Difference between revisions of "Float2Sci"

From Second Life Wiki
Jump to navigation Jump to search
m
m (→‎Code: i should have compiled the code, I would have realized that I forgot some stuff.)
Line 18: Line 18:
     string mantissa = (string)frac;//this may be a string of about 47 characters long.
     string mantissa = (string)frac;//this may be a string of about 47 characters long.
     integer exponent = -6;//default exponent for optical method
     integer exponent = -6;//default exponent for optical method
     if(frac != (float)(mantissa = llDeleteSubString(mantissa, -7, -7)))
     if(frac == (float)(mantissa = llDeleteSubString(mantissa, -7, -7)))
     {//optical failed
        jump optical;
        //Ugly Math version; ugly in the sense that it is slow and not as elegant as working with it as a string.
 
        //A) calculate the exponent via approximation of C log2()
     //optical failed
        //B) use kludge to avert fatal error in approximation of log2 result (only a problem with values >= 0x1.FFFFF8p127)
    //Ugly Math version; ugly in the sense that it is slow and not as elegant as working with it as a string.
        //      the exponent is sometimes reported as 128, which will bork float math, so we subtract the test for 128.
    //A) calculate the exponent via approximation of C log2()
        //      max_float btw is 0x1.FFFFFEp127, so we are only talking a very small number of numbers.
    //B) use kludge to avert fatal error in approximation of log2 result (only a problem with values >= 0x1.FFFFF8p127)
        //C) normalize the float with questionable exponent
    //      the exponent is sometimes reported as 128, which will bork float math, so we subtract the test for 128.
        //D) calculate rounding error left from log2 approximation and add to normalization value.
    //      max_float btw is 0x1.FFFFFEp127, so we are only talking a very small number of numbers.
        //      the '|' acts like a '+' in this instance but saves us one byte.
    //C) normalize the float with questionable exponent
        integer position = (24 | (3 <= frac)) - (integer)( //D
    //D) calculate rounding error left from log2 approximation and add to normalization value.
                frac /= (float)("0x1p"+(string)( //C
    //      the '|' acts like a '+' in this instance but saves us one byte.
                exponent = (exponent - (( //B
    integer position = (24 | (3 <= frac)) - (integer)( //D
                    exponent = llFloor(llLog(frac) / 0.69314718055994530941723212145818) //A
            frac /= (float)("0x1p"+(string)( //C
                ) == 128))
            exponent = (exponent - (( //B
                ))
                exponent = llFloor(llLog(frac) / 0.69314718055994530941723212145818) //A
                );
            ) == 128))
            ))
            );
 
    //this pushes the float into the integer buffer exactly.
    //since the shift is within integer range, we don't need to make a float.
    integer int = (integer)(frac * (1 << position));
    integer target = (integer)(frac = 0.0);//since the float is in the integer buffer, we need to clear the float buffer.
   
    //we don't use a traditional while loop, and instead opt for a do-while, because it's faster
    //since we may have to do about 128 iteration, this savings is important,
    //the exponent needs one final adjustment because of the shift, we do it here to save memory & it's faster.
      
      
        //this pushes the float into the integer buffer exactly.
    //The two loops try to make exponent == position by shifting and multiplying.
        //since the shift is within integer range, we don't need to make a float.
    //when they are equal, then this should be true ((int * llPow(10, exponent)) == llFabs(input))
        integer int = (integer)(frac * (1 << position));
    //That is of course assuming that the llPow(10, exponent) result has enough precision.
        integer target = (integer)(frac = 0.0);//since the float is in the integer buffer, we need to clear the float buffer.
   
