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Math3D.pas
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Math3D.pas
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unit Math3D;
interface
uses math;
type
TSMatrix2 = array[0..1, 0..1] of Single;
TMatrix3 = array[0..2, 0..2] of Double;
TSMatrix3 = array[0..2, 0..3] of Single;
TSMatrix4 = array[0..3, 0..3] of Single;
TPSMatrix2 = ^TSMatrix2;
TPMatrix3 = ^TMatrix3;
TPSMatrix3 = ^TSMatrix3;
TPSMatrix4 = ^TSMatrix4;
TPos3D = array[0..2] of Double;
TVec3D = array[0..2] of Double;
TVec4D = array[0..3] of Double;
TSVec = array[0..3] of Single;
TPPos3D = ^TPos3D;
TPVec3D = ^TVec3D;
TPVec4D = ^TVec4D;
TPSVec = ^TSVec;
TSPoint = array[0..1] of Single;
TPSPoint = ^TSPoint;
TCAVWproc = procedure(V1, V2, V3: TPVec3D; const W: Double);
TAVWproc = procedure(V1, V2: TPVec3D; const W: Double);
T2Vproc = procedure(V1, V2: TPVec3D);
T2Vproc4 = procedure(V1, V2: TPVec4D);
TSVfunc = function(const V1: TSVec): TSVec;
TSVfunc2 = function(const smin, smax: Single; const V1: TSVec): TSVec;
TSVfunc3 = procedure(sv1: TPSVec);
Double7B = array[0..6] of Byte;
PDouble7B = ^Double7B;
TQuaternion = array[0..3] of Double;
TPQuaternion = ^TQuaternion;
ShortFloat = array[0..1] of Shortint;
PShortFloat = ^ShortFloat;
TComplex = array[0..1] of Double;
TPComplex = ^TComplex;
T4Cardinal = array[0..3] of Cardinal;
T4SVec = array[0..3] of TSVec;
TP4SVec = ^T4SVec;
T3SVec = array[0..2] of TSVec;
TLNormals = array[0..2] of Smallint;
TPLNormals = ^TLNormals;
function LengthOfSVec(const V: TSVec): Single;
function SVectorCross(const V1, V2: TSVec): TSVec;
function AddSVectors(const V1, V2: TSVec): TSVec; overload;
procedure AddSVectors(V1: TPSVec; const V2: TSVec); overload;
function AddSVectorsToDVec(const V1, V2: TSVec): TVec3D;
procedure AddVec(V1, V2: TPVec3D); overload;
procedure AddVec(V1: TPVec3D; const V2: TVec3D); overload;
function AddVecF(const V1, V2: TVec3D): TVec3D;
function AddSVec2Vec3(V1: TPSVec; V2: TPVec3D): TVec3D;
procedure AddSVec2Vec3d(const V1: TSVec; V2: TPVec3D);
procedure mAddVecWeight(V1, V2: TPVec3D; const W: Double);
procedure AddSVecWeight(V1, V2: TPSVec; W: Double);
procedure ChangeMathFuncsToSSE2;
procedure mCopyVec(Vd, Vs: TPVec3D);
procedure CopyVec4(V1, V2: TPVec4D);
procedure mCopyAddVecWeight(V1, V2, V3: TPVec3D; const W: Double);
procedure CopyAddSVecWeight(V1, V2: TPVec3D; V3: TPSVec; const W: Double);
procedure AddSubVecWeight(V1, V2, V3: TPVec3D; const W: Double);
procedure BuildRotMatrix(const xa, ya, za: Double; M: TPMatrix3);
procedure BuildRotMatrixS(const xa, ya, za: Double; M: TPSMatrix3);
procedure InvertSMatrix(M: TPSMatrix3);
procedure RotateVector(V: TPVec3D; M: TPMatrix3);
procedure ScaleMatrix(const s: Double; M: TPMatrix3);
procedure ScaleSMatrix(const s: Double; M: TPSMatrix3);
procedure Multiply2Matrix(M1, M2: TPMatrix3);
procedure Multiply2SMatrix(M1, M2: TPSMatrix3);
//procedure BuildRotMatrixFOV(var xa, ya: Double; M: TPMatrix3);
//function InvertMatrix(m: TPMatrix3): TMatrix3;
procedure MatrixToQuat(M1: TMatrix3; var Q: TQuaternion);
procedure SMatrixToQuat(M1: TSMatrix3; var Q: TQuaternion);
procedure QuatToAxisAngle(var xAxes, yAxes, zAxes, angle: Double; Quat: TQuaternion);
function AxisAngleToQuat(var x, y, z, angle: Double): TQuaternion;
procedure CreateMatrixFromQuat(var M: TMatrix3; var Q: TQuaternion);
procedure CreateSMatrixFromQuat(var M: TSMatrix3; var Q: TQuaternion);
function SlerpQuat(Q1, Q2: TQuaternion; const w2: Double): TQuaternion;
//function LerpQuat(Q1, Q2: TQuaternion; w2: Double): TQuaternion;
function InvertQuat(const Q: TQuaternion): TQuaternion;
//procedure BuildRotMatrixX(var xa: Double; M: TPMatrix3);
//procedure BuildRotMatrixY(var ya: Double; M: TPMatrix3);
function NormaliseMatrixTo(const n: Double; M: TPMatrix3): TMatrix3;
