diff options
| author | Vadim Dashevskiy <watcherhd@gmail.com> | 2012-10-08 18:43:29 +0000 |
|---|---|---|
| committer | Vadim Dashevskiy <watcherhd@gmail.com> | 2012-10-08 18:43:29 +0000 |
| commit | 864081102a5f252415f41950b3039a896b4ae9c5 (patch) | |
| tree | c6b764651e9dd1f8f53b98eab05f16ba4a492a79 /plugins/Libs/kolmath.pas | |
| parent | db5149b48346c417e18add5702a9dfe7f6e28dd0 (diff) | |
Awkwars's plugins - welcome to our trunk
git-svn-id: http://svn.miranda-ng.org/main/trunk@1822 1316c22d-e87f-b044-9b9b-93d7a3e3ba9c
Diffstat (limited to 'plugins/Libs/kolmath.pas')
| -rw-r--r-- | plugins/Libs/kolmath.pas | 1845 |
1 files changed, 1845 insertions, 0 deletions
diff --git a/plugins/Libs/kolmath.pas b/plugins/Libs/kolmath.pas new file mode 100644 index 0000000000..9e06418343 --- /dev/null +++ b/plugins/Libs/kolmath.pas @@ -0,0 +1,1845 @@ +{=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
+
+ KKKKK KKKKK OOOOOOOOO LLLLL
+ KKKKK KKKKK OOOOOOOOOOOOO LLLLL
+ KKKKK KKKKK OOOOO OOOOO LLLLL
+ KKKKK KKKKK OOOOO OOOOO LLLLL
+ KKKKKKKKKK OOOOO OOOOO LLLLL
+ KKKKK KKKKK OOOOO OOOOO LLLLL
+ KKKKK KKKKK OOOOO OOOOO LLLLL
+ KKKKK KKKKK OOOOOOOOOOOOO LLLLLLLLLLLLL
+ KKKKK KKKKK OOOOOOOOO LLLLLLLLLLLLL
+
+ Key Objects Library (C) 2000 by Kladov Vladimir.
+
+ mailto: vk@kolmck.net
+ Home: http://kolmck.net
+
+ =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-}
+{
+ This code is grabbed from standard math.pas unit,
+ provided by Borland Delphi. This unit is for working with
+ engineering (mathematical) functions. The main difference
+ is that err unit specially designed to handle exceptions
+ for KOL is used instead of SysUtils. This allows to make
+ size of the executable smaller for about 5K. though this
+ value is insignificant for project made with VCL, it can
+ be more than 15% of executable file size made with KOL.
+}
+
+{*******************************************************}
+{ }
+{ Borland Delphi Runtime Library }
+{ Math Unit }
+{ }
+{ Copyright (C) 1996,99 Inprise Corporation }
+{ }
+{*******************************************************}
+
+unit kolmath;
+
+{ This unit contains high-performance arithmetic, trigonometric, logorithmic,
+ statistical and financial calculation routines which supplement the math
+ routines that are part of the Delphi language or System unit. }
+
+{$N+,S-}
+
+{$I KOLDEF.INC}
+
+interface
+
+uses {$IFNDEF MATH_NOERR} err, {$ENDIF} kol;
+
+const { Ranges of the IEEE floating point types, including denormals }
+ MinSingle = 1.5e-45;
+ MaxSingle = 3.4e+38;
+ MinDouble = 5.0e-324;
+ MaxDouble = 1.7e+308;
+ MinExtended = 3.4e-4932;
+ MaxExtended = 1.1e+4932;
+ MinComp = -9.223372036854775807e+18;
+ MaxComp = 9.223372036854775807e+18;
+
+{-----------------------------------------------------------------------
+References:
+
+1) P.J. Plauger, "The Standard C Library", Prentice-Hall, 1992, Ch. 7.
+2) W.J. Cody, Jr., and W. Waite, "Software Manual For the Elementary
+ Functions", Prentice-Hall, 1980.
+3) Namir Shammas, "C/C++ Mathematical Algorithms for Scientists and Engineers",
+ McGraw-Hill, 1995, Ch 8.
+4) H.T. Lau, "A Numerical Library in C for Scientists and Engineers",
+ CRC Press, 1994, Ch. 6.
+5) "Pentium(tm) Processor User's Manual, Volume 3: Architecture
+ and Programming Manual", Intel, 1994
++6)Уоррен Младший, "Арифметические трюки для программистов", исправленное изд.,
+ 2004
+
+All angle parameters and results of trig functions are in radians.
+
+Most of the following trig and log routines map directly to Intel 80387 FPU
+floating point machine instructions. Input domains, output ranges, and
+error handling are determined largely by the FPU hardware.
+Routines coded in assembler favor the Pentium FPU pipeline architecture.
+-----------------------------------------------------------------------}
+
+function EAbs( D: Double ): Double;
+function EMax( const Values: array of Double ): Double;
+function EMin( const Values: array of Double ): Double;
+function ESign( X: Extended ): Integer;
+function iMax( const Values: array of Integer ): Integer;
+function iMin( const Values: array of Integer ): Integer;
+function iSign( i: Integer ): Integer;
+
+{ Trigonometric functions }
+function ArcCos(X: Extended): Extended; { IN: |X| <= 1 OUT: [0..PI] radians }
+function ArcSin(X: Extended): Extended; { IN: |X| <= 1 OUT: [-PI/2..PI/2] radians }
+
+{ ArcTan2 calculates ArcTan(Y/X), and returns an angle in the correct quadrant.
+ IN: |Y| < 2^64, |X| < 2^64, X <> 0 OUT: [-PI..PI] radians }
+function ArcTan2(Y, X: Extended): Extended;
+
+{ SinCos is 2x faster than calling Sin and Cos separately for the same angle }
+procedure SinCos(Theta: Extended; var Sin, Cos: Extended) register;
+function Tan(X: Extended): Extended;
+function Cotan(X: Extended): Extended; { 1 / tan(X), X <> 0 }
+function Hypot(X, Y: Extended): Extended; { Sqrt(X**2 + Y**2) }
+
+{ Angle unit conversion routines }
+function DegToRad(Degrees: Extended): Extended; { Radians := Degrees * PI / 180}
+function RadToDeg(Radians: Extended): Extended; { Degrees := Radians * 180 / PI }
+function GradToRad(Grads: Extended): Extended; { Radians := Grads * PI / 200 }
+function RadToGrad(Radians: Extended): Extended; { Grads := Radians * 200 / PI }
+function CycleToRad(Cycles: Extended): Extended; { Radians := Cycles * 2PI }
+function RadToCycle(Radians: Extended): Extended;{ Cycles := Radians / 2PI }
+
+{ Hyperbolic functions and inverses }
+function Cosh(X: Extended): Extended;
+function Sinh(X: Extended): Extended;
+function Tanh(X: Extended): Extended;
+function ArcCosh(X: Extended): Extended; { IN: X >= 1 }
+function ArcSinh(X: Extended): Extended;
+function ArcTanh(X: Extended): Extended; { IN: |X| <= 1 }
+
+{ Logorithmic functions }
+function LnXP1(X: Extended): Extended; { Ln(X + 1), accurate for X near zero }
+function Log10(X: Extended): Extended; { Log base 10 of X}
+function Log2(X: Extended): Extended; { Log base 2 of X }
+function LogN(Base, X: Extended): Extended; { Log base N of X }
+
+{ Exponential functions }
+
+{ IntPower: Raise base to an integral power. Fast. }
+//function IntPower(Base: Extended; Exponent: Integer): Extended register;
+// -- already defined in kol.pas
+
+{ Power: Raise base to any power.
+ For fractional exponents, or |exponents| > MaxInt, base must be > 0. }
+function Power(Base, Exponent: Extended): Extended;
+{$IFNDEF _D6orHigher}
+function Trunc( X: Extended ): Int64;
+{$ENDIF}
+
+{ Miscellaneous Routines }
+
+{ Frexp: Separates the mantissa and exponent of X. }
+procedure Frexp(X: Extended; var Mantissa: Extended; var Exponent: Integer) register;
+
+{ Ldexp: returns X*2**P }
+function Ldexp(X: Extended; P: Integer): Extended register;
+
+{ Ceil: Smallest integer >= X, |X| < MaxInt }
+function Ceil(X: Extended):Integer;
+
+{ Floor: Largest integer <= X, |X| < MaxInt }
+function Floor(X: Extended): Integer;
+
+{ Poly: Evaluates a uniform polynomial of one variable at value X.
