Difference between revisions of "Float2Hex"

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===Safe===
===Safe===
This version isn't as fast but will work in LSLEditor, LSO and Mono.
This version isn't as fast but will work in LSLEditor, LSO and Mono.
<lsl>
<lsl>string hexc="0123456789ABCDEF";//faster
string hexc="0123456789ABCDEF";//faster


string Float2Hex(float input)// LSLEditor Safe, LSO Safe, Mono Safe
string Float2Hex(float input)// LSLEditor Safe, LSO Safe, Mono Safe
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         integer exponent = llFloor((llLog(unsigned) / 0.69314718055994530941723212145818));//floor(log2(b)) + rounding error
         integer exponent = llFloor((llLog(unsigned) / 0.69314718055994530941723212145818));//floor(log2(b)) + rounding error


         integer mantissa_a = (integer)(unsigned = ((unsigned / llPow(2., exponent += ~((exponent >> 31) & -2))) * 0x4000000));
         integer mantissa_a = (integer)(unsigned = ((unsigned / llPow(2., exponent -= ((exponent >> 31) | 1))) * 0x4000000));
         integer index = (integer)(llLog(mantissa_a & -mantissa_a) / 0.69314718055994530941723212145818);//index of first 'on' bit
         integer index = (integer)(llLog(mantissa_a & -mantissa_a) / 0.69314718055994530941723212145818);//index of first 'on' bit
         string str = "p" + (string)(exponent + index - 26);//final exponent for single or simple double
         string str = "p" + (string)(exponent + index - 26);//final exponent for single or simple double
Line 52: Line 51:
     }//integers pack well so anything that qualifies as an integer we dump as such, supports netative zero
     }//integers pack well so anything that qualifies as an integer we dump as such, supports netative zero
     return llDeleteSubString((string)input,-7,-1);//trim off the float portion, return an integer
     return llDeleteSubString((string)input,-7,-1);//trim off the float portion, return an integer
}
}</lsl>
</lsl>


===Double Unsafe===
===Double Unsafe===
Fast & accurate in LSO and Mono but will not work properly in [[LSLEditor]].
Fast & accurate in LSO and Mono but will not work properly in [[LSLEditor]].
<lsl>
<lsl>string hexc="0123456789ABCDEF";//faster
string hexc="0123456789ABCDEF";//faster


string Float2Hex(float input)// LSLEditor Unsafe, LSO Safe, Mono Safe
string Float2Hex(float input)// LSLEditor Unsafe, LSO Safe, Mono Safe
Line 67: Line 64:
         integer exponent = llFloor((llLog(unsigned) / 0.69314718055994530941723212145818));//floor(log2(b)) + rounding error
         integer exponent = llFloor((llLog(unsigned) / 0.69314718055994530941723212145818));//floor(log2(b)) + rounding error


         integer mantissa = (integer)((unsigned / llPow(2., exponent += ~((exponent >> 31) & -2))) * 0x4000000);//shift up into integer range
         integer mantissa = (integer)((unsigned / llPow(2., exponent -= ((exponent >> 31) | 1))) * 0x4000000);//shift up into integer range
         integer index = (integer)(llLog(mantissa & -mantissa) / 0.69314718055994530941723212145818);//index of first 'on' bit
         integer index = (integer)(llLog(mantissa & -mantissa) / 0.69314718055994530941723212145818);//index of first 'on' bit
         string str = "p" + (string)(exponent + index - 25);
         string str = "p" + (string)(exponent + index - 25);
Line 80: Line 77:
     }//integers pack well so anything that qualifies as an integer we dump as such, supports netative zero
     }//integers pack well so anything that qualifies as an integer we dump as such, supports netative zero
     return llDeleteSubString((string)input,-7,-1);//trim off the float portion, return an integer
     return llDeleteSubString((string)input,-7,-1);//trim off the float portion, return an integer
}
}</lsl>
</lsl>