function NormaliseSMatrixTo(const n: Double; M: TPSMatrix3): TSMatrix3;
function NormaliseMatrixToS(const n: Double; M: TPMatrix3): TSMatrix3;
function GetQuatFromEuler(const A: TVec3D): TQuaternion;
function GetEulerFromQuat(const Q: TQuaternion): TVec3D;
function DotOfQuats(const Q1, Q2: TQuaternion): Double;
function DotOfVectors(V1, V2: TPVec3D): Double;
function DotOfVectorsNormalize(V1, V2: TPVec3D): Double;
function DotOfSVectors(const V1, V2: TSVec): Single;
function SubtractVectors2s(const V1, V2: TVec3D): TSVec;
function SubtractVectors(const V1, V2: TVec3D): TVec3D; overload;
function SubtractVectors(V1: TPVec3D; const V2: TVec3D): TVec3D; overload;
function SubtractVectors(const V1: TVec3D; V2: TPVec3D): TVec3D; overload;
function SubtractSVectors(V1: TPSVec; const V2: TSVec): TSVec;
function ScaleVector(const V1: TVec3D; const s: Double): TVec3D;
function ScaleSVector(const V1: TSVec; const s: Single): TSVec;
function ScaleSVector4(const V1: TSVec; const s: Single): TSVec;
function ScaleSVectorD(V1: TPSVec; const d: Double): TSVec;
procedure ScaleVectorV(V1: TPVec3D; const s: Double);
procedure ScaleSVectorV(V1: TPSVec; const s: Single);
function NormaliseVector(V: TPVec3D): TVec3D;
function NormaliseVectorF(const V: TVec3D): TVec3D;
procedure NormaliseVectorVar(var V: TVec3D);
function NormaliseSVectorTo(const n: Double; const V: TSVec): TVec3D;
function NormaliseSVectorToS2(const n: Double; const V: TSVec): TSVec;
//procedure NormaliseSVectorToS(n: Double; var V: TSVec);
function NormaliseVectorTo(const n: Double; const V: TVec3D): TVec3D; overload;
procedure NormaliseVectorTo(const n: Double; V: TPVec3D); overload;
function NormaliseSVector(const V: TSVec): TSVec;
procedure NormaliseSVectorVar(var V: TSVec);
procedure BuildViewVectorDFOV(var xa, ya: Double; v: TPVec3D);
procedure BuildViewVectorFOV(var xa, ya: Double; v: TPSVec);
procedure BuildViewVectorDSphereFOV(var xa, ya: Double; v: TPVec3D);
procedure BuildViewVectorSphereFOV(var xa, ya: Double; v: TPSVec);
procedure TranslatePos(V, VT: TPVec3D; M: TPMatrix3);
procedure RotateSVector(V: TPSVec; M: TPMatrix3);
procedure RotateSVectorReverse(V: TPSVec; M: TPMatrix3);
procedure RotateVectorReverse(V: TPVec3D; M: TPMatrix3);
procedure RotateSVectorS(V: TPSVec; M: TPSMatrix3);
procedure RotateVectorS(V: TPVec3D; M: TPSMatrix3);
procedure RotateVectorReverseS(V: TPVec3D; M: TPSMatrix3);
procedure RotateSVectorReverseS(V: TPSVec; M: TPSMatrix3);
function SingleToShortFloat(s: Single): ShortFloat;
function ShortFloatToSingle(sf: PShortFloat): Single;
function SlerpSVec(V1, V2: TPSVec; const t: Single): TSVec;
//procedure BuildRotMatrixXY(var xa, ya: Double; M: TPMatrix3);
function LengthOfVec(const V: TVec3D): Double;
function SqrLengthOfVec(const V: TVec3D): Double;
function SqrLengthOfSVec(const V: TSVec): Single;
function QBezier(const Q0, Q1, Q2: TQuaternion; const t: Double): TQuaternion;
//function QCubic(Q0, Q1, Q2, Q3: TQuaternion; t: Double): TQuaternion;
function CubicIpol4SVecs(SV1, SV2, SV3, SV4: TPSVec; const t: Double): TSVec;
function BezierIpol3SVecs(SV1, SV2, SV3: TPSVec; const t: Double): TSVec;
function DistanceOf2Vecs(V1, V2: TPVec3D): Double;
//procedure BuildViewVectorFOVprecalc(var ya: Double; Ysincos: TPVec3D; v: TPSVec);
function aMedian(const Count: Integer; var List: array of Double;
const select: Single): Double;
function RotAxisSVecToQuat(const SVec: TSVec; const angle: Single): TQuaternion;
function ArcCosSafe(const d: Double): Double;
function ArcSinSafe(const d: Double): Double;
function MakeRotQuatFromSNormals(const NVec: TSVec): TQuaternion;
procedure AddSVecWeightS(V1, V2: TPSVec; const W: Single); overload;
procedure AddSVecWeightS(var V1: TSVec; const V2: TSVec; const W: Single); overload;
function MultiplySVectors(const V1, V2: TSVec): TSVec;
procedure MultiplySVectorsV(V1, V2: TPSVec); overload;
