(09-25-2021 01:25 AM)robve Wrote: Sharp EL-5100(S): 93 keystrokes
I'll buy the first person who finds this keystroke sequence a beer. If no one found it in 7 days, then I'll report the solution next week anyway.
Just 92 keystrokes is also possible. So I have to restate the challenge slightly: the first person who finds a keystroke sequence of 93 or less gets a beer.
Alas, no submitted solutions.
A solution with 91 keystrokes
saves the value B/2 in M in the AER setup. Instead of typing B/2 in the execution, the RM key suffices to obtain B/2:
AER-switch 1 AER mode
[2ndF][f()=]AB= 5 enter formula LHS
/2[=>M] 3 save B/2 in M
A[x^2]+A-[LN]B,[LN]B[x^2] 11 enter formula RHS
Setup: 20 keystrokes.
Code:
COMP-switch 1 comp mode
COMP 1 activate AER formula
3.12[COMP] 5
2.56[COMP] 5 displays X
[COMP] 1 displays Y
[COMP] 1 A is unchanged
RM[COMP] 2 displays X
[COMP] 1 displays Y
[COMP] 1 A is unchanged
RM[COMP] 2 displays X
[COMP] 1 displays Y
2A[COMP] 3
[COMP] 1 B is unchanged displays X
[COMP] 1 displays Y
2A[COMP] 3
[COMP] 1 B unchanged displays X
[COMP] 1 displays Y
2A[COMP] 3
RM[COMP] 2 displays X
[COMP] 1 displays Y
[COMP] 1 A is unchanged
RM[COMP] 2 displays X
[COMP] 1 displays Y
[COMP] 1 A is unchanged
RM[COMP] 2 displays X
[COMP] 1 displays Y
18.59[COMP] 6
[COMP] 1 B is unchanged, displays X
[COMP] 1 displays Y
17.63[COMP] 6
[COMP] 1 B is unchanged, displays X
[COMP] 1 displays Y
[COMP] 1 A is unchanged
2B[COMP] 3 displays X
[COMP] 1 displays Y
[COMP] 1 A is unchanged
2B[COMP] 3 displays X
[COMP] 1 displays Y
Execution: 71 keystrokes.
Sharp EL-5100(S): 91 keystrokes
The EL-5100(S) was the first calculator to introduce algebraic notation. The expression syntax is internally still handled by the traditional operand and operator stacks combined with an X register to hold the last result. This means that
/2[=>M] is legal, because
/2 takes the last value stored in register X then divides it by 2. In this case X holds the last value entered. Because an internal register X is used to hold the last value and the syntax of infix and postfix operators allows omitting the first operand, a slew of tricks and hacks is possible to reduce the size of AER formulas and, consequently, reduce keystrokes.
There appears to be no requirement to use a comma in an AER formula to chain multiple expressions, despite what the SHARP manual says. The comma produces a value, which is not always desirable. Omitting the comma in a formula simply continues executing the next expression in the AER formula. This is what you would normally expect a simple calculator to do. Perhaps SHARP didn't want to reveal that the implementation of algebraic expression evaluation is a simple "
shunting yard" algorithm to parse expressions.
Below is a list of EL-5100(S) tricks and hacks. Most aren't documented by SHARP or posted elsewhere:
Code:
After STO ⇒M M+ the last value is still usable as an operand for the next
operator. For example:
1;A STO B +1 STO C saves A to B and B+1 to C
When using an infix or postfix operator (+ - × ÷ Yˣ ˣ√ ℙ ℂ STO →POL →REC ² ⁻¹ !
⇒M M+ M- →DEG →DMS) at the start of an expression, this operator uses the last
value calculated as its first operand. For example:
1;f(A)=+1 STO A ×2 STO B takes A then saves A+1 to A and 2A to B
In fact, this method also works without a function, but a value must be
calculated first and displayed before pressing COMP. For example:
1;STO A
Open parenthesis '(' can be omitted when using ')' or '=' in an expression. A
'=' closes all parentheses of an expression. For example:
1;f(A)=2A-1)² computes (2A-1)²
1;f(A)=1+(2×(A-3=² computes (1+(2×(A-3)))²
All parentheses before STO ⇒M M+ , ◣ are automatically closed. For example:
1;f(A)=2×(A-1 STO B takes A then saves 2×(A-1) to B
A comma ',' can be omitted (display value) when the next expression starts with
an operand. For example:
1;A+1 STO A 2B STO B saves A+1 to A and 2B to B
A f()= function can be defined within an AER entry to start of the next
expression. For example:
1;f(A)=²,f(A)=√A takes A, displays A², then takes A
again, displays √A
A f()= function does not require the closing ')', a '=' suffices. For example:
1;f(AB=√(A²+B² computes hypotenuse of A,B
A value specified with COMP for f(A)= can also use some of the same tricks.
For example:
1;2 STO B f(A)=
COMP
1;A=?
enter ×2
1;ANS 1= 4.
Implied multiplication when applied to parentheses like A(1+2) is not possible,
except when applying after the closing ')' for memory or π: For example:
1;1+B)A computes A×(1+B)
Always use (-) for unary minus, otherwise - (minus) takes X as an operand.
Powers Yˣ do not accept negative Y, use ² and repeated multiplications or use
√A²YˣB to compute |A|YˣB.
To compute the absolute value |A|, use √A².
To compute trunc(A) integer part of A, use A+ᴱ10-ᴱ10
To compute round(A) for positive A, use A+.5+ᴱ10-ᴱ10
To compute frac(A), use A-(A+ᴱ10-ᴱ10)
In COMP mode, when the COMP key is mixed with other key presses (except memory
operations), COMP always reverts to 1;. Therefore, put repetitive calculations
preferably in 1;.
