0.9.0 - complex numbers

• 0.9.0 (2024-01-06)
  • Breaking: Change names and internal formats of various appVars
    • STK list variable replaced with RPN83STK
    • REGS list variable replaced with RPN83REG
    • RPN83SAV remains unchanged
    • the old STK and REGS variables can be manually removed
    • see TI-OS Interaction for more
      details
  • Breaking: Add CPLX menu at the previous location of CONV
    • CPLX menu seemed most convenient on row 1 of the ROOT menu where
      the old CONV was located
    • CONV got pushed to row 2, where the UNIT menu was previously
      located
    • UNIT got pushed to row 3, into an empty slot
    • the RPN83P home menu row now has exactly the same items as the MATH
      menu on the TI-OS:
      • RPN83P: MATH, NUM, PROB, CPLX
      • TI-OS: MATH, NUM, CPX, PROB
  • Support more than 14 digits during edit/input
    • When more than 14 digits are entered, the left most digits scroll off
      to the left, with the left most digit replaced with an ellipsis
      character indicates existence of extra digits.
    • Normal mode:
      • accepts maximum of 20 digits, which supports entering all 14
        digits encoded by the TI-OS floating point number format
    • Complex mode:
      • accepts maximum of 41 digits to allow 2 floating point numbers
    • BASE BIN mode
      • accepts up to 32 digits, to allow a 32-bit binary number when the
        WSIZ is 32.
    • see Input Limits and Long
      Numbers for more
      details
  • PROB
    • Expand range of COMB(n,r) and PERM(n,r) arguments to n,r<=65535
      from n,r<=255.
    • Improve performance of COMB(n,r) when r>(n-r) by taking advantage
      of the symmetry of COMB(n,r)==COMB(n,n-r).
    • Eliminate floating point round-off errors in computing COMB(n,r) by
      incrementing the divisor from 1 to r, instead of decrementing it
      from r to 1.
  • Complex Numbers
    • redesign RPN stack and storage registers to support both real and
      complex numbers
    • extend arithmetic, algebraic, transcendental handlers to support
      complex numbers
    • add explicit CPLX menu group with: REAL, IMAG, CONJ, CABS, CANG
    • support RRES (real result) and CRES (complex result) menu settings
    • support RECT (rectangular), PRAD (polar radian), PDEG (polar degree)
      menu settings
    • display complex numbers in RPN stack in rect and polar modes
    • support complex numbers in SHOW in rect and polar modes
    • support Linking/Unlinking a complex number and its 2 real components
      using 2ND LINK (equivalent to COMPLEX button on the HP-42S)
    • support entry of complex numbers on a single line in RECT, PRAD, and
      PDEG modes using the 2ND i and 2ND ANGLE keys.
    • see Complex Numbers for more
      details.
  • Save and restore app MODE settings independently from the TI-OS settings
    • decouple the TI-OS MODE settings from the RPN83P MODE settings
    • the TI-OS MODE settings are saved upon app start, and restored upon
      app exit
    • the app MODE settings are saved and restore independently
    • for example, it is now possible to set the TI-OS to FIX(2) and DEG,
      while setting RPN83P to SCI(4) and RAD and the 2 settings are managed
      separately, even though there is only a single set of global OS
      settings
  • Bug Fix: Render 3-digit EE exponents correctly in SHOW mode.
    • 3-digit exponents can only be shown for complex numbers, so the bug
      was latent until complex numbers were added
  • Bug Fix: Fix overflow in rectangular to polar conversion >POL
    • the built-in TI-OS RToP() function has a bug which throws an
      exception when x^2+y^2 becomes >=1e100, which can happen for x
      or y as low as 7.07e49.
    • reimplement using a custom rectToPolar() without the scaling bug