procedure MultiplySVectorsV(V1: TPSVec; const V2: TSVec); overload;
function AddSVecS(const V1: TSVec; const s: Single): TSVec;
procedure NormaliseQuat(var Quat: TQuaternion);
function MaxCS(s1, s2: Single): Single;
function MinCS(const s1, s2: Single): Single;
function MinMaxCS(const smin, s, smax: Single): Single;
function Min0MaxCS(const s, smax: Single): Single;
function Min0MaxCD(const d, dmax: Double): Double;
function MinMaxCD(const dmin, d, dmax: Double): Double;
function MinCD(const s1, s2: Double): Double;
function MaxCD(const s1, s2: Double): Double;
function Clamp0D(const d: Double): Double;
procedure CreateXYVecsFromNormals(N, VX, VY: TPVec3D);
function MaxAbsCD(const s1, s2: Double): Double;
function MinAbsCD(const s1, s2: Double): Double;
procedure BuildSMatrix4(const dXWrot, dYWrot, dZWrot: Double; var Smatrix4: TSMatrix4);
procedure Rotate4Dex(Vin: TPVec3D; Vout: TPVec4D; SM4: TPSMatrix4);
//procedure Rotate4D(V4: TPVec4D; SM4: TPSMatrix4);
procedure BuildRotMatrix4d(angles: array of Double; var ms4: TSMatrix4);
//function q_pow(const qa, qb: TQuaternion): TQuaternion;
function VectorCross(const V1, V2: TVec3D): TVec3D;
function SVecToDVec(const V1: TSVec): TVec3D;
function DVecToSVec(const V1: TVec3D): TSVec;
procedure SVectorChangeSign(V1: TPSVec);
function mSqrtSVec(const V1: TSVec): TSVec;
function SqrtPosSVec(const V1: TSVec): TSVec;
procedure ChangeMathFuncsToSSE;
function MinMaxSVecPas(const smin, smax: Single; const V1: TSVec): TSVec;
function MinMaxSVecSSE(const smin, smax: Single; const V1: TSVec): TSVec;
function MakeSVecMultiplierFromDynFogCol(sv: TSVec): TSVec;
function MakeSVecFromNormals(PsiLight: Pointer): TSVec;
function MakeDVecFromNormals(PsiLight: Pointer): TVec3D;
function FastPow(const x, y: Single): Single;
function MaxSVec(const V1, V2: TSVec): TSVec;
function MinMaxSVecMC(const V1: TSVec): TSVec;
procedure ClearSVec(var sv: TSVec);
function SqrSVec(const V1: TSVec): TSVec;
procedure ClearDVec(var dv: TVec3D);
function DistanceOf2lines(const P1, P2, V1, V2: TVec3D): Double;
procedure SinCosD(const a: Double; var Sin, Cos: Double);
procedure SinCosS(const a: Double; var Sin, Cos: Single);
procedure SVecToNormals(const sv: TSVec; pn: Pointer);
function LinInterpolate2SVecs(const sv1, sv2: TSVec; const w1: Single): TSVec;
function Add2SVecsWeight(const sv1, sv2: TSVec; const w1, w2: Single): TSVec;
function Add2SVecsWeight2(const sv1, sv2: TSVec; const w2: Single): TSVec;
function MakeSVecFromNormalsD(PsiLight: Pointer): TSVec;
function Add3SVectors(const V1, V2, V3: TSVec): TSVec;
function MakeSplineCoeff(const xs: Double): TSVec;
function SqrDistSV(const sv1, sv2: TSVec): Single;
function FastIntPow(const base: Single; const expo: Integer): Single; //powers with expo in 2^x
procedure MinMaxSvar(const smin, smax: Single; var s: Single);
function Clamp01S(const sv: Single): Single;
function Clamp01D(const dv: Double): Double;
procedure Clamp01Svar(var sv: Single);
function Max0S(s: Single): Single;
procedure MakeWNormalsFromDVec(PsiLight: TPLNormals; PDVec: TPVec3D);
function D7BtoDouble(const D7B: Double7B): Double;
function DoubleToD7B(const D: Double): Double7B;
//procedure CopyD(PDsrc, PDdest: Pointer);
procedure MaxCDvar(var ds, ddest: Double);
procedure Clamp1Svar(var s: Single);
function D7Bequal(d1, d2: Double7B): LongBool;
function AbsSVec(sv: TSVec): TSVec;
procedure AbsSVecVar(var sv: TSVec);
function YofSVec(sv: TPSVec): Single;
function MaxOfSVec(sv: TPSVec): Single;
function SVecPow(const sv: TSVec; const sExp: Single): TSVec;
procedure FlipVecs(V1, V2: TPVec3D);
function sNotZero(s: Single): Single;
//function EulerToQuat(x, y, z: Double): TQuaternion;
function MatrixToAngles(var v3: TVec3D; M: TPMatrix3): LongBool;
procedure MakeOrthoVecs(Vin: TPVec3D; Vortho: TPSVec); //Vortho = TPLightSD !!!