<br /> Usage:<br />
<br /> Usage:<br />
Line 137: Line 133:
string hexc="0123456789ABCDEF";//faster
string hexc="0123456789ABCDEF";//faster


string Float2Hex(float a)
string Float2Hex(float input)// LSLEditor Safe, LSO Safe, Mono Safe
{// Copyright Strife Onizuka, 2006-2007, LGPL, http://www.gnu.org/copyleft/lesser.html
{// Copyright Strife Onizuka, 2006-2007, LGPL, http://www.gnu.org/copyleft/lesser.html or (cc-by) http://creativecommons.org/licenses/by/3.0/
     //If it's zero, the zero stripper will hang, lets avoid that
     //LL screwed up hex integers support in rotation & vector string typecasting
     if(a)
     if(input != (integer)input)
     {//we need to find the exponent, but to do that we need to take the log of the number (or run a while loop)
     {
         float b = llFabs(a);//logs don't work on negatives.
         //logs don't work on negatives.
         string f = "p";//This is a trade off, slightly slower (only slightly) for a couple bytes savings (10)
         float unsigned = llFabs(input);
         //To get the exponent we need to round the integer portion down or the log2(b)
         //calculate the exponent, this value is approxomit and it unfortunately will be rounded towards the extreams
        //  LSL doesn't have log2, so we use one of the laws of logs to get it from the natural log
         integer exponent = llFloor((llLog(unsigned) / 0.69314718055994530941723212145818));//floor(log2(b)) + rounding error
         integer c = llFloor(llLog(b) / 0.69314718055994530941723212145818);//floor(log2(b))
         //adjust the exponent so it errors towards zero
         //There is a rounding error in the exponent that causes it to round up, this usualy isn't a problem as the
         //if we don't adjust it, it will crash the script on overflow (bad)
         // exponent only is only used to shift the number. It becomes a problem when dealing with float max as
         exponent -= ((exponent >> 31) | 1);
        //  it will round up to 128; which will crash llPow.
        //using the exponent calculate the upper part of the mantisa with a few extra bits
         if(c > 127) c = 127;//catch fatal rounding error in exponent.
         unsigned = (unsigned / llPow(2., exponent)) * 0x4000000;
         //Q: why not do (b * llPow(2,-c))? A: because the range of floats are different at the top and bottom
         //store it to an integer
         // at the top it's 2^127 at the bottom it's 2^-149; and if you tried to do this otherwise,
        integer mantissa_a = (integer)unsigned;
         // llPow would crash with an overflow. Then we multiply it by 2 ^ 24, floats only use 23 bits for the mantisa,
         //find the first turned on bit, this also corrects for the rounding errors in the exponent
         // we cannot add it into c because we could overflow llPow; we correct the value of c later.
         integer index = (integer)(llLog(mantissa_a & -mantissa_a) / 0.69314718055994530941723212145818);//index of first 'on' bit
         // Instead of using llPow(2.0, c) we are using (float)("0x1p"+(string)c), it's 10% faster and 16 bytes lighter.
         //write the final exponent for single or simple double
         integer d = (integer)((b / (float)("0x1p"+(string)c)) * 0x1000000);//shift up into integer range
        string str = "p" + (string)(exponent + index - 26);
        while(!(d & 0xf))
        //subtract the upper part of the mantisa from the mantisa so that we have the fpart left
        {//strip extra zeros off before converting or they break "p"
         integer mantissa_b = (integer)((unsigned - mantissa_a) * 0x10000000);
             //a catch22 of sorts, you cannot know exactly how far to shift it till after you have shifted it
        //check to see if there is an fpart
             d = d >> 4;
        if(mantissa_b)
             c+=4; //for each zero stripped we must adjust the exponent
        {
            //this code only gets activated if the lower bytes of the double mantissa are set
            //this code won't get activated in single percission environments
            //there was an fpart so the shift and final exponenet are wrong
            index = (integer)(llLog(mantissa_b & -mantissa_b) / 0.69314718055994530941723212145818);
            //generate the new final exponent
            str = "p" + (string)(exponent + index - 54);
             //apply the shift and adds some bits from the upper part
            //mask it so it so we can shift check
             mantissa_b = (mantissa_b >> index) | ((mantissa_a << (28 - index)) & 0x0FFFFFFF);
             //use the shift checking exclusively if there is no upper part to the mantissa
            //we recycle exponent
            exponent = -7 * !!mantissa_a;
            //if there is an upper part to the mantissa then the loop must run 7 times; otherwise run as many times as needed (less then 7 maybe)
            //we do this by peaking at the sine on exponent
            do
                str = llGetSubString(hexc, 15 & mantissa_b, 15 & mantissa_b) + str;
            while((mantissa_b = (mantissa_b >> 4)) | ((exponent = -~exponent) & 0x80000000));//dodge bugs in LSLEditor
         }
         }
         do//convert to hex
         //mantissa_a will always be non-zero before shifting unless it is in the denormalized range.
             f = llGetSubString(hexc,15&d,15&d) + f;
        //if it is double then after the shifting we can't be sure
        while(d = d >> 4);
        //we wouldn't want to pad the output with an extra zero by accident.
         if(a < 0)//final formating & c adjustment (from making it an integer)
        if((mantissa_a = (mantissa_a >> index)))
             return "-0x" + f +(string)(c - 24);
             do
         return "0x" + f +(string)(c - 24);
                str = llGetSubString(hexc, 15 & mantissa_a, 15 & mantissa_a) + str;
     }//no point in this getting special formating.
            while((mantissa_a = (mantissa_a >> 4)) );
     return "0";//zero would hang the zero stripper.
}
         if(input < 0)
</lsl>
             return "-0x" + str;
         return "0x" + str;
     }
    //integers pack well so anything that qualifies as an integer we dump as such, supports netative zero
     //trim off the float portion, return an integer
    return llDeleteSubString((string)input,-7,-1);
}</lsl>