       
    //We recycle position for these loops as a temporary buffer. This is so we can save a few operations.
        //we don't use a traditional while loop, and instead opt for a do-while, because it's faster
    //If we didn't, then we could actualy optimize the variable out of the code; though it would be slower.
        //since we may have to do about 128 iteration, this savings is important,
    if(target > (exponent -= position))
        //the exponent needs one final adjustment because of the shift, we do it here to save memory & it's faster.
    {//apply the rest of the bit shift if |input| < 1
       
        do
        //The two loops try to make exponent == position by shifting and multiplying.
        {
        //when they are equal, then this should be true ((int * llPow(10, exponent)) == llFabs(input))
            if(int < 0x19999999)//(0x80000000 / 5)
        //That is of course assuming that the llPow(10, exponent) result has enough precision.
            {//won't overflow, multiply in 5
       
                int = int * 5 + (position = (integer)(frac *= 5.0));
        //We recycle position for these loops as a temporary buffer. This is so we can save a few operations.
                frac -= (float)position;
        //If we didn't, then we could actualy optimize the variable out of the code; though it would be slower.
                target = ~-target;
        if(target > (exponent -= position))
            }
        {//apply the rest of the bit shift if |input| < 1
            else
            do
            {//overflow predicted, devide by 2
            {
                frac = (frac + (int & 1))/2;
                if(int < 0x19999999)//(0x80000000 / 5)
                int = int >> 1;
                {//won't overflow, multiply in 5
                exponent = -~exponent;
                    int = int * 5 + (position = (integer)(frac *= 5.0));
             }
                    frac -= (float)position;
         }while(target ^ exponent);
                    target = ~-target;
                }
                else
                {//overflow predicted, devide by 2
                    frac = (frac + (int & 1))/2;
                    int = int >> 1;
                    exponent = -~exponent;
                }
             }while(target ^ exponent);
        }
        else if(target ^ exponent)//target < exponent
         {//apply the rest of the bit shift if |input| > 1
            do
            {
                if(int < 0x40000000) //(0x80000000 / 2)
                {//won't overflow, multiply in 2
                    int = (int << 1) + (position = (integer)(frac *= 2.0));
                    frac -= (float)position;
                    exponent = ~-exponent;
                }
                else
                {//overflow predicted, divide by 5
                    frac = (frac + int%5) / 5.0;
                    int /= 5;
                    target = -~target;
                }
            }while(target ^ exponent);
        }
        //int is now properly calculated, it holds enough data to accurately describe the input in conjunction with exponent.
        //we feed this through optical to clean up the answer.
        mantissa = (string)int;
     }
     }
    else if(target ^ exponent)//target < exponent
    {//apply the rest of the bit shift if |input| > 1
        do
        {
            if(int < 0x40000000) //(0x80000000 / 2)
            {//won't overflow, multiply in 2
                int = (int << 1) + (position = (integer)(frac *= 2.0));
                frac -= (float)position;
                exponent = ~-exponent;
            }
            else
            {//overflow predicted, divide by 5
                frac = (frac + int%5) / 5.0;
                int /= 5;
                target = -~target;
            }
        }while(target ^ exponent);
    }
    //int is now properly calculated, it holds enough data to accurately describe the input in conjunction with exponent.
    //we feed this through optical to clean up the answer.
    mantissa = (string)int;
   
    @optical;
     //it's not an issue that we may be jumping over the initialization of some of the variables,
     //it's not an issue that we may be jumping over the initialization of some of the variables,
     //we initialize everything we use here.
     //we initialize everything we use here.
Line 132: Line 135:
     string mantissa = (string)frac;//this may be a string of about 47 characters long.
     string mantissa = (string)frac;//this may be a string of about 47 characters long.
     integer exponent = -6;//default exponent for optical method
     integer exponent = -6;//default exponent for optical method
     if(frac != (float)(mantissa = llDeleteSubString(mantissa, -7, -7)))
     if(frac == (float)(mantissa = llDeleteSubString(mantissa, -7, -7)))
     {//optical failed
        jump optical;
        //Ugly Math version; ugly in the sense that it is slow and not as elegant as working with it as a string.
   
