+++ /dev/null
-// Written in the D programming language.
-
-/**
- * Computes SHA1 digests of arbitrary data, using an optimized algorithm with SSSE3 instructions.
- *
- * Authors:
- * The general idea is described by Dean Gaudet.
- * Another important observation is published by Max Locktyukhin.
- * (Both implementations are public domain.)
- * Translation to X86 and D by Kai Nacke <kai@redstar.de>
- *
- * References:
- * $(LINK2 http://arctic.org/~dean/crypto/sha1.html)
- * $(LINK2 http://software.intel.com/en-us/articles/improving-the-performance-of-the-secure-hash-algorithm-1/, Fast implementation of SHA1)
- */
-module std.internal.digest.sha_SSSE3;
-
-version (D_InlineAsm_X86)
-{
- version (D_PIC) {} // Bugzilla 9378
- else
- {
- private version = USE_SSSE3;
- private version = _32Bit;
- }
-}
-else version (D_InlineAsm_X86_64)
-{
- private version = USE_SSSE3;
- private version = _64Bit;
-}
-
-/*
- * The idea is quite simple. The SHA-1 specification defines the following message schedule:
- * W[i] = (W[i-3] ^ W[i-8] ^ W[i-14] ^ W[i-16]) rol 1
- *
- * To employ SSE, simply write down the formula four times:
- * W[i ] = (W[i-3] ^ W[i-8] ^ W[i-14] ^ W[i-16]) rol 1
- * W[i+1] = (W[i-2] ^ W[i-7] ^ W[i-13] ^ W[i-15]) rol 1
- * W[i+2] = (W[i-1] ^ W[i-6] ^ W[i-12] ^ W[i-14]) rol 1
- * W[i+3] = (W[i ] ^ W[i-5] ^ W[i-11] ^ W[i-13]) rol 1
- * The last formula requires value W[i] computed with the first formula.
- * Because the xor operation and the rotate operation are commutative, we can replace the
- * last formula with
- * W[i+3] = ( 0 ^ W[i-5] ^ W[i-11] ^ W[i-13]) rol 1
- * and then calculate
- * W[i+3] ^= W[i] rol 1
- * which unfortunately requires many additional operations. This approach was described by
- * Dean Gaudet.
- *
- * Max Locktyukhin observed that
- * W[i] = W[i-A] ^ W[i-B]
- * is equivalent to
- * W[i] = W[i-2*A] ^ W[i-2*B]
- * (if the indices are still in valid ranges). Using this observation, the formula is
- * translated to
- * W[i] = (W[i-6] ^ W[i-16] ^ W[i-28] ^ W[i-32]) rol 2
- * Again, to employ SSE the formula is used four times.
- *
- * Later on, the expression W[i] + K(i) is used. (K(i) is the constant used in round i.)
- * Once the 4 W[i] are calculated, we can also add the four K(i) values with one SSE instruction.
- *
- * The 32bit and 64bit implementations are almost identical. The main difference is that there
- * are only 8 XMM registers in 32bit mode. Therefore, space on the stack is needed to save
- * computed values.
- */
-
-version (USE_SSSE3)
-{
- /*
- * The general idea is to use the XMM registers as a sliding window over
- * message schedule. XMM0 to XMM7 are used to store the last 64 byte of
- * the message schedule. In 64 bit mode this is fine because of the number of
- * registers. The main difference of the 32 bit code is that a part of the
- * calculated message schedule is saved on the stack because 2 temporary
- * registers are needed.
- */
-
- /* Number of message words we are precalculating. */
- private immutable int PRECALC_AHEAD = 16;
-
- /* T1 and T2 are used for intermediate results of computations. */
- private immutable string T1 = "EAX";
- private immutable string T2 = "EBX";
-
- /* The registers used for the SHA-1 variables. */
- private immutable string A = "ECX";
- private immutable string B = "ESI";
- private immutable string C = "EDI";
- private immutable string D = "EBP";
- private immutable string E = "EDX";
-
- /* */
- version (_32Bit)
- {
- private immutable string SP = "ESP";
- private immutable string BUFFER_PTR = "EAX";
- private immutable string STATE_PTR = "EBX";
-
- // Control byte for shuffle instruction (only used in round 0-15)
- private immutable string X_SHUFFLECTL = "XMM6";
-
- // Round constant (only used in round 0-15)
- private immutable string X_CONSTANT = "XMM7";
- }
- version (_64Bit)
- {
- private immutable string SP = "RSP";
- private immutable string BUFFER_PTR = "R9";
- private immutable string STATE_PTR = "R8";
- private immutable string CONSTANTS_PTR = "R10";
-
- // Registers for temporary results (XMM10 and XMM11 are also used temporary)
- private immutable string W_TMP = "XMM8";
- private immutable string W_TMP2 = "XMM9";
-
- // Control byte for shuffle instruction (only used in round 0-15)
- private immutable string X_SHUFFLECTL = "XMM12";
-
- // Round constant
- private immutable string X_CONSTANT = "XMM13";
- }
-
- /* The control words for the byte shuffle instruction and the round constants. */
- align(16) public immutable uint[20] constants =
- [
- // The control words for the byte shuffle instruction.
- 0x0001_0203, 0x0405_0607, 0x0809_0a0b, 0x0c0d_0e0f,
- // Constants for round 0-19
- 0x5a827999, 0x5a827999, 0x5a827999, 0x5a827999,
- // Constants for round 20-39
- 0x6ed9eba1, 0x6ed9eba1, 0x6ed9eba1, 0x6ed9eba1,
- // Constants for round 40-59
- 0x8f1bbcdc, 0x8f1bbcdc, 0x8f1bbcdc, 0x8f1bbcdc,
- // Constants for round 60-79
- 0xca62c1d6, 0xca62c1d6, 0xca62c1d6, 0xca62c1d6
- ];
-
- /** Simple version to produce numbers < 100 as string. */
- private nothrow pure string to_string(uint i)
- {
- if (i < 10)
- return "0123456789"[i .. i + 1];
-
- assert(i < 100);
- char[2] s;
- s[0] = cast(char)(i / 10 + '0');
- s[1] = cast(char)(i % 10 + '0');
- return s.idup;
- }
-
- /** Returns the reference to the byte shuffle control word. */
- private nothrow pure string bswap_shufb_ctl()
- {
- version (_64Bit)
- return "["~CONSTANTS_PTR~"]";
- else
- return "[constants]";
- }
-
- /** Returns the reference to constant used in round i. */
- private nothrow pure string constant(uint i)
- {
- version (_64Bit)
- return "16 + 16*"~to_string(i/20)~"["~CONSTANTS_PTR~"]";
- else
- return "[constants + 16 + 16*"~to_string(i/20)~"]";
- }
-
- /** Returns the XMM register number used in round i */
- private nothrow pure uint regno(uint i)
- {
- return (i/4)&7;
- }
-
- /** Returns reference to storage of vector W[i .. i+4]. */
- private nothrow pure string WiV(uint i)
- {
- return "["~SP~" + WI_PTR + "~to_string((i/4)&7)~"*16]";
- }
-
- /** Returns reference to storage of vector (W + K)[i .. i+4]. */
- private nothrow pure string WiKiV(uint i)
- {
- return "["~SP~" + WI_PLUS_KI_PTR + "~to_string((i/4)&3)~"*16]";
- }
-
- /** Returns reference to storage of value W[i] + K[i]. */
- private nothrow pure string WiKi(uint i)
- {
- return "["~SP~" + WI_PLUS_KI_PTR + 4*"~to_string(i&15)~"]";
- }
-
- /**
- * Chooses the instruction sequence based on the 32bit or 64bit model.
- */
- private nothrow pure string[] swt3264(string[] insn32, string[] insn64)
- {
- version (_32Bit)
- {
- return insn32;
- }
- version (_64Bit)
- {
- return insn64;
- }
- }
-
- /**
- * Flattens the instruction sequence and wraps it in an asm block.
- */
- private nothrow pure string wrap(string[] insn)
- {
- string s = "asm pure nothrow @nogc {";
- foreach (t; insn) s ~= (t ~ "; \n");
- s ~= "}";
- return s;
- // Is not CTFE:
- // return "asm pure nothrow @nogc { " ~ join(insn, "; \n") ~ "}";
- }
-
- /**
- * Weaves the 2 instruction sequences together.
- */
- private nothrow pure string[] weave(string[] seq1, string[] seq2, uint dist = 1)
- {
- string[] res = [];
- auto i1 = 0, i2 = 0;
- while (i1 < seq1.length || i2 < seq2.length)
- {
- if (i2 < seq2.length)
- {
- res ~= seq2[i2 .. i2+1];
- i2 += 1;
- }
- if (i1 < seq1.length)
- {
- import std.algorithm.comparison : min;
-
- res ~= seq1[i1 .. min(i1+dist, $)];
- i1 += dist;
- }
- }
- return res;
- }
-
- /**
- * Generates instructions to load state from memory into registers.
- */
- private nothrow pure string[] loadstate(string base, string a, string b, string c, string d, string e)
- {
- return ["mov "~a~",["~base~" + 0*4]",
- "mov "~b~",["~base~" + 1*4]",
- "mov "~c~",["~base~" + 2*4]",
- "mov "~d~",["~base~" + 3*4]",
- "mov "~e~",["~base~" + 4*4]" ];
- }
-
- /**
- * Generates instructions to update state from registers, saving result in memory.
