; Multi Precision Library v.1.1
; Large Integer = {Int:Sign, UInt:LenInUInts, UInts:LSword..MSword}
;  = little endian, signed magnitude (not 2's complement!)

; TODO:
;  MP_TML(z,y,x,H,L) truncated multiplitaction: words L..H of the product
;  MP_RCP(y,n,x) n-bit reciprocal
;  MP_MPW(z,y,x,m) modular power: z <- Mod(y**x,m)
;  primality tests, Legendre/Jacobi symbol
;  update-reuse ints: MP_ADD(x,x,y), MP_SUB(x,y,x)...

MP_Init() ; Initialize Multi Precision Library


bits(n) {                      ; Binary representation of Int64 n>=0
   Return n>1 ? bits(n>>1) . n&1 : n
}

MP_PowIpp(ByRef y, V32, U32) { ; y <- V32 ** U32, left-to-right exponent scan
   If U32 < 1
      Return MP_SET(y,1)
   MP_SET(y,V32)
   b := SubStr(bits(U32),2)    ; bits of the exponent from MS-1..0
   Loop Parse, b
   {
      MP_MUL(z,y,y)            ; z := y*y
      If A_LoopField           ; next exponent bit
           MP_MulIpp(y,z,V32)  ; y := z*x (V32) <- faster when x is small
      Else MP_CPY(y,z)         ; y := z
  }
}

MP_POW(ByRef y, ByRef x, U32) { ; y <- x ** U32, left-to-right exponent scan
   If U32 < 1
      Return MP_SET(y,1)
   b := SubStr(bits(U32),2)    ; bits of the exponent from MS-1..0
   MP_CPY(y,x)
   Loop Parse, b
   {
      MP_MUL(z,y,y)            ; z := y*y
      If A_LoopField           ; next exponent bit
           MP_MUL(y,z,x)       ; y := z*x
      Else MP_CPY(y,z)         ; y := z
  }
}

MP_POW2(ByRef y, ByRef x, U32) { ; y <- x ** U32, Right-to-left expoent scan
   MP_SET(y,1), MP_CPY(u,x)
   Loop {
      If (U32 & 1)
         MP_MUL(z,y,u), MP_CPY(y,z) ; y *= x (u)
      If (U32 >>= 1)
         MP_MUL(z,u,u), MP_CPY(u,z) ; x *= x (u)
      Else Return
  }
}

MP_CMP(ByRef x, ByRef y, ByRef eq="") { ; -0+  for x <=> y, eq = #equal MS words
   Global CMPpp
   eq := 0
   SX := NumGet(x,0,"Int"), SY := NumGet(y,0,"Int")
   If (SX < SY)
      Return -1
   If (SX > SY)
      Return 1
   LX := NumGet(x,4), LY := NumGet(y,4)
   If (LX < LY)
      Return -SX
   If (LX > LY)
      Return SX
   Return SX*dllcall(&CMPpp,"Int",LX, "UInt*",eq, "UInt",&x+8, "UInt",&y+8, "CDECL Int") ; same sign, length
}

MP_SFT(ByRef y, ByRef x, s) {       ; s>0: y <- x << s, s<0: y <- x >> -s
   Global SFL, SFR, LEN
   L8 := NumGet(x,4)
   If (s > 0) {                     ; shift left
      offs := s//32, s &= 31
      VarSetCapacity(y,(L8+offs)*4+8,0)
      NumPut(NumGet(x,0,"Int"),y)      ; sign
      NumPut(L8+offs,y,4)              ; new length
      dllcall(&SFL, "UInt",&y+8+4*offs, "Int",L8, "UInt",&x+8, "UInt",s, "CDECL")
      Return
   }                                ; shift right
   s := -s, offs := s//32, s &= 31
   If (offs >= L8) {                   ; too large shift: nothing remains
      VarSetCapacity(y,12,0)
      NumPut(1,y), NumPut(1,y,4)
      Return
   }
   VarSetCapacity(y,(L8-offs)*4+8,0)
   NumPut(NumGet(x,0,"Int"),y) ; sign
   dllcall(&SFR, "UInt",&y+8, "Int",L8-offs, "UInt",&x+8+4*offs, "UInt",s, "CDECL")
   NumPut(dllcall(&LEN,"Int",L8-offs,"UInt",&y+8, "CDECL Int"), y, 4)
}

MP_ADD(ByRef z, ByRef y, ByRef x) { ; z <- y + x
   Global CMPpp, ADDpp, SUBpp, LEN
   SX := NumGet(x,0,"Int"), SY := NumGet(y,0,"Int")
   LX := NumGet(x,4), LY := NumGet(y,4), LZ := LX > LY ? LX : LY