+ The coefficients are ordered in increasing powers of X:
+ Coefficients[0] + Coefficients[1]*X + ... + Coefficients[N]*(X**N) }
+function Poly(X: Extended; const Coefficients: array of Double): Extended;
+
+{-----------------------------------------------------------------------
+Statistical functions.
+
+Common commercial spreadsheet macro names for these statistical and
+financial functions are given in the comments preceding each function.
+-----------------------------------------------------------------------}
+
+{ Mean: Arithmetic average of values. (AVG): SUM / N }
+function Mean(const Data: array of Double): Extended;
+
+{ Sum: Sum of values. (SUM) }
+function Sum(const Data: array of Double): Extended register;
+function SumInt(const Data: array of Integer): Integer register;
+function SumOfSquares(const Data: array of Double): Extended;
+procedure SumsAndSquares(const Data: array of Double;
+ var Sum, SumOfSquares: Extended) register;
+
+{ MinValue: Returns the smallest signed value in the data array (MIN) }
+function MinValue(const Data: array of Double): Double;
+function MinIntValue(const Data: array of Integer): Integer;
+
+function Min(A,B: Integer): Integer;
+{$IFDEF _D4orHigher}
+overload;
+function Min(A,B: I64): I64; overload;
+function Min(A,B: Int64): Int64; overload;
+function Min(A,B: Single): Single; overload;
+function Min(A,B: Double): Double; overload;
+function Min(A,B: Extended): Extended; overload;
+{$ENDIF}
+
+{ MaxValue: Returns the largest signed value in the data array (MAX) }
+function MaxValue(const Data: array of Double): Double;
+function MaxIntValue(const Data: array of Integer): Integer;
+
+function Max(A,B: Integer): Integer;
+{$IFDEF _D4orHigher}
+overload;
+function Max(A,B: I64): I64; overload;
+function Max(A,B: Single): Single; overload;
+function Max(A,B: Double): Double; overload;
+function Max(A,B: Extended): Extended; overload;
+{$ENDIF}
+
+{ Standard Deviation (STD): Sqrt(Variance). aka Sample Standard Deviation }
+function StdDev(const Data: array of Double): Extended;
+
+{ MeanAndStdDev calculates Mean and StdDev in one call. }
+procedure MeanAndStdDev(const Data: array of Double; var Mean, StdDev: Extended);
+
+{ Population Standard Deviation (STDP): Sqrt(PopnVariance).
+ Used in some business and financial calculations. }
+function PopnStdDev(const Data: array of Double): Extended;
+
+{ Variance (VARS): TotalVariance / (N-1). aka Sample Variance }
+function Variance(const Data: array of Double): Extended;
+
+{ Population Variance (VAR or VARP): TotalVariance/ N }
+function PopnVariance(const Data: array of Double): Extended;
+
+{ Total Variance: SUM(i=1,N)[(X(i) - Mean)**2] }
+function TotalVariance(const Data: array of Double): Extended;
+
+{ Norm: The Euclidean L2-norm. Sqrt(SumOfSquares) }
+function Norm(const Data: array of Double): Extended;
+
+{ MomentSkewKurtosis: Calculates the core factors of statistical analysis:
+ the first four moments plus the coefficients of skewness and kurtosis.
+ M1 is the Mean. M2 is the Variance.
+ Skew reflects symmetry of distribution: M3 / (M2**(3/2))
+ Kurtosis reflects flatness of distribution: M4 / Sqr(M2) }
+procedure MomentSkewKurtosis(const Data: array of Double;
+ var M1, M2, M3, M4, Skew, Kurtosis: Extended);
+
+{ RandG produces random numbers with Gaussian distribution about the mean.
+ Useful for simulating data with sampling errors. }
+function RandG(Mean, StdDev: Extended): Extended;
+
+{-----------------------------------------------------------------------
+Financial functions. Standard set from Quattro Pro.
+
+Parameter conventions:
+
+From the point of view of A, amounts received by A are positive and
+amounts disbursed by A are negative (e.g. a borrower's loan repayments
+are regarded by the borrower as negative).
+
+Interest rates are per payment period. 11% annual percentage rate on a
+loan with 12 payments per year would be (11 / 100) / 12 = 0.00916667
+
+-----------------------------------------------------------------------}
+
+type
+ TPaymentTime = (ptEndOfPeriod, ptStartOfPeriod);
+
+{ Double Declining Balance (DDB) }
+function DoubleDecliningBalance(Cost, Salvage: Extended;
+ Life, Period: Integer): Extended;
+
+{ Future Value (FVAL) }
+function FutureValue(Rate: Extended; NPeriods: Integer; Payment, PresentValue:
+ Extended; PaymentTime: TPaymentTime): Extended;
+
+{ Interest Payment (IPAYMT) }
+function InterestPayment(Rate: Extended; Period, NPeriods: Integer; PresentValue,
+ FutureValue: Extended; PaymentTime: TPaymentTime): Extended;
+
+{ Interest Rate (IRATE) }
+function InterestRate(NPeriods: Integer;
+ Payment, PresentValue, FutureValue: Extended; PaymentTime: TPaymentTime): Extended;
+
+{ Internal Rate of Return. (IRR) Needs array of cash flows. }
+function InternalRateOfReturn(Guess: Extended;
+ const CashFlows: array of Double): Extended;
+
+{ Number of Periods (NPER) }
+function NumberOfPeriods(Rate, Payment, PresentValue, FutureValue: Extended;
+ PaymentTime: TPaymentTime): Extended;
+
+{ Net Present Value. (NPV) Needs array of cash flows. }
+function NetPresentValue(Rate: Extended; const CashFlows: array of Double;
+ PaymentTime: TPaymentTime): Extended;
+
+{ Payment (PAYMT) }
+function Payment(Rate: Extended; NPeriods: Integer;
+ PresentValue, FutureValue: Extended; PaymentTime: TPaymentTime): Extended;
+
+{ Period Payment (PPAYMT) }
+function PeriodPayment(Rate: Extended; Period, NPeriods: Integer;
+ PresentValue, FutureValue: Extended; PaymentTime: TPaymentTime): Extended;
+
+{ Present Value (PVAL) }
+function PresentValue(Rate: Extended; NPeriods: Integer;
