ZERO (Truncation to zero): If the sign bit is 1, and either the most significant deleted bit or at least one other deleted bit is 1, add 1 to the remaining bits.

TRN is default. RND and TRN are usually the most implementation friendly. However, note that it is RND_INF that corresponds to "ordinary rounding" and TRN_ZERO that corresponds to "ordinary truncation".

Note

Fix, Fixed, CFix and CFixed apply this restriction during initialization and right-shift operations only.

Statistics object pointer

Supported statistics object pointer values: either a pointer to an itpp::Stat object or 0. 0 is default.

The sample method in the statistics object is called during initializations and assignments. A single statistics object can collect statistics from more than one fixed-point variable.

Output mode

Supported output modes (itpp::output_mode), used by the output stream operator <<:

• OUTPUT_FIX: Output fixed-point representation only
• OUTPUT_FIX_SHIFT: Output fixed-point representation followed by <shift>
• OUTPUT_FLOAT: Output floating-point value
• OUTPUT_FLOAT_SHIFT: Output floating-point value followed by <<shift

OUTPUT_FIX_SHIFT is default. Unlike the other modes, output_mode is a static data member of Fix_Base, i.e. the output_mode is common for all fixed-point variables. Use the following commands to change output_mode:

Fix_Base::set_output_mode(OUTPUT_FIX);
Fix_Base::set_output_mode(OUTPUT_FIX_SHIFT);
Fix_Base::set_output_mode(OUTPUT_FLOAT);
Fix_Base::set_output_mode(OUTPUT_FLOAT_SHIFT);

// Alternative using a string parameter
Fix_Base::set_output_mode("OUTPUT_FIX");
Fix_Base::set_output_mode("OUTPUT_FIX_SHIFT");
Fix_Base::set_output_mode("OUTPUT_FLOAT");
Fix_Base::set_output_mode("OUTPUT_FLOAT_SHIFT");

// Alternative using an ostream modifier
cout << OUTPUT_FIX;
cout << OUTPUT_FIX_SHIFT;
cout << OUTPUT_FLOAT;
cout << OUTPUT_FLOAT_SHIFT;

Fix and Fixed

Fix and Fixed are real-valued fixed-point data types primarily intended to replace double when a design is refined from floating- to fixed-point implementation. The data is stored in the least significant bits of a 64-bit integer variable.

The following example shows how to declare a two's complement (i.e. a signed) 20-bit variable with wrap-around as overflow handling with the initial value 3.14 shifted up 10 bits:

Fix a(3.14, 10, 20, TC, WRAP);
Fixed<20, TC, WRAP> b(3.14, 10);

Note that Fix takes the initial values as well as the fixed-point restrictions as constructor arguments. Fixed also takes the initial values as constructor arguments but it takes the fixed-point restrictions as template arguments. Choose Fix or Fixed depending on your needs. There are three main reasons why you would want to choose Fix instead of Fixed. First, if you want to change the fixed-point restrictions for a variable during run time, you have to use Fix, since the fixed-point restrictions for Fixed have been "fixed" at compile time. Second, if your code is using a lot of templating, you might end up with many more template arguments if you use Fixed than you would if you use Fix, since each set of fixed-point restrictions that you want to use will correspond to another type (based on the class template Fixed) instead of just different configurations of a single type (Fix). Third, the vector and matrix operations currently work better for Fix than for Fixed.

Note

Fixed is derived from Fix, which means that operators, methods and functions for Fix can be used for Fixed as well. However, the functions for Vec<Fix> (fixvec) and Mat<Fix> (fixmat) cannot be used for Vec<Fixed> and Mat<Fixed>.

If you choose Fix, you should also read the section Fix_Factory. If you choose Fixed, you may find it convenient to use the following typedefs:

typedef Fixed<1, TC, WRAP> fixed1;  // for Fixed with 1 bit
...
typedef Fixed<64, TC, WRAP> fixed64;  // for Fixed with 64 bits

typedef Fixed<1, US, WRAP> ufixed1;  // for Unsigned Fixed with 1 bit
...
typedef Fixed<64, US, WRAP> ufixed64;  // for Unsigned Fixed with 64 bits

typedef Fixed<1, TC, SAT> sfixed1;  // for Saturated Fixed with 1 bit
...
typedef Fixed<64, TC, SAT> sfixed64;  // for Saturated Fixed with 64 bits

typedef Fixed<1, US, SAT> sufixed1;  // for Saturated Unsigned Fixed with 1 bit
...
typedef Fixed<64, US, SAT> sufixed64;  // for Saturated Unsigned Fixed with 64 bits

Note

These typedefs use the default values for quantization mode (TRN) and statistics object pointer value (0). Also note that U stands for Unsigned but S stands for Saturated, NOT for Signed.

