Android Question I Need Sub Code that Can Compute Large and Very Large Exponential

Theera said:

I think you can use AI Prompt "I need b4x code that can compute large and very large exponential like 3^935687429879864897 or more. Answer to this sample should be: 2.19222399769E+446436360569697305 in B4X's function module"

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emexes said:

B4X:

Dim A As Double = 3
Dim B As Double = 935687429879864897

If True Then    'test case that doesn't overflow Double precision type
    A = 123
    B = 45
    Log(A & TAB & B & TAB & Power(A, B))
End If

Dim LogA As Double = Logarithm(A, 10)
Dim LogApowerB As Double = LogA * B

Dim IntLog As Double = Floor(LogApowerB)
Dim FracLog As Double = LogApowerB - IntLog

Dim ResultMantissa As Double = Power(10, FracLog)
Dim ResultExponent As Double = IntLog

Log(A & TAB & B)
Log(LogA & TAB & LogApowerB)
Log(FracLog & TAB & IntLog)

'''Log(ResultMantissa & " E " & ResultExponent)    'only displays first ~17 digits of ResultExponent
Log(ResultMantissa & " E " & NumberFormat2(ResultExponent, 1, 3, 3, False))

Log output for 123 ^ 45:

Waiting for debugger to connect...
Program started.
123    45    1.1110408185131957E94
123    45
2.0899051114393976    94.04573001477289
0.04573001477288585    94
1.1110408185131417 E 94.000
Program terminated (StartMessageLoop was not called).

Log output for 3 ^ 935687429879864897:

Waiting for debugger to connect...
Program started
3    9.3568742987986496E17
0.47712125471966244    4.4643636056969734E17
0    4.4643636056969734E17
1 E 446436360569697340.000
Program terminated (StartMessageLoop was not called).

The exponent is in the ballpark of your (presumably) correct 446436360569697305, ie first 16 digits match, but precision beyond that has been lost due to Double floating point mantissa being 53-54 bits out of 64.

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Peter Simpson said:

Hello,
I've not tried this myself, it may help, it may not. I just know that this library has something to do with big numbers.

BigNumbers library

If you need to do very accurate claculations using decimal numbers then the normal Java numeric types are not appropriate because, being finite length binary numbers, they cannot accurately represent every possible decimal number. The Java libraries contain a BigDecimal class that is optimised...

www.b4x.com

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emexes said:

I tried same thing in PowerBasic with 80-bit floats instead of 64:

B4X:

DEFEXT A-Z

A = 3
B = 935687429879864897

IF 0 THEN    'test case that doesn't overflow Double precision type
    A = 123
    B = 45
    PRINT A, B, A ^ B
END IF

LogA = LOG10(A)
LogApowerB = LogA * B

IntLog = INT(LogApowerB)
FracLog = LogApowerB - IntLog

ResultMantissa = 10 ^ FracLog
ResultExponent = IntLog

PRINT A, B
PRINT LogA, LogApowerB
PRINT FracLog, IntLog

PRINT ResultMantissa; "E"; ResultExponent    'only displays first ~16 digits of ResultExponent
PRINT ResultMantissa; "E " ; FORMAT$(ResultExponent, "0.000")

and it got closer to the full result (exponent is correct, but only a few bits of precision were left for the mantissa) :

Program output:

 3             9.35687429879865E+17
 .477121254719662            4.46436360569697E+17
 .375          4.46436360569697E+17
 2.37137370566166 E 4.46436360569697E+17
 2.37137370566166 E 446436360569697305.000

so all we need to do now is find ourselves a working VAX running BASIC and we'd probably have a matching mantissa too:

View attachment 166387

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Daestrum said:

Got this result
Result: 3.6573543923 E446436360569697303

using this code (written with help of Copilot)

B4X:

#if java
import java.math.BigDecimal;
import java.math.MathContext;
import java.math.RoundingMode;

public static void power(String n, String exp) {
    BigDecimal base = new BigDecimal(n);
    BigDecimal exponent = new BigDecimal(exp);

    MathContext mc = new MathContext(60, RoundingMode.HALF_UP); // High precision

    // log10(3) ≈ 0.47712125472
    BigDecimal log10Base = new BigDecimal(Math.log10(base.doubleValue()), mc);
    BigDecimal log10Result = exponent.multiply(log10Base, mc);

    // Extract exponent and fractional part
    BigDecimal exponentPart = log10Result.setScale(0, RoundingMode.FLOOR);
    BigDecimal fractionalPart = log10Result.subtract(exponentPart, mc);

    // Use fractional part to estimate mantissa via log rules:
    // mantissa ≈ 10^fractionalPart
    double mantissa = Math.pow(10, fractionalPart.doubleValue());

    System.out.printf("Result: %.10f E%s%n", mantissa, exponentPart.toPlainString());
}
#End If

called like

B4X:

Me.as(JavaObject).RunMethod("power",Array("3","935687429879864897"))

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rwblinn said:

Here another example.

B4X pages project using this library with Inline Java. Tested with B4J.

The result: 2.19222399769E+446436360569697305

Copy big-math-2.3.2.jar to the B4J additional libraries folder.