        //A) calculate the exponent via approximation of C log2()
     //optical failed
        //B) use kludge to avert fatal error in approximation of log2 result (only a problem with values >= 0x1.FFFFF8p127)
    //Ugly Math version; ugly in the sense that it is slow and not as elegant as working with it as a string.
        //      the exponent is sometimes reported as 128, which will bork float math, so we subtract the test for 128.
    //A) calculate the exponent via approximation of C log2()
        //      max_float btw is 0x1.FFFFFEp127, so we are only talking a very small number of numbers.
    //B) use kludge to avert fatal error in approximation of log2 result (only a problem with values >= 0x1.FFFFF8p127)
        //      but max_double is much larger but we aren't supporting those, we don't have the precision.
    //      the exponent is sometimes reported as 128, which will bork float math, so we subtract the test for 128.
        //C) normalize the float with questionable exponent
    //      max_float btw is 0x1.FFFFFEp127, so we are only talking a very small number of numbers.
        //D) calculate rounding error left from log2 approximation and add to normalization value.
    //      but max_double is much larger but we aren't supporting those, we don't have the precision.
        //      the '|' acts like a '+' in this instance but saves us one byte.
    //C) normalize the float with questionable exponent
       
    //D) calculate rounding error left from log2 approximation and add to normalization value.
        if((exponent = llFloor(llLog(frac) / 0.69314718055994530941723212145818)) >= 128)//A
    //      the '|' acts like a '+' in this instance but saves us one byte.
            exponent = ~-exponent;//B
   
        frac /= (float)("0x1p"+(string)(exponent));//C
    if((exponent = llFloor(llLog(frac) / 0.69314718055994530941723212145818)) >= 128)//A
        integer position = (24 | (integer)(3 <= frac)) - (integer)(frac); //D
        exponent = ~-exponent;//B
       
    frac /= (float)("0x1p"+(string)(exponent));//C
        //this pushes the float into the integer buffer exactly.
    integer position = (24 | (integer)(3 <= frac)) - (integer)(frac); //D
        //since the shift is within integer range, we don't need to make a float.
   
        integer int = (integer)(frac * (1 << position));
    //this pushes the float into the integer buffer exactly.
        integer target = (integer)(frac = 0.0);//since the float is in the integer buffer, we need to clear the float buffer.
    //since the shift is within integer range, we don't need to make a float.
       
    integer int = (integer)(frac * (1 << position));
        //we don't use a traditional while loop, and instead opt for a do-while, because it's faster
    integer target = (integer)(frac = 0.0);//since the float is in the integer buffer, we need to clear the float buffer.
        //since we may have to do about 128 iteration, this savings is important,
   
        //the exponent needs one final adjustment because of the shift, we do it here to save memory & it's faster.
    //we don't use a traditional while loop, and instead opt for a do-while, because it's faster
       
    //since we may have to do about 128 iteration, this savings is important,
        //The two loops try to make exponent == position by shifting and multiplying.
    //the exponent needs one final adjustment because of the shift, we do it here to save memory & it's faster.
        //when they are equal, then this should be true ((int * llPow(10, exponent)) == llFabs(input))
   
        //That is of course assuming that the llPow(10, exponent) result has enough precision.
    //The two loops try to make exponent == position by shifting and multiplying.
       
    //when they are equal, then this should be true ((int * llPow(10, exponent)) == llFabs(input))
        //We recycle position for these loops as a temporary buffer. This is so we can save a few operations.
    //That is of course assuming that the llPow(10, exponent) result has enough precision.
        //If we didn't, then we could actually optimize the variable out of the code; though it would be slower.
   
