Developer Reference for Intel® oneAPI Math Kernel Library - C

Developer Reference

Contents

Special Value Notations

This
topic
 defines notations of special values for complex functions. The definitions are provided in text, tables, or formulas.
  • z
    ,
    z1
    ,
    z2
    , etc. denote complex numbers.
  • i
    ,
    i
    2
    =-1
     is the imaginary unit.
  • x
    ,
    X
    ,
    x1
    ,
    x2
    , etc. denote real imaginary parts.
  • y
    ,
    Y
    ,
    y1
    ,
    y2
    , etc. denote imaginary parts.
  • X
     and
    Y
     represent any finite positive IEEE-754 floating point values, if not stated otherwise.
  • Quiet
    NaN
     and signaling
    NaN
     are denoted with
    QNAN
     and
    SNAN
    , respectively.
  • The IEEE-754 positive infinities or floating-point numbers are denoted with a
    +
     sign before
    X
    ,
    Y
    , etc.
  • The IEEE-754 negative infinities or floating-point numbers are denoted with a
    -
     sign before
    X
    ,
    Y
    , etc.
CONJ(z)
 and
CIS(z)
 are defined as follows:
CONJ(x+i
·
y)=x-i
·
y
CIS(y)=cos(y)+i
·
sin(y)
.
The special value tables show the result of the function for the
z
 argument at the intersection of the
RE(z)
 column and the
i*IM(z)
 row. If the function raises an exception on the argument
z
, the lower part of this cell shows the raised exception and the VM Error Status. An empty cell indicates that this argument is normal and the result is defined mathematically.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.