Comparison QB64 compiled with gcc optimizations and without

[Coolman]

i hate the c c++ language but i must admit that it is very powerful. it's a pity that qb64 doesn't generate an optimized code like this. i found this code here :

https://benchmarksgame-team.pages.debian...gpp-3.html

compile :
g++ -c -pipe -O3 -fomit-frame-pointer -std=c++17 n-body.cpp -o n-body.o && g++ n-body.o -o n-body

test :
time ./n-body 50000000

results :
-0.169075164
-0.169059907

real 0m3,352s
user 0m3,348s

n-body.cpp

Code: (Select All)

/* The Computer Language Benchmarks Game
   https://salsa.debian.org/benchmarksgame-team/benchmarksgame/

   contributed by Martin Jambrek
   based off the Java #2 program contributed by Mark C. Lewis and modified slightly by Chad Whipkey
*/

#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <utility>

static constexpr double PI = 3.141592653589793;
static constexpr double SOLAR_MASS = 4 * PI * PI;
static constexpr double DAYS_PER_YEAR = 365.24;

template <auto start, auto stop, auto step = 1, class F>
constexpr void static_for(F&& f)
{
    if constexpr (start < stop) {
        f(std::integral_constant<decltype(start), start>());
        static_for<start + step, stop, step>(std::move(f));
    }
}

struct alignas(32) Body {
    double x, y, z, pad0;
    double vx, vy, vz, pad1;
    double mass;

    constexpr Body(double x, double y, double z,
        double vx, double vy, double vz,
        double mass)
        : x(x)
        , y(y)
        , z(z)
        , pad0()
        , vx(vx)
        , vy(vy)
        , vz(vz)
        , pad1()
        , mass(mass)
    {
    }
};

static constexpr size_t N_BODIES = 5;
using System = Body[N_BODIES];

static constexpr Body sun = {
    0, 0, 0, 0, 0, 0, SOLAR_MASS
};

static constexpr Body jupiter = {
    4.84143144246472090e+00,
    -1.16032004402742839e+00,
    -1.03622044471123109e-01,
    1.66007664274403694e-03 * DAYS_PER_YEAR,
    7.69901118419740425e-03 * DAYS_PER_YEAR,
    -6.90460016972063023e-05 * DAYS_PER_YEAR,
    9.54791938424326609e-04 * SOLAR_MASS
};

static constexpr Body saturn = {
    8.34336671824457987e+00,
    4.12479856412430479e+00,
    -4.03523417114321381e-01,
    -2.76742510726862411e-03 * DAYS_PER_YEAR,
    4.99852801234917238e-03 * DAYS_PER_YEAR,
    2.30417297573763929e-05 * DAYS_PER_YEAR,
    2.85885980666130812e-04 * SOLAR_MASS
};

static constexpr Body uranus = {
    1.28943695621391310e+01,
    -1.51111514016986312e+01,
    -2.23307578892655734e-01,
    2.96460137564761618e-03 * DAYS_PER_YEAR,
    2.37847173959480950e-03 * DAYS_PER_YEAR,
    -2.96589568540237556e-05 * DAYS_PER_YEAR,
    4.36624404335156298e-05 * SOLAR_MASS
};

static constexpr Body neptune = {
    1.53796971148509165e+01,
    -2.59193146099879641e+01,
    1.79258772950371181e-01,
    2.68067772490389322e-03 * DAYS_PER_YEAR,
    1.62824170038242295e-03 * DAYS_PER_YEAR,
    -9.51592254519715870e-05 * DAYS_PER_YEAR,
    5.15138902046611451e-05 * SOLAR_MASS
};

constexpr void offset_momentum(System& bodies)
{
    double px = 0.0;
    double py = 0.0;
    double pz = 0.0;

    static_for<0, N_BODIES>([&](auto i) {
        px += bodies[i].vx * bodies[i].mass;
        py += bodies[i].vy * bodies[i].mass;
        pz += bodies[i].vz * bodies[i].mass;
    });

    bodies[0].vx = -px / SOLAR_MASS;
    bodies[0].vy = -py / SOLAR_MASS;
    bodies[0].vz = -pz / SOLAR_MASS;
}

constexpr void advance(System& bodies, double dt)
{
    static_for<0, N_BODIES>([&](auto i) {
        static_for<i + 1, N_BODIES>([&](auto j) {
            double dx = bodies[i].x - bodies[j].x;
            double dy = bodies[i].y - bodies[j].y;
            double dz = bodies[i].z - bodies[j].z;

            double dSquared = dx * dx + dy * dy + dz * dz;
            double mag = dt / (dSquared * std::sqrt(dSquared));

