User:Strife Onizuka/Float Functions
LSL Portal | Functions | Events | Types | Operators | Constants | Flow Control | Script Library | Categorized Library | Tutorials |
Float <-Union-> Integer
<lsl> integer fui(float a)//Mono Safe, LSO Safe, Doubles Unsupported, LSLEditor Unsafe {//union float to integer
if((a)){//is it greater than or less than 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. if(a > 3.4028234663852885981170418348452e+38)//Round up to infinity return b | 0x7F800000;//Positive or negative infinity 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); }//the previous requires a lot of unwinding to understand it. if(a == 0)//Just because it's not greater than or less than zero doesn't mean it's non-zero. return ((string)a == (string)(-0.0)) << 31;//for grins, detect the sign on zero. it's not pretty but it works. //Mono does not support indeterminates so I'm not going to worry about it. return 0x7FFFFFFF;//NaN time! We have no way to tell NaN's apart so lets just choose one.
}
float iuf(integer a) {//union integer to float
if((a & 0x7F800000) == 0x7F800000) return (1 | (a >> 31)) * (float)llList2String(["NaN","Infinity"], !(a & 0x7FFFFF)); 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 greater than or less than 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 if(a > 3.4028234663852885981170418348452e+38)//Round up to infinity b = b | 0x7F800000;//Positive or negative infinity 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 >> 31) | 1)))))))) << 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(a != 0) return "f////w"; if((string)a == (string)(0.0)) return "AAAAAA"; return "gAAAAA";
}
float siuf(string b) {//base64ed integer union to float
integer a = llBase64ToInteger(b); if((a & 0x7F800000) == 0x7F800000) return (1 | (a >> 31)) * (float)llList2String(["NaN","Infinity"], !(a & 0x7FFFFF)); 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>
Half-Precision
<lsl> integer fui16(float a)//Mono Safe, LSO Safe, Doubles Unsupported, LSLEditor Unsafe {//union half-precision float to short integer
if((a)){//is it greater than or less than zero? integer b = (integer)(a < 0) << 15;//the sign, but later this variable is reused to store the shift if((a = llFabs(a)) < 0.0001220703125)//Denormalized range check & last stride of normalized range return b | (integer)(a * 16777216.0);//the math overlaps; saves cpu time. if(a > 65504.0)//Round up to infinity return b | 0x7C00;//Positive or negative infinity integer c = llFloor((llLog(a) / 0.69314718055994530941723212145818)) + 14;//extremes will error towards extremes. following yuch corrects it. return (0x3FF & (integer)(a * (0x800 >> b))) | (((c + (b = ((integer)a - (3 <= (a *= (0.0000152587890625 * (0x40000000 >> c)))))) << 10 ) | b); }//the previous requires a lot of unwinding to understand it. if(a == 0)//Just because it's not greater than or less than zero doesn't mean it's non-zero. return ((string)a == (string)(-0.0)) << 15;//for grins, detect the sign on zero. it's not pretty but it works. //Mono does not support indeterminates so I'm not going to worry about it. return 0x7FFF;//NaN time! We have no way to tell NaN's apart so lets just choose one.
}
float i16uf(integer a) {//union short integer to half-precision float
if((a & 0x7C00) == 0x7C00) return (1 | ((a << 16) >> 31)) * (float)llList2String(["NaN","Infinity"], !(a & 0x3FF)); return 0.000000059604644775390625 * (1 << (a - !!a)) * ((!!(a = (0x1f & (a >> 10))) << 10) | ((a & 0x3ff))) * (1 | ((a << 16) >> 31));
} </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>