donna_sse.cpp

// donna_sse.cpp - written and placed in public domain by Jeffrey Walton
//                 This is a integration of Andrew Moon's public domain code.
//                 Also see https://github.com/floodyberry/curve25519-donna.

// This is a integration of Andrew Moon's public domain code. The port was
// clean, but it has one potential problem. The original code is C and relies
// upon unions. Accessing the inactive union member is undefined behavior in
// C++. That means copying the array into packedelem8.u is OK; but then using
// packedelem8.v in a calculation is UB. Fortunately most (all?) compilers
// take pity on C++ developers and compile the code. We will have to keep an
// eye on things or rewrite significant portions of this code.

// If needed, see Moon's commit "Go back to ignoring 256th bit [sic]",
// https://github.com/floodyberry/curve25519-donna/commit/57a683d18721a658

#include "pch.h"

#include "config.h"
#include "donna.h"
#include "secblock.h"
#include "misc.h"

// The data is aligned, but Clang issues warning based on type
// and not the actual alignment of the variable and data.
#if CRYPTOPP_GCC_DIAGNOSTIC_AVAILABLE
# pragma GCC diagnostic ignored "-Wcast-align"
# pragma GCC diagnostic ignored "-Wunused-function"
#endif

#if CRYPTOPP_MSC_VERSION
# pragma warning(disable: 4244)
#endif

// Squash MS LNK4221 and libtool warnings
extern const char DONNA_SSE_FNAME[] = __FILE__;

#if (CRYPTOPP_CURVE25519_SSE2)

#include "donna_sse.h"

ANONYMOUS_NAMESPACE_BEGIN

using CryptoPP::byte;
using CryptoPP::word32;
using CryptoPP::sword32;
using CryptoPP::word64;
using CryptoPP::sword64;
using CryptoPP::GetBlock;
using CryptoPP::LittleEndian;

// Bring in all the symbols from the SSE header
using namespace CryptoPP::Donna::ArchSSE;

/* Copy a bignum to another: out = in */
inline void
curve25519_copy(bignum25519 out, const bignum25519 in) {
    xmmi x0,x1,x2;
    x0 = _mm_load_si128((xmmi*)in + 0);
    x1 = _mm_load_si128((xmmi*)in + 1);
    x2 = _mm_load_si128((xmmi*)in + 2);
    _mm_store_si128((xmmi*)out + 0, x0);
    _mm_store_si128((xmmi*)out + 1, x1);
    _mm_store_si128((xmmi*)out + 2, x2);
}

/* Take a little-endian, 32-byte number and expand it into polynomial form */
inline void
curve25519_expand(bignum25519 out, const byte in[32]) {
    word32 x0,x1,x2,x3,x4,x5,x6,x7;

    x0 = *(word32 *)(in + 0);
    x1 = *(word32 *)(in + 4);
    x2 = *(word32 *)(in + 8);
    x3 = *(word32 *)(in + 12);
    x4 = *(word32 *)(in + 16);
    x5 = *(word32 *)(in + 20);
    x6 = *(word32 *)(in + 24);
    x7 = *(word32 *)(in + 28);

    out[0] = (                      x0       ) & reduce_mask_26;
    out[1] = ((((word64)x1 << 32) | x0) >> 26) & reduce_mask_25;
    out[2] = ((((word64)x2 << 32) | x1) >> 19) & reduce_mask_26;
    out[3] = ((((word64)x3 << 32) | x2) >> 13) & reduce_mask_25;
    out[4] = ((                     x3) >>  6) & reduce_mask_26;
    out[5] = (                      x4       ) & reduce_mask_25;
    out[6] = ((((word64)x5 << 32) | x4) >> 25) & reduce_mask_26;
    out[7] = ((((word64)x6 << 32) | x5) >> 19) & reduce_mask_25;
    out[8] = ((((word64)x7 << 32) | x6) >> 12) & reduce_mask_26;
    out[9] = ((                     x7) >>  6) & reduce_mask_25; /* ignore the top bit */

    out[10] = 0;
    out[11] = 0;
}

/* Take a fully reduced polynomial form number and contract it into a
 * little-endian, 32-byte array
 */
inline void
curve25519_contract(byte out[32], const bignum25519 in) {
    ALIGN(16) bignum25519 f;

    curve25519_copy(f, in);

    #define carry_pass() \
        f[1] += f[0] >> 26; f[0] &= reduce_mask_26; \
        f[2] += f[1] >> 25; f[1] &= reduce_mask_25; \
        f[3] += f[2] >> 26; f[2] &= reduce_mask_26; \
        f[4] += f[3] >> 25; f[3] &= reduce_mask_25; \
        f[5] += f[4] >> 26; f[4] &= reduce_mask_26; \
        f[6] += f[5] >> 25; f[5] &= reduce_mask_25; \
        f[7] += f[6] >> 26; f[6] &= reduce_mask_26; \
        f[8] += f[7] >> 25; f[7] &= reduce_mask_25; \
        f[9] += f[8] >> 26; f[8] &= reduce_mask_26;

    #define carry_pass_full() \
        carry_pass() \
        f[0] += 19 * (f[9] >> 25); f[9] &= reduce_mask_25;

    #define carry_pass_final() \
        carry_pass() \
        f[9] &= reduce_mask_25;

    carry_pass_full()
    carry_pass_full()

    /* now t is between 0 and 2^255-1, properly carried. */
    /* case 1: between 0 and 2^255-20. case 2: between 2^255-19 and 2^255-1. */
    f[0] += 19;
    carry_pass_full()

    /* now between 19 and 2^255-1 in both cases, and offset by 19. */
    f[0] += (1 << 26) - 19;
    f[1] += (1 << 25) - 1;
    f[2] += (1 << 26) - 1;
    f[3] += (1 << 25) - 1;
    f[4] += (1 << 26) - 1;
    f[5] += (1 << 25) - 1;
    f[6] += (1 << 26) - 1;
    f[7] += (1 << 25) - 1;
    f[8] += (1 << 26) - 1;
    f[9] += (1 << 25) - 1;

    /* now between 2^255 and 2^256-20, and offset by 2^255. */
    carry_pass_final()

    #undef carry_pass
    #undef carry_full
    #undef carry_final

    *(word32 *)(out +  0) = ((f[0]      ) | (f[1] << 26));
    *(word32 *)(out +  4) = ((f[1] >>  6) | (f[2] << 19));
    *(word32 *)(out +  8) = ((f[2] >> 13) | (f[3] << 13));
    *(word32 *)(out + 12) = ((f[3] >> 19) | (f[4] <<  6));
    *(word32 *)(out + 16) = ((f[5]      ) | (f[6] << 25));
    *(word32 *)(out + 20) = ((f[6] >>  7) | (f[7] << 19));
    *(word32 *)(out + 24) = ((f[7] >> 13) | (f[8] << 12));
    *(word32 *)(out + 28) = ((f[8] >> 20) | (f[9] <<  6));
}