- */
- private nothrow pure string[] savestate(string base, string a, string b, string c, string d, string e)
- {
- return ["add ["~base~" + 0*4],"~a,
- "add ["~base~" + 1*4],"~b,
- "add ["~base~" + 2*4],"~c,
- "add ["~base~" + 3*4],"~d,
- "add ["~base~" + 4*4],"~e ];
- }
-
- /** Calculates Ch(x, y, z) = z ^ (x & (y ^ z)) */
- private nothrow pure string[] Ch(string x, string y, string z)
- {
- return ["mov "~T1~","~y,
- "xor "~T1~","~z,
- "and "~T1~","~x,
- "xor "~T1~","~z ];
- }
-
- /** Calculates Parity(x, y, z) = x ^ y ^ z */
- private nothrow pure string[] Parity(string x, string y, string z)
- {
- return ["mov "~T1~","~z,
- "xor "~T1~","~y,
- "xor "~T1~","~x ];
- }
-
- /** Calculates Maj(x, y, z) = (x & y) | (z & (x ^ y)) */
- private nothrow pure string[] Maj(string x, string y, string z)
- {
- return ["mov "~T1~","~y,
- "mov "~T2~","~x,
- "or "~T1~","~x,
- "and "~T2~","~y,
- "and "~T1~","~z,
- "or "~T1~","~T2 ];
- }
-
- /** Returns function for round i. Function returns result in T1 and may destroy T2. */
- private nothrow pure string[] F(int i, string b, string c, string d)
- {
- string[] insn;
- if (i >= 0 && i <= 19) insn = Ch(b, c, d);
- else if (i >= 20 && i <= 39) insn = Parity(b, c, d);
- else if (i >= 40 && i <= 59) insn = Maj(b, c, d);
- else if (i >= 60 && i <= 79) insn = Parity(b, c, d);
- else assert(false, "Coding error");
- return insn;
- }
-
- /** Returns instruction used to setup a round. */
- private nothrow pure string[] xsetup(int i)
- {
- if (i == 0)
- {
- return swt3264(["movdqa "~X_SHUFFLECTL~","~bswap_shufb_ctl(),
- "movdqa "~X_CONSTANT~","~constant(i)],
- ["movdqa "~X_SHUFFLECTL~","~bswap_shufb_ctl(),
- "movdqa "~X_CONSTANT~","~constant(i)]);
- }
- version (_64Bit)
- {
- if (i%20 == 0)
- {
- return ["movdqa "~X_CONSTANT~","~constant(i)];
- }
- }
- return [];
- }
-
- /**
- * Loads the message words and performs the little to big endian conversion.
- * Requires that the shuffle control word and the round constant is loaded
- * into required XMM register. The BUFFER_PTR register must point to the
- * buffer.
- */
- private nothrow pure string[] precalc_00_15(int i)
- {
- int regno = regno(i);
-
- string W = "XMM" ~ to_string(regno);
- version (_32Bit)
- {
- string W_TMP = "XMM" ~ to_string(regno+2);
- }
- version (_64Bit)
- {
- string W_TMP = "XMM" ~ to_string(regno+8);
- }
-
- if ((i & 3) == 0)
- {
- return ["movdqu "~W~",["~BUFFER_PTR~" + "~to_string(regno)~"*16]"];
- }
- else if ((i & 3) == 1)
- {
- return ["pshufb "~W~","~X_SHUFFLECTL] ~
- swt3264(["movdqa "~WiV(i)~","~W], []);
- }
- else if ((i & 3) == 2)
- {
- return ["movdqa "~W_TMP~","~W,
- "paddd "~W_TMP~","~X_CONSTANT,
- ];
- }
- else
- {
- return ["movdqa "~WiKiV(i)~","~W_TMP,
- ];
- }
- }
-
- /**
- * Done on 4 consequtive W[i] values in a single XMM register
- * W[i ] = (W[i-3] ^ W[i-8] ^ W[i-14] ^ W[i-16]) rol 1
- * W[i+1] = (W[i-2] ^ W[i-7] ^ W[i-13] ^ W[i-15]) rol 1
- * W[i+2] = (W[i-1] ^ W[i-6] ^ W[i-12] ^ W[i-14]) rol 1
- * W[i+3] = ( 0 ^ W[i-5] ^ W[i-11] ^ W[i-13]) rol 1
- *
- * This additional calculation unfortunately requires many additional operations
- * W[i+3] ^= W[i] rol 1
- *
- * Once we have 4 W[i] values in XMM we can also add four K values with one instruction
- * W[i:i+3] += {K,K,K,K}
- */
- private nothrow pure string[] precalc_16_31(int i)
- {
- int regno = regno(i);
-
- string W = "XMM" ~ to_string(regno);
- string W_minus_4 = "XMM" ~ to_string((regno-1)&7);
- string W_minus_8 = "XMM" ~ to_string((regno-2)&7);
- string W_minus_12 = "XMM" ~ to_string((regno-3)&7);
- string W_minus_16 = "XMM" ~ to_string((regno-4)&7);
- version (_32Bit)
- {
- string W_TMP = "XMM" ~ to_string((regno+1)&7);
- string W_TMP2 = "XMM" ~ to_string((regno+2)&7);
- }
-
- if ((i & 3) == 0)
- {
- return ["movdqa "~W~","~W_minus_12,
- "palignr "~W~","~W_minus_16~",8", // W[i] = W[i-14]
- "pxor "~W~","~W_minus_16, // W[i] ^= W[i-16]
- "pxor "~W~","~W_minus_8, // W[i] ^= W[i-8]
- "movdqa "~W_TMP~","~W_minus_4,
- ];
- }
- else if ((i & 3) == 1)
- {
- return ["psrldq "~W_TMP~",4", // W[i-3]
- "pxor "~W~","~W_TMP, // W[i] ^= W[i-3]
- "movdqa "~W_TMP~","~W,
- "psrld "~W~",31",
- "pslld "~W_TMP~",1",
- ];
- }
- else if ((i & 3) == 2)
- {
- return ["por "~W~","~W_TMP,
- "movdqa "~W_TMP~","~W,
- "pslldq "~W_TMP~",12",
- "movdqa "~W_TMP2~","~W_TMP,
- "pslld "~W_TMP~",1",
- ];
- }
- else
- {
- return ["psrld "~W_TMP2~",31",
- "por "~W_TMP~","~W_TMP2,
- "pxor "~W~","~W_TMP,
- "movdqa "~W_TMP~","~W ] ~
- swt3264(["movdqa "~WiV(i)~","~W,
- "paddd "~W_TMP~","~constant(i) ],
- ["paddd "~W_TMP~","~X_CONSTANT ]) ~
- ["movdqa "~WiKiV(i)~","~W_TMP];
- }
- }
-
- /** Performs the main calculation as decribed above. */
- private nothrow pure string[] precalc_32_79(int i)
- {
- int regno = regno(i);
-
- string W = "XMM" ~ to_string(regno);
- string W_minus_4 = "XMM" ~ to_string((regno-1)&7);
- string W_minus_8 = "XMM" ~ to_string((regno-2)&7);
- string W_minus_16 = "XMM" ~ to_string((regno-4)&7);
- version (_32Bit)
- {
- string W_minus_28 = "[ESP + WI_PTR + "~ to_string((regno-7)&7)~"*16]";
- string W_minus_32 = "[ESP + WI_PTR + "~ to_string((regno-8)&7)~"*16]";
- string W_TMP = "XMM" ~ to_string((regno+1)&7);
- string W_TMP2 = "XMM" ~ to_string((regno+2)&7);
- }
- version (_64Bit)
- {
- string W_minus_28 = "XMM" ~ to_string((regno-7)&7);
- string W_minus_32 = "XMM" ~ to_string((regno-8)&7);
- }
-
- if ((i & 3) == 0)
- {
- return swt3264(["movdqa "~W~","~W_minus_32], []) ~
- ["movdqa "~W_TMP~","~W_minus_4,
- "pxor "~W~","~W_minus_28, // W is W_minus_32 before xor
- "palignr "~W_TMP~","~W_minus_8~",8",
- ];
- }
- else if ((i & 3) == 1)
- {
- return ["pxor "~W~","~W_minus_16,
- "pxor "~W~","~W_TMP,
- "movdqa "~W_TMP~","~W,
- ];
- }
- else if ((i & 3) == 2)
- {
- return ["psrld "~W~",30",
- "pslld "~W_TMP~",2",
- "por "~W_TMP~","~W,
- ];
- }
- else
- {
- if (i < 76)
- return ["movdqa "~W~","~W_TMP] ~
- swt3264(["movdqa "~WiV(i)~","~W,
- "paddd "~W_TMP~","~constant(i)],
- ["paddd "~W_TMP~","~X_CONSTANT]) ~
- ["movdqa "~WiKiV(i)~","~W_TMP];
- else
- return swt3264(["paddd "~W_TMP~","~constant(i)],
- ["paddd "~W_TMP~","~X_CONSTANT]) ~
- ["movdqa "~WiKiV(i)~","~W_TMP];
- }
- }
-
- /** Choose right precalc method. */
- private nothrow pure string[] precalc(int i)
- {
- if (i >= 0 && i < 16) return precalc_00_15(i);
- if (i >= 16 && i < 32) return precalc_16_31(i);
- if (i >= 32 && i < 80) return precalc_32_79(i);
- return [];
- }
-
- /**
- * Return code for round i and i+1.
