math/mpx-mul4-*.S: Fix up some of the commentary.

[catacomb] / math / mpx-mul4-amd64-sse2.S

/// -*- mode: asm; asm-comment-char: ?/; comment-start: "// " -*-
///
/// Large SIMD-based multiplications
///
/// (c) 2016 Straylight/Edgeware
///

///----- Licensing notice ---------------------------------------------------
///
/// This file is part of Catacomb.
///
/// Catacomb is free software; you can redistribute it and/or modify
/// it under the terms of the GNU Library General Public License as
/// published by the Free Software Foundation; either version 2 of the
/// License, or (at your option) any later version.
///
/// Catacomb is distributed in the hope that it will be useful,
/// but WITHOUT ANY WARRANTY; without even the implied warranty of
/// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
/// GNU Library General Public License for more details.
///
/// You should have received a copy of the GNU Library General Public
/// License along with Catacomb; if not, write to the Free
/// Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
/// MA 02111-1307, USA.

///--------------------------------------------------------------------------
/// Preliminaries.

#include "config.h"
#include "asm-common.h"

        .arch   pentium4

        .text

///--------------------------------------------------------------------------
/// Theory.
///
/// We define a number of primitive fixed-size multipliers from which we can
/// construct more general variable-length multipliers.
///
/// The basic trick is the same throughout.  In an operand-scanning
/// multiplication, the inner multiplication loop multiplies a multiple-
/// precision operand by a single precision factor, and adds the result,
/// appropriately shifted, to the result.  A `finely integrated operand
/// scanning' implementation of Montgomery multiplication also adds the
/// product of a single-precision `Montgomery factor' and the modulus,
/// calculated in the same pass.  The more common `coarsely integrated
/// operand scanning' alternates main multiplication and Montgomery passes,
/// which requires additional carry propagation.
///
/// Throughout both plain-multiplication and Montgomery stages, then, one of
/// the factors remains constant throughout the operation, so we can afford
/// to take a little time to preprocess it.  The transformation we perform is
/// as follows.  Let b = 2^16, and B = b^2 = 2^32.  Suppose we're given a
/// 128-bit factor v = v_0 + v_1 B + v_2 B^2 + v_3 B^3.  Split each v_i into
/// two sixteen-bit pieces, so v_i = v'_i + v''_i b.  These eight 16-bit
/// pieces are placed into 32-bit cells, and arranged as two 128-bit SSE
/// operands, as follows.
///
///     Offset     0       4        8      12
///        0    v'_0    v'_1    v''_0   v''_1
///       16    v'_2    v'_3    v''_2   v''_3
///
/// A `pmuludqd' instruction ignores the odd positions in its operands; thus,
/// it will act on (say) v'_0 and v''_0 in a single instruction.  Shifting
/// this vector right by 4 bytes brings v'_1 and v''_1 into position.  We can
/// multiply such a vector by a full 32-bit scalar to produce two 48-bit
/// results in 64-bit fields.  The sixteen bits of headroom allows us to add
/// many products together before we must deal with carrying; it also allows
/// for some calculations to be performed on the above expanded form.
///
/// We maintain four `carry' registers XMM12--XMM15 accumulating intermediate
/// results.  The registers' precise roles rotate during the computation; we
/// name them `c0', `c1', `c2', and `c3'.  Each carry register holds two
/// 64-bit halves: the register c0, for example, holds c'_0 (low half) and
/// c''_0 (high half), and represents the value c_0 = c'_0 + c''_0 b; the
/// carry registers collectively represent the value c_0 + c_1 B + c_2 B^2 +
/// c_3 B^3.  The `pmuluqdq' instruction acting on a scalar operand
/// (broadcast across all lanes of its vector) and an operand in the expanded
/// form above produces a result which can be added directly to the
/// appropriate carry register.  Following a pass of four multiplications, we
/// perform some limited carry propagation: let t = c''_0 mod B, and let d =
/// c'_0 + t b; then we output z = d mod B, add (floor(d/B), floor(c''_0/B))
/// to c1, and cycle the carry registers around, so that c1 becomes c0, and
/// the old (implicitly) zeroed c0 becomes c3.
///
/// On 64-bit AMD64, we have a reasonable number of registers: the expanded
/// operands are kept in registers.  The packed operands are read from memory
/// into working registers XMM4 and XMM5; XMM0--XMM3 are used for the actual
/// multiplications; and XMM6 and XMM7 are used for combining the results.
/// The following conventional argument names and locations are used
/// throughout.
///
/// Arg Format      Location    Notes
///
/// U   packed      [RAX]
/// X   packed      [RBX]       In Montgomery multiplication, X = N
/// V   expanded    XMM8/XMM9
/// Y   expanded    XMM10/XMM11 In Montgomery multiplication, Y = (A + U V) M
/// M   expanded    (see below) Montgomery factor, M = -N^{-1} (mod B^4)
/// N                           Modulus, for Montgomery multiplication
/// A   packed      [RDI]       Destination/accumulator
/// C   carry       XMM12--XMM15
///
/// The calculation is some variant of
///
///     A' + C' B^4 <- U V + X Y + A + C
///
/// The low-level functions fit into a fairly traditional (finely-integrated)
/// operand scanning loop over operand pairs (U, X) (indexed by j) and (V, Y)
/// (indexed by i).
///
/// The variants are as follows.
///
/// Function    Variant                 Use             i       j
///
/// mmul4       A = C = 0, Y = M        Montgomery      0       0
/// dmul4       A = 0                   Montgomery      0       +
/// mmla4       C = 0, Y = M            Montgomery      +       0
/// dmla4       exactly as shown        Montgomery      +       +
/// mont4       U = C = 0, V = M        Montgomery      any     0
///
/// mul4zc      U = V = A = C = 0       Plain           0       0
/// mul4        U = V = A = 0           Plain           0       +
/// mla4zc      U = V = C = 0           Plain           +       0
/// mla4        U = V = 0               Plain           +       +
///
/// The `mmul4' and `mmla4' functions are also responsible for calculating
/// the Montgomery reduction factor Y = (A + U V) M used by the rest of the
/// inner loop.

///--------------------------------------------------------------------------
/// Macro definitions.

.macro  mulcore r, i, slo, shi, d0, d1=nil, d2=nil, d3=nil
        // Multiply R_I by the expanded operand SLO/SHI, and leave the pieces
        // of the product in registers D0, D1, D2, D3.
        pshufd  \d0, \r, SHUF(\i, 3, \i, 3) // (r_i, ?; r_i, ?)
  .ifnes "\d1", "nil"
        movdqa  \d1, \slo               // (s'_0, s'_1; s''_0, s''_1)
  .endif
  .ifnes "\d3", "nil"
        movdqa  \d3, \shi               // (s'_2, s'_3; s''_2, s''_3)
  .endif
  .ifnes "\d1", "nil"
        psrldq  \d1, 4                  // (s'_1, s''_0; s''_1, 0)
  .endif
  .ifnes "\d2", "nil"
        movdqa  \d2, \d0                // another copy of (r_i, ?; r_i, ?)
  .endif
  .ifnes "\d3", "nil"
        psrldq  \d3, 4                  // (s'_3, s''_2; s''_3, 0)
  .endif
  .ifnes "\d1", "nil"
        pmuludq \d1, \d0                // (r_i s'_1; r_i s''_1)
  .endif
  .ifnes "\d3", "nil"
        pmuludq \d3, \d0                // (r_i s'_3; r_i s''_3)
  .endif
  .ifnes "\d2", "nil"
        pmuludq \d2, \shi               // (r_i s'_2; r_i s''_2)
  .endif
        pmuludq \d0, \slo               // (r_i s'_0; r_i s''_0)
.endm