+ Payment, FutureValue: Extended; PaymentTime: TPaymentTime): Extended;
+
+{ Straight Line depreciation (SLN) }
+function SLNDepreciation(Cost, Salvage: Extended; Life: Integer): Extended;
+
+{ Sum-of-Years-Digits depreciation (SYD) }
+function SYDDepreciation(Cost, Salvage: Extended; Life, Period: Integer): Extended;
+
+{type
+ EInvalidArgument = class(EMathError) end;}
+
+{------------------------------------------------------------------------------}
+{ Integer and logical functions }
+function IsPowerOf2( i: Integer ): Boolean;
+{* TRUE, если число является степенью числа 2 }
+
+function Low1( i: Integer ): Integer;
+{* Выделяет младший бит 1 из числа i. }
+
+function Low0( i: Integer ): Integer;
+{* Выделяет младший справа бит 0 из числа i, например, 1100011 -> 100 }
+
+function count_1_bits_in_byte( x: Byte ): Byte;
+{* Подсчитывает число единичных битов в байте }
+
+function count_1_bits_in_dword( x: Integer ): Integer;
+{* Подсчитывает число единичных битов в 32-битном }
+
+
+implementation
+
+{$IFNDEF _D2orD3}
+uses SysConst;
+{$ENDIF}
+
+function EAbs( D: Double ): Double;
+begin
+ Result := D;
+ if Result < 0.0 then
+ Result := -Result;
+end;
+
+function EMax( const Values: array of Double ): Double;
+var I: Integer;
+begin
+ Result := Values[ 0 ];
+ for I := 1 to High( Values ) do
+ if Result < Values[ I ] then Result := Values[ I ];
+end;
+
+function EMin( const Values: array of Double ): Double;
+var I: Integer;
+begin
+ Result := Values[ 0 ];
+ for I := 1 to High( Values ) do
+ if Result > Values[ I ] then Result := Values[ I ];
+end;
+
+function ESign( X: Extended ): Integer;
+begin
+ if X < 0 then Result := -1
+ else if X > 0 then Result := 1
+ else Result := 1;
+end;
+
+function iMax( const Values: array of Integer ): Integer;
+var I: Integer;
+begin
+ Result := Values[ 0 ];
+ for I := 1 to High( Values ) do
+ if Result < Values[ I ] then Result := Values[ I ];
+end;
+
+function iMin( const Values: array of Integer ): Integer;
+var I: Integer;
+begin
+ Result := Values[ 0 ];
+ for I := 1 to High( Values ) do
+ if Result > Values[ I ] then Result := Values[ I ];
+end;
+
+{$IFDEF PAS_VERSION}
+function iSign( i: Integer ): Integer;
+begin
+ if i < 0 then Result := -1
+ else if i > 0 then Result := 1
+ else Result := 0;
+end;
+{$ELSE}
+function iSign( i: Integer ): Integer;
+asm
+ XOR EDX, EDX
+ TEST EAX, EAX
+ JZ @@exit
+ MOV DL, 1
+ JG @@exit
+ OR EDX, -1
+@@exit:
+ XCHG EAX, EDX
+end;
+{$ENDIF}
+
+function Annuity2(R: Extended; N: Integer; PaymentTime: TPaymentTime;
+ var CompoundRN: Extended): Extended; Forward;
+function Compound(R: Extended; N: Integer): Extended; Forward;
+function RelSmall(X, Y: Extended): Boolean; Forward;
+
+type
+ TPoly = record
+ Neg, Pos, DNeg, DPos: Extended
+ end;
+
+const
+ MaxIterations = 15;
+
+{$IFNDEF MATH_NOERR}
+procedure ArgError(const Msg: string);
+begin
+ raise Exception.Create(e_Math_InvalidArgument, Msg);
+end;
+{$ENDIF}
+
+function DegToRad(Degrees: Extended): Extended; { Radians := Degrees * PI / 180 }
+begin
+ Result := Degrees * (PI / 180);
+end;
+
+function RadToDeg(Radians: Extended): Extended; { Degrees := Radians * 180 / PI }
+begin
+ Result := Radians * (180 / PI);
+end;
+
+function GradToRad(Grads: Extended): Extended; { Radians := Grads * PI / 200 }
+begin
+ Result := Grads * (PI / 200);
+end;
+
+function RadToGrad(Radians: Extended): Extended; { Grads := Radians * 200 / PI}
+begin
+ Result := Radians * (200 / PI);
+end;
+
+function CycleToRad(Cycles: Extended): Extended; { Radians := Cycles * 2PI }
+begin
+ Result := Cycles * (2 * PI);
+end;
+
+function RadToCycle(Radians: Extended): Extended;{ Cycles := Radians / 2PI }
+begin
+ Result := Radians / (2 * PI);
+end;
+
+function LnXP1(X: Extended): Extended;
+{ Return ln(1 + X). Accurate for X near 0. }
+asm
+ FLDLN2
+ MOV AX,WORD PTR X+8 { exponent }
+ FLD X
+ CMP AX,$3FFD { .4225 }
+ JB @@1
+ FLD1
+ FADD
+ FYL2X
+ JMP @@2
+@@1:
+ FYL2XP1
+@@2:
+ FWAIT
+end;
+
+{ Invariant: Y >= 0 & Result*X**Y = X**I. Init Y = I and Result = 1. }
+{function IntPower(X: Extended; I: Integer): Extended;
+var
+ Y: Integer;
+begin
+ Y := Abs(I);
+ Result := 1.0;
+ while Y > 0 do begin
+ while not Odd(Y) do
+ begin
+ Y := Y shr 1;
+ X := X * X
+ end;
+ Dec(Y);
+ Result := Result * X
+ end;
+ if I < 0 then Result := 1.0 / Result
+end;
+}
+(* -- already defined in kol.pas
+function IntPower(Base: Extended; Exponent: Integer): Extended;
+asm
+ mov ecx, eax
+ cdq
+ fld1 { Result := 1 }
+ xor eax, edx
+ sub eax, edx { eax := Abs(Exponent) }
+ jz @@3
+ fld Base
+ jmp @@2
+@@1: fmul ST, ST { X := Base * Base }
+@@2: shr eax,1
+ jnc @@1
+ fmul ST(1),ST { Result := Result * X }
+ jnz @@1
+ fstp st { pop X from FPU stack }
+ cmp ecx, 0
+ jge @@3
+ fld1
+ fdivrp { Result := 1 / Result }
+@@3:
+ fwait
+end;
+*)
+
+function Compound(R: Extended; N: Integer): Extended;
+{ Return (1 + R)**N. }
+begin
+ Result := IntPower(1.0 + R, N)
+end;
+
+function Annuity2(R: Extended; N: Integer; PaymentTime: TPaymentTime;
+ var CompoundRN: Extended): Extended;
+{ Set CompoundRN to Compound(R, N),
+ return (1+Rate*PaymentTime)*(Compound(R,N)-1)/R;
+}
+begin
+ if R = 0.0 then
+ begin
+ CompoundRN := 1.0;
+ Result := N;
+ end
+ else
+ begin
+ { 6.1E-5 approx= 2**-14 }
+ if EAbs(R) < 6.1E-5 then
+ begin
+ CompoundRN := Exp(N * LnXP1(R));
+ Result := N*(1+(N-1)*R/2);
+ end
+ else
+ begin
+ CompoundRN := Compound(R, N);
+ Result := (CompoundRN-1) / R
+ end;
+ if PaymentTime = ptStartOfPeriod then
+ Result := Result * (1 + R);
+ end;
+end; {Annuity2}
+
+
+procedure PolyX(const A: array of Double; X: Extended; var Poly: TPoly);
+{ Compute A[0] + A[1]*X + ... + A[N]*X**N and X * its derivative.