            bodies[i].vx -= dx * bodies[j].mass * mag;
            bodies[i].vy -= dy * bodies[j].mass * mag;
            bodies[i].vz -= dz * bodies[j].mass * mag;

            bodies[j].vx += dx * bodies[i].mass * mag;
            bodies[j].vy += dy * bodies[i].mass * mag;
            bodies[j].vz += dz * bodies[i].mass * mag;
        });
    });

    static_for<0, N_BODIES>([&](auto i) {
        bodies[i].x += dt * bodies[i].vx;
        bodies[i].y += dt * bodies[i].vy;
        bodies[i].z += dt * bodies[i].vz;
    });
}

constexpr double energy(const System& bodies)
{
    double e = 0.0;

    static_for<0, N_BODIES>([&](auto i) {
        const Body& iBody = bodies[i];
        e += 0.5 * iBody.mass * (iBody.vx * iBody.vx + iBody.vy * iBody.vy + iBody.vz * iBody.vz);

        static_for<i + 1, N_BODIES>([&](auto j) {
            double dx = iBody.x - bodies[j].x;
            double dy = iBody.y - bodies[j].y;
            double dz = iBody.z - bodies[j].z;

            double distance = std::sqrt(dx * dx + dy * dy + dz * dz);
            e -= (iBody.mass * bodies[j].mass) / distance;
        });
    });

    return e;
}

int main(int argc, char* argv[])
{
    const auto n = std::atoi(argv[1]);

    System system = {
        sun,
        jupiter,
        saturn,
        uranus,
        neptune
    };

    offset_momentum(system);

    std::printf("%.9f\n", energy(system));

    for (size_t i = 0; i < n; ++i)
        advance(system, 0.01);

    std::printf("%.9f\n", energy(system));
}

[madscijr]

i hate the c c++ language but i must admit that it is very powerful. it's a pity that qb64 doesn't generate an optimized code like this. 

The good news is, with research and feedback like yours, the developers can always improve QB64 and its C code generator. No programming language or compiler was built in a day!

[Coolman]

i hate the c c++ language but i must admit that it is very powerful. it's a pity that qb64 doesn't generate an optimized code like this. 

The good news is, with research and feedback like yours, the developers can always improve QB64 and its C code generator. No programming language or compiler was built in a day!

indeed. qb64 can be improved to generate a more clear and efficient code...

[Fifi]

So, the question is: QB64 should it be compiled with the -O3 option by default?
Are the results the same on Linux, macOS and Windows?
What are the Pros Vs Cons?
TIA

[madscijr]

So, the question is: QB64 should it be compiled with the -O3 option by default?
Are the results the same on Linux, macOS and Windows?
What are the Pros Vs Cons?
TIA

I think we'll need the developers to answer this one!

[DSMan195276]

> QB64 should it be compiled with the -O3 option by default?

> Are the results the same on Linux, macOS and Windows?
> What are the Pros Vs Cons?


There's two aspect that I think need to be considered: technical, and practical.

From the technical side, I'm still hesitant to recommend it as there are some coding patterns in

libqb.cpp

that are very likely to get optimized wrong, resulting in a broken program. It does appear that this isn't as big of a problem as I first assumed it would be, as we do have several successful uses of it, but I still don't think it makes sense as a default just yet.

From the practical side, QB64 itself probably shouldn't be compiled with

-O3

due to the length of time and amount of memory it can take. I haven't tried it on Linux (I think the situation might be much better) but on Windows it ends up taking several GBs of RAM and many minutes (10 or 15) to finish compiling. For Linux and MacOS, since they have to build QB64 themselves during the setup script I think that's just too long to expect people to sit through.

[madscijr]

...
but on Windows it ends up taking several GBs of RAM and many minutes (10 or 15) to finish compiling. For Linux and MacOS, since they have to build QB64 themselves during the setup script I think that's just too long to expect people to sit through.

Good point - when I'm developing a game, the first 1000 times I run (compile) it, it's development & unit testing, not for someone to run, so the performance benefit doesn't matter so much at this stage as the ability to develop rapidly. If I had to wait 10-15 mins every time I wanted to rerun my code to see if some minor change worked, that could be a problem. When my app is far enough along where I'm ready to compile to performance test, if it's just the one time, I can wait for it to compile. But 10-15 minutes can add up, so I would probably mainly use that feature for the build before a release.

[Coolman]

personally, i decided to compile qb64 with option O3 because the editor is faster under linux but i agree with DSMan195276, the compilation of programs is slower with this option. that said it depends on the power and memory available in your computer. if not if you have a light program, it could be ok. otherwise it's better to use the original version of qb64 and when the program is finished. consider compiling it with option O3...