.macro  accum   c0, c1=nil, c2=nil, c3=nil
        // Accumulate 64-bit pieces in XMM0--XMM3 into the corresponding
        // carry registers C0--C3.  Any or all of C1--C3 may be `nil' to skip
        // updating that register.
        paddq   \c0, xmm0
  .ifnes "\c1", "nil"
        paddq   \c1, xmm1
  .endif
  .ifnes "\c2", "nil"
        paddq   \c2, xmm2
  .endif
  .ifnes "\c3", "nil"
        paddq   \c3, xmm3
  .endif
.endm

.macro  mulacc  r, i, slo, shi, c0=nil, c1=nil, c2=nil, c3=nil, z3p=nil
        // Multiply R_I by the expanded operand SLO/SHI, and accumulate in
        // carry registers C0, C1, C2, C3.  If Z3P is `t' then C3 notionally
        // contains zero, but needs clearing; in practice, we store the
        // product directly rather than attempting to add.  On completion,
        // XMM0, XMM1, and XMM2 are clobbered, as is XMM3 if Z3P is not `t'.
  .ifeqs "\z3p", "t"
        mulcore \r, \i, \slo, \shi, xmm0, xmm1, xmm2, \c3
        accum                       \c0,  \c1,  \c2
  .else
        mulcore \r, \i, \slo, \shi, xmm0, xmm1, xmm2, xmm3
        accum                       \c0,  \c1,  \c2,  \c3
  .endif
.endm

.macro  propout d, pos, c, cc=nil
        // Calculate an output word from C, and store it at POS in D;
        // propagate carries out from C to CC in preparation for a rotation
        // of the carry registers.  D is an XMM register; the POS is either
        // `lo' or `hi' according to whether the output word should be in
        // lane 0 or 1 of D; the high two lanes of D are clobbered.  On
        // completion, XMM3 is clobbered.  If CC is `nil', then the
        // contribution which would have been added to it is left in C.
        pshufd  xmm3, \c, SHUF(3, 3, 3, 2) // (?, ?; ?, t = c'' mod B)
        psrldq  xmm3, 12                // (t, 0; 0, 0) = (t; 0)
        pslldq  xmm3, 2                 // (t b; 0)
        paddq   \c, xmm3                // (c' + t b; c'')
  .ifeqs "\pos", "lo"
        movdqa  \d, \c
  .else
        punpckldq \d, \c
  .endif
        psrlq   \c, 32                  // floor(c/B)
  .ifnes "\cc", "nil"
        paddq   \cc, \c                 // propagate up
  .endif
.endm

.macro endprop d, pos, c, t
        // On entry, C contains a carry register.  On exit, the low 32 bits
        // of the value represented in C are written at POS in D, and the
        // remaining bits are left at the bottom of T.
        movdqa  \t, \c
        psllq   \t, 16                  // (?; c'' b)
        pslldq  \c, 8                   // (0; c')
        paddq   \t, \c                  // (?; c' + c'' b)
        psrldq  \t, 8                   // (c' + c'' b; 0) = (c; 0)
  .ifeqs "\pos", "lo"
        movdqa  \d, \t
  .else
        punpckldq \d, \t
  .endif
        psrldq  \t, 4                   // (floor(c/B); 0)
.endm

.macro  expand  z, a, b, c=nil, d=nil
        // On entry, A and C hold packed 128-bit values, and Z is zero.  On
        // exit, A:B and C:D together hold the same values in expanded
        // form.  If C is `nil', then only expand A to A:B.
        movdqa  \b, \a                  // (a_0, a_1; a_2, a_3)
  .ifnes "\c", "nil"
        movdqa  \d, \c                  // (c_0, c_1; c_2, c_3)
  .endif
        punpcklwd \a, \z                // (a'_0, a''_0; a'_1, a''_1)
        punpckhwd \b, \z                // (a'_2, a''_2; a'_3, a''_3)
  .ifnes "\c", "nil"
        punpcklwd \c, \z                // (c'_0, c''_0; c'_1, c''_1)
        punpckhwd \d, \z                // (c'_2, c''_2; c'_3, c''_3)
  .endif
        pshufd  \a, \a, SHUF(0, 2, 1, 3) // (a'_0, a'_1; a''_0, a''_1)
        pshufd  \b, \b, SHUF(0, 2, 1, 3) // (a'_2, a'_3; a''_2, a''_3)
  .ifnes "\c", "nil"
        pshufd  \c, \c, SHUF(0, 2, 1, 3) // (c'_0, c'_1; c''_0, c''_1)
        pshufd  \d, \d, SHUF(0, 2, 1, 3) // (c'_2, c'_3; c''_2, c''_3)
  .endif
.endm

.macro  squash  c0, c1, c2, c3, t, u, lo, hi=nil
        // On entry, C0, C1, C2, C3 are carry registers representing a value
        // Y.  On exit, LO holds the low 128 bits of the carry value; C1, C2,
        // C3, T, and U are clobbered; and the high bits of Y are stored in
        // HI, if this is not `nil'.

        // The first step is to eliminate the `double-prime' pieces -- i.e.,
        // the ones offset by 16 bytes from a 32-bit boundary -- by carrying
        // them into the 32-bit-aligned pieces above and below.  But before
        // we can do that, we must gather them together.
        movdqa  \t, \c0
        movdqa  \u, \c1
        punpcklqdq \t, \c2              // (y'_0; y'_2)
        punpckhqdq \c0, \c2             // (y''_0; y''_2)
        punpcklqdq \u, \c3              // (y'_1; y'_3)
        punpckhqdq \c1, \c3             // (y''_1; y''_3)

        // Now split the double-prime pieces.  The high (up to) 48 bits will
        // go up; the low 16 bits go down.
        movdqa  \c2, \c0
        movdqa  \c3, \c1
        psllq   \c2, 48
        psllq   \c3, 48
        psrlq   \c0, 16                 // high parts of (y''_0; y''_2)
        psrlq   \c1, 16                 // high parts of (y''_1; y''_3)
        psrlq   \c2, 32                 // low parts of (y''_0; y''_2)
        psrlq   \c3, 32                 // low parts of (y''_1; y''_3)
  .ifnes "\hi", "nil"
        movdqa  \hi, \c1
  .endif
        pslldq  \c1, 8                  // high part of (0; y''_1)

        paddq   \t, \c2                 // propagate down
        paddq   \u, \c3
        paddq   \t, \c1                 // and up: (y_0; y_2)
        paddq   \u, \c0                 // (y_1; y_3)
  .ifnes "\hi", "nil"
        psrldq  \hi, 8                  // high part of (y''_3; 0)
  .endif