Declaration corresponding to the above Fixed example but using one of the typedefs:

fixed20 b(3.14, 10);

CFix and CFixed

CFix and CFixed are complex-valued fixed-point data types primarily intended to replace complex<double> when a design is refined from floating- to fixed-point implementation. The data is stored in the least significant bits of two 64-bit integer variables: one for the real part and one for the imaginary part. The two parts have a common shift factor (the one inherited from Fix_Base), so it is not possible to shift only one of them.

The following example shows two ways to declare a two's complement (i.e. a signed) 20-bit variable with wrap-around as overflow handling with the initial value 1.11 + 2.22i shifted up 10 bits:

CFix a(1.11, 2.22, 10, 20, TC, WRAP);
CFixed<20, TC, WRAP> b(1.11, 2.22, 10);

CFix c(complex<double>(1.11, 2.22), 0.0, 10, 20, TC, WRAP);
CFixed<20, TC, WRAP> d(complex<double>(1.11, 2.22), 0.0, 10);

Note

The shift factor is passed as the third argument to the CFix/CFixed constructors. If the first argument is complex, the second argument is a dummy (that was set to 0.0 in the examples above).

Choose CFix or CFixed depending on your needs; see section Fix and Fixed. If you choose CFix, you should also read the section Fix_Factory.

Note

CFixed is derived from CFix, which means that operators, methods and functions for CFix can be used for CFixed as well. However, the functions for Vec<CFix> (cfixvec) and Mat<CFix> (cfixmat) cannot be used for Vec<CFixed> and Mat<CFixed>.

If you choose CFixed, you may find it convenient to use the following typedefs, which are predefined in IT++:

typedef CFixed<1, TC, WRAP> cfixed1;  // for CFixed with 1 bit
...
typedef CFixed<64, TC, WRAP> cfixed64;  // for CFixed with 64 bits

typedef CFixed<1, TC, SAT> scfixed1;  // for Saturated CFixed with 1 bit
...
typedef CFixed<64, TC, SAT> scfixed64;  // for Saturated CFixed with 64 bits

Note

These typedefs use the default values for sign encoding mode (TC), quantization mode (TRN) and statistics object pointer value (0). Also note that S stands for Saturated, NOT for Signed.

Declarations corresponding to the above CFixed examples but using one of the typedefs:

cfixed20 b(1.11, 2.22, 10);

cfixed20 d(complex<double>(1.11, 2.22), 0.0, 10);

Fix_Factory

IF you choose to use Fix/CFix (instead of Fixed/CFixed) AND you want to declare an Array/Vec/Mat with Fix/CFix elements AND you wish to specify some non-default fixed-point restrictions for these elements (i.e. something else than 64-bit word length, two's complement as sign encoding mode, wrap-around as overflow mode, truncation as quantization mode, and no statistics object), THEN you will need to use a Fix_Factory when declaring the Array/Vec/Mat of Fix/CFix. Here is how it works, somewhat simplified: you give the fixed-point restrictions as parameters to the Fix_Factory, then you give the Fix_Factory as a parameter to the Array/Vec/Mat, and finally the Array/Vec/Mat uses the Fix_Factory to create Fix/CFix elements with those fixed-point restrictions. All constructors for Array, Vec and Mat can take a Fix_Factory (or any other Factory for that matter) as their last, optional argument. It is assumed that all elements in the Array/Vec/Mat should have the same fixed-point restrictions (and use a common statistics object, if any). Note that a Fix_Factory can create both Fix and CFix objects. For information on Factory in general and Fix_Factory in particular, see the Detailed Descriptions for itpp::Factory and itpp::Fix_Factory, respectively.

The following example shows how to declare a vector of length 7 with Fix elements that are two's complement 20-bit variables with wrap-around as overflow handling:

Vec<Fix> a(7, FIX20);

FIX20 is one of many predefined Fix_Factory; see the Detailed Description for itpp::Fix_Factory.

