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Commit 6feee1e1 by Iain Buclaw Committed by Iain Buclaw
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Remove unused modules from libphobos std.internal package. 

libphobos/ChangeLog:

2018-11-19  Iain Buclaw  <ibuclaw@gdcproject.org>

	* src/Makefile.am: Remove std.internal.digest.sha_SSSE3 and
	std.internal.math.biguintx86 modules.
	* src/Makefile.in: Rebuild.
	* src/std/internal/digest/sha_SSSE3.d: Remove.
	* src/std/internal/math/biguintx86.d: Remove.

From-SVN: r266256
parent bee39274
Showing with 12 additions and 2103 deletions
libphobos/ChangeLog
2018-11-19 Iain Buclaw <ibuclaw@gdcproject.org>
* src/Makefile.am: Remove std.internal.digest.sha_SSSE3 and
std.internal.math.biguintx86 modules.
* src/Makefile.in: Rebuild.
* src/std/internal/digest/sha_SSSE3.d: Remove.
* src/std/internal/math/biguintx86.d: Remove.
2018-11-02 Iain Buclaw <ibuclaw@gdcproject.org> 2018-11-02 Iain Buclaw <ibuclaw@gdcproject.org>
PR d/87827 PR d/87827
......
libphobos/src/Makefile.am
...@@ -156,9 +156,8 @@ PHOBOS_DSOURCES = etc/c/curl.d etc/c/sqlite3.d etc/c/zlib.d \ ...@@ -156,9 +156,8 @@ PHOBOS_DSOURCES = etc/c/curl.d etc/c/sqlite3.d etc/c/zlib.d \
std/experimental/logger/multilogger.d \ std/experimental/logger/multilogger.d \
std/experimental/logger/nulllogger.d std/experimental/logger/package.d \ std/experimental/logger/nulllogger.d std/experimental/logger/package.d \
std/experimental/typecons.d std/file.d std/format.d std/functional.d \ std/experimental/typecons.d std/file.d std/format.d std/functional.d \
std/getopt.d std/internal/cstring.d std/internal/digest/sha_SSSE3.d \ std/getopt.d std/internal/cstring.d std/internal/math/biguintcore.d \
std/internal/math/biguintcore.d std/internal/math/biguintnoasm.d \ std/internal/math/biguintnoasm.d std/internal/math/errorfunction.d \
std/internal/math/biguintx86.d std/internal/math/errorfunction.d \
std/internal/math/gammafunction.d std/internal/scopebuffer.d \ std/internal/math/gammafunction.d std/internal/scopebuffer.d \
std/internal/test/dummyrange.d std/internal/test/range.d \ std/internal/test/dummyrange.d std/internal/test/range.d \
std/internal/test/uda.d std/internal/unicode_comp.d \ std/internal/test/uda.d std/internal/unicode_comp.d \
......
libphobos/src/Makefile.in
...@@ -193,10 +193,8 @@ am__objects_1 = etc/c/curl.lo etc/c/sqlite3.lo etc/c/zlib.lo \ ...@@ -193,10 +193,8 @@ am__objects_1 = etc/c/curl.lo etc/c/sqlite3.lo etc/c/zlib.lo \
std/experimental/logger/package.lo \ std/experimental/logger/package.lo \
std/experimental/typecons.lo std/file.lo std/format.lo \ std/experimental/typecons.lo std/file.lo std/format.lo \
std/functional.lo std/getopt.lo std/internal/cstring.lo \ std/functional.lo std/getopt.lo std/internal/cstring.lo \
std/internal/digest/sha_SSSE3.lo \
std/internal/math/biguintcore.lo \ std/internal/math/biguintcore.lo \
std/internal/math/biguintnoasm.lo \ std/internal/math/biguintnoasm.lo \
std/internal/math/biguintx86.lo \
std/internal/math/errorfunction.lo \ std/internal/math/errorfunction.lo \
std/internal/math/gammafunction.lo std/internal/scopebuffer.lo \ std/internal/math/gammafunction.lo std/internal/scopebuffer.lo \
std/internal/test/dummyrange.lo std/internal/test/range.lo \ std/internal/test/dummyrange.lo std/internal/test/range.lo \
...@@ -282,10 +280,8 @@ am__DEPENDENCIES_1 = etc/c/curl.t.lo etc/c/sqlite3.t.lo \ ...@@ -282,10 +280,8 @@ am__DEPENDENCIES_1 = etc/c/curl.t.lo etc/c/sqlite3.t.lo \