        // Finally extract the answer.  This complicated dance is better than
        // storing to memory and loading, because the piecemeal stores
        // inhibit store forwarding.
        movdqa  \c3, \t                 // (y_0; ?)
        movdqa  \lo, \t                 // (y^*_0, ?; ?, ?)
        psrldq  \t, 8                   // (y_2; 0)
        psrlq   \c3, 32                 // (floor(y_0/B); ?)
        paddq   \c3, \u                 // (y_1 + floor(y_0/B); ?)
        movdqa  \c1, \c3                // (y^*_1, ?; ?, ?)
        psrldq  \u, 8                   // (y_3; 0)
        psrlq   \c3, 32                 // (floor((y_1 B + y_0)/B^2; ?)
        paddq   \c3, \t                 // (y_2 + floor((y_1 B + y_0)/B^2; ?)
        punpckldq \lo, \c3              // (y^*_0, y^*_2; ?, ?)
        psrlq   \c3, 32             // (floor((y_2 B^2 + y_1 B + y_0)/B^3; ?)
        paddq   \c3, \u       // (y_3 + floor((y_2 B^2 + y_1 B + y_0)/B^3; ?)
  .ifnes "\hi", "nil"
        movdqa  \t, \c3
        pxor    \u, \u
  .endif
        punpckldq \c1, \c3              // (y^*_1, y^*_3; ?, ?)
  .ifnes "\hi", "nil"
        psrlq   \t, 32                  // very high bits of y
        paddq   \hi, \t
        punpcklqdq \hi, \u              // carry up
  .endif
        punpckldq \lo, \c1              // y mod B^4
.endm

.macro  carryadd
        // On entry, RDI points to a packed addend A, and XMM12, XMM13, XMM14
        // hold the incoming carry registers c0, c1, and c2 representing a
        // carry-in C.
        //
        // On exit, the carry registers, including XMM15, are updated to hold
        // C + A; XMM0, XMM1, XMM2, and XMM3 are clobbered.  The other
        // registers are preserved.
        movd    xmm0, [rdi +  0]        // (a_0; 0)
        movd    xmm1, [rdi +  4]        // (a_1; 0)
        movd    xmm2, [rdi +  8]        // (a_2; 0)
        movd    xmm15, [rdi + 12]       // (a_3; 0)
        paddq   xmm12, xmm0             // (c'_0 + a_0; c''_0)
        paddq   xmm13, xmm1             // (c'_1 + a_1; c''_1)
        paddq   xmm14, xmm2             // (c'_2 + a_2; c''_2 + a_3 b)
.endm

///--------------------------------------------------------------------------
/// Primitive multipliers and related utilities.

INTFUNC(carryprop)
        // On entry, XMM12, XMM13, and XMM14 hold a 144-bit carry in an
        // expanded form.  Store the low 128 bits of the represented carry to
        // [RDI] as a packed 128-bit value, and leave the remaining 16 bits
        // in the low 32 bits of XMM12.  On exit, XMM0, XMM1, XMM3, XMM13 and
        // XMM14 are clobbered.
  endprologue

        propout xmm0, lo, xmm12, xmm13
        propout xmm1, lo, xmm13, xmm14
        propout xmm0, hi, xmm14, nil
        endprop xmm1, hi, xmm14, xmm12
        punpckldq xmm0, xmm1
        movdqu  [rdi], xmm0

        ret
ENDFUNC

INTFUNC(dmul4)
        // On entry, RDI points to the destination buffer; RAX and RBX point
        // to the packed operands U and X; XMM8/XMM9 and XMM10/XMM11 hold the
        // expanded operands V and Y; and XMM12, XMM13, XMM14 hold the
        // incoming carry registers c0, c1, and c2; c3 is assumed to be zero.
        //
        // On exit, we write the low 128 bits of the sum C + U V + X Y to
        // [RDI], and update the carry registers with the carry out.  The
        // registers XMM0--XMM7, and XMM15 are clobbered; the general-purpose
        // registers are preserved.
  endprologue

        movdqu  xmm4, [rax]
        movdqu  xmm5, [rbx]

        mulacc  xmm4, 0,   xmm8,  xmm9,  xmm12, xmm13, xmm14, xmm15, t
        mulacc  xmm5, 0,   xmm10, xmm11, xmm12, xmm13, xmm14, xmm15
        propout xmm6, lo,                xmm12, xmm13

        mulacc  xmm4, 1,   xmm8,  xmm9,  xmm13, xmm14, xmm15, xmm12, t
        mulacc  xmm5, 1,   xmm10, xmm11, xmm13, xmm14, xmm15, xmm12
        propout xmm7, lo,                xmm13, xmm14

        mulacc  xmm4, 2,   xmm8,  xmm9,  xmm14, xmm15, xmm12, xmm13, t
        mulacc  xmm5, 2,   xmm10, xmm11, xmm14, xmm15, xmm12, xmm13
        propout xmm6, hi,                xmm14, xmm15

        mulacc  xmm4, 3,   xmm8,  xmm9,  xmm15, xmm12, xmm13, xmm14, t
        mulacc  xmm5, 3,   xmm10, xmm11, xmm15, xmm12, xmm13, xmm14
        propout xmm7, hi,                xmm15, xmm12

        punpckldq xmm6, xmm7
        movdqu  [rdi], xmm6

        ret
ENDFUNC

INTFUNC(dmla4)
        // On entry, RDI points to the destination buffer, which also
        // contains an addend A to accumulate; RAX and RBX point to the
        // packed operands U and X; XMM8/XMM9 and XMM10/XMM11 hold the
        // expanded operands V and Y; and XMM12, XMM13, XMM14 hold the
        // incoming carry registers c0, c1, and c2 representing a carry-in C;
        // c3 is assumed to be zero.
        //
        // On exit, we write the low 128 bits of the sum A + C + U V + X Y to
        // [RDI], and update the carry registers with the carry out.  The
        // registers XMM0--XMM7, and XMM15 are clobbered; the general-purpose
        // registers are preserved.
  endprologue

        movdqu  xmm4, [rax]
        movdqu  xmm5, [rbx]
        carryadd

        mulacc  xmm4, 0,   xmm8,  xmm9,  xmm12, xmm13, xmm14, xmm15
        mulacc  xmm5, 0,   xmm10, xmm11, xmm12, xmm13, xmm14, xmm15
        propout xmm6, lo,                xmm12, xmm13

        mulacc  xmm4, 1,   xmm8,  xmm9,  xmm13, xmm14, xmm15, xmm12, t
        mulacc  xmm5, 1,   xmm10, xmm11, xmm13, xmm14, xmm15, xmm12
        propout xmm7, lo,                xmm13, xmm14

        mulacc  xmm4, 2,   xmm8,  xmm9,  xmm14, xmm15, xmm12, xmm13, t
        mulacc  xmm5, 2,   xmm10, xmm11, xmm14, xmm15, xmm12, xmm13
        propout xmm6, hi,                xmm14, xmm15

        mulacc  xmm4, 3,   xmm8,  xmm9,  xmm15, xmm12, xmm13, xmm14, t
        mulacc  xmm5, 3,   xmm10, xmm11, xmm15, xmm12, xmm13, xmm14
        propout xmm7, hi,                xmm15, xmm12

        punpckldq xmm6, xmm7
        movdqu  [rdi], xmm6

        ret
ENDFUNC

INTFUNC(mul4zc)
        // On entry, RDI points to the destination buffer; RBX points to a
        // packed operand X; and XMM10/XMM11 hold an expanded operand Y.
        //
        // On exit, we write the low 128 bits of the product X Y to [RDI],
        // and set the carry registers XMM12, XMM13, XMM14 to the carry out.
        // The registers XMM0--XMM3, XMM5--XMM7, and XMM15 are clobbered; the
        // general-purpose registers are preserved.
  endprologue

        movdqu  xmm5, [rbx]

        mulcore xmm5, 0,   xmm10, xmm11, xmm12, xmm13, xmm14, xmm15
        propout xmm6, lo,                xmm12, xmm13

