DATAMATH CALCULATOR MUSEUM 
The TI35X and TI36X SOLAR introduced in 1991 an algorithm problem still present in calculators sold in 2013, e.g. the TI30Xa and the TI36X SOLAR. This article explains the bug, its effect on the y^{x }function, lists all affected calculator models and compares the precision of different calculators developed in a timeframe of almost 30 years. Last but not least the article mentiones
the "Logarithm Bug  Reloaded". The Bug
Essentially, the TI35X calculates inaccurate values for ln(1 + x) where
x is a small number,
The y^{x} FunctionA strange side effect of the logarithm bug is the
related y^{x} function, most calculators use the rule Example: 5^{3}: e^{(3 * ln(5))} = 125
The best way to demonstrate the logarithm bug could be found with the exponential function, one of the most important functions in mathematics. It is written as e^{x} and can be defined as a limit of a sequence:

The following table compares the results of the above expression for some values of n using four different calculators (rounded to 8 digits, RED numbers indicate wrong results):
n  SR51 (1975) 
TI35 PLUS (1986) 
TI30X (1994) 
TI36X SOLAR (2004) 
10  2.5937425  2.5937425  2.5937425  2.5937425 
100  2.7048138  2.7048138  2.7048138  2.7048138 
1,000  2.7169239  2.7169239  2.7169239  2.7169239 
10,000  2.7181459  2.7181459  2.7181459  2.7181459 
100,000  2.7182682  2.7182682  2.7182683  2.7182683 
1,000,000  2.7182805  2.7182805  2.7182814  2.7182814 
10,000,000  2.7182818  2.7182817  2.7182888  2.7182888 
100,000,000  2.7182818  2.7182818  2.7183727  2.7183727 
1,000,000,000  2.7182818  2.7182818  2.7191928  2.7191928 
The Logarithm Bug is present in all calculators based on the algorithm of the Toshiba T6A57 (TI36X Solar) , T6A58 (TI35X), T6A61 (TI30X), T6M38 (TI30X Solar), T6M79 (TI30Xa Solar, TI30Xa SE) and T6M80 (TI30Xa).
These calculators could identified by a result of 9.00000229461 running Mike Sebastian's "Calculator forensics". A typical feature of the affected calculators is a 10digit display and 12digit precision of the internal calculations.
During the research of the calculating precision realized in different calculators we noticed some strange results:
n  TI25 (1978) 
TI66 (1983) 
BASOLAR (1986) 
TI65 (1987) 
TI34,
SC10 (1987..1989) 
10  2.59374__  2.5937425  2.5937425  2.5937425  2.5937425 
100  2.70481__  2.7048138  2.7048138  2.7048138  2.7048138 
1,000  2.71692__  2.7169239  2.7169239  2.7169239  2.7169239 
10,000  2.71815__  2.7181459  2.7181459  2.7181459  2.7181459 
100,000  2.71827__  2.7182682  2.7182682  2.7182682  2.7182682 
1,000,000  2.71828__  2.7182805  2.7182818  2.7182818  2.7182805 
10,000,000  2.71828__  2.7182817  2.7182818  2.7182818  2.7182817 
100,000,000  2.71828__  2.7182818  2.7182818  2.7182818  2.7182818 
1,000,000,000  1.0000000  2.7182818  2.7182818  2.7182818  2.7182818 
n  TI68 (1989) 
Math Explorer (1991) 
BAII Plus (1991) 
TI40 Solar (1995) 
TI15, TI30X IIB ( 1999) 
10  2.5937425  2.5937425  2.5937425  2.5937425  2.5937425 
100  2.7048138  2.7048138  2.7048138  2.7048138  2.7048138 
1,000  2.7169239  2.7169238  2.7169239  2.7169239  2.7169239 
10,000  2.7181459  2.7181459  2.7181459  2.7181459  2.7181459 
100,000  2.7182682  2.7182546  2.7182682  2.7182682  2.7182682 
1,000,000  2.7182805  2.7182818  2.7182805  2.7182806  2.7182805 
10,000,000  2.7182817  Error U  2.7182817  2.7182801  2.7182817 
100,000,000  2.7182813  2.7182818  2.7182913  2.7182818  
1,000,000,000  2.7182788  2.7182818  2.7183790  2.7182818 
Texas Instruments stopped in 2000 the production of the new twoline calculators TI30X IIB, TI30X IIS, TI34 II, and TI40 Collège II and announced a replacement offer running through January 31, 2001. What happened?