- * Performs the following rotation:
- * in=>out: A=>D, B=>E, C=>A, D=>B, E=>C
- */
- private nothrow pure string[] round(int i, string a, string b, string c, string d, string e)
- {
- return xsetup(PRECALC_AHEAD + i) ~
- weave(F(i, b, c, d) ~ // Returns result in T1; may destroy T2
- ["add "~e~","~WiKi(i),
- "ror "~b~",2",
- "mov "~T2~","~a,
- "add "~d~","~WiKi(i+1),
- "rol "~T2~",5",
- "add "~e~","~T1 ],
- precalc(PRECALC_AHEAD + i), 2) ~
- weave(
- ["add "~T2~","~e, // T2 = (A <<< 5) + F(B, C, D) + Wi + Ki + E
- "mov "~e~","~T2,
- "rol "~T2~",5",
- "add "~d~","~T2 ] ~
- F(i+1, a, b, c) ~ // Returns result in T1; may destroy T2
- ["add "~d~","~T1,
- "ror "~a~",2"],
- precalc(PRECALC_AHEAD + i+1), 2);
- }
-
- // Offset into stack (see below)
- version (_32Bit)
- {
- private enum { STATE_OFS = 4, WI_PLUS_KI_PTR = 8, WI_PTR = 72 };
- }
- version (_64Bit)
- {
- private enum { WI_PLUS_KI_PTR = 0 };
- }
-
- /** The prologue sequence. */
- private nothrow pure string[] prologue()
- {
- version (_32Bit)
- {
- /*
- * Parameters:
- * EAX contains pointer to input buffer
- *
- * Stack layout as follows:
- * +----------------+
- * | ptr to state |
- * +----------------+
- * | return address |
- * +----------------+
- * | EBP |
- * +----------------+
- * | ESI |
- * +----------------+
- * | EDI |
- * +----------------+
- * | EBX |
- * +----------------+
- * | Space for |
- * | Wi | <- ESP+72
- * +----------------+
- * | Space for |
- * | Wi+Ki | <- ESP+8
- * +----------------+ <- 16byte aligned
- * | ptr to state | <- ESP+4
- * +----------------+
- * | old ESP | <- ESP
- * +----------------+
- */
- static assert(BUFFER_PTR == "EAX");
- static assert(STATE_PTR == "EBX");
- return [// Save registers according to calling convention
- "push EBP",
- "push ESI",
- "push EDI",
- "push EBX",
- // Load parameters
- "mov EBX, [ESP + 5*4]", //pointer to state
- // Align stack
- "mov EBP, ESP",
- "sub ESP, 4*16 + 8*16",
- "and ESP, 0xffff_fff0",
- "push EBX",
- "push EBP",
- ];
- }
- version (_64Bit)
- {
- /*
- * Parameters:
- * RDX contains pointer to state
- * RSI contains pointer to input buffer
- * RDI contains pointer to constants
- *
- * Stack layout as follows:
- * +----------------+
- * | return address |
- * +----------------+
- * | RBP |
- * +----------------+
- * | RBX |
- * +----------------+
- * | Unused |
- * +----------------+
- * | Space for |
- * | Wi+Ki | <- RSP
- * +----------------+ <- 16byte aligned
- */
- return [// Save registers according to calling convention
- "push RBP",
- "push RBX",
- // Save parameters
- "mov "~STATE_PTR~", RDX", //pointer to state
- "mov "~BUFFER_PTR~", RSI", //pointer to buffer
- "mov "~CONSTANTS_PTR~", RDI", //pointer to constants to avoid absolute addressing
- // Align stack
- "sub RSP, 4*16+8",
- ];
- }
- }
-
- /**
- * The epilogue sequence. Just pop the saved registers from stack and return to caller.
- */
- private nothrow pure string[] epilogue()
- {
- version (_32Bit)
- {
- return ["pop ESP",
- "pop EBX",
- "pop EDI",
- "pop ESI",
- "pop EBP",
- "ret 4",
- ];
- }
- version (_64Bit)
- {
- return ["add RSP,4*16+8",
- "pop RBX",
- "pop RBP",
- "ret 0",
- ];
- }
- }
-
- // constants as extra argument for PIC, see Bugzilla 9378
- import std.meta : AliasSeq;
- version (_64Bit)
- alias ExtraArgs = AliasSeq!(typeof(&constants));
- else
- alias ExtraArgs = AliasSeq!();
-
- /**
- *
- */
- public void transformSSSE3(uint[5]* state, const(ubyte[64])* buffer, ExtraArgs) pure nothrow @nogc
- {
- mixin(wrap(["naked;"] ~ prologue()));
- // Precalc first 4*16=64 bytes
- mixin(wrap(xsetup(0)));
- mixin(wrap(weave(precalc(0)~precalc(1)~precalc(2)~precalc(3),
- precalc(4)~precalc(5)~precalc(6)~precalc(7))));
- mixin(wrap(weave(loadstate(STATE_PTR, A, B, C, D, E),
- weave(precalc(8)~precalc(9)~precalc(10)~precalc(11),
- precalc(12)~precalc(13)~precalc(14)~precalc(15)))));
- // Round 1
- mixin(wrap(round( 0, A, B, C, D, E)));
- mixin(wrap(round( 2, D, E, A, B, C)));
- mixin(wrap(round( 4, B, C, D, E, A)));
- mixin(wrap(round( 6, E, A, B, C, D)));
- mixin(wrap(round( 8, C, D, E, A, B)));
- mixin(wrap(round(10, A, B, C, D, E)));
- mixin(wrap(round(12, D, E, A, B, C)));
- mixin(wrap(round(14, B, C, D, E, A)));
- mixin(wrap(round(16, E, A, B, C, D)));
- mixin(wrap(round(18, C, D, E, A, B)));
- // Round 2
- mixin(wrap(round(20, A, B, C, D, E)));
- mixin(wrap(round(22, D, E, A, B, C)));
- mixin(wrap(round(24, B, C, D, E, A)));
- mixin(wrap(round(26, E, A, B, C, D)));
- mixin(wrap(round(28, C, D, E, A, B)));
- mixin(wrap(round(30, A, B, C, D, E)));
- mixin(wrap(round(32, D, E, A, B, C)));
- mixin(wrap(round(34, B, C, D, E, A)));
- mixin(wrap(round(36, E, A, B, C, D)));
- mixin(wrap(round(38, C, D, E, A, B)));
- // Round 3
- mixin(wrap(round(40, A, B, C, D, E)));
- mixin(wrap(round(42, D, E, A, B, C)));
- mixin(wrap(round(44, B, C, D, E, A)));
- mixin(wrap(round(46, E, A, B, C, D)));
- mixin(wrap(round(48, C, D, E, A, B)));
- mixin(wrap(round(50, A, B, C, D, E)));
- mixin(wrap(round(52, D, E, A, B, C)));
- mixin(wrap(round(54, B, C, D, E, A)));
- mixin(wrap(round(56, E, A, B, C, D)));
- mixin(wrap(round(58, C, D, E, A, B)));
- // Round 4
- mixin(wrap(round(60, A, B, C, D, E)));
- mixin(wrap(round(62, D, E, A, B, C)));
- mixin(wrap(round(64, B, C, D, E, A)));
- mixin(wrap(round(66, E, A, B, C, D)));
- mixin(wrap(round(68, C, D, E, A, B)));
- mixin(wrap(round(70, A, B, C, D, E)));
- mixin(wrap(round(72, D, E, A, B, C)));
- mixin(wrap(round(74, B, C, D, E, A)));
- mixin(wrap(round(76, E, A, B, C, D)));
- mixin(wrap(round(78, C, D, E, A, B)));
- version (_32Bit)
- {
- // Load pointer to state
- mixin(wrap(["mov "~STATE_PTR~",[ESP + STATE_OFS]"]));
- }
- mixin(wrap(savestate(STATE_PTR, A, B, C, D, E)));
- mixin(wrap(epilogue()));
- }
-}
+++ /dev/null
-/** Optimised asm arbitrary precision arithmetic ('bignum')
- * routines for X86 processors.
- *
- * All functions operate on arrays of uints, stored LSB first.
- * If there is a destination array, it will be the first parameter.
- * Currently, all of these functions are subject to change, and are
- * intended for internal use only.
- * The symbol [#] indicates an array of machine words which is to be
- * interpreted as a multi-byte number.
- */
-
-/* Copyright Don Clugston 2008 - 2010.
- * Distributed under the Boost Software License, Version 1.0.
- * (See accompanying file LICENSE_1_0.txt or copy at
- * http://www.boost.org/LICENSE_1_0.txt)
- */
-/**
- * In simple terms, there are 3 modern x86 microarchitectures:
- * (a) the P6 family (Pentium Pro, PII, PIII, PM, Core), produced by Intel;
- * (b) the K6, Athlon, and AMD64 families, produced by AMD; and
- * (c) the Pentium 4, produced by Marketing.
- *
- * This code has been optimised for the Intel P6 family.
- * Generally the code remains near-optimal for Intel Core2/Corei7, after
- * translating EAX-> RAX, etc, since all these CPUs use essentially the same
- * pipeline, and are typically limited by memory access.
- * The code uses techniques described in Agner Fog's superb Pentium manuals
- * available at www.agner.org.
- * Not optimised for AMD, which can do two memory loads per cycle (Intel
- * CPUs can only do one). Despite this, performance is superior on AMD.
- * Performance is dreadful on P4.
- *
- * Timing results (cycles per int)
- * --Intel Pentium-- --AMD--
- * PM P4 Core2 K7
- * +,- 2.25 15.6 2.25 1.5
- * <<,>> 2.0 6.6 2.0 5.0
- * (<< MMX) 1.7 5.3 1.5 1.2
- * * 5.0 15.0 4.0 4.3
- * mulAdd 5.7 19.0 4.9 4.0
- * div 30.0 32.0 32.0 22.4
- * mulAcc(32) 6.5 20.0 5.4 4.9
- *
- * mulAcc(32) is multiplyAccumulate() for a 32*32 multiply. Thus it includes
- * function call overhead.
- * The timing for Div is quite unpredictable, but it's probably too slow
- * to be useful. On 64-bit processors, these times should
- * halve if run in 64-bit mode, except for the MMX functions.
- */
-
-module std.internal.math.biguintx86;
-
-@system:
-pure:
-nothrow:
-
-/*
- Naked asm is used throughout, because:
- (a) it frees up the EBP register
- (b) compiler bugs prevent the use of .ptr when a frame pointer is used.
-*/
-
-version (D_InlineAsm_X86)
-{
-
-private:
-
-/* Duplicate string s, with n times, substituting index for '@'.
- *
- * Each instance of '@' in s is replaced by 0,1,...n-1. This is a helper
- * function for some of the asm routines.
