mirror of
https://github.com/louisrubet/rpn
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283 lines
8.7 KiB
Markdown
283 lines
8.7 KiB
Markdown
# **rpn** - reference manual
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**rpn**
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- is a **math-oriented language** inspired by Hewlett-Packard **R**everse **P**olish **L**isp (**HP28S** user manual is provided as a reference), it includes at least **stack**, **store**, **branch**, **test**, **trig** and **logs** commands
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- is implemented as a a **command-line calculator** for GNU/Linux
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- brings powerfull calculation facilities on floating point numbers with __arbitrary precision__, provided by **GNU MP** and **GNU MPFR** libraries
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- uses that so cool **reverse polish notation**
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## Quick examples
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### easy calculation with **stacked results**
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```
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rpn> 1 2 +
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3
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rpn> 2 sqrt
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2> 3
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1> 1.4142135623730950488
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```
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### **programs** and **variables**
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```
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rpn> << rot * swap 2 / neg dup sq rot - sqrt >> 'quadratic_solution' sto
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rpn> 1 2 -3 quadratic_solution
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2> -1
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1> 2
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rpn> vars
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var 1: name 'quadratic_solution', type program, value << rot * swap 2 / chs dup sq rot - sqrt >>
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```
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### **local variables**
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```
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rpn> << -> x y << x y + ln >> >> 'P' sto
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rpn> 1 2 P
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rpn> 1.0986122886681096914
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```
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### **arbitrary precision**
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Precision can be really high, up to 0x7FFFFFFFFFFFFFFF bits with GNU MPFR
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```
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rpn> 256 prec 200 std
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rpn> pi 3 * 4 / cos
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-0.70710678118654752440084436210484903928483593768847403658833986899536623923105962592591087473479525356117497671223960240783675485777817360566073272153486395308799122357513534343724299243077135552002446
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rpn>
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```
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### Objects
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Following objects are managed: **floating numbers**, **symbols**, **strings**, **programs**, plus language **keywords** (commands and flow controls)
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```
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4> 'symbol'
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3> "string"
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2> 12.3456
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1> << -> n << 0 1 n for i i 2 * inv + next >> >>
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rpn>
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```
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### Command line
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**rpn** is a cli interface with an **interactive editor** with autocompletion provided by **linenoise-ng**, see https://github.com/arangodb/linenoise-ng
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```
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rpn>
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Display all 128 possibilities? (y or n)
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!= -> > acosh atan cosh drop e exit for ifte max not pos r->d rot sinh sqrt sto+ tan unti xor
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% ->str >= alog atanh d->r drop2 edit exp h inv min num pow rcl round sinv start sto- tanh until xpon
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%CH / ? alog2 chr dec dropn else exp10 help ln mod or prec repea same size std sto/ test vars
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* < ^ and chs default dup end exp2 hex log neg over purge repeat sci sneg step str-> then version
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+ <= abs asin clusr depth dup2 erase fact if log2 next pi q roll sign sq sto sub type whil
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- == acos asinh cos do dupn eval fix ift mant nop pick quit rolld sin sqr sto* swap uname while
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rpn>
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```
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## keywords
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### general
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|keyword|description|
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|-|-|
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|nop | no operation |
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|help | (or h or ?) this help message
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|quit | (or q or exit) quit software
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|version | show rpn version
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|uname | show rpn complete identification string
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|type | show type of stack first entry
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|default | set float representation and precision to default
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### real and complex
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|keyword|description|
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|-|-|
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|+| addition
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|-| substraction
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|neg| negation
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|*| multiplication
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|/| division
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|inv| inverse
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|^| (or pow) power
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|sqrt| square root
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|sq| (or sqr) square
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|abs| absolute value for a number or sqrt(re*re+im*im) for a complex
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|dec| decimal representation
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|hex| hexadecimal representation
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|prec| get float precision in bits when first stack is not a number, set float precision in bits when first stack entry is a number. ex: ```256 prec```
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|round| set float rounding mode. Authoerized values are: ```["nearest", "toward zero", "toward +inf", "toward -inf", "away from zero"] round```. ex: ```"nearest" round```
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|sign| 1 if number at stack level 1 is > 0, 0 if == 0, -1 if <= 0
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### real
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|%| purcent
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|%|CH inverse purcent
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|mod| modulo
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|fact| n! for integer n or Gamma(x+1) for fractional x
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|mant| mantissa of a real number
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|xpon| exponant of a real number
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|min| min of 2 real numbers
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|max| max of 2 real numbers
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### complex
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|re| complex real part
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|im| complex imaginary part
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|conj| complex conjugate
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|arg| complex argument in radians
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|r->p| rectangular to polar coordinates
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|p->r| polar to rectangular coordinates
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|r->c| transform 2 reals in a complex
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|c->r| transform a complex in 2 reals
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### mode
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|keyword|description|
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|-|-|
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|std| standard floating numbers representation. ex: [25] std
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|fix| fixed point representation. ex: 6 fix
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|sci| scientific floating point representation. ex: 20 sci
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### test
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|keyword|description|
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|-|-|
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|>| binary operator >