/*
 * Maybe swap the contents of two felem arrays (@a and @b), each 5 elements
 * long. Perform the swap iff @swap is non-zero.
 */
inline void
curve25519_swap_conditional(bignum25519 a, bignum25519 b, word32 iswap) {
    const word32 swap = (word32)(-(sword32)iswap);
    xmmi a0,a1,a2,b0,b1,b2,x0,x1,x2;
    xmmi mask = _mm_cvtsi32_si128(swap);
    mask = _mm_shuffle_epi32(mask, 0);
    a0 = _mm_load_si128((xmmi *)a + 0);
    a1 = _mm_load_si128((xmmi *)a + 1);
    a2 = _mm_load_si128((xmmi *)a + 2);
    b0 = _mm_load_si128((xmmi *)b + 0);
    b1 = _mm_load_si128((xmmi *)b + 1);
    b2 = _mm_load_si128((xmmi *)b + 2);
    b0 = _mm_xor_si128(a0, b0);
    b1 = _mm_xor_si128(a1, b1);
    b2 = _mm_xor_si128(a2, b2);
    x0 = _mm_and_si128(b0, mask);
    x1 = _mm_and_si128(b1, mask);
    x2 = _mm_and_si128(b2, mask);
    x0 = _mm_xor_si128(x0, a0);
    x1 = _mm_xor_si128(x1, a1);
    x2 = _mm_xor_si128(x2, a2);
    a0 = _mm_xor_si128(x0, b0);
    a1 = _mm_xor_si128(x1, b1);
    a2 = _mm_xor_si128(x2, b2);
    _mm_store_si128((xmmi *)a + 0, x0);
    _mm_store_si128((xmmi *)a + 1, x1);
    _mm_store_si128((xmmi *)a + 2, x2);
    _mm_store_si128((xmmi *)b + 0, a0);
    _mm_store_si128((xmmi *)b + 1, a1);
    _mm_store_si128((xmmi *)b + 2, a2);
}

/* interleave two bignums */
inline void
curve25519_tangle32(packedelem32 *out, const bignum25519 x, const bignum25519 z) {
    xmmi x0,x1,x2,z0,z1,z2;

    x0 = _mm_load_si128((xmmi *)(x + 0));
    x1 = _mm_load_si128((xmmi *)(x + 4));
    x2 = _mm_load_si128((xmmi *)(x + 8));
    z0 = _mm_load_si128((xmmi *)(z + 0));
    z1 = _mm_load_si128((xmmi *)(z + 4));
    z2 = _mm_load_si128((xmmi *)(z + 8));

    out[0].v = _mm_unpacklo_epi32(x0, z0);
    out[1].v = _mm_unpackhi_epi32(x0, z0);
    out[2].v = _mm_unpacklo_epi32(x1, z1);
    out[3].v = _mm_unpackhi_epi32(x1, z1);
    out[4].v = _mm_unpacklo_epi32(x2, z2);
}

/* split a packed bignum in to it's two parts */
inline void
curve25519_untangle64(bignum25519 x, bignum25519 z, const packedelem64 *in) {
    _mm_store_si128((xmmi *)(x + 0), _mm_unpacklo_epi64(_mm_unpacklo_epi32(in[0].v, in[1].v), _mm_unpacklo_epi32(in[2].v, in[3].v)));
    _mm_store_si128((xmmi *)(x + 4), _mm_unpacklo_epi64(_mm_unpacklo_epi32(in[4].v, in[5].v), _mm_unpacklo_epi32(in[6].v, in[7].v)));
    _mm_store_si128((xmmi *)(x + 8), _mm_unpacklo_epi32(in[8].v, in[9].v)                                                          );
    _mm_store_si128((xmmi *)(z + 0), _mm_unpacklo_epi64(_mm_unpackhi_epi32(in[0].v, in[1].v), _mm_unpackhi_epi32(in[2].v, in[3].v)));
    _mm_store_si128((xmmi *)(z + 4), _mm_unpacklo_epi64(_mm_unpackhi_epi32(in[4].v, in[5].v), _mm_unpackhi_epi32(in[6].v, in[7].v)));
    _mm_store_si128((xmmi *)(z + 8), _mm_unpackhi_epi32(in[8].v, in[9].v)                                                          );
}

/* add two packed bignums */
inline void
curve25519_add_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) {
    out[0].v = _mm_add_epi32(r[0].v, s[0].v);
    out[1].v = _mm_add_epi32(r[1].v, s[1].v);
    out[2].v = _mm_add_epi32(r[2].v, s[2].v);
    out[3].v = _mm_add_epi32(r[3].v, s[3].v);
    out[4].v = _mm_add_epi32(r[4].v, s[4].v);
}

/* subtract two packed bignums */
inline void
curve25519_sub_packed32(packedelem32 *out, const packedelem32 *r, const packedelem32 *s) {
    xmmi r0,r1,r2,r3,r4;
    xmmi s0,s1,s2,s3;
    xmmi c1,c2;

    r0 = _mm_add_epi32(r[0].v, packed32zeromodp0.v);
    r1 = _mm_add_epi32(r[1].v, packed32zeromodp1.v);
    r2 = _mm_add_epi32(r[2].v, packed32zeromodp1.v);
    r3 = _mm_add_epi32(r[3].v, packed32zeromodp1.v);
    r4 = _mm_add_epi32(r[4].v, packed32zeromodp1.v);
    r0 = _mm_sub_epi32(r0, s[0].v); /* 00 11 */
    r1 = _mm_sub_epi32(r1, s[1].v); /* 22 33 */
    r2 = _mm_sub_epi32(r2, s[2].v); /* 44 55 */
    r3 = _mm_sub_epi32(r3, s[3].v); /* 66 77 */
    r4 = _mm_sub_epi32(r4, s[4].v); /* 88 99 */

    s0 = _mm_unpacklo_epi64(r0, r2); /* 00 44 */
    s1 = _mm_unpackhi_epi64(r0, r2); /* 11 55 */
    s2 = _mm_unpacklo_epi64(r1, r3); /* 22 66 */
    s3 = _mm_unpackhi_epi64(r1, r3); /* 33 77 */

    c1 = _mm_srli_epi32(s0, 26); c2 = _mm_srli_epi32(s2, 26); s0 = _mm_and_si128(s0, packedmask26262626.v); s2 = _mm_and_si128(s2, packedmask26262626.v); s1 = _mm_add_epi32(s1, c1); s3 = _mm_add_epi32(s3, c2);
    c1 = _mm_srli_epi32(s1, 25); c2 = _mm_srli_epi32(s3, 25); s1 = _mm_and_si128(s1, packedmask25252525.v); s3 = _mm_and_si128(s3, packedmask25252525.v); s2 = _mm_add_epi32(s2, c1); r4 = _mm_add_epi32(r4, _mm_srli_si128(c2, 8)); s0 = _mm_add_epi32(s0,  _mm_slli_si128(c2, 8));

    out[0].v = _mm_unpacklo_epi64(s0, s1); /* 00 11 */
    out[1].v = _mm_unpacklo_epi64(s2, s3); /* 22 33 */
    out[2].v = _mm_unpackhi_epi64(s0, s1); /* 44 55 */
    out[3].v = _mm_unpackhi_epi64(s2, s3); /* 66 77 */
    out[4].v = r4;                         /* 88 99 */
}

/* multiply two packed bignums */
inline void
curve25519_mul_packed64(packedelem64 *out, const packedelem64 *r, const packedelem64 *s) {
    xmmi r1,r2,r3,r4,r5,r6,r7,r8,r9;
    xmmi r1_2,r3_2,r5_2,r7_2,r9_2;
    xmmi c1,c2;

