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, i2=-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.