#
# 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-10: log10(x)
; Color: green
; Style: blank
; ----------  Card-Pocket-End  ---------------------------------------------
;
SFJ $210
    SQRT        ; The series converges faster when x is closer to 1.
    SQRT
    SQRT
    SQRT
;
; 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 + ... )
;       =  2 (y + (y**3)/3 + (y**5)/5 + (y**7)/7 + (y**9)/9 + ... )
;
; where y = (x - 1) / (x + 1)
;
; M14 => odd denominator
; M13 => previous numerator
; M12 => series sum
; M11 => y**2
;
    SM13        ; x (temporarily)
    1
    SM14
    M13         ; m13 = x + 1
    -=          ; x - 1
    /
    RM13        ; x + 1
    +=          ; "y" = (x - 1) / (x + 1)
    SM13        ; first term numerator
    SM12        ; series sum
    *
    +=
    SM11        ; y**2
FJ $307
    2
    M14         ; bump denominator
    RM13        ; previous numerator
    *
    RM11        ; y**2
    /
    SM13        ; save numerator
    RM14
    +=
    M12         ; add to series sum
    MJ $307
    CS
    MJ $307
    RM12        ; correct for the sqrts above, and the missing 2*
    *           ; and also convert from ln(x) to log10(x)
    13.8974234209045 ; = 32/ln(10)
    +=
    SRJ