# Cannon Shot (On Target) # What is the elevation angle to hit a target 20 000 m away? # Enter a number in the Display Register then press Return. # The calculator displays a positive or negative distance if you overshoot or undershoot. # It displays 9.9999999 if you score a hit within 100 m of the target. # Check the History to narrow down the angle. # Source: "TI-57 Making Tracks into Programming.pdf#page=210", p. 11-7 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 # Angle (0-90) x = 40 # 40 mem[0] = x # STO 0 (32 0) # Distance (1 000-40 000) x = 20000 # 20000 mem[3] = x # STO 3 (32 0) # Hit Range x = 100 # 100 mem[5] = x # STO 5 (32 0) # Data Processing (38 steps) rounding = 2 # 2nd Fix 2 (48) x = 1 # 1 mem[4] += x # SUM 4 (34 0) x = 80000 # 80000 mem[1] = x # STO 1 (32 0) x = mem[0] # RCL 0 (33 0) x = tan(unit2rad(x)) # 2nd tan (20) stack.append(x) # X (55) x = mem[0] # RCL 0 (33 0) x = cos(unit2rad(x)) # 2nd cos (29) x *= x # x^2 (23) y = stack.pop() # X (55) x = y * x stack.append(x) x = mem[1] # RCL 1 (33 0) y = stack.pop() # = (85) x = y * x mem[2] = x # STO 2 (32 0) x = mem[5] # RCL 5 (33 0) y = mem[7] # x<>t (22) mem[7] = x x = y x = mem[2] # RCL 2 (33 0) stack.append(x) # - (65) x = mem[3] # RCL 3 (33 0) y = stack.pop() # = (85) x = y - x x = abs(x) # 2nd |x| (40) if x < mem[7]: # INV 2nd x>=t (- 76) goto .label_1 # GTO 1 (51 0) x = mem[2] # RCL 2 (33 0) stack.append(x) # - (65) x = mem[3] # RCL 3 (33 0) y = stack.pop() # = (85) x = y - x regx.append(fix(x)) # 2nd Pause (36) raise UserWarning('R/S') # R/S (81) label .label_1 # 2nd Lbl 1 (86 0) rounding = None # INV 2nd Fix (- 48) x = 0 # CLR (15) ee = False stack = [] x = 1 / x # 1/x (25) # 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)