==Double2Hex==
==Double2Hex==

Revision as of 23:31, 31 January 2008

About

Use to encode floats in hex notation, minimal overhead, does not introduce errors. No special decoder needed. Try it.

Use this instead of (string) when converting floats to strings.

LSL (float) typecast supports C99 hex floats. This is good because with hex you can store floats without the need for a special decoder (just use (float)) and since hex is a power of 2 format, floats can be stored without any loss or rounding errors.

A similar function (also by me) Float to Scientific Notation, works much the same way (except it uses base 10). The trouble is it has to emulates higher precision math, in a scripting language this is a bad solution. Because of the base conversion using logs would introduce a huge accumulated error (read as: floats suck). Resulting in the need to do the shifting with a while loop. This wasn't good enough, even with 32 bits small numbers would still be corrupted by the shifting. An integer and a float (or in one rewrite two integers) were used, one to store the integer portion, and the other the float. This worked, but was slow as all get out for large and small numbers (2 seconds). Finaly some optical approches were used to do the conversion which sped up large numbers. While accurate, the function was slow and used alot of memory.

This function is much faster, it requires about 900 instructions with little deviation from that number. In the sceme of things it's not too costly (on a not too lagged sim that is about 0.12 seconds). There isn't much that can be done to reduce the number of instructions executed, unless LL wants to give us an llInteger2HexString or an llFloat2HexString.

Update

Auto adjust so doubles can be used instead of floats. The safe version should be Mono ready.

Float2Hex

When SVC-1342 & SVC-1376 are fixed these version will be updated.

Safe

This version isn't as fast but will work in LSLEditor, LSO and Mono. <lsl>string hexc="0123456789ABCDEF";//faster

string Float2Hex(float input)// LSLEditor Safe, LSO Safe, Mono Safe {// Copyright Strife Onizuka, 2006-2007, LGPL, http://www.gnu.org/copyleft/lesser.html or (cc-by) http://creativecommons.org/licenses/by/3.0/ 

   if(input != (integer)input)//LL screwed up hex integers support in rotation & vector string typecasting
   {//this also keeps zero from hanging the zero stripper.
       float unsigned = llFabs(input);//logs don't work on negatives.
       integer exponent = llFloor((llLog(unsigned) / 0.69314718055994530941723212145818));//floor(log2(b)) + rounding error