   If (SX = SY) {                   ; ADD
      VarSetCapacity(z, LZ*4+12)       ; room for carry
      If (LY > LX)
           dllcall(&ADDpp,"UInt",&z+8, "Int",LY,"UInt",&y+8, "Int",LX,"UInt",&x+8, "CDECL")
      Else dllcall(&ADDpp,"UInt",&z+8, "Int",LX,"UInt",&x+8, "Int",LY,"UInt",&y+8, "CDECL")
      NumPut(SX,z)  ; set sign(z)
      NumPut(dllcall(&LEN,"Int",LZ+1,"UInt",&z+8, "CDECL Int"), z, 4)
      Return
   }                                ; SUBTRACT
   NumPut(1,x), NumPut(1,y)            ; set both positive
   c := MP_CMP(x,y,eq)                 ; compare, find same MS part
   eq -= eq = LZ                       ; leave at least one word
   VarSetCapacity(z,(LZ-eq)*4+8,0)     ; no room needed for equal MS parts (fill 0 for x=y)
   If (c = 0)                          ; x = y
      NumPut(1,z), NumPut(1,z,4)       ; z <- 0
   Else If (c < 0) {                ; x < y
      dllcall(&SUBpp,"UInt",&z+8, "Int",LY-eq,"UInt",&y+8, "Int",LX-eq,"UInt",&x+8, "CDECL")
      NumPut(Sy,z)                     ; sign(z) <- Sy
   }
   Else {                           ; x > y
      dllcall(&SUBpp,"UInt",&z+8, "Int",LX-eq,"UInt",&x+8, "Int",LY-eq,"UInt",&y+8, "CDECL")
      NumPut(Sx,z)                     ; sign(z) <- Sx
   }
   NumPut(dllcall(&LEN,"Int",LZ,"UInt",&z+8, "CDECL Int"), z, 4)
   NumPut(Sx,x), NumPut(Sy,y)          ; reset both signs
}

MP_SUB(ByRef z, ByRef y, ByRef x) { ; z <- y - x
   SX := NumGet(x,0,"Int")
   NumPut(-SX,x)  ; x <- (-x)
   MP_ADD(z,y,x)  ; z <- y + (-x)
   NumPut( SX,x)  ; reset sign(x)
}

MP_MUL(ByRef z, ByRef y, ByRef x) { ; z <- y * x
   Global MULpp, LEN
   SX := NumGet(x,0,"Int"), SY := NumGet(y,0,"Int")
   LX := NumGet(x,4), LY := NumGet(y,4), LZ := LX + LY
   VarSetCapacity(z, LZ*4+8, 0)
   dllcall(&MULpp,"UInt",&z+8, "Int",LY,"UInt",&y+8, "Int",LX,"UInt",&x+8, "CDECL")
   NumPut(dllcall(&LEN,"Int",LZ,"UInt",&z+8, "CDECL Int"), z, 4)
   NumPut(Sy*Sx,z)                     ; sign(z) <- Sy*Sx
}

MP_DIV(ByRef q, ByRef r, ByRef y, ByRef x) { ; q <- y/x, r <- Mod(y,x), sign(q) = SY*SX, sign(r) = SY
   Global DIVpq, LEN, CPY
   SX := NumGet(x,0,"Int"), SY := NumGet(y,0,"Int")
   LX := NumGet(x,4), LY := NumGet(y,4)
   If (Lx = 1) {                    ; Single digit x
      If (NumGet(x,8) = 0)
         Return "ERROR: Divide by 0"
      rem := MP_DivIpp(q, y, NumGet(x,8))
      VarSetCapacity(r,12)             ; put rem in MP format
      NumPut(SY,r), NumPut(1,r,4), NumPut(rem,r,8)
      NumPut(Sy*Sx,q)                  ; set lengths, signs
      Return
   }                                ; Multi-digit x
   If (MP_CMP(y,x) < 0) {              ; y < x
      VarSetCapacity(q,12,0)
      NumPut(SY*Sx,q), NumPut(1,q,4)   ; q <- 0
      MP_CPY(r,y)                      ; r <- y
      Return
   }                                ; Multi-digits, y >= x
   LQ := LY > LX ? LY-LX+1 : 1
   VarSetCapacity(q, LQ*4+ 8, 0)       ; q initialized to all 0!
   VarSetCapacity(r, LY*4+12, 0)       ; r <- y, 0-padded on both ends
   dllcall(&CPY, "UInt",&r+8, "UInt",&y+8, "Int",LY*4, "CDECL")

   dllcall(&DIVpq,"UInt",&q+8, "Int",LY,"UInt",&r+8, "Int",LX,"UInt",&x+8, "CDECL")

