Hex

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Revision as of 20:22, 17 October 2007 by Ppaatt Lynagh (talk | contribs) (adopt Talk:Hex suggestion of lsn = least significant nybble, rather than lsbs)
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Function: string hex(integer value);

Returns the hexadecimal nybbles of the signed integer value in order. Specifically returns the nybbles from most to least significant, starting with the first nonzero nybble, folding every nybble to lower case, and beginning with the nonnegative prefix "0x" or the negative prefix "-0x".

Parameters:

• integer value – signed value to be expressed as signed hex

Note: Results with eight nybbles begin always with one of the positive signed nybbles 1 2 3 4 5 6 7, never with a zero or unsigned nybble 0 8 9 A B C D E F.

Caution: This page was a work in progress as of 2007-10. The specification, the implementations, the demo, the demo results, and the alternatives may not yet be totally consistent. See the discussion tab.

Implementations

Here you see code that implements the hex function specification, demo code that calls the hex function, and a copy of exactly the results you should see when you run the demo.

You see three kinds of code that implement the one specification. The concise & conventional code explains and implements the specification. The small code reduces the code size reported by llGetFreeMemory. The fast code reduces the run time reported by llGetTimestamp.

Concise & Conventional

You should choose this code when you care more about concise & conventional than about small & fast.

You should feel that this concise & conventional code is easy to review and modify. For example, you should immediately understand the comment that tells you how to substitute the easy-to-read upper case A B C D E F nybbles of IBM style for the easy-to-type lower case a b c d e f nybbles of AT&T style. Also you should immediately see what results to expect this code to return for any input. 

// http://wiki.secondlife.com/wiki/hex

string XDIGITS = "0123456789abcdef"; // could be "0123456789ABCDEF"

string bits2nybbles(integer bits)
{
    string nybbles = "";
    while (bits)
    {
        integer lsn = bits & 0xF; // least significant nybble
        string nybble = llGetSubString(XDIGITS, lsn, lsn);
        nybbles = nybble + nybbles;
        bits = bits >> 4; // discard the least significant bits at right
        bits = bits & 0xfffFFFF; // discard the sign bits at left
    }
    return nybbles;
}

string hex(integer value)
{
    if (value < 0)
    {
        return "-0x" + bits2nybbles(-value);
    }
    else if (value == 0)
    {
        return "0x0"; // bits2nybbles(value) == "" when (value == 0)
    }
    else // if (0 < value)
    {
        return "0x" + bits2nybbles(value);
    }
}

347 bytes of code reported by llGetFreeMemory -- more than the small code and more than the fast code

FIXME milliseconds of run time to calculate "-0x80000000" reported by llGetTimestamp -- more than the small code and more than the fast code

Small

You should choose this code when you care more about small & fast than about concise & conventional.

We wrote this small code to show how to reduce the code size reported by llGetFreeMemory. We think this small code produces the same results as the concise & conventional code. After adequate education & review, you should agree. 

// http://wiki.secondlife.com/wiki/hex

string hex(integer value)
{
    string lead = "0x";
    if (value & 0x80000000) // means (integer < 0) but is smaller and faster
    {
        lead = "-0x";
        value = -value;
    }
    string nybbles = "";
    do
    {
        integer lsn = value & 0xF; // least significant nybble
        nybbles = llGetSubString("0123456789abcdef", lsn, lsn) + nybbles;
    } while ((value = (0xfffFFFF & (value >> 4))));
    return lead + nybbles;
}

197 bytes of code reported by llGetFreeMemory -- less than the concise & conventional code and less than the fast code

FIXME milliseconds of run time to calculate "-0x80000000" reported by llGetTimestamp -- less than the concise & conventional code, but more than the fast code

Fast

You should choose this code when you care more about fast & small than about concise & conventional.

We wrote this fast code to show how to reduce the run time reported by llGetTimestamp. We think this fast code produces the same results as the concise & conventional code. After adequate education & review, you should agree. This code leaves as little work inside the loop as possible. This code might not be as fast as code that unrolls the loop completely. This code might not be as fast as code which implements hex as one function rather than as two functions. 

// http://wiki.secondlife.com/wiki/hex

string XDIGITS = "0123456789abcdef"; // could be "0123456789ABCDEF"

string hexu(integer bits)
{
    integer lsn = (bits & 0xF); // least significant nybble
    string nybbles = llGetSubString(XDIGITS, lsn, lsn);
    if ((bits = (0xfffFFFF & (bits >> 4))))
    {
        do
        {
            nybbles = llGetSubString(XDIGITS, lsn = (bits & 0xF), lsn) + nybbles;
        } while ((bits = (bits >> 4)));
    }
    return "0x" + nybbles;
}

string hex(integer value)
{
    //saves one byte over "value < 0" and is faster.
    if (value & 0x80000000) return "-" + hexu(-value);
    return hexu(value);
}

337 bytes of code reported by llGetFreeMemory - less than concise & conventional code, but more than the small code

FIXME milliseconds of run time to calculate "-0x80000000" reported by llGetTimestamp - less than the concise & conventional code and less than the small code

Demo

Run this demo code to confirm that you get exactly the expected demo results below. We chose test cases that astonish people new to hex.