procedure MakeOrthoVecsD(Vin, Vx, Vy: TPVec3D);
function NotZero(d: Double): Double;
procedure Clamp0SvecPas(sv1: TPSVec);
//procedure Clamp08SvecPas(sv1: TPSVec);
{procedure RGB2YUV(sv1: TPSVec);
procedure YUV2RGB(sv1: TPSVec); }
procedure YUV2RGBd(vec: TPVec3D);
function SignedSqr(d: Double): Double;
function SignedSqrt(d: Double): Double;
function NotZeroSVec(sv: TPSVec): LongBool;
function FracSingle(const s: Single): Single;
function SingleToPosShortF(s: Single): Word;
function PosShortFToSingle(psf: Word): Single;
procedure mClampSqrtSVecV(v: TPSVec);
procedure mClampSqrSVecV(v: TPSVec);
function MakeVec(d1, d2, d3: Double): TVec3D;
//{$ALIGN 16}
var
// mAddVecWeight: TAVWproc = AddVecWeight;
// mCopyVec: T2Vproc = CopyVec;
// mCopyAddVecWeight: TCAVWproc = CopyAddVecWeight;
mAddSubVecWeight: TCAVWproc = AddSubVecWeight;
mCopyVec4: T2Vproc4 = CopyVec4;
// mSqrtSVec: TSVfunc = SqrtSVecPas;
mMinMaxSVec: TSVfunc2 = MinMaxSVecPas;
mClamp0SVec: TSVfunc3 = Clamp0SVecPas;
// mClamp08SVec: TSVfunc3 = Clamp08SVecPas;
implementation
uses DivUtils, TypeDefinitions;
{$CODEALIGN 16}
function MakeVec(d1, d2, d3: Double): TVec3D;
begin
Result[0] := d1;
Result[1] := d2;
Result[2] := d3;
end;
function NotZeroSVec(sv: TPSVec): LongBool; //eax 0, $FFFFFFFF
//begin //eax
// Result := (sv[0] <> 0) or (sv[1] <> 0) or (sv[2] <> 0);
asm
mov edx, [eax]
or edx, [eax + 4]
or edx, [eax + 8]
xor eax, eax
test edx, edx
jz @@1
mov eax, $FFFFFFFF
@@1:
end;
function SignedSqr(d: Double): Double;
begin
if d < 0 then Result := - Sqr(d) else Result := Sqr(d);
end;
function SignedSqrt(d: Double): Double;
begin
if d < 0 then Result := - Sqrt(- d) else Result := Sqrt(d);
end;
function sNotZero(s: Single): Single;
begin
if Abs(s) > 0.01 then Result := s else
if s < 0 then Result := -0.01 else Result := 0.01;
end;
function NotZero(d: Double): Double;
begin
if Abs(d) > 1e-16 then Result := d else
if d < 0 then Result := d * 0.5 - 0.5e-16
else Result := d * 0.5 + 0.5e-16;
end;
procedure Clamp0SvecPas(sv1: TPSVec);
begin
if sv1[0] < 0 then sv1[0] := 0;
if sv1[1] < 0 then sv1[1] := 0;
if sv1[2] < 0 then sv1[2] := 0;
end;
procedure Clamp0SvecSSE(sv1: TPSVec);
asm
movups xmm0, [eax]
xorps xmm1, xmm1
maxps xmm0, xmm1
movups [eax], xmm0
end;
{procedure Clamp08SvecPas(sv1: TPSVec);
begin
if sv1[0] < 0 then sv1[0] := 0 else if sv1[0] > 8 then sv1[0] := 8;
if sv1[1] < 0 then sv1[1] := 0 else if sv1[1] > 8 then sv1[1] := 8;
if sv1[2] < 0 then sv1[2] := 0 else if sv1[2] > 8 then sv1[2] := 8;
end;
procedure Clamp08SvecSSE(sv1: TPSVec);
const s8: array[0..3] of Single = (8,8,8,8);
asm
movups xmm0, [eax]
movups xmm1, s8
xorps xmm2, xmm2
minps xmm0, xmm1
maxps xmm0, xmm2
movups [eax], xmm0
end;
{procedure RGB2YUV(sv1: TPSVec);
var y: Single;
begin
y := 0.299 * sv1[0] + 0.587 * sv1[1] + 0.114 * sv1[2];
sv1[1] := (sv1[2] - y) * 0.493;
sv1[2] := (sv1[0] - y) * 0.877;
sv1[0] := y;
end;
procedure YUV2RGB(sv1: TPSVec);
var y, u: Single;
begin
y := sv1[0];
u := sv1[1];