+ Accumulate positive and negative terms separately. }
+var
+ I: Integer;
+ Neg, Pos, DNeg, DPos: Extended;
+begin
+ Neg := 0.0;
+ Pos := 0.0;
+ DNeg := 0.0;
+ DPos := 0.0;
+ for I := High(A) downto Low(A) do
+ begin
+ DNeg := X * DNeg + Neg;
+ Neg := Neg * X;
+ DPos := X * DPos + Pos;
+ Pos := Pos * X;
+ if A[I] >= 0.0 then
+ Pos := Pos + A[I]
+ else
+ Neg := Neg + A[I]
+ end;
+ Poly.Neg := Neg;
+ Poly.Pos := Pos;
+ Poly.DNeg := DNeg * X;
+ Poly.DPos := DPos * X;
+end; {PolyX}
+
+
+function RelSmall(X, Y: Extended): Boolean;
+{ Returns True if X is small relative to Y }
+const
+ C1: Double = 1E-15;
+ C2: Double = 1E-12;
+begin
+ Result := EAbs(X) < (C1 + C2 * EAbs(Y))
+end;
+
+{ Math functions. }
+
+function ArcCos(X: Extended): Extended;
+begin
+ if X > 0.999999999999999 then
+ Result := 0 {иначе -NAN !}
+ else
+ if X < -0.999999999999999 then
+ Result := PI
+ else
+ Result := ArcTan2(Sqrt(1 - X*X), X);
+end;
+
+function ArcSin(X: Extended): Extended;
+begin
+ Result := ArcTan2(X, Sqrt(1 - X*X))
+end;
+
+function ArcTan2(Y, X: Extended): Extended;
+asm
+ FLD Y
+ FLD X
+ FPATAN
+ FWAIT
+end;
+
+function Tan(X: Extended): Extended;
+{ Tan := Sin(X) / Cos(X) }
+asm
+ FLD X
+ FPTAN
+ FSTP ST(0) { FPTAN pushes 1.0 after result }
+ FWAIT
+end;
+
+function CoTan(X: Extended): Extended;
+{ CoTan := Cos(X) / Sin(X) = 1 / Tan(X) }
+asm
+ FLD X
+ FPTAN
+ FDIVRP
+ FWAIT
+end;
+
+function Hypot(X, Y: Extended): Extended;
+{ formula: Sqrt(X*X + Y*Y)
+ implemented as: |Y|*Sqrt(1+Sqr(X/Y)), |X| < |Y| for greater precision
+var
+ Temp: Extended;
+begin
+ X := Abs(X);
+ Y := Abs(Y);
+ if X > Y then
+ begin
+ Temp := X;
+ X := Y;
+ Y := Temp;
+ end;
+ if X = 0 then
+ Result := Y
+ else // Y > X, X <> 0, so Y > 0
+ Result := Y * Sqrt(1 + Sqr(X/Y));
+end;
+}
+asm
+ FLD Y
+ FABS
+ FLD X
+ FABS
+ FCOM
+ FNSTSW AX
+ TEST AH,$45
+ JNZ @@1 // if ST > ST(1) then swap
+ FXCH ST(1) // put larger number in ST(1)
+@@1: FLDZ
+ FCOMP
+ FNSTSW AX
+ TEST AH,$40 // if ST = 0, return ST(1)
+ JZ @@2
+ FSTP ST // eat ST(0)
+ JMP @@3
+@@2: FDIV ST,ST(1) // ST := ST / ST(1)
+ FMUL ST,ST // ST := ST * ST
+ FLD1
+ FADD // ST := ST + 1
+ FSQRT // ST := Sqrt(ST)
+ FMUL // ST(1) := ST * ST(1); Pop ST
+@@3: FWAIT
+end;
+
+
+procedure SinCos(Theta: Extended; var Sin, Cos: Extended);
+asm
+ FLD Theta
+ FSINCOS
+ FSTP tbyte ptr [edx] // Cos
+ FSTP tbyte ptr [eax] // Sin
+ FWAIT
+end;
+
+{ Extract exponent and mantissa from X }
+procedure Frexp(X: Extended; var Mantissa: Extended; var Exponent: Integer);
+{ Mantissa ptr in EAX, Exponent ptr in EDX }
+asm
+ FLD X
+ PUSH EAX
+ MOV dword ptr [edx], 0 { if X = 0, return 0 }
+
+ FTST
+ FSTSW AX
+ FWAIT
+ SAHF
+ JZ @@Done
+
+ FXTRACT // ST(1) = exponent, (pushed) ST = fraction
+ FXCH
+
+// The FXTRACT instruction normalizes the fraction 1 bit higher than
+// wanted for the definition of frexp() so we need to tweak the result
+// by scaling the fraction down and incrementing the exponent.
+
+ FISTP dword ptr [edx]
+ FLD1
+ FCHS
+ FXCH
+ FSCALE // scale fraction
+ INC dword ptr [edx] // exponent biased to match
+ FSTP ST(1) // discard -1, leave fraction as TOS
+
+@@Done:
+ POP EAX
+ FSTP tbyte ptr [eax]
+ FWAIT
+end;
+
+function Ldexp(X: Extended; P: Integer): Extended;
+ { Result := X * (2^P) }
+asm
+ PUSH EAX
+ FILD dword ptr [ESP]
+ FLD X
+ FSCALE
+ POP EAX
+ FSTP ST(1)
+ FWAIT
+end;
+
+function Ceil(X: Extended): Integer;
+begin
+ Result := Integer(Trunc(X));
+ if Frac(X) > 0 then
+ Inc(Result);
+end;
+
+function Floor(X: Extended): Integer;
+begin
+ Result := Integer(Trunc(X));
+ if Frac(X) < 0 then
+ Dec(Result);
+end;
+
+{ Conversion of bases: Log.b(X) = Log.a(X) / Log.a(b) }
+
+function Log10(X: Extended): Extended;
+ { Log.10(X) := Log.2(X) * Log.10(2) }
+asm
+ FLDLG2 { Log base ten of 2 }
+ FLD X
+ FYL2X
+ FWAIT
+end;
+
+function Log2(X: Extended): Extended;
+asm
+ FLD1
+ FLD X
+ FYL2X
+ FWAIT
+end;
+
+function LogN(Base, X: Extended): Extended;
+{ Log.N(X) := Log.2(X) / Log.2(N) }
+asm
+ FLD1
+ FLD X
+ FYL2X
+ FLD1
+ FLD Base
+ FYL2X
+ FDIV
+ FWAIT
+end;
+
+function Poly(X: Extended; const Coefficients: array of Double): Extended;
+{ Horner's method }
+var
+ I: Integer;
+begin
+ Result := Coefficients[High(Coefficients)];
+ for I := High(Coefficients)-1 downto Low(Coefficients) do
+ Result := Result * X + Coefficients[I];
+end;
+
+function Power(Base, Exponent: Extended): Extended;
+begin
+ if Exponent = 0.0 then
+ Result := 1.0 { n**0 = 1 }
+ else if (Base = 0.0) and (Exponent > 0.0) then
+ Result := 0.0 { 0**n = 0, n > 0 }
+ else if (Frac(Exponent) = 0.0) and (EAbs(Exponent) <= MaxInt) then
+ Result := IntPower(Base, Integer(Trunc(Exponent)))
+ else
+ Result := Exp(Exponent * Ln(Base))
+end;
+
+{$IFNDEF _D6orHigher}
+(*function Trunc1( X: Extended ): Int64;
+begin
+ Result := System.Trunc( X );
+end;
+asm
+ FLD qword ptr [ESP+4]
+ { -> FST(0) Extended argument }
+ { <- EDX:EAX Result }
+
+
+ SUB ESP,12
+ FNSTCW [ESP].Word // save
+ FNSTCW [ESP+2].Word // scratch
+ FWAIT
+ OR [ESP+2].Word, $0F00 // trunc toward zero, full precision
+ FLDCW [ESP+2].Word
+ FISTP qword ptr [ESP+4]
+ FWAIT
+ FLDCW [ESP].Word
+ POP ECX
+ POP EAX
+ POP EDX
+end;*)
+
+function Trunc( X: Extended ): Int64;
+begin
+ if Abs( X ) < 1 then Result := 0 else
+ if X < 0 then Result := -System.Trunc( -X )
+ else Result := System.Trunc( X );
+end;
+{$ENDIF}
+
+
+{ Hyperbolic functions }
+
+function CoshSinh(X: Extended; Factor: Double): Extended;
+begin
+ Result := Exp(X) / 2;
+ Result := Result + Factor / Result;
+end;
+
+function Cosh(X: Extended): Extended;
+begin
+ Result := CoshSinh(X, 0.25)
+end;
+
+function Sinh(X: Extended): Extended;
+begin
+ Result := CoshSinh(X, -0.25)
+end;
+
+const
+ MaxTanhDomain = 5678.22249441322; // Ln(MaxExtended)/2
+
+function Tanh(X: Extended): Extended;
+begin
+ if X > MaxTanhDomain then
+ Result := 1.0
+ else if X < -MaxTanhDomain then
+ Result := -1.0
+ else
+ begin
+ Result := Exp(X);
+ Result := Result * Result;
+ Result := (Result - 1.0) / (Result + 1.0)
+ end;
+end;
+
+function ArcCosh(X: Extended): Extended;
+begin
+ if X <= 1.0 then
+ Result := 0.0
+ else if X > 1.0e10 then
+ Result := Ln(2) + Ln(X)
+ else