We also chose test cases that astonish people new to LSL permission masks. You'll get the permission mask results we show if you create a New Script to run this demo in. If instead you tried modifying some old script to run this demo, then you might have to edit its permission masks to get the demo results that we show here. 

default
{
    state_entry()
    {
        llOwnerSay("Hello");
        llOwnerSay(hex(0) + " == 0");
        llOwnerSay(hex(0x00FEDC00 & -0x00FEDC00) + " == (0x00FEDC00 & -0x00FEDC00)");
        llOwnerSay(hex(1 << 30) + " == (1 << 30)");
        llOwnerSay(hex(0x80000000) + " == 0x80000000");
        llOwnerSay(hex(0xFEDC9876) + " == 0xFEDC9876");
        llOwnerSay(hex(-1) + " == -1");
        llOwnerSay(hex(0x123456789) + " == 0x123456789");
        llOwnerSay("OK");
        
        llOwnerSay("Hello again");
        string item = llGetScriptName();
        llOwnerSay(hex(llGetInventoryPermMask(item, MASK_BASE)) + " as base");
        llOwnerSay(hex(llGetInventoryPermMask(item, MASK_OWNER)) + " by owner");
        llOwnerSay(hex(llGetInventoryPermMask(item, MASK_GROUP)) + " by group");
        llOwnerSay(hex(llGetInventoryPermMask(item, MASK_EVERYONE)) + " by anyone");
        llOwnerSay(hex(llGetInventoryPermMask(item, MASK_NEXT)) + " by next owner");
        llOwnerSay("aka " + (string) llGetInventoryPermMask(item, MASK_NEXT));
        llOwnerSay("OK");
    }
}
Demo Results:

Running the demo to call your choice of code should produce exactly these results: 

Hello
0x0 == 0
0x400 == (0x00FEDC00 & -0x00FEDC00)
0x40000000 == (1 << 30)
-0x80000000 == 0x80000000
-0x123678a == 0xFEDC9876
-0x1 == -1
-0x1 == 0x123456789
OK
Hello again
0x7fffffff as base
0x7fffffff by owner
0x0 by group
0x0 by anyone
0x82000 by next owner
aka 532480
OK

Design Rationale

The specification requires exactly the same results as the hex function of the Python scripting language.

The specification reproduces how hex integer literals often appear in LSL script, conforming to such arbitrary and traditional AT&T C conventions as:

  1. return lower case a b c d e f rather than upper case A B C D E F,
  2. return a signed 31-bit result if negative, rather than an unsigned 32-bit result,
  3. omit the leading quads of zeroed bits, except returns "0x0" rather than "0x" when the result is zero,
  4. return a meaningless "0" before the "x", as LSL and C compilers require,
  5. return the "x" on the left as in LSL and C, not the "h" on the right as in Assembly code, and
  6. return the nybbles listed from most to least significant as in English, not listed from least to most significant as in Arabic.

Brief doc for the Python hex function appears buried deep within http://docs.python.org/lib/built-in-funcs.html

Disputes over the detailed specification of the Python hex function appear buried deep within http://www.python.org/dev/peps/pep-0237/

As you read this page, you have to wade thru more than one implementation because our LSL wiki serves more than one community of LSL authors. New authors need to see a concise & conventional exemplar, experts find appropriate uses for the small & fast exemplars.

We don't know how to write LSL that implements a hex function that is as concise as our most concise, as conventional as our most conventional, as small as our smallest, and as fast as our fastest, all simultaneously. We think that goal is an impossibility.

Alternatives

You can make the code smaller and faster still whenever you can accept the cost of abandoning the conventional specification.

Different & Small - Signed Only

Calling bits2nybbles alone may be smaller than any implementation of the hex function.

Different & Small - Signed or Unsigned

This version returns a signed or an unsigned result, bizarrely raising code size and run time to give you a run time choice of whichever you prefer.

Here is a version where we have merged bits2nybbles into hex. This merge allows for a considerable savings in bytecode. This savings evaporates if the function is explicitly called from more than 10 places in the script (as compared to the double function size implementation). This of course assumes you need both sets of functionality -- an assumption entirely outside the specification. 

// http://wiki.secondlife.com/wiki/hex

string hex(integer value, integer signed)
{
    string lead = "0x";
    if((value & 0x80000000) && signed)
    {//saves one byte over "value < 0" and is faster.
        lead = "-0x";
        value = -value;
    }
    string nybbles = "";
    do //variable recycling is ugly but it saves bytecode
        nybbles = llGetSubString("0123456789abcdef", signed = (value & 0xF), signed) + nybbles;
    while ((value = (0xfffFFFF & (value >> 4))));
    return lead + nybbles;
}

200 bytes of code reported by llGetFreeMemory

TBD milliseconds of run time to calculate "-0x80000000" reported by llGetTimestamp

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