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4.2 Elementary functions
Each of the classes cl_N
, cl_R
, cl_RA
, cl_I
,
cl_F
, cl_SF
, cl_FF
, cl_DF
, cl_LF
defines the following operations:
type operator + (const type&, const type&)
-
Addition.
type operator - (const type&, const type&)
-
Subtraction.
type operator - (const type&)
Returns the negative of the argument.
type plus1 (const type& x)
-
Returns
x + 1
. type minus1 (const type& x)
-
Returns
x - 1
. type operator * (const type&, const type&)
-
Multiplication.
type square (const type& x)
-
Returns
x * x
.
Each of the classes cl_N
, cl_R
, cl_RA
,
cl_F
, cl_SF
, cl_FF
, cl_DF
, cl_LF
defines the following operations:
type operator / (const type&, const type&)
-
Division.
type recip (const type&)
-
Returns the reciprocal of the argument.
The class cl_I
doesn’t define a ‘/’ operation because
in the C/C++ language this operator, applied to integral types,
denotes the ‘floor’ or ‘truncate’ operation (which one of these,
is implementation dependent). (See section Rounding functions.)
Instead, cl_I
defines an “exact quotient” function:
The following exponentiation functions are defined:
cl_I expt_pos (const cl_I& x, const cl_I& y)
cl_RA expt_pos (const cl_RA& x, const cl_I& y)
y
must be > 0. Returnsx^y
.cl_RA expt (const cl_RA& x, const cl_I& y)
cl_R expt (const cl_R& x, const cl_I& y)
cl_N expt (const cl_N& x, const cl_I& y)
Returns
x^y
.
Each of the classes cl_R
, cl_RA
, cl_I
,
cl_F
, cl_SF
, cl_FF
, cl_DF
, cl_LF
defines the following operation:
The class cl_N
implements this as follows:
cl_R abs (const cl_N x)
Returns the absolute value of
x
.
Each of the classes cl_N
, cl_R
, cl_RA
, cl_I
,
cl_F
, cl_SF
, cl_FF
, cl_DF
, cl_LF
defines the following operation:
type signum (const type& x)
-
Returns the sign of
x
, in the same number format asx
. This is defined asx / abs(x)
ifx
is non-zero, andx
ifx
is zero. Ifx
is real, the value is either 0 or 1 or -1.
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