       integer mantissa_a = (integer)(unsigned = ((unsigned / llPow(2., exponent -= ((exponent >> 31) | 1))) * 0x4000000));
       integer index = (integer)(llLog(mantissa_a & -mantissa_a) / 0.69314718055994530941723212145818);//index of first 'on' bit
       string str = "p" + (string)(exponent + index - 26);//final exponent for single or simple double
       integer mantissa_b = (integer)((unsigned - mantissa_a) * 0x10000000);
       if(mantissa_b)//this code only gets activated if the lower bytes of the double mantissa are set
       {//this code won't get activated in single percission environments
           str = "p" + (string)(exponent + (index = (integer)(llLog(mantissa_b & -mantissa_b) / 0.69314718055994530941723212145818)) - 54);//final exponent
           mantissa_b = (mantissa_b >> index) | ((mantissa_a << (28 - index)) & 0x0FFFFFFF);//mask it so it so we can shift check
           exponent = -7 * !!mantissa_a;// use the shift checking exclusively if there is no mantissa_a
           do// if there is mantissa_a then the loop must run 7 times; otherwise run as many times as needed
               str = llGetSubString(hexc, 15 & mantissa_b, 15 & mantissa_b) + str;
           while((mantissa_b = (mantissa_b >> 4)) | ((exponent = -~exponent) & 0x80000000));//dodge bugs in LSLEditor
       }// mantissa_a will always be non-zero before shifting unless it is in the denormalized range.
       if((mantissa_a = (mantissa_a >> index)))//if it is double then after the shifting we can't be sure
           do//we wouldn't want to pad the output with an extra zero by accident.
               str = llGetSubString(hexc, 15 & mantissa_a, 15 & mantissa_a) + str;
           while((mantissa_a = (mantissa_a >> 4)) );

       if(input < 0)
           return "-0x" + str;
       return "0x" + str;
   }//integers pack well so anything that qualifies as an integer we dump as such, supports netative zero
   return llDeleteSubString((string)input,-7,-1);//trim off the float portion, return an integer

}</lsl>

Double Unsafe

Fast & accurate in LSO and Mono but will not work properly in LSLEditor. <lsl>string hexc="0123456789ABCDEF";//faster

string Float2Hex(float input)// LSLEditor Unsafe, LSO Safe, Mono Safe {// Copyright Strife Onizuka, 2006-2007, LGPL, http://www.gnu.org/copyleft/lesser.html or (cc-by) http://creativecommons.org/licenses/by/3.0/ 

   if(input != (integer)input)//LL screwed up hex integers support in rotation & vector string typecasting
   {//this also keeps zero from hanging the zero stripper.
       float unsigned = llFabs(input);//logs don't work on negatives.
       integer exponent = llFloor((llLog(unsigned) / 0.69314718055994530941723212145818));//floor(log2(b)) + rounding error

       integer mantissa = (integer)((unsigned / llPow(2., exponent -= ((exponent >> 31) | 1))) * 0x4000000);//shift up into integer range
       integer index = (integer)(llLog(mantissa & -mantissa) / 0.69314718055994530941723212145818);//index of first 'on' bit
       string str = "p" + (string)(exponent + index - 25);
       mantissa = mantissa >> index;
       do
           str = llGetSubString(hexc, 15 & mantissa, 15 & mantissa) + str;
       while(mantissa = mantissa >> 4);

       if(input < 0)
           return "-0x" + str;
       return "0x" + str;
   }//integers pack well so anything that qualifies as an integer we dump as such, supports netative zero
   return llDeleteSubString((string)input,-7,-1);//trim off the float portion, return an integer

}</lsl>


Usage:

<lsl> string a = Float2Hex(100.000000); // a == "100" string b = Float2Hex(14353.344727); // b == 0xE04561p-10 float c = (float)a;//c == 100.000000 float d = (float)b;//d == 14353.344727 </lsl>


Helper Functions:

<lsl> string Rot2Hex(rotation a) { 

   return "<"+Float2Hex(a.x)+","+Float2Hex(a.y)+","+Float2Hex(a.z)+","+Float2Hex(a.s)+">";

}

string Vec2Hex(vector a) { 

   return "<"+Float2Hex(a.x)+","+Float2Hex(a.y)+","+Float2Hex(a.z)+">";