- */
-string indexedLoopUnroll(int n, string s) pure @safe
-{
- string u;
- for (int i = 0; i<n; ++i)
- {
- string nstr= (i>9 ? ""~ cast(char)('0'+i/10) : "") ~ cast(char)('0' + i%10);
-
- int last = 0;
- for (int j = 0; j<s.length; ++j)
- {
- if (s[j]=='@')
- {
- u ~= s[last .. j] ~ nstr;
- last = j+1;
- }
- }
- if (last<s.length) u = u ~ s[last..$];
-
- }
- return u;
-}
-@safe unittest
-{
- assert(indexedLoopUnroll(3, "@*23;")=="0*23;1*23;2*23;");
-}
-
-public:
-
-alias BigDigit = uint; // A Bignum is an array of BigDigits. Usually the machine word size.
-
-// Limits for when to switch between multiplication algorithms.
-enum : int { KARATSUBALIMIT = 18 }; // Minimum value for which Karatsuba is worthwhile.
-enum : int { KARATSUBASQUARELIMIT=26 }; // Minimum value for which square Karatsuba is worthwhile
-
-/** Multi-byte addition or subtraction
- * dest[#] = src1[#] + src2[#] + carry (0 or 1).
- * or dest[#] = src1[#] - src2[#] - carry (0 or 1).
- * Returns carry or borrow (0 or 1).
- * Set op == '+' for addition, '-' for subtraction.
- */
-uint multibyteAddSub(char op)(uint[] dest, const uint [] src1, const uint []
- src2, uint carry) pure
-{
- // Timing:
- // Pentium M: 2.25/int
- // P6 family, Core2 have a partial flags stall when reading the carry flag in
- // an ADC, SBB operation after an operation such as INC or DEC which
- // modifies some, but not all, flags. We avoid this by storing carry into
- // a resister (AL), and restoring it after the branch.
-
- enum { LASTPARAM = 4*4 } // 3* pushes + return address.
- asm pure nothrow {
- naked;
- push EDI;
- push EBX;
- push ESI;
- mov ECX, [ESP + LASTPARAM + 4*4]; // dest.length;
- mov EDX, [ESP + LASTPARAM + 3*4]; // src1.ptr
- mov ESI, [ESP + LASTPARAM + 1*4]; // src2.ptr
- mov EDI, [ESP + LASTPARAM + 5*4]; // dest.ptr
- // Carry is in EAX
- // Count UP to zero (from -len) to minimize loop overhead.
- lea EDX, [EDX + 4*ECX]; // EDX = end of src1.
- lea ESI, [ESI + 4*ECX]; // EBP = end of src2.
- lea EDI, [EDI + 4*ECX]; // EDI = end of dest.
-
- neg ECX;
- add ECX, 8;
- jb L2; // if length < 8 , bypass the unrolled loop.
-L_unrolled:
- shr AL, 1; // get carry from EAX
- }
- mixin(" asm pure nothrow {"
- ~ indexedLoopUnroll( 8,
- "mov EAX, [@*4-8*4+EDX+ECX*4];"
- ~ ( op == '+' ? "adc" : "sbb" ) ~ " EAX, [@*4-8*4+ESI+ECX*4];"
- ~ "mov [@*4-8*4+EDI+ECX*4], EAX;")
- ~ "}");
- asm pure nothrow {
- setc AL; // save carry
- add ECX, 8;
- ja L_unrolled;
-L2: // Do the residual 1 .. 7 ints.
-
- sub ECX, 8;
- jz done;
-L_residual:
- shr AL, 1; // get carry from EAX
- }
- mixin(" asm pure nothrow {"
- ~ indexedLoopUnroll( 1,
- "mov EAX, [@*4+EDX+ECX*4];"
- ~ ( op == '+' ? "adc" : "sbb" ) ~ " EAX, [@*4+ESI+ECX*4];"
- ~ "mov [@*4+EDI+ECX*4], EAX;") ~ "}");
- asm pure nothrow {
- setc AL; // save carry
- add ECX, 1;
- jnz L_residual;
-done:
- and EAX, 1; // make it O or 1.
- pop ESI;
- pop EBX;
- pop EDI;
- ret 6*4;
- }
-}
-
-@system unittest
-{
- uint [] a = new uint[40];
- uint [] b = new uint[40];
- uint [] c = new uint[40];
- for (int i=0; i<a.length; ++i)
- {
- if (i&1) a[i]=0x8000_0000 + i;
- else a[i]=i;
- b[i]= 0x8000_0003;
- }
- c[19]=0x3333_3333;
- uint carry = multibyteAddSub!('+')(c[0 .. 18], a[0 .. 18], b[0 .. 18], 0);
- assert(carry == 1);
- assert(c[0]==0x8000_0003);
- assert(c[1]==4);
- assert(c[19]==0x3333_3333); // check for overrun
- for (int i=0; i<a.length; ++i)
- {
- a[i]=b[i]=c[i]=0;
- }
- a[8]=0x048D159E;
- b[8]=0x048D159E;
- a[10]=0x1D950C84;
- b[10]=0x1D950C84;
- a[5] =0x44444444;
- carry = multibyteAddSub!('-')(a[0 .. 12], a[0 .. 12], b[0 .. 12], 0);
- assert(a[11]==0);
- for (int i=0; i<10; ++i) if (i != 5) assert(a[i]==0);
-
- for (int q=3; q<36;++q)
- {
- for (int i=0; i<a.length; ++i)
- {
- a[i]=b[i]=c[i]=0;
- }
- a[q-2]=0x040000;
- b[q-2]=0x040000;
- carry = multibyteAddSub!('-')(a[0 .. q], a[0 .. q], b[0 .. q], 0);
- assert(a[q-2]==0);
- }
-}
-
-/** dest[#] += carry, or dest[#] -= carry.
- * op must be '+' or '-'
- * Returns final carry or borrow (0 or 1)
- */
-uint multibyteIncrementAssign(char op)(uint[] dest, uint carry) pure
-{
- enum { LASTPARAM = 1*4 } // 0* pushes + return address.
- asm pure nothrow {
- naked;
- mov ECX, [ESP + LASTPARAM + 0*4]; // dest.length;
- mov EDX, [ESP + LASTPARAM + 1*4]; // dest.ptr
- // EAX = carry
-L1: ;
- }
- static if (op=='+')
- asm pure nothrow { add [EDX], EAX; }
- else
- asm pure nothrow { sub [EDX], EAX; }
- asm pure nothrow {
- mov EAX, 1;
- jnc L2;
- add EDX, 4;
- dec ECX;
- jnz L1;
- mov EAX, 2;
-L2: dec EAX;
- ret 2*4;
- }
-}
-
-/** dest[#] = src[#] << numbits
- * numbits must be in the range 1 .. 31
- * Returns the overflow
- */
-uint multibyteShlNoMMX(uint [] dest, const uint [] src, uint numbits) pure
-{
- // Timing: Optimal for P6 family.
- // 2.0 cycles/int on PPro .. PM (limited by execution port p0)
- // 5.0 cycles/int on Athlon, which has 7 cycles for SHLD!!
- enum { LASTPARAM = 4*4 } // 3* pushes + return address.
- asm pure nothrow {
- naked;
- push ESI;
- push EDI;
- push EBX;
- mov EDI, [ESP + LASTPARAM + 4*3]; //dest.ptr;
- mov EBX, [ESP + LASTPARAM + 4*2]; //dest.length;
- mov ESI, [ESP + LASTPARAM + 4*1]; //src.ptr;
- mov ECX, EAX; // numbits;
-
- mov EAX, [-4+ESI + 4*EBX];
- mov EDX, 0;
- shld EDX, EAX, CL;
- push EDX; // Save return value
- cmp EBX, 1;
- jz L_last;
- mov EDX, [-4+ESI + 4*EBX];
- test EBX, 1;
- jz L_odd;
- sub EBX, 1;
-L_even:
- mov EDX, [-4+ ESI + 4*EBX];
- shld EAX, EDX, CL;
- mov [EDI+4*EBX], EAX;
-L_odd:
- mov EAX, [-8+ESI + 4*EBX];
- shld EDX, EAX, CL;
- mov [-4+EDI + 4*EBX], EDX;
- sub EBX, 2;
- jg L_even;
-L_last:
- shl EAX, CL;
- mov [EDI], EAX;
- pop EAX; // pop return value
- pop EBX;
- pop EDI;
- pop ESI;
- ret 4*4;
- }
-}
-
-/** dest[#] = src[#] >> numbits
- * numbits must be in the range 1 .. 31
- * This version uses MMX.
- */
-uint multibyteShl(uint [] dest, const uint [] src, uint numbits) pure
-{
- // Timing:
- // K7 1.2/int. PM 1.7/int P4 5.3/int
- enum { LASTPARAM = 4*4 } // 3* pushes + return address.