sv1[0] := y + sv1[2] * 1.1402508551881414;
sv1[1] := y - 0.58080920903 * sv1[2] - 0.39393070275 * u;
sv1[2] := y + u * 2.0283975659229209;
end; }
procedure YUV2RGBd(vec: TPVec3D);
var y, u: Double;
begin
y := vec[0];
u := vec[1];
vec[0] := y + vec[2] * 1.1402508551881414;
vec[1] := y - 0.58080920903 * vec[2] - 0.39393070275 * u;
vec[2] := y + u * 2.0283975659229209;
end;
{function SVectorCross(const V1, V2: TSVec): TSVec;
Result[0] := V1[1] * V2[2] - V1[2] * V2[1];
Result[1] := V1[2] * V2[0] - V1[0] * V2[2];
Result[2] := V1[0] * V2[1] - V1[1] * V2[0]; }
procedure MakeOrthoVecs(Vin: TPVec3D; Vortho: TPSVec);
var NVec: TVec3D;
d: Double;
begin
NVec := NormaliseVector(Vin);
if Abs(NVec[0]) > 0.1 then
begin
d := 1 / Sqrt(Sqr(NVec[0]) + Sqr(NVec[2]));
Vortho[0] := NVec[2] * d;
Vortho[1] := 0;
Vortho[2] := -NVec[0] * d;
end else begin
d := 1 / Sqrt(Sqr(NVec[1]) + Sqr(NVec[2]));
Vortho[0] := 0;
Vortho[1] := -NVec[2] * d;
Vortho[2] := NVec[1] * d;
end;
// NormaliseSVectorVar(Vortho^);
TPLightSD(Vortho)^[1][0] := Vortho[1] * NVec[2] - Vortho[2] * NVec[1];
TPLightSD(Vortho)^[1][1] := Vortho[2] * NVec[0] - Vortho[0] * NVec[2];
TPLightSD(Vortho)^[1][2] := Vortho[0] * NVec[1] - Vortho[1] * NVec[0];
// TPLightSD(Vortho)^[1] := SVectorCross(Vortho^, NVec);
end;
procedure MakeOrthoVecsD(Vin, Vx, Vy: TPVec3D);
var NVec: TVec3D;
begin
NVec := NormaliseVector(Vin);
if Abs(NVec[0]) > 0.1 then
begin
Vx[0] := NVec[2];
Vx[1] := 0;
Vx[2] := -NVec[0];
end else begin
Vx[0] := 0;
Vx[1] := -NVec[2];
Vx[2] := NVec[1];
end;
NormaliseVectorVar(Vx^);
Vy^ := VectorCross(Vx^, NVec);
end;
procedure FlipVecs(V1, V2: TPVec3D);
asm
fld qword [eax]
fld qword [eax + 8]
fld qword [eax + 16]
fld qword [edx]
fld qword [edx + 8]
fld qword [edx + 16]
fstp qword [eax + 16]
fstp qword [eax + 8]
fstp qword [eax]
fstp qword [edx + 16]
fstp qword [edx + 8]
fstp qword [edx]
end;
function SVecPow(const sv: TSVec; const sExp: Single): TSVec;
begin
Result[0] := Power(sv[0], sExp);
Result[1] := Power(sv[1], sExp);
Result[2] := Power(sv[2], sExp);
Result[3] := 0;
end;
function YofSVec(sv: TPSVec): Single;
asm // Result := sv[0] * s03 + sv[1] * s059 + sv[2] * s011;
fld dword [eax]
fmul s03
fld dword [eax + 4]
fmul s059
faddp
fld dword [eax + 8]
fmul s011
faddp
ftst
fnstsw ax
shr ah, 1
jnc @@1
fstp st
fldz
@@1:
end;
function MaxOfSVec(sv: TPSVec): Single;
{begin
Result := sv[0];
if sv[1] > Result then Result := sv[1];
if sv[2] > Result then Result := sv[2];
end; }
asm
cmp SupportSSE, 0
jz @@1
push edx
movss xmm0, [eax]
maxss xmm0, [eax + 4]
maxss xmm0, [eax + 8]
movss [esp], xmm0
fld dword [esp]
pop edx
ret
@@1:
mov edx, eax
fld dword [eax]
fcom dword [edx + 4]
fnstsw ax
and ah, 41H
jz @@up1
fstp st
fld dword [edx + 4]
@@up1:
fcom dword [edx + 8]
fnstsw ax
and ah, 41H
jz @@up2
fstp st
fld dword [edx + 8]
@@up2:
end;
procedure AbsSVecVar(var sv: TSVec);
begin
sv[0] := Abs(sv[0]);
sv[1] := Abs(sv[1]);
sv[2] := Abs(sv[2]);
end;
function AbsSVec(sv: TSVec): TSVec;
begin
