Maths: sinLo

       Name: sinLo                                                   [Show more]
       Type: Variable
   Category: Maths
    Summary: Low byte of the sine lookup table
  Deep dive: Trigonometry
    Context: See this variable in context in the source code
 References: This variable is used as follows:
             * Sine16Bit uses sinLo


 This table contains sine values for a quarter of a circle, i.e. for the range
 0 to 90 degrees, or 0 to PI/2 radians. The table contains values for indexes
 0 to 256, which cover the quarter from 0 to PI/2 radians. Entry X in the table
 is therefore (X / 256) * (PI / 2) radians of the way round the quarter circle,
 so the table at index X contains the sine of this value.

 The value of sine across the quarter circle ranges from 0 to 1:

   sin(0) = 0

   sin(90) = sin(PI/2) = 1

 but assembly language doesn't support fractions, so instead we store the sine
 in a 16-bit number that contains the sine multiplied by 65536, so the range of
 (sinHi sinLo) over the course of the quarter circle is 0 to 65536. It might
 help to think of sinHi as an integer ranging from 0 to 256 across the quarter
 circle, with sinLo as the fractional part ranging from 0 to 255; this is the
 approach taken in the Sine16Bit routine.

 In other words, entry X in this table contains sin(X) * 65536, where X ranges
 from 0 to 256 over the course of a quarter circle.


.sinLo

 FOR I%, 0, 256

  N = SIN((I% / 256) * (PI / 2))

  IF N >= 1
   B% = 255
  ELSE
   B% = LO(INT(N * 65536))
  ENDIF

  EQUB B%

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