[Coolman]

This code has many calculation functions, different nesting, use of for next loop, select case, intensive string manipulation, function call and even use of goto instruction from basic language. It's ideal to compare processing speed with qb64 compiled in O3 and without.

more information here : https://staging.qb64phoenix.com/showthread.php?tid=770

to get 3.14, i used 750. deactivate print in the processing loop to speed up the processing. here is the result :

928.2x seconds : program compiled with qb64 (v0.5.0) -O3

1481.6x seconds : program compiled with qb64 (v0.5.0) original

Code: (Select All)

Dim Shared betatest%: betatest% = -1
Width 160, 42
_Delay 0.2
_ScreenMove _Middle
Color 14, 0: Print "Wait...": Color 7, 0
limit&& = 500
j = -1
start = Timer(.001)
For i = 1 To 750
    j = j + 2

    If oldd$ = "" Then
        d$ = "1": oldd$ = "1": oldn$ = "1": n$ = "1"
    Else
        d$ = LTrim$(Str$(j))
        ' 2nd denominator * 1st numerator.
        a$ = d$: b$ = oldn$: op$ = "*"
        Call string_math(a$, op$, b$, x$, limit&&)
        m1$ = x$
        ' 1st denominator * 2nd numerator.
        a$ = oldd$: b$ = n$
        Call string_math(a$, op$, b$, x$, limit&&)
        m2$ = x$
        ' Get common denominator
        a$ = d$: b$ = oldd$
        Call string_math(a$, op$, b$, x$, limit&&)
        d$ = x$
        a$ = m1$: b$ = m2$: If i / 2 = i \ 2 Then op$ = "-" Else op$ = "+"
        Call string_math(a$, op$, b$, x$, limit&&)
        Rem  PRINT "oldn$ = "; oldn$; " oldd$ = "; oldd$, "n$ = "; x$; " d$ = "; d$
        'Print "n$ = "; x$; " d$ = "; d$;: Color 14, 0: Print j: Color 7, 0
        oldn$ = x$: oldd$ = d$
    End If
Next

Rem CALL greatest_common_factor(x$, d$, limit&&) ' Too slow.

n$ = x$
a$ = x$: b$ = d$: op$ = "/"

'speed reduction
If Len(a$) > 16 Then
    j = Len(a$)
    k = Len(b$)
    i = j - k
    a$ = Mid$(a$, 1, 16 + i): b$ = Mid$(b$, 1, 16)
End If

Call string_math(a$, op$, b$, x$, limit&&)
a$ = x$: b$ = "4": op$ = "*"
Call string_math(a$, op$, b$, x$, limit&&)
Print: Print "pi = "; x$
Color 3: Print: Print Timer(.001) - start; "seconds"
End

Sub string_math (stringmatha$, operator$, stringmathb$, runningtotal$, limit&&)
    Select Case operator$
        Case "+", "-"
            GoTo string_add_subtract
        Case "*"
            GoTo string_multiply
        Case "/"
            GoTo string_divide
        Case Else
            Print "Error, no operator selected. operator$ = "; operator$
    End Select

    string_divide:
    divsign% = 0: divremainder& = 0: divremainder$ = "": divplace& = 0: divplace2& = 0: quotient$ = "": divcarry& = 0
    operationdivision% = -1
    divbuffer& = Len(stringmathb$) - Len(stringmatha$)
    If divbuffer& < 0 Then divbuffer& = 0
    d2dividend$ = stringmatha$
    d1divisor$ = stringmathb$
    If Left$(d1divisor$, 1) = "0" And Len(d1divisor$) = 1 Then Print "Division by zero not allowed.": divsign% = 0: operationdivision% = 0: Exit Sub
    If Left$(d1divisor$, 1) = "-" Then divsign% = -1: d1divisor$ = Mid$(d1divisor$, 2)
    If Left$(d2dividend$, 1) = "-" Then
        If divsign% Then
            divsign% = 0
        Else
            divsign% = -1
        End If
        d2dividend$ = Mid$(d2dividend$, 2)
    End If
    If InStr(d1divisor$, ".") <> 0 Then
        Do Until Right$(d1divisor$, 1) <> "0"
            d1divisor$ = Mid$(d1divisor$, 1, Len(d1divisor$) - 1) ' Strip off trailing zeros
        Loop
        divplace& = Len(d1divisor$) - InStr(d1divisor$, ".")
        d1divisor$ = Mid$(d1divisor$, 1, InStr(d1divisor$, ".") - 1) + Mid$(d1divisor$, InStr(d1divisor$, ".") + 1) ' Strip off decimal point.
        Do Until Left$(d1divisor$, 1) <> "0"
            d1divisor$ = Mid$(d1divisor$, 2) ' Strip off leading zeros for divisors smaller than .1
        Loop
    End If

