HP 15C User manual

HP-15C
HP-15C Quick Reference
 A. Thimet
Memory & Display
Memory Approx. 462 bytes of memory corresponding to 66 registers 7 bytes each
4-level stack Last-X index register I.
Nonvolatile memory mostly merged program commands (1 byte per
instruction)
Pr Error Displayed when the contents of the nonvolatile (continuous memory) has
been lost
Number
separator
Turn off press & hold ON press "." release ON release "."
This toggles between using a dot or comma for the decimal separator.
Global
reset
Turn off press & hold ON press "-" release ON release "-"
This clears all permanent memory!
MEM Displays memory assignment in the form "RR UU pp – n" with:
RR: Number of highest storage register. At least 1 which means that R0 R1
and the index register I are always present. Register 0-19 correspond to
0-9 & .0-.9 and can be accessed directly by STO/RCL. Higher registers
can be reached thru indirect addressing only.
UU: Number of uncommitted registers. Use DIM to commit them to storage
registers. Uncommitted registers are automatically converted to
program space when needed.
pp: Number of registers containing program instructions. One register
consists of 7 bytes and can hold 7 program steps (except for a few
instructions that occupy two bytes).
n: Number of bytes left before next uncommitted register is converted to
program space.
In total there are 66 registers corresponding to 462 bytes.
The initial setup is "19 46 0-0": 20 storage registers (0-19) 46 uncommitted
registers corresponding to approx. 322 program steps.
DIM (i) Use this command to select the number of registers committed to storage.
The argument must be passed in X. It specifies the highest storage register
number.
Registers containing program instructions cannot be converted to storage
registers!
X must be at least 1 so there will always be R0 and R1 available.
The maximum is 65
FIX 0-9 Select fix-point format
SCI 0-9 Select scientific format with exponent
ENG 0-9 Select engineering format with exponent always being a multiple of 3
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HP-15C
Clearing Data
←RUN mode: Deletes either the last digit during number entry or the
entire X-register in case number entry has been
terminated.
PRGM mode: Delete the currently displayed program step
CLEAR ∑Clear stack and summation registers 0-5
CLEAR PRGM RUN mode: Set program counter to 000
PRGM mode: Erase entire program memory
CLEAR REG Clear all storage registers
CLEAR PREFIX Clear prefix key and briefly display all 10 digits of the mantissa
CL X RUN mode: Clear X-register
PRGM mode: Store the CLX command as a program command
Storage Registers & In irect A ressing
STO 0-9 .0-.9 Store X in the specified storage register.
By default 20 registers are available
STO + 0-9 .0-.9
STO – 0-9 .0-.9
STO x 0-9 .0-.9
STO ÷ 0-9 .0-.9
Register store arithmetic: Register OP X → Register.
RCL 0-9 .0-.9 Recall number from storage register to X-register
RCL + 0-9 .0-.9
RCL – 0-9 .0-.9
RCL x 0-9 .0-.9
RCL ÷ 0-9 .0-.9
Register recall arithmetic: X OP Register → X.
X↔ 0-9 .0-.9 Exchange X with one of the storage registers
STO I Store X in index register
STO +–x÷ I Register store arithmetic with index reister
RCL I Recall value from index register
RCL +–x÷ I Register recall arithmetic with index reister
X↔ I Exchange X with index register
STO (i) Store X in the register pointed to by I.
Values of I and corresponding registers:
0-9 → R0-R9, 10-19 → R.0-R.9, 10 → I
STO +–x÷ (i) Perform indirect register storage arithmetic
RCL (i) Recall value from the register pointed to by I
X↔ (i) Exchange X with the register pointed to by I
FIX I SCI I ENG I Use the index register to specify the number of digits
RCL ∑+ Recall ∑x and ∑y from the summation registers into X & Y
LST X Recall last value of X-register as it was before the previous operation
STO A-E Used to enter elements in matrices see Matrix Operations
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HP-15C
Functions (Selection)
RAN# Create random number 0 ≤ X < 1
STO f RAN# Store X as the new random number seed
→ P Convert (X=x Y=x) from orthogonal to polar coordinates (X=r Y=θ)
See label on the back of the calculator
→ R Convert (X=r Y=θ) from polar to orthogonal coordinates (X=x Y=x)
→ H.MS Convert fractional hours to hours minutes & seconds: H.MMSSs
→ H Convert hours minutes & seconds H.MMSSs to fractional hours
→ RAD Convert degress (360) to radians (2π)
→ DEG Convert radians (2π) to degress (360)
Py x Permutations = Y! / (Y-X)!