Note

One might wonder why the Array/Vec/Mat classes themselves cannot take the fixed-point restrictions as parameters directly and create the Fix/CFix elements without help from a Fix_Factory. The main benefit with the chosen solution is that the Array/Vec/Mat classes are not "contaminated" with knowledge (parameters, methods, etc) that is specific to the Fix/CFix types. If the user for some reason prefers to use some other type (i.e. a type not known by IT++) as the Array/Vec/Mat element type, this should work fine as long as he or she creates a corresponding Factory. And this is exactly the way that Fix/CFix and Fix_Factory work.

Fix/CFix should not need to know about Fix_Factory, but for the sake of uniform syntax in declarations, an exception has been made:

Fix a(FIX20);

i.e. a Fix/CFix declaration can take a Fix_Factory as an argument, just like the Vec<Fix> declaration above did.

Note

All declarations with a Fix_Factory as a constructor argument also work in templated code; see the Detailed Description for itpp::Fix_Factory.

Operators and methods

Initialization and assignment

Fixed-point variables can be initialized with a fixed- or a floating-point value:

// Initialize a with the floating-point value double(3.14*pow2(10))
// and word length 20, two's complement, wrap-around and rounding
Fix a(3.14, 10, 20, TC, WRAP, RND);

// Initialize b with the fixed-point value a
// and word length 7, two's complement, wrap-around and rounding
Fix b(a, 7, TC, WRAP, RND);

In this example, b was initialized with the same value as a but with smaller word length resulting in overflow, since round(3.14*pow2(10)) does not fit in the 7-bit variable b.

Warning

All fixed-point data types have default constructors. For Fix/CFix, the default constructor gives full word length (64 bits). If you call templated functions with Fix/CFix as the template argument, they might use these default constructors for declaration of temporary variables, which may then contain unrestricted (64-bit) temporary results. If you want these temporary results to be restricted, then you may have to modify the function to introduce fixed-point restrictions for the temporary results, and even introduce new temporary variables in order to avoid more than one operation per expression (demonstrated in an example below). For Fixed/CFixed, on the other hand, the default constructor gives certain fixed-point restrictions, but note that it may still be necessary to introduce other fixed-point restrictions as well as new temporary variables in the function.

The assignment operators =, +=, -=, *=, /=, <<= and >>= are supported. For =, +=, -=, *= and /=, the right-hand operand can be another fixed-point variable or an integer value. If it is an integer value, it is interpreted as a fixed-point value with shift factor 0. The = operator simply copies the shift factor from the right side to the left side. For information on how the other operators treat the shift factor, see sections Addition and subtraction, Multiplication and division and Bit-shifting.

If assignment to a scaled double is desired (when initialization has already taken place), the itpp::Fix::set method can be used.

// Initialize c with the floating-point value double(3.14*pow2(10))
// The shift factor is set to 10
Fix c(3.14, 10);

// Set c equal to 123. The shift factor is set to 0
// Note that the old shift factor 10 is discarded
c = 123;

// Set c equal to the integer portion of double(3.14*pow2(10))
// The shift factor is set to 10 (again)
c.set(3.14, 10);

// Achieve the same result using a temporary variable
// Note that the assignment operator copies the shift factor
c = Fix(3.14, 10);

When the floating-point value is quantized, the quantization mode of the fixed-point variable (TRN in the example above, since c has this quantization mode) will be used, unless some other quantization mode (e.g. RND) is specified as a third argument to set:

c.set(3.14, 10, RND);

Note

If you write templated code, you are better off if you use the set_fix function described in section Function set_fix instead of the set method.

There are also methods for setting data representation and shift directly: itpp::Fix::set_re, itpp::CFix::set_im and itpp::Fix_Base::set_shift. They are mainly intended for internal use.

Addition and subtraction

Addition and subtraction between two fixed-point variables as well as between a fixed-point variable and an integer variable is supported. The unary minus operator is also defined. For Fix and CFix, several vector and matrix operations are also supported.

// Declare a fixed-point vector with 7 elements
// (using the predefined Fix_Factory FIX20)
Vec<Fix> d(7, FIX20);

// Set all 7 elements equal to 77 with shift factor 0
d = Fix(77);

// Declare an integer vector with 7 elements
ivec e = "1 2 3 4 5 6 7";

// Add fixed-point vector d and integer vector e. Both have shift factor 0
Vec<Fix> f(d + e, FIX20);

Note

The addition and subtraction operators require that both operands have the same shift factor, unless at least one of the operands is zero. If d had been assigned with a different shift factor than 0 in the above example (and ASSERT_LEVEL > 0), the addition d + e would have failed, resulting in termination with the error message "assert_shifts: Different shifts not allowed!".