}

string DumpList2String(list input, string seperator)// for csv use ", " as the seperator. { 

   integer b = (input != []);
   string c;
   string d;
   integer e;
   if(b)
   {
       @top;
       if((e = llGetListEntryType(input,--b)) == TYPE_FLOAT)
           d=Float2Hex(llList2Float(input,b));
       else if(e == TYPE ROTATION)
           d=Rot2Hex(llList2Rot(input,b));
       else if(e == TYPE_VECTOR)
           d=Vec2Hex(llList2Vector(input,b));
       else
           d=llList2String(input,b);
       if(b)
       {
           c = d + (c=seperator) + c;
           jump top;
       }
   }
   return (c=d) + c;

} </lsl>


How it works:

<lsl> string hexc="0123456789ABCDEF";//faster

string Float2Hex(float input)// LSLEditor Safe, LSO Safe, Mono Safe {// Copyright Strife Onizuka, 2006-2007, LGPL, http://www.gnu.org/copyleft/lesser.html or (cc-by) http://creativecommons.org/licenses/by/3.0/ 

   //LL screwed up hex integers support in rotation & vector string typecasting
   if(input != (integer)input)
   {
       //logs don't work on negatives.
       float unsigned = llFabs(input);
       //calculate the exponent, this value is approxomit and it unfortunately will be rounded towards the extreams
       integer exponent = llFloor((llLog(unsigned) / 0.69314718055994530941723212145818));//floor(log2(b)) + rounding error
       //adjust the exponent so it errors towards zero
       //if we don't adjust it, it will crash the script on overflow (bad)
       exponent -= ((exponent >> 31) | 1);
       //using the exponent calculate the upper part of the mantisa with a few extra bits
       unsigned = (unsigned / llPow(2., exponent)) * 0x4000000;
       //store it to an integer
       integer mantissa_a = (integer)unsigned;
       //find the first turned on bit, this also corrects for the rounding errors in the exponent
       integer index = (integer)(llLog(mantissa_a & -mantissa_a) / 0.69314718055994530941723212145818);//index of first 'on' bit
       //write the final exponent for single or simple double
       string str = "p" + (string)(exponent + index - 26);
       //subtract the upper part of the mantisa from the mantisa so that we have the fpart left
       integer mantissa_b = (integer)((unsigned - mantissa_a) * 0x10000000);
       //check to see if there is an fpart
       if(mantissa_b)
       {
           //this code only gets activated if the lower bytes of the double mantissa are set
           //this code won't get activated in single percission environments
           //there was an fpart so the shift and final exponenet are wrong
           index = (integer)(llLog(mantissa_b & -mantissa_b) / 0.69314718055994530941723212145818);
           //generate the new final exponent
           str = "p" + (string)(exponent + index - 54);
           //apply the shift and adds some bits from the upper part
           //mask it so it so we can shift check
           mantissa_b = (mantissa_b >> index) | ((mantissa_a << (28 - index)) & 0x0FFFFFFF);
           //use the shift checking exclusively if there is no upper part to the mantissa
           //we recycle exponent 
           exponent = -7 * !!mantissa_a;
           //if there is an upper part to the mantissa then the loop must run 7 times; otherwise run as many times as needed (less then 7 maybe)
           //we do this by peaking at the sine on exponent
           do
               str = llGetSubString(hexc, 15 & mantissa_b, 15 & mantissa_b) + str;
           while((mantissa_b = (mantissa_b >> 4)) | ((exponent = -~exponent) & 0x80000000));//dodge bugs in LSLEditor
       }
       //mantissa_a will always be non-zero before shifting unless it is in the denormalized range.
       //if it is double then after the shifting we can't be sure
       //we wouldn't want to pad the output with an extra zero by accident.
       if((mantissa_a = (mantissa_a >> index)))
           do
               str = llGetSubString(hexc, 15 & mantissa_a, 15 & mantissa_a) + str;
           while((mantissa_a = (mantissa_a >> 4)) );

       if(input < 0)
           return "-0x" + str;
       return "0x" + str;
   }
   //integers pack well so anything that qualifies as an integer we dump as such, supports netative zero
   //trim off the float portion, return an integer
   return llDeleteSubString((string)input,-7,-1);

}</lsl>

Double2Hex

LongDouble2Hex

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