Number of possibilities to select X elements from a group of Y different
elements where different sequences count separately.
Cy x Combinations = Y! / [X! • (Y-X)!]
Number of possibilities to select X elements from a group of Y different
elements where different sequences do not count separately.
x! Faculty and Gamma. Calculates Γ(x+1)=n! for positive and non-integer
negative numbers
RND Rounds X to the number of currently displayed digits
FRAC Returns the fractional part of X
INT Returns the integer part of X
yxY to the power of X. Works also for negative Y in case X is integer
% Calculates X percent of Y. Does not pop the stack!
∆%Percential difference from Y to X. Does not pop the stack!
Trigonometric Functions
DEG Set trig mode "degrees" (360)
RAD Set trig mode "radians" (2π) indicated in display
GRD Set trig mode "grad" (400) indicated in display
SIN COS TAN Trigonometric functions performed in current
mode (DEG RAD GRD)
SIN-1 COS-1 TAN-1 Inverse trig functions
HYP SIN HYP COS HYP TAN Hyperbolic functions (independent of trig mode!)
HYP-1 SIN HYP-1 COS HYP-1 TAN Inverse hyperbolic functions
Summation & Statistics
General The statistics registers occupy the storage registers 2-7 see calculator's
back label. See section Clearing Data for statistics register deletion.
Stats registers can also be used for vector addition and substraction!
Register usage: 2=n 3=∑x 4=∑x2 5=∑y 6=∑y2 7=∑xy
∑+
STO ∑+
Add X and Y to the stats registers.
This will display the total number of entries and disable stack lift so that
the next entry will overwrite the count.
∑-Substract X and Y from the stats registers
RCL ∑+ Recall ∑x and ∑y from the summation registers into X & Y
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HP-15C
x Calculate ∑x & ∑y mean value and place result in X & Y.
Requires n>0
s Calculate ∑x & ∑y standard deviation and place result in X & Y.
sx = SQRT[ {n∑x2 – (∑x) 2} / {n(n-1)} ] accordingly for sy.
Requires n>1
L.R. Linear regression. Calculates a straight line thru the (X Y) data points and
returns the slope of the line in Y and the y-offset in X.
Requires n>1
y r This function assumes a straight line thru the (X Y) data points and
calculates for a given X the approximatedy value which is returned in X.
In Y this function returns an estimate how close the data points come to a
straight line. +1 indicates that all points lie on a line with positive slope -1
indicates that all points lie on a line with negative slope 0 indicates that an
approximation by a straight line isn't possible.
Requires n>1
Programming
P/R Toggles between RUN (program execution) and PRGM (program
entry) mode. See section Clearing Data for program memory and
program step deletion.
SST RUN: Display and execute next program step
PRGM: Step forward thru program scolls when held down
BST RUN: Display and go back to previous program step but do not
execute any program code
PRGM: Step backwards thru program scolls when held down
Inserting steps Program entry starts with line number 1.
Line "000-" indicates the start of the program space.
Commands are inserted after the currently displayed line.
Program code values indicate the row & column of a command with
the exception that numbers are displayed as such. Prefix keys have
their own code. Example:
001-42.21. 0 corresponds to "LBL 1" (42=f 21=SST/LBL 0=0)
f A-E RUN: Execute program starting at the given label. An error occurs
if the label is not found. Any keypress will halt the program!
PRGM: Insert a "GSB label" command
USER Normally "f A-E" must be pressed to execute a program see above.
In USER mode the prefix-f is not needed ie. pressing ex will
immediately execute the program starting at label B.
Use the prefix-f to reach the key's normal function.