As hinted earlier, the fixed-point restrictions are applied during initialization, assignment and bit-shifting operations only. This means that the result of an addition or subtraction is unrestricted (64 bits).

Fix g(0, 0, 8, TC, SAT);
Fix h(100, 0, 8, TC, SAT);
Fix i(100, 0, 8, TC, SAT);
Fix j(-100, 0, 8, TC, SAT);

// The result of h + i is unrestricted (64 bits) but when it is assigned to g,
// it is restricted according to the fixed-point restrictions of g (8 bits).
// We get overflow, since 100+100=200 doesn't fit in an 8-bit signed variable.
// The saturated result will be 127
g = h + i;

// But now we don't get overflow since 100+100-100=100 does fit!
g = h + i + j;

// If we do want the temporary result to be restricted, we have to make
// an explicit temporary variable (with appropriate restrictions) for it
Fix tmp(0, 0, 8, TC, SAT);
// The first sum will be saturated to 127
tmp = h + i;
// The final sum will be 127-100=27, i.e. we got a different
// result when we introduced a restricted temporary variable
g = tmp + j;

Multiplication and division

Multiplication and division between two fixed-point variables as well as between a fixed-point variable and an integer variable is supported. For Fix and CFix, several vector and matrix operations are also supported.

As stated earlier, the fixed-point restrictions are applied during initialization, assignment and bit-shifting operations only. This means that the result of a multiplication or division is unrestricted (64 bits) in the same way as for an addition or subtraction; see section Addition and subtraction.

The resulting shift factor after a multiplication is the sum of the two shift factors, while the resulting shift factor after a division is the difference between the numerator shift factor and the denominator shift factor. The result of a division is always quantized using truncation, i.e. the quantization modes of the involved fixed-point variables do not matter. Note that sometimes divisions can be replaced with multiplications and/or bit-shifting operations; see section Bit-shifting.

Warning

Complex multiplications and divisions are supported, but they utilize temporary variables with full word length (64 bits).

Bit-shifting

The <<= and >>= operators are defined for the fixed-point data types. As an alternative, you can use the itpp::Fix::lshift and itpp::Fix::rshift methods. The appropriate fixed-point restrictions of the variable are applied, i.e. for left-shifting the overflow mode is applied and for right-shifting the quantization mode is applied. There is also a version of rshift that takes a quantization mode as the last argument (but there is no corresponding version of the >>= operator since it cannot take an extra argument).

// Declare a fixed-point variable with the default quantization mode (TRN)
Fix a(3.14, 10);

// Right shift 5 bits using the quantization mode of a (i.e. TRN)
a.rshift(5);

// Right shift 5 bits using the specified quantization mode (i.e. RND)
a.rshift(5, RND);

Note

If you write templated code, you are better off if you use the lshift_fix and rshift_fix functions described in section Functions lshift_fix and rshift_fix instead of the <<= and >>= operators and the lshift and rshift methods.

The << and >> operators are not defined for the fixed-point data types since it is not clear what quantization mode that should be applied for the >> operator.

Conversion

Fix and Fixed can be converted to double, while CFix and CFixed can be converted to complex<double>. The conversion operators "un-shift" the data by multiplying the fixed-point bit representation with pow2(-shift).

The itpp::Fix::unfix and itpp::CFix::unfix methods can always be used:

Fix a(3.14, 5);

cout << a.unfix() << endl;

The resulting output is 3.125.

Note

If you write templated code, you are better off if you use the functions unfix or to<T> described in sections Function unfix and Function to<T> instead of the unfix method.

Equivalently, the double(Fix&) and complex<double>(CFix&) operators can be used, unless you define NO_IMPLICIT_FIX_CONVERSION before you include IT++ in your program.

Fix a(3.14, 5);

cout << double(a) << endl;

The resulting output is 3.125.

Finally, Fix/Fixed can be converted to CFix/CFixed using the appropriate CFix/CFixed constructors.

