gh-150534: Add C23 half-turn trigonometric *pi functions (GH-150555)

Add the the following functions to the math module:
acospi, asinpi, atanpi, atan2pi, cospi, sinpi, tanpi.

Author: jepler

Doc/library/math.rst

@@ -83,13 +83,20 @@ noted otherwise, all return values are floats.
 
 **Trigonometric functions**
 --------------------------------------------------------------------------------------------------
-:func:`acos(x) <acos>`                                Arc cosine of *x*
-:func:`asin(x) <asin>`                                Arc sine of *x*
-:func:`atan(x) <atan>`                                Arc tangent of *x*
-:func:`atan2(y, x) <atan2>`                           ``atan(y / x)``
-:func:`cos(x) <cos>`                                  Cosine of *x*
-:func:`sin(x) <sin>`                                  Sine of *x*
-:func:`tan(x) <tan>`                                  Tangent of *x*
+:func:`acos(x) <acos>`                                Arc cosine of *x*, in radians
+:func:`acospi(x) <acospi>`                            Arc cosine of *x*, in half-turns
+:func:`asin(x) <asin>`                                Arc sine of *x*, in radians
+:func:`asinpi(x) <asinpi>`                            Arc sine of *x*, in half-turns
+:func:`atan(x) <atan>`                                Arc tangent of *x*, in radians
+:func:`atanpi(x) <atanpi>`                            Arc tangent of *x*, in half-turns
+:func:`atan2(y, x) <atan2>`                           ``atan(y / x)``, in radians
+:func:`atan2pi(y, x) <atan2pi>`                       ``atan(y / x)``, in half-turns
+:func:`cos(x) <cos>`                                  Cosine of *x* radians
+:func:`cospi(x) <cospi>`                              Cosine of *x⋅π* radians
+:func:`sin(x) <sin>`                                  Sine of *x* radians
+:func:`sinpi(x) <sinpi>`                              Sine of *x⋅π* radians
+:func:`tan(x) <tan>`                                  Tangent of *x* radians
+:func:`tanpi(x) <tanpi>`                              Tangent of *x⋅π* radians
 
 **Hyperbolic functions**
 --------------------------------------------------------------------------------------------------
@@ -599,18 +606,42 @@ Trigonometric functions
    ``pi``.
 
 
+.. function:: acospi(x)
+
+   Return the arc cosine of *x*, in half-turns. The result is between ``0`` and
+   ``1``.
+
+   .. versionadded:: next
+
+
 .. function:: asin(x)
 
    Return the arc sine of *x*, in radians. The result is between ``-pi/2`` and
    ``pi/2``.
 
 
+.. function:: asinpi(x)
+
+   Return the arc sine of *x*, in half-turns. The result is between ``-0.5`` and
+   ``0.5``.
+
+   .. versionadded:: next
+
+
 .. function:: atan(x)
 
    Return the arc tangent of *x*, in radians. The result is between ``-pi/2`` and
    ``pi/2``.
 
 
+.. function:: atanpi(x)
+
+   Return the arc tangent of *x*, in half-turns. The result is between ``-0.5`` and
+   ``0.5``.
+
+   .. versionadded:: next
+
+
 .. function:: atan2(y, x)
 
    Return ``atan(y / x)``, in radians. The result is between ``-pi`` and ``pi``.
@@ -621,21 +652,54 @@ Trigonometric functions
    -1)`` is ``-3*pi/4``.
 
 
+.. function:: atan2pi(y, x)
+
+   Return ``atanpi(y / x)``, in half-turns. The result is between ``-1`` and ``1``.
+   The vector in the plane from the origin to point ``(x, y)`` makes this angle
+   with the positive X axis. The point of :func:`atan2pi` is that the signs of both
+   inputs are known to it, so it can compute the correct quadrant for the angle.
+   For example, ``atanpi(1)`` and ``atan2pi(1, 1)`` are both ``0.25``, but
+   ``atan2pi(-1, -1)`` is ``-0.75``.
+
+   .. versionadded:: next
+
+
 .. function:: cos(x)
 
    Return the cosine of *x* radians.
 
 
+.. function:: cospi(x)
+
+   Return the cosine of *x* half-turns (*x⋅π* radians).
+
+   .. versionadded:: next
+
+
 .. function:: sin(x)
 
    Return the sine of *x* radians.
 
 
+.. function:: sinpi(x)
+
+   Return the sine of *x* half-turns (*x⋅π* radians).
+
+   .. versionadded:: next
+
+
 .. function:: tan(x)
 
    Return the tangent of *x* radians.
 
 
+.. function:: tanpi(x)
+
+   Return the tangent of *x* half-turns (*x⋅π* radians).
+
+   .. versionadded:: next
+
+
 Hyperbolic functions
 --------------------
 

Doc/whatsnew/3.16.rst

@@ -113,6 +113,17 @@ logging
   before the rotation interval expires.
   (Contributed by Iván Márton and Serhiy Storchaka in :gh:`84649`.)
 
+math
+----
+
+* Added trigonometric functions that work in units of half turns, rather than
+  radians. The new functions :func:`math.acospi`, :func:`math.asinpi`,
+  :func:`math.atanpi`, and :func:`math.atan2pi` return half-turn angles. The
+  new functions :func:`math.cospi`, :func:`math.sinpi`, and :func:`math.tanpi`
+  take half-turn angle arguments. These functions are recommended by IEEE
+  754-2019 and standardized in C23.
+  (Contributed by Jeff Epler in :gh:`150534`.)
+
 os
 --