   NumPut(dllcall(&LEN,"Int",LQ,"UInt",&q+8, "CDECL Int"), q, 4)
   NumPut(dllcall(&LEN,"Int",LX,"UInt",&r+8, "CDECL Int"), r, 4)
   NumPut(Sy*Sx,q), NumPut(Sy,r)       ; sign(q) <- Sy*Sx, sign(r) <- Sy
}

MP_GCD(ByRef g, ByRef c, ByRef d, ByRef x, ByRef y) { ; Extended shifting Euclidean GCD = g = c*x + d*y
   Global xGCD, CPY
   If (MP_IS0(x)) {
      MP_CPY(g,y), MP_SET(c,0), MP_SET(d,1)
      Return
   }
   If (MP_IS0(y)) {
      MP_CPY(g,x), MP_SET(c,1), MP_SET(d,0)
      Return
   }
   L := ((MP_LEN(x) > MP_LEN(y) ? MP_LEN(x) : MP_LEN(y)) + 3) * 4       ; temp length in bytes
   VarSetCapacity(Z, 6*L, 0)
   dllcall(&CPY, "UInt", &Z,  "UInt",&x, "Int",MP_LEN(x)*4+8, "CDECL") ; copy input
   dllcall(&CPY, "UInt",&Z+L, "UInt",&y, "Int",MP_LEN(y)*4+8, "CDECL") ; copy destroyed in xGCD

   dllcall(&xGCD, "UInt*",f,"UInt*",a,"UInt*",b, "UInt",&Z,"UInt",&Z+L ; do the work
                , "UInt",&Z+2*L,"UInt",&Z+3*L,"UInt",&Z+4*L,"UInt",&Z+5*L)

   s := NumGet(f+0,4)*4+8, VarSetCapacity(g,s)                         ; copy result from buffer
   dllcall(&CPY, "UInt",&g,  "UInt",f, "Int",s, "CDECL")
   s := NumGet(a+0,4)*4+8, VarSetCapacity(c,s)
   dllcall(&CPY, "UInt",&c,  "UInt",a, "Int",s, "CDECL")
   s := NumGet(b+0,4)*4+8, VarSetCapacity(d,s)
   dllcall(&CPY, "UInt",&d,  "UInt",b, "Int",s, "CDECL")
}

MP_AddIpp(ByRef y, ByRef x, I32) {  ; add a 32-bit integer (pos+pos) to x
   Global AddIpp
   L8 := NumGet(x,4)
   VarSetCapacity(y,L8*4+12)           ; one extra word for carry
   c := dllcall(&AddIpp, "UInt",&y+8, "Int",L8, "UInt",&x+8, "UInt",I32, "CDECL UInt")
   NumPut(1,y)                         ; positive
   NumPut(c>0 ? L8+1 : L8,y,4)         ; true length
}

MP_SubIpp(ByRef y, ByRef x, I32) {  ; subtract a 32-bit integer (pos+pos) from x
   Global SubIpp, LEN
   L8 := NumGet(x,4)
   If (L8 < 2) {
      VarSetCapacity(y,12)
      d := NumGet(x,8,"UInt") - I32
      s := d < 0 ? -1 : 1
      NumPut(s,y), NumPut(1,y,4), NumPut(s*d,y,8)
      Return
   }
   VarSetCapacity(y,L8*4+8)            ; no borrow
   c := dllcall(&SubIpp, "UInt",&y+8, "Int",L8, "UInt",&x+8, "UInt",I32, "CDECL UInt")
   NumPut(1,y)                         ; positive
   NumPut(dllcall(&LEN,"Int",L8,"UInt",&y+8, "CDECL Int"), y, 4)
}

MP_MulIpp(ByRef y, ByRef x, I32) {  ; multiply x with max 32-bit integer (pos*pos)
   Global MulIpp
   L8 := NumGet(x,4)
   VarSetCapacity(y,L8*4+12)           ; one extra word for carry
   c := dllcall(&MulIpp,"UInt",&y+8, "Int",L8, "UInt",&x+8, "UInt",I32, "CDECL UInt")
   NumPut(1,y)                         ; positive
   NumPut(c>0 ? L8+1 : L8,y,4)         ; true length
}