- asm pure nothrow {
- naked;
- push ESI;
- push EDI;
- push EBX;
- mov EDI, [ESP + LASTPARAM + 4*3]; //dest.ptr;
- mov EBX, [ESP + LASTPARAM + 4*2]; //dest.length;
- mov ESI, [ESP + LASTPARAM + 4*1]; //src.ptr;
-
- movd MM3, EAX; // numbits = bits to shift left
- xor EAX, 63;
- align 16;
- inc EAX;
- movd MM4, EAX ; // 64-numbits = bits to shift right
-
- // Get the return value into EAX
- and EAX, 31; // EAX = 32-numbits
- movd MM2, EAX; // 32-numbits
- movd MM1, [ESI+4*EBX-4];
- psrlq MM1, MM2;
- movd EAX, MM1; // EAX = return value
- test EBX, 1;
- jz L_even;
-L_odd:
- cmp EBX, 1;
- jz L_length1;
-
- // deal with odd lengths
- movq MM1, [ESI+4*EBX-8];
- psrlq MM1, MM2;
- movd [EDI +4*EBX-4], MM1;
- sub EBX, 1;
-L_even: // It's either singly or doubly even
- movq MM2, [ESI + 4*EBX - 8];
- psllq MM2, MM3;
- sub EBX, 2;
- jle L_last;
- movq MM1, MM2;
- add EBX, 2;
- test EBX, 2;
- jz L_onceeven;
- sub EBX, 2;
-
- // MAIN LOOP -- 128 bytes per iteration
- L_twiceeven: // here MM2 is the carry
- movq MM0, [ESI + 4*EBX-8];
- psrlq MM0, MM4;
- movq MM1, [ESI + 4*EBX-8];
- psllq MM1, MM3;
- por MM2, MM0;
- movq [EDI +4*EBX], MM2;
-L_onceeven: // here MM1 is the carry
- movq MM0, [ESI + 4*EBX-16];
- psrlq MM0, MM4;
- movq MM2, [ESI + 4*EBX-16];
- por MM1, MM0;
- movq [EDI +4*EBX-8], MM1;
- psllq MM2, MM3;
- sub EBX, 4;
- jg L_twiceeven;
-L_last:
- movq [EDI +4*EBX], MM2;
-L_alldone:
- emms; // NOTE: costs 6 cycles on Intel CPUs
- pop EBX;
- pop EDI;
- pop ESI;
- ret 4*4;
-
-L_length1:
- // length 1 is a special case
- movd MM1, [ESI];
- psllq MM1, MM3;
- movd [EDI], MM1;
- jmp L_alldone;
- }
-}
-
-void multibyteShr(uint [] dest, const uint [] src, uint numbits) pure
-{
- enum { LASTPARAM = 4*4 } // 3* pushes + return address.
- asm pure nothrow {
- naked;
- push ESI;
- push EDI;
- push EBX;
- mov EDI, [ESP + LASTPARAM + 4*3]; //dest.ptr;
- mov EBX, [ESP + LASTPARAM + 4*2]; //dest.length;
-align 16;
- mov ESI, [ESP + LASTPARAM + 4*1]; //src.ptr;
- lea EDI, [EDI + 4*EBX]; // EDI = end of dest
- lea ESI, [ESI + 4*EBX]; // ESI = end of src
- neg EBX; // count UP to zero.
-
- movd MM3, EAX; // numbits = bits to shift right
- xor EAX, 63;
- inc EAX;
- movd MM4, EAX ; // 64-numbits = bits to shift left
-
- test EBX, 1;
- jz L_even;
-L_odd:
- // deal with odd lengths
- and EAX, 31; // EAX = 32-numbits
- movd MM2, EAX; // 32-numbits
- cmp EBX, -1;
- jz L_length1;
-
- movq MM0, [ESI+4*EBX];
- psrlq MM0, MM3;
- movd [EDI +4*EBX], MM0;
- add EBX, 1;
-L_even:
- movq MM2, [ESI + 4*EBX];
- psrlq MM2, MM3;
-
- movq MM1, MM2;
- add EBX, 4;
- cmp EBX, -2+4;
- jz L_last;
- // It's either singly or doubly even
- sub EBX, 2;
- test EBX, 2;
- jnz L_onceeven;
- add EBX, 2;
-
- // MAIN LOOP -- 128 bytes per iteration
- L_twiceeven: // here MM2 is the carry
- movq MM0, [ESI + 4*EBX-8];
- psllq MM0, MM4;
- movq MM1, [ESI + 4*EBX-8];
- psrlq MM1, MM3;
- por MM2, MM0;
- movq [EDI +4*EBX-16], MM2;
-L_onceeven: // here MM1 is the carry
- movq MM0, [ESI + 4*EBX];
- psllq MM0, MM4;
- movq MM2, [ESI + 4*EBX];
- por MM1, MM0;
- movq [EDI +4*EBX-8], MM1;
- psrlq MM2, MM3;
- add EBX, 4;
- jl L_twiceeven;
-L_last:
- movq [EDI +4*EBX-16], MM2;
-L_alldone:
- emms; // NOTE: costs 6 cycles on Intel CPUs
- pop EBX;
- pop EDI;
- pop ESI;
- ret 4*4;
-
-L_length1:
- // length 1 is a special case
- movd MM1, [ESI+4*EBX];
- psrlq MM1, MM3;
- movd [EDI +4*EBX], MM1;
- jmp L_alldone;
-
- }
-}
-
-/** dest[#] = src[#] >> numbits
- * numbits must be in the range 1 .. 31
- */
-void multibyteShrNoMMX(uint [] dest, const uint [] src, uint numbits) pure
-{
- // Timing: Optimal for P6 family.
- // 2.0 cycles/int on PPro .. PM (limited by execution port p0)
- // Terrible performance on AMD64, which has 7 cycles for SHRD!!
- enum { LASTPARAM = 4*4 } // 3* pushes + return address.
- asm pure nothrow {
- naked;
- push ESI;
- push EDI;
- push EBX;
- mov EDI, [ESP + LASTPARAM + 4*3]; //dest.ptr;
- mov EBX, [ESP + LASTPARAM + 4*2]; //dest.length;
- mov ESI, [ESP + LASTPARAM + 4*1]; //src.ptr;
- mov ECX, EAX; // numbits;
-
- lea EDI, [EDI + 4*EBX]; // EDI = end of dest
- lea ESI, [ESI + 4*EBX]; // ESI = end of src
- neg EBX; // count UP to zero.
- mov EAX, [ESI + 4*EBX];
- cmp EBX, -1;
- jz L_last;
- mov EDX, [ESI + 4*EBX];
- test EBX, 1;
- jz L_odd;
- add EBX, 1;
-L_even:
- mov EDX, [ ESI + 4*EBX];
- shrd EAX, EDX, CL;
- mov [-4 + EDI+4*EBX], EAX;
-L_odd:
- mov EAX, [4 + ESI + 4*EBX];
- shrd EDX, EAX, CL;
- mov [EDI + 4*EBX], EDX;
- add EBX, 2;
- jl L_even;
-L_last:
- shr EAX, CL;
- mov [-4 + EDI], EAX;
-
- pop EBX;
- pop EDI;
- pop ESI;
- ret 4*4;
- }
-}
-
-@system unittest
-{
-
- uint [] aa = [0x1222_2223, 0x4555_5556, 0x8999_999A, 0xBCCC_CCCD, 0xEEEE_EEEE];
- multibyteShr(aa[0..$-1], aa, 4);
- assert(aa[0] == 0x6122_2222 && aa[1]==0xA455_5555
- && aa[2]==0xD899_9999 && aa[3]==0x0BCC_CCCC);
-
- aa = [0x1222_2223, 0x4555_5556, 0x8999_999A, 0xBCCC_CCCD, 0xEEEE_EEEE];
- multibyteShr(aa[2..$-1], aa[2..$-1], 4);
- assert(aa[0] == 0x1222_2223 && aa[1]==0x4555_5556
- && aa[2]==0xD899_9999 && aa[3]==0x0BCC_CCCC);
-
- aa = [0x1222_2223, 0x4555_5556, 0x8999_999A, 0xBCCC_CCCD, 0xEEEE_EEEE];
- multibyteShr(aa[0..$-2], aa, 4);
- assert(aa[1]==0xA455_5555 && aa[2]==0x0899_9999);
- assert(aa[0]==0x6122_2222);
- assert(aa[3]==0xBCCC_CCCD);
-
-
- aa = [0xF0FF_FFFF, 0x1222_2223, 0x4555_5556, 0x8999_999A, 0xBCCC_CCCD, 0xEEEE_EEEE];
- uint r = multibyteShl(aa[2 .. 4], aa[2 .. 4], 4);
- assert(aa[0] == 0xF0FF_FFFF && aa[1]==0x1222_2223
- && aa[2]==0x5555_5560 && aa[3]==0x9999_99A4 && aa[4]==0xBCCC_CCCD);
- assert(r == 8);
-
- aa = [0xF0FF_FFFF, 0x1222_2223, 0x4555_5556, 0x8999_999A, 0xBCCC_CCCD, 0xEEEE_EEEE];
- r = multibyteShl(aa[1 .. 4], aa[1 .. 4], 4);
- assert(aa[0] == 0xF0FF_FFFF
- && aa[2]==0x5555_5561);
- assert(aa[3]==0x9999_99A4 && aa[4]==0xBCCC_CCCD);
- assert(r == 8);
- assert(aa[1]==0x2222_2230);
-
- aa = [0xF0FF_FFFF, 0x1222_2223, 0x4555_5556, 0x8999_999A, 0xBCCC_CCCD, 0xEEEE_EEEE];
- r = multibyteShl(aa[0 .. 4], aa[1 .. 5], 31);
-}
-
-/** dest[#] = src[#] * multiplier + carry.
- * Returns carry.
- */
-uint multibyteMul(uint[] dest, const uint[] src, uint multiplier, uint carry)
- pure
-{
- // Timing: definitely not optimal.
- // Pentium M: 5.0 cycles/operation, has 3 resource stalls/iteration
- // Fastest implementation found was 4.6 cycles/op, but not worth the complexity.
-
- enum { LASTPARAM = 4*4 } // 4* pushes + return address.
- // We'll use p2 (load unit) instead of the overworked p0 or p1 (ALU units)
- // when initializing variables to zero.
- version (D_PIC)
- {
- enum { zero = 0 }
- }
- else
- {
- __gshared int zero = 0;
- }
- asm pure nothrow {
- naked;
- push ESI;
- push EDI;
- push EBX;
-
- mov EDI, [ESP + LASTPARAM + 4*4]; // dest.ptr
- mov EBX, [ESP + LASTPARAM + 4*3]; // dest.length
- mov ESI, [ESP + LASTPARAM + 4*2]; // src.ptr
- align 16;
- lea EDI, [EDI + 4*EBX]; // EDI = end of dest
- lea ESI, [ESI + 4*EBX]; // ESI = end of src
- mov ECX, EAX; // [carry]; -- last param is in EAX.
- neg EBX; // count UP to zero.