    If InStr(d2dividend$, ".") <> 0 Then
        d2dividend$ = d2dividend$ + String$(divplace& - Len(d2dividend$) - InStr(d2dividend$, "."), "0") ' Add any zeros based on the length of dividend at decimal - length of divisor at decimal. If less than zero, nothing added.
        divplace2& = InStr(d2dividend$, ".")
        Do Until Right$(d2dividend$, 1) <> "0"
            d2dividend$ = Mid$(d2dividend$, 1, Len(d2dividend$) - 1) ' Strip off trailing zeros
        Loop
        d2dividend$ = Mid$(d2dividend$, 1, InStr(d2dividend$, ".") - 1) + Mid$(d2dividend$, InStr(d2dividend$, ".") + 1) ' Strip off decimal point.
    Else
        d2dividend$ = d2dividend$ + String$(divplace&, "0") ' Add any zeros based on the length of dividend at decimal - length of divisor at decimal. If less than zero, nothing added.
        divplace& = 0
    End If
    Do
        Do
            divremainder& = divremainder& + 1: divremainder$ = divremainder$ + Mid$(d2dividend$, divremainder&, 1)
            If Mid$(d2dividend$, divremainder&, 1) = "" Then
                If divremainder$ = String$(Len(divremainder$), "0") And Len(quotient$) > Len(d2dividend$) Then divflag% = -1: Exit Do
                divcarry& = divcarry& + 1
                If divcarry& = 1 Then divplace3& = divremainder& - 1
                If divcarry& > limit&& + 1 + divbuffer& Then
                    divflag% = -2: Exit Do
                End If
                divremainder$ = divremainder$ + "0" ' No more digits to bring down.
            End If
            If Len(divremainder$) > Len(d1divisor$) Or Len(divremainder$) = Len(d1divisor$) And divremainder$ >= d1divisor$ Then Exit Do
            quotient$ = quotient$ + "0"
        Loop
        If divflag% Then divflag% = 0: Exit Do
        For div_i% = 9 To 1 Step -1
            stringmatha$ = LTrim$(Str$(div_i%)): stringmathb$ = d1divisor$
            m_product$ = "": GoSub string_multiply
            tempcutd$ = divremainder$ ' divremainder$ can be 00 or other leading zero values.
            Do
                If Len(tempcutd$) = 1 Then Exit Do
                If Left$(tempcutd$, 1) = "0" Then
                    tempcutd$ = Mid$(tempcutd$, 2)
                Else
                    Exit Do
                End If
            Loop
            If Len(tempcutd$) > Len(m_product$) Or Len(tempcutd$) = Len(m_product$) And m_product$ <= tempcutd$ Then Exit For
        Next
        quotient$ = quotient$ + LTrim$(Str$(div_i%))
        stringmatha$ = LTrim$(Str$(div_i%)): stringmathb$ = d1divisor$
        m_product$ = "": GoSub string_multiply
        operator$ = "-"
        stringmatha$ = divremainder$
        stringmathb$ = m_product$
        GoSub string_add_subtract
        divremainder$ = stringmatha$
        operator$ = "/"
    Loop
    If divplace& = 0 And divplace2& = 0 Then divplace& = divplace3&
    If divplace2& Then divplace& = divplace& + divplace2& - 1
    If quotient$ = "" Then divplace& = 0 ' dividend is zero.
    If divplace& Or divplace2& Then
        quotient$ = Mid$(quotient$, 1, divplace&) + "." + Mid$(quotient$, divplace& + 1)
        Do Until Right$(quotient$, 1) <> "0"
            quotient$ = Mid$(quotient$, 1, Len(quotient$) - 1) ' Strip off trailing zeros
        Loop
        If Right$(quotient$, 1) = "." Then quotient$ = Mid$(quotient$, 1, Len(quotient$) - 1) ' Strip off abandoned decimal.
    End If
    Do Until Left$(quotient$, 1) <> "0"
        quotient$ = Mid$(quotient$, 2) ' Strip off leading zeros
    Loop
    If quotient$ = "" Then quotient$ = "0": divsign% = 0
    operationdivision% = 0
    stringmathb$ = quotient$: quotient$ = ""

    If stringmathb$ = "overflow" Then divsign% = 0: operationdivision% = 0: Exit Sub

    runningtotal$ = stringmathb$: stringmathb$ = ""
    If divsign% Then runningtotal$ = "-" + runningtotal$