Get data members

This example shows how to get the data members of fixed-point variables:

Fix a;

int64_t the_bit_representation = a.get_re();
int the_shift_factor = a.get_shift();
int the_word_length = a.get_wordlen();
e_mode the_sign_encoding_mode = a.get_e_mode();
o_mode the_overflow_mode = a.get_o_mode();
q_mode the_quantization_mode = a.get_q_mode();

int64_t max_bit_representation = a.get_max();
int64_t min_bit_representation = a.get_min();

Note

For CFix and CFixed, you get the bit representation for the imaginary part with the method get_im().

Input and output

The print() method outputs the entire state; see section Get data members.

Fix a;
a.print();

This code example shows how to input and output fixed-point numbers:

CFix a(FIX8);
a.set(0.0, 0.0, 4);

cout << "Old a: " << a << endl;
cout << "New a? ";
cin >> a;
cout << "New a: " << a << endl;

Complex numbers can be input on both the C++ form and the IT++ form:

Old a: 0+0i<4>
New a? 1+2i
New a: 1+2i<4>

Old a: 0+0i<4>
New a? (1,2)
New a: 1+2i<4>

Note

The output_mode is OUTPUT_FIX_SHIFT in these examples; see section Output mode.

In the above examples, only the data representation was changed, while the shift (4) was kept. It is however possible to enter another (positive or negative) shift factor as well:

Old a: 0+0i<4>
New a? 1+2i<5>
New a: 1+2i<5>

It is also possible to enter a floating-point value and a (positive or negative) shift, rather than the data representation and a shift, if a slightly different format is used:

Old a: 0+0i<4>
New a? 1+2i<<5
New a: 32+64i<5>

The resulting data representation is the entered floating-point value 1+2i multiplied by 2^5.

Note

In order to enter a negative shift, write 1+2i<<-5. It is not possible to write 1+2i>>5.

Vectors and matrices support the same formats for fixed-point numbers. However, all old elements are assumed to have the same shift factor, and the shift factor of the first old element becomes the default shift factor for all elements of the vector or matrix. The same holds in e.g. an Array of vectors, i.e. the shift factor of the first old element in each vector becomes the default shift factor for all elements of that vector. The default shift factor in an empty vector or matrix is zero.

Functions

Function is_fix

The function itpp::is_fix returns true only if the argument is of type Fix or CFix or an Array/Vec/Mat of Fix or CFix.

Array<Array<Vec<Fix> > > aavf(FIX20);
bool will_be_true = is_fix(aavf);

Warning

Unfortunately, the function is_fix returns false if the argument is of type Fixed or CFixed.

Function set_fix

The function itpp::set_fix sets y = x * pow2(n) if the first argument is of type Fix or CFix or an Array/Vec/Mat of Fix or CFix. If the first argument is of type double or complex<double> or an Array/Vec/Mat of double or complex<double>, the function just sets y = x.

Fix fix_var(FIX20);
set_fix(fix_var, 3.14, 10);
// fix_var will equal the integer portion of 3.14 * pow2(10)

double double_var(FIX20);
set_fix(double_var, 3.14, 10);
// double_var will just equal 3.14

When the floating-point value is quantized, the quantization mode of the first argument (TRN in the example above, since fix_var has this quantization mode) will be used, unless some other quantization mode (e.g. RND) is specified as a fourth argument to set_fix:

set_fix(fix_var, 3.14, 10, RND);

Functions lshift_fix and rshift_fix

The functions itpp::lshift_fix and itpp::rshift_fix perform left and right bit-shifts, respectively, if the first argument is of type Fix or CFix or an Array/Vec/Mat of Fix or CFix. If the first argument is of type double or complex<double> or an Array/Vec/Mat of double or complex<double>, the functions do not do anything at all.

// This will right-shift fix_var 10 bits
rshift_fix(fix_var, 10);

// This will not affect double_var
rshift_fix(double_var, 10);

When a fixed-point value is right-shifted using rshift_fix, the quantization mode of the first argument (TRN in the example above, since fix_var has this quantization mode) will be used, unless some other quantization mode (e.g. RND) is specified as a third argument to rshift_fix:

rshift_fix(fix_var, 10, RND);

When a fixed-point value is left-shifted using lshift_fix, on the other hand, the overflow mode of the first argument is always used.

Function assert_fixshift

The itpp::assert_fixshift function can be used to verify that the shift factor has the expected value:

Fix a(3.14, 5);

// We will pass this check since 5 = 5
assert_fixshift(a, 5);

// The program will terminate (if ASSERT_LEVEL > 0) since 5 != 6
assert_fixshift(a, 6);

If the first argument is of type double or complex<double> instead, no test will be performed (since they have no shift factors).

