#
# 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-18: atanh(x)
; Conditions: -1 < x < 1
; Accuracy: 10 digits
; Color: green
; Style: blank
; ----------  Card-Pocket-End  ---------------------------------------------
;
; http://en.wikipedia.org/wiki/Hyperbolic_function
;
; Calculated using the formula
;
;     atanh(x) = 0.5 * ln((1 + x) / (1 - x))
;
; M14 => sign of result
; M13 => |x|
; M12 => y**2
; M11 => series sum
; M10 => odd denominator
;
SFJ $304
    SM13
    MJ $406
    1
    SM14
    RV
    UJ $407
FJ $406
    1
    CS
    SM14
    RV
    CS
FJ $407
    1
    -=
    /
    2
    RV
    -=
    1
    -=

    SQRT
    SQRT
    SQRT
    SQRT

    1
    +=
    /
    2
    RV
    -=
    1
    SM10
    +=          ; "y"
    SM13
    SM11
    *
    +=          ; y**2
    SM12
FJ $408
    2
    M10
    RM13
    *
    RM12
    /
    SM13
    RM10
    +=
    M11         ; add to series sum
    CS
    MJ $408
    RM11
    *
    16          ; compensate for the 4 sqrt, above
    *
    RM14        ; sign of the result
    +=
    SRJ