- test EBX, 1;
- jnz L_odd;
- add EBX, 1;
- L1:
- mov EAX, [-4 + ESI + 4*EBX];
- mul int ptr [ESP+LASTPARAM]; //[multiplier];
- add EAX, ECX;
- mov ECX, zero;
- mov [-4+EDI + 4*EBX], EAX;
- adc ECX, EDX;
-L_odd:
- mov EAX, [ESI + 4*EBX]; // p2
- mul int ptr [ESP+LASTPARAM]; //[multiplier]; // p0*3,
- add EAX, ECX;
- mov ECX, zero;
- adc ECX, EDX;
- mov [EDI + 4*EBX], EAX;
- add EBX, 2;
- jl L1;
-
- mov EAX, ECX; // get final carry
-
- pop EBX;
- pop EDI;
- pop ESI;
- ret 5*4;
- }
-}
-
-@system unittest
-{
- uint [] aa = [0xF0FF_FFFF, 0x1222_2223, 0x4555_5556, 0x8999_999A, 0xBCCC_CCCD, 0xEEEE_EEEE];
- multibyteMul(aa[1 .. 4], aa[1 .. 4], 16, 0);
- assert(aa[0] == 0xF0FF_FFFF && aa[1] == 0x2222_2230 &&
- aa[2]==0x5555_5561 && aa[3]==0x9999_99A4 && aa[4]==0x0BCCC_CCCD);
-}
-
-// The inner multiply-and-add loop, together with the Even entry point.
-// Multiples by M_ADDRESS which should be "ESP+LASTPARAM" or "ESP". OP must be "add" or "sub"
-// This is the most time-critical code in the BigInt library.
-// It is used by both MulAdd, multiplyAccumulate, and triangleAccumulate
-string asmMulAdd_innerloop(string OP, string M_ADDRESS) pure {
- // The bottlenecks in this code are extremely complicated. The MUL, ADD, and ADC
- // need 4 cycles on each of the ALUs units p0 and p1. So we use memory load
- // (unit p2) for initializing registers to zero.
- // There are also dependencies between the instructions, and we run up against the
- // ROB-read limit (can only read 2 registers per cycle).
- // We also need the number of uops in the loop to be a multiple of 3.
- // The only available execution unit for this is p3 (memory write). Unfortunately we can't do that
- // if Position-Independent Code is required.
-
- // Register usage
- // ESI = end of src
- // EDI = end of dest
- // EBX = index. Counts up to zero (in steps of 2).
- // EDX:EAX = scratch, used in multiply.
- // ECX = carry1.
- // EBP = carry2.
- // ESP = points to the multiplier.
-
- // The first member of 'dest' which will be modified is [EDI+4*EBX].
- // EAX must already contain the first member of 'src', [ESI+4*EBX].
-
- version (D_PIC) { bool using_PIC = true; } else { bool using_PIC = false; }
- return "
- // Entry point for even length
- add EBX, 1;
- mov EBP, ECX; // carry
-
- mul int ptr [" ~ M_ADDRESS ~ "]; // M
- mov ECX, 0;
-
- add EBP, EAX;
- mov EAX, [ESI+4*EBX];
- adc ECX, EDX;
-
- mul int ptr [" ~ M_ADDRESS ~ "]; // M
- " ~ OP ~ " [-4+EDI+4*EBX], EBP;
- mov EBP, zero;
-
- adc ECX, EAX;
- mov EAX, [4+ESI+4*EBX];
-
- adc EBP, EDX;
- add EBX, 2;
- jnl L_done;
-L1:
- mul int ptr [" ~ M_ADDRESS ~ "];
- " ~ OP ~ " [-8+EDI+4*EBX], ECX;
- adc EBP, EAX;
- mov ECX, zero;
- mov EAX, [ESI+4*EBX];
- adc ECX, EDX;
-" ~
- (using_PIC ? "" : " mov storagenop, EDX; ") // make #uops in loop a multiple of 3, can't do this in PIC mode.
-~ "
- mul int ptr [" ~ M_ADDRESS ~ "];
- " ~ OP ~ " [-4+EDI+4*EBX], EBP;
- mov EBP, zero;
-
- adc ECX, EAX;
- mov EAX, [4+ESI+4*EBX];
-
- adc EBP, EDX;
- add EBX, 2;
- jl L1;
-L_done: " ~ OP ~ " [-8+EDI+4*EBX], ECX;
- adc EBP, 0;
-";
- // final carry is now in EBP
-}
-
-string asmMulAdd_enter_odd(string OP, string M_ADDRESS) pure
-{
- return "
- mul int ptr [" ~M_ADDRESS ~"];
- mov EBP, zero;
- add ECX, EAX;
- mov EAX, [4+ESI+4*EBX];
-
- adc EBP, EDX;
- add EBX, 2;
- jl L1;
- jmp L_done;
-";
-}
-
-
-
-/**
- * dest[#] += src[#] * multiplier OP carry(0 .. FFFF_FFFF).
- * where op == '+' or '-'
- * Returns carry out of MSB (0 .. FFFF_FFFF).
- */
-uint multibyteMulAdd(char op)(uint [] dest, const uint [] src, uint
- multiplier, uint carry) pure {
- // Timing: This is the most time-critical bignum function.
- // Pentium M: 5.4 cycles/operation, still has 2 resource stalls + 1load block/iteration
-
- // The main loop is pipelined and unrolled by 2,
- // so entry to the loop is also complicated.
-
- // Register usage
- // EDX:EAX = multiply
- // EBX = counter
- // ECX = carry1
- // EBP = carry2
- // EDI = dest
- // ESI = src
-
- enum string OP = (op=='+')? "add" : "sub";
- version (D_PIC)
- {
- enum { zero = 0 }
- }
- else
- {
- // use p2 (load unit) instead of the overworked p0 or p1 (ALU units)
- // when initializing registers to zero.
- __gshared int zero = 0;
- // use p3/p4 units
- __gshared int storagenop; // write-only
- }
-
- enum { LASTPARAM = 5*4 } // 4* pushes + return address.
- asm pure nothrow {
- naked;
-
- push ESI;
- push EDI;
- push EBX;
- push EBP;
- mov EDI, [ESP + LASTPARAM + 4*4]; // dest.ptr
- mov EBX, [ESP + LASTPARAM + 4*3]; // dest.length
- align 16;
- nop;
- mov ESI, [ESP + LASTPARAM + 4*2]; // src.ptr
- lea EDI, [EDI + 4*EBX]; // EDI = end of dest
- lea ESI, [ESI + 4*EBX]; // ESI = end of src
- mov EBP, 0;
- mov ECX, EAX; // ECX = input carry.
- neg EBX; // count UP to zero.
- mov EAX, [ESI+4*EBX];
- test EBX, 1;
- jnz L_enter_odd;
- }
- // Main loop, with entry point for even length
- mixin("asm pure nothrow {" ~ asmMulAdd_innerloop(OP, "ESP+LASTPARAM") ~ "}");
- asm pure nothrow {
- mov EAX, EBP; // get final carry
- pop EBP;
- pop EBX;
- pop EDI;
- pop ESI;
- ret 5*4;
- }
-L_enter_odd:
- mixin("asm pure nothrow {" ~ asmMulAdd_enter_odd(OP, "ESP+LASTPARAM") ~ "}");
-}
-
-@system unittest
-{
-
- uint [] aa = [0xF0FF_FFFF, 0x1222_2223, 0x4555_5556, 0x8999_999A, 0xBCCC_CCCD, 0xEEEE_EEEE];
- uint [] bb = [0x1234_1234, 0xF0F0_F0F0, 0x00C0_C0C0, 0xF0F0_F0F0, 0xC0C0_C0C0];
- multibyteMulAdd!('+')(bb[1..$-1], aa[1..$-2], 16, 5);
- assert(bb[0] == 0x1234_1234 && bb[4] == 0xC0C0_C0C0);
- assert(bb[1] == 0x2222_2230 + 0xF0F0_F0F0+5 && bb[2] == 0x5555_5561+0x00C0_C0C0+1
- && bb[3] == 0x9999_99A4+0xF0F0_F0F0 );
-}
-
-/**
- Sets result[#] = result[0 .. left.length] + left[#] * right[#]
-
- It is defined in this way to allow cache-efficient multiplication.
- This function is equivalent to:
- ----
- for (int i = 0; i< right.length; ++i)
- {
- dest[left.length + i] = multibyteMulAdd(dest[i .. left.length+i],
- left, right[i], 0);
- }
- ----
- */
-void multibyteMultiplyAccumulate(uint [] dest, const uint[] left,
- const uint [] right) pure {
- // Register usage
- // EDX:EAX = used in multiply
- // EBX = index
- // ECX = carry1
- // EBP = carry2
- // EDI = end of dest for this pass through the loop. Index for outer loop.
- // ESI = end of left. never changes
- // [ESP] = M = right[i] = multiplier for this pass through the loop.
- // right.length is changed into dest.ptr+dest.length
- version (D_PIC)
- {
- enum { zero = 0 }
- }
- else
- {
- // use p2 (load unit) instead of the overworked p0 or p1 (ALU units)
- // when initializing registers to zero.
- __gshared int zero = 0;
- // use p3/p4 units
- __gshared int storagenop; // write-only
- }
-
- enum { LASTPARAM = 6*4 } // 4* pushes + local + return address.
- asm pure nothrow {
- naked;
-
- push ESI;
- push EDI;
- align 16;
- push EBX;
- push EBP;
- push EAX; // local variable M
- mov EDI, [ESP + LASTPARAM + 4*5]; // dest.ptr
- mov EBX, [ESP + LASTPARAM + 4*2]; // left.length
- mov ESI, [ESP + LASTPARAM + 4*3]; // left.ptr
- lea EDI, [EDI + 4*EBX]; // EDI = end of dest for first pass
-
- mov EAX, [ESP + LASTPARAM + 4*0]; // right.length
- lea EAX, [EDI + 4*EAX];
- mov [ESP + LASTPARAM + 4*0], EAX; // last value for EDI
-
- lea ESI, [ESI + 4*EBX]; // ESI = end of left
- mov EAX, [ESP + LASTPARAM + 4*1]; // right.ptr
- mov EAX, [EAX];
- mov [ESP], EAX; // M
-outer_loop:
- mov EBP, 0;
- mov ECX, 0; // ECX = input carry.