std/experimental/logger/package.t.lo \ std/experimental/logger/package.t.lo \
std/experimental/typecons.t.lo std/file.t.lo std/format.t.lo \ std/experimental/typecons.t.lo std/file.t.lo std/format.t.lo \
std/functional.t.lo std/getopt.t.lo std/internal/cstring.t.lo \ std/functional.t.lo std/getopt.t.lo std/internal/cstring.t.lo \
std/internal/digest/sha_SSSE3.t.lo \
std/internal/math/biguintcore.t.lo \ std/internal/math/biguintcore.t.lo \
std/internal/math/biguintnoasm.t.lo \ std/internal/math/biguintnoasm.t.lo \
std/internal/math/biguintx86.t.lo \
std/internal/math/errorfunction.t.lo \ std/internal/math/errorfunction.t.lo \
std/internal/math/gammafunction.t.lo \ std/internal/math/gammafunction.t.lo \
std/internal/scopebuffer.t.lo \ std/internal/scopebuffer.t.lo \
...@@ -392,10 +388,8 @@ am__DEPENDENCIES_4 = etc/c/curl.t.o etc/c/sqlite3.t.o etc/c/zlib.t.o \ ...@@ -392,10 +388,8 @@ am__DEPENDENCIES_4 = etc/c/curl.t.o etc/c/sqlite3.t.o etc/c/zlib.t.o \
std/experimental/logger/package.t.o \ std/experimental/logger/package.t.o \
std/experimental/typecons.t.o std/file.t.o std/format.t.o \ std/experimental/typecons.t.o std/file.t.o std/format.t.o \
std/functional.t.o std/getopt.t.o std/internal/cstring.t.o \ std/functional.t.o std/getopt.t.o std/internal/cstring.t.o \
std/internal/digest/sha_SSSE3.t.o \
std/internal/math/biguintcore.t.o \ std/internal/math/biguintcore.t.o \
std/internal/math/biguintnoasm.t.o \ std/internal/math/biguintnoasm.t.o \
std/internal/math/biguintx86.t.o \
std/internal/math/errorfunction.t.o \ std/internal/math/errorfunction.t.o \
std/internal/math/gammafunction.t.o \ std/internal/math/gammafunction.t.o \
std/internal/scopebuffer.t.o std/internal/test/dummyrange.t.o \ std/internal/scopebuffer.t.o std/internal/test/dummyrange.t.o \
...@@ -788,9 +782,8 @@ PHOBOS_DSOURCES = etc/c/curl.d etc/c/sqlite3.d etc/c/zlib.d \ ...@@ -788,9 +782,8 @@ PHOBOS_DSOURCES = etc/c/curl.d etc/c/sqlite3.d etc/c/zlib.d \
std/experimental/logger/multilogger.d \ std/experimental/logger/multilogger.d \
std/experimental/logger/nulllogger.d std/experimental/logger/package.d \ std/experimental/logger/nulllogger.d std/experimental/logger/package.d \
std/experimental/typecons.d std/file.d std/format.d std/functional.d \ std/experimental/typecons.d std/file.d std/format.d std/functional.d \
std/getopt.d std/internal/cstring.d std/internal/digest/sha_SSSE3.d \ std/getopt.d std/internal/cstring.d std/internal/math/biguintcore.d \
std/internal/math/biguintcore.d std/internal/math/biguintnoasm.d \ std/internal/math/biguintnoasm.d std/internal/math/errorfunction.d \
std/internal/math/biguintx86.d std/internal/math/errorfunction.d \
std/internal/math/gammafunction.d std/internal/scopebuffer.d \ std/internal/math/gammafunction.d std/internal/scopebuffer.d \
std/internal/test/dummyrange.d std/internal/test/range.d \ std/internal/test/dummyrange.d std/internal/test/range.d \
std/internal/test/uda.d std/internal/unicode_comp.d \ std/internal/test/uda.d std/internal/unicode_comp.d \
...@@ -1032,16 +1025,11 @@ std/internal/$(am__dirstamp): ...@@ -1032,16 +1025,11 @@ std/internal/$(am__dirstamp):
@$(MKDIR_P) std/internal @$(MKDIR_P) std/internal
@: > std/internal/$(am__dirstamp) @: > std/internal/$(am__dirstamp)
std/internal/cstring.lo: std/internal/$(am__dirstamp) std/internal/cstring.lo: std/internal/$(am__dirstamp)
std/internal/digest/$(am__dirstamp):
@$(MKDIR_P) std/internal/digest
@: > std/internal/digest/$(am__dirstamp)