    out[0].v = _mm_mul_epu32(r[0].v, s[0].v);
    out[1].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[1].v), _mm_mul_epu32(r[1].v, s[0].v));
    r1_2 = _mm_slli_epi32(r[1].v, 1);
    out[2].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r1_2  , s[1].v), _mm_mul_epu32(r[2].v, s[0].v)));
    out[3].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[1].v), _mm_mul_epu32(r[3].v, s[0].v))));
    r3_2 = _mm_slli_epi32(r[3].v, 1);
    out[4].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r1_2  , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r3_2  , s[1].v), _mm_mul_epu32(r[4].v, s[0].v)))));
    out[5].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[1].v), _mm_mul_epu32(r[5].v, s[0].v))))));
    r5_2 = _mm_slli_epi32(r[5].v, 1);
    out[6].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r1_2  , s[5].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r3_2  , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r5_2  , s[1].v), _mm_mul_epu32(r[6].v, s[0].v)))))));
    out[7].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[7].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[5].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[1].v), _mm_mul_epu32(r[7].v  , s[0].v))))))));
    r7_2 = _mm_slli_epi32(r[7].v, 1);
    out[8].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[8].v), _mm_add_epi64(_mm_mul_epu32(r1_2  , s[7].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r3_2  , s[5].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r5_2  , s[3].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r7_2  , s[1].v), _mm_mul_epu32(r[8].v, s[0].v)))))))));
    out[9].v = _mm_add_epi64(_mm_mul_epu32(r[0].v, s[9].v), _mm_add_epi64(_mm_mul_epu32(r[1].v, s[8].v), _mm_add_epi64(_mm_mul_epu32(r[2].v, s[7].v), _mm_add_epi64(_mm_mul_epu32(r[3].v, s[6].v), _mm_add_epi64(_mm_mul_epu32(r[4].v, s[5].v), _mm_add_epi64(_mm_mul_epu32(r[5].v, s[4].v), _mm_add_epi64(_mm_mul_epu32(r[6].v, s[3].v), _mm_add_epi64(_mm_mul_epu32(r[7].v, s[2].v), _mm_add_epi64(_mm_mul_epu32(r[8].v, s[1].v), _mm_mul_epu32(r[9].v, s[0].v))))))))));

    r1 = _mm_mul_epu32(r[1].v, packednineteen.v);
    r2 = _mm_mul_epu32(r[2].v, packednineteen.v);
    r1_2 = _mm_slli_epi32(r1, 1);
    r3 = _mm_mul_epu32(r[3].v, packednineteen.v);
    r4 = _mm_mul_epu32(r[4].v, packednineteen.v);
    r3_2 = _mm_slli_epi32(r3, 1);
    r5 = _mm_mul_epu32(r[5].v, packednineteen.v);
    r6 = _mm_mul_epu32(r[6].v, packednineteen.v);
    r5_2 = _mm_slli_epi32(r5, 1);
    r7 = _mm_mul_epu32(r[7].v, packednineteen.v);
    r8 = _mm_mul_epu32(r[8].v, packednineteen.v);
    r7_2 = _mm_slli_epi32(r7, 1);
    r9 = _mm_mul_epu32(r[9].v, packednineteen.v);
    r9_2 = _mm_slli_epi32(r9, 1);

    out[0].v = _mm_add_epi64(out[0].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[1].v), _mm_add_epi64(_mm_mul_epu32(r8, s[2].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[3].v), _mm_add_epi64(_mm_mul_epu32(r6, s[4].v), _mm_add_epi64(_mm_mul_epu32(r5_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r4, s[6].v), _mm_add_epi64(_mm_mul_epu32(r3_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r2, s[8].v), _mm_mul_epu32(r1_2, s[9].v))))))))));
    out[1].v = _mm_add_epi64(out[1].v, _mm_add_epi64(_mm_mul_epu32(r9  , s[2].v), _mm_add_epi64(_mm_mul_epu32(r8, s[3].v), _mm_add_epi64(_mm_mul_epu32(r7  , s[4].v), _mm_add_epi64(_mm_mul_epu32(r6, s[5].v), _mm_add_epi64(_mm_mul_epu32(r5  , s[6].v), _mm_add_epi64(_mm_mul_epu32(r4, s[7].v), _mm_add_epi64(_mm_mul_epu32(r3  , s[8].v), _mm_mul_epu32(r2, s[9].v)))))))));
    out[2].v = _mm_add_epi64(out[2].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[3].v), _mm_add_epi64(_mm_mul_epu32(r8, s[4].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r6, s[6].v), _mm_add_epi64(_mm_mul_epu32(r5_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r4, s[8].v), _mm_mul_epu32(r3_2, s[9].v))))))));
    out[3].v = _mm_add_epi64(out[3].v, _mm_add_epi64(_mm_mul_epu32(r9  , s[4].v), _mm_add_epi64(_mm_mul_epu32(r8, s[5].v), _mm_add_epi64(_mm_mul_epu32(r7  , s[6].v), _mm_add_epi64(_mm_mul_epu32(r6, s[7].v), _mm_add_epi64(_mm_mul_epu32(r5  , s[8].v), _mm_mul_epu32(r4, s[9].v)))))));
    out[4].v = _mm_add_epi64(out[4].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[5].v), _mm_add_epi64(_mm_mul_epu32(r8, s[6].v), _mm_add_epi64(_mm_mul_epu32(r7_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r6, s[8].v), _mm_mul_epu32(r5_2, s[9].v))))));
    out[5].v = _mm_add_epi64(out[5].v, _mm_add_epi64(_mm_mul_epu32(r9  , s[6].v), _mm_add_epi64(_mm_mul_epu32(r8, s[7].v), _mm_add_epi64(_mm_mul_epu32(r7  , s[8].v), _mm_mul_epu32(r6, s[9].v)))));
    out[6].v = _mm_add_epi64(out[6].v, _mm_add_epi64(_mm_mul_epu32(r9_2, s[7].v), _mm_add_epi64(_mm_mul_epu32(r8, s[8].v), _mm_mul_epu32(r7_2, s[9].v))));
    out[7].v = _mm_add_epi64(out[7].v, _mm_add_epi64(_mm_mul_epu32(r9  , s[8].v), _mm_mul_epu32(r8, s[9].v)));
    out[8].v = _mm_add_epi64(out[8].v, _mm_mul_epu32(r9_2, s[9].v));

    c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
    c1 = _mm_srli_epi64(out[1].v, 25); c2 = _mm_srli_epi64(out[5].v, 25); out[1].v = _mm_and_si128(out[1].v, packedmask25.v); out[5].v = _mm_and_si128(out[5].v, packedmask25.v); out[2].v = _mm_add_epi64(out[2].v, c1); out[6].v = _mm_add_epi64(out[6].v, c2);
    c1 = _mm_srli_epi64(out[2].v, 26); c2 = _mm_srli_epi64(out[6].v, 26); out[2].v = _mm_and_si128(out[2].v, packedmask26.v); out[6].v = _mm_and_si128(out[6].v, packedmask26.v); out[3].v = _mm_add_epi64(out[3].v, c1); out[7].v = _mm_add_epi64(out[7].v, c2);
    c1 = _mm_srli_epi64(out[3].v, 25); c2 = _mm_srli_epi64(out[7].v, 25); out[3].v = _mm_and_si128(out[3].v, packedmask25.v); out[7].v = _mm_and_si128(out[7].v, packedmask25.v); out[4].v = _mm_add_epi64(out[4].v, c1); out[8].v = _mm_add_epi64(out[8].v, c2);
                                       c2 = _mm_srli_epi64(out[8].v, 26);                                                     out[8].v = _mm_and_si128(out[8].v, packedmask26.v);                                         out[9].v = _mm_add_epi64(out[9].v, c2);
                                       c2 = _mm_srli_epi64(out[9].v, 25);                                                     out[9].v = _mm_and_si128(out[9].v, packedmask25.v);                                         out[0].v = _mm_add_epi64(out[0].v, _mm_mul_epu32(c2, packednineteen.v));
    c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
}