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|>=| binary operator >=
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|<| binary operator <
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|<=| binary operator <=
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|!=| binary operator != (different)
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|==| binary operator == (equal)
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|and| boolean operator and
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|or| boolean operator or
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|xor| boolean operator xor
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|not| boolean operator not
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|same| boolean operator same (equal)
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### stack
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|keyword|description|
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|-|-|
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|swap| swap 2 first stack entries
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|drop| drop first stack entry
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|drop2| drop 2 first stack entries
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|dropn| drop n first stack entries
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|erase| drop all stack entries
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|rot| rotate 3 first stack entries
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|dup| duplicate first stack entry
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|dup2| duplicate 2 first stack entries
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|dupn| duplicate n first stack entries
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|pick| push a copy of the given stack level onto the stack
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|depth| give stack depth
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|roll| move a stack entry to the top of the stack
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|rolld| move the element on top of the stack to a higher stack position
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|over| push a copy of the element in stack level 2 onto the stack
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### string
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|keyword|description|
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|-|-|
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|->str| convert an object into a string
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|str->| convert a string into an object
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|chr| convert ASCII character code in stack level 1 into a string
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|num| return ASCII code of the first character of the string in stack level 1 as a real number
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|size| return the length of the string
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|pos| seach for the string in level 1 within the string in level 2
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|sub| return a substring of the string in level 3
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### branch
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|keyword|description|
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|-|-|
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|if| if <test-instruction> then <true-instructions> else <false-instructions> end
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|then| used with if
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|else| used with if
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|end| used with various branch instructions
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|ift| similar to if-then-end, <test-instruction> <true-instruction> ift"
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|ifte| similar to if-then-else-end, <test-instruction> <true-instruction> <false-instruction> ifte"
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|start| start> <end> start <instructions> next|<step> step
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|for| start> <end> for <variable> <instructions> next|<step> step
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|next| used with start and for
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|step| used with start and for
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|do| do <instructions> until <condition> end
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|until | (or unti) used with do
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|while| (or whil) while <test-instruction> repeat <loop-instructions> end
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|repeat| (or repea) used with while
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### store
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|keyword|description|
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|-|-|
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|sto| store a variable. ex: ```1 'name' sto```
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|rcl| recall a variable. ex: ```'name' rcl```
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|purge| delete a variable. ex: ```'name' purge```
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|vars| list all variables
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|clusr| erase all variables
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|edit| edit a variable content
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|sto+| add to a stored variable. ex: 1 'name' sto+ 'name' 2 sto+
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|sto-| substract to a stored variable. ex: 1 'name' sto- 'name' 2 sto-
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|sto*| multiply a stored variable. ex: 3 'name' sto* 'name' 2 sto*
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|sto/| divide a stored variable. ex: 3 'name' sto/ 'name' 2 sto/
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|sneg| negate a variable. ex: 'name' sneg
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|sinv| inverse a variable. ex: 1 'name' sinv
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### program
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|keyword|description|
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|-|-|
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|eval| evaluate (run) a program, or recall a variable. ex: ```'my_prog' eval```
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|->| load program local variables. ex: ```<< -> n m << 0 n m for i i + next >> >>```
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### trig
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|keyword|description|
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|-|-|
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|pi| pi constant
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|sin| sinus
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|asin| arg sinus
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|cos| cosinus
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|acos| arg cosinus
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|tan| tangent
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|atan| arg tangent
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|d|->r convert degrees to radians
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|r|->d convert radians to degrees
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### logs
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|keyword|description|
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|-|-|
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|e| exp(1) constant
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|log| logarithm base 10
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|alog| (or exp10) exponential base 10
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|log2| logarithm base 2
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|alog2| (or exp2) exponential base 2
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|ln| logarithm base e
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|exp| exponential
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|sinh| hyperbolic sine
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|asinh| inverse hyperbolic sine
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|cosh| hyperbolic cosine
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|acosh| inverse hyperbolic cosine
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|tanh| hyperbolic tangent
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|atanh| inverse hyperbolic tangent
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### default
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Default float mode is 'std' with 20 digits
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Default floating point precision is 128 bits
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Default rounding mode is 'nearest'
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## Tests
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Unit tests are given as txt files in the test subdirectory.
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Use the command 'test' to run a test file, eg
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```
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# cd src_directory/
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# rpn
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rpn> "test/01-all.txt"
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rpn> test
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## ENTRY TEST
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(...)
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# real decimal PASSED
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# real hex PASSED
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# real binary PASSED
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(...)
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```
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Test output is done on stdout and is not stacked in rpn.
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