Result[0] := Abs(sv[0]);
Result[1] := Abs(sv[1]);
Result[2] := Abs(sv[2]);
Result[3] := 0;
end;
// eax, edx
function D7Bequal(d1, d2: Double7B): LongBool;
{begin
Result := (d1[0] = d2[0]) and (d1[1] = d2[1]) ...; }
asm
push ecx
mov ecx, [eax]
cmp ecx, [edx]
jne @@1
mov cx, [eax + 4]
cmp cx, word [edx + 4]
jne @@1
mov cl, [eax + 6]
cmp cl, byte [edx + 6]
jne @@1
mov eax, $FFFFFFFF
jmp @@2
@@1:
xor eax, eax
@@2:
pop ecx
end;
// eax st
function D7BtoDouble(const D7B: Double7B): Double;
//begin
// Result := PDouble(Integer(@D7B) - 1)^; //and $FFFFFFFFFFFFFF00;
asm
add esp, -8
xor edx, edx
mov [esp], edx
mov edx, [eax]
mov [esp + 1], edx
mov edx, [eax + 3]
mov [esp + 4], edx
fld qword [esp]
add esp, 8
end;
// ebp+8 eax
function DoubleToD7B(const D: Double): Double7B;
{begin
PInteger(@Result)^ := PInteger(Integer(@D) + 1)^;
PWord(Integer(@Result) + 4)^ := PWord(Integer(@D) + 5)^;
PByte(Integer(@Result) + 6)^ := PByte(Integer(@D) + 7)^; }
asm
mov edx, [ebp + 9]
mov [eax], edx
mov edx, [ebp + 12]
mov [eax + 3], edx
end;
// eax edx
procedure MakeWNormalsFromDVec(PsiLight: TPLNormals; PDVec: TPVec3D);
{var dt2: Double;
begin
dT2 := 32767 / Sqrt(Sqr(PDVec[0]) + Sqr(PDVec[1]) + Sqr(PDVec[2]) + d1em100);
PsiLight[0] := Round(PDVec[0] * dT2); //3 normals a 16bit
PsiLight[1] := Round(PDVec[1] * dT2);
PsiLight[2] := Round(PDVec[2] * dT2); }
asm
fld qword [edx]
fld st
fmul st, st //x²,x
fld qword [edx + 8]
fld st
fmul st, st //y²,y,x²,x
faddp st(2), st //y,x²+y²,x
fld qword [edx + 16]
fld st
fmul st, st //z²,z,y,x²+y²,x
faddp st(3), st //z,y,x²+y²+z²,x
fxch st(2) //x²+y²+z²,y,z,x
fadd d1em100
fsqrt
fdivr d32767
fmul st(3), st
fmul st(2), st
fmulp //y',z',x'
fistp word [eax + 2]
fistp word [eax + 4]
fistp word [eax]
end;
// ebp+8 eax st
function FastIntPow(const base: Single; const expo: Integer): Single; //powers with expo in 2^x x in[1..much] for spec painting, if ipol, expo could be float!
{var i: Integer;
begin
if base < 0 then Result := 0 else
begin
Result := base;
i := expo shr 1;
while i > 0 do
begin
Result := Result * Result;
i := i shr 1;
end;
end; }
asm
fld dword [ebp + 8]
mov edx, eax
ftst
fnstsw ax
shr ah, 1
jnc @@1
fstp st
fldz
jmp @@end
@@1:
shr edx, 1
@@2:
fmul st, st
shr edx, 1
jnz @@2
@@end:
end;
// ebp+8 st
function Clamp0D(const d: Double): Double;
{begin
if d <= 0 then Result := 0
else Result := d; }
asm
fld qword [ebp + 8]
ftst
fnstsw ax
shr ah, 1
jnc @@end
fstp st
fldz
@@end:
end;
//ebp+8 st
function Clamp01S(const sv: Single): Single;
{begin
if sv <= 0 then Result := 0 else
if sv > 1 then Result := 1 else Result := sv; }
asm
fld dword [ebp + 8]
ftst
fnstsw ax
shr ah, 1
jnc @@1
fstp st
fldz
jmp @@end
@@1:
fld1
fcomp st(1)
fnstsw ax
shr ah, 1
jnc @@end
fstp st
fld1
@@end:
end; //ret 4
function Clamp01D(const dv: Double): Double;
asm
fld qword [ebp + 8]
ftst
fnstsw ax
shr ah, 1
jnc @@1
fstp st
fldz
jmp @@end
@@1:
fld1
fcomp st(1)
fnstsw ax
shr ah, 1
jnc @@end
fstp st
fld1
@@end:
end;
procedure Clamp01Svar(var sv: Single);
