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Sin Cepat dan Kos pada ASM tertanam untuk Delphi

Halo semuanya!

Ada kebutuhan untuk menulis perhitungan cepat Sin dan Cos. Dasar perhitungannya adalah ekspansi dalam seri Taylor. Saya menggunakannya dalam sistem 3D (OpenGL dan perpustakaan grafik pengembangan saya). Sayangnya, tidak mungkin untuk mengurangi jumlah "ideal" untuk Double, tetapi ini diimbangi dengan akselerasi yang baik. Kode ini ditulis dalam assembler di Delphi XE6. Digunakan oleh SSE2.

Tidak cocok untuk komputasi ilmiah, tetapi sepenuhnya untuk digunakan dalam game.
Akurasinya cukup untuk menutupi panjang jumlah Single, yang digunakan
untuk perkalian dengan matriks.

Singkatnya:

  1. Akurasi yang diperoleh adalah: 10.e-13
  2. Perbedaan maksimum dengan CPU adalah 0,000000000000045.
  3. Kecepatan meningkat dibandingkan dengan CPU sebesar 4,75 kali.
  4. Kecepatannya meningkat dibandingkan dengan Math.Sin dan Math.Cos sebesar 2,6 kali.

Untuk pengujian saya menggunakan prosesor Intel Core-i7 6950X Extreme 3.0 GHz.
Kode sumber delphi tertanam dalam komentar assembler.

Kode Sumber:

Judul spoiler
var gSinTab: array of Double; gSinAddr: UInt64; const AbsMask64: UInt64 = ($7FFFFFFFFFFFFFFF); PI90: Double = (PI / 2.0); FSinTab: array[0..7] of Double = (1.0 / 6.0, //3! 1.0 / 120.0, //5! 1.0 / 5040.0, //7! 1.0 / 362880.0, //9! 1.0 / 39916800.0, //11! 1.0 / 6227020800.0, //13! 1.0 / 1307674368000.0, //15! 1.0 / 355687428096000.0); //17! //  Sin    QSinMaxP: array[0..3] of Double = (0.0, 1.0, 0.0, -1.0); //  Sin    QSinMaxM: array[0..3] of Double = (0.0, -1.0, 0.0, 1.0); //     QSinSignP: array[0..3] of Double = (1.0, 1.0, -1.0, -1.0); //     QSinSignM: array[0..3] of Double = (-1.0, -1.0, 1.0, 1.0); function Sinf(const A: Double): Double; asm .NOFRAME //   A  xmm0 //   // X := IntFMod(Abs(A), PI90, D); // Result := FNum - (Trunc(FNum / FDen) * FDen); pxor xmm3, xmm3 comisd A, xmm3 jnz @ANZ ret // Result := 0.0; @ANZ: //   //Minus := (A < 0.0); setc cl movsd xmm1, [AbsMask64] //Abs(A) pand A, xmm1 movsd xmm1, [PI90] //PI90 = FDen movsd xmm2, A // A = FNum divsd xmm2, xmm1 //(FNum / FDen) roundsd xmm2, xmm2, 11b //11b - Trunc cvtsd2si rax, xmm2 //  (X  EAX) mulsd xmm2, xmm1 subsd xmm0, xmm2 //----------------------------------- //  and rax, 3 // D := (D and 3); //----------------------------------- //     // if (X = 0.0) then // begin // if Minus then // Exit(QSinMaxM[D]) else // Exit(QSinMaxP[D]); // end; comisd xmm0, xmm3 jnz @XNZ shl rax, 3 //     Double (8 ) cmp cl, 1 //  ,   je @MaxMinus @MaxPlus: lea rdx, qword ptr [QSinMaxP] movsd xmm0, qword ptr [rdx + rax] ret @MaxMinus: lea rdx, qword ptr [QSinMaxM] movsd xmm0, qword ptr [rdx + rax] ret //----------------------------------- @XNZ: //        // if (D and 1) <> 0 then X := (PI90 - X); mov edx, eax and edx, 1 cmp edx, 0 je @DZ subsd xmm1, xmm0 movsd xmm0, xmm1 //----------------------------------- @DZ: // Result   xmm0 // X  xmm0 // N := (X * X)  xmm2 // F := (N * X)  xmm1 // N movsd xmm2, xmm0 //  X mulsd xmm2, xmm2 // N := (X * X) // F movsd xmm1, xmm2 //  N mulsd xmm1, xmm0 // F := (N * X) //     mov rdx, [gSinTab] movaps xmm4, dqword ptr [rdx] movaps xmm6, dqword ptr [rdx + 16] movaps xmm8, dqword ptr [rdx + 32] movaps xmm10, dqword ptr [rdx + 48] //    movhlps xmm5, xmm4 movhlps xmm7, xmm6 movhlps xmm9, xmm8 movhlps xmm11, xmm10 // Result := X - F * PDouble(gSinAddr)^; mulsd xmm4, xmm1 //FSinTab[0] subsd xmm0, xmm4 // F := (F * N); // Result := Result + F * PDouble(gSinAddr + 8)^; mulsd xmm1, xmm2 mulsd xmm5, xmm1 //FSinTab[1] addsd xmm0, xmm5 // F := (F * N); // Result := Result - F * PDouble(gSinAddr + 16)^; mulsd xmm1, xmm2 mulsd xmm6, xmm1 //FSinTab[2] subsd xmm0, xmm6 // F := (F * N); // Result := Result + F * PDouble(gSinAddr + 24)^; mulsd xmm1, xmm2 mulsd xmm7, xmm1 //FSinTab[3] addsd xmm0, xmm7 // F := (F * N); // Result := Result - F * PDouble(gSinAddr + 32)^; mulsd xmm1, xmm2 mulsd xmm8, xmm1 //FSinTab[4] subsd xmm0, xmm8 // F := (F * N); // Result := Result + F * PDouble(gSinAddr + 40)^; mulsd xmm1, xmm2 mulsd xmm9, xmm1 //FSinTab[5] addsd xmm0, xmm9 // F := (F * N); // Result := Result - F * PDouble(gSinAddr + 48)^; mulsd xmm1, xmm2 mulsd xmm10, xmm1 //FSinTab[6] subsd xmm0, xmm10 // F := (F * N); // Result := Result + F * PDouble(gSinAddr + 56)^; mulsd xmm1, xmm2 mulsd xmm11, xmm1 //FSinTab[7] addsd xmm0, xmm11 //----------------------------------- // if Minus then // Result := (Result * QSinSignM[D]) else // Result := (Result * QSinSignP[D]); shl rax, 3 //  8 cmp cl, 1 je @Minus lea rdx, qword ptr [QSinSignP] mulsd xmm0, qword ptr [rdx + rax] ret @Minus: lea rdx, qword ptr [QSinSignM] mulsd xmm0, qword ptr [rdx + rax] end; //------------------------------------ function Cosf(const A: Double): Double; asm .NOFRAME // A  xmm0 //   // X := IntFMod(AMod, PI90, D); // Result := FNum - (Trunc(FNum / FDen) * FDen); pxor xmm3, xmm3 comisd A, xmm3 jnz @ANZ movsd xmm0, [DoubleOne] ret // Result := 1.0; //----------------------------------- @ANZ: //   //Minus := (A < 0.0); setc cl movsd xmm1, [AbsMask64] //Abs(A) pand A, xmm1 //----------------------------------- movsd xmm1, [PI90] //PI90 = FDen //----------------------------------- // if Minus then // AMod := Abs(A) - PI90 else // AMod := Abs(A) + PI90; cmp cl, 1 je @SubPI90 addsd A, xmm1 jmp @IntFMod @SubPI90: subsd A, xmm1 //----------------------------------- @IntFMod: movsd xmm2, A // A = FNum divsd xmm2, xmm1 //(FNum / FDen) roundsd xmm2, xmm2, 11b //11b - Trunc cvtsd2si rax, xmm2 //  (X  EAX) mulsd xmm2, xmm1 subsd xmm0, xmm2 //----------------------------------- //  and rax, 3 // D := (D and 3); //----------------------------------- //     // if (X = 0.0) then // begin // if Minus then // Exit(QSinMaxM[D]) else // Exit(QSinMaxP[D]); // end; comisd xmm0, xmm3 jnz @XNZ shl rax, 3 //     Double (8 ) cmp cl, 1 //  ,   je @MaxMinus @MaxPlus: lea rdx, qword ptr [QSinMaxP] movsd xmm0, qword ptr [rdx + rax] ret @MaxMinus: lea rdx, qword ptr [QSinMaxM] movsd xmm0, qword ptr [rdx + rax] ret //----------------------------------- @XNZ: //        // if (D and 1) <> 0 then X := (PI90 - X); mov edx, eax and edx, 1 cmp edx, 0 je @DZ subsd xmm1, xmm0 movsd xmm0, xmm1 @DZ: // Result   xmm0 // X  xmm0 // N := (X * X)  xmm2 // F := (N * X)  xmm1 // N movsd xmm2, xmm0 //  X mulsd xmm2, xmm2 // N := (X * X) // F movsd xmm1, xmm2 //  N mulsd xmm1, xmm0 // F := (N * X) //     mov rdx, [gSinTab] movaps xmm4, dqword ptr [rdx] movaps xmm6, dqword ptr [rdx + 16] movaps xmm8, dqword ptr [rdx + 32] movaps xmm10, dqword ptr [rdx + 48] //    movhlps xmm5, xmm4 movhlps xmm7, xmm6 movhlps xmm9, xmm8 movhlps xmm11, xmm10 // Result := X - F * PDouble(gSinAddr)^; mulsd xmm4, xmm1 //FSinTab[0] subsd xmm0, xmm4 // F := (F * N); // Result := Result + F * PDouble(gSinAddr + 8)^; mulsd xmm1, xmm2 mulsd xmm5, xmm1 //FSinTab[1] addsd xmm0, xmm5 // F := (F * N); // Result := Result - F * PDouble(gSinAddr + 16)^; mulsd xmm1, xmm2 mulsd xmm6, xmm1 //FSinTab[2] subsd xmm0, xmm6 // F := (F * N); // Result := Result + F * PDouble(gSinAddr + 24)^; mulsd xmm1, xmm2 mulsd xmm7, xmm1 //FSinTab[3] addsd xmm0, xmm7 // F := (F * N); // Result := Result - F * PDouble(gSinAddr + 32)^; mulsd xmm1, xmm2 mulsd xmm8, xmm1 //FSinTab[4] subsd xmm0, xmm8 // F := (F * N); // Result := Result + F * PDouble(gSinAddr + 40)^; mulsd xmm1, xmm2 mulsd xmm9, xmm1 //FSinTab[5] addsd xmm0, xmm9 // F := (F * N); // Result := Result - F * PDouble(gSinAddr + 48)^; mulsd xmm1, xmm2 mulsd xmm10, xmm1 //FSinTab[6] subsd xmm0, xmm10 // F := (F * N); // Result := Result + F * PDouble(gSinAddr + 56)^; mulsd xmm1, xmm2 mulsd xmm11, xmm1 //FSinTab[7] addsd xmm0, xmm11 //----------------------------------- // if Minus then // Result := (Result * QSinSignM[D]) else // Result := (Result * QSinSignP[D]); shl rax, 3 //  8 cmp cl, 1 je @Minus lea rdx, qword ptr [QSinSignP] mulsd xmm0, qword ptr [rdx + rax] ret @Minus: lea rdx, qword ptr [QSinSignM] mulsd xmm0, qword ptr [rdx + rax] end; Initialization //  SetLength(gSinTab, 8); //  gSinAddr := UInt64(@FSinTab[0]); //     Move(FSinTab[0], gSinTab[0], SizeOf(Double) * 8); Finalization SetLength(gSinTab, 0);


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Source: https://habr.com/ru/post/id429786/

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