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```#On the name of ALLAH and may the blessing and peace of Allah
#be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam.
#Date : 10/07/10
#version :2.6

"""
maclaurin_ln is a function to compute ln(x) using maclaurin series
and the interval of convergence is -1 < x < +1
ln(y) = ln(1+x/1-x)= 2(x + x^3/3 + x^5/5 + x^7/7 ...........)
"""

def maclaurin_ln(value, k):
"""
Compute maclaurin's series approximation for ln(value).
"""

global first_value
first_value = 0.0

#attempt to Approximate ln(x) for a given value
try:
value_x = (value - 1)/float(value + 1)
for item in xrange(1,k,2):
next_value = value_x **item/item
first_value += next_value

return 2*(first_value)

#Raise TypeError if input is not a number
except TypeError:
print 'Please enter an integer or a float value'

if __name__ == "__main__":

maclaurin_ln_1 = maclaurin_ln(2,100)
print maclaurin_ln_1
maclaurin_ln_2 = maclaurin_ln(5,100)
print maclaurin_ln_2
maclaurin_ln_3 = maclaurin_ln(777,10000)
print maclaurin_ln_3
print
for arg in xrange(7,28,10):
print "ln(%s) = %s " %\
(arg, maclaurin_ln(arg,10000))
###########################################################################

#"C: python \Maclaurin_ln
#0.69314718056
#1.60943791243
#6.65544035037

#ln(7) = 1.94591014906
#ln(17) = 2.83321334406
#ln(27) = 3.295836866
######################################################################################

#On the name of ALLAH and may the blessing and peace of Allah
#be upon the Messenger of Allah Mohamed Salla Allahu Aliahi Wassalam.

# ln(x) decimal version

from decimal import Decimal as D,Context, localcontext
def maclaurin_ln(value, k):
"""
Compute maclaurin's series approximation for ln(value).
"""

first_value = 0

#attempt to Approximate ln(x) for a given value
try:
value_x = (value - D("1.0"))/(value + D("1.0"))
for item in xrange(1,k,2):
next_value = value_x**item/item
first_value += next_value

return 2*(first_value)

#Raise TypeError if input is not a number
except TypeError:
print 'Please enter an integer or a float value'

if __name__ == "__main__":
with localcontext(Context(prec=67)):
for arg in xrange(7,28,10):
print "ln(%s) = %s " %\
(arg, maclaurin_ln(arg,D("10000")))

#######################################################################

FT  "C:\Maclaurin_lndecimal1.py"
ln(7) = 1.945910149055313305105352743443179729637084729581861188459390149937
ln(17) = 2.833213344056216080249534617873126535588203012585744787297237737878
ln(27) = 3.295836866004329074185735710767577113942471673468248355204083000896
```

Diff to Previous Revision

```--- revision 4 2010-07-15 10:50:46
+++ revision 5 2010-07-15 10:59:15
@@ -46,14 +46,14 @@
(arg, maclaurin_ln(arg,10000))
###########################################################################

-"C: python \Maclaurin_ln
-0.69314718056
-1.60943791243
-6.65544035037
+#"C: python \Maclaurin_ln
+#0.69314718056
+#1.60943791243
+#6.65544035037

-ln(7) = 1.94591014906
-ln(17) = 2.83321334406
-ln(27) = 3.295836866
+#ln(7) = 1.94591014906
+#ln(17) = 2.83321334406
+#ln(27) = 3.295836866
######################################################################################

```