RPN Reverse Polish Notation Calculator -- in Fortran

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

Build with CMake or Fortran package manager (FPM).

CMake:

```sh cmake -B build

cmake --build build

ctest --test-dir build # optional, compare with SciPy output. ```

Fortran Package Manager (FPM):

```sh fpm build

fpm run ```

Usage

Run the "rpncalc" executable like:

sh build/rpncalc

or with:

sh fpm run

Enter 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 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

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