    If stringmathround$ <> "" Then runningtotal$ = runningtotal$ + stringmathround$
    operationdivision% = 0
    Exit Sub

    string_multiply:
    m_decimal_places& = 0: m_product$ = ""
    fac1$ = stringmatha$: fac2$ = stringmathb$ ' Make numbers whole numbers and remove any - sign.
    If Left$(fac1$, 1) = "-" Then fac1$ = Mid$(fac1$, 2): m_sign% = -1
    If Left$(fac2$, 1) = "-" Then fac2$ = Mid$(fac2$, 2): If m_sign% Then m_sign% = 0 Else m_sign% = -1
    If InStr(fac1$, ".") <> 0 Then m_decimal_places& = Len(fac1$) - InStr(fac1$, "."): fac1$ = Mid$(fac1$, 1, InStr(fac1$, ".") - 1) + Mid$(fac1$, InStr(fac1$, ".") + 1)
    If InStr(fac2$, ".") <> 0 Then m_decimal_places& = m_decimal_places& + Len(fac2$) - InStr(fac2$, "."): fac2$ = Mid$(fac2$, 1, InStr(fac2$, ".") - 1) + Mid$(fac2$, InStr(fac2$, ".") + 1)
    For m_i& = Len(fac2$) To 1 Step -1 ' Multiply each charater top and bottom.
        m_k& = m_l&
        m_x2$ = Mid$(fac2$, m_i&, 1)
        For m_j& = Len(fac1$) To 1 Step -1
            m_x1$ = Mid$(fac1$, m_j&, 1)
            If m_product$ <> "" Then
                m_add$ = LTrim$(Str$(Val(m_x1$) * Val(m_x2$))) + String$(m_k&, "0")
                m_t& = 0: m_xproduct$ = "": m_carry% = 0
                Do ' Add multiplied characters together.
                    m_x3$ = Mid$(m_add$, Len(m_add$) - m_t&, 1)
                    m_x4$ = Mid$(m_product$, Len(m_product$) - m_t&, 1)
                    If m_x3$ = "" And m_x4$ = "" Then
                        If m_carry% Then m_xproduct$ = "1" + m_xproduct$
                        Exit Do
                    End If
                    m_g% = Val(m_x3$) + Val(m_x4$) + m_carry%
                    If m_g% >= 10 Then m_g% = m_g% - 10: m_carry% = 1 Else m_carry% = 0
                    m_xproduct$ = LTrim$(Str$(m_g%)) + m_xproduct$
                    m_t& = m_t& + 1
                Loop
                m_product$ = m_xproduct$: m_xproduct$ = ""
            Else
                m_product$ = LTrim$(Str$(Val(m_x1$) * Val(m_x2$))) + String$(m_k&, "0") ' First loop makes variable here.
            End If
            m_k& = m_k& + 1 ' Adds trailing zeros multiplication
        Next
        m_l& = m_l& + 1 ' Used to reset value for m_k& adding one trailing zer for each loop.
    Next
    fac1$ = "": fac2$ = "": m_l& = 0: m_k& = 0: m_t& = 0
    If m_decimal_places& > Len(m_product$) Then m_product$ = String$(m_decimal_places& - Len(m_product$), "0") + m_product$ ' Add any leading zeros to a decimal. Ex: .02 * .01 is factored as 002. It needs one leading zero before adding the decimal point, .0002.
    If m_decimal_places& And m_product$ <> "0" Then ' Replace any decimal point.
        m_product$ = Mid$(m_product$, 1, Len(m_product$) - m_decimal_places&) + "." + Mid$(m_product$, Len(m_product$) - m_decimal_places& + 1)
    End If
    Do Until Left$(m_product$, 1) <> "0" ' Remove leading zeros.
        m_product$ = Mid$(m_product$, 2)
    Loop
    If m_decimal_places& Then
        Do Until Right$(m_product$, 1) <> "0" ' Remove trailing zeros in a decimal sum.
            m_product$ = Mid$(m_product$, 1, Len(m_product$) - 1)
        Loop
    End If
    If m_product$ = "" Then m_product$ = "0": m_sign% = 0
    If Right$(m_product$, 1) = "." Then m_product$ = Mid$(m_product$, 1, Len(m_product$) - 1) ' Remove decimal from the end of an integer total.
    If operationdivision% Then m_sign% = 0: Return
    stringmathb$ = m_product$: m_product$ = ""