        if(target > (exponent -= position))
    //We recycle position for these loops as a temporary buffer. This is so we can save a few operations.
        {//apply the rest of the bit shift if |input| < 1
    //If we didn't, then we could actually optimize the variable out of the code; though it would be slower.
            do
    if(target > (exponent -= position))
            {
    {//apply the rest of the bit shift if |input| < 1
                if(int < 0x19999999)//(0x80000000 / 5)
        do
                {//won't overflow, multiply in 5
        {
                    int = int * 5 + (position = (integer)(frac *= 5.0));
            if(int < 0x19999999)//(0x80000000 / 5)
                    frac -= (float)position;
            {//won't overflow, multiply in 5
                    target = ~-target;
                int = int * 5 + (position = (integer)(frac *= 5.0));
                }
                frac -= (float)position;
                else
                target = ~-target;
                {//overflow predicted, devide by 2
            }
                    frac = (frac + (int & 1))/2;
            else
                    int = int >> 1;
            {//overflow predicted, devide by 2
                    exponent = -~exponent;
                frac = (frac + (int & 1))/2;
                }
                int = int >> 1;
             }while(target ^ exponent);
                exponent = -~exponent;
        }
             }
        else if(target ^ exponent)//target < exponent
         }while(target ^ exponent);
         {//apply the rest of the bit shift if |input| > 1
            do
            {
                if(int < 0x40000000) //(0x80000000 / 2)
                {//won't overflow, multiply in 2
                    int = (int << 1) + (position = (integer)(frac *= 2.0));
                    frac -= (float)position;
                    exponent = ~-exponent;
                }
                else
                {//overflow predicted, divide by 5
                    frac = (frac + int%5) / 5.0;
                    int /= 5;
                    target = -~target;
                }
            }while(target ^ exponent);
        }
        //int is now properly calculated, it holds enough data to accurately describe the input in conjunction with exponent.
        //we feed this through optical to clean up the answer.
        mantissa = (string)int;
     }
     }
    else if(target ^ exponent)//target < exponent
    {//apply the rest of the bit shift if |input| > 1
        do
        {
            if(int < 0x40000000) //(0x80000000 / 2)
            {//won't overflow, multiply in 2
                int = (int << 1) + (position = (integer)(frac *= 2.0));
                frac -= (float)position;
                exponent = ~-exponent;
            }
            else
            {//overflow predicted, divide by 5
                frac = (frac + int%5) / 5.0;
                int /= 5;
                target = -~target;
            }
        }while(target ^ exponent);
    }
    //int is now properly calculated, it holds enough data to accurately describe the input in conjunction with exponent.
    //we feed this through optical to clean up the answer.
    mantissa = (string)int;
   
    @optical;
     //it's not an issue that we may be jumping over the initialization of some of the variables,
     //it's not an issue that we may be jumping over the initialization of some of the variables,
     //we initialize everything we use here.
     //we initialize everything we use here.

Revision as of 11:04, 24 August 2012

A script for passing floats through strings without loosing precision. Wrote this ages ago, it isn't very fast but it is accurate. If you want fast and accurate but don't care so much about human readable try Float2Hex.

Works flawlessly and LSL can parse directly to floats again without any special code :-) just use a (float) typecast.

Changes:

Code

<lsl> string Float2Sci(float input) {// LSLEditor Unsafe, LSO Safe, Mono Safe 

   if(input == 0.0)//handles negative zero
       return llDeleteSubString((string)input, -5, -1);//trim off the trailing zero's, don't need them.
   
   float frac = llFabs(input);//we put the negative back at the end.
   string mantissa = (string)frac;//this may be a string of about 47 characters long.
   integer exponent = -6;//default exponent for optical method
   if(frac == (float)(mantissa = llDeleteSubString(mantissa, -7, -7)))
       jump optical;

   //optical failed
   //Ugly Math version; ugly in the sense that it is slow and not as elegant as working with it as a string.
   //A) calculate the exponent via approximation of C log2()
   //B) use kludge to avert fatal error in approximation of log2 result (only a problem with values >= 0x1.FFFFF8p127)
   //       the exponent is sometimes reported as 128, which will bork float math, so we subtract the test for 128.
   //       max_float btw is 0x1.FFFFFEp127, so we are only talking a very small number of numbers.
   //C) normalize the float with questionable exponent
   //D) calculate rounding error left from log2 approximation and add to normalization value.
   //       the '|' acts like a '+' in this instance but saves us one byte.
   integer position = (24 | (3 <= frac)) - (integer)( //D
           frac /= (float)("0x1p"+(string)( //C
           exponent = (exponent - (( //B
               exponent = llFloor(llLog(frac) / 0.69314718055994530941723212145818) //A
           ) == 128))
           ))
           );

   //this pushes the float into the integer buffer exactly.
   //since the shift is within integer range, we don't need to make a float.
   integer int = (integer)(frac * (1 << position));
   integer target = (integer)(frac = 0.0);//since the float is in the integer buffer, we need to clear the float buffer.
   