USER mode is indicated in the display
R/S RUN: Continue program at current program counter
PRGM: Insert R/S command which will halt the program at this
location
RTN RUN: Set program counter to 000
PRGM: Insert a RTN instruction. This will return from a subroutine
or at the top level end the program and set the program
counter to 000
GTO CHS nnn RUN & PRGM mode: Jump to program line nnn
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HP-15C
LBL 0-9 .0-.9 A-E Insert label
GT0 0-9 .0-.9 A-E RUN: Set program counter to the specified label
PRGM: Insert a GTO instruction
GSB 0-9 .0-.9 A-E RUN: Execute the program starting at the given label
PRGM: Insert a GSB instruction. A maximum of seven subroutine
calls can be nested
Flags There are 10 flags 0-7 are user flags. Flag 8 & 9:
8: Complex flag. Automatically set when complex mode is activated.
To deactivate complex mode explicitly clear this flag. Indicated by
"C" in the display. See section Complex Numbers
9: Overflow flag. Automatically set by an overflow condition (result
≥1E100). Causes the display to blink. If the overflow occurs
during program execution the program continues using a value of
9.99...E99 and the display blinks when the program finally stops.
Cleared by CF9 or pressing "←". Can be used to provide
program-controlled visual feedback.
SF n: Set flag n CF n: Clear flag n
F? n: Execute next step if flag is set skip next step if flag is clear
TEST comparisns Only two comparisn are directly available on the keyboard:
X≤Y and X=0
Others must be entered using the TEST n command:
0: X≠0 1: X>0 2: X<0 3: X≥0 4: X≤0
5: X=Y 6: X≠Y 7: X>Y 8: X<Y 9: X≥Y
If camparisn is false: Skip the next program step
If camparisn is true : Execute the next program step
ISG 0-9 .0-.9 I Increment and skip if greater.
This loop command uses the specified register which must contain a
value in the form nnnnn.xxxyy where:
±nnnnn: Current (initial) loop counter value
xxx: Comparisn value for loop counter
yy: Loop counter increment (or decrement for DSE) if y=0
then 1 is used instead
ISG first increments n by y and then compares the new n to x:
If n>x the next program step is skipped
If n≤x the next program step is executed
Ie. if initially I=0.023 then the loop will run from 0 to 22 (or 1 to 23)
DSE 0-9 .0-.9 I Decrement and skip if equal (or smaller).
DSE first decrements n by y and then compares the new n to x:
If n≤x the next program step is skipped
If n>x the next program step is executed
GTO I Jump to the label indicated by the I register. Only the integer part of
I will be used! Values of I and associated labels:
I≥0: 0...9 → LBL 0...LBL 9 10...14 → LBL A...LBL E
I<0: Jump to the line number indicated by the absolute value of I.
Ie. if I=–5.3 the jump will go to line number 5.
GSB I Perform subroutine call to the label indicated by the I register
PSE Halt program for about 1 second and display the X-register
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HP-15C
Complex Numbers
Memory In complex mode a complex stack including Last-X register exists.
The needed five registers are allocated from the uncommitted
memory space see MEM.
f I -or-
Re↔Im
Automatically turns on the complex mode. Indicated by "C" in the
display. To turn off complex mode clear flag 8 (CF8).
NOTE: If stack lift is enabled and a number is keyed in a stack lift
occurs and the imaginary part is set to 0!
Real number If stack lift is enabled: Enter real part
Imaginary
number
If stack lift is enabled: Enter real part press Re↔Im
f I Complex number input: <real part> ENTER <imaginary part> f I
f (i) Display imaginary part of number while (i) is held down
Re↔Im Exchange real and imaginary part
CHS Changes sign of real part only! Use Re↔Im to negate the imaginary
part as well
CLx or ←Clears only the real part. However this disables stack lift for both the
real and imaginary stack so the entry of a complex number after "←"
will do the expected thing
STO & RCL STO & RCL only act on the real part of the number!
Store: STO 1 Re↔Im STO 2 Re↔Im
Recall: RCL 2 RCL 1 f I -or-
RCL 2 Re↔Im ← RCL 1 (this does not disturb the stack)
x↔yReplace both real and imaginary part of X and Y register
R↓ R↑Shift both the real and imaginary part
Sqrt x² Ln Log
1/x ex
hyp sin cos tan
hyp-1 sin cos tan
All these unary functions work in complex mode as well.