Some examples to demonstrate these hacks.
Simpson's rule of integration:
Code:
1;f(ABC)=0 STO I 1 STO J 2 STO H A STO E B-A)÷C STO D◣
2;EEE+2E²-E+2 STO F ×J+I STO I E+D STO E 6-H STO H STO J C-1 STO C◣
3;I-F)D÷3
where:
1; specifies integration range A to B in C parts, where C must be even
2; evaluates one step of the function
3; computes the final result
The function is specified in 2; up to STO F, with E as x.
Press 1; or COMP to specify A, B and C, then press 2; and repeat COMP until the
counter C value displayed is -1. Press 3; to obtain the integral value. To
restart, press 1;. The values of A and B are retained, but C must be specified.
Example to compute the integral of x^3+2x^2-x+2 for x=1..5 in 8 steps:
Press 1; then enter the value 1 for A, 5 for B and 8 for C:
1;A=1 COMP
1;B=5 COMP
1;C=8 COMP
1;ANS 1= 0.5
Press 2; then press COMP until -1 is displayed:
2;ANS 1= 7.
COMP
...
2;ANS 1=-1.
Press 3;
3;ANS 1= 234.6666667
erf() approximation with maximum relative error 0.00013 (note that (-) means unary minus):
Code:
1;f(A)=² STO B √B÷A×√(1-e((-)B×(4÷π+.147B)÷(1+.147B
Note: erf(0)=0 but AER produces an error because √B÷A is used to determine the
sign of A.
GCD(A,B):
Code:
1;A-(A÷B+ᴱ10-ᴱ10)B STO C B STO A C STO B
Press COMP until zero is displayed (or when an error occurred), then A holds
the GCD result. Negative A or B may produce a negative GCD in A. In that case
ignore the sign of A or correct it with √A².
Example:
5040 STO A
411 STO B
COMP
1;ANS 1= 108.
COMP
1;ANS 1= 87.
COMP
1;ANS 1= 21.
COMP
1;ANS 1= 3.
COMP
1;ANS 1= 0.
RCL A
3.
Rational approximation by continued fractions:
Code:
1;E+ᴱ10-ᴱ10 STO D E-D STO E BD+J STO F B STO J F STO B CD+I STO F C STO I F STO C B÷C STO D E⁻¹ STO E A-D◣
2;f(A)=1 STO B STO I 0 STO C STO J A STO E
Press 2; to enter a value
Press 1; to compute the first approximation D=B/C~A, displays the difference A-D
Press COMP to compute the next approximation D=B/C~A, displays the difference A-D
Repeat COMP until the difference (error) is sufficiently small or zero
Result: B is the numerator, C the denominator and D=B/C~A
Example:
Press 2; then enter π
2;A=π
COMP
Press 1;
1;ANS 1= 0.141592654
COMP
1;ANS 1=-0.001264489
RCL B
22.
RCL C
7.
COMP
1;ANS 1= 0.00008322
RCL B
333.
RCL C
106.
COMP
1;ANS 1= 0.00000267
RCL B
355.
RCL C
113.
This gives 355/133 as an approximation of π with 5 digits precision.
Complex arithmetic:
Code:
1;f(BJ)=A+B STO A,I+J STO I◣
2;f(BJ)=A STO HAB-IJ STO A,BI+HJ STO I◣
3;f(BJ)=²+B² STO GA STO HAB+IJ)/G STO A,BI-HJ)/G STO I
where
1; adds B+Ji to A+Ii
2; multiplies A+Ii by B+Ji
3; divides A+Ii by B+Ji
Example:
12.5 STO A re of first argument
(-)7 STO I im of first argument
2ndF-G
2;B=3 re of second argument
2;J=2 im of second argument
2;ANS 1= 51.5 re of the product
2;ANS 2= 4. im of the product
t-test:
Code:
1;f(A)=F÷E-A)÷√((G-E×(F÷E)²)÷(E²-E
STAT mode to enter the data.
COMP mode then COMP to compute the t test statistic for a theoretical mean
value given as A.
Example:
STAT mode
72 DATA
67 DATA
69 DATA
85 DATA
91 DATA
68 DATA
77 DATA
74 DATA
70 DATA
82 DATA
COMP mode
COMP
1;A=70
1;ANS 1= 2.147
Numerical differentiation:
Code:
1;f(A)=√A²+ᴱ‐9)×ᴱ‐4 STO H A+H÷2 STO A 0 STO D◣
2;SIN A=÷H+D STO D A-H STO A (‐)H STO H D
where:
1; specifies the differentiation point
2; evaluates the function, which must be done twice
The function is specified in 2; up to = with A as x.
Press 1; or COMP to specify A then press 2; and COMP to obtain the
differential of the function at point A.
Example to compute derivative of SIN at π/3 which is COS(π/3)=0.5:
Press DRG until RAD annunciator lights up
Press 1; then enter π÷3 for A:
1;A=π÷3 COMP
1;ANS 1= 0
Press 2; then press COMP:
2;ANS 1= 8270.183412
COMP
2;ANS 1= 0.5
Sterling's Gamma approximation:
Code:
1;f(A)=√2π×AYˣ(A-.5)×e(1÷12A-A
These fun concoctions are mine, except the last one, which is based on the Gamma function shown in
http://rskey.org/el5100
Edit: after posting I noticed that the HP forum "machinery" replaced the E exponent symbol U+1D53C with a question mark. Is this a bug? I replaced the double stroke E with the ᴱ symbol. Ugly, but close enough. Also clarified the floor/round tricks, added the f(A= hack and added a complex arithmetic example.
Edit 2: further reduced to 91 keystrokes by replacing
)= requiring two keystrokes [2ndF][f()=] with just one keystroke
= as a shortcut.
- Rob
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