A foreword: calculators nowadays may be sold in three main modes: algebraic (as classic '80 calculators), equation (modern calculators) and RPN (some HP model), and often they can be used in multiple ways. For calculators that are both RPN and 'something else', they have been treated as if they were RPN tout-court. This is the usage I prefer. If you want to conduct the test for the same calculators in a different mode, you're welcome.
THE TEST
This test does not aim to criticize this or that
calculator, this or that brand. It only wants to show the
potential incoherence some calculators bring. What we learned at
school is the best way we can use to tell if a calculator is
fit for us or if we must fit the calculator itself.
Since I love calculators like sons, I tend to be severe like a parent,
and like a parent I know how to judge them.
Thanks to professor
Thimbleby, who opened my eyes.
***
The
score for each calculator is the sum of all the scores for each
applicable section divided by the maximum reachable score.
Thus, the
best score is 1.00 (total coherence), while the worst score
is 0.00 (no coherence at all). Each
section score is a value in the range 0÷3, where 3 means the
best and 0 the
worst behavior. Should a test yield a
value less than zero,
the score will be set to zero.
This test is composed by the following sections (the number in brackets
refers to the exercises proposed here):
1. The explicit
negative operand (2 sections) [2]
The calculator must be able to perform the following:
1.1
4 x -5 = -20
1.2
-4 x 5 = -20 The "minus" sign should operate as in normal mathematical
language and as common sense requires. The
use of [(-)] in place of the minus sign or [+/-] or [CHS] is permitted
if any
previous format fails, but the score will be deducted by 1,
and will be set to zero if this section
fails.
Note: The use of the
"change sign" key for RPN calculators is admitted with no score
deduction, because of its proper usage.
2. Consign a result
to memory [4]
The calculator must be able to store a result in memory with
one
store
key, eventually followed by a character (or more), identifying
a
cell or a register. The score is calculated this way:
3 points for one typed key + 1 register
(among many
available, e.g. STO 6; the same score if two or more keys are
needed for register identification, e.g. STO 13)
3 points for one typed key if
there's only one available register (e.g. x->M)
2 points if two typed keys are required
for the store key (that is, STO it's behind a shift key)
0 point if there's only an M+ key (the
operation is
possible, but only with 5 typed keys, as demonstrated by prof.
Thimbleby) or if there's no store key at all.
It's considered
bad design the impossibility to consign a calculated result to memory
without a simple storing.
3. (For
calculators with the % key) Percentage calculation (2
sections) [3]
The algebraic calculator must be able to perform the
following:
3.1
50
+ 5% = 52.5
3.2
50
- 5% = 47.5
This should be performed in a rigorous, friendly way
(friendly way means, for algebraic calculators, 50 + 5 % =, that is as
in normal speech). It's
considered bad design any operation that differs from the friendly way,
or that requires a multiplication to reach, unnaturally, the same
result; score will be set to zero for any non-conforming machine.
RPN machines
follow their own input mode, and the result should be performed as:
3.1
50
ENTER 5 % +
3.2
50
ENTER 5 % -
The calculator must be able to perform the following:
4 + 5 x 6 = 34
(and NOT 54)
The absence of precedence rules is considered a very bad
feature in
an algebraic
scientific calculator; in this case, score will be set to zero.
RPN machines won't be considered for this
section, as well as any non-scientific basic calculator.
5. Easy calculation
of combinations/permutations into
operations
The calculator must be able to perform the following:
5 100 - ( ) = 90 2
The whole operation should be performed, more or less, in this way:
100 - 5 nCr 2
or in
whatever disguise the nCr
operation is performed. Any more key will cost one point. A wrong
result will cause score to be set to zero.
Note: RPN
calculators should
perform the same task as: 100 ENTER 5
ENTER 2 nCr -
6.
Special calculation of 2^-π [5]
It should be executed as near as possible to the sequence 2 ^ - π
The result should be 0.113314732297...
or a proper approximation. The
use of [(-)] or the "change sign" keys
[+/-] or [CHS] in place of the minus sign is permitted
if any
previous function format fails, but score will be deducted by
one; it will be set to zero if this calculation fails even
with the
"change sign" keys.
Note: the use of the
"change sign" keys for RPN calculators is admitted with no score
deduction due to their proper input mode.
7. Rounding errors [10]
The calculator must be able to perform the following: 1
/ 6 should yield 1.666...67 (notice the ending 7, which is a correct rounding). The
absence of a correct rounding is considered a very bad
feature, potentially error prone, and will cause score to be set to
zero.
8. (For
complex-mode-enabled machines) Special calculation of ii
It should yield the real number 0.207879576351...
or a proper approximation. The lacking of such result or the
impossibility to practically reach this calculation is considered a bad
design, and will cause score to be set to zero.
9. (For
complex-mode-enabled machines) Special calculation
of square root of -1[6]
It should of course yield i
(see section 10).
This result is considered a "must" for complex-mode-enable machines.
The lacking of such result or the impossibility to practically reach
this calculation is considered a bad design, and will cause
score to be set to zero.
10. (For
complex-mode-enabled machines) Special calculation of i2
It should of course yield the real number -1 (see section 9).
This result is considered a "must" for complex-mode-enable machines.
The lacking of such result or the impossibility to practically reach
this calculation is considered a bad design, and will cause
score to be set to zero. The use of i
x i
is not admitted, because it's considered a trivial workout.
11. (For mode-enabled
machines) Modes interaction
This section evidences that sometimes calculators are
built with modes that are not mutually interactive, that is while
operating in mode A, functions of mode B are not available
or
not reachable. Such behavior is considered bad design; one
point
will be deducted for each non-interactive mode.
