#
# canola - canon canola 1614p emulator
# Copyright (C) 2011 Peter Miller
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License, version 3, as
# published by the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
# General Public License for more details.
#
# You should have received a copy of the GNU General Public License along
# with this program. If not, see <http://www.gnu.org/licenses/>.
#
# ----------  Card-Pocket-Begin  -------------------------------------------
# Title: MS-1: sin(x)
# Conditions:
#     -10**16 < x < 10**16
#     x: Degree
# Accuracy: 10 digits
# Style: blank
# ----------  Card-Pocket-End  ---------------------------------------------
;
;
; This uses a Taylor series expansion of sin(x)
; See http://en.wikipedia.org/wiki/Trigonometric_functions#Series_definitions
; for more information.
;
;              x**3   x**5   x**7
; sin(x) = x - ---- + ---- - ---- + ...
;               3!     5!     7!
;
; initial X in degress is in the X register
; M14 contains the series sum
; M13 contains the (2n+1)! being constructed
; M12 contains the x**2
;
; Rather than convert into the -pi..pi range, it converts into the
; 0..2*pi range, so it is going to converge slightly more slowly for
; values > pi.
;
SFJ $201
/                       ; first we must turn degrees into radians
360
*
SM14
1
FLOOR 0                 ; this modifies the following += to truncate to integer
-=                      ; negatively, so that we subtract it from
RM14                    ; the unbounded angle
+=                      ; now we have a value in the range 0..<1
*
6.28318530718           ; and convert to radians [first source of inaccuracy]
+=                      ; in the range 0..<2*pi
SM14                    ; M14 = x
2
SM13                    ; M13 = 2
RM14
*
-=
SM12                    ; M12 = -x ** 2
FJ $200
RV
*
RM12
/
RM13
+=
1
M13
RV
/
RM13
+=
M14
1
M13
RV
*
.1
+=
MJ $200                 ; only stop when it's zero
CS
MJ $200
RM14                    ; recall series sum
SRJ