The funcs.90 module provides over 100 elemental functions not found in Fortran instrinsics.
Bessel, complex gamma, psi and a few others come are vendored and modernized from Netlib Specfun under the specfun/ directory.
RPNcalc works on Linux, Mac and Windows.
The stack size is set by the user with command line option. Default size is 4.
Authors:
- Fortran 77 code: David G. Simpson
- Fortran 2018 code: Michael Hirsch
We have created some self-tests using Python SciPy, which is not necessary for normal use -- this is a standalone Fortran program.
Build with CMake or Fortran package manager (FPM).
CMake:
cmake -B build
cmake --build build
ctest --test-dir build # optional, compare with SciPy output.Fortran Package Manager (FPM):
fpm build
fpm runRun the "rpncalc" executable like:
build/rpncalcor with:
fpm runEnter numbers and operations separated by blanks or carriage returns. The contents of the X register will be printed after each carriage return. For example:
X
2 3 + 5.0000
6 * 30.0000
SIN 0.5000
To exit the program, type:
q
To get a brief help:
help
Stack size: default stack size is 4, and may be betweeen 2..99 levels. Set the stack size at runtime, say 25 by:
rpncalc 25
Show what modes the calculator is in with:
MODES Print modes
The Fortran 2018 RPN calculator has 3 operating modes. The default mode is REAL
COMPLEX COMPLEX mode
REAL REAL mode
RATIONAL Rational (fraction) mode
Additionally, angle modes can be selected like any scientific calculator:
DEFAULT Restore default modes
GRAD Grads mode
RAD Radians mode
DEG Degrees mode
Number base selection:
DEC Decimal mode ( default )
BIN Binary mode
HEX Hexadecimal mode
OCT Octal mode
Stack operations are fundamental to RPN use, and constitute some of RPN's key advantages over other calculating methods.
R Roll stack down
U Roll stack up
D Drop lowest (X) register from stack
CLALL Clear all
CLREG Clear general registers
CLS Clear summation registers
CLSTK Clear stack
CLX Clear X
RESET Reset calculator to initial state
LASTX Recall last X
PR Print registers
PS Print stack
PSUMS Print sums
Registers:
There are ten registers (0..9) accessed with:
STOx Store, where x ~ 0..9 e.g. STO3 STO6
RCLx Recall, where x ~ 0..9 e.g. RCL3 RCL6
Digits of precision display:
For each case, x ~ (0..9) digits of DISPLAYED precision. Iinternal precision remains at 32 or 64 bits, set when compiled.
ENGx Engineering notation
FIXx Fix notation
SCIx Scientific notation
Other display modes:
IMPROPER Improper fraction display mode
MIXED Mixed fraction display mode
ALL ALL digits display mode
Common Functions:
+ Addition
- Subtraction
* Multiplication
/ Division
^ Exponentiation
RECIP Reciprocal
2X 2^x
SQR Square
SQRT Square root
HYPOT Compute SQRT(X^2+Y^2)
HYPOT3 Compute SQRT(X^2+Y^2+Z^2)
CUBE Cube
CBRT Cube root
! Factorial (= GAMMA(n+1))
ROUND Round to integer
CHS Change sign
FRAC Fractional part
FRACTOL Set fraction tolerance
Complex functions:
These utility functions are for operations with numbers having a real and imaginary component. Most of the functions overall in the program can handle real and complex numbers, using Fortran 2003+ polymorphism.