    If stringmathb$ = "overflow" Then Exit Sub

    runningtotal$ = stringmathb$: stringmathb$ = ""
    If m_sign% Then runningtotal$ = "-" + runningtotal$: m_sign% = 0
    Exit Sub

    string_add_subtract:
    If InStr(stringmatha$, ".") <> 0 Then ' Evaluate sum for decimal fraction.
        sumplace& = Len(stringmatha$) - InStr(stringmatha$, ".")
        stringmatha$ = Mid$(stringmatha$, 1, InStr(stringmatha$, ".") - 1) + Mid$(stringmatha$, InStr(stringmatha$, ".") + 1) ' Strip out decimal
    End If
    If InStr(stringmathb$, ".") <> 0 Then ' Evaluate number for decimal fraction.
        numplace& = Len(stringmathb$) - InStr(stringmathb$, ".")
        stringmathb$ = Mid$(stringmathb$, 1, InStr(stringmathb$, ".") - 1) + Mid$(stringmathb$, InStr(stringmathb$, ".") + 1) ' Strip out decimal
    End If
    If sumplace& > numplace& Then addsubplace& = sumplace& Else addsubplace& = numplace&
    If sumplace& > addsubplace& Then
        stringmatha$ = stringmatha$ + String$(sumplace& - addsubplace&, "0")
    ElseIf addsubplace& > sumplace& Then
        stringmatha$ = stringmatha$ + String$(addsubplace& - sumplace&, "0")
    End If
    If numplace& > addsubplace& Then
        stringmathb$ = stringmathb$ + String$(numplace& - addsubplace&, "0")
    ElseIf addsubplace& > numplace& Then
        stringmathb$ = stringmathb$ + String$(addsubplace& - numplace&, "0")
    End If ' END Decimal evaluations.

    If Left$(stringmatha$, 1) = "-" Then sign_input$ = "-" Else sign_input$ = "+"
    If Left$(stringmathb$, 1) = "-" Then sign_total$ = "-" Else sign_total$ = "+"

    addsubsign% = 0
    Select Case sign_input$ + operator$ + sign_total$
        Case "+++", "+--"
            operator$ = "+"
            If Left$(stringmathb$, 1) = "-" Then stringmathb$ = Mid$(stringmathb$, 2)
        Case "++-", "+-+"
            operator$ = "-"
            If Left$(stringmathb$, 1) = "-" Then stringmathb$ = Mid$(stringmathb$, 2)
            GoSub string_comp
            If gl% < 0 Then Swap stringmatha$, stringmathb$: addsubsign% = -1
        Case "---", "-++"
            operator$ = "-"
            If Left$(stringmatha$, 1) = "-" Then stringmatha$ = Mid$(stringmatha$, 2)
            If Left$(stringmathb$, 1) = "-" Then stringmathb$ = Mid$(stringmathb$, 2)
            GoSub string_comp
            If gl% < 0 Then Swap stringmatha$, stringmathb$: addsubsign% = -1
        Case "--+", "-+-"
            operator$ = "+"
            If Left$(stringmatha$, 1) = "-" Then stringmatha$ = Mid$(stringmatha$, 2)
            If Left$(stringmathb$, 1) = "-" Then stringmathb$ = Mid$(stringmathb$, 2)
            addsubsign% = -1
    End Select

    If Len(stringmatha$) > Len(stringmathb$) Then
        stringmathb$ = String$(Len(stringmatha$) - Len(stringmathb$), "0") + stringmathb$
    ElseIf Len(stringmatha$) < Len(stringmathb$) Then
        stringmatha$ = String$(Len(stringmathb$) - Len(stringmatha$), "0") + stringmatha$
    End If
    addsubx1$ = ""

    Select Case operator$
        Case "+", "="
            For addsubii& = Len(stringmatha$) To 1 Step -1
                addsubx1% = Val(Mid$(stringmatha$, addsubii&, 1)) + Val(Mid$(stringmathb$, addsubii&, 1)) + addsubcarry%
                If addsubx1% > 9 Then addsubx1% = addsubx1% - 10: addsubcarry% = 1 Else addsubcarry% = 0
                addsubx1$ = LTrim$(Str$(addsubx1%)) + addsubx1$
            Next
            If addsubcarry% Then addsubx1$ = "1" + addsubx1$: addsubcarry% = 0
            GoSub replace_decimal
        Case "-"
            For addsubii& = Len(stringmatha$) To 1 Step -1
                addsubx1% = Val(Mid$(stringmatha$, addsubii&, 1)) - Val(Mid$(stringmathb$, addsubii&, 1)) + addsubcarry%
                If addsubx1% < 0 Then addsubx1% = addsubx1% + 10: addsubcarry% = -1 Else addsubcarry% = 0
                addsubx1$ = LTrim$(Str$(addsubx1%)) + addsubx1$
            Next
            If addsubx1$ <> "" And addsubx1$ <> String$(Len(addsubx1$), "0") Then GoSub replace_decimal
            Do Until Left$(addsubx1$, 1) <> "0" ' Remove leading zeros.
                addsubx1$ = Mid$(addsubx1$, 2)
            Loop
            If addsubx1$ = "" Then
                addsubx1$ = "0": addsubsign% = 0
            Else
                If addsubcarry% Then addsubx1$ = "-" + addsubx1$: addsubcarry% = 0
            End If
    End Select

