Developer Reference

  • 0.10
  • 10/21/2020
  • Public Content
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

Intel's compilers may or may not optimize to the same degree for non-Intel microprocessors for optimizations that are not unique to Intel microprocessors. These optimizations include SSE2, SSE3, and SSSE3 instruction sets and other optimizations. Intel does not guarantee the availability, functionality, or effectiveness of any optimization on microprocessors not manufactured by Intel. Microprocessor-dependent optimizations in this product are intended for use with Intel microprocessors. Certain optimizations not specific to Intel microarchitecture are reserved for Intel microprocessors. Please refer to the applicable product User and Reference Guides for more information regarding the specific instruction sets covered by this notice.

Notice revision #20110804