The Display Register or X Register shows the result after the execution of a Program.
In the Python code, the X Register corresponds to the variable "x".
The Display History shows the values of the Display Register each time the Program encounters the "2nd Pause" key.
The real Calculator would pause for a second while the Emulator keeps track of the X Register.
In the Python code, the Display History is stored in the "regx" list.
The Display Register is editable. Enter a list of numbers separated by spaces to change the Data. Then click elsewhere to see the effect of the change in the Program. Or press the Enter key to run the Program with the new Data. For example, suppose the Data begins with 10 STO 1 20 STO 2 30 STO 3 and you want to replace the first two with 11 STO 1 22 STO 2. You can either edit the program directly or enter 11 22 in the Display Register. This is handy especially with games.
# | History |
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Program Instructions/Keys
# Master Mind
# How many guesses will you take to discover a 4-digit number with digits ranging from 1 to 6?
# Enter a number in the Display Register then press Return!
# The calculator will return the number of digits placed correctly.
# Keep trying until you get 4 and check the History to narrow down the number.
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
# Your guess
x = 0 # 0
mem[3] = x # STO 3 (32 0)
regx.append(fix(x)) # 2nd Pause (36)
# Data Preprocessing
x = 0 # 0
mem[7] = x # STO 7 (32 0)
x = mem[1] # RCL 1 (33 0)
# Seed != 0?
if x != mem[7]: # INV 2nd x=t (- 66)
goto .label_0 # GTO 0 (51 0)
# Set the seed
x = 0.721015 # 0.721015
mem[1] = x # STO 1 (32 0)
label .label_0 # 2nd Lbl 0 (86 0)
x = 4 # 4
mem[7] = x # STO 7 (32 0)
x = mem[6] # RCL 6 (33 0)
# Digit found != 4?
if x != mem[7]: # INV 2nd x=t (- 66)
# Keep trying
goto .label_1 # GTO 1 (51 0)
# New game
x = 0 # 0
mem[2] = x # STO 2 (32 0)
label .label_1 # 2nd Lbl 1 (86 0)
x = 0 # 0
mem[7] = x # STO 7 (32 0)
x = mem[2] # RCL 2 (33 0)
# Secret = 0?
if x == mem[7]: # 2nd x=t (66)
# Generate secret
sbr_4() # SBR 4 (61 0)
# Data Processing (70 steps)
# Digit position
x = 4 # 4
mem[0] = x # STO 0 (32 0)
# Number of correctly placed digits
x = 0 # 0
mem[6] = x # STO 6 (32 0)
# Copy the target number
x = mem[2] # RCL 2 (33 0)
mem[4] = x # STO 4 (32 0)
label .label_2 # 2nd Lbl 2 (86 0)
# Shift one digit of the target number right
# Fractional part
x = mem[4] # RCL 4 (33 0)
stack.append(x) # : (45)
x = 10 # 10
y = stack.pop() # = (85)
x = y / x
stack.append(x) # - (65)
x = int(x) # 2nd Int (49)
mem[4] = x # STO 4 (32 0)
y = stack.pop() # = (85)
x = y - x
mem[5] = x # STO 5 (32 0)
# Shift one digit of the guessed number right
# Fractional part
x = mem[3] # RCL 3 (33 0)
stack.append(x) # : (45)
x = 10 # 10
y = stack.pop() # = (85)
x = y / x
stack.append(x) # - (65)
x = int(x) # 2nd Int (49)
mem[3] = x # STO 3 (32 0)
y = stack.pop() # = (85)
x = y - x
# Digit difference (Fract difference)
mem[5] -= x # INV SUM 5 (- 34 0)
x = 0.01 # 0.01
mem[7] = x # STO 7 (32 0)
# Digit difference
x = mem[5] # RCL 5 (33 0)
x = abs(x) # 2nd |x| (40)
# Digit difference > 0.01?
if x >= mem[7]: # 2nd x>=t (76)
goto .label_3 # GTO 3 (51 0)
# Add on digit correctly placed
x = 1 # 1
mem[6] += x # SUM 6 (34 0)
label .label_3 # 2nd Lbl 3 (86 0)
# Digits left?
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:
goto .label_2 # GTO 2 (51 0)
# Correctly placed digits
x = mem[6] # RCL 6 (33 0)
regx.append(fix(x)) # 2nd Pause (36)
return # R/S (81)
# Subroutine: Generate a 4-digit random number
@with_goto
def sbr_4():
global ee, mem, rounding, stack, unit, x
label .label_4 # 2nd Lbl 4 (86 0)
# Number of digits
x = 4 # 4
mem[0] = x # STO 0 (32 0)
# Initialize the number
x = 0 # 0
mem[2] = x # STO 2 (32 0)
label .label_5 # 2nd Lbl 5 (86 0)
# Shift previous digits left
x = 10 # 10
mem[2] *= x # 2nd Prd 2 (39 0)
sbr_6() # SBR 6 (61 0)
# Add a digit to the number
mem[2] += x # SUM 2 (34 0)
# Digits left?
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:
# Yep
goto .label_5 # GTO 5 (51 0)
# 4-digit number ready
label .end # INV SBR (- 61)
# Subroutine: Generate a random digit from 1 to 6
@with_goto
def sbr_6():
global ee, mem, rounding, stack, unit, x
label .label_6 # 2nd Lbl 6 (86 0)
# i = π + A
x = pi # 2nd pi (30)
stack.append(x) # + (75)
x = mem[1] # RCL 1 (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[1] = x # STO 1 (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)
label .end # INV SBR (- 61)
# Note that this program would not fit in a real calculator!
# 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)