    If addsubsign% Then
        If Left$(addsubx1$, 1) = "-" Then addsubx1$ = Mid$(addsubx1$, 2) Else addsubx1$ = "-" + addsubx1$
    End If
    stringmatha$ = addsubx1$: addsubx1$ = ""
    If operationdivision% Then Return
    stringmathb$ = stringmatha$: stringmatha$ = ""
    If Left$(stringmathb$, 1) = "-" Then
        stringmathb$ = Mid$(stringmathb$, 2)
        n2sign$ = "-"
    Else
        n2sign$ = ""
    End If

    If stringmathb$ = "overflow" Then n2sign$ = "": Exit Sub

    runningtotal$ = n2sign$ + stringmathb$: n2sign$ = ""
    Exit Sub

    replace_decimal:
    If addsubplace& Then
        addsubx1$ = String$(addsubplace& - Len(addsubx1$), "0") + addsubx1$
        addsubx1$ = Mid$(addsubx1$, 1, Len(addsubx1$) - addsubplace&) + "." + Mid$(addsubx1$, Len(addsubx1$) - addsubplace& + 1)
        Do Until Right$(addsubx1$, 1) <> "0" ' Remove trailing zeros in a decimal sum.
            addsubx1$ = Mid$(addsubx1$, 1, Len(addsubx1$) - 1)
            addsubplace& = addsubplace& - 1
        Loop
        If Right$(addsubx1$, 1) = "." Then addsubx1$ = Mid$(addsubx1$, 1, Len(addsubx1$) - 1) ' Number is now an integer.
    End If
    Return

    string_comp:
    Do
        Rem Remove trailing zeros after a decimal point.
        If InStr(acomp$, ".") Then
            Do Until Right$(acomp$, 1) <> "0" And Right$(acomp$, 1) <> "." And Right$(acomp$, 1) <> "-"
                acomp$ = Mid$(acomp$, 1, Len(acomp$) - 1)
            Loop
        End If
        If InStr(bcomp$, ".") Then
            Do Until Right$(bcomp$, 1) <> "0" And Right$(bcomp$, 1) <> "." And Right$(bcomp$, 1) <> "-"
                bcomp$ = Mid$(bcomp$, 1, Len(bcomp$) - 1)
            Loop
        End If

        If Mid$(acomp$, 1, 2) = "-0" Or acomp$ = "" Or acomp$ = "-" Then acomp$ = "0"
        If Mid$(bcomp$, 1, 2) = "-0" Or bcomp$ = "" Or bcomp$ = "-" Then bcomp$ = "0"

        ' A - and +
        If Left$(acomp$, 1) = "-" Then j% = -1
        If Left$(bcomp$, 1) = "-" Then k% = -1
        If k% = 0 And j% Then gl% = -1: Exit Do
        If j% = 0 And k% Then gl% = 1: Exit Do

        ' A decimal and non-decimal.
        j% = InStr(acomp$, ".")
        k% = InStr(bcomp$, ".")
        If j% = 0 And k% Then
            If acomp$ = "0" Then gl% = -1 Else gl% = 1
            Exit Do
        End If
        If k% = 0 And j% Then
            If bcomp$ = "0" Then gl% = 1 Else gl% = -1
            Exit Do
        End If

        ' Both decimals.
        If j% Then
            If acomp$ > bcomp$ Then
                gl% = 1
            ElseIf acomp$ = bcomp$ Then gl% = 0
            ElseIf acomp$ < bcomp$ Then gl% = -1
            End If
            Exit Do
        End If

        ' Both positive or both negative whole numbers.
        Select Case Len(acomp$)
            Case Is < Len(bcomp$)
                gl% = -1
            Case Is = Len(bcomp$)
                If acomp$ = bcomp$ Then
                    gl% = 0
                ElseIf acomp$ > bcomp$ Then gl% = 1
                ElseIf acomp$ < bcomp$ Then gl% = -1
                End If
            Case Is > Len(bcomp$)
                gl% = 1
        End Select
        Exit Do
    Loop
    Return
End Sub

Sub greatest_common_factor (gfca$, gfcb$, limit&&)
    hold_gfca$ = gfca$
    hold_gfcb$ = gfcb$
    numerator$ = gfca$: denominator$ = gfcb$
    ' Make both numbers positive.
    If Mid$(gfca$, 1, 1) = "-" Then gfca$ = Mid$(gfca$, 2)
    If Mid$(gfcb$, 1, 1) = "-" Then gfcb$ = Mid$(gfcb$, 2)