MP_DivIpp(ByRef y, ByRef x, U32) {  ; y := x // 32-bit integer (pos/pos), RETURN remainder
   Global LEN, DivIpp
   L8 := NumGet(x,4)
   VarSetCapacity(y,L8*4+8)
   r := dllcall(&DivIpp,"UInt",&y+8, "Int",L8, "UInt",&x+8, "UInt",U32, "CDECL UInt")
   NumPut(1,y)                         ; positive
   NumPut(dllcall(&LEN,"Int",L8,"UInt",&y+8, "CDECL Int"), y, 4)
   Return r
}

MP_Cpy(ByRef y, ByRef x) {          ; y <- x
   Global CPY
   L8 := NumGet(x,4)
   VarSetCapacity(y,L8*4+8)
   dllcall(&CPY, "UInt",&y, "UInt",&x, "Int",L8*4+8, "CDECL")
}

MP_Set(ByRef x, h) {                ; x <- string (hex, decimal integer, double precision float)
   Global U32toHex
   Static D52 := 4503599627370496.0, d := 0x1234567890123456, mk = 0xFFFFFFFFFFFFF
   If (SubStr(h,1,1) = "-")
      sign := -1, h := SubStr(h,2)     ; negative
   Else
      sign := 1                        ; positive

   If (SubStr(h,1,2) = "0x") {      ; arbitrary long hex
      L8 := (StrLen(h)+5)//8
      VarSetCapacity(x,L8*4+8)
      Loop % L8-1
         NumPut("0x" . SubStr(h,1-A_Index*8,8), x, 4+A_Index*4)
      NumPut(SubStr(h,1,StrLen(h)+8-L8*8), x, 4+L8*4)
      NumPut(L8,x,4)
   }
   Else If h contains e,.           ; decimal double
   {
      If (h <= D52)                    ; 52-bit precise AHK conversion
         MP_Set(x, Round(h))           ; sign fixed at the end
      Else {
         NumPut(h,d,0,"Double")
         e := (NumGet(d,6,"Short")>>4) - 1075 ; power_of_2 exponent (0x3ff+52)
         f := NumGet(d,0,"Int64") & mk | D52  ; fraction 1..2 * 2.**-52
         If e < 11
            MP_Set(x, f<<e)            ; h < 2**63 (Int64)
         Else {
            fm := f >> 32
            fl := f & 0xffffffff
            el := e & 31, ek := e >> 5
            If (el < 12) {             ; 2 words
               VarSetCapacity(x,16+4*ek,0)
               NumPut(2+ek,x,4)
               NumPut(fl<<el,x,8+4*ek)
               NumPut(fm<<el | fl>>(32-el), x ,12+4*ek)
            }
            Else {                     ; 3 words
               VarSetCapacity(x,20+4*ek,0)
               NumPut(3+ek,x,4)
               NumPut(fl<<el,x,8+4*ek)
               NumPut(fm<<el | fl>>(32-el), x ,12+4*ek)
               NumPut(fm>>(32-el), x ,16+4*ek)
            }
         }
      }
   }
   Else If (StrLen(h) < 19)         ; decimal integer
      If (h > 0xffffffff) {
         VarSetCapacity(x,16)          ; 63 bits
         NumPut(h & 0xffffffff,x,8)
         NumPut(h>>32,x,12)
         NumPut(2,x,4)
      } Else {                         ; 32 bits
         VarSetCapacity(x,12)
         NumPut(h,x,8)
         NumPut(1,x,4)
      }
   Else {                              ; > 18 digits
      d := Mod(StrLen(h)-1,9) + 1      ; 1..9
      MP_Set(x,SubStr(h,1,d))          ; MS 1..9 digits
      StringTrimLeft h, h, d
      Loop % StrLen(h)//9 {
         MP_MulIpp(y, x, 1000000000)
         MP_AddIpp(x, y, SubStr(h,1,9))
         StringTrimLeft h, h, 9
      }
   }

   NumPut(sign,x)
}

MP_Hex(ByRef x, tab="") {             ; HEX representation of MP integer x, tab before every 8 digits
   Global U32toHex, U32to8Hex
   Static S := "12345678"
   L8 := NumGet(x,4)
   VarSetCapacity(h,3+L8*8)
   DllCall(&U32toHex, "Str",h, "UInt",NumGet(x,4+L8*4), "CDECL")
   h := NumGet(x)=1 ? "0x" . h : "-0x" . h
   Loop % L8-1
      DllCall(&U32to8Hex, "UInt",&S, "UInt",NumGet(x,L8*4+4-A_Index*4), "CDECL"), h .= tab . S
   Return h
}