+ Result := Ln(X + Sqrt((X - 1.0) * (X + 1.0)));
+end;
+
+function ArcSinh(X: Extended): Extended;
+var
+ Neg: Boolean;
+begin
+ if X = 0 then
+ Result := 0
+ else
+ begin
+ Neg := (X < 0);
+ X := EAbs(X);
+ if X > 1.0e10 then
+ Result := Ln(2) + Ln(X)
+ else
+ begin
+ Result := X*X;
+ Result := LnXP1(X + Result / (1 + Sqrt(1 + Result)));
+ end;
+ if Neg then Result := -Result;
+ end;
+end;
+
+function ArcTanh(X: Extended): Extended;
+var
+ Neg: Boolean;
+begin
+ if X = 0 then
+ Result := 0
+ else
+ begin
+ Neg := (X < 0);
+ X := EAbs(X);
+ if X >= 1 then
+ Result := MaxExtended
+ else
+ Result := 0.5 * LnXP1((2.0 * X) / (1.0 - X));
+ if Neg then Result := -Result;
+ end;
+end;
+
+{ Statistical functions }
+
+function Mean(const Data: array of Double): Extended;
+begin
+ Result := SUM(Data) / (High(Data) - Low(Data) + 1)
+end;
+
+function MinValue(const Data: array of Double): Double;
+var
+ I: Integer;
+begin
+ Result := Data[Low(Data)];
+ for I := Low(Data) + 1 to High(Data) do
+ if Result > Data[I] then
+ Result := Data[I];
+end;
+
+function MinIntValue(const Data: array of Integer): Integer;
+var
+ I: Integer;
+begin
+ Result := Data[Low(Data)];
+ for I := Low(Data) + 1 to High(Data) do
+ if Result > Data[I] then
+ Result := Data[I];
+end;
+
+{$IFDEF ASM_VERSION}
+function Min(A,B: Integer): Integer;
+asm
+ CMP EAX, EDX
+ JL @@1
+ XCHG EAX, EDX
+@@1:
+end;
+{$ELSE}
+function Min(A,B: Integer): Integer;
+begin
+ if A < B then
+ Result := A
+ else
+ Result := B;
+end;
+{$ENDIF}
+
+{$IFDEF _D4orHigher}
+function Min(A,B: I64): I64;
+begin
+ if Cmp64( A, B ) < 0 then
+ Result := A
+ else
+ Result := B;
+end;
+
+function Min(A,B: Int64): Int64;
+begin
+ if A < B then
+ Result := A
+ else
+ Result := B;
+end;
+
+function Min(A,B: Single): Single;
+begin
+ if A < B then
+ Result := A
+ else
+ Result := B;
+end;
+
+function Min(A,B: Double): Double;
+begin
+ if A < B then
+ Result := A
+ else
+ Result := B;
+end;
+
+function Min(A,B: Extended): Extended;
+begin
+ if A < B then
+ Result := A
+ else
+ Result := B;
+end;
+{$ENDIF}
+
+function MaxValue(const Data: array of Double): Double;
+var
+ I: Integer;
+begin
+ Result := Data[Low(Data)];
+ for I := Low(Data) + 1 to High(Data) do
+ if Result < Data[I] then
+ Result := Data[I];
+end;
+
+function MaxIntValue(const Data: array of Integer): Integer;
+var
+ I: Integer;
+begin
+ Result := Data[Low(Data)];
+ for I := Low(Data) + 1 to High(Data) do
+ if Result < Data[I] then
+ Result := Data[I];
+end;
+
+{$IFDEF ASM_VERSION}
+function Max(A,B: Integer): Integer;
+asm
+ CMP EAX, EDX
+ JG @@1
+ XCHG EAX, EDX
+@@1:
+end;
+{$ELSE}
+function Max(A,B: Integer): Integer;
+begin
+ if A > B then
+ Result := A
+ else
+ Result := B;
+end;
+{$ENDIF}
+
+{$IFDEF _D4orHigher}
+function Max(A,B: I64): I64;
+begin
+ if Cmp64( A, B ) > 0 then
+ Result := A
+ else
+ Result := B;
+end;
+
+function Max(A,B: Single): Single;
+begin
+ if A > B then
+ Result := A
+ else
+ Result := B;
+end;
+
+function Max(A,B: Double): Double;
+begin
+ if A > B then
+ Result := A
+ else
+ Result := B;
+end;
+
+function Max(A,B: Extended): Extended;
+begin
+ if A > B then
+ Result := A
+ else
+ Result := B;
+end;
+{$ENDIF}
+
+procedure MeanAndStdDev(const Data: array of Double; var Mean, StdDev: Extended);
+var
+ S: Extended;
+ N,I: Integer;
+begin
+ N := High(Data)- Low(Data) + 1;
+ if N = 1 then
+ begin
+ Mean := Data[0];
+ StdDev := Data[0];
+ Exit;
+ end;
+ Mean := Sum(Data) / N;
+ S := 0; // sum differences from the mean, for greater accuracy
+ for I := Low(Data) to High(Data) do
+ S := S + Sqr(Mean - Data[I]);
+ StdDev := Sqrt(S / (N - 1));
+end;
+
+procedure MomentSkewKurtosis(const Data: array of Double;
+ var M1, M2, M3, M4, Skew, Kurtosis: Extended);
+var
+ Sum, SumSquares, SumCubes, SumQuads, OverN, Accum, M1Sqr, S2N, S3N: Extended;
+ I: Integer;
+begin
+ OverN := 1 / (High(Data) - Low(Data) + 1);
+ Sum := 0;
+ SumSquares := 0;
+ SumCubes := 0;
+ SumQuads := 0;
+ for I := Low(Data) to High(Data) do
+ begin
+ Sum := Sum + Data[I];
+ Accum := Sqr(Data[I]);
+ SumSquares := SumSquares + Accum;
+ Accum := Accum*Data[I];
+ SumCubes := SumCubes + Accum;
+ SumQuads := SumQuads + Accum*Data[I];
+ end;
+ M1 := Sum * OverN;
+ M1Sqr := Sqr(M1);
+ S2N := SumSquares * OverN;
+ S3N := SumCubes * OverN;
+ M2 := S2N - M1Sqr;
+ M3 := S3N - (M1 * 3 * S2N) + 2*M1Sqr*M1;
+ M4 := (SumQuads * OverN) - (M1 * 4 * S3N) + (M1Sqr*6*S2N - 3*Sqr(M1Sqr));
+ Skew := M3 * Power(M2, -3/2); // = M3 / Power(M2, 3/2)
+ Kurtosis := M4 / Sqr(M2);
+end;
+
+function Norm(const Data: array of Double): Extended;
+begin
+ Result := Sqrt(SumOfSquares(Data));
+end;
+
+function PopnStdDev(const Data: array of Double): Extended;
+begin
+ Result := Sqrt(PopnVariance(Data))
+end;
+
+function PopnVariance(const Data: array of Double): Extended;
+begin
+ Result := TotalVariance(Data) / (High(Data) - Low(Data) + 1)
+end;
+
+function RandG(Mean, StdDev: Extended): Extended;
+{ Marsaglia-Bray algorithm }
+var
+ U1, S2: Extended;
+begin
+ repeat
+ U1 := 2*Random - 1;
+ S2 := Sqr(U1) + Sqr(2*Random-1);
+ until S2 < 1;
+ Result := Sqrt(-2*Ln(S2)/S2) * U1 * StdDev + Mean;
+end;
+
+function StdDev(const Data: array of Double): Extended;
+begin
+ Result := Sqrt(Variance(Data))
+end;
+
+procedure RaiseOverflowError; forward;
+
+function SumInt(const Data: array of Integer): Integer;
+{var
+ I: Integer;
+begin
+ Result := 0;
+ for I := Low(Data) to High(Data) do
+ Result := Result + Data[I]
+end; }
+asm // IN: EAX = ptr to Data, EDX = High(Data) = Count - 1
+ // loop unrolled 4 times, 5 clocks per loop, 1.2 clocks per datum
+ PUSH EBX
+ MOV ECX, EAX // ecx = ptr to data
+ MOV EBX, EDX
+ XOR EAX, EAX
+ AND EDX, not 3
+ AND EBX, 3
+ SHL EDX, 2
+ JMP @Vector.Pointer[EBX*4]
+@Vector:
+ DD @@1
+ DD @@2
+ DD @@3
+ DD @@4
+@@4:
+ ADD EAX, [ECX+12+EDX]
+ JO @@RaiseOverflowError
+@@3:
+ ADD EAX, [ECX+8+EDX]
+ JO @@RaiseOverflowError
+@@2:
+ ADD EAX, [ECX+4+EDX]
+ JO @@RaiseOverflowError
+@@1:
+ ADD EAX, [ECX+EDX]
+ JO @@RaiseOverflowError
+ SUB EDX,16
+ JNS @@4
+ POP EBX
+ RET
+@@RaiseOverflowError:
+ POP EBX
+ POP ECX
+ JMP RaiseOverflowError
+end;
+
+procedure RaiseOverflowError;
+begin
