#
# 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-17: acosh(x)
; Color: green
; Style: blank
; ----------  Card-Pocket-End  ---------------------------------------------
;
; http://en.wikipedia.org/wiki/Hyperbolic_function
;
; Evaluated using the formula
;
;     acosh(x) = ln(x + sqrt(x**2 - 1))
;
SFJ $303
    SM14        ; x
    *
    +=
    1
    -=
    SQRT
    RM14
    +=          ; x + sqrt(x**2 - 1)

    SQRT        ; this next is similar to the MS-12 ln(x) code
    SQRT
    SQRT
    SQRT
;
; M14 => previous numerator
; M13 => y**2
; M12 => series sum
; M11 => odd denominator
;
    1           ; 1 - 2 / (x + 1)
    +=          ; is the same as
    /           ; (x - 1) / (x + 1)
    2
    RV
    -=
    1
    SM11        ; odd denominator
    +=          ; "y" = (x - 1) / (x + 1)
    SM14        ; previous numerator
    SM12        ; series sum
    *
    +=
    SM13        ; y**2
FJ $405
    2           ; bump denominator
    M11
    RM14        ; previous numerator
    *
    RM13        ; y**2
    /
    SM14        ; save numerator
    RM11        ; odd denominator
    +=
    M12         ; add to series sum
    CS
    MJ $405
    RM12
    *
    32          ; cope with those 4 sqrt, above, and the missing 2*
    +=
    SRJ