        mulacc  xmm5, 1,   xmm10, xmm11, xmm13, xmm14, xmm15, xmm12, t
        propout xmm7, lo,                xmm13, xmm14

        mulacc  xmm5, 2,   xmm10, xmm11, xmm14, xmm15, xmm12, xmm13, t
        propout xmm6, hi,                xmm14, xmm15

        mulacc  xmm5, 3,   xmm10, xmm11, xmm15, xmm12, xmm13, xmm14, t
        propout xmm7, hi,                xmm15, xmm12

        punpckldq xmm6, xmm7
        movdqu  [rdi], xmm6

        ret
ENDFUNC

INTFUNC(mul4)
        // On entry, RDI points to the destination buffer; RBX points to a
        // packed operand X; XMM10/XMM11 hold an expanded operand Y; and
        // XMM12, XMM13, XMM14 hold the incoming carry registers c0, c1, and
        // c2, representing a carry-in C; c3 is assumed to be zero.
        //
        // On exit, we write the low 128 bits of the sum C + X Y to [RDI],
        // and update the carry registers with the carry out.  The registers
        // XMM0--XMM3, XMM5--XMM7, and XMM15 are clobbered; the
        // general-purpose registers are preserved.
  endprologue

        movdqu  xmm5, [rbx]

        mulacc  xmm5, 0,   xmm10, xmm11, xmm12, xmm13, xmm14, xmm15, t
        propout xmm6, lo,                xmm12, xmm13

        mulacc  xmm5, 1,   xmm10, xmm11, xmm13, xmm14, xmm15, xmm12, t
        propout xmm7, lo,                xmm13, xmm14

        mulacc  xmm5, 2,   xmm10, xmm11, xmm14, xmm15, xmm12, xmm13, t
        propout xmm6, hi,                xmm14, xmm15

        mulacc  xmm5, 3,   xmm10, xmm11, xmm15, xmm12, xmm13, xmm14, t
        propout xmm7, hi,                xmm15, xmm12

        punpckldq xmm6, xmm7
        movdqu  [rdi], xmm6

        ret
ENDFUNC

INTFUNC(mla4zc)
        // On entry, RDI points to the destination buffer, which also
        // contains an addend A to accumulate; RBX points to a packed operand
        // X; and XMM10/XMM11 points to an expanded operand Y.
        //
        // On exit, we write the low 128 bits of the sum A + X Y to [RDI],
        // and set the carry registers XMM12, XMM13, XMM14 to the carry out.
        // The registers XMM0--XMM3, XMM5--XMM7, and XMM15 are clobbered; the
        // general-purpose registers are preserved.
  endprologue

        movdqu  xmm5, [rbx]
        movd    xmm12, [rdi +  0]
        movd    xmm13, [rdi +  4]
        movd    xmm14, [rdi +  8]
        movd    xmm15, [rdi + 12]

        mulacc  xmm5, 0,   xmm10, xmm11, xmm12, xmm13, xmm14, xmm15
        propout xmm6, lo,                xmm12, xmm13

        mulacc  xmm5, 1,   xmm10, xmm11, xmm13, xmm14, xmm15, xmm12, t
        propout xmm7, lo,                xmm13, xmm14

        mulacc  xmm5, 2,   xmm10, xmm11, xmm14, xmm15, xmm12, xmm13, t
        propout xmm6, hi,                xmm14, xmm15

        mulacc  xmm5, 3,   xmm10, xmm11, xmm15, xmm12, xmm13, xmm14, t
        propout xmm7, hi,                xmm15, xmm12

        punpckldq xmm6, xmm7
        movdqu  [rdi], xmm6

        ret
ENDFUNC

INTFUNC(mla4)
        // On entry, RDI points to the destination buffer, which also
        // contains an addend A to accumulate; RBX points to a packed operand
        // X; XMM10/XMM11 holds an expanded operand Y; and XMM12, XMM13,
        // XMM14 hold the incoming carry registers c0, c1, and c2,
        // representing a carry-in C; c3 is assumed to be zero.
        //
        // On exit, we write the low 128 bits of the sum A + C + X Y to
        // [RDI], and update the carry registers with the carry out.  The
        // registers XMM0--XMM3, XMM5--XMM7, and XMM15 are clobbered; the
        // general-purpose registers are preserved.
  endprologue

        movdqu  xmm5, [rbx]
        carryadd

        mulacc  xmm5, 0,    xmm10, xmm11, xmm12, xmm13, xmm14, xmm15
        propout xmm6, lo,                xmm12, xmm13

        mulacc  xmm5, 1,    xmm10, xmm11, xmm13, xmm14, xmm15, xmm12, t
        propout xmm7, lo,                xmm13, xmm14

        mulacc  xmm5, 2,    xmm10, xmm11, xmm14, xmm15, xmm12, xmm13, t
        propout xmm6, hi,                xmm14, xmm15

        mulacc  xmm5, 3,    xmm10, xmm11, xmm15, xmm12, xmm13, xmm14, t
        propout xmm7, hi,                xmm15, xmm12

        punpckldq xmm6, xmm7
        movdqu  [rdi], xmm6

        ret
ENDFUNC

INTFUNC(mmul4)
        // On entry, RDI points to the destination buffer; RAX and RBX point
        // to the packed operands U and N; and XMM8/XMM9 and XMM10/XMM11 hold
        // the expanded operands V and M.  The stack pointer must be 8 modulo
        // 16 (as usual for AMD64 ABIs).
        //
        // On exit, we store Y = U V M mod B in XMM10/XMM11, and write the
        // low 128 bits of the sum U V + N Y to [RDI], leaving the remaining
        // carry in XMM12, XMM13, and XMM14.  The registers XMM0--XMM7, and
        // XMM15 are clobbered; the general-purpose registers are preserved.
        movdqu  xmm4, [rax]
#if ABI_WIN
        stalloc 48 + 8                  // space for the carries
#endif
  endprologue

        // Calculate W = U V, and leave it in XMM7.  Stash the carry pieces
        // for later.
        mulcore xmm4, 0,   xmm8,  xmm9,  xmm12, xmm13, xmm14, xmm15
        propout xmm7, lo,                xmm12, xmm13
        jmp     5f
ENDFUNC

INTFUNC(mmla4)
        // On entry, RDI points to the destination buffer, which also
        // contains an addend A to accumulate; RAX and RBX point to the
        // packed operands U and N; and XMM8/XMM9 and XMM10/XMM11 hold the
        // expanded operands V and M.  The stack pointer must be 8 modulo 16
        // (as usual for AMD64 ABIs).
        //
        // On exit, we store Y = (A + U V) M mod B in XMM10/XMM11, and write
        // the low 128 bits of the sum A + U V + N Y to [RDI], leaving the
        // remaining carry in XMM12, XMM13, and XMM14.  The registers
        // XMM0--XMM7, and XMM15 are clobbered; the general-purpose registers
        // are preserved.
        movdqu  xmm4, [rax]
#if ABI_WIN
        stalloc 48 + 8                  // space for the carries
#  define STKTMP(i) [SP + i]
#endif
#if ABI_SYSV
#  define STKTMP(i) [SP + i - 48 - 8]   // use red zone
#endif
  endprologue

        movd    xmm12, [rdi +  0]
        movd    xmm13, [rdi +  4]
        movd    xmm14, [rdi +  8]
        movd    xmm15, [rdi + 12]