NOTE: To calculate sqrt(-1) the complex mode must be already
enabled or otherwise an error occurs!
ABS Calculates magnitude of complex number
+ - x ÷ yxAll these binary functions work in complex mode as well
sin cos tan
sin-1 cos-1 tan-1
Trigonometric functions are only executed in radians (2π)
→ P Convert from rectangular coordinates (real=X imaginary=Y) to polar
coordinates (real=R imaginary=θ).
This operation is affected by the current trigonometric setting
(DEG RAD GRD)
→ R Convert from polar coordinates (real=R imaginary=θ) to rectangular
coordinates (real=X imaginary=Y).
This operation is affected by the current trigonometric setting
(DEG RAD GRD)
Conditional tests These tests work for complex numbers and operate on both the real
and imaginary part: x=y TEST 0 (X≠0) TEST 5 (X=Y) TEST 6 (X≠Y)
All other tests ignore the imaginary part of the complex number
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HP-15C
Matrix Operations
Memory A total of 64 matrix elements can be used in a total of 5 matrices
named A-E. Different matrices can have different size; sometimes
the result of a matrix operation can overwrite the input matrix.
The registers for the matrix elements are allocated from the
uncommitted registers space see MEM.
See further down for complex matrices.
MATRIX 0 Redimensions all matrices to 0x0 thus freeing up all memory
occupied by matrices
Matrix descriptors The stack registers Last-X and index register I as well as ordinary
storage registers can contain " matrix descriptors " which refer to one
of the matrices A-E. Ie. if there are two matrix descriptors in X and
Y then pressing "+" will add them and put the result in the result
matrix. Matrix descriptors can be moved around in the stack and
to/from storage registers like ordinary numbers
DIM A-E Dimensions one of the matrices A-E. It will have as many rows as
specified in Y and as many columns as specified in X.
Whan an existing matrix is redimensioned values are lost or zeros
inserted. Refer to pg. 142 of the Owner's Handbook
DIM (i) If I contains a matrix descriptor then the DIM operation will be
performed on the matrix specified in I.
This indirect method applies to other matrix operations see below.
RCL DIM A-E (i) Places the matrix' dimensions in X and Y. A non-exisiting matrix has
dimensions 0x0
RCL MATRIX A-E Put a matrix descriptor in the X register. This displays the matrix'
name and its dimensions
STO 0-9 .0-.9 I
RCL 0-9 .0-.9 I
Matrix descriptors can be stored in and recalled from ordinary
storage registers
MATRIX 1 Stores 1 in R0 and R1 which are used to index matrix elements.
Useful in preparation of matrix element input
STO A-E (i)
RCL A-E (i)
Store X in the matrix element of matrix A-E which is addressed by
registers R0 and R1. R0 is the row and R1 the column number
starting from 1. RCL recalls the matrix element.
While the A-E key is held down the matrix name row and column
are displayed. R1 & R0 are automatically incremented in USER
mode see below
USER When user mode is active a STO A-E (i) or RCL A-E (i) operation
will automatically increment the column index in R1 until it wraps
back to 1 in which case the row index R0 is increment until it wraps
back to 1 as well.
So in user mode all matrix elements can quickly be entered and
recalled
STO +–x÷ A-E (i)
RCL +–x÷ A-E (i)
Matrix element arithmentic. Does not increment R1/R0 in USER
mode
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HP-15C
STO g A-E (i) Same as above but the stack's Y register contains the row number and
X the column number starting from 1.
The value must be present in Z.
Both X & Y will be popped from the stack so that the value ends up in
X.
STO g A-E (i)
RCL g A-E (i)
Same as above but the stack's Y register contains the row number and
X the column number starting from 1.
RCL will pop X & Y from the stack and then push the matrix element
into X
STO MATRIX
A-E
X is a number: Store the value of X in all matrix elements.
X is a matrix: Copy matrix in X to the specified matrix. The destination
matrix will be redimensioned
RCL MATRIX
A-E
Put the matrix descriptor of the specified matrix in X
x↔ A-E (i) Exchange X with the matrix element of A-E specified by R1/R0.