/* multiply a bignum */
void
curve25519_mul(bignum25519 out, const bignum25519 r, const bignum25519 s) {
    xmmi m01,m23,m45,m67,m89;
    xmmi m0123,m4567;
    xmmi s0123,s4567;
    xmmi s01,s23,s45,s67,s89;
    xmmi s12,s34,s56,s78,s9;
    xmmi r0,r2,r4,r6,r8;
    xmmi r1,r3,r5,r7,r9;
    xmmi r119,r219,r319,r419,r519,r619,r719,r819,r919;
    xmmi c1,c2,c3;

    s0123 = _mm_load_si128((xmmi*)s + 0);
    s01 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,1,2,0));
    s12 = _mm_shuffle_epi32(s0123, _MM_SHUFFLE(2,2,1,1));
    s23 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,3,2,2));
    s4567 = _mm_load_si128((xmmi*)s + 1);
    s34 = _mm_unpacklo_epi64(_mm_srli_si128(s0123,12),s4567);
    s45 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,1,2,0));
    s56 = _mm_shuffle_epi32(s4567, _MM_SHUFFLE(2,2,1,1));
    s67 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,3,2,2));
    s89 = _mm_load_si128((xmmi*)s + 2);
    s78 = _mm_unpacklo_epi64(_mm_srli_si128(s4567,12),s89);
    s89 = _mm_shuffle_epi32(s89,_MM_SHUFFLE(3,1,2,0));
    s9 = _mm_shuffle_epi32(s89, _MM_SHUFFLE(3,3,2,2));

    r0 = _mm_load_si128((xmmi*)r + 0);
    r1 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(1,1,1,1));
    r1 = _mm_add_epi64(r1, _mm_and_si128(r1, sse2_top64bitmask.v));
    r2 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(2,2,2,2));
    r3 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(3,3,3,3));
    r3 = _mm_add_epi64(r3, _mm_and_si128(r3, sse2_top64bitmask.v));
    r0 = _mm_shuffle_epi32(r0, _MM_SHUFFLE(0,0,0,0));
    r4 = _mm_load_si128((xmmi*)r + 1);
    r5 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(1,1,1,1));
    r5 = _mm_add_epi64(r5, _mm_and_si128(r5, sse2_top64bitmask.v));
    r6 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(2,2,2,2));
    r7 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(3,3,3,3));
    r7 = _mm_add_epi64(r7, _mm_and_si128(r7, sse2_top64bitmask.v));
    r4 = _mm_shuffle_epi32(r4, _MM_SHUFFLE(0,0,0,0));
    r8 = _mm_load_si128((xmmi*)r + 2);
    r9 = _mm_shuffle_epi32(r8, _MM_SHUFFLE(3,1,3,1));
    r9 = _mm_add_epi64(r9, _mm_and_si128(r9, sse2_top64bitmask.v));
    r8 = _mm_shuffle_epi32(r8, _MM_SHUFFLE(3,0,3,0));

    m01 = _mm_mul_epu32(r1,s01);
    m23 = _mm_mul_epu32(r1,s23);
    m45 = _mm_mul_epu32(r1,s45);
    m67 = _mm_mul_epu32(r1,s67);
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r3,s01));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r3,s23));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r3,s45));
    m89 = _mm_mul_epu32(r1,s89);
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r5,s01));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r5,s23));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r3,s67));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r7,s01));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r5,s45));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r7,s23));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r9,s01));

    /* shift up */
    m89 = _mm_unpackhi_epi64(m67,_mm_slli_si128(m89,8));
    m67 = _mm_unpackhi_epi64(m45,_mm_slli_si128(m67,8));
    m45 = _mm_unpackhi_epi64(m23,_mm_slli_si128(m45,8));
    m23 = _mm_unpackhi_epi64(m01,_mm_slli_si128(m23,8));
    m01 = _mm_unpackhi_epi64(_mm_setzero_si128(),_mm_slli_si128(m01,8));

    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r0,s01));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r0,s23));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r0,s45));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r0,s67));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r2,s01));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r2,s23));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r4,s23));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r0,s89));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r4,s01));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r2,s45));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r2,s67));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r6,s01));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r4,s45));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r6,s23));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r8,s01));

    r219 = _mm_mul_epu32(r2, packednineteen.v);
    r419 = _mm_mul_epu32(r4, packednineteen.v);
    r619 = _mm_mul_epu32(r6, packednineteen.v);
    r819 = _mm_mul_epu32(r8, packednineteen.v);
    r119 = _mm_shuffle_epi32(r1,_MM_SHUFFLE(0,0,2,2)); r119 = _mm_mul_epu32(r119, packednineteen.v);
    r319 = _mm_shuffle_epi32(r3,_MM_SHUFFLE(0,0,2,2)); r319 = _mm_mul_epu32(r319, packednineteen.v);
    r519 = _mm_shuffle_epi32(r5,_MM_SHUFFLE(0,0,2,2)); r519 = _mm_mul_epu32(r519, packednineteen.v);
    r719 = _mm_shuffle_epi32(r7,_MM_SHUFFLE(0,0,2,2)); r719 = _mm_mul_epu32(r719, packednineteen.v);
    r919 = _mm_shuffle_epi32(r9,_MM_SHUFFLE(0,0,2,2)); r919 = _mm_mul_epu32(r919, packednineteen.v);

    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r919,s12));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r919,s34));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r919,s56));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r919,s78));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r719,s34));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r719,s56));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r719,s78));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r719,s9));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r519,s56));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r519,s78));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r519,s9));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r819,s89));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r319,s78));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r319,s9));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r619,s89));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r919,s9));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r819,s23));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r819,s45));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r819,s67));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r619,s45));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r619,s67));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r419,s67));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r419,s89));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r219,s89));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r119,s9));

    r0 = _mm_unpacklo_epi64(m01, m45);
    r1 = _mm_unpackhi_epi64(m01, m45);
    r2 = _mm_unpacklo_epi64(m23, m67);
    r3 = _mm_unpackhi_epi64(m23, m67);
    r4 = _mm_unpacklo_epi64(m89, m89);
    r5 = _mm_unpackhi_epi64(m89, m89);

    c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
    c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
    c1 = _mm_srli_epi64(r4, 26);                                                                      r4 = _mm_and_si128(r4, packedmask26.v);                             r5 = _mm_add_epi64(r5, c1);
    c1 = _mm_srli_epi64(r5, 25);                                                                      r5 = _mm_and_si128(r5, packedmask25.v);                             r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
    c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);

    m0123 = _mm_unpacklo_epi32(r0, r1);
    m4567 = _mm_unpackhi_epi32(r0, r1);
    m0123 = _mm_unpacklo_epi64(m0123, _mm_unpacklo_epi32(r2, r3));
    m4567 = _mm_unpacklo_epi64(m4567, _mm_unpackhi_epi32(r2, r3));
    m89 = _mm_unpackhi_epi32(r4, r5);

    _mm_store_si128((xmmi*)out + 0, m0123);
    _mm_store_si128((xmmi*)out + 1, m4567);
    _mm_store_si128((xmmi*)out + 2, m89);
}

typedef struct bignum25519mulprecomp_t {
    xmmi r0,r2,r4,r6,r8;
    xmmi r1,r3,r5,r7,r9;
    xmmi r119,r219,r319,r419,r519,r619,r719,r819,r919;
} bignum25519mulprecomp;