        // Calculate W = U V, and leave it in XMM7.  Stash the carry pieces
        // for later.
        mulacc  xmm4, 0,   xmm8,  xmm9,  xmm12, xmm13, xmm14, xmm15
        propout xmm7, lo,                xmm12, xmm13

5:      mulacc  xmm4, 1,   xmm8,  xmm9,  xmm13, xmm14, xmm15, xmm12, t
        propout xmm6, lo,                xmm13, xmm14

        mulacc  xmm4, 2,   xmm8,  xmm9,  xmm14, xmm15, xmm12, xmm13, t
        propout xmm7, hi,                xmm14, xmm15

        mulacc  xmm4, 3,   xmm8,  xmm9,  xmm15, xmm12, xmm13, xmm14, t
        propout xmm6, hi,                xmm15, xmm12

        // Prepare W, and stash carries for later.
        punpckldq xmm7, xmm6
        movdqa  STKTMP( 0), xmm12
        movdqa  STKTMP(16), xmm13
        movdqa  STKTMP(32), xmm14

        // Calculate Y = W M.  We just about have enough spare registers to
        // make this work.
        mulcore xmm7, 0,   xmm10, xmm11, xmm3,  xmm4,  xmm5,  xmm6

        // Start expanding W back into the main carry registers...
        pxor    xmm15, xmm15
        movdqa  xmm12, xmm7
        movdqa  xmm14, xmm7

        mulcore xmm7, 1,   xmm10, xmm11, xmm0,  xmm1,  xmm2
        accum                            xmm4,  xmm5,  xmm6

        punpckldq xmm12, xmm15          // (w_0, 0; w_1, 0)
        punpckhdq xmm14, xmm15          // (w_2, 0; w_3, 0)

        mulcore xmm7, 2,   xmm10, xmm11, xmm0,  xmm1
        accum                            xmm5,  xmm6

        pxor    xmm2, xmm2
        movdqa  xmm13, xmm12
        movdqa  xmm15, xmm14

        mulcore xmm7, 3,   xmm10, xmm11, xmm0
        accum                            xmm6

        punpckldq xmm12, xmm2           // (w_0, 0; 0, 0)
        punpckldq xmm14, xmm2           // (w_2, 0; 0, 0)
        punpckhdq xmm13, xmm2           // (w_1, 0; 0, 0)
        punpckhdq xmm15, xmm2           // (w_3, 0; 0, 0)

        // That's lots of pieces.  Now we have to assemble the answer.
        squash  xmm3, xmm4, xmm5, xmm6,  xmm0, xmm1,  xmm10

        // Expand it.
        movdqu  xmm5, [rbx]
        expand  xmm2, xmm10, xmm11

        // Finish the calculation by adding the Montgomery product.
        mulacc  xmm5, 0    xmm10, xmm11, xmm12, xmm13, xmm14, xmm15
        propout xmm6, lo,                xmm12, xmm13

        mulacc  xmm5, 1    xmm10, xmm11, xmm13, xmm14, xmm15, xmm12, t
        propout xmm7, lo,                xmm13, xmm14

        mulacc  xmm5, 2    xmm10, xmm11, xmm14, xmm15, xmm12, xmm13, t
        propout xmm6, hi,                xmm14, xmm15

        mulacc  xmm5, 3    xmm10, xmm11, xmm15, xmm12, xmm13, xmm14, t
        propout xmm7, hi,                xmm15, xmm12

        punpckldq xmm6, xmm7

        // Add add on the carry we calculated earlier.
        paddq   xmm12, STKTMP( 0)
        paddq   xmm13, STKTMP(16)
        paddq   xmm14, STKTMP(32)

        // And, with that, we're done.
        movdqu  [rdi], xmm6
#if ABI_WIN
        stfree  56
#endif
        ret

#undef STKTMP

ENDFUNC

INTFUNC(mont4)
        // On entry, RDI points to the destination buffer holding a packed
        // value W; RBX points to a packed operand N; and XMM8/XMM9 hold an
        // expanded operand M.
        //
        // On exit, we store Y = W M mod B in XMM10/XMM11, and write the low
        // 128 bits of the sum W + N Y to [RDI], leaving the remaining carry
        // in XMM12, XMM13, and XMM14.  The registers XMM0--XMM3, XMM5--XMM7,
        // and XMM15 are clobbered; the general-purpose registers are
        // preserved.
  endprologue

        movdqu  xmm7, [rdi]

        // Calculate Y = W M.  Avoid the standard carry registers, because
        // we're setting something else up there.
        mulcore xmm7, 0,   xmm8,  xmm9,  xmm3,  xmm4,  xmm5,  xmm6

        // Start expanding W back into the main carry registers...
        pxor    xmm15, xmm15
        movdqa  xmm12, xmm7
        movdqa  xmm14, xmm7

        mulcore xmm7, 1,   xmm8,  xmm9,  xmm0,  xmm1,  xmm2
        accum                            xmm4,  xmm5,  xmm6

        punpckldq xmm12, xmm15          // (w_0, 0; w_1, 0)
        punpckhdq xmm14, xmm15          // (w_2, 0; w_3, 0)

        mulcore xmm7, 2,   xmm8,  xmm9,  xmm0,  xmm1
        accum                            xmm5,  xmm6

        pxor    xmm2, xmm2
        movdqa  xmm13, xmm12
        movdqa  xmm15, xmm14

        mulcore xmm7, 3,   xmm8,  xmm9,  xmm0
        accum                            xmm6

        punpckldq xmm12, xmm2           // (w_0, 0; 0, 0)
        punpckldq xmm14, xmm2           // (w_2, 0; 0, 0)
        punpckhdq xmm13, xmm2           // (w_1, 0; 0, 0)
        punpckhdq xmm15, xmm2           // (w_3, 0; 0, 0)

        // That's lots of pieces.  Now we have to assemble the answer.
        squash  xmm3, xmm4, xmm5, xmm6,  xmm0, xmm1,  xmm10

        // Expand it.
        movdqu  xmm5, [rbx]
        expand  xmm2, xmm10, xmm11

        // Finish the calculation by adding the Montgomery product.
        mulacc  xmm5, 0    xmm10, xmm11, xmm12, xmm13, xmm14, xmm15
        propout xmm6, lo,                xmm12, xmm13

        mulacc  xmm5, 1    xmm10, xmm11, xmm13, xmm14, xmm15, xmm12, t
        propout xmm7, lo,                xmm13, xmm14

        mulacc  xmm5, 2    xmm10, xmm11, xmm14, xmm15, xmm12, xmm13, t
        propout xmm6, hi,                xmm14, xmm15

        mulacc  xmm5, 3    xmm10, xmm11, xmm15, xmm12, xmm13, xmm14, t
        propout xmm7, hi,                xmm15, xmm12

        punpckldq xmm6, xmm7

        // And, with that, we're done.
        movdqu  [rdi], xmm6
        ret
ENDFUNC

///--------------------------------------------------------------------------
/// Bulk multipliers.