R1 & R0 are not affected
DSE A-E (i)
ISG A-E (i)
Decrements/increments the matrix element of A-E or (i) specified by
R1/R0. R1 & R0 are not affected. See DSE & ISG in section
Programming
RESULT A-E Specifies the result matrix (default is A). This is the matrix that will hold
the result of a matrix operation. Not all operations require a result
matrix. The result matrix will automatically be dimensioned so that it
can properly hold the result. For some matrix operations the result
matrix can be identical to one of the input matrices
STO RESULT When a matrix descriptor is already present in X then this matrix will be
used as the result matrix
RCL RESULT Recalls the descriptor of the result matrix into X
Unary matrix
operations
Result in X Effect on matrix
specified in X
Effect on RESULT
matrix
CHS None Changes sign of all
matrix elements
None as long as
X<>RESULT
1/x Descriptor of RESULT.
X must be square
None as long as
X<>RESULT
Inverse of matrix X.
If it is singular then
1/x will calculate the
inverse of a matrix
that is close to X.
MATRIX 4 None Replaced by
transpose XT
None as long as
X<>RESULT
MATRIX 7 Row norm: Largest sum
of absolute values of all
rows
None None
MATRIX 8 Frobenius or Euclidian
norm of X: Square root
of the sum of all matrix
elements
None None
MATRIX 9 Determinat of matrix.
X must be square
None as long as
X<>RESULT
LU decomposition of
matrix X
Scalar matrix operations
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HP-15C
Operation between a matrix and a scaler (=a plain number)
+ If X is a matrix and Y a scalar (or vice versa) the scalar will be added to
each element of the matrix
x If X is a matrix an Y a scalar (or vice versa) each element of the matrix
will be multiplied by the scalar
X=scalar Y=matrix X=matrix Y=scalar
- Substract scalar from each matrix
element
Substracts each matrix element
from scalar
÷Divide each matrix element by
scalar
Calculates the inverse of the
matrix and then multiplies each
matrix element with scalar
Binary matrix operations
X and Y contain matrix descriptors
+Add X+Y → RESULT where RESULT may be X or Y.
X & Y must have the same dimensions
-Substract Y-X → RESULT where RESULT may be X or Y.
X & Y must have the same dimensions
xMultiply Y•X→ RESULT where RESULT may neither be X or Y.
X & Y must have the compatible dimensions
÷Calculate X-1•Y→ RESULT where RESULT may be Y but not X.
X will be replaced by its LU decomposition. If X is singular it is replaced
by a non-singular matrix close to X.
Note that the order of X and Y is reversed! It corresponds to the Y/X
order. X must be square and have dimensions compatible with Y
MATRIX 5 Calculate YT•X→ RESULT where RESULT may neither be X nor Y.
X & Y must have compatible dimension
MATRIX 6 Calulatest the residual: RESULT – Y•X→ RESULT
The descriptor of RESULT is placed in X.
RESULT may neither be X nor Y. X & Y must have compatible dimension
Matrix in LU
form
Its descriptor is displayed with two dashes after the matrix name A-E.
Operations ÷ and determinate (MATRIX 9) calculate a LU decompsed
matrix. The following operations can be performed with the LU
decomposition as with the original matrix: 1/x ÷ (X=matrix) and
MATRIX 9
Complex matrices
Refer to pg. 160ff of the Owner's Manual.
Complex matrix operations are not supported directly. However these operations can be
rewritten so that they can be solved using only real matrices. The HP-15C provides a
number of functions to simplify the conversions between complex and corresponding real
matrixes
Py x Converts XC → XP. Number of rows of X must be even
Cy x Converts XP → XC. Number of columns of X must be even
MATRIX 2 Expand XP toX. Number of rows of X must be even
MATRIX 3 CollapseX to XP. Number of columns of X must be even
GSB I GTO I If I contains a matrix then the natrix name A-E is used as the target
label of the GSB or GTO
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HP-15C
X=0 Always returns false if X contains a matrix descriptor
TEST 0 (X≠0) Always returns true if X contains a matrix descriptor
TEST 5 (X=Y) Returns true if X and Y contain the same matrix descriptor. This does
not compare any matrix elements!