MP_Dec(ByRef z, tab="") {             ; DECIMAL representation of MP integer x, tab before every 9 digits
   Static d9 := 1000000000
   MP_CPY(x,z)                        ; copy of input (destroyed)
   sign := NumGet(x)
   VarSetCapacity(d,NumGet(x,4)*10)   ; allocate enough memory
   Loop {
     c := MP_DivIpp(y, x, d9)         ; no leading 0's
     If MP_IS0(y)
        Break
     d := SubStr(c+d9,-8) . tab . d   ; attach to the left with leaging 0's
     c := MP_DivIpp(x, y, d9)         ; no leading 0's
     If MP_IS0(x)
        Break
     d := SubStr(c+d9,-8) . tab . d   ; pad-left, prepend
   }
   Return (sign = 1 ? "" : "-") . c . tab . d
}

MP_LEN(ByRef x) {
   Return NumGet(x,4)
}

MP_IS0(ByRef x) {
   Return NumGet(x,4)=1 && NumGet(x,8)=0
}

PI(digits) { ; Newton's method, 2 accurate bits/iteration, less rounding errors, < 905 million digits
   VarSetCapacity(y,digits*1.3,Asc("0"))
   MP_SET(x, 3 . y)    ; initial estimate pi = 3
   MP_CPY(y,x)
   Loop {
      i := 2*A_Index-1 ; for better speed: start with a large i and good initial value
      MP_SET(n,i*i)
      MP_MUL(z,y,n)

      MP_SET(d,4*(i+1)*(i+2)) ; up to 63 bits, i < 1.4 * 2**30, up to 1.4*2**31 accurate bits
      MP_DIV(y,n,z,d)  ; the remainder in n can be used for rounding: fewer guard digits

      MP_ADD(z,x,y)
      MP_CPY(x,z)

      If (MP_LEN(y)<2) ; last few terms can be floats
         Break
   }
   Return SubStr(MP_DEC(x),1,digits)
}

PI0(digits) { ; Newton's method, little faster, for less than 20,000 digits
   VarSetCapacity(y,digits+sqrt(2*digits),Asc("0")) ; digits+sqrt(digits) is expected to be OK
   MP_SET(x, 3 . y)    ; x = estimate of pi, x0 = 3
   MP_CPY(y,x)         ; y = current term to be added
   Loop {
      i := 2*A_Index-1
      MP_MulIpp(z,y,i*i)    ; 32-bit UInt parameter
      d := 4*(i+1)*(i+2)    ; i < 2**15 ==> accuracy < 2**16 bits =~ 19,728 digits
      r := MP_DivIpp(w,z,d) ; remainder used for rounding: fewer guard digits
      MP_AddIpp(y,w,r>=d//2)

      MP_ADD(z,x,y)
      MP_CPY(x,z)

      If (MP_LEN(y) < 2)
         Break
   }
   Return SubStr(MP_DEC(x),1,digits)
}

SQT(value,digits) { ; Newton iteration, value <= 16 digits integer
   VarSetCapacity(z,digits,Asc("0"))
   StringLeft z, z, digits          ; trailing 0's
   a = %value%%z%%z%                ; scaled input
   s := Round(sqrt(value)*1.e16, 1) ; float form, to have more than 18 digits
   StringTrimRight s, s, 2          ; remove ".0" from end
   s .= z                           ; pad with 0's
   StringTrimRight s, s, 16         ; initial value

   MP_SET(V, a)
   MP_SET(X, s)

   Loop {
      MP_DIV(y,z,V,X)
      MP_ADD(z,X,y)
      MP_SFT(X,z,-1)
      If MP_CMP(X,y) = 0
         Break
   }
   Return  SubStr(MP_DEC(x),1,digits)
}

Factorial(n) { ; 0 <= n < 2**32 AHK integer  ==> string of decimal digits
    If n < 4
       Return SubStr("1261",n,1)
    MP_Set(x,n), i := n
    Loop % n//2-2
        MP_MulIpp(y,x,--i)
       ,MP_MulIpp(x,y,--i)
    MP_MulIpp(y, x, i=4 ? 6 : 24)
    Return MP_Dec(y)
}

Factorial0(n) { ; shorter code
    MP_Set(result, 1)
    Loop %n%
        MP_MulIpp(tmpVal, result, A_Index)
       ,MP_Cpy(result, tmpVal)
    Return MP_Dec(result)
}