- neg EBX; // count UP to zero.
- mov EAX, [ESI+4*EBX];
- test EBX, 1;
- jnz L_enter_odd;
- }
- // -- Inner loop, with even entry point
- mixin("asm pure nothrow { " ~ asmMulAdd_innerloop("add", "ESP") ~ "}");
- asm pure nothrow {
- mov [-4+EDI+4*EBX], EBP;
- add EDI, 4;
- cmp EDI, [ESP + LASTPARAM + 4*0]; // is EDI = &dest[$]?
- jz outer_done;
- mov EAX, [ESP + LASTPARAM + 4*1]; // right.ptr
- mov EAX, [EAX+4]; // get new M
- mov [ESP], EAX; // save new M
- add int ptr [ESP + LASTPARAM + 4*1], 4; // right.ptr
- mov EBX, [ESP + LASTPARAM + 4*2]; // left.length
- jmp outer_loop;
-outer_done:
- pop EAX;
- pop EBP;
- pop EBX;
- pop EDI;
- pop ESI;
- ret 6*4;
- }
-L_enter_odd:
- mixin("asm pure nothrow {" ~ asmMulAdd_enter_odd("add", "ESP") ~ "}");
-}
-
-/** dest[#] /= divisor.
- * overflow is the initial remainder, and must be in the range 0 .. divisor-1.
- * divisor must not be a power of 2 (use right shift for that case;
- * A division by zero will occur if divisor is a power of 2).
- * Returns the final remainder
- *
- * Based on public domain code by Eric Bainville.
- * (http://www.bealto.com/) Used with permission.
- */
-uint multibyteDivAssign(uint [] dest, uint divisor, uint overflow) pure
-{
- // Timing: limited by a horrible dependency chain.
- // Pentium M: 18 cycles/op, 8 resource stalls/op.
- // EAX, EDX = scratch, used by MUL
- // EDI = dest
- // CL = shift
- // ESI = quotient
- // EBX = remainderhi
- // EBP = remainderlo
- // [ESP-4] = mask
- // [ESP] = kinv (2^64 /divisor)
- enum { LASTPARAM = 5*4 } // 4* pushes + return address.
- enum { LOCALS = 2*4} // MASK, KINV
- asm pure nothrow {
- naked;
-
- push ESI;
- push EDI;
- push EBX;
- push EBP;
-
- mov EDI, [ESP + LASTPARAM + 4*2]; // dest.ptr
- mov EBX, [ESP + LASTPARAM + 4*1]; // dest.length
-
- // Loop from msb to lsb
- lea EDI, [EDI + 4*EBX];
- mov EBP, EAX; // rem is the input remainder, in 0 .. divisor-1
- // Build the pseudo-inverse of divisor k: 2^64/k
- // First determine the shift in ecx to get the max number of bits in kinv
- xor ECX, ECX;
- mov EAX, [ESP + LASTPARAM]; //divisor;
- mov EDX, 1;
-kinv1:
- inc ECX;
- ror EDX, 1;
- shl EAX, 1;
- jnc kinv1;
- dec ECX;
- // Here, ecx is a left shift moving the msb of k to bit 32
-
- mov EAX, 1;
- shl EAX, CL;
- dec EAX;
- ror EAX, CL ; //ecx bits at msb
- push EAX; // MASK
-
- // Then divide 2^(32+cx) by divisor (edx already ok)
- xor EAX, EAX;
- div int ptr [ESP + LASTPARAM + LOCALS-4*1]; //divisor;
- push EAX; // kinv
- align 16;
-L2:
- // Get 32 bits of quotient approx, multiplying
- // most significant word of (rem*2^32+input)
- mov EAX, [ESP+4]; //MASK;
- and EAX, [EDI - 4];
- or EAX, EBP;
- rol EAX, CL;
- mov EBX, EBP;
- mov EBP, [EDI - 4];
- mul int ptr [ESP]; //KINV;
-
- shl EAX, 1;
- rcl EDX, 1;
-
- // Multiply by k and subtract to get remainder
- // Subtraction must be done on two words
- mov EAX, EDX;
- mov ESI, EDX; // quot = high word
- mul int ptr [ESP + LASTPARAM+LOCALS]; //divisor;
- sub EBP, EAX;
- sbb EBX, EDX;
- jz Lb; // high word is 0, goto adjust on single word
-
- // Adjust quotient and remainder on two words
-Ld: inc ESI;
- sub EBP, [ESP + LASTPARAM+LOCALS]; //divisor;
- sbb EBX, 0;
- jnz Ld;
-
- // Adjust quotient and remainder on single word
-Lb: cmp EBP, [ESP + LASTPARAM+LOCALS]; //divisor;
- jc Lc; // rem in 0 .. divisor-1, OK
- sub EBP, [ESP + LASTPARAM+LOCALS]; //divisor;
- inc ESI;
- jmp Lb;
-
- // Store result
-Lc:
- mov [EDI - 4], ESI;
- lea EDI, [EDI - 4];
- dec int ptr [ESP + LASTPARAM + 4*1+LOCALS]; // len
- jnz L2;
-
- pop EAX; // discard kinv
- pop EAX; // discard mask
-
- mov EAX, EBP; // return final remainder
- pop EBP;
- pop EBX;
- pop EDI;
- pop ESI;
- ret 3*4;
- }
-}
-
-@system unittest
-{
- uint [] aa = new uint[101];
- for (int i=0; i<aa.length; ++i) aa[i] = 0x8765_4321 * (i+3);
- uint overflow = multibyteMul(aa, aa, 0x8EFD_FCFB, 0x33FF_7461);
- uint r = multibyteDivAssign(aa, 0x8EFD_FCFB, overflow);
- for (int i=0; i<aa.length-1; ++i) assert(aa[i] == 0x8765_4321 * (i+3));
- assert(r == 0x33FF_7461);
-}
-
-// Set dest[2*i .. 2*i+1]+=src[i]*src[i]
-void multibyteAddDiagonalSquares(uint [] dest, const uint [] src) pure
-{
- /* Unlike mulAdd, the carry is only 1 bit,
- since FFFF*FFFF+FFFF_FFFF = 1_0000_0000.
- Note also that on the last iteration, no carry can occur.
- As for multibyteAdd, we save & restore carry flag through the loop.
-
- The timing is entirely dictated by the dependency chain. We could
- improve it by moving the mov EAX after the adc [EDI], EAX. Probably not worthwhile.
- */
- enum { LASTPARAM = 4*5 } // 4* pushes + return address.
- asm pure nothrow {
- naked;
- push ESI;
- push EDI;
- push EBX;
- push ECX;
- mov EDI, [ESP + LASTPARAM + 4*3]; //dest.ptr;
- mov EBX, [ESP + LASTPARAM + 4*0]; //src.length;
- mov ESI, [ESP + LASTPARAM + 4*1]; //src.ptr;
- lea EDI, [EDI + 8*EBX]; // EDI = end of dest
- lea ESI, [ESI + 4*EBX]; // ESI = end of src
- neg EBX; // count UP to zero.
- xor ECX, ECX; // initial carry = 0.
-L1:
- mov EAX, [ESI + 4*EBX];
- mul EAX, EAX;
- shr CL, 1; // get carry
- adc [EDI + 8*EBX], EAX;
- adc [EDI + 8*EBX + 4], EDX;
- setc CL; // save carry
- inc EBX;
- jnz L1;
-
- pop ECX;
- pop EBX;
- pop EDI;
- pop ESI;
- ret 4*4;
- }
-}
-
-@system unittest
-{
- uint [] aa = new uint[13];
- uint [] bb = new uint[6];
- for (int i=0; i<aa.length; ++i) aa[i] = 0x8000_0000;
- for (int i=0; i<bb.length; ++i) bb[i] = i;
- aa[$-1]= 7;
- multibyteAddDiagonalSquares(aa[0..$-1], bb);
- assert(aa[$-1]==7);
- for (int i=0; i<bb.length; ++i) { assert(aa[2*i]==0x8000_0000+i*i); assert(aa[2*i+1]==0x8000_0000); }
-}
-
-void multibyteTriangleAccumulateD(uint[] dest, uint[] x) pure
-{
- for (int i = 0; i < x.length-3; ++i)
- {
- dest[i+x.length] = multibyteMulAdd!('+')(
- dest[i+i+1 .. i+x.length], x[i+1..$], x[i], 0);
- }
- ulong c = cast(ulong)(x[$-3]) * x[$-2] + dest[$-5];
- dest[$-5] = cast(uint) c;
- c >>= 32;
- c += cast(ulong)(x[$-3]) * x[$-1] + dest[$-4];
- dest[$-4] = cast(uint) c;
- c >>= 32;
-length2:
- c += cast(ulong)(x[$-2]) * x[$-1];
- dest[$-3] = cast(uint) c;
- c >>= 32;
- dest[$-2] = cast(uint) c;
-}
-
-//dest += src[0]*src[1...$] + src[1]*src[2..$] + ... + src[$-3]*src[$-2..$]+ src[$-2]*src[$-1]
-// assert(dest.length = src.length*2);
-// assert(src.length >= 3);
-void multibyteTriangleAccumulateAsm(uint[] dest, const uint[] src) pure
-{
- // Register usage
- // EDX:EAX = used in multiply
- // EBX = index
- // ECX = carry1
- // EBP = carry2
- // EDI = end of dest for this pass through the loop. Index for outer loop.
- // ESI = end of src. never changes
- // [ESP] = M = src[i] = multiplier for this pass through the loop.
- // dest.length is changed into dest.ptr+dest.length
- version (D_PIC)
- {
- enum { zero = 0 }
- }
- else
- {
- // use p2 (load unit) instead of the overworked p0 or p1 (ALU units)
- // when initializing registers to zero.