Customers reported the calculators with production date codes earlier than N1299 or C1299 returned incorrect answers on specific, multidecimalplace values in combination with specific functions. The chance of this situation occuring in an individual's average use is remote but engineers of Texas Instruments fixed the software bug.
Please find the original announcement retrieved from the Texas Instruments calculator website:
This replacement offer is good through January 31, 2001.
We listen to our customers, especially when you tell us things you don't
like.
We've been pleased to hear that you like our new, twoline calculators, and we're proud of the benefits they provide. But we were extremely
surprised and concerned when we heard that when specific, multidecimalplace values are used in combination with specific
functions in our TI30X IIS, TI30X IIB, TI34 II, and our TI40 College
II, an incorrect answer is returned.
We halted production of these products and fixed the software. As we
did so, our engineers concluded that the chance of this situation occurring in an individual's average use is remote, given the specific
functions and combinations needed. (These are detailed below.)
However, these errors are not consistent with our efforts to provide you
with the best possible educational products for your needs.
New, revised product is now shipping to stores. If, however, you have
affected product*, and you're concerned about its performance, please contact us at the phone numbers or email address listed below and we
will replace your product.
* In order to confirm that the above issue impacts your calculator, please check the date code, which is stamped into the plastic, or on a
small, plastic label, on the back of your calculator. Date codes begin with either an "N" or a "C", and then four numbers follow. Only
calculators with date codes earlier than 1299 are affected, for example N0699 or C0899.
[Telephone numbers and email addess omitted.]
For the TI34 II and the TI40 College II, the following functions and ranges will give incorrect results for products with date codes earlier than 1299. The result for the range limits shown will be correct and the values between these limits will be incorrect.
Also Y^{X} if Y is inside the range shwn and X is any value other than
an integer in the range {0,9}.
Also X ROOT Y if Y is inside the range shown and X is not equal to one or negative one.
Also CUBE ROOT X if X is inside the range shown.
Entry Value between 1.221402765935 and 1.222222222223
Entry Value between 1.020201346154 and 1.020202020203
Entry Value between 1.002002001340 and 1.002002002003
Entry Value between 1.000200020001 and 1.000200020003
Entry Value between 0.9801980198019 and 0.9801986674200
Entry Value between 0.9980019980019 and 0.9980019986620
For the TI30X IIS and the TI30X IIB, the following functions and ranges will give incorrect results for products with date codes earlier than 1299. The results for the range limits shown will be correct and the values between these limits will be incorrect.
Also Y^{X} if Y is inside the range shwn and X is any value other than
an integer in the range {0,9}.
Also X ROOT Y if Y is inside the range shown and X is not equal to one or negative one.
Also CUBE ROOT X if X is inside the range shown.
Entry Value between 1.221402765935 and 1.222222222223
Entry Value between 1.020201346154 and 1.020202020203
Entry Value between 1.002002001340 and 1.002002002003
Entry Value between 1.000200020001 and 1.000200020003
Entry Value between 0.9801980198019 and 0.9801986674200
Entry Value between 0.9980019980019 and 0.9980019986620
Also gives incorrect results for the negatives of the values below:
Entry Value between 9.966799777635 e02 and 1.0 e01
Entry Value between 9.999669682703 e03 and 1.0 e02
Entry Value between 9.999996696697 e04 and 1.0 e03
Entry Value between 9.999999966966 e05 and 1.0 e04
Entry Value between 9.999999999669 e06 and 1.0 e05
Entry Value between 9.999999999996 e07 and 1.0 e06
Entry Value between 1.005004168374 and 1.005037815260
Entry Value between 1.000050000446 and 1.000050003751
Also gives incorrect results for the negatives of the values listed below:
Entry Value between 1.001667532187 e01 and 1.005037815259 e01
Entry Value between 1.000016967064 e02 and 1.000050003750 e02
Entry Value between 1.000000169669 e03 and 1.000000500000 e0
Entry Value between 1.000000001696 e04 and 1.000000005000 e04
Entry Value between 1.000000000016 e05 and 1.000000000050 e05
(c) Copyright 2000 Texas Instruments Incorporated. All rights reserved.
If you have additions to the above article please email: joerg@datamath.org.
© Bob Senzer, Mike Sebastian and Joerg Woerner, July 12, 2004 and October 11, 2005. No reprints without written permission.