User:Strife Onizuka/Float Functions

Float <-Union-> Integer

<lsl> integer fui(float a)//Mono Safe, LSO Safe, Doubles Unsupported, LSLEditor Unsafe {//union float to integer

   if((a)){//is it non zero?
       integer b = (a < 0) << 31;//the sign, but later this variable is reused to store the shift
       if((a = llFabs(a)) < 2.3509887016445750159374730744445e-38)//Denormalized range check & last stride of normalized range
           return b | (integer)(a / 1.4012984643248170709237295832899e-45);//the math overlaps; saves cpu time.
       integer c = llFloor((llLog(a) / 0.69314718055994530941723212145818));//extremes will error towards extremes. following yuch corrects it.
       return (0x7FFFFF & (integer)(a * (0x1000000 >> b))) | (((c + 126 + (b = ((integer)a - (3 <= (a /= (float)("0x1p"+(string)(c -= ((c >> 31) | 1)))))))) << 23 ) | b);
   }//for grins, detect the sign on zero. it's not pretty but it works. the previous requires a lot of unwinding to understand it.
   return ((string)a == (string)(-0.0)) << 31;

}

float iuf(integer a) {//union integer to float

   return ((float)("0x1p"+(string)((a | !a) - 150))) * ((!!(a = (0xff & (a >> 23))) << 23) | ((a & 0x7fffff))) * (1 | (a >> 31));

}//will crash if the raw exponent == 0xff; reason for crash deviates from float standard; though a crash is warranted. </lsl>

Base64-Float

As a specialized mode of transport, this is faster then Float2Hex and just as lossless. <lsl> string fuis(float a){//float union to base64ed integer

   if(a){//is it non zero?
       integer b = (a < 0) << 31;//the sign, but later this variable is reused to store the shift
       if((a = llFabs(a)) < 2.3509887016445750159374730744445e-38)//Denormalized range check & last stride of normalized range
           b = b | (integer)(a / 1.4012984643248170709237295832899e-45);//the math overlaps; saves cpu time.
       else
       {
           integer c = llFloor(llLog(a) / 0.69314718055994530941723212145818);//extremes will error towards extremes. following yuch corrects it.
           b = (0x7FFFFF & (integer)(a * (0x1000000 >> b))) | (((c + 126 + (b = ((integer)a - (3 <= (a /= (float)("0x1p"+(string)(c -= (c == 128)))))))) << 23 ) | b);
       }
       return llGetSubString(llIntegerToBase64(b),0,5);
   }//for grins, detect the sign on zero. it's not pretty but it works. the previous requires a lot of unwinding to understand it.
   if((string)a == (string)(0.0))
       return "AAAAAA";
   return "gAAAAA";

}

float siuf(string b) {//base64ed integer union to float

   integer a = llBase64ToInteger(b);
   return ((float)("0x1p"+(string)((a | !a) - 150))) * ((!!(a = (0xff & (a >> 23))) << 23) | ((a & 0x7fffff))) * (1 | (a >> 31));

}//will crash if the raw exponent == 0xff; reason for crash deviates from float standard; though a crash is warranted. </lsl>

Float Compare

<lsl>integer FloatCompare(float a, float b, integer c) {//compare floats and allow for a margin of error, requires fui().

   if(a - b)//(c) Strife Onizuka 2006 
   {//they are not equal
       //First we convert the floats to integer form, as they would be in memory;
       integer a_i = fui(a);
       integer b_i = fui(b);
       integer a_e = (a_i >> 23) & 0xff;
       integer b_e = (b_i >> 23) & 0xff;
       if(!(a_e || b_e) || //to disable the +/- roll under support put a // just before the !
           ((a_i & 0x80000000) == (b_i & 0x80000000)))//sign match check
       {//start by getting and testing the difference, this is what limits c
           integer diff = a_e - b_e;//ugly is fast, basically, it gets the mantissa, sets the sign on the mantissa,
           if(diff >= -1 || diff <= 1)//shifts it depending on exponent, finally executes the test.
               if(llAbs(((((a_i & 0x7FFFFF) | (!!a_e << 23)) * ((a_i >> 31) | 1)) >> !~-diff) - 
                        ((((b_i & 0x7FFFFF) | (!!b_e << 23)) * ((b_i >> 31) | 1)) >> !~diff)) <= c)
                   jump out;
       }
       return (a > b) - (a < b);
   }
   @out;
   return 0;

}</lsl>

FUI2HexFloat

<lsl> //This implementation isn't meant to create the most compact hexfloat and makes no effort to. //It was designed to quickly produce an accurate hexfloat. //Do keep in mind it does not handle NAN or INF. string FUI2HexFloat(integer b) {//Dump FUI float-integer to a hex-float string

   string c = "";
   integer d = 0;
   integer e = 0xff & (b >> 23);
   string f = "0x"+(string)(!!e) + ".";
   if(b & 0x80000000)
       f = "-"+ f;
   if(e ^ 127) c = "p" + (string)((e | !e) - 127);
   if((e = 0xfffffe & (b << 1)))
   {
       while(!((e >> d) & 0xf))
           d+=4;
       while(d < 24)
       {
           c = llGetSubString(hexc, b = 0xf & (e >> d), b) + c;
           d += 4;
       }
   }
   return f + c;

}

string Float2Hex(float a) {//Another way to do Float2Hex, i wrote this for the heck of it; not because it's a good idea.

   return FUI2HexFloat(fui(a));

} </lsl>