std/internal/digest/sha_SSSE3.lo: std/internal/digest/$(am__dirstamp)
std/internal/math/$(am__dirstamp): std/internal/math/$(am__dirstamp):
@$(MKDIR_P) std/internal/math @$(MKDIR_P) std/internal/math
@: > std/internal/math/$(am__dirstamp) @: > std/internal/math/$(am__dirstamp)
std/internal/math/biguintcore.lo: std/internal/math/$(am__dirstamp) std/internal/math/biguintcore.lo: std/internal/math/$(am__dirstamp)
std/internal/math/biguintnoasm.lo: std/internal/math/$(am__dirstamp) std/internal/math/biguintnoasm.lo: std/internal/math/$(am__dirstamp)
std/internal/math/biguintx86.lo: std/internal/math/$(am__dirstamp)
std/internal/math/errorfunction.lo: std/internal/math/$(am__dirstamp) std/internal/math/errorfunction.lo: std/internal/math/$(am__dirstamp)
std/internal/math/gammafunction.lo: std/internal/math/$(am__dirstamp) std/internal/math/gammafunction.lo: std/internal/math/$(am__dirstamp)
std/internal/scopebuffer.lo: std/internal/$(am__dirstamp) std/internal/scopebuffer.lo: std/internal/$(am__dirstamp)
...@@ -1174,8 +1162,6 @@ mostlyclean-compile: ...@@ -1174,8 +1162,6 @@ mostlyclean-compile:
-rm -f std/experimental/logger/*.lo -rm -f std/experimental/logger/*.lo
-rm -f std/internal/*.$(OBJEXT) -rm -f std/internal/*.$(OBJEXT)
-rm -f std/internal/*.lo -rm -f std/internal/*.lo
-rm -f std/internal/digest/*.$(OBJEXT)
-rm -f std/internal/digest/*.lo
-rm -f std/internal/math/*.$(OBJEXT) -rm -f std/internal/math/*.$(OBJEXT)
-rm -f std/internal/math/*.lo -rm -f std/internal/math/*.lo
-rm -f std/internal/test/*.$(OBJEXT) -rm -f std/internal/test/*.$(OBJEXT)
...@@ -1401,7 +1387,6 @@ clean-libtool: ...@@ -1401,7 +1387,6 @@ clean-libtool:
-rm -rf std/experimental/allocator/building_blocks/.libs std/experimental/allocator/building_blocks/_libs -rm -rf std/experimental/allocator/building_blocks/.libs std/experimental/allocator/building_blocks/_libs
-rm -rf std/experimental/logger/.libs std/experimental/logger/_libs -rm -rf std/experimental/logger/.libs std/experimental/logger/_libs
-rm -rf std/internal/.libs std/internal/_libs -rm -rf std/internal/.libs std/internal/_libs
-rm -rf std/internal/digest/.libs std/internal/digest/_libs
-rm -rf std/internal/math/.libs std/internal/math/_libs -rm -rf std/internal/math/.libs std/internal/math/_libs
-rm -rf std/internal/test/.libs std/internal/test/_libs -rm -rf std/internal/test/.libs std/internal/test/_libs
-rm -rf std/internal/windows/.libs std/internal/windows/_libs -rm -rf std/internal/windows/.libs std/internal/windows/_libs
...@@ -1529,7 +1514,6 @@ distclean-generic: ...@@ -1529,7 +1514,6 @@ distclean-generic:
-rm -f std/experimental/allocator/building_blocks/$(am__dirstamp) -rm -f std/experimental/allocator/building_blocks/$(am__dirstamp)
-rm -f std/experimental/logger/$(am__dirstamp) -rm -f std/experimental/logger/$(am__dirstamp)
-rm -f std/internal/$(am__dirstamp) -rm -f std/internal/$(am__dirstamp)
-rm -f std/internal/digest/$(am__dirstamp)
-rm -f std/internal/math/$(am__dirstamp) -rm -f std/internal/math/$(am__dirstamp)
-rm -f std/internal/test/$(am__dirstamp) -rm -f std/internal/test/$(am__dirstamp)
-rm -f std/internal/windows/$(am__dirstamp) -rm -f std/internal/windows/$(am__dirstamp)
......
libphobos/src/std/internal/digest/sha_SSSE3.d deleted 100644 → 0
// 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()));
}
}
libphobos/src/std/internal/math/biguintx86.d deleted 100644 → 0
/** 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)
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