/* precompute a constant to multiply by */
inline void
curve25519_mul_precompute(bignum25519mulprecomp *pre, const bignum25519 r) {
    pre->r0 = _mm_load_si128((xmmi*)r + 0);
    pre->r1 = _mm_shuffle_epi32(pre->r0, _MM_SHUFFLE(1,1,1,1));
    pre->r1 = _mm_add_epi64(pre->r1, _mm_and_si128(pre->r1, sse2_top64bitmask.v));
    pre->r2 = _mm_shuffle_epi32(pre->r0, _MM_SHUFFLE(2,2,2,2));
    pre->r3 = _mm_shuffle_epi32(pre->r0, _MM_SHUFFLE(3,3,3,3));
    pre->r3 = _mm_add_epi64(pre->r3, _mm_and_si128(pre->r3, sse2_top64bitmask.v));
    pre->r0 = _mm_shuffle_epi32(pre->r0, _MM_SHUFFLE(0,0,0,0));
    pre->r4 = _mm_load_si128((xmmi*)r + 1);
    pre->r5 = _mm_shuffle_epi32(pre->r4, _MM_SHUFFLE(1,1,1,1));
    pre->r5 = _mm_add_epi64(pre->r5, _mm_and_si128(pre->r5, sse2_top64bitmask.v));
    pre->r6 = _mm_shuffle_epi32(pre->r4, _MM_SHUFFLE(2,2,2,2));
    pre->r7 = _mm_shuffle_epi32(pre->r4, _MM_SHUFFLE(3,3,3,3));
    pre->r7 = _mm_add_epi64(pre->r7, _mm_and_si128(pre->r7, sse2_top64bitmask.v));
    pre->r4 = _mm_shuffle_epi32(pre->r4, _MM_SHUFFLE(0,0,0,0));
    pre->r8 = _mm_load_si128((xmmi*)r + 2);
    pre->r9 = _mm_shuffle_epi32(pre->r8, _MM_SHUFFLE(3,1,3,1));
    pre->r9 = _mm_add_epi64(pre->r9, _mm_and_si128(pre->r9, sse2_top64bitmask.v));
    pre->r8 = _mm_shuffle_epi32(pre->r8, _MM_SHUFFLE(3,0,3,0));

    pre->r219 = _mm_mul_epu32(pre->r2, packednineteen.v);
    pre->r419 = _mm_mul_epu32(pre->r4, packednineteen.v);
    pre->r619 = _mm_mul_epu32(pre->r6, packednineteen.v);
    pre->r819 = _mm_mul_epu32(pre->r8, packednineteen.v);
    pre->r119 = _mm_shuffle_epi32(pre->r1,_MM_SHUFFLE(0,0,2,2)); pre->r119 = _mm_mul_epu32(pre->r119, packednineteen.v);
    pre->r319 = _mm_shuffle_epi32(pre->r3,_MM_SHUFFLE(0,0,2,2)); pre->r319 = _mm_mul_epu32(pre->r319, packednineteen.v);
    pre->r519 = _mm_shuffle_epi32(pre->r5,_MM_SHUFFLE(0,0,2,2)); pre->r519 = _mm_mul_epu32(pre->r519, packednineteen.v);
    pre->r719 = _mm_shuffle_epi32(pre->r7,_MM_SHUFFLE(0,0,2,2)); pre->r719 = _mm_mul_epu32(pre->r719, packednineteen.v);
    pre->r919 = _mm_shuffle_epi32(pre->r9,_MM_SHUFFLE(0,0,2,2)); pre->r919 = _mm_mul_epu32(pre->r919, packednineteen.v);
}


/* multiply a bignum by a pre-computed constant */
inline void
curve25519_mul_precomputed(bignum25519 out, const bignum25519 s, const bignum25519mulprecomp *r) {
    xmmi m01,m23,m45,m67,m89;
    xmmi m0123,m4567;
    xmmi s0123,s4567;
    xmmi s01,s23,s45,s67,s89;
    xmmi s12,s34,s56,s78,s9;
    xmmi r0,r1,r2,r3,r4,r5;
    xmmi c1,c2,c3;

    s0123 = _mm_load_si128((xmmi*)s + 0);
    s01 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,1,2,0));
    s12 = _mm_shuffle_epi32(s0123, _MM_SHUFFLE(2,2,1,1));
    s23 = _mm_shuffle_epi32(s0123,_MM_SHUFFLE(3,3,2,2));
    s4567 = _mm_load_si128((xmmi*)s + 1);
    s34 = _mm_unpacklo_epi64(_mm_srli_si128(s0123,12),s4567);
    s45 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,1,2,0));
    s56 = _mm_shuffle_epi32(s4567, _MM_SHUFFLE(2,2,1,1));
    s67 = _mm_shuffle_epi32(s4567,_MM_SHUFFLE(3,3,2,2));
    s89 = _mm_load_si128((xmmi*)s + 2);
    s78 = _mm_unpacklo_epi64(_mm_srli_si128(s4567,12),s89);
    s89 = _mm_shuffle_epi32(s89,_MM_SHUFFLE(3,1,2,0));
    s9 = _mm_shuffle_epi32(s89, _MM_SHUFFLE(3,3,2,2));

    m01 = _mm_mul_epu32(r->r1,s01);
    m23 = _mm_mul_epu32(r->r1,s23);
    m45 = _mm_mul_epu32(r->r1,s45);
    m67 = _mm_mul_epu32(r->r1,s67);
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r3,s01));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r3,s23));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r3,s45));
    m89 = _mm_mul_epu32(r->r1,s89);
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r5,s01));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r5,s23));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r3,s67));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r7,s01));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r5,s45));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r7,s23));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r9,s01));

    /* shift up */
    m89 = _mm_unpackhi_epi64(m67,_mm_slli_si128(m89,8));
    m67 = _mm_unpackhi_epi64(m45,_mm_slli_si128(m67,8));
    m45 = _mm_unpackhi_epi64(m23,_mm_slli_si128(m45,8));
    m23 = _mm_unpackhi_epi64(m01,_mm_slli_si128(m23,8));
    m01 = _mm_unpackhi_epi64(_mm_setzero_si128(),_mm_slli_si128(m01,8));

    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r0,s01));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r0,s23));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r0,s45));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r0,s67));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r2,s01));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r2,s23));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r4,s23));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r0,s89));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r4,s01));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r2,s45));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r2,s67));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r6,s01));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r4,s45));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r6,s23));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r8,s01));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r919,s12));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r919,s34));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r919,s56));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r919,s78));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r719,s34));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r719,s56));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r719,s78));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r719,s9));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r519,s56));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r519,s78));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r519,s9));
    m67 = _mm_add_epi64(m67,_mm_mul_epu32(r->r819,s89));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r319,s78));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r319,s9));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r619,s89));
    m89 = _mm_add_epi64(m89,_mm_mul_epu32(r->r919,s9));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r819,s23));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r819,s45));
    m45 = _mm_add_epi64(m45,_mm_mul_epu32(r->r819,s67));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r619,s45));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r619,s67));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r419,s67));
    m23 = _mm_add_epi64(m23,_mm_mul_epu32(r->r419,s89));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r219,s89));
    m01 = _mm_add_epi64(m01,_mm_mul_epu32(r->r119,s9));

    r0 = _mm_unpacklo_epi64(m01, m45);
    r1 = _mm_unpackhi_epi64(m01, m45);
    r2 = _mm_unpacklo_epi64(m23, m67);
    r3 = _mm_unpackhi_epi64(m23, m67);
    r4 = _mm_unpacklo_epi64(m89, m89);
    r5 = _mm_unpackhi_epi64(m89, m89);

    c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
    c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
    c1 = _mm_srli_epi64(r4, 26);                                                                      r4 = _mm_and_si128(r4, packedmask26.v);                             r5 = _mm_add_epi64(r5, c1);
    c1 = _mm_srli_epi64(r5, 25);                                                                      r5 = _mm_and_si128(r5, packedmask25.v);                             r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
    c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);

    m0123 = _mm_unpacklo_epi32(r0, r1);
    m4567 = _mm_unpackhi_epi32(r0, r1);
    m0123 = _mm_unpacklo_epi64(m0123, _mm_unpacklo_epi32(r2, r3));
    m4567 = _mm_unpacklo_epi64(m4567, _mm_unpackhi_epi32(r2, r3));
    m89 = _mm_unpackhi_epi32(r4, r5);

    _mm_store_si128((xmmi*)out + 0, m0123);
    _mm_store_si128((xmmi*)out + 1, m4567);
    _mm_store_si128((xmmi*)out + 2, m89);
}