B4X:

Sub Class_Globals
    Private Root As B4XView
    Private xui As XUI
    ' Inline Java object
    Private joInlineJava As JavaObject = Me
End Sub

Public Sub Initialize
'    B4XPages.GetManager.LogEvents = True
End Sub

'This event will be called once, before the page becomes visible.
Private Sub B4XPage_Created (Root1 As B4XView)
    Root = Root1
    Root.LoadLayout("MainPage")
End Sub

Private Sub Button1_Click
    ' Example: compute 3^935687429879864897 with 12 digits
    Dim result As String
    result = joInlineJava.RunMethod("HugePowerSci", Array("3", "935687429879864897", 12))
   
    Log(result)    ' > 2.19222399769E+446436360569697305
    xui.MsgboxAsync($"3^935687429879864897 with 12 digits: ${result}"$, "HugePower Result")
End Sub

#If JAVA
import ch.obermuhlner.math.big.BigDecimalMath;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;

public String HugePowerSci(String baseStr, String expStr, int digits) {
    try {
        import java.math.BigDecimal;
        import java.math.BigInteger;
        import java.math.MathContext;
        import ch.obermuhlner.math.big.BigDecimalMath;

        BigDecimal base = new BigDecimal(baseStr);
        BigInteger exp = new BigInteger(expStr);
        MathContext mc = new MathContext(digits + 50); // high precision

        // log10(base)
        BigDecimal log10Base = BigDecimalMath.log10(base, mc);

        // exponent * log10(base)
        BigDecimal exponentTimesLog = new BigDecimal(exp).multiply(log10Base, mc);

        // integer and fractional parts
        BigInteger intPart = exponentTimesLog.toBigInteger();
        BigDecimal fracPart = exponentTimesLog.subtract(new BigDecimal(intPart), mc);

        // significand = 10^fractional_part
        BigDecimal significand = BigDecimalMath.pow(BigDecimal.TEN, fracPart, mc);

        // round to requested digits
        significand = significand.round(new MathContext(digits));

        return significand.toPlainString() + "E+" + intPart.toString();
    } catch (Exception e) {
        return "Error: " + e.getMessage();
    }
}
#End If

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rwblinn said:

Here another example.

B4X pages project using this library with Inline Java. Tested with B4J.

The result: 2.19222399769E+446436360569697305

Copy big-math-2.3.2.jar to the B4J additional libraries folder.

B4X:

Sub Class_Globals
    Private Root As B4XView
    Private xui As XUI
    ' Inline Java object
    Private joInlineJava As JavaObject = Me
End Sub

Public Sub Initialize
'    B4XPages.GetManager.LogEvents = True
End Sub

'This event will be called once, before the page becomes visible.
Private Sub B4XPage_Created (Root1 As B4XView)
    Root = Root1
    Root.LoadLayout("MainPage")
End Sub

Private Sub Button1_Click
    ' Example: compute 3^935687429879864897 with 12 digits
    Dim result As String
    result = joInlineJava.RunMethod("HugePowerSci", Array("3", "935687429879864897", 12))
 
    Log(result)    ' > 2.19222399769E+446436360569697305
    xui.MsgboxAsync($"3^935687429879864897 = ${result}"$, "HugePower Result")
End Sub

#If JAVA
import ch.obermuhlner.math.big.BigDecimalMath;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.math.MathContext;

public String HugePowerSci(String baseStr, String expStr, int digits) {
    try {
        import java.math.BigDecimal;
        import java.math.BigInteger;
        import java.math.MathContext;
        import ch.obermuhlner.math.big.BigDecimalMath;

        BigDecimal base = new BigDecimal(baseStr);
        BigInteger exp = new BigInteger(expStr);
        MathContext mc = new MathContext(digits + 50); // high precision

        // log10(base)
        BigDecimal log10Base = BigDecimalMath.log10(base, mc);

        // exponent * log10(base)
        BigDecimal exponentTimesLog = new BigDecimal(exp).multiply(log10Base, mc);

        // integer and fractional parts
        BigInteger intPart = exponentTimesLog.toBigInteger();
        BigDecimal fracPart = exponentTimesLog.subtract(new BigDecimal(intPart), mc);

        // significand = 10^fractional_part
        BigDecimal significand = BigDecimalMath.pow(BigDecimal.TEN, fracPart, mc);

        // round to requested digits
        significand = significand.round(new MathContext(digits));

        return significand.toPlainString() + "E+" + intPart.toString();
    } catch (Exception e) {
        return "Error: " + e.getMessage();
    }
}
#End If

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omo said:

the reason why I was getting 1E at the mantissa while exponent was always correct. So, it was due to precision lost

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omo said:

Can you use bigdecimals for this your logarithm approach? Are we going to get all correct answer without loss in precision?

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omo said:

while the exponent is correct, but I can't still rely on such answer because this difference is still huge

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emexes said:

recursive sum of the digits

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emexes said:

Bear in mind that even if you calculate an answer accurate to a million significant digits, the remaining 446,436,360,568,697,306 digits will be randomlike gibberish.

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emexes said:

Apparently the correct name for this is digital root which would not have been my first guess at the definition of that term

https://x.com/i/grok/share/8NXsl7ipGLG22SXjQ5XZ40xLB

x.com

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