FUNC(mpx_umul4_amd64_avx)
        .arch   .avx
        vzeroupper
  endprologue
        .arch   pentium4
ENDFUNC

FUNC(mpx_umul4_amd64_sse2)
        // void mpx_umul4_amd64_sse2(mpw *dv, const mpw *av, const mpw *avl,
        //                           const mpw *bv, const mpw *bvl);

        // Establish the arguments and do initial setup.
        //
        //                      sysv    win
        // inner loop dv        rdi     rdi*
        // inner loop av        rbx*    rbx*
        // outer loop dv        r10     rcx
        // outer loop bv        rcx     r9
        // av base              rsi     rdx
        // av limit             rdx     r8
        // bv limit             r8      r10

#if ABI_SYSV
#  define DV r10
#  define AV rsi
#  define AVL rdx
#  define BV rcx
#  define BVL r8

        pushreg rbx
  endprologue

        mov     DV, rdi
#endif

#if ABI_WIN
#  define DV rcx
#  define AV rdx
#  define AVL r8
#  define BV r9
#  define BVL r10

        pushreg rbx
        pushreg rdi
        stalloc 160 + 8

        savexmm xmm6,    0
        savexmm xmm7,   16
        savexmm xmm8,   32
        savexmm xmm9,   48
        savexmm xmm10,  64
        savexmm xmm11,  80
        savexmm xmm12,  96
        savexmm xmm13, 112
        savexmm xmm14, 128
        savexmm xmm15, 144

  endprologue

        mov     rdi, DV
        mov     BVL, [SP + 224]
#endif

        // Prepare for the first iteration.
        pxor    xmm0, xmm0
        movdqu  xmm10, [BV]             // bv[0]
        mov     rbx, AV
        add     DV, 16
        add     BV, 16
        expand  xmm0, xmm10, xmm11
        call    mul4zc
        add     rbx, 16
        add     rdi, 16
        cmp     rbx, AVL                // all done?
        jae     8f

        .p2align 4
        // Continue with the first iteration.
0:      call    mul4
        add     rbx, 16
        add     rdi, 16
        cmp     rbx, AVL                // all done?
        jb      0b

        // Write out the leftover carry.  There can be no tail here.
8:      call    carryprop
        cmp     BV, BVL                 // more passes to do?
        jae     9f

        .p2align 4
        // Set up for the next pass.
1:      movdqu  xmm10, [BV]             // bv[i]
        mov     rdi, DV                 // -> dv[i]
        pxor    xmm0, xmm0
        expand  xmm0, xmm10, xmm11
        mov     rbx, AV                 // -> av[0]
        add     DV, 16
        add     BV, 16
        call    mla4zc
        add     rbx, 16
        add     rdi, 16
        cmp     rbx, AVL                // done yet?
        jae     8f

        .p2align 4
        // Continue...
0:      call    mla4
        add     rbx, 16
        add     rdi, 16
        cmp     rbx, AVL
        jb      0b

        // Finish off this pass.  There was no tail on the previous pass, and
        // there can be none on this pass.
8:      call    carryprop
        cmp     BV, BVL
        jb      1b

        // All over.
9:

#if ABI_SYSV
        popreg  rbx
#endif

#if ABI_WIN
        rstrxmm xmm6,    0
        rstrxmm xmm7,   16
        rstrxmm xmm8,   32
        rstrxmm xmm9,   48
        rstrxmm xmm10,  64
        rstrxmm xmm11,  80
        rstrxmm xmm12,  96
        rstrxmm xmm13, 112
        rstrxmm xmm14, 128
        rstrxmm xmm15, 144

        stfree  160 + 8
        popreg  rdi
        popreg  rbx
#endif

        ret

#undef DV
#undef AV
#undef AVL
#undef BV
#undef BVL

ENDFUNC

FUNC(mpxmont_mul4_amd64_avx)
        .arch   .avx
        vzeroupper
  endprologue
        .arch   pentium4
ENDFUNC

FUNC(mpxmont_mul4_amd64_sse2)
        // void mpxmont_mul4_amd64_sse2(mpw *dv, const mpw *av, const mpw *bv,
        //                           const mpw *nv, size_t n, const mpw *mi);

        // Establish the arguments and do initial setup.
        //
        //                      sysv    win
        // inner loop dv        rdi     rdi*
        // inner loop av        rax     rax
        // inner loop nv        rbx*    rbx*
        // mi                   r9      r10
        // outer loop dv        r10     rcx
        // outer loop bv        rdx     r8
        // av base              rsi     rdx
        // av limit             r11     r11
        // bv limit             r8      r12*
        // nv base              rcx     r9
        // n                    r8      r12*

#if ABI_SYSV
#  define DV r10
#  define AV rsi
#  define AVL r11
#  define BV rdx
#  define BVL r8
#  define NV rcx
#  define N r8
#  define MI r9

        pushreg rbx
  endprologue

        mov     DV, rdi
#endif

#if ABI_WIN
#  define DV rcx
#  define AV rdx
#  define AVL r11
#  define BV r8
#  define BVL r12
#  define NV r9
#  define N r12
#  define MI r10

        pushreg rbx
        pushreg rdi
        pushreg r12
        stalloc 160

        savexmm xmm6,    0
        savexmm xmm7,   16
        savexmm xmm8,   32
        savexmm xmm9,   48
        savexmm xmm10,  64
        savexmm xmm11,  80
        savexmm xmm12,  96
        savexmm xmm13, 112
        savexmm xmm14, 128
        savexmm xmm15, 144

  endprologue

        mov     rdi, DV
        mov     N, [SP + 224]
        mov     MI, [SP + 232]
#endif

        // Establish the expanded operands.
        pxor    xmm0, xmm0
        movdqu  xmm8, [BV]              // bv[0]
        movdqu  xmm10, [MI]             // mi
        expand  xmm0, xmm8, xmm9, xmm10, xmm11

        // Set up the outer loop state and prepare for the first iteration.
        mov     rax, AV                 // -> U = av[0]
        mov     rbx, NV                 // -> X = nv[0]
        lea     AVL, [AV + 4*N]         // -> av[n/4] = av limit
        lea     BVL, [BV + 4*N]         // -> bv[n/4] = bv limit
        add     BV, 16
        add     DV, 16
        call    mmul4
        add     rdi, 16
        add     rax, 16
        add     rbx, 16
        cmp     rax, AVL                // done already?
        jae     8f

        .p2align 4
        // Complete the first inner loop.
0:      call    dmul4
        add     rdi, 16
        add     rax, 16
        add     rbx, 16
        cmp     rax, AVL                // done yet?
        jb      0b

        // Still have carries left to propagate.
        call    carryprop
        movd    [rdi + 16], xmm12

        .p2align 4
        // Embark on the next iteration.  (There must be one.  If n = 1, then
        // we would have bailed above, to label 8.  Similarly, the subsequent
        // iterations can fall into the inner loop immediately.)
1:      pxor    xmm0, xmm0
        movdqu  xmm8, [BV]              // bv[i]
        movdqu  xmm10, [MI]             // mi
        mov     rdi, DV                 // -> Z = dv[i]
        mov     rax, AV                 // -> U = av[0]
        mov     rbx, NV                 // -> X = nv[0]
        expand  xmm0, xmm8, xmm9, xmm10, xmm11
        add     BV, 16
        add     DV, 16
        call    mmla4
        add     rdi, 16
        add     rax, 16
        add     rbx, 16

        .p2align 4
        // Complete the next inner loop.
0:      call    dmla4
        add     rdi, 16
        add     rax, 16
        add     rbx, 16
        cmp     rax, AVL
        jb      0b

        // Still have carries left to propagate, and they overlap the
        // previous iteration's final tail, so read that in and add it.
        movd    xmm0, [rdi]
        paddq   xmm12, xmm0
        call    carryprop
        movd    [rdi + 16], xmm12

        // Back again, maybe.
        cmp     BV, BVL
        jb      1b

        // All done.
9:

#if ABI_SYSV
        popreg  rbx
#endif

#if ABI_WIN
        rstrxmm xmm6,    0
        rstrxmm xmm7,   16
        rstrxmm xmm8,   32
        rstrxmm xmm9,   48
        rstrxmm xmm10,  64
        rstrxmm xmm11,  80
        rstrxmm xmm12,  96
        rstrxmm xmm13, 112
        rstrxmm xmm14, 128
        rstrxmm xmm15, 144

        stfree  160
        popreg  r12
        popreg  rdi
        popreg  rbx
#endif

        ret

        // First iteration was short.  Write out the carries and we're done.
        // (This could be folded into the main loop structure, but that would
        // penalize small numbers more.)
8:      call    carryprop
        movd    [rdi + 16], xmm12
#if ABI_SYSV
        popreg  rbx
        ret
#endif
#if ABI_WIN
        jmp     9b
#endif

#undef DV
#undef AV
#undef AVL
#undef BV
#undef BVL
#undef NV
#undef N
#undef MI

ENDFUNC

FUNC(mpxmont_redc4_amd64_avx)
        .arch   .avx
        vzeroupper
  endprologue
        .arch   pentium4
ENDFUNC

FUNC(mpxmont_redc4_amd64_sse2)
        // void mpxmont_redc4_amd64_sse2(mpw *dv, mpw *dvl, const mpw *nv,
        //                             size_t n, const mpw *mi);

        // Establish the arguments and do initial setup.
        //
        //                      sysv    win
        // inner loop dv        rdi     rdi*
        // dv limit             rax     rax
        // blocks-of-4 dv limit rsi     rdx
        // inner loop nv        rbx*    rbx*
        // mi                   r8      r10
        // outer loop dv        r10     rcx
        // outer loop dv limit  r11     r11
        // nv base              rdx     r8
        // nv limit             r9      r12*
        // n                    rcx     r9
        // c                    rcx     r9

#if ABI_SYSV
#  define DVL rax
#  define DVL4 rsi
#  define MI r8
#  define DV r10
#  define DVLO r11
#  define NV rdx
#  define NVL r9
#  define N rcx
#  define C ecx

        pushreg rbx
  endprologue

        mov     DV, rdi
#endif

#if ABI_WIN
#  define DVL rax
#  define DVL4 rdx
#  define MI r10
#  define DV rcx
#  define DVLO r11
#  define NV r8
#  define NVL r12
#  define N r9
#  define C r9d

        pushreg rbx
        pushreg rdi
        pushreg r12
        stalloc 160

        savexmm xmm6,    0
        savexmm xmm7,   16
        savexmm xmm8,   32
        savexmm xmm9,   48
        savexmm xmm10,  64
        savexmm xmm11,  80
        savexmm xmm12,  96
        savexmm xmm13, 112
        savexmm xmm14, 128
        savexmm xmm15, 144

  endprologue

        mov     rdi, DV
        mov     MI, [SP + 224]
#endif

        // Establish the expanded operands and the blocks-of-4 dv limit.
        pxor    xmm0, xmm0
        mov     DVL, DVL4               // -> dv[n] = dv limit
        sub     DVL4, DV                // length of dv in bytes
        movdqu  xmm8, [MI]              // mi
        and     DVL4, ~15               // mask off the tail end
        expand  xmm0, xmm8, xmm9
        add     DVL4, DV                // find limit

        // Set up the outer loop state and prepare for the first iteration.
        mov     rbx, NV                 // -> X = nv[0]
        lea     DVLO, [DV + 4*N]        // -> dv[n/4] = outer dv limit
        lea     NVL, [NV + 4*N]         // -> nv[n/4] = nv limit
        add     DV, 16
        call    mont4
        add     rbx, 16
        add     rdi, 16
        cmp     rbx, NVL                // done already?
        jae     8f

        .p2align 4
        // Complete the first inner loop.
5:      call    mla4
        add     rbx, 16
        add     rdi, 16
        cmp     rbx, NVL                // done yet?
        jb      5b

        // Still have carries left to propagate.
8:      carryadd
        psllq   xmm15, 16
        pslldq  xmm15, 8
        paddq   xmm14, xmm15
        call    carryprop
        movd    C, xmm12
        add     rdi, 16
        cmp     rdi, DVL4
        jae     7f

        .p2align 4
        // Continue carry propagation until the end of the buffer.
0:      add     [rdi], C
        mov     C, 0                    // preserves flags
        adcd    [rdi + 4], 0
        adcd    [rdi + 8], 0
        adcd    [rdi + 12], 0
        adc     C, 0
        add     rdi, 16
        cmp     rdi, DVL4
        jb      0b

        // Deal with the tail end.
7:      add     [rdi], C
        mov     C, 0                    // preserves flags
        add     rdi, 4
        adc     C, 0
        cmp     rdi, DVL
        jb      7b

        // All done for this iteration.  Start the next.  (This must have at
        // least one follow-on iteration, or we'd not have started this outer
        // loop.)
8:      mov     rdi, DV                 // -> Z = dv[i]
        mov     rbx, NV                 // -> X = nv[0]
        cmp     rdi, DVLO               // all done yet?
        jae     9f
        add     DV, 16
        call    mont4
        add     rdi, 16
        add     rbx, 16
        jmp     5b

        // All over.
9:

#if ABI_SYSV
        popreg  rbx
#endif

#if ABI_WIN
        rstrxmm xmm6,    0
        rstrxmm xmm7,   16
        rstrxmm xmm8,   32
        rstrxmm xmm9,   48
        rstrxmm xmm10,  64
        rstrxmm xmm11,  80
        rstrxmm xmm12,  96
        rstrxmm xmm13, 112
        rstrxmm xmm14, 128
        rstrxmm xmm15, 144

        stfree  160
        popreg  r12
        popreg  rdi
        popreg  rbx
#endif

        ret

#undef DVL
#undef DVL4
#undef MI
#undef DV
#undef DVLO
#undef NV
#undef NVL
#undef N
#undef C

ENDFUNC

///--------------------------------------------------------------------------
/// Testing and performance measurement.

#ifdef TEST_MUL4

#if ABI_SYSV
#  define ARG0 rdi
#  define ARG1 rsi
#  define ARG2 rdx
#  define ARG3 rcx
#  define ARG4 r8
#  define ARG5 r9
#  define ARG6 STKARG(0)
#  define ARG7 STKARG(1)
#  define ARG8 STKARG(2)
#  define STKARG_OFFSET 16
#endif
#if ABI_WIN
#  define ARG0 rcx
#  define ARG1 rdx
#  define ARG2 r8
#  define ARG3 r9
#  define ARG4 STKARG(0)
#  define ARG5 STKARG(1)
#  define ARG6 STKARG(2)
#  define ARG7 STKARG(3)
#  define ARG8 STKARG(4)
#  define STKARG_OFFSET 224
#endif
#define STKARG(i) [SP + STKARG_OFFSET + 8*(i)]

//                sysv                          win
//                dmul  smul  mmul  mont        dmul  smul  mmul  mont
// A    rax
// D    rdx
// z    rdi       rdi   rdi   rdi    rdi        rcx   rcx   rcx    rcx
// c    rcx       rsi   rsi   rsi    rsi        rdx   rdx   rdx    rdx
// y    r10       --    --    rdx    rdx        --    --    r8     r8
// u    r11       rdx   --    rcx    --         r8    --    r9     --
// x    rbx       rcx   rdx   r8     rcx        r9    r8    stk0   r9
// vv   xmm8/9    r8    --    r9     r8         stk0  --    stk1   stk0
// yy   xmm10/11  r9    rcx   stk0   --         stk1  r9    stk2   --
// n    r8        stk0  r8    stk1   r9         stk2  stk0  stk3   stk1
// cyv  r9        stk1  r9    stk2   stk0       stk3  stk1  stk4   stk2