- __gshared int zero = 0;
- // use p3/p4 units
- __gshared int storagenop; // write-only
- }
-
- enum { LASTPARAM = 6*4 } // 4* pushes + local + return address.
- asm pure nothrow {
- naked;
-
- push ESI;
- push EDI;
- align 16;
- push EBX;
- push EBP;
- push EAX; // local variable M= src[i]
- mov EDI, [ESP + LASTPARAM + 4*3]; // dest.ptr
- mov EBX, [ESP + LASTPARAM + 4*0]; // src.length
- mov ESI, [ESP + LASTPARAM + 4*1]; // src.ptr
-
- lea ESI, [ESI + 4*EBX]; // ESI = end of left
- add int ptr [ESP + LASTPARAM + 4*1], 4; // src.ptr, used for getting M
-
- // local variable [ESP + LASTPARAM + 4*2] = last value for EDI
- lea EDI, [EDI + 4*EBX]; // EDI = end of dest for first pass
-
- lea EAX, [EDI + 4*EBX-3*4]; // up to src.length - 3
- mov [ESP + LASTPARAM + 4*2], EAX; // last value for EDI = &dest[src.length*2 -3]
-
- cmp EBX, 3;
- jz length_is_3;
-
- // We start at src[1], not src[0].
- dec EBX;
- mov [ESP + LASTPARAM + 4*0], EBX;
-
-outer_loop:
- mov EBX, [ESP + LASTPARAM + 4*0]; // src.length
- mov EBP, 0;
- mov ECX, 0; // ECX = input carry.
- dec [ESP + LASTPARAM + 4*0]; // Next time, the length will be shorter by 1.
- neg EBX; // count UP to zero.
-
- mov EAX, [ESI + 4*EBX - 4*1]; // get new M
- mov [ESP], EAX; // save new M
-
- mov EAX, [ESI+4*EBX];
- test EBX, 1;
- jnz L_enter_odd;
- }
- // -- Inner loop, with even entry point
- mixin("asm pure nothrow { " ~ asmMulAdd_innerloop("add", "ESP") ~ "}");
- asm pure nothrow {
- mov [-4+EDI+4*EBX], EBP;
- add EDI, 4;
- cmp EDI, [ESP + LASTPARAM + 4*2]; // is EDI = &dest[$-3]?
- jnz outer_loop;
-length_is_3:
- mov EAX, [ESI - 4*3];
- mul EAX, [ESI - 4*2];
- mov ECX, 0;
- add [EDI-2*4], EAX; // ECX:dest[$-5] += x[$-3] * x[$-2]
- adc ECX, EDX;
-
- mov EAX, [ESI - 4*3];
- mul EAX, [ESI - 4*1]; // x[$-3] * x[$-1]
- add EAX, ECX;
- mov ECX, 0;
- adc EDX, 0;
- // now EDX: EAX = c + x[$-3] * x[$-1]
- add [EDI-1*4], EAX; // ECX:dest[$-4] += (EDX:EAX)
- adc ECX, EDX; // ECX holds dest[$-3], it acts as carry for the last row
-// do length == 2
- mov EAX, [ESI - 4*2];
- mul EAX, [ESI - 4*1];
- add ECX, EAX;
- adc EDX, 0;
- mov [EDI - 0*4], ECX; // dest[$-2:$-3] = c + x[$-2] * x[$-1];
- mov [EDI + 1*4], EDX;
-
- pop EAX;
- pop EBP;
- pop EBX;
- pop EDI;
- pop ESI;
- ret 4*4;
- }
-L_enter_odd:
- mixin("asm pure nothrow {" ~ asmMulAdd_enter_odd("add", "ESP") ~ "}");
-}
-
-@system unittest
-{
- uint [] aa = new uint[200];
- uint [] a = aa[0 .. 100];
- uint [] b = new uint [100];
- aa[] = 761;
- a[] = 0;
- b[] = 0;
- a[3] = 6;
- b[0]=1;
- b[1] = 17;
- b[50 .. 100]=78;
- multibyteTriangleAccumulateAsm(a, b[0 .. 50]);
- uint [] c = new uint[100];
- c[] = 0;
- c[1] = 17;
- c[3] = 6;
- assert(a[]==c[]);
- assert(a[0]==0);
- aa[] = 0xFFFF_FFFF;
- a[] = 0;
- b[] = 0;
- b[0]= 0xbf6a1f01;
- b[1]= 0x6e38ed64;
- b[2]= 0xdaa797ed;
- b[3] = 0;
-
- multibyteTriangleAccumulateAsm(a[0 .. 8], b[0 .. 4]);
- assert(a[1]==0x3a600964);
- assert(a[2]==0x339974f6);
- assert(a[3]==0x46736fce);
- assert(a[4]==0x5e24a2b4);
-
- b[3] = 0xe93ff9f4;
- b[4] = 0x184f03;
- a[]=0;
- multibyteTriangleAccumulateAsm(a[0 .. 14], b[0 .. 7]);
- assert(a[3]==0x79fff5c2);
- assert(a[4]==0xcf384241);
- assert(a[5]== 0x4a17fc8);
- assert(a[6]==0x4d549025);
-}
-
-
-void multibyteSquare(BigDigit[] result, const BigDigit [] x) pure
-{
- if (x.length < 4)
- {
- // Special cases, not worth doing triangular.
- result[x.length] = multibyteMul(result[0 .. x.length], x, x[0], 0);
- multibyteMultiplyAccumulate(result[1..$], x, x[1..$]);
- return;
- }
- // Do half a square multiply.
- // dest += src[0]*src[1...$] + src[1]*src[2..$] + ... + src[$-3]*src[$-2..$]+ src[$-2]*src[$-1]
- result[x.length] = multibyteMul(result[1 .. x.length], x[1..$], x[0], 0);
- multibyteTriangleAccumulateAsm(result[2..$], x[1..$]);
- // Multiply by 2
- result[$-1] = multibyteShlNoMMX(result[1..$-1], result[1..$-1], 1);
- // And add the diagonal elements
- result[0] = 0;
- multibyteAddDiagonalSquares(result, x);
-}
-
-version (BignumPerformanceTest)
-{
-import core.stdc.stdio;
-int clock() { asm { push EBX; xor EAX, EAX; cpuid; pop EBX; rdtsc; } }
-
-__gshared uint [2200] X1;
-__gshared uint [2200] Y1;
-__gshared uint [4000] Z1;
-
-void testPerformance() pure
-{
- // The performance results at the top of this file were obtained using
- // a Windows device driver to access the CPU performance counters.
- // The code below is less accurate but more widely usable.
- // The value for division is quite inconsistent.
- for (int i=0; i<X1.length; ++i) { X1[i]=i; Y1[i]=i; Z1[i]=i; }
- int t, t0;
- multibyteShl(Z1[0 .. 2000], X1[0 .. 2000], 7);
- t0 = clock();
- multibyteShl(Z1[0 .. 1000], X1[0 .. 1000], 7);
- t = clock();
- multibyteShl(Z1[0 .. 2000], X1[0 .. 2000], 7);
- auto shltime = (clock() - t) - (t - t0);
- t0 = clock();
- multibyteShr(Z1[2 .. 1002], X1[4 .. 1004], 13);
- t = clock();
- multibyteShr(Z1[2 .. 2002], X1[4 .. 2004], 13);
- auto shrtime = (clock() - t) - (t - t0);
- t0 = clock();
- multibyteAddSub!('+')(Z1[0 .. 1000], X1[0 .. 1000], Y1[0 .. 1000], 0);
- t = clock();
- multibyteAddSub!('+')(Z1[0 .. 2000], X1[0 .. 2000], Y1[0 .. 2000], 0);
- auto addtime = (clock() - t) - (t-t0);
- t0 = clock();
- multibyteMul(Z1[0 .. 1000], X1[0 .. 1000], 7, 0);
- t = clock();
- multibyteMul(Z1[0 .. 2000], X1[0 .. 2000], 7, 0);
- auto multime = (clock() - t) - (t - t0);
- multibyteMulAdd!('+')(Z1[0 .. 2000], X1[0 .. 2000], 217, 0);
- t0 = clock();
- multibyteMulAdd!('+')(Z1[0 .. 1000], X1[0 .. 1000], 217, 0);
- t = clock();
- multibyteMulAdd!('+')(Z1[0 .. 2000], X1[0 .. 2000], 217, 0);
- auto muladdtime = (clock() - t) - (t - t0);
- multibyteMultiplyAccumulate(Z1[0 .. 64], X1[0 .. 32], Y1[0 .. 32]);
- t = clock();
- multibyteMultiplyAccumulate(Z1[0 .. 64], X1[0 .. 32], Y1[0 .. 32]);
- auto accumtime = clock() - t;
- t0 = clock();
- multibyteDivAssign(Z1[0 .. 2000], 217, 0);
- t = clock();
- multibyteDivAssign(Z1[0 .. 1000], 37, 0);
- auto divtime = (t - t0) - (clock() - t);
- t= clock();
- multibyteSquare(Z1[0 .. 64], X1[0 .. 32]);
- auto squaretime = clock() - t;
-
- printf("-- BigInt asm performance (cycles/int) --\n");
- printf("Add: %.2f\n", addtime/1000.0);
- printf("Shl: %.2f\n", shltime/1000.0);
- printf("Shr: %.2f\n", shrtime/1000.0);
- printf("Mul: %.2f\n", multime/1000.0);
- printf("MulAdd: %.2f\n", muladdtime/1000.0);
- printf("Div: %.2f\n", divtime/1000.0);
- printf("MulAccum32: %.2f*n*n (total %d)\n", accumtime/(32.0*32.0), accumtime);
- printf("Square32: %.2f*n*n (total %d)\n\n", squaretime/(32.0*32.0), squaretime);
-}
-
-static this()
-{
- testPerformance();
-}
-}
-
-} // version (D_InlineAsm_X86)
projects / gcc.git / commitdiff