Function unfix

The itpp::unfix function converts a fixed-point variable to a floating-point variable (or an Array/Vec/Mat of fixed-point variables to an Array/Vec/Mat of floating-point variables) by multiplying the fixed-point bit representation with pow2(-shift), using the unfix method mentioned above.

Fix a(3.14, 5);
double b = unfix(a);

Array<Mat<CFix> > c(FIX40);
cin >> c;
Array<cmat> d = unfix(c);

If the argument is a floating-point variable (or an Array/Vec/Mat of floating-point variables) instead, the function just returns the argument.

Function to<T>

The itpp::to<T> function is a very general conversion function. It converts a floating- or fixed-point variable to a floating- or fixed-point variable (or a floating- or fixed-point Array/Vec/Mat to a floating- or fixed-point Array/Vec/Mat) depending on the types of the argument and of the specified template parameter.

// Convert a Vec<double> to a Vec<Fix> and assign it to f
Vec<double> e = "1.0 2.0 3.0";
Vec<Fix> f;
f = to<Fix>(e);  // convert e "to Fix"

// Convert an Array<Array<Mat<Fix> > > called g to
// an Array<Array<Mat<CFix> > > and assign it to h
Array<Array<Mat<CFix> > > h;
h = to<CFix>(g);  // convert g "to CFix"

Note

The variants to<double>(x) and to<complex<double> >(x) provide the same functionality as unfix(x).

Warning

Be aware that the variants to<Fix>(x) and to<CFix>(x) will return a fixed-point variable with the shift factor(s) set to zero if x is a floating-point variable. However, if x is a fixed-point variable, the shift will be copied to the return variable.

Other functions

• itpp::abs
• itpp::real
• itpp::imag
• itpp::conj

Enumeration Type Documentation

enum itpp::e_mode

Sign encoding modes (aligned with SystemC)

Enumerator:

TC	Two's complement.
US	Unsigned.

Definition at line 942 of file fix_base.h.

enum itpp::o_mode

Overflow modes (aligned with SystemC)

Enumerator:

SAT	Saturation.
SAT_ZERO	Saturation to zero (Not implemented)
SAT_SYM	Symmetrical saturation (Not implemented)
WRAP	Wrap-around.
WRAP_SM	Sign magnitued wrap-around (Not implemented)

Definition at line 948 of file fix_base.h.

enum itpp::q_mode

Quantization modes (aligned with SystemC)

Enumerator:

RND	Rounding to plus infinity.
RND_ZERO	Rounding to zero.
RND_MIN_INF	Rounding to minus infinity.
RND_INF	Rounding to infinity.
RND_CONV	Convergent rounding with half-way value rounded to even value.
RND_CONV_ODD	Convergent rounding with half-way value rounded to odd value (not defined in SystemC)
TRN	Truncation.
TRN_ZERO	Truncation to zero.

Definition at line 957 of file fix_base.h.

enum itpp::output_mode

Output modes.

Enumerator:

OUTPUT_FIX	Output fixed-point representation only.
OUTPUT_FIX_SHIFT	Output fixed-point representation followed by <shift> (default)
OUTPUT_FLOAT	Output floating-point value.
OUTPUT_FLOAT_SHIFT	Output floating-point value followed by <<shift.

Definition at line 969 of file fix_base.h.

Function Documentation

cvec itpp::unfix ( const fixvec &  x )

inline

Convert fixvec to vec by multiplying the bit representations with pow2(-shift)

Convert cfixvec to cvec by multiplying the bit representations with pow2(-shift)

Definition at line 467 of file fix_functions.h.

References itpp::to_vec().

cmat itpp::unfix ( const fixmat &  x )

inline

Convert fixmat to mat by multiplying the bit representations with pow2(-shift)

Convert cfixmat to cmat by multiplying the bit representations with pow2(-shift)

Definition at line 471 of file fix_functions.h.

