For the difference between Euclidean and truncated resuls and code compare with Trancate division.
A screen capture of the demo results.
Note - The last two lines of LONG and QUAD shows the difference between Euclidean and truncate with remainder results.
The Euclidean Division functions should compile and run as-is in any version of PowerBASIC from PBWin 8 and PBCC 4 to PBWin 10 and PBCC 6, maybe earier. Compiling with the PBMAIN function, the demonstration, requires PBWin 10 Will compile in either PBWin 10 or PBCC 6. The FUNCTIONs can be SUBs instead. To retain divide by zero detection replace "FUNCTION = %err_divisionbyzero" with "ERROR %err_divisionbyzero".
''The remainder/modulo operation performed by Intel math coprocessors (FPREM
''and FPREM1 instructions) is not Euclidean, Intel's idiv assembly instruction
''is not Euclidean division. They are both IEEE Standard 754.
''In Euclidean division the remainder is never negative. For negative dividends
''the quotient is 1 different than expected.
''From Google- "An example use of Euclidean division with a negative dividend
''is finding a repeating time or calendar offset, such as calculating what hour
''of the day it was a certain number of hours ago.
#compile exe
#dim all
#if %def(%pb_cc32) 'if PBCC
#console off 'don't create a console window
#endif
'========================== Euclidean Division Of LONGs ========================
function EuclidDivide (byval Dividend as long, _
byval Divisor as long, _
byref Quotient as long, _
byref Remainder as long) as long
'
! mov ebx, Divisor
! cmp ebx, 0
! jne DoDivide
! mov function, %err_divisionbyzero
! jmp Done
DoDivide:
! mov esi, Quotient 'Quotient and Remainder pointers to registers
! mov edi, Remainder
'
! mov eax, Dividend 'load the dividend
! cdq 'sign-extend EAX into EDX:EAX
! idiv ebx 'EDX:EAX / ECX
'
'adjust to Euclidean results
! cmp edx, 0 'remainder < 0
! jl RmndrLT0
! jmp Results
RmndrLT0:
! cmp ebx, 0 'divisor > 0
! jg DvsrGT0
! add eax, 1
! sub edx, ebx
! jmp Results
DvsrGT0:
! sub eax, 1
! add edx, ebx
'
'set result variables
Results:
! mov [esi], eax
! mov [edi], edx
Done:
end function
'
'========================== Euclidean Division Of QUADs ========================
'For QUAD the only change is the type of the parameters.
function EuclidDivideQuad (byval Dividend as quad, _
byval Divisor as quad, _
byref Quotient as quad, _
byref Remainder as quad) as long
'------------------------
if Divisor = 0 then
Quotient = 0
Remainder = 0
function = %err_divisionbyzero
exit function
end if
'
Quotient = Dividend \ Divisor
Remainder = Dividend mod Divisor
'
if Remainder < 0 then
if Divisor > 0 then
Quotient -= 1
Remainder += Divisor
else
Quotient += 1
Remainder -= Divisor
end if
end if
end function
'
'/\/\/\/\/\/\/\/\/\/\/\ Demonstrate Euclidian Division /\/\/\/\/\/\/\/\/\/\/\/\
function pbmain () as long
local hTWin as dword
local QuotientQ, RemainderQ as quad
local Quotient, Remainder, ErrNum as long
local FmtLg, FmtQd as string
txt.window("Euclidian Division Demonstration", 200, 200, 18, 64) to hTWin
'
FmtLg = " #;-#; 0"
FmtQd = " ###########;-###########; 0"
'================================== Long =====================================
txt.print "type LONG"
ErrNum = EuclidDivide(9, 0, Quotient, Remainder)
txt.print " 9 / 0 = " + format$(Quotient, FmtLg) + " R" + _
format$(Remainder, FmtLg) + " error code = " + dec$(ErrNum, 2)
'
ErrNum = EuclidDivide(9, 4, Quotient, Remainder)
txt.print " 9 / 4 = " + format$(Quotient, FmtLg) + " R" + _
format$(Remainder, FmtLg) + " error code = " + dec$(ErrNum, 2)
'
ErrNum = EuclidDivide(9, -4, Quotient, Remainder)
txt.print " 9 / -4 = " + format$(Quotient, FmtLg) + " R" + _
format$(Remainder, FmtLg) + " error code = " + dec$(ErrNum, 2)
'
ErrNum = EuclidDivide(-9, 4, Quotient, Remainder)
txt.print "-9 / 4 = " + format$(Quotient, FmtLg) + " R" + _
format$(Remainder, FmtLg) + " error code = " + dec$(ErrNum, 2)
'
ErrNum = EuclidDivide(-9, -4, Quotient, Remainder)
txt.print "-9 / -4 = " + format$(Quotient, FmtLg) + " R" + _
format$(Remainder, FmtLg) + " error code = " + dec$(ErrNum, 2)
'
'================================== Quad =====================================
txt.print
txt.print "type QUAD"
ErrNum = EuclidDivideQuad(90000000000, 0, QuotientQ, RemainderQ)
txt.print " 90000000000 / 0 = " + _
format$(QuotientQ, FmtQd) + " R" + format$(RemainderQ, FmtQd) + _
" error code " + dec$(ErrNum, 2)
'
ErrNum = EuclidDivideQuad(90000000000, 40000000000, QuotientQ, RemainderQ)
txt.print " 90000000000 / 40000000000 = " + _
format$(QuotientQ, FmtQd) + " R" + format$(RemainderQ, FmtQd) + _
" error code " + dec$(ErrNum, 2)
'
ErrNum = EuclidDivideQuad(90000000000, -40000000000, QuotientQ, RemainderQ)
txt.print " 90000000000 / -40000000000 = " + _
format$(QuotientQ, FmtQd) + " R" + format$(RemainderQ, FmtQd) + _
" error code " + dec$(ErrNum, 2)
'
ErrNum = EuclidDivideQuad(-90000000000, 40000000000, QuotientQ, RemainderQ)
txt.print "-90000000000 / 40000000000 = " + _
format$(QuotientQ, FmtQd) + " R" + format$(RemainderQ, FmtQd) + _
" error code " + dec$(ErrNum, 2)
'
ErrNum = EuclidDivideQuad(-90000000000, -40000000000, QuotientQ, RemainderQ)
txt.print "-90000000000 / -40000000000 = " + _
format$(QuotientQ, FmtQd) + " R" + format$(RemainderQ, FmtQd) + _
" error code " + dec$(ErrNum, 2)
'
txt.print
txt.print
txt.color = &h0000C000
txt.print "Any key to close."
txt.waitkey$
txt.end
end function
Source and compiled code partial copyleft (ↄ), the limitation is you
may not claim creation and attempt to copyright it.
This page is copyright © 2026, all rights reserved Dale Yarker.
Created on 30 August 2026.
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