MCode(ByRef code, hex) { ; allocate memory and write Machine Code there
   VarSetCapacity(code,StrLen(hex)//2)
   Loop % StrLen(hex)//2
      NumPut("0x" . SubStr(hex,2*A_Index-1,2), code, A_Index-1, "Char")
}

MP_Init() {                         ; INITIALIZE global machine code functions
GLOBAL
MCode(CPY,"568B74241085F67E118B4C240C8B4424088A11881040414E75F75EC3") ; ~memcpy, copy BYTES
MCode(LEN,"8B442404EB0A8B4C2408833C810077054879F333C040C3")
MCode(SFL,"558BEC8B450C568B7508576A205A2B551433FF85C07E2489450C8B4510538B188B4D14D3E38BCA0BDF891E8B3883C604D3EF"
. "83C004FF4D0C75E45B893E5F5E5DC3")
MCode(SFR,"558BEC8B551053568B7508578B7D0C6A208BCFC1E102582B451433DB03F103D185FF7E1F897D0C8B4D1483EA048B3AD3EF83"
. "EE048BC80BFB893E8B1AD3E3FF4D0C75E45F895EFC5E5B5DC3")
MCode(UDIV,"8B4424048B5424088B4C2410F774240C8911C3") ; ErrorLevel = 0xc0000095: Integer Overflow
MCode(ADC, "33D28B4C240C8B010344240883D2000344240483D2008911C3") ; x+y+*c, c <- carry
MCode(SBB, "33D28B4C240C8B4424042B0183D2002B44240883D2008911C3") ; x-y-*b, b <- borrow
MCode(MulIpp,"558BEC518365FC008B4D08578B7D0C85FF7E2153568B75108B06F7651433DB83C6040345FC13D3890183C1044F8955FC75E6"
. "5E5B8B45FC89015FC9C3")
MCode(DivIpp,"558BEC83EC0C8365FC00578B7D0C4F78398D45FC538B5D1089450C8B4508568D34B82BD88B45FC8945F88B04338945F48B45"
. "F48B55F88B4D0CF77514891189064F83EE0485FF7DDC5E5B8B45FC5FC9C3")
MCode(AddIpp,"558BEC8B45148B4D08568B750C85F67E1F8B5510578B3A03F8893983C20483C1043BF8730533C040EB0233C04E75E65F8901"
. "5E5DC3")
MCode(SubIpp,"558BEC8B550C85D27E2C8B45108B4D08568B302B751489318B3083C10483C0043B75147309C7451401000000EB048365140"
. "04A75DC5E8B45145DC3")
MCode(CMPpp,"558BEC8B550C8B450883220048535657781C8B75148B7D108D0C862BFE8B1C0F3B197511FF024883E90485C07DEF33C05F5E"
. "5B5DC38B4D10C1E0028B0C08390C301BC083E00248EBE7")
MCode(ADDpp,"558BEC83EC108B45148365FC0085C053568B7508578B7D107E3B8B5D188D4DFC894DF08945F88B038945F48B0789450833D2"
. "8B4DF08B010345F483D20003450883D2008911890683C60483C70483C304FF4DF875D18B450C2B451485C07E2D8D4DFC894D148BD88B07"
. "89450833D28B4D148B0183C00083D20003450883D2008911890683C60483C7044B75DB8B45FC5F89065E5BC9C3")
MCode(SUBpp,"558BEC83EC148B45148365FC0085C053568B7508578B7D107E3B8B5D188D4DFC894DEC8945F88B038945F48B078945F033D2"
. "8B4DEC8B45F02B0183D2002B45F483D2008911890683C60483C70483C304FF4DF875D18B450C2B451485C07E2D8D4DFC894D0C8BD88B07"
. "89451433D28B4D0C8B45142B0183D20083E80083D2008911890683C60483C7044B75DB5F5E5BC9C3")
MCode(MULpp,"558BEC8B451483EC0C85C07E628B4D08538B5D18568B751057894D142BF18945F48B450C8B4D1433D285C08955FC7E2B8945"
. "F88B040EF72333FF0345FC13D701018B3983C1043BF8730533C040EB0233C003D0FF4DF88955FC75D88345140483C30483EE04FF4DF489"
. "1175B55F5E5BC9C3")
MCode(DIVpp,"558BEC83EC288B4D1856578B7D148B44B9FC0FBDD08955FC6A1F5E2BF28B54B9F88B4DFCD3EA8BCED3E08975ECD1EA0BD08B"