/* square a bignum 'count' times */
#define curve25519_square(r,x) curve25519_square_times(r,x,1)

void
curve25519_square_times(bignum25519 r, const bignum25519 in, int count) {
    xmmi m01,m23,m45,m67,m89;
    xmmi r0,r1,r2,r3,r4,r5,r6,r7,r8,r9;
    xmmi r0a,r1a,r2a,r3a,r7a,r9a;
    xmmi r0123,r4567;
    xmmi r01,r23,r45,r67,r6x,r89,r8x;
    xmmi r12,r34,r56,r78,r9x;
    xmmi r5619;
    xmmi c1,c2,c3;

    r0123 = _mm_load_si128((xmmi*)in + 0);
    r01 = _mm_shuffle_epi32(r0123,_MM_SHUFFLE(3,1,2,0));
    r23 = _mm_shuffle_epi32(r0123,_MM_SHUFFLE(3,3,2,2));
    r4567 = _mm_load_si128((xmmi*)in + 1);
    r45 = _mm_shuffle_epi32(r4567,_MM_SHUFFLE(3,1,2,0));
    r67 = _mm_shuffle_epi32(r4567,_MM_SHUFFLE(3,3,2,2));
    r89 = _mm_load_si128((xmmi*)in + 2);
    r89 = _mm_shuffle_epi32(r89,_MM_SHUFFLE(3,1,2,0));

    do {
        r12 = _mm_unpackhi_epi64(r01, _mm_slli_si128(r23, 8));
        r0 = _mm_shuffle_epi32(r01, _MM_SHUFFLE(0,0,0,0));
        r0 = _mm_add_epi64(r0, _mm_and_si128(r0, sse2_top64bitmask.v));
        r0a = _mm_shuffle_epi32(r0,_MM_SHUFFLE(3,2,1,2));
        r1 = _mm_shuffle_epi32(r01, _MM_SHUFFLE(2,2,2,2));
        r2 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(0,0,0,0));
        r2 = _mm_add_epi64(r2, _mm_and_si128(r2, sse2_top64bitmask.v));
        r2a = _mm_shuffle_epi32(r2,_MM_SHUFFLE(3,2,1,2));
        r3 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(2,2,2,2));
        r34 = _mm_unpackhi_epi64(r23, _mm_slli_si128(r45, 8));
        r4 = _mm_shuffle_epi32(r45, _MM_SHUFFLE(0,0,0,0));
        r4 = _mm_add_epi64(r4, _mm_and_si128(r4, sse2_top64bitmask.v));
        r56 = _mm_unpackhi_epi64(r45, _mm_slli_si128(r67, 8));
        r5619 = _mm_mul_epu32(r56, packednineteen.v);
        r5 = _mm_shuffle_epi32(r5619, _MM_SHUFFLE(1,1,1,0));
        r6 = _mm_shuffle_epi32(r5619, _MM_SHUFFLE(3,2,3,2));
        r78 = _mm_unpackhi_epi64(r67, _mm_slli_si128(r89, 8));
        r6x = _mm_unpacklo_epi64(r67, _mm_setzero_si128());
        r7 = _mm_shuffle_epi32(r67, _MM_SHUFFLE(2,2,2,2));
        r7 = _mm_mul_epu32(r7, packed3819.v);
        r7a = _mm_shuffle_epi32(r7, _MM_SHUFFLE(3,3,3,2));
        r8x = _mm_unpacklo_epi64(r89, _mm_setzero_si128());
        r8 = _mm_shuffle_epi32(r89, _MM_SHUFFLE(0,0,0,0));
        r8 = _mm_mul_epu32(r8, packednineteen.v);
        r9  = _mm_shuffle_epi32(r89, _MM_SHUFFLE(2,2,2,2));
        r9x  = _mm_slli_epi32(_mm_shuffle_epi32(r89, _MM_SHUFFLE(3,3,3,2)), 1);
        r9 = _mm_mul_epu32(r9, packed3819.v);
        r9a = _mm_shuffle_epi32(r9, _MM_SHUFFLE(2,2,2,2));

        m01 = _mm_mul_epu32(r01, r0);
        m23 = _mm_mul_epu32(r23, r0a);
        m45 = _mm_mul_epu32(r45, r0a);
        m45 = _mm_add_epi64(m45, _mm_mul_epu32(r23, r2));
        r23 = _mm_slli_epi32(r23, 1);
        m67 = _mm_mul_epu32(r67, r0a);
        m67 = _mm_add_epi64(m67, _mm_mul_epu32(r45, r2a));
        m89 = _mm_mul_epu32(r89, r0a);
        m89 = _mm_add_epi64(m89, _mm_mul_epu32(r67, r2a));
        r67 = _mm_slli_epi32(r67, 1);
        m89 = _mm_add_epi64(m89, _mm_mul_epu32(r45, r4));
        r45 = _mm_slli_epi32(r45, 1);

        r1 = _mm_slli_epi32(r1, 1);
        r3 = _mm_slli_epi32(r3, 1);
        r1a = _mm_add_epi64(r1, _mm_and_si128(r1, sse2_bot64bitmask.v));
        r3a = _mm_add_epi64(r3, _mm_and_si128(r3, sse2_bot64bitmask.v));

        m23 = _mm_add_epi64(m23, _mm_mul_epu32(r12, r1));
        m45 = _mm_add_epi64(m45, _mm_mul_epu32(r34, r1a));
        m67 = _mm_add_epi64(m67, _mm_mul_epu32(r56, r1a));
        m67 = _mm_add_epi64(m67, _mm_mul_epu32(r34, r3));
        r34 = _mm_slli_epi32(r34, 1);
        m89 = _mm_add_epi64(m89, _mm_mul_epu32(r78, r1a));
        r78 = _mm_slli_epi32(r78, 1);
        m89 = _mm_add_epi64(m89, _mm_mul_epu32(r56, r3a));
        r56 = _mm_slli_epi32(r56, 1);

        m01 = _mm_add_epi64(m01, _mm_mul_epu32(_mm_slli_epi32(r12, 1), r9));
        m01 = _mm_add_epi64(m01, _mm_mul_epu32(r34, r7));
        m23 = _mm_add_epi64(m23, _mm_mul_epu32(r34, r9));
        m01 = _mm_add_epi64(m01, _mm_mul_epu32(r56, r5));
        m23 = _mm_add_epi64(m23, _mm_mul_epu32(r56, r7));
        m45 = _mm_add_epi64(m45, _mm_mul_epu32(r56, r9));
        m01 = _mm_add_epi64(m01, _mm_mul_epu32(r23, r8));
        m01 = _mm_add_epi64(m01, _mm_mul_epu32(r45, r6));
        m23 = _mm_add_epi64(m23, _mm_mul_epu32(r45, r8));
        m23 = _mm_add_epi64(m23, _mm_mul_epu32(r6x, r6));
        m45 = _mm_add_epi64(m45, _mm_mul_epu32(r78, r7a));
        m67 = _mm_add_epi64(m67, _mm_mul_epu32(r78, r9));
        m45 = _mm_add_epi64(m45, _mm_mul_epu32(r67, r8));
        m67 = _mm_add_epi64(m67, _mm_mul_epu32(r8x, r8));
        m89 = _mm_add_epi64(m89, _mm_mul_epu32(r9x, r9a));

        r0 = _mm_unpacklo_epi64(m01, m45);
        r1 = _mm_unpackhi_epi64(m01, m45);
        r2 = _mm_unpacklo_epi64(m23, m67);
        r3 = _mm_unpackhi_epi64(m23, m67);
        r4 = _mm_unpacklo_epi64(m89, m89);
        r5 = _mm_unpackhi_epi64(m89, m89);