begin
if sv <= 0 then sv := 0 else
if sv > 1 then sv := 1;
end;
function MinDistSV(const sv1, sv2: TSVec): TSVec;
begin
Result[0] := sv1[1] * sv2[2] - sv1[2] * sv2[1];
Result[1] := sv1[2] * sv2[0] - sv1[0] * sv2[2];
Result[2] := sv1[0] * sv2[1] - sv1[1] * sv2[0];
end;
function SqrDistSV(const sv1, sv2: TSVec): Single;
begin
Result := SqrLengthOfSVec(MinDistSV(sv1, SubtractSVectors(@sv1, sv2)));
end;
//ebp+8 eax
function MakeSplineCoeff(const xs: Double): TSVec;
{begin
Result[3] := d1d6 * xs * xs * xs;
Result[0] := d1d6 + 0.5 * xs * (xs - 1.0) - Result[3];
Result[2] := xs + Result[0] - 2.0 * Result[3];
Result[1] := 1.0 - Result[0] - Result[2] - Result[3]; }
asm
fld d1d6
fld qword [ebp + 8]
fld st
fmul st, st
fmul st, st(1)
fmul st, st(2)
fst dword [eax + 12] //Result[3],xs,d1d6
fld1
fsub st, st(2) //1-xs,Result[3],xs,d1d6
fmul st, st(2)
fmul s05
fsubp st(3), st //Result[3],xs,d1d6 + 0.5 * xs * (xs - 1.0)
fsub st(2), st //Result[3],xs,Result[0]
fxch //xs,Result[3],Result[0]
fadd st, st(2)
fsub st, st(1)
fsub st, st(1) //Result[2],Result[3],Result[0]
fst dword [eax + 8]
fld1
fsubrp //1-Result[2],Result[3],Result[0]
fsubrp //1-Result[2]-Result[3],Result[0]
fsub st, st(1) //1-Result[2]-Result[3]-Result[0],Result[0]
fstp dword [eax + 4]
fstp dword [eax]
end;
// eax edx ebp+8 ecx
function Add2SVecsWeight2(const sv1, sv2: TSVec; const w2: Single): TSVec;
asm
{ cmp SupportSSE, 0
jz @@1
movss xmm2, [ebp + 8]
movups xmm1, [edx]
shufps xmm2, xmm2, $C0
movups xmm0, [eax]
mulps xmm1, xmm2
addps xmm0, xmm1
movups [ecx], xmm0
pop ebp
ret 4
@@1: }
fld dword [edx]
fld dword [edx + 4]
fld dword [edx + 8]
fld dword [ebp + 8]
fmul st(3), st
fmul st(2), st
fmulp
fadd dword [eax + 8]
fstp dword [ecx + 8]
fadd dword [eax + 4]
fstp dword [ecx + 4]
fadd dword [eax]
fstp dword [ecx]
xor eax, eax
mov [ecx + 12], eax
end;
// eax edx ebp+8 ecx
function LinInterpolate2SVecs(const sv1, sv2: TSVec; const w1: Single): TSVec;
{begin
Result[0] := sv1[0] * w1 + sv2[0] * (1 - w1); = sv2[0] + w1 * (sv1[0] - sv2[0]);
Result[1] := sv1[1] * w1 + sv2[1] * (1 - w1);
Result[2] := sv1[2] * w1 + sv2[2] * (1 - w1);
Result[3] := sv1[3] * w1 + sv2[3] * (1 - w1); }
asm
cmp SupportSSE, 0
jz @@1
movss xmm2, [ebp + 8]
movups xmm0, [eax]
movups xmm1, [edx]
shufps xmm2, xmm2, 0
subps xmm0, xmm1
mulps xmm0, xmm2
addps xmm0, xmm1
movups [ecx], xmm0
pop ebp
ret 4
@@1:
fld dword [edx]
fld dword [edx + 4]
fld dword [edx + 8]
fld dword [edx + 12]
fld dword [ebp + 8]
fld dword [eax]
fld dword [eax + 4]
fld dword [eax + 8] //s12,s11,s10,w1,s23,s22,s21,s20
fsub st, st(5)
fmul st, st(3)
faddp st(5), st //s11,s10,w1,s23,result2,s21,s20
fsub st, st(5)
fmul st, st(2)
faddp st(5), st //s10,w1,s23,result2,result1,s20
fsub st, st(5)
fmul st, st(1)
faddp st(5), st //w1,s23,result2,result1,result0
fld dword [eax + 12]
fsub st, st(2) //..,w1,s23,result2,result1,result0
fmulp //..*w1,s23,result2,result1,result0
faddp
fstp dword [ecx + 12]
fstp dword [ecx + 8]