.macro  cysetup v, n
        rdtsc
        shl     rdx, 32
        or      rax, rdx
        mov     [\v + 8*\n - 8], rax
.endm

.macro  cystore v, n
        rdtsc
        shl     rdx, 32
        or      rax, rdx
        sub     rax, [\v + 8*\n - 8]
        mov     [\v + 8*\n - 8], rax
        dec     \n
.endm

.macro  testprologue mode
        pushreg rbx
#if ABI_SYSV
  endprologue
  .ifeqs "\mode", "dmul"
        mov     rbx, rcx
        movdqu  xmm8, [r8]
        movdqu  xmm10, [r9]
        mov     r8d, STKARG(0)
        mov     r9, STKARG(1)
        mov     r11, rdx
        mov     rcx, rsi
  .endif
  .ifeqs "\mode", "smul"
        mov     rbx, rdx
        movdqu  xmm10, [rcx]
        mov     rcx, rsi
  .endif
  .ifeqs "\mode", "mmul"
        mov     rax, STKARG(0)
        mov     rbx, r8
        movdqu  xmm8, [r9]
        movdqu  xmm10, [rax]
        mov     r8d, STKARG(1)
        mov     r9, STKARG(2)
        mov     r10, rdx
        mov     r11, rcx
        mov     rcx, rsi
  .endif
  .ifeqs "\mode", "mont"
        mov     rbx, rcx
        movdqu  xmm8, [r8]
        mov     r8d, r9d
        mov     r9, STKARG(0)
        mov     r10, rdx
        mov     rcx, rsi
  .endif
#endif
#if ABI_WIN
        pushreg rdi
        stalloc 168
        savexmm xmm6,    0
        savexmm xmm7,   16
        savexmm xmm8,   32
        savexmm xmm9,   48
        savexmm xmm10,  64
        savexmm xmm11,  80
        savexmm xmm12,  96
        savexmm xmm13, 112
        savexmm xmm14, 128
        savexmm xmm15, 144
  endprologue
  .ifeqs "\mode", "dmul"
        mov     r10, STKARG(0)
        mov     r11, STKARG(1)
        mov     rdi, rcx
        mov     rcx, rdx
        mov     rbx, r9
        movdqu  xmm8, [r10]
        movdqu  xmm10, [r11]
        mov     r11, r8
        mov     r8d, STKARG(2)
        mov     r9, STKARG(3)
  .endif
  .ifeqs "\mode", "smul"
        mov     rdi, rcx
        mov     rcx, rdx
        mov     rbx, r8
        movdqu  xmm10, [r9]
        mov     r8d, STKARG(0)
        mov     r9, STKARG(1)
  .endif
  .ifeqs "\mode", "mmul"
        mov     r10, STKARG(1)
        mov     r11, STKARG(2)
        mov     rdi, rcx
        mov     rcx, rdx
        mov     rbx, STKARG(0)
        movdqu  xmm8, [r10]
        movdqu  xmm10, [r11]
        mov     r10, r8
        mov     r11, r9
        mov     r8d, STKARG(3)
        mov     r9, STKARG(4)
  .endif
  .ifeqs "\mode", "mont"
        mov     r10, STKARG(0)
        mov     rdi, rcx
        mov     rcx, rdx
        mov     rbx, r9
        movdqu  xmm8, [r10]
        mov     r10, r8
        mov     r8d, STKARG(1)
        mov     r9, STKARG(2)
  .endif
#endif

        pxor    xmm0, xmm0
  .ifeqs "\mode", "dmul"
        expand  xmm0, xmm8, xmm9, xmm10, xmm11
  .endif
  .ifeqs "\mode", "smul"
        expand  xmm0, xmm10, xmm11
  .endif
  .ifeqs "\mode", "mmul"
        expand  xmm0, xmm8, xmm9, xmm10, xmm11
  .endif
  .ifeqs "\mode", "mont"
        expand  xmm0, xmm8, xmm9
  .endif
.endm

.macro  testepilogue
#if ABI_WIN
        rstrxmm xmm6,    0
        rstrxmm xmm7,   16
        rstrxmm xmm8,   32
        rstrxmm xmm9,   48
        rstrxmm xmm10,  64
        rstrxmm xmm11,  80
        rstrxmm xmm12,  96
        rstrxmm xmm13, 112
        rstrxmm xmm14, 128
        rstrxmm xmm15, 144
        stfree  168
        popreg  rdi
#endif
        popreg  rbx
        ret
.endm

.macro  testldcarry
        movdqu  xmm12, [rcx +  0]       // (c'_0; c''_0)
        movdqu  xmm13, [rcx + 16]       // (c'_1; c''_1)
        movdqu  xmm14, [rcx + 32]       // (c'_2; c''_2)
.endm

.macro  testtop u=nil
        .p2align 4
0:
        cysetup r9, r8
  .ifnes "\u", "nil"
        mov     rax, \u
  .endif
.endm

.macro  testtail
        cystore r9, r8
        jnz     0b
.endm

.macro  testcarryout
        movdqu  [rcx +  0], xmm12
        movdqu  [rcx + 16], xmm13
        movdqu  [rcx + 32], xmm14
.endm

FUNC(test_dmul4)
        testprologue dmul
        testldcarry
        testtop r11
        call    dmul4
        testtail
        testcarryout
        testepilogue
ENDFUNC

FUNC(test_dmla4)
        testprologue dmul
        testldcarry
        testtop r11
        call    dmla4
        testtail
        testcarryout
        testepilogue
ENDFUNC

FUNC(test_mul4)
        testprologue smul
        testldcarry
        testtop nil
        call    mul4
        testtail
        testcarryout
        testepilogue
ENDFUNC

FUNC(test_mul4zc)
        testprologue smul
        testldcarry
        testtop nil
        call    mul4zc
        testtail
        testcarryout
        testepilogue
ENDFUNC

FUNC(test_mla4)
        testprologue smul
        testldcarry
        testtop nil
        call    mla4
        testtail
        testcarryout
        testepilogue
ENDFUNC

FUNC(test_mla4zc)
        testprologue smul
        testldcarry
        testtop nil
        call    mla4zc
        testtail
        testcarryout
        testepilogue
ENDFUNC

FUNC(test_mmul4)
        testprologue mmul
        testtop r11
        call    mmul4
        testtail
        movdqu  [r10 +  0], xmm10
        movdqu  [r10 + 16], xmm11
        testcarryout
        testepilogue
ENDFUNC

FUNC(test_mmla4)
        testprologue mmul
        testtop r11
        call    mmla4
        testtail
        movdqu  [r10 +  0], xmm10
        movdqu  [r10 + 16], xmm11
        testcarryout
        testepilogue
ENDFUNC

FUNC(test_mont4)
        testprologue mont
        testtop
        call    mont4
        testtail
        movdqu  [r10 +  0], xmm10
        movdqu  [r10 + 16], xmm11
        testcarryout
        testepilogue
ENDFUNC

#endif

///----- That's all, folks --------------------------------------------------