+ {$IFNDEF MATH_NOERR}
+ raise Exception.Create(e_IntOverflow, SIntOverflow);
+ {$ENDIF}
+end;
+
+function SUM(const Data: array of Double): Extended;
+{var
+ I: Integer;
+begin
+ Result := 0.0;
+ for I := Low(Data) to High(Data) do
+ Result := Result + Data[I]
+end; }
+asm // IN: EAX = ptr to Data, EDX = High(Data) = Count - 1
+ // Uses 4 accumulators to minimize read-after-write delays and loop overhead
+ // 5 clocks per loop, 4 items per loop = 1.2 clocks per item
+ FLDZ
+ MOV ECX, EDX
+ FLD ST(0)
+ AND EDX, not 3
+ FLD ST(0)
+ AND ECX, 3
+ FLD ST(0)
+ SHL EDX, 3 // count * sizeof(Double) = count * 8
+ JMP @Vector.Pointer[ECX*4]
+@Vector:
+ DD @@1
+ DD @@2
+ DD @@3
+ DD @@4
+@@4: FADD qword ptr [EAX+EDX+24] // 1
+ FXCH ST(3) // 0
+@@3: FADD qword ptr [EAX+EDX+16] // 1
+ FXCH ST(2) // 0
+@@2: FADD qword ptr [EAX+EDX+8] // 1
+ FXCH ST(1) // 0
+@@1: FADD qword ptr [EAX+EDX] // 1
+ FXCH ST(2) // 0
+ SUB EDX, 32
+ JNS @@4
+ FADDP ST(3),ST // ST(3) := ST + ST(3); Pop ST
+ FADD // ST(1) := ST + ST(1); Pop ST
+ FADD // ST(1) := ST + ST(1); Pop ST
+ FWAIT
+end;
+
+function SumOfSquares(const Data: array of Double): Extended;
+var
+ I: Integer;
+begin
+ Result := 0.0;
+ for I := Low(Data) to High(Data) do
+ Result := Result + Sqr(Data[I]);
+end;
+
+procedure SumsAndSquares(const Data: array of Double; var Sum, SumOfSquares: Extended);
+{var
+ I: Integer;
+begin
+ Sum := 0;
+ SumOfSquares := 0;
+ for I := Low(Data) to High(Data) do
+ begin
+ Sum := Sum + Data[I];
+ SumOfSquares := SumOfSquares + Data[I]*Data[I];
+ end;
+end; }
+asm // IN: EAX = ptr to Data
+ // EDX = High(Data) = Count - 1
+ // ECX = ptr to Sum
+ // Est. 17 clocks per loop, 4 items per loop = 4.5 clocks per data item
+ FLDZ // init Sum accumulator
+ PUSH ECX
+ MOV ECX, EDX
+ FLD ST(0) // init Sqr1 accum.
+ AND EDX, not 3
+ FLD ST(0) // init Sqr2 accum.
+ AND ECX, 3
+ FLD ST(0) // init/simulate last data item left in ST
+ SHL EDX, 3 // count * sizeof(Double) = count * 8
+ JMP @Vector.Pointer[ECX*4]
+@Vector:
+ DD @@1
+ DD @@2
+ DD @@3
+ DD @@4
+@@4: FADD // Sqr2 := Sqr2 + Sqr(Data4); Pop Data4
+ FLD qword ptr [EAX+EDX+24] // Load Data1
+ FADD ST(3),ST // Sum := Sum + Data1
+ FMUL ST,ST // Data1 := Sqr(Data1)
+@@3: FLD qword ptr [EAX+EDX+16] // Load Data2
+ FADD ST(4),ST // Sum := Sum + Data2
+ FMUL ST,ST // Data2 := Sqr(Data2)
+ FXCH // Move Sqr(Data1) into ST(0)
+ FADDP ST(3),ST // Sqr1 := Sqr1 + Sqr(Data1); Pop Data1
+@@2: FLD qword ptr [EAX+EDX+8] // Load Data3
+ FADD ST(4),ST // Sum := Sum + Data3
+ FMUL ST,ST // Data3 := Sqr(Data3)
+ FXCH // Move Sqr(Data2) into ST(0)
+ FADDP ST(3),ST // Sqr1 := Sqr1 + Sqr(Data2); Pop Data2
+@@1: FLD qword ptr [EAX+EDX] // Load Data4
+ FADD ST(4),ST // Sum := Sum + Data4
+ FMUL ST,ST // Sqr(Data4)
+ FXCH // Move Sqr(Data3) into ST(0)
+ FADDP ST(3),ST // Sqr1 := Sqr1 + Sqr(Data3); Pop Data3
+ SUB EDX,32
+ JNS @@4
+ FADD // Sqr2 := Sqr2 + Sqr(Data4); Pop Data4
+ POP ECX
+ FADD // Sqr1 := Sqr2 + Sqr1; Pop Sqr2
+ FXCH // Move Sum1 into ST(0)
+ MOV EAX, SumOfSquares
+ FSTP tbyte ptr [ECX] // Sum := Sum1; Pop Sum1
+ FSTP tbyte ptr [EAX] // SumOfSquares := Sum1; Pop Sum1
+ FWAIT
+end;
+
+function TotalVariance(const Data: array of Double): Extended;
+var
+ Sum, SumSquares: Extended;
+begin
+ SumsAndSquares(Data, Sum, SumSquares);
+ Result := SumSquares - Sqr(Sum)/(High(Data) - Low(Data) + 1);
+end;
+
+function Variance(const Data: array of Double): Extended;
+begin
+ Result := TotalVariance(Data) / (High(Data) - Low(Data))
+end;
+
+
+{ Depreciation functions. }
+
+function DoubleDecliningBalance(Cost, Salvage: Extended; Life, Period: Integer): Extended;
+{ dv := cost * (1 - 2/life)**(period - 1)
+ DDB = (2/life) * dv
+ if DDB > dv - salvage then DDB := dv - salvage
+ if DDB < 0 then DDB := 0
+}
+var
+ DepreciatedVal, Factor: Extended;
+begin
+ Result := 0;
+ if (Period < 1) or (Life < Period) or (Life < 1) or (Cost <= Salvage) then
+ Exit;
+
+ {depreciate everything in period 1 if life is only one or two periods}
+ if ( Life <= 2 ) then
+ begin
+ if ( Period = 1 ) then
+ DoubleDecliningBalance:=Cost-Salvage
+ else
+ DoubleDecliningBalance:=0; {all depreciation occurred in first period}
+ exit;
+ end;
+ Factor := 2.0 / Life;
+
+ DepreciatedVal := Cost * IntPower((1.0 - Factor), Period - 1);
+ {DepreciatedVal is Cost-(sum of previous depreciation results)}
+
+ Result := Factor * DepreciatedVal;
+ {Nominal computed depreciation for this period. The rest of the
+ function applies limits to this nominal value. }
+
+ {Only depreciate until total depreciation equals cost-salvage.}
+ if Result > DepreciatedVal - Salvage then
+ Result := DepreciatedVal - Salvage;
+
+ {No more depreciation after salvage value is reached. This is mostly a nit.
+ If Result is negative at this point, it's very close to zero.}
+ if Result < 0.0 then
+ Result := 0.0;
+end;
+
+function SLNDepreciation(Cost, Salvage: Extended; Life: Integer): Extended;
+{ Spreads depreciation linearly over life. }
+begin
+ {$IFNDEF MATH_NOERR}
+ if Life < 1 then ArgError('SLNDepreciation');
+ {$ENDIF}
+ Result := (Cost - Salvage) / Life
+end;
+
+function SYDDepreciation(Cost, Salvage: Extended; Life, Period: Integer): Extended;
+{ SYD = (cost - salvage) * (life - period + 1) / (life*(life + 1)/2) }
+{ Note: life*(life+1)/2 = 1+2+3+...+life "sum of years"
+ The depreciation factor varies from life/sum_of_years in first period = 1
+ downto 1/sum_of_years in last period = life.
+ Total depreciation over life is cost-salvage.}
+var
+ X1, X2: Extended;
+begin
+ Result := 0;
+ if (Period < 1) or (Life < Period) or (Cost <= Salvage) then Exit;
+ X1 := 2 * (Life - Period + 1);
+ X2 := Life * (Life + 1);
+ Result := (Cost - Salvage) * X1 / X2
+end;
+
+{ Discounted cash flow functions. }
+
+function InternalRateOfReturn(Guess: Extended; const CashFlows: array of Double): Extended;
+{
+Use Newton's method to solve NPV = 0, where NPV is a polynomial in
+x = 1/(1+rate). Split the coefficients into negative and postive sets:
+ neg + pos = 0, so pos = -neg, so -neg/pos = 1
+Then solve:
+ log(-neg/pos) = 0
+
+ Let t = log(1/(1+r) = -LnXP1(r)
+ then r = exp(-t) - 1
+Iterate on t, then use the last equation to compute r.
