Round-Half-Up

[Greg Lyon]

#COMPILE EXE
#DIM ALL
'---------------------------------------------------
' Round-Half-Up - Round EXT to LONG
'---------------------------------------------------
' The tricky point is what "up" means for negative numbers. Does it mean increasing
' in size towards negative infinity? Or does it mean increasing towards positive
' infinity? If it means increasing towards negative infinity then the algorithm
' is 'symmetric' with respect to zero for positive and negative values. If it means
' increasing towards positive infinity then the algorithm is 'asymmetric' with
' respect to zero for positive and negative values.
' .NET Math.Round(x, System.MidpointRounding.AwayFromZero) is symmetric.
' Python round() is symmetric.
' MATHLAB round() is symmetric.
' Java round() is assymmetric.
'---------------------------------------------------
FUNCTION RoundHalfUp_S (BYVAL extVal AS EXT) AS LONG
    ' symmetric implementation (-5.5 rounds to -6)
    FUNCTION = FIX(extVal + (SGN(extVal) * 0.5##))
END FUNCTION
'---------------------------------------------------
FUNCTION RoundHalfUp_A(BYVAL extVal AS EXT) AS LONG
    ' asymmetric implementation (-5.5 rounds to -5).
    FUNCTION = FIX(extVal + IIF(SGN(extVal)=1, 0.5##, 0.0##))
END FUNCTION
'---------------------------------------------------
FUNCTION PBMAIN() AS LONG

    LOCAL x AS EXT

    STDOUT "Symmetric"
    FOR x = 9.5## TO -9.5## STEP -0.5##
        STDOUT FORMAT$(x, "0.0") & " = " & FORMAT$(RoundHalfUp_S(x), "0")
    NEXT x

    STDOUT

    STDOUT "Asymmetric"
    FOR x = 9.5## TO -9.5## STEP -0.5##
        STDOUT FORMAT$(x, "0.0") & " = " & FORMAT$(RoundHalfUp_A(x), "0")
    NEXT x

    STDOUT $CRLF & "Press any key to exit ... ";
    WAITKEY$
    STDOUT

END FUNCTION

[Greg Lyon]

Round-Half-Up ASM Version

ASM version.

#COMPILE EXE
#DIM ALL
'---------------------------------------------------
' Round-Half-Up - Round EXT to LONG
'---------------------------------------------------
' The tricky point is what "up" means for negative numbers. Does it mean increasing
' in size towards negative infinity? Or does it mean increasing towards positive
' infinity? If it means increasing towards negative infinity then the algorithm
' is 'symmetric' with respect to zero for positive and negative values. If it means
' increasing towards positive infinity then the algorithm is 'asymmetric' with
' respect to zero for positive and negative values.
' .NET Math.Round(x, System.MidpointRounding.AwayFromZero) is symmetric.
' Python round() is symmetric.
' MATHLAB round() is symmetric.
' Java round() is assymmetric.
'
' I got the idea for this code from: http://ldesoras.free.fr/doc/articles/rounding_en.pdf
' Greg Lyon
'--------------------------------------------------
FUNCTION RoundHalfUp_A(BYREF e AS EXT) AS LONG
    ' Asymmetric implementation (-5.5 rounds to -5).
    #REGISTER NONE

    LOCAL OneHalf AS EXT
    LOCAL i AS LONG

    OneHalf = 0.5##

    ! mov eax, e
    ! finit
    ! fld TBYTE PTR [eax]
    ! fadd st(0), st(0)
    ! fld OneHalf
    ! fadd
    ! fistp i
    ! sar i, 1

    FUNCTION = i

END FUNCTION
'---------------------------------------------------
FUNCTION RoundHalfUp_S(BYREF e AS EXT) AS LONG
    ' Symmetric implementation (-5.5 rounds to -6)
    #REGISTER NONE

    LOCAL OneHalf AS EXT
    LOCAL i AS LONG

    OneHalf  = 0.5##

    ! mov eax, e
    ! finit
    ! fld TBYTE PTR [eax]
    ! fadd st(0), st(0)
    ! fld OneHalf

    ! mov eax, e
    ! add eax, 9
    ! movzx edx, DWORD PTR [eax]
    ! bt edx, 7
    ! jnc positive
    ! fchs

  positive:
    ! fadd
    ! fistp i
    ! sar i, 1

    FUNCTION = i

END FUNCTION
'----------------------------------------------------
FUNCTION PBMAIN() AS LONG

    LOCAL x AS EXT

    STDOUT "Symmetric"
    FOR x = 9.5## TO -9.5## STEP -0.5##
        STDOUT FORMAT$(x, "0.0") & " = " & FORMAT$(RoundHalfUp_S(x), "0")
    NEXT x
    
    STDOUT
    
    STDOUT "Asymmetric"
    FOR x = 9.5## TO -9.5## STEP -0.5##
        STDOUT FORMAT$(x, "0.0") & " = " & FORMAT$(RoundHalfUp_A(x), "0")
    NEXT x

    STDOUT $CRLF & "Press any key to exit ... ";
    WAITKEY$
    STDOUT

END FUNCTION
'---------------------------------------------------