This is a simple stack machine that can carry out arbitrarily complex mathematical computations. It’s not a universal machine as it lacks logical operators, conditional branching, and iteration, but the language it accepts can nevertheless approximate a wide range of functions.

A program for the machine is fed through the “run” method as a list of instructions and numbers. This serves as the input tape. Instructions are strings that are defined in the opcode tables below. These functions all take their arguments from the stack and return their results to the stack. Numbers can be integers or floats.

If the input tape’s read-head encounters a number, it gets pushed onto the stack. If it comes across an instruction, it will check that there are an adequate number of arguments on the stack, pop them if there are, carry out the instruction, and push the result back on to the stack. Invalid items on the tape are ignored.

If there are no relevant arguments on the stack, the instruction gets skipped. The run method returns the number at the stop of the stack after the read-head comes to the end of the tape. Empty and invalid programs return 0.

Example programs:

stack = Marula()

stack.run([5, 5, “op_mul”]) #returns 25

stack.run([2, 80, “op_div”]) #80/2 returns 40.0

stack.run([5.7, “op_tanh”]) #returns 0.999978

stack.run([17, 8, “op_argmax”]) #returns 17

   


import math 
import collections




class Marula:
    
    
    def __init__(self):
          
        #Initiate stack
          
        self.STACK = collections.deque()
        
        
        #OPCode dictionaries
        
        self.STACK_OPS = {
            
            "op_size" : self.size,
            "op_peek" : self.peek,
            "op_pop"  : self.pop,
            "op_push" : self.push
            
             }
        
    
        self.MATH_OPS = {
        
            "op_add" : self.add,
            "op_sub" : self.sub,
            "op_mul" : self.mul,
            "op_div" : self.div,
            "op_mod" : self.mod,
            "op_floor" : self.floor, 
            "op_ceil" : self.ceil,
            "op_sign" : self.sign,
            "op_abs" : self.fabs,
            "op_neg" : self.neg,
            "op_argmin" : self.argmin,
            "op_argmax" : self.argmax,
            "op_sqrt" : self.sqrt,
            "op_pwr" : self.pwr,
            "op_log" : self.log,
            "op_exp" : self.exp,
            "op_fctl" : self.fctl,
            "op_gamma": self.gamma,
            "op_sin" : self.sin,
            "op_cos" : self.cos,
            "op_tan" : self.tan,
            "op_asin" : self.asin,
            "op_acos" : self.acos,
            "op_atan" : self.atan,
            "op_sinh" : self.sinh,
            "op_cosh" : self.cosh,
            "op_tanh" : self.tanh,
            "op_asinh" : self.sinh,
            "op_acosh" : self.acosh,
            "op_atanh" : self.atanh

            }
        
        
        self.OP_CODES = {
            
            **self.STACK_OPS, 
            **self.MATH_OPS
            
            }
    
    
    #Stack manipulation methods
    
    def size(self):
        """Get size of stack"""
        return len(self.STACK)
    
    def peek(self):
        """Get the top items of the
        stack without removing it."""
        if self.STACK:
            return self.STACK[0]
        else:
            return 0

    
    def pop(self):
        "Pop item off the stack"
        return self.STACK.pop()
    
    def push(self, num):
        "Push item onto the stack"
        return self.STACK.append(round(num, 6))
    
    
    #Mathematical operations
    
    def add(self):
        if self.size() > 1:
            a = self.pop()
            b = self.pop()
            self.push(a + b)
    
    def sub(self):
        if self.size() > 1:
            a = self.pop()
            b = self.pop()
            self.push(a - b)
    
    def mul(self):
        if self.size() > 1:
            a = self.pop()
            b = self.pop()
            self.push(a * b)
    
    def div (self):
        if self.size() > 1 and all(
            [self.peek(), self.peek()]):
            a = self.pop()
            b = self.pop()
            self.push(a / b)
    
    def mod(self):
        """C standard modulo"""
        if self.size() > 1 and all(
            [self.peek(), self.peek()]):
            a = self.pop()
            b = self.pop()
            self.push(math.fmod(a,b))
    
    def floor(self):
        if self.size() > 0 and type(
            self.peek()[0]) == float:
            a = self.pop()
            self.push(math.floor(a))
    
    def ceil(self):
        if self.size() > 0 and type(
            self.peek()[0]) == float:
            a = self.pop()
            self.push(math.ceil(a))
    
    def sign(self):
        """Get sign bit of number"""
        if self.size() > 0:
            a = self.pop()
            if a > 0:
                return self.push(1)
            elif a < 0:
                return self.push(-1)
            else:
                return self.push(0)
    
    def fabs(self):
        """Absolute value"""
        if self.size() > 0:
            a = self.pop()
            self.push(math.fabs(a))
    
    def neg(self):
        """Inverter"""
        if self.size() > 0:
            a = self.pop()
            self.push(-a)
    
    def argmin(self):
        if self.size() > 1:
            a = self.pop()
            b = self.pop()
            self.push(min(a,b))

    def argmax(self):
        if self.size() > 1:
            a = self.pop()
            b = self.pop()
            self.push(max(a,b))
    
    def sqrt(self):
        if (self.size() > 0 
            and self.peek() > 0):
            a = self.pop()
            self.push(math.sqrt(a))
    
    def pwr(self):
        if self.size() > 1:
            a = self.pop()
            b = self.pop()
            self.push(a ** b) 
    
    def log(self):
        if (self.size() > 0 
            and self.peek() > 0):
            a = self.pop()
            self.push(math.log(a))
    
    def exp(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.exp(a))
    
    def fctl(self):
        "Factorial"
        if (self.size() > 0 
            and self.peek() > 0
            and type(
                self.peek()) == int):
            a = self.pop()
            self.push(math.factorial(a))
    
    def gamma(self):
        if (self.size() > 0
            and self.peek > 0): 
            a = self.pop()
            self.push(math.gamma(a))
    
    def sin(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.sin(a))
    
    def cos(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.cos(a))
    
    def tan(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.tan(a))
    
    def asin(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.asin(a))
    
    def acos(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.acos(a))
    
    def atan(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.atan(a))
    
    def sinh(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.sinh(a))
    
    def cosh(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.cosh(a))
    
    def tanh(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.tanh(a))
    
    def asinh(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.asinh(a))
            
    def acosh(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.acosh(a))
    
    def atanh(self):
        if self.size() > 0:
            a = self.pop()
            self.push(math.gamma(a))
    
    
    
    # Main method
    
    
    def run(self, program):
        
        """

        This is the input tape for the stack machine.
        Programs must be in the in the form of a list
        of instructions and numbers.
        
        """
        
        if not type(program) == list:
            raise ValueError(
                "Inputs must be in a list.")
        
        for element in program:
            if type(element) in [int, float]:
                self.push(element)
            elif element in self.OP_CODES:
                self.OP_CODES[element]()
            else:
                continue
               
        if self.STACK:
            return self.STACK[0]
        else:
            self.push(0)
            return self.STACK[0]

                
        
        



   

Full code repo available on Github

 

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Interleaved Neighborhood Algorithm: Fully Exploratory Optimization

 

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