Maths (Geometry): ACT

       Name: ACT                                                     [Show more]
       Type: Variable
   Category: Maths (Geometry)
    Summary: Arctan table
  Deep dive: The sine, cosine and arctan tables
    Context: See this variable in context in the source code
 References: No direct references to this variable in this source file


 This table contains lookup values for arctangent calculations involving angles
 in the range 0 to 45 degrees (or 0 to PI / 4 radians).

 To calculate the value of theta in the following:

   theta = arctan(t)

 where 0 <= t < 1, we look up the value in:

   ACT + (t * 32)

 The result will be an integer representing the angle in radians, where 256
 represents a full circle of 360 degrees (2 * PI radians). The result of the
 lookup will therefore be an integer in the range 0 to 31, as this represents
 0 to 45 degrees (0 to PI / 4 radians).

 The table does not support values of t >= 1 or t < 0 directly, so if we need
 to calculate the arctangent for an angle greater than 45 degrees, we can apply
 the following calculation to the result from the table:

   * For t > 1, arctan(t) = 64 - arctan(1 / t)

 For negative values of t where -1 < t < 0, we can apply the following
 calculation to the result from the table:

   * For t < 0, arctan(-t) = 128 - arctan(t)

 Finally, if t < -1, we can do the first calculation to get arctan(|t|), and
 the second to get arctan(-|t|).


.ACT

 FOR I%, 0, 31

  EQUB INT((128 / PI) * ATN(I% / 32) + 0.5)

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