. "450C3BC78955E88945F00F8C210100008B4D102BC78D048189450C8B45082BC1538945D8EB038B4D108B5DF0C1E3028D740BFC8B068B76"
. "FC03D98B4DFC8BD0D3EA8B4DEC895DE48B1BD3E38B4DFCD3EE8B4DECD3E0D1EAD1EE0BD30BF03B55E88955F88975E073168D45148945F4"
. "8B45E08B55F88B4DF4F775E88911EB0383C8FF836514008365F80085FF8945F47E328B750C8B4DF88B45188B0488F765F433C903451413"
. "D18B0E3BC81BDBF7DB2BC803DAFF45F8890E83C604397DF8895D147CD18B45148B4DE43901744233DB3BFB895D147E368B750C8D451489"
. "45DC8B45188B04988945F88B068945E033D28B4DDC8B010345F883D2000345E083D200891189064383C6043BDF7CD3FF4DF48B45E48320"
. "008B550CFF4DF08B45D88B4DF4836D0C04397DF0890C100F8DF6FEFFFF5B5F5EC9C3") ; shortest code 359 bytes
MCode(DIVpq,"558BEC83EC2C538B5D1856578B7D148B44BBFC0FBDC88B54BBF8894DFC6A1F592B4DFC8BF2894DF48B4DFCD3EE8B4DF4D3E0"
. "D3E2D1EE0BF083FF028975E48955E87E0E8B44BBF48B4DFCD3E8D1E80945E88B450C3BC78945EC0F8C300100002BC7C1E0028945F88B5D"
. "EC8B4D10C1E3028D740BFC8B068B76FC03D98B4DFC8BD0D3EA8B4DF4895DE08B1BD3E38B4DFCD3EE8B4DF4D3E0D1EAD1EE0BD30BF03B55"
. "E48955F08975DC732A8D451489450C8B45DC8B55F08B4D0CF775E4891189450CF765E88945D48B4514403BD07609FF4D0CEB04834D0CFF"
. "836514008365F00085FF7E388B45F88B4D108D34088B4DF08B45188B0488F7650C33C903451413D18B0E3BC81BDBF7DB2BC803DAFF45F0"
. "890E83C604397DF0895D147CD18B45148B4DE03901744833DB3BFB895D147E3C8B4D108D45148945D88B45F88D34088B45188B04988945"
. "F08B068945DC33D28B4DD88B010345F083D2000345DC83D200891189064383C6043BDF7CD3FF4D0C8B45E08320008B55F8FF4DEC8B4508"
. "8B4D0C836DF804397DEC890C020F8DD8FEFFFF5F5E5BC9C3") ; Quotient correction 404 bytes, 20..30% faster @ large args!
/*
MCode(DIVpr,"558BEC8B5518D9EE83EC38538B5D148B449AFC85C0567504D9C0EB2E0FBDC8894DF08B75F06A1F592BCED3E081C61F040000"
. "C1E61403C08BC8C1E90C0BF1C1E0148975E48945E0DD45E08B449AF885C07504D9C1EB2E0FBDC8894DF08B55F06A1F592BCAD3E081C2FF"
. "030000C1E21403C08BC8C1E90C0BD1C1E0148955E48945E0DD45E08B450CDEC13BC38945F80F8CBA010000D9E82BC3C1E002DEF18945FC"
. "578B55F88B7510C1E2028D04328945F08B0085C07504D9C1EB2E0FBDC8894D0C8B7D0C6A1F592BCFD3E081C73F040000C1E71403C08BC8"
. "C1E90C0BF9C1E014897DDC8945D8DD45D88D5432F88B420485C07504D9C2EB2E0FBDC8894D0C8B7D0C6A1F592BCFD3E081C71F040000C1"
. "E71403C08BC8C1E90C0BF9C1E014897DD48945D0DD45D08B0285C07504D9C3EB2E0FBDC8894D0C8B550C6A1F592BCAD3E081C2FF030000"
. "C1E21403C08BC8C1E90C0BD1C1E0148955CC8945C8DD45C8DEC1DEC1D8C9DD5DE08B55E481FA0000F03F0F82C800000081FA0000F04172"
. "06834D0CFFEB218B4DE08BC20D0000F0FFC1E915C1E00B0BC1C1EA14B91E0400002BCAD3E889450C33FF33DB397D147E2E8B45FC03F08B"
. "45188B04B8F7650C33C903C313D18B0E3BC81BDBF7DB2BC803DA890E4783C6043B7D147CDA8B75108B45F03918744633FF397D14897DF4"
. "7E398D45F48945E48B45FC03F08B45188B04B88945E88B068945EC33D28B4DE48B010345E883D2000345EC83D200891189064783C6043B"
. "7D147CD2FF4D0C8B45F08320008B45088B4DFC8B550C8B5D14891401FF4DF8836DFC04395DF80F8D54FEFFFF5FDDD95EDDD85BC9C3")