ABS Absolute value
CONJ Complex conjugate
I i (imaginary unit)
IM Imaginary component
RE Real component
ARG Argument of a complex number
RI Exchange real and imaginary parts
Conversions:
P>R Polar to rectangular
R>D Radians to degrees
R>P Rectangular to polar
D>F Decimal to fraction
D>R Degrees to radians
C>F Celsius to Fahrenheit
CM>IN Centimeter to inches
F>C Fahrenheit to Celsius
GAL>L Gallons to liters
HMS>H HMS to hours
KG>LB Kilograms to pounds
L>GAL Liters to gallons
H>HMS Hours to HMS
LB>KG Pounds to kilograms
IN>CM Inches to centimeters
Trigonometric:
SIN Sine
ASIN Inverse sine
COS Cosine
ACOS Inverse cosine
COT Cotangent
ACOT Inverse cotangent
ACOT2 Inverse cotangent (2 args)
CSC Cosecant
ACSC Inverse cosecant
SEC Secant
ASEC Inverse secant
TAN Tangent
ATAN Inverse tangent
ATAN2 Inverse tangent (2 args)
AHAV Inverse haversine
HAV Haversine
Hyperbolic:
ACOSH Inverse hyperbolic cosine
ACOTH Inverse hyperbolic cotangent
COSH Hyperbolic cosine
COTH Hyperbolic cotangent
ASECH Inverse hyperbolic secant
ACSCH Inverse hyperbolic cosecant
ASINH Inverse hyperbolic sine
ATANH Inverse hyperbolic tangent
SINH Hyperbolic sine
TANH Hyperbolic tangent
SECH Hyperbolic secant
CSCH Hyperbolic cosecant
Logarithms:
XRT X root of Y
EXP exp(x)
10X 10^x
LN Natural logarithm
LOG Common logarithm
LOG2 Logarithm base 2
Rational numbers:
GCD Greatest common divisor
LCM Least common multiple
INT Integer part
INT/ Integer division
Statistics:
CNR Combinations
PNR Permutations
LR Linear regression (leaves b in X, m in Y)
X^ Linear estimate X
XMEAN Mean of X
XS Sample standard deviation of X
XSIG Population standard deviation of X
XY X-Y exchange
Y^ Linear estimate Y
YMEAN Mean of Y
YS Sample standard deviation of Y
YSIG Population standard deviation of Y
Constants:
AMU Atomic mass unit (kg)
AU Astronomical unit (m)
C Speed of light in vacuum (m/s)
ECHG Elementary charge e (C)
EPS0 Permittivity of free space (F/m)
EULER Euler-Mascheroni constant
G Standard acceleration due to gravity (m/s^2)
GOLDEN Golden ratio
GRAV Gravitational constant G (m^3/kg s^2)
H Planck constant (J s)
HBAR Planck constant (J s)
KB Boltzmann constant (J/K)
ME Electron mass (kg)
MN Neutron mass (kg)
MP Proton mass (kg)
MU0 Permeability of free space (N/A^2)
MUB Bohr magneton (A m^2)
MUN Nuclear magneton (A m^2)
NA Avogadro's number (mol^-1)
PI Pi ( ~ 22/7)
2PI 2 * pi
2PII 2 * pi * i
RGAS Gas constant (J/mol K)
REARTH Earth radius (m)
STEFAN Stefan-Boltzmann constant (W/m^2 K^4)
logical:
AND Logical AND
NOT Logical NOT
OR Logical OR
XOR Logical XOR
Other Functions:
Many functions not commonly found in RPN calculators are included:
% Percent
%CHG Percent change
!! Double factorial
A0 Bohr radius (m)
ACOVERS Inverse coversine
ACRD Inverse chord (of Ptolemy)
AEXSEC Inverse exsecant
AVERS Inverse versine
BESSELJ0 Bessel function of the first kind, order 0
BESSELJ1 Bessel function of the first kind, order 1
BESSELJ1P first derivative J'1(x)
BESSELJ Bessel function of the first kind, real order
BESSELY0 Bessel function of the second kind, order 0
BESSELY1 Bessel function of the second kind, order 1
BESSELY Bessel function of the second kind, real order
BESSELI0 Modified Bessel function of the first kind, order 0
BESSELI1 Modified Bessel function of the first kind, order 1
BESSELI Modified Bessel function of the first kind, real order
BESSELK0 Modified Bessel function of the second kind, order 0
BESSELK1 Modified Bessel function of the second kind, order 1
BESSELK Modified Bessel function of the second kind, real order
JINC [JINC sombrero function](https://en.wikipedia.org/wiki/Sombrero_function) J1(x)/x
BETA Beta function
COVERS Coversine
CRD Chord (of Ptolemy)
DIGAMMA Digamma function
DUP Duplicate X
ERF Error function
ERFC Complementary error function
EXSEC Exsecant
GAMMA Gamma function
HMS+ HMS add
HMS- HMS subtract
KEPLER Solves elliptical Kepler's equation (e,M -> E)
MOD Modulo
N Number of points in summation
RAND Random number
RCORR Linear regression correlation coefficient
REDUCE Reduce an angle
REV Revs mode
RZETA Riemann zeta function
S Summation
S- Delete summation
SGN Signum
SINC [cardinal sine (sinc) function sin(x) / x](https://en.wikipedia.org/wiki/Sinc_function)
SINHC Sinhc function
SUMX Summation of X
SUMX2 Summation of X^2
SUMXY Summation of XY
SUMY Summation of Y
SUMY2 Summation of Y^2
TANC Tanc function
TANHC Tanhc function
TIME Current date and time
VER Print software version
VERS Versine
Possible future operations:
? Incomplete gamma functions (upper and lower)
? Incomplete beta function
? Spherical Bessel functions j, n
? Legendre functions Pnm, Qnm (various normalizations)
? Legendre polynomials
? Elliptic integrals
? Jacobi elliptic functions sn, cn, dn
? Jacobi amplitude function am
? Exponential integrals
? Hypergeometric functions
? Hermite polynomials
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