   //we don't use a traditional while loop, and instead opt for a do-while, because it's faster
   //since we may have to do about 128 iteration, this savings is important,
   //the exponent needs one final adjustment because of the shift, we do it here to save memory & it's faster.
   
   //The two loops try to make exponent == position by shifting and multiplying.
   //when they are equal, then this should be true ((int * llPow(10, exponent)) == llFabs(input))
   //That is of course assuming that the llPow(10, exponent) result has enough precision.
   
   //We recycle position for these loops as a temporary buffer. This is so we can save a few operations.
   //If we didn't, then we could actualy optimize the variable out of the code; though it would be slower.
   if(target > (exponent -= position))
   {//apply the rest of the bit shift if |input| < 1
       do
       {
           if(int < 0x19999999)//(0x80000000 / 5)
           {//won't overflow, multiply in 5
               int = int * 5 + (position = (integer)(frac *= 5.0));
               frac -= (float)position;
               target = ~-target;
           }
           else
           {//overflow predicted, devide by 2
               frac = (frac + (int & 1))/2;
               int = int >> 1;
               exponent = -~exponent;
           }
       }while(target ^ exponent);
   }
   else if(target ^ exponent)//target < exponent
   {//apply the rest of the bit shift if |input| > 1
       do
       {
           if(int < 0x40000000) //(0x80000000 / 2)
           {//won't overflow, multiply in 2
               int = (int << 1) + (position = (integer)(frac *= 2.0));
               frac -= (float)position;
               exponent = ~-exponent;
           }
           else
           {//overflow predicted, divide by 5
               frac = (frac + int%5) / 5.0;
               int /= 5;
               target = -~target;
           }
       }while(target ^ exponent);
   }
   //int is now properly calculated, it holds enough data to accurately describe the input in conjunction with exponent.
   //we feed this through optical to clean up the answer.
   mantissa = (string)int;
   
   @optical;
   //it's not an issue that we may be jumping over the initialization of some of the variables,
   //we initialize everything we use here.
   
   //to accurately describe a float you only need 9 decimal places; so we throw the extra's away
   if(9 < (target = position = llStringLength(mantissa)))
       position = 9;
   //chop off the tailing zero's; we don't need them.
   do; while(llGetSubString(mantissa, position, position) == "0" && (position = ~-position));//faster then a while loop
   
   //we do a bad thing, we recycle 'target' here, position is one less then target,
   //"target + ~position" is the same as "target - (position + 1)" saves 6 bytes.
   //this block of code actually does the cutting.
   if(target + ~position) mantissa = llGetSubString(mantissa, 0, position);
   
   //insert the decimal point (not strictly needed). We add the extra zero for aesthetics.
   //by adding in the decimal point, it simplifies some of the code.
   mantissa = llInsertString(mantissa, 1, llGetSubString(".0", 0, !position));

   //adjust exponent from having added the decimal place
   if((exponent += ~-target))
       mantissa += "e" + (string)exponent;
   //return with the correct sign.
   if(input < 0)
       return "-" + mantissa;
   return mantissa;

} </lsl>

LSLEditor

Some people will want to run this in LSLEditor where the execution order is reversed and where booleans aren't integers. Do keep in mind this will only work support float precision, not double precision. I have no intention of adding double precision.

<lsl> string Float2Sci(float input) {// LSLEditor Safe, LSO Safe, Mono Safe 

   if(input == 0.0)//handles negative zero
       return llDeleteSubString((string)input, -5, -1);//trim off the trailing zero's, don't need them.
   
   float frac = llFabs(input);//we put the negative back at the end.
   string mantissa = (string)frac;//this may be a string of about 47 characters long.
   integer exponent = -6;//default exponent for optical method
   if(frac == (float)(mantissa = llDeleteSubString(mantissa, -7, -7)))
       jump optical;
   
   //optical failed
   //Ugly Math version; ugly in the sense that it is slow and not as elegant as working with it as a string.
   //A) calculate the exponent via approximation of C log2()
   //B) use kludge to avert fatal error in approximation of log2 result (only a problem with values >= 0x1.FFFFF8p127)
   //       the exponent is sometimes reported as 128, which will bork float math, so we subtract the test for 128.
   //       max_float btw is 0x1.FFFFFEp127, so we are only talking a very small number of numbers.
   //       but max_double is much larger but we aren't supporting those, we don't have the precision.
   //C) normalize the float with questionable exponent
   //D) calculate rounding error left from log2 approximation and add to normalization value.
   //       the '|' acts like a '+' in this instance but saves us one byte.
   