fstp dword [ecx + 4]
fstp dword [ecx]
end;
// eax edx ebp+12 ebp+8 ecx
function Add2SVecsWeight(const sv1, sv2: TSVec; const w1, w2: Single): TSVec;
{begin
Result[0] := sv1[0] * w1 + sv2[0] * w2;
Result[1] := sv1[1] * w1 + sv2[1] * w2;
Result[2] := sv1[2] * w1 + sv2[2] * w2;
Result[3] := 0; }
asm
cmp SupportSSE, 0
jz @@1
movss xmm2, [ebp + 12]
movss xmm3, [ebp + 8]
movups xmm0, [eax]
movups xmm1, [edx]
shufps xmm2, xmm2, $C0
shufps xmm3, xmm3, $C0
mulps xmm0, xmm2
mulps xmm1, xmm3
addps xmm0, xmm1
movups [ecx], xmm0
pop ebp
ret 8
@@1:
fld dword [edx]
fld dword [edx + 4]
fld dword [edx + 8]
fld dword [ebp + 8]
fmul st(3), st
fmul st(2), st
fmulp
fld dword [eax]
fld dword [eax + 4]
fld dword [eax + 8]
fld dword [ebp + 12]
fmul st(3), st
fmul st(2), st
fmulp //s12,s11,s10,s22,s21,s20
xor eax, eax
faddp st(3), st //s11,s10,result2,s21,s20
faddp st(3), st
faddp st(3), st //result2,result1,result0
fstp dword [ecx + 8]
fstp dword [ecx + 4]
fstp dword [ecx]
mov [ecx + 12], eax
end;
function AddSVectorsToDVec(const V1, V2: TSVec): TVec3D;
begin
Result[0] := V1[0] + V2[0];
Result[1] := V1[1] + V2[1];
Result[2] := V1[2] + V2[2];
end;
function DistanceOf2lines(const P1, P2, V1, V2: TVec3D): Double; //not used
var n, p: TVec3D;
begin
p := SubtractVectors(@P1, P2);
n := VectorCross(V1, V2);
Result := (p[0] * n[0] + p[1] * n[1] + p[2] * n[2]) / LengthOfVec(n);
end;
procedure ClearSVec(var sv: TSVec);
asm
xor edx, edx
mov [eax], edx
mov [eax + 4], edx
mov [eax + 8], edx
mov [eax + 12], edx
end;
procedure ClearDVec(var dv: TVec3D);
asm
fldz
fst qword [eax]
fst qword [eax + 8]
fstp qword [eax + 16]
end;
function MaxSVec(const V1, V2: TSVec): TSVec; //not used
begin
Result[0] := MaxCS(V1[0], V2[0]);
Result[1] := MaxCS(V1[1], V2[1]);
Result[2] := MaxCS(V1[2], V2[2]);
Result[3] := 0;
end;
function SqrSVec(const V1: TSVec): TSVec;
begin
Result[0] := Sqr(V1[0]);
Result[1] := Sqr(V1[1]);
Result[2] := Sqr(V1[2]);
Result[3] := 0;
end;
procedure mClampSqrtSVecV(v: TPSVec);
asm
xor edx, edx
mov [eax + 12], edx
cmp SupportSSE, 0
jz @@1
movups xmm0, [eax]
xorps xmm1, xmm1
maxps xmm0, xmm1
sqrtps xmm0, xmm0
movups [eax], xmm0
ret
@@1:
mov edx, eax
fld dword [edx]
ftst
fnstsw ax
shr ah, 1
jnc @@2
fstp st
fldz
jmp @@21
@@2:
fsqrt
@@21:
fstp dword [edx]
fld dword [edx + 4]
ftst
fnstsw ax
shr ah, 1
jnc @@3
fstp st
fldz
jmp @@31
@@3:
fsqrt
@@31:
fstp dword [edx + 4]
fld dword [edx + 8]
ftst
fnstsw ax
shr ah, 1
jnc @@4
fstp st
fldz
jmp @@41
@@4:
fsqrt
@@41:
fstp dword [edx + 8]
end;
procedure mClampSqrSVecV(v: TPSVec);
asm
xor edx, edx
mov [eax + 12], edx
cmp SupportSSE, 0
jz @@1
movups xmm0, [eax]
xorps xmm1, xmm1
maxps xmm0, xmm1
mulps xmm0, xmm0
movups [eax], xmm0
ret
@@1:
mov edx, eax
fld dword [edx]
ftst
fnstsw ax
shr ah, 1
jnc @@2
fstp st
fldz
@@2:
fmul st, st
fstp dword [edx]
fld dword [edx + 4]
ftst
fnstsw ax
shr ah, 1
jnc @@3
fstp st
fldz
@@3:
fmul st, st
fstp dword [edx + 4]
fld dword [edx + 8]
ftst
fnstsw ax
shr ah, 1
jnc @@4
fstp st
fldz
@@4: