To: J3                                                     J3/19-157r1
From: Lorri Menard
Subject: IEEE Circular trigonometric functions
Date: 2019-February-22
Reference:  m215/18-139r1, m217/18-276r1

1 Introduction

Addition of the circular trigonometric functions was approved for further
work at m217.  This paper attempts to craft specifications.

2 Specifications

These elemental intrinsics are generic and not specific.
All would be similar to their radian counterparts except that the
argument(s) or return values would be half-revolutions.

3 Syntax

    ACOSPI (X)
    Description: Inverse circular cosine function.
    Class: Elemental function.
    Argument: X shall be of type real with a value that satisfies the
              inequality |X| <= 1.
    Result Characteristics:  Same as X.
    Result Value: The result has a value equal to a processor-dependent
    approximation to arccos(X)/pi. It is expressed in
    half-revolutions and lies in the range of -1 to 1.

    ASINPI (X)
    Description: Inverse circular sine function.
    Class: Elemental function.
    Argument: X shall be of type real with a value that satisfies the
              inequality |X| <= 1.
    Result Characteristics:  Same as X.
    Result Value: The result has a value equal to a processor-dependent
    approximation to arcsin(X)/pi. It is expressed in half-revolutions
    and lies in the range of -1 to 1.

    ATANPI (X) or ATANPI (Y,X)
    Description: Inverse circular tangent function.
    Class: Elemental function.
    Arguments:
     Y     shall be of type real.
     X     If Y appears, X shall be of type real with the same kind type
           parameter as Y. If Y has the value zero, X shall not have the
           value zero. If Y does not appear, X shall be of type real.
    Result Characteristics:  Same as X.
    Result Value: If Y appears, the result is the same as the result of
    ATAN2PI (Y,X). If Y does not appear, the result has a value equal to a
    processor-dependent approximation to arctan(X)/pi.

    ATAN2PI (Y,X)
    Description: Inverse circular tangent function.
    Class: Elemental function.
    Arguments:
     Y     shall be of type real.
     X     X shall be of the same type and kind type
           parameter as Y. If Y has the value zero, X shall not have the
           value zero.
    Result Characteristics:  Same as X
    Result Value: The result has a value equal to a processor-dependent
    approximation to arctan(Y/X)/pi if X != 0. If Y > zero, the result is
    positive. If Y < zero, the result is negative.  If Y = zero, the
    result is zero (if X > zero) or 1 (if X < zero).
    If X = zero, the result is zero.  If X is minus zero the result is
    one.

    COSPI (X)
    Description: Circular cosine function.
    Class: Elemental function.
    Argument: X shall be of type real.
    Result Characteristics:  Same as X.
    Result Value: The result has a value equal to a processor-dependent
    approximation to cos(X * pi). It is regarded as a value in
    half-revolutions.

    SINPI (X)
    Description: Circular sine function.
    Class: Elemental function.
    Argument: X shall be of type real.
    Result Characteristics:  Same as X.
    Result Value: The result has a value equal to a processor-dependent
    approximation to sin(X * pi). It is regarded as a value in
    half-revolutions.

    TANPI (X)
    Description: Circular tangent function.
    Class: Elemental function.
    Argument: X shall be of type real.
    Result Characteristics:  Same as X.
    Result Value: The result has a value equal to a processor-dependent
    approximation to tan(X * pi). It is regarded as a value in
    half-revolutions.

4 Edits
   To be supplied later