        c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);
        c1 = _mm_srli_epi64(r1, 25); c2 = _mm_srli_epi64(r3, 25); r1 = _mm_and_si128(r1, packedmask25.v); r3 = _mm_and_si128(r3, packedmask25.v); r2 = _mm_add_epi64(r2, c1); r4 = _mm_add_epi64(r4, c2); c3 = _mm_slli_si128(c2, 8);
        c1 = _mm_srli_epi64(r4, 26);                                                                      r4 = _mm_and_si128(r4, packedmask26.v);                             r5 = _mm_add_epi64(r5, c1);
        c1 = _mm_srli_epi64(r5, 25);                                                                      r5 = _mm_and_si128(r5, packedmask25.v);                             r0 = _mm_add_epi64(r0, _mm_unpackhi_epi64(_mm_mul_epu32(c1, packednineteen.v), c3));
        c1 = _mm_srli_epi64(r0, 26); c2 = _mm_srli_epi64(r2, 26); r0 = _mm_and_si128(r0, packedmask26.v); r2 = _mm_and_si128(r2, packedmask26.v); r1 = _mm_add_epi64(r1, c1); r3 = _mm_add_epi64(r3, c2);

        r01 = _mm_unpacklo_epi64(r0, r1);
        r45 = _mm_unpackhi_epi64(r0, r1);
        r23 = _mm_unpacklo_epi64(r2, r3);
        r67 = _mm_unpackhi_epi64(r2, r3);
        r89 = _mm_unpackhi_epi64(r4, r5);
    } while (--count);

    r0123 = _mm_shuffle_epi32(r23, _MM_SHUFFLE(2,0,3,3));
    r4567 = _mm_shuffle_epi32(r67, _MM_SHUFFLE(2,0,3,3));
    r0123 = _mm_or_si128(r0123, _mm_shuffle_epi32(r01, _MM_SHUFFLE(3,3,2,0)));
    r4567 = _mm_or_si128(r4567, _mm_shuffle_epi32(r45, _MM_SHUFFLE(3,3,2,0)));
    r89 = _mm_shuffle_epi32(r89, _MM_SHUFFLE(3,3,2,0));

    _mm_store_si128((xmmi*)r + 0, r0123);
    _mm_store_si128((xmmi*)r + 1, r4567);
    _mm_store_si128((xmmi*)r + 2, r89);
}

/* square two packed bignums */
inline void
curve25519_square_packed64(packedelem64 *out, const packedelem64 *r) {
    xmmi r0,r1,r2,r3;
    xmmi r1_2,r3_2,r4_2,r5_2,r6_2,r7_2;
    xmmi d5,d6,d7,d8,d9;
    xmmi c1,c2;

    r0 = r[0].v;
    r1 = r[1].v;
    r2 = r[2].v;
    r3 = r[3].v;

    out[0].v = _mm_mul_epu32(r0, r0);
    r0 = _mm_slli_epi32(r0, 1);
    out[1].v = _mm_mul_epu32(r0, r1);
    r1_2 = _mm_slli_epi32(r1, 1);
    out[2].v = _mm_add_epi64(_mm_mul_epu32(r0, r2    ), _mm_mul_epu32(r1, r1_2));
    r1 = r1_2;
    out[3].v = _mm_add_epi64(_mm_mul_epu32(r0, r3    ), _mm_mul_epu32(r1, r2  ));
    r3_2 = _mm_slli_epi32(r3, 1);
    out[4].v = _mm_add_epi64(_mm_mul_epu32(r0, r[4].v), _mm_add_epi64(_mm_mul_epu32(r1, r3_2  ), _mm_mul_epu32(r2, r2)));
    r2 = _mm_slli_epi32(r2, 1);
    out[5].v = _mm_add_epi64(_mm_mul_epu32(r0, r[5].v), _mm_add_epi64(_mm_mul_epu32(r1, r[4].v), _mm_mul_epu32(r2, r3)));
    r5_2 = _mm_slli_epi32(r[5].v, 1);
    out[6].v = _mm_add_epi64(_mm_mul_epu32(r0, r[6].v), _mm_add_epi64(_mm_mul_epu32(r1, r5_2  ), _mm_add_epi64(_mm_mul_epu32(r2, r[4].v), _mm_mul_epu32(r3, r3_2  ))));
    r3 = r3_2;
    out[7].v = _mm_add_epi64(_mm_mul_epu32(r0, r[7].v), _mm_add_epi64(_mm_mul_epu32(r1, r[6].v), _mm_add_epi64(_mm_mul_epu32(r2, r[5].v), _mm_mul_epu32(r3, r[4].v))));
    r7_2 = _mm_slli_epi32(r[7].v, 1);
    out[8].v = _mm_add_epi64(_mm_mul_epu32(r0, r[8].v), _mm_add_epi64(_mm_mul_epu32(r1, r7_2  ), _mm_add_epi64(_mm_mul_epu32(r2, r[6].v), _mm_add_epi64(_mm_mul_epu32(r3, r5_2  ), _mm_mul_epu32(r[4].v, r[4].v)))));
    out[9].v = _mm_add_epi64(_mm_mul_epu32(r0, r[9].v), _mm_add_epi64(_mm_mul_epu32(r1, r[8].v), _mm_add_epi64(_mm_mul_epu32(r2, r[7].v), _mm_add_epi64(_mm_mul_epu32(r3, r[6].v), _mm_mul_epu32(r[4].v, r5_2  )))));

    d5 = _mm_mul_epu32(r[5].v, packedthirtyeight.v);
    d6 = _mm_mul_epu32(r[6].v, packednineteen.v);
    d7 = _mm_mul_epu32(r[7].v, packedthirtyeight.v);
    d8 = _mm_mul_epu32(r[8].v, packednineteen.v);
    d9 = _mm_mul_epu32(r[9].v, packedthirtyeight.v);

    r4_2 = _mm_slli_epi32(r[4].v, 1);
    r6_2 = _mm_slli_epi32(r[6].v, 1);
    out[0].v = _mm_add_epi64(out[0].v, _mm_add_epi64(_mm_mul_epu32(d9, r1                   ), _mm_add_epi64(_mm_mul_epu32(d8, r2  ), _mm_add_epi64(_mm_mul_epu32(d7, r3    ), _mm_add_epi64(_mm_mul_epu32(d6, r4_2), _mm_mul_epu32(d5, r[5].v))))));
    out[1].v = _mm_add_epi64(out[1].v, _mm_add_epi64(_mm_mul_epu32(d9, _mm_srli_epi32(r2, 1)), _mm_add_epi64(_mm_mul_epu32(d8, r3  ), _mm_add_epi64(_mm_mul_epu32(d7, r[4].v), _mm_mul_epu32(d6, r5_2  )))));
    out[2].v = _mm_add_epi64(out[2].v, _mm_add_epi64(_mm_mul_epu32(d9, r3                   ), _mm_add_epi64(_mm_mul_epu32(d8, r4_2), _mm_add_epi64(_mm_mul_epu32(d7, r5_2  ), _mm_mul_epu32(d6, r[6].v)))));
    out[3].v = _mm_add_epi64(out[3].v, _mm_add_epi64(_mm_mul_epu32(d9, r[4].v               ), _mm_add_epi64(_mm_mul_epu32(d8, r5_2), _mm_mul_epu32(d7, r[6].v))));
    out[4].v = _mm_add_epi64(out[4].v, _mm_add_epi64(_mm_mul_epu32(d9, r5_2                 ), _mm_add_epi64(_mm_mul_epu32(d8, r6_2), _mm_mul_epu32(d7, r[7].v))));
    out[5].v = _mm_add_epi64(out[5].v, _mm_add_epi64(_mm_mul_epu32(d9, r[6].v               ), _mm_mul_epu32(d8, r7_2  )));
    out[6].v = _mm_add_epi64(out[6].v, _mm_add_epi64(_mm_mul_epu32(d9, r7_2                 ), _mm_mul_epu32(d8, r[8].v)));
    out[7].v = _mm_add_epi64(out[7].v, _mm_mul_epu32(d9, r[8].v));
    out[8].v = _mm_add_epi64(out[8].v, _mm_mul_epu32(d9, r[9].v));