This section tends to underline the fact that sometimes calculators are
built
with modes that consume some register while operating in a different
mode than normal computation; this may cause the accidental and
unaware loss of data by users that do not know about this feature or
press inadvertently the wrong key. Such behavior is considered
bad
design; one point will be deducted for each register-consuming mode.
13. (For
scientific machines) Function Names on keys
Function names as learned at school often differ from what is depicted
on calculators (e.g. arc
sin is often written as sin-1),
or sometimes the chosen names are not clearly understood without a manual.
Such behavior is considered bad design; one point will be
deducted
for each of the following non-conforming classes:
A) trigonometric functions (sin-1, cos-1, tan-1) B) hyperbolic functions (hyp-1 key) C) RND and RAN adjacent keys (they mean Round and Random,
but they may be easily confused).
Note: in USA people often write arcsin as sin-1,
but I guess this is a bad behavior even if this is widely accepted.
Note: I (and maybe
some of you) have been taught to call logarithms this way: the natural
logarithm as log the decimal
logarithm as log10 This is not a general
rule. In many other countries they are called respectively ln and log.
This second habit reflects on most calculators (quite all,
effectively). So I cannot consider this as a non-conforming class.
14. (For
scientific machines) Precision of trigonometric function
The calculator is able to perform TAN 89.999
Claimed scientific models cannot be erratic. Errors in calculating
simple trigonometric functions, even in tough conditions, are not
acceptable. This section has been added after a post in the MoHPC site
(see References),
where the TAN(89.999) question arose. The correct answer in
DEG mode should be 57295.7795073,
or a proper approximation. A point will be deduced for any pair of
wrong decimals, and 0 will be scored if the error propagates to the
integer part.
***
THE RESULTS
If a cell is marked N/A, the calculator is not be able to perform the
relative test section.
Calculator
Coherence
1
neg.op.
2
STO
3
perc.
4
preced.
5
comb.
6
2 ^ -pi
7
round.
8
i ^ i
9
sqrt(i)
10
i ^ 2
11
modes
12
reg.
13
names
14
precis.
Canon
Palmtronic LE-84
Canon
P35-D
Casio
AS-8D
Casio
fx-10F
Casio
fx-100
Casio
fx-180P
0.667
22
2
0
3
N/A
2
0
N/A
N/A
N/A
3
3
2
3
Casio
fx-350MS
Casio
fx-500US
Casio
fx-570MW
Casio
fx-3600Pv
Casio
fx-3900Pv
Casio
fx-4100P
Casio
fx-4800P
Casio
fx-5000F
Casio
fx-7700GB
Casio
fx-8500G
Casio
fx-P401
Casio
HR-8L
Casio
PB-220
Casio
PB-80
Citizen
CBL-200
Hermes
5700
HP-9G
HP-9S
HP-11C
0.926
3
3
3
N/A
3
3
3
N/A
N/A
N/A
N/A
26
2
3
HP-12C/12CP/12C
25th (financial)
1.00
3
3
3
N/A
N/A
N/A
3
N/A
N/A
N/A
N/A
N/A
N/A
N/A
HP-15C
HP-17BII
(financial)
HP-17BII+
(financial)
HP-20S
HP-32S
0.923
3
3
3
N/A
3
3
3
3
23
23
3
24
3
3
HP-32SII
0.923
3
3
3
N/A
3
3
3
3
23
23
3
24
3
3
HP-33S
HP-35S
0.846
3
2
3
N/A
3
3
3
3
29
29
3
210
3
1
HP-38G
HP-40G
HP-49G
HP-49g+/HP-50g
0.972
3
3
3
N/A
21
3
3
3
3
3
N/A
3
3
3
Karce
KC-S3500
Lexibook
SC200
Lexibook
SC300
Lexibook
SC300 (evolution)
Sharp
EL-508A
Sharp
EL-509W
Sharp
EL-510
Sharp
EL-512
0.815
22
2
3
2
3
25
3
2
3
Sharp
EL-545
Sharp
EL-5250
Sharp
PC-1401
0.722
27
3
0
3
N/A
2.58
0
N/A
N/A
N/A
N/A
3
3
3
Sharp
PC-1500
Sharp
PC-E500
TI-30
Galaxy
Welco
1220PD
1. The HP-49g+ has a rather cumbersome way to
find the right COMB command, so one point is deducted
2. The Casio fx-180P
and the Sharp EL-512 return a correct result for the second formula; so
the score is not the lowest one
3. The HP-32S and HP-32SII execute the operation through the y^x key,
which is cumbersome; the score is deducted by one
4. The HP-32S and HP-32SII consume memory for integration, so the score
is deducted by one
5. The Sharp EL-512 has a STAT mode that excludes programs to be
executed, but enables all the other functions.
6. The HP-11C consumes registers for statistics, so the score is
deducted by one
7. The Sharp PC-1401 returns the wrong answer in algebraic mode, but
the right one in BASIC mode, so the score is deducted by 1 only
8. The Sharp PC-1401 uses the +/- keys in algebraic mode, but returns
the correct answer in BASIC mode.
9. The HP-35S calculates i^2 and square root of -1 (written as -1i0) through the y^x key; the score is deducted by one.
10. The HP-35S consumes registers for statistics and integration, so the score is
deducted by two.
Coherence results ordered by highest score:
Calculator
Coherence
THE REFERENCES
H. Thimbleby wrote these essays, which I find delightful and
very coherent:
He and his ingenious son also conceived some
other tests for your own calculator.
You can find the MoHPC post about the TAN(89.999) problem (original
referred to the HP-33S) here. Back to Main page