   if((exponent = llFloor(llLog(frac) / 0.69314718055994530941723212145818)) >= 128)//A
       exponent = ~-exponent;//B
   frac /= (float)("0x1p"+(string)(exponent));//C
   integer position = (24 | (integer)(3 <= frac)) - (integer)(frac); //D
   
   //this pushes the float into the integer buffer exactly.
   //since the shift is within integer range, we don't need to make a float.
   integer int = (integer)(frac * (1 << position));
   integer target = (integer)(frac = 0.0);//since the float is in the integer buffer, we need to clear the float buffer.
   
   //we don't use a traditional while loop, and instead opt for a do-while, because it's faster
   //since we may have to do about 128 iteration, this savings is important,
   //the exponent needs one final adjustment because of the shift, we do it here to save memory & it's faster.
   
   //The two loops try to make exponent == position by shifting and multiplying.
   //when they are equal, then this should be true ((int * llPow(10, exponent)) == llFabs(input))
   //That is of course assuming that the llPow(10, exponent) result has enough precision.
   
   //We recycle position for these loops as a temporary buffer. This is so we can save a few operations.
   //If we didn't, then we could actually optimize the variable out of the code; though it would be slower.
   if(target > (exponent -= position))
   {//apply the rest of the bit shift if |input| < 1
       do
       {
           if(int < 0x19999999)//(0x80000000 / 5)
           {//won't overflow, multiply in 5
               int = int * 5 + (position = (integer)(frac *= 5.0));
               frac -= (float)position;
               target = ~-target;
           }
           else
           {//overflow predicted, devide by 2
               frac = (frac + (int & 1))/2;
               int = int >> 1;
               exponent = -~exponent;
           }
       }while(target ^ exponent);
   }
   else if(target ^ exponent)//target < exponent
   {//apply the rest of the bit shift if |input| > 1
       do
       {
           if(int < 0x40000000) //(0x80000000 / 2)
           {//won't overflow, multiply in 2
               int = (int << 1) + (position = (integer)(frac *= 2.0));
               frac -= (float)position;
               exponent = ~-exponent;
           }
           else
           {//overflow predicted, divide by 5
               frac = (frac + int%5) / 5.0;
               int /= 5;
               target = -~target;
           }
       }while(target ^ exponent);
   }
   //int is now properly calculated, it holds enough data to accurately describe the input in conjunction with exponent.
   //we feed this through optical to clean up the answer.
   mantissa = (string)int;
   
   @optical;
   //it's not an issue that we may be jumping over the initialization of some of the variables,
   //we initialize everything we use here.
   
   //to accurately describe a float you only need 9 decimal places; so we throw the extra's away
   if(9 < (target = position = llStringLength(mantissa)))
       position = 9;
   //chop off the tailing zero's; we don't need them.
   do
       position = ~-position;
   while(llGetSubString(mantissa, position, position) == "0" && position);//faster then a while loop
   
   //we do a bad thing, we recycle 'target' here, position is one less then target,
   //"target + ~position" is the same as "target - (position + 1)" saves 6 bytes.
   //this block of code actually does the cutting.
   if(target + ~position) mantissa = llGetSubString(mantissa, 0, position);
   
   //insert the decimal point (not strictly needed). We add the extra zero for aesthetics.
   //by adding in the decimal point, it simplifies some of the code.
   mantissa = llInsertString(mantissa, 1, llGetSubString(".0", 0, !position));

   //adjust exponent from having added the decimal place
   if((exponent += ~-target))
       mantissa += "e" + (string)exponent;
   //return with the correct sign.
   if(input < 0)
       return "-" + mantissa;
   return mantissa;

} </lsl>

Retrieved from "https://wiki.secondlife.com/w/index.php?title=Float2Sci&oldid=1172134"