    c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
    c1 = _mm_srli_epi64(out[1].v, 25); c2 = _mm_srli_epi64(out[5].v, 25); out[1].v = _mm_and_si128(out[1].v, packedmask25.v); out[5].v = _mm_and_si128(out[5].v, packedmask25.v); out[2].v = _mm_add_epi64(out[2].v, c1); out[6].v = _mm_add_epi64(out[6].v, c2);
    c1 = _mm_srli_epi64(out[2].v, 26); c2 = _mm_srli_epi64(out[6].v, 26); out[2].v = _mm_and_si128(out[2].v, packedmask26.v); out[6].v = _mm_and_si128(out[6].v, packedmask26.v); out[3].v = _mm_add_epi64(out[3].v, c1); out[7].v = _mm_add_epi64(out[7].v, c2);
    c1 = _mm_srli_epi64(out[3].v, 25); c2 = _mm_srli_epi64(out[7].v, 25); out[3].v = _mm_and_si128(out[3].v, packedmask25.v); out[7].v = _mm_and_si128(out[7].v, packedmask25.v); out[4].v = _mm_add_epi64(out[4].v, c1); out[8].v = _mm_add_epi64(out[8].v, c2);
                                       c2 = _mm_srli_epi64(out[8].v, 26);                                                     out[8].v = _mm_and_si128(out[8].v, packedmask26.v);                                         out[9].v = _mm_add_epi64(out[9].v, c2);
                                       c2 = _mm_srli_epi64(out[9].v, 25);                                                     out[9].v = _mm_and_si128(out[9].v, packedmask25.v);                                         out[0].v = _mm_add_epi64(out[0].v, _mm_mul_epu32(c2, packednineteen.v));
    c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
}

/* make [nqx+nqz,nqpqx+nqpqz], [nqpqx-nqpqz,nqx-nqz] from [nqx+nqz,nqpqx+nqpqz], [nqx-nqz,nqpqx-nqpqz] */
inline void
curve25519_make_nqpq(packedelem64 *primex, packedelem64 *primez, const packedelem32 *pqx, const packedelem32 *pqz) {
    primex[0].v = _mm_shuffle_epi32(pqx[0].v, _MM_SHUFFLE(1,1,0,0));
    primex[1].v = _mm_shuffle_epi32(pqx[0].v, _MM_SHUFFLE(3,3,2,2));
    primex[2].v = _mm_shuffle_epi32(pqx[1].v, _MM_SHUFFLE(1,1,0,0));
    primex[3].v = _mm_shuffle_epi32(pqx[1].v, _MM_SHUFFLE(3,3,2,2));
    primex[4].v = _mm_shuffle_epi32(pqx[2].v, _MM_SHUFFLE(1,1,0,0));
    primex[5].v = _mm_shuffle_epi32(pqx[2].v, _MM_SHUFFLE(3,3,2,2));
    primex[6].v = _mm_shuffle_epi32(pqx[3].v, _MM_SHUFFLE(1,1,0,0));
    primex[7].v = _mm_shuffle_epi32(pqx[3].v, _MM_SHUFFLE(3,3,2,2));
    primex[8].v = _mm_shuffle_epi32(pqx[4].v, _MM_SHUFFLE(1,1,0,0));
    primex[9].v = _mm_shuffle_epi32(pqx[4].v, _MM_SHUFFLE(3,3,2,2));
    primez[0].v = _mm_shuffle_epi32(pqz[0].v, _MM_SHUFFLE(0,0,1,1));
    primez[1].v = _mm_shuffle_epi32(pqz[0].v, _MM_SHUFFLE(2,2,3,3));
    primez[2].v = _mm_shuffle_epi32(pqz[1].v, _MM_SHUFFLE(0,0,1,1));
    primez[3].v = _mm_shuffle_epi32(pqz[1].v, _MM_SHUFFLE(2,2,3,3));
    primez[4].v = _mm_shuffle_epi32(pqz[2].v, _MM_SHUFFLE(0,0,1,1));
    primez[5].v = _mm_shuffle_epi32(pqz[2].v, _MM_SHUFFLE(2,2,3,3));
    primez[6].v = _mm_shuffle_epi32(pqz[3].v, _MM_SHUFFLE(0,0,1,1));
    primez[7].v = _mm_shuffle_epi32(pqz[3].v, _MM_SHUFFLE(2,2,3,3));
    primez[8].v = _mm_shuffle_epi32(pqz[4].v, _MM_SHUFFLE(0,0,1,1));
    primez[9].v = _mm_shuffle_epi32(pqz[4].v, _MM_SHUFFLE(2,2,3,3));
}

/* make [nqx+nqz,nqx-nqz] from [nqx+nqz,nqpqx+nqpqz], [nqx-nqz,nqpqx-nqpqz] */
inline void
curve25519_make_nq(packedelem64 *nq, const packedelem32 *pqx, const packedelem32 *pqz) {
    nq[0].v = _mm_unpacklo_epi64(pqx[0].v, pqz[0].v);
    nq[1].v = _mm_unpackhi_epi64(pqx[0].v, pqz[0].v);
    nq[2].v = _mm_unpacklo_epi64(pqx[1].v, pqz[1].v);
    nq[3].v = _mm_unpackhi_epi64(pqx[1].v, pqz[1].v);
    nq[4].v = _mm_unpacklo_epi64(pqx[2].v, pqz[2].v);
    nq[5].v = _mm_unpackhi_epi64(pqx[2].v, pqz[2].v);
    nq[6].v = _mm_unpacklo_epi64(pqx[3].v, pqz[3].v);
    nq[7].v = _mm_unpackhi_epi64(pqx[3].v, pqz[3].v);
    nq[8].v = _mm_unpacklo_epi64(pqx[4].v, pqz[4].v);
    nq[9].v = _mm_unpackhi_epi64(pqx[4].v, pqz[4].v);
}

/* compute [nqx+nqz,nqx-nqz] from nqx, nqz */
inline void
curve25519_compute_nq(packedelem64 *nq, const bignum25519 nqx, const bignum25519 nqz) {
    xmmi x0,x1,x2;
    xmmi z0,z1,z2;
    xmmi a0,a1,a2;
    xmmi s0,s1,s2;
    xmmi r0,r1;
    xmmi c1,c2;
    x0 = _mm_load_si128((xmmi*)nqx + 0);
    x1 = _mm_load_si128((xmmi*)nqx + 1);
    x2 = _mm_load_si128((xmmi*)nqx + 2);
    z0 = _mm_load_si128((xmmi*)nqz + 0);
    z1 = _mm_load_si128((xmmi*)nqz + 1);
    z2 = _mm_load_si128((xmmi*)nqz + 2);
    a0 = _mm_add_epi32(x0, z0);
    a1 = _mm_add_epi32(x1, z1);
    a2 = _mm_add_epi32(x2, z2);
    s0 = _mm_add_epi32(x0, packed2p0.v);
    s1 = _mm_add_epi32(x1, packed2p1.v);
    s2 = _mm_add_epi32(x2, packed2p2.v);
    s0 = _mm_sub_epi32(s0, z0);
    s1 = _mm_sub_epi32(s1, z1);
    s2 = _mm_sub_epi32(s2, z2);
    r0 = _mm_and_si128(_mm_shuffle_epi32(s0, _MM_SHUFFLE(2,2,0,0)), sse2_bot32bitmask.v);
    r1 = _mm_and_si128(_mