# Introduction to programming the TI-57 (Dice Roll) # The TI-57 Programmable Calculator was made by Texas Instruments around 1980. # It has a LED Display, 50 Program steps and 8 memory registers. # A TI-57 Program is a set of basic instructions that can perform calculations, # read or write memory, test a value, go to a program step to make a loop or call a subroutine. # The TI-57 Program Emulator (this web site) translates the instructions into Python then runs it. # The Python code can be checked below along with the Calculator Internal State. # The following program generates a random number (R) from 2 to 12 to simulate two dice rolls. # Here is the algorithm: R = Int(A X 6 + 1) where A = Fract[(π + A)^8] and A = 0 to start. # Run the Program to roll the dice then check the details in the History. # Source: [https://en.wikipedia.org/wiki/TI-57 TI-57] on Wikipedia import re from math import * from goto import with_goto # pip install goto-statement @with_goto def main(): global ee, mem, rounding, stack, unit, x label .label_rst # Data Input # Number of dice x = 2 # 2 mem[0] = x # STO 0 (32 0) # Data Processing (25 steps) # Reset the total x = 0 # 0 mem[1] = x # STO 1 (32 0) label .label_1 # 2nd Lbl 1 (86 0) # i = π + A x = pi # 2nd pi (30) stack.append(x) # + (75) x = mem[2] # RCL 2 (33 0) y = stack.pop() # = (85) x = y + x # A = Fract[i^8] stack.append(x) # y^x (35) x = 8 # 8 y = stack.pop() # = (85) x = pow(y, x) x = x - int(x) # INV 2nd Int (- 49) mem[2] = x # STO 2 (32 0) # R = Int(A X 6 + 1) stack.append(x) # X (55) x = 6 # 6 y = stack.pop() # + (75) x = y * x stack.append(x) x = 1 # 1 y = stack.pop() # = (85) x = y + x x = int(x) # 2nd Int (49) # Keep track of the number regx.append(fix(x)) # 2nd Pause (36) # Update the total mem[1] += x # SUM 1 (34 0) # Dice left to roll? mem[0] = floor(mem[0]) # 2nd DSZ (56) if mem[0] > 0: mem[0] -= 1 elif mem[0] < 0: mem[0] += 1 if mem[0] != 0: # Yes, roll the next dice goto .label_1 # GTO 1 (51 0) # No, display the total x = mem[1] # RCL 1 (33 0) regx.append(fix(x)) # 2nd Pause (36) return # R/S (81) # Internal functions def degrees2dms(degrees): """Convert decimal degrees to degrees, minutes, seconds.""" degrees = float(degrees) is_positive = degrees >= 0 if not is_positive: degrees = -degrees minutes, seconds = divmod(degrees * 3600, 60) degrees, minutes = divmod(minutes, 60) # Internal mantissa has 11 digits on TI-57 seconds = f"{seconds:016.13f}".replace(".", "") dms = f"{int(degrees)}.{int(minutes):02}{seconds}".rstrip("0") if not is_positive: dms = "-" + dms return dms def dms2degrees(dms): """Convert degrees, minutes, seconds to decimal degrees.""" match = re.fullmatch( r"(?P[+-])?(?P[0-9]+)\.?(?P[0-9]{1,2})?(?P[0-9]{1,2})?(?P[0-9]*)", str(dms), ) if match is None: raise Exception(f"Calculator error: invalid DMS angle {dms}") angle = match.groupdict() degrees = float(angle["degrees"]) if angle["minutes"]: if len(angle["minutes"]) == 1: angle["minutes"] += "0" degrees += float(angle["minutes"]) / 60 if angle["seconds"]: if len(angle["seconds"]) == 1: angle["seconds"] += "0" degrees += float(angle["seconds"]) / 3600 if angle["remainder"]: degrees += float("0." + angle["remainder"]) / 3600 if angle["sign"] == "-": degrees = -degrees return degrees def fix(number): """Round a number and/or convert it to the scientific notation.""" global ee, rounding if ee: # The scientific notation is on if rounding is None: # Default to the calculator 7 digit precision number = f"{number:.7E}" # Remove trailing 0s number = re.sub("0+E", "E", number) else: # Round as exponent with the given precision number = f"{number:.{rounding}E}" elif rounding is not None: # Rounding is on number = f"{number:.{rounding}f}" else: # No rounding number = str(number) return number def grd2rad(gradian): """Convert gradian to radian.""" return (gradian / 200) * pi def get_calculator_state(): """Return the calculator sate.""" global ee, error, mem, regx, rounding, stack, unit, x return { "ee": ee, "error": error, "fixed_x": fix(x), "mem": mem, "regx": regx, "rounding": rounding, "stack": stack, "unit": unit, "x": x, } def init_calculator_state(state={}): """Initialize the calculator state. Must be called before running the program, see run(). ee -- Scientific notation (EE) error -- Syntax error etc. mem -- Memories (STO) regx -- History of values displayed before a pause (2nd pause) rounding -- Number of digit after the decimal point (2nd Fix) stack -- Internal memory stack used for computing nested operations unit -- Angle unit (2nd Deg, 2nd Rad, 2nd Grad) x -- Display register or X register """ global ee, error, mem, regx, rounding, stack, unit, x ee = state["ee"] if "ee" in state else False error = state["error"] if "error" in state else None mem = state["mem"] if "mem" in state else [0 for i in range(8)] regx = state["regx"] if "regx" in state else [] rounding = state["rounding"] if "rounding" in state else None stack = state["stack"] if "stack" in state else [] unit = state["unit"] if "unit" in state else "Deg" x = state["x"] if "x" in state else 0 def rad2grd(radian): """Convert radian to gradian.""" return (radian / pi) * 200 def rad2unit(number): """Convert radian to degree or gradian.""" global unit number = float(number) if unit == "Deg": number = degrees(number) elif unit == "Grd": number = rad2grd(number) return number def run_program(): """Run the program (the entry point). The calculator must be initialized beforehand, see init_calculator_state(). """ global error, x try: main() except ZeroDivisionError: x = 9.9999999 except UserWarning: # R/S key pass except Exception as e: error = str(e) def unit2rad(number): """Convert degree or gradian to radian.""" global unit number = float(number) if unit == "Deg": number = radians(number) elif unit == "Grd": number = grd2rad(number) return number # Program execution, uncomment to run the file on its own. # init_calculator_state() # run_program() # calculator_state = get_calculator_state() # print(calculator_state)