;  598 bytes. uses real (double) division internally. Workaround compiler bugs!!
*/
MCode(U32toHex,"8B542404566A1C33F6598B44240CD3E883E00F03F0750485C9750E83F80976040437EB02043088024283E90479DCC602005EC3")
MCode(U32to8Hex,"8B5424046A1C598B442408D3E883E00F83F8097E040437EB02043088024283E90479E4C60200C3")
MCode(xGCD, "558BEC8B551C836208008B4D2433C0408942048901894104894108830AFF8B4D2083EC20538B5D1489018941048941088B4D"
. "28836108008309FF56578941048B43048B55188BC82B4A04740A3BC81BC083E00248EB234083F8027C1B8BFB8D34822BFA8B0C372B0E0F"
. "85C60000004883EE0483F8027DEC33C085C00F840B0400007D228B4D1C8BC38945188B4524894D248B4D2089451C8B45288BDA8B551889"
. "4D288945208B43040FBD4C8304894D148B4A040FBD748A048B7D142BFE8975EC8BF02BF185FF897D147D054E83451420408D7E023BC789"
. "45EC7E426A1F592B4D142BC68D0482894DF88945F08B78FC8B4DF88B00D3EF8B4D14D3E08B4DECD1EF0BF88B048B2BC775338B45F04983"
. "E8048D7E023BCF894DEC8945F07FCF8B4D148B42088B3CBBD3E08BC88BC72BC174173BC7EB0B3B0C83E912FFFFFF3B048B1BC083E00248"
. "EB138D4601EB07833C830077154883F8027DF433C085C00F842A0300007D03FF4D14837D14007D054E834514208B4D148365FC008D45FC"
. "8945F48B4208D3E08D7CB3088945EC8B078945F033D28B4DF48B45F02B0183D2002B45EC83D200891189078B4B048D4603413BC18945F4"
. "77608D4DFC894DE86A1F592B4D142BC6894DF88B4D188D3C818B4DF88B47FC8B17D3E88B4D14D3E2D1E80BC28945EC8B45F48B04838945"
. "F033D28B4DE88B45F02B0183D2002B45EC83D20089118B4DF4FF45F489048B8B430483C704403945F476B78B430433C94140EB07833C83"
. "0075084883F80277F4EB038D48FF894B04837C8B04000F844C0200008B4D148365FC008D45FC8945F08B451C8B4008D3E08945EC8B4524"
. "8D7CB0088B078945E833D28B4DF08B010345EC83D2000345E883D200891189078B451C8B40048D7C30018B45248B4004403BF873028BF8"
. "8D46033BC78945F4776C8D4DFC894DE46A1F592B4D142BC6894DF88B4D1C8D04818945F0EB038B45F08B50FC8B4DF88B00D3EA8B4D14D3"
. "E08B4DF4D1EA0BD08B45248D04888945E08B008955EC8945E833D28B4DE48B010345EC83D2000345E883D20089118B4DE0FF45F48345F0"
. "04397DF4890176B08B551C8D45FC8945E86A1F8BC72BC68B0482592B4D14D3E8894DF8D1E88945E48B45248B44B8048945E033D28B4DE8"
. "8B010345E483D2000345E083D20089118B4D248944B9048B45FC85C089790476098944B908FF4104EB0B837CB9040075044F8979048B4D"
. "148B7D288365FC008D45FC8945E88B45208B4008D3E08945E48B44B7088945E033D28B4DE88B010345E483D2000345E083D20089118B4D"
. "208944B7088B41048D5430018B4704403BD08955F473038945F48D46033B45F48945F0775D2BC68D55FC8D04818955E88945ECEB038B45"
. "EC8B50FC8B4DF88B00D3EA8B4D14D3E0D1EA0BD08B45F08B04878955E48945E033D28B4DE88B010345E483D2000345E083D20089118B4D"
. "F08345EC0489048F413B4DF4894DF076B68B4D208D45FC8945E48B45F48BD02BD68B14918B4DF8D3EA8D7487048B06894514D1EA8955E0"
. "33D28B4DE48B010345E083D20003451483D20089118B4DFC85C989068B45F4894704760C894C8708FF4704E9C8FBFFFF833E000F85BFFB"
. "FFFF8B4D2848E9B3FBFFFF8B55188B45088B4D1C89108B450C89088B45108B4D205F5E89085BC9C3") ; 1190 bytes
}