    GoSub string_comp
    If gl% Then Swap gfca$, gfcb$

    Do
        stringmatha$ = gfca$: stringmathb$ = gfcb$
        operator$ = "/": Call string_math(stringmatha$, operator$, stringmathb$, runningtotal$, limit&&)
        If InStr(runningtotal$, ".") Then runningtotal$ = Mid$(runningtotal$, 1, InStr(runningtotal$, ".") - 1)
        stringmatha$ = runningtotal$: stringmathb$ = gfcb$
        operator$ = "*": Call string_math(stringmatha$, operator$, stringmathb$, runningtotal$, limit&&)
        stringmatha$ = gfca$: stringmathb$ = runningtotal$
        operator$ = "-": Call string_math(stringmatha$, operator$, stringmathb$, runningtotal$, limit&&)
        Swap gfca$, gfcb$: gfcb$ = runningtotal$
        If runningtotal$ = "0" Then Exit Do
    Loop

    stringmatha$ = numerator$: stringmathb$ = gfca$
    operator$ = "/": Call string_math(stringmatha$, operator$, stringmathb$, runningtotal$, limit&&)
    numerator$ = runningtotal$
    stringmatha$ = denominator$: stringmathb$ = gfca$
    operator$ = "/": Call string_math(stringmatha$, operator$, stringmathb$, runningtotal$, limit&&)
    denominator$ = runningtotal$
    If betatest% Then
        Print "GFC = "; gfca$; ": Previous fraction: "; hold_gfca$; " / "; hold_gfcb$, "Reduced: "; numerator$; " / "; denominator$
    End If
    gfca$ = numerator$: gfcb$ = denominator$
    Exit Sub

    string_comp:
    Do
        Rem Remove trailing zeros after a decimal point.
        If InStr(a$, ".") Then
            Do Until Right$(a$, 1) <> "0" And Right$(a$, 1) <> "." And Right$(a$, 1) <> "-"
                a$ = Mid$(a$, 1, Len(a$) - 1)
            Loop
        End If
        If InStr(b$, ".") Then
            Do Until Right$(b$, 1) <> "0" And Right$(b$, 1) <> "." And Right$(b$, 1) <> "-"
                b$ = Mid$(b$, 1, Len(b$) - 1)
            Loop
        End If

        If Mid$(a$, 1, 2) = "-0" Or a$ = "" Or a$ = "-" Then a$ = "0"
        If Mid$(b$, 1, 2) = "-0" Or b$ = "" Or b$ = "-" Then b$ = "0"

        ' A - and +
        If Left$(a$, 1) = "-" Then j% = -1
        If Left$(b$, 1) = "-" Then k% = -1
        If k% = 0 And j% Then gl% = -1: Exit Do
        If j% = 0 And k% Then gl% = 1: Exit Do

        ' A decimal and non-decimal.
        j% = InStr(a$, ".")
        k% = InStr(b$, ".")
        If j% = 0 And k% Then
            If a$ = "0" Then gl% = -1 Else gl% = 1
            Exit Do
        End If
        If k% = 0 And j% Then
            If b$ = "0" Then gl% = 1 Else gl% = -1
            Exit Do
        End If

        ' Both decimals.
        If j% Then
            If a$ > b$ Then
                gl% = 1
            ElseIf a$ = b$ Then gl% = 0
            ElseIf a$ < b$ Then gl% = -1
            End If
            Exit Do
        End If

        ' Both positive or both negative whole numbers.
        Select Case Len(a$)
            Case Is < Len(b$)
                gl% = -1
            Case Is = Len(b$)
                If a$ = b$ Then
                    gl% = 0
                ElseIf a$ > b$ Then gl% = 1
                ElseIf a$ < b$ Then gl% = -1
                End If
            Case Is > Len(b$)
                gl% = 1
        End Select
        Exit Do
    Loop
    Return
End Sub

[Pete]

Nice! Thanks for speed testing.

I developed my string math routine as a way to never get caught in "computer" binary math errors. VAL() even fails when strings get too big, so I took that into account, too. I find this to be a great system for big number accounting, probably useful for chemistry molar calculations, but too slow for the kinds of massive numbers produced, as when calculating pi.

BTW: The pi algorithm I used is based on Leibniz's formula. There are other methods, but I'm not sure which is the fastest or most accurate. What's funny is the stone age method of putting a thread around a cylinder of known diameter is faster at getting to 3.14. I imagine at 15min to get that with my routine using Leibniz calculations, it would take several hours to get anything better than 3.14159.

Pete