#
# 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-8: a**x
;    a => m14 (a > 0)
;    x => m13
; Color: green
; Style: blank
; ----------  Card-Pocket-End  ---------------------------------------------
;
SFJ $208
    RM14        ; by moving "a" closer to 1, we increase rate of convergence
    SQRT
    SQRT
    SQRT
    SM14
;
; http://en.wikipedia.org/wiki/Natural_logarithm
;
; ln(x) = ln((1+y)/(1-y))
;       = 2y (1 + (y**2)/3 + (y**4)/5 + (y**6)/7 + (y**8)/9 + ... )
;
; where y = (x - 1) / (x + 1)
;
    1
    SM12
    M14         ; m14 = x + 1
    -=          ; x - 1
    /
    RM14
    +=          ; "y" = (x - 1) / (x + 1)
    SM11        ; series sum
    *
    +=
    SM14        ; y**2
FJ $304
    RV            ; previous term
    *
    RM12
    *
    RM14
    /
    2
    M12
    RV
    RM12
    *
    M11         ; series sum += term
    .1
    +=
    MJ $304
    CS
    MJ $304
    16          ; 2 * 8 (where 8 is to compensite for the three zert, above,
    *           ;        and the 2 is because of series expansion)
    RM11        ; ln(a)
    *
    RM13        ; x  (from a**x, above)
    +=

;
; At this point we start calculating e**x using the Taylor series
;
;     e**x = sigma((x**n)/(n!))
;          = 1 + x + (x**2)/2 + (x**3)/6 + ...
;
; Strangely, this is a slightly different implementation than MS-9
;
    SM14        ; x
    1
    SM12        ; series sum
    SM13        ; previous series term
    CM11        ; factorial denominator
FJ $305
    1
    M11         ; bump factorial denominator
    RM13        ; previous term
    *
    RM14        ; x
    /
    RM11        ; factorial denominator
    +=
    SM13        ; save term
    M12         ; add to series sum
    MJ $305
    CS
    MJ $305
    RM12        ; series sum
    SRJ