+}
+var
+ T, Y: Extended;
+ Poly: TPoly;
+ K, Count: Integer;
+
+ function ConditionP(const CashFlows: array of Double): Integer;
+ { Guarantees existence and uniqueness of root. The sign of payments
+ must change exactly once, the net payout must be always > 0 for
+ first portion, then each payment must be >= 0.
+ Returns: 0 if condition not satisfied, > 0 if condition satisfied
+ and this is the index of the first value considered a payback. }
+ var
+ X: Double;
+ I, K: Integer;
+ begin
+ K := High(CashFlows);
+ while (K >= 0) and (CashFlows[K] >= 0.0) do Dec(K);
+ Inc(K);
+ if K > 0 then
+ begin
+ X := 0.0;
+ I := 0;
+ while I < K do begin
+ X := X + CashFlows[I];
+ if X >= 0.0 then
+ begin
+ K := 0;
+ Break
+ end;
+ Inc(I)
+ end
+ end;
+ ConditionP := K
+ end;
+
+begin
+ InternalRateOfReturn := 0;
+ K := ConditionP(CashFlows);
+ {$IFNDEF MATH_NOERR}
+ if K < 0 then ArgError('InternalRateOfReturn');
+ {$ENDIF}
+ if K = 0 then
+ begin
+ {$IFNDEF MATH_NOERR}
+ if Guess <= -1.0 then ArgError('InternalRateOfReturn');
+ {$ENDIF}
+ T := -LnXP1(Guess)
+ end else
+ T := 0.0;
+ for Count := 1 to MaxIterations do
+ begin
+ PolyX(CashFlows, Exp(T), Poly);
+ {$IFNDEF MATH_NOERR}
+ if Poly.Pos <= Poly.Neg then ArgError('InternalRateOfReturn');
+ {$ENDIF}
+ if (Poly.Neg >= 0.0) or (Poly.Pos <= 0.0) then
+ begin
+ InternalRateOfReturn := -1.0;
+ Exit;
+ end;
+ with Poly do
+ Y := Ln(-Neg / Pos) / (DNeg / Neg - DPos / Pos);
+ T := T - Y;
+ if RelSmall(Y, T) then
+ begin
+ InternalRateOfReturn := Exp(-T) - 1.0;
+ Exit;
+ end
+ end;
+ {$IFNDEF MATH_NOERR}
+ ArgError('InternalRateOfReturn');
+ {$ENDIF}
+end;
+
+function NetPresentValue(Rate: Extended; const CashFlows: array of Double;
+ PaymentTime: TPaymentTime): Extended;
+{ Caution: The sign of NPV is reversed from what would be expected for standard
+ cash flows!}
+var
+ rr: Extended;
+ I: Integer;
+begin
+ {$IFNDEF MATH_NOERR}
+ if Rate <= -1.0 then ArgError('NetPresentValue');
+ {$ENDIF}
+ rr := 1/(1+Rate);
+ result := 0;
+ for I := High(CashFlows) downto Low(CashFlows) do
+ result := rr * result + CashFlows[I];
+ if PaymentTime = ptEndOfPeriod then result := rr * result;
+end;
+
+{ Annuity functions. }
+
+{---------------
+From the point of view of A, amounts received by A are positive and
+amounts disbursed by A are negative (e.g. a borrower's loan repayments
+are regarded by the borrower as negative).
+
+Given interest rate r, number of periods n:
+ compound(r, n) = (1 + r)**n "Compounding growth factor"
+ annuity(r, n) = (compound(r, n)-1) / r "Annuity growth factor"
+
+Given future value fv, periodic payment pmt, present value pv and type
+of payment (start, 1 , or end of period, 0) pmtTime, financial variables satisfy:
+
+ fv = -pmt*(1 + r*pmtTime)*annuity(r, n) - pv*compound(r, n)
+
+For fv, pv, pmt:
+
+ C := compound(r, n)
+ A := (1 + r*pmtTime)*annuity(r, n)
+ Compute both at once in Annuity2.
+
+ if C > 1E16 then A = C/r, so:
+ fv := meaningless
+ pv := -pmt*(pmtTime+1/r)
+ pmt := -pv*r/(1 + r*pmtTime)
+ else
+ fv := -pmt(1+r*pmtTime)*A - pv*C
+ pv := (-pmt(1+r*pmtTime)*A - fv)/C
+ pmt := (-pv*C-fv)/((1+r*pmtTime)*A)
+---------------}
+
+function PaymentParts(Period, NPeriods: Integer; Rate, PresentValue,
+ FutureValue: Extended; PaymentTime: TPaymentTime; var IntPmt: Extended):
+ Extended;
+var
+ Crn:extended; { =Compound(Rate,NPeriods) }
+ Crp:extended; { =Compound(Rate,Period-1) }
+ Arn:extended; { =AnnuityF(Rate,NPeriods) }
+
+begin
+ {$IFNDEF MATH_NOERR}
+ if Rate <= -1.0 then ArgError('PaymentParts');
+ {$ENDIF}
+ Crp:=Compound(Rate,Period-1);
+ Arn:=Annuity2(Rate,NPeriods,PaymentTime,Crn);
+ IntPmt:=(FutureValue*(Crp-1)-PresentValue*(Crn-Crp))/Arn;
+ PaymentParts:=(-FutureValue-PresentValue)*Crp/Arn;
+end;
+
+function FutureValue(Rate: Extended; NPeriods: Integer; Payment, PresentValue:
+ Extended; PaymentTime: TPaymentTime): Extended;
+var
+ Annuity, CompoundRN: Extended;
+begin
+ {$IFNDEF MATH_NOERR}
+ if Rate <= -1.0 then ArgError('FutureValue');
+ {$ENDIF}
+ Annuity := Annuity2(Rate, NPeriods, PaymentTime, CompoundRN);
+ {$IFNDEF MATH_NOERR}
+ if CompoundRN > 1.0E16 then ArgError('FutureValue');
+ {$ENDIF}
+ FutureValue := -Payment * Annuity - PresentValue * CompoundRN
+end;
+
+function InterestPayment(Rate: Extended; Period, NPeriods: Integer; PresentValue,
+ FutureValue: Extended; PaymentTime: TPaymentTime): Extended;
+var
+ Crp:extended; { compound(rate,period-1)}
+ Crn:extended; { compound(rate,nperiods)}
+ Arn:extended; { annuityf(rate,nperiods)}
+begin
+ {$IFNDEF MATH_NOERR}
+ if (Rate <= -1.0)
+ or (Period < 1) or (Period > NPeriods) then ArgError('InterestPayment');
+ {$ENDIF}
+ Crp:=Compound(Rate,Period-1);
+ Arn:=Annuity2(Rate,Nperiods,PaymentTime,Crn);
+ InterestPayment:=(FutureValue*(Crp-1)-PresentValue*(Crn-Crp))/Arn;
+end;
+
+function InterestRate(NPeriods: Integer;
+ Payment, PresentValue, FutureValue: Extended; PaymentTime: TPaymentTime): Extended;
+{
+Given:
+ First and last payments are non-zero and of opposite signs.
+ Number of periods N >= 2.
+Convert data into cash flow of first, N-1 payments, last with
+first < 0, payment > 0, last > 0.
+Compute the IRR of this cash flow:
+ 0 = first + pmt*x + pmt*x**2 + ... + pmt*x**(N-1) + last*x**N
+where x = 1/(1 + rate).
+Substitute x = exp(t) and apply Newton's method to
+ f(t) = log(pmt*x + ... + last*x**N) / -first
+which has a unique root given the above hypotheses.
+}
+var
+ X, Y, Z, First, Pmt, Last, T, ET, EnT, ET1: Extended;
+ Count: Integer;
+ Reverse: Boolean;
+
+ function LostPrecision(X: Extended): Boolean;
+ asm
+ XOR EAX, EAX
+ MOV BX,WORD PTR X+8
+ INC EAX
+ AND EBX, $7FF0
+ JZ @@1
+ CMP EBX, $7FF0
+ JE @@1
+ XOR EAX,EAX
+ @@1:
+ end;
+
+begin
+ Result := 0;
+ {$IFNDEF MATH_NOERR}
+ if NPeriods <= 0 then ArgError('InterestRate');
+ {$ENDIF}
+ Pmt := Payment;
+ if PaymentTime = ptEndOfPeriod then
+ begin
+ X := PresentValue;
+ Y := FutureValue + Payment
+ end
+ else
+ begin
+ X := PresentValue + Payment;
+ Y := FutureValue
+ end;
+ First := X;
+ Last := Y;
+ Reverse := False;
+ if First * Payment > 0.0 then
+ begin
+ Reverse := True;
+ T := First;
+ First := Last;
+ Last := T
+ end;
+ if first > 0.0 then
+ begin
+ First := -First;
+ Pmt := -Pmt;
+ Last := -Last
+ end;
+ {$IFNDEF MATH_NOERR}
+ if (First = 0.0) or (Last < 0.0) then ArgError('InterestRate');
+ {$ENDIF}
+ T := 0.0; { Guess at solution }
+ for Count := 1 to MaxIterations do
+ begin
+ EnT := Exp(NPeriods * T);
+ if {LostPrecision(EnT)} ent=(ent+1) then
+ begin
+ Result := -Pmt / First;
+ if Reverse then
+ Result := Exp(-LnXP1(Result)) - 1.0;
+ Exit;
+ end;
+ ET := Exp(T);
+ ET1 := ET - 1.0;
+ if ET1 = 0.0 then
+ begin
+ X := NPeriods;
+ Y := X * (X - 1.0) / 2.0
+ end
+ else
+ begin
+ X := ET * (Exp((NPeriods - 1) * T)-1.0) / ET1;
+ Y := (NPeriods * EnT - ET - X * ET) / ET1
+ end;
+ Z := Pmt * X + Last * EnT;
+ Y := Ln(Z / -First) / ((Pmt * Y + Last * NPeriods *EnT) / Z);
+ T := T - Y;
+ if RelSmall(Y, T) then
+ begin
+ if not Reverse then T := -T;
+ InterestRate := Exp(T)-1.0;
+ Exit;
+ end
+ end;
+ {$IFNDEF MATH_NOERR}
+ ArgError('InterestRate');
+ {$ENDIF}
+end;
+
+function NumberOfPeriods(Rate, Payment, PresentValue, FutureValue: Extended;
+ PaymentTime: TPaymentTime): Extended;
+
+{ If Rate = 0 then nper := -(pv + fv) / pmt
+ else cf := pv + pmt * (1 + rate*pmtTime) / rate
+ nper := LnXP1(-(pv + fv) / cf) / LnXP1(rate) }
+
+var
+ PVRPP: Extended; { =PV*Rate+Payment } {"initial cash flow"}
+ T: Extended;
+
+begin
+ {$IFNDEF MATH_NOERR}
+ if Rate <= -1.0 then ArgError('NumberOfPeriods');
+ {$ENDIF}
+
+{whenever both Payment and PaymentTime are given together, the PaymentTime has the effect
+ of modifying the effective Payment by the interest accrued on the Payment}
+
+ if ( PaymentTime=ptStartOfPeriod ) then
+ Payment:=Payment*(1+Rate);
+
+{if the payment exactly matches the interest accrued periodically on the
+ presentvalue, then an infinite number of payments are going to be
+ required to effect a change from presentvalue to futurevalue. The
+ following catches that specific error where payment is exactly equal,
+ but opposite in sign to the interest on the present value. If PVRPP
+ ("initial cash flow") is simply close to zero, the computation will
+ be numerically unstable, but not as likely to cause an error.}
+
+ PVRPP:=PresentValue*Rate+Payment;
+ {$IFNDEF MATH_NOERR}
+ if PVRPP=0 then ArgError('NumberOfPeriods');
+ {$ENDIF}
+
+ { 6.1E-5 approx= 2**-14 }
+ if ( EAbs(Rate)<6.1E-5 ) then
+ Result:=-(PresentValue+FutureValue)/PVRPP
+ else
+ begin
+
+{starting with the initial cash flow, each compounding period cash flow
+ should result in the current value approaching the final value. The
+ following test combines a number of simultaneous conditions to ensure
+ reasonableness of the cashflow before computing the NPER.}
+
+ T:= -(PresentValue+FutureValue)*Rate/PVRPP;
+ {$IFNDEF MATH_NOERR}
+ if T<=-1.0 then ArgError('NumberOfPeriods');
+ {$ENDIF}
+ Result := LnXP1(T) / LnXP1(Rate)
+ end;
+ NumberOfPeriods:=Result;
+end;
+
+function Payment(Rate: Extended; NPeriods: Integer; PresentValue, FutureValue:
+ Extended; PaymentTime: TPaymentTime): Extended;
+var
+ Annuity, CompoundRN: Extended;
+begin
+ {$IFNDEF MATH_NOERR}
+ if Rate <= -1.0 then ArgError('Payment');
+ {$ENDIF}
+ Annuity := Annuity2(Rate, NPeriods, PaymentTime, CompoundRN);
+ if CompoundRN > 1.0E16 then
+ Payment := -PresentValue * Rate / (1 + Integer(PaymentTime) * Rate)
+ else
+ Payment := (-PresentValue * CompoundRN - FutureValue) / Annuity
+end;
+
+function PeriodPayment(Rate: Extended; Period, NPeriods: Integer;
+ PresentValue, FutureValue: Extended; PaymentTime: TPaymentTime): Extended;
+var
+ Junk: Extended;
+begin
+ {$IFNDEF MATH_NOERR}
+ if (Rate <= -1.0) or (Period < 1) or (Period > NPeriods) then ArgError('PeriodPayment');
+ {$ENDIF}
+ PeriodPayment := PaymentParts(Period, NPeriods, Rate, PresentValue,
+ FutureValue, PaymentTime, Junk);
+end;
+
+function PresentValue(Rate: Extended; NPeriods: Integer; Payment, FutureValue:
+ Extended; PaymentTime: TPaymentTime): Extended;
+var
+ Annuity, CompoundRN: Extended;
+begin
+ {$IFNDEF MATH_NOERR}
+ if Rate <= -1.0 then ArgError('PresentValue');
+ {$ENDIF}
+ Annuity := Annuity2(Rate, NPeriods, PaymentTime, CompoundRN);
+ if CompoundRN > 1.0E16 then
+ PresentValue := -(Payment / Rate * Integer(PaymentTime) * Payment)
+ else
+ PresentValue := (-Payment * Annuity - FutureValue) / CompoundRN
+end;
+
+{------------------------------------------------------------------------------}
+
+function IsPowerOf2( i: Integer ): Boolean; { Result = (i <> 0) and (i and (i-1) = 0); }
+asm
+ OR EAX,EAX
+ JZ @@exit // 0 не является степенью числа 2
+ LEA EDX, [EAX-1]
+ OR EAX,EDX
+ SETZ AL // число является степенью 2, если (i & (i-1)) = 0, т.е. если после
+ // обнуления младшей 1 в числе больше не осталось битов 1.
+@@exit:
+end;
+
+function Low1( i: Integer ): Integer; { Result := i and (-i); }
+asm
+ MOV EDX, EAX
+ NEG EAX
+ AND EAX, EDX
+end;
+
+function Low0( i: Integer ): Integer; { Result := -i and (i+1); }
+asm
+ LEA EDX, [EAX+1]
+ NEG EAX
+ AND EAX, EDX
+end;
+
+function count_1_bits_in_byte( x: Byte ): Byte;
+ asm
+ MOV CL, AL
+@@loop:
+ SHR CL, 1
+ JZ @@exit
+ SUB AL, CL
+ JMP @@loop
+@@exit:
+ end;
+
+function count_1_bits_in_dword( x: Integer ): Integer;
+ asm
+ MOV ECX, EAX
+ JMP @@go
+@@loop:
+ SUB EAX, ECX
+@@go:
+ SHR ECX, 1
+ JNZ @@loop
+ end;
+
+end.
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