TEST 6 (X≠Y) Returns true if X and Y contain a different matrix descriptor or if X or Y
doesn't contain a matrix at all
Last X Operations which affect the RESULT matrix or produce a scalar in X also
affect Last X in the usual way
Maxtrix operations in a program
USER mode When USER mode is on STO & RCL operations on matrix elements
increment the R1/R0 register (see above).
When such an instruction is entered in a program a "u" replaces the
dash after the program line number to indicate that the command will
increment R1/R0.
If in programmed USER STO & USER RCL mode the R1/R0 registers
wrap around to (1 1) the next program line is skipped. This can be
helpful when accessing all matrix elements without explicit knowledge of
the matrix dimensions
MATRIX 7
MATRIX 8
Row norm & Frobenius norm. Puts original X into Last X. Then if X is a
matrix the norm is calculated and placed in X and the next program line
is executed. If X is a scalar it remains unchanged and the next program
line is skipped. This can be used to test whether X contains a matrix or
a scalar
Root Fin ing (Solver)
Memory The solver needs 5 registers. These are allocated from the uncommitted
registers space see MEM. The solver and the numerical integrator (see
below) share their registers
SOLVE 0-9
.0-.9 A-E
Finds real root of a function. This is a value X where the function f(X)
evaluates to 0.
•SOLVE expects two initial guesses for X in X and Y. These values can
be used to narrow down the serach for a root in case f(x) has
multiple roots. X=Y is permissable
•It then makes repeated GSB calls to the label with the current X
value being present in the stack's X Y Z and T register
•The program at the label must calculate the function f(X) and return
the result in X before it executes the RTN
•When SOLVE finally ends the stack will contain the following values:
X: Value for which f(X)=0 this is the "root"
Y: X value of the 2nd to last evaluation step
Z: f(X) at the root value – should be 0!
•If no root can be found Error 8 occurs (in RUN mode)
•Note that SOLVE eats up two of the seven possible GSB levels: One
for SOLVE and one for the calls to the user function
•The program which calculates f(x) must not call SOLVE (no nesting)
Complex mode SOLVE ignores the complex stack and can only calculate real roots
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HP-15C
SOLVE in a
program
If SOLVE can find a root the next program line is executed otherwise
skipped
Misc •To speed up the root finding process rewrite your function f(x) so
that it returns 0 if |f(x)|<ε. Or count the number of iterations inside
the calculation of f(x) and stop when a limit has been reached
•Even if no root can be found the stack registers contain the above
mentioned values. These often give a hint why the root finding
failed
•To find multiple roots eliminate an already known root R by dividing
the function by (x-R)
•Fore more details see HP-15C Owner's Handbook Appendix D
pg.220ff and The HP-15C Advanced Functions Handbook
Numerical Integration
Memory The integrator needs 23 registers. These are allocated from the uncommitted
registers space see MEM.
The integrator and the solver (see above) share their registers
∫xy 0-9
.0-.9 A-E
Integrates function f(X) at the given label for X values running from Y to X
• ∫xy makes repeated GSB calls to the specified label with the current X
value being present in the stack's X Y Z and T register
•The program at the label must calculate the function f(X) and return the
result in X before it executes the RTN
•When ∫xy ends the stack wil contain these values:
X: The integral of f(x)
Y: The uncertainty of the result: ∫xy f(x) = X±Y
Z: Upper integration limit
T: Lower integration limit
•Note that ∫xy eats up two of the seven possible GSB levels: One for ∫xy and
one for the calls to the user function
•The program which calculates f(x) must not call ∫xy (no nesting). However
SOLVE and ∫xy can be nested
Accuracy The integral is only evaluated to the accuracy specified by the current FIX
SCI or ENG format! The more digits have been specified the more accurate
the integral will be – but calculating it will take longer
Misc •Initially ∫xy will evaluate f(x) only at a few sample points. Then the
number of sample points are increased until the calculated integral
doesn't change any more. This has one important consequence: The
integration limits should be close to the area where the function is
"interesting". Ie. exp(-x²) around x=0 – if this function is integrated from
1E-50 to 1E+50 then the result will be 0 because the algorithm missed
the interesting part around 0
•Fore more details see HP-15C Owner's Handbook Appendix E pg.240ff
and The HP-15C Advanced Functions Handbook
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