References itpp::to_mat().

cfixvec itpp::operator+ ( const fixvec &  v, const int  s  )

inline

fixvec + int

cfixvec + int

Definition at line 75 of file fix_operators.h.

cfixvec itpp::operator+ ( const int  s, const fixvec &  v  )

inline

int + fixvec

int + cfixvec

Definition at line 77 of file fix_operators.h.

cfixvec itpp::operator- ( const fixvec &  v, const int  s  )

inline

fixvec - int

cfixvec - int

Definition at line 79 of file fix_operators.h.

cfixvec itpp::operator- ( const int  s, const fixvec &  v  )

inline

int - fixvec

int - cfixvec

Definition at line 81 of file fix_operators.h.

cfixvec itpp::operator* ( const fixvec &  v, const int  s  )

inline

fixvec * int

cfixvec * int

Definition at line 83 of file fix_operators.h.

cfixvec itpp::operator* ( const int  s, const fixvec &  v  )

inline

int * fixvec

int * cfixvec

Definition at line 85 of file fix_operators.h.

cfixvec itpp::operator/ ( const fixvec &  v, const int  s  )

inline

fixvec / int using quantization mode TRN

cfixvec / int using quantization mode TRN

Definition at line 87 of file fix_operators.h.

cfixmat itpp::operator+ ( const fixmat &  v, const int  s  )

inline

fixmat + int

cfixmat + int

Definition at line 90 of file fix_operators.h.

cfixmat itpp::operator+ ( const int  s, const fixmat &  v  )

inline

int + fixmat

int + cfixmat

Definition at line 92 of file fix_operators.h.

cfixmat itpp::operator- ( const fixmat &  v, const int  s  )

inline

fixmat - int

cfixmat - int

Definition at line 94 of file fix_operators.h.

cfixmat itpp::operator- ( const int  s, const fixmat &  v  )

inline

int - fixmat

int - cfixmat

Definition at line 96 of file fix_operators.h.

cfixmat itpp::operator* ( const fixmat &  v, const int  s  )

inline

fixmat * int

cfixmat * int

Definition at line 98 of file fix_operators.h.

cfixmat itpp::operator* ( const int  s, const fixmat &  v  )

inline

int * fixmat

int * cfixmat

Definition at line 100 of file fix_operators.h.

cfixmat itpp::operator/ ( const fixmat &  v, const int  s  )

inline

fixmat / int using quantization mode TRN

cfixmat / int using quantization mode TRN

Definition at line 102 of file fix_operators.h.

ITPP_EXPORT cfixvec itpp::operator+	(	const fixvec &	a,
		const ivec &	b
	)

fixvec + ivec

cfixvec + ivec

Definition at line 125 of file fix_operators.cpp.

References it_assert_debug, and itpp::Vec< Num_T >::size().

cfixvec itpp::operator+ ( const ivec &  a, const fixvec &  b  )

inline

ivec + fixvec

ivec + cfixvec

Definition at line 107 of file fix_operators.h.

cfixvec itpp::operator- ( const fixvec &  a, const ivec &  b  )

inline

fixvec - ivec

cfixvec - ivec

Definition at line 109 of file fix_operators.h.

cfixvec itpp::operator- ( const ivec &  a, const fixvec &  b  )

inline

ivec - fixvec

ivec - cfixvec

Definition at line 111 of file fix_operators.h.

ITPP_EXPORT CFix itpp::operator*	(	const fixvec &	a,
		const ivec &	b
	)

fixvec * ivec

cfixvec * ivec

Definition at line 135 of file fix_operators.cpp.

References it_assert_debug, and itpp::Vec< Num_T >::size().

CFix itpp::operator* ( const ivec &  a, const fixvec &  b  )

inline

ivec * fixvec

ivec * cfixvec

Definition at line 115 of file fix_operators.h.

ITPP_EXPORT cfixmat itpp::operator+	(	const fixmat &	a,
		const imat &	b
	)

fixmat + imat

cfixmat + imat

Definition at line 145 of file fix_operators.cpp.

References itpp::Mat< Num_T >::cols(), it_assert_debug, and itpp::Mat< Num_T >::rows().

cfixmat itpp::operator+ ( const imat &  a, const fixmat &  b  )

inline

imat + fixmat

imat + cfixmat

Definition at line 120 of file fix_operators.h.

cfixmat itpp::operator- ( const fixmat &  a, const imat &  b  )

inline

fixmat - imat

cfixmat - imat

Definition at line 122 of file fix_operators.h.

cfixmat itpp::operator- ( const imat &  a, const fixmat &  b  )

inline

imat - fixmat

imat - cfixmat

Definition at line 124 of file fix_operators.h.

ITPP_EXPORT cfixmat itpp::operator*	(	const fixmat &	a,
		const imat &	b
	)

fixmat * imat

cfixmat * imat

Definition at line 158 of file fix_operators.cpp.

References itpp::Mat< Num_T >::_data(), itpp::Mat< Num_T >::cols(), it_assert_debug, and itpp::Mat< Num_T >::rows().

cfixmat itpp::operator* ( const imat &  a, const fixmat &  b  )

inline

imat * fixmat

imat * cfixmat

Definition at line 128 of file fix_operators.h.

cfixvec itpp::operator+ ( const cfixvec &  a, const fixvec &  b  )

inline

cfixvec + fixvec

fixvec + cfixvec

Definition at line 352 of file fix_operators.cpp.

References it_assert_debug, and itpp::Vec< Num_T >::size().

cfixvec itpp::operator- ( const cfixvec &  a, const fixvec &  b  )

inline

cfixvec - fixvec

fixvec - cfixvec

Definition at line 302 of file fix_operators.h.

CFix itpp::operator* ( const cfixvec &  a, const fixvec &  b  )

inline

cfixvec * fixvec

fixvec * cfixvec

Definition at line 362 of file fix_operators.cpp.

References it_assert_debug, and itpp::Vec< Num_T >::size().

cfixmat itpp::operator+ ( const cfixmat &  a, const fixmat &  b  )

inline

cfixmat + fixmat

fixmat + cfixmat

Definition at line 372 of file fix_operators.cpp.

References itpp::Mat< Num_T >::cols(), it_assert_debug, and itpp::Mat< Num_T >::rows().

cfixmat itpp::operator- ( const cfixmat &  a, const fixmat &  b  )

inline

cfixmat - fixmat

fixmat - cfixmat

Definition at line 315 of file fix_operators.h.

cfixmat itpp::operator* ( const cfixmat &  a, const fixmat &  b  )

inline

cfixmat * fixmat

fixmat * cfixmat

Definition at line 385 of file fix_operators.cpp.

References itpp::Mat< Num_T >::_data(), itpp::Mat< Num_T >::cols(), it_assert_debug, and itpp::Mat< Num_T >::rows().

Variable Documentation

const uint64_t itpp::UINT64_POW2[64]

Initial value:

= {
  uint64_t(1),     uint64_t(1) << 1,  uint64_t(1) << 2,  uint64_t(1) << 3,  uint64_t(1) << 4,
  uint64_t(1) << 5,  uint64_t(1) << 6,  uint64_t(1) << 7,  uint64_t(1) << 8,  uint64_t(1) << 9,
  uint64_t(1) << 10, uint64_t(1) << 11, uint64_t(1) << 12, uint64_t(1) << 13, uint64_t(1) << 14,
  uint64_t(1) << 15, uint64_t(1) << 16, uint64_t(1) << 17, uint64_t(1) << 18, uint64_t(1) << 19,
  uint64_t(1) << 20, uint64_t(1) << 21, uint64_t(1) << 22, uint64_t(1) << 23, uint64_t(1) << 24,
  uint64_t(1) << 25, uint64_t(1) << 26, uint64_t(1) << 27, uint64_t(1) << 28, uint64_t(1) << 29,
  uint64_t(1) << 30, uint64_t(1) << 31, uint64_t(1) << 32, uint64_t(1) << 33, uint64_t(1) << 34,
  uint64_t(1) << 35, uint64_t(1) << 36, uint64_t(1) << 37, uint64_t(1) << 38, uint64_t(1) << 39,
  uint64_t(1) << 40, uint64_t(1) << 41, uint64_t(1) << 42, uint64_t(1) << 43, uint64_t(1) << 44,
  uint64_t(1) << 45, uint64_t(1) << 46, uint64_t(1) << 47, uint64_t(1) << 48, uint64_t(1) << 49,
  uint64_t(1) << 50, uint64_t(1) << 51, uint64_t(1) << 52, uint64_t(1) << 53, uint64_t(1) << 54,
  uint64_t(1) << 55, uint64_t(1) << 56, uint64_t(1) << 57, uint64_t(1) << 58, uint64_t(1) << 59,
  uint64_t(1) << 60, uint64_t(1) << 61, uint64_t(1) << 62, uint64_t(1) << 63
}

Table for fast multiplication or division by 2^n.

Definition at line 889 of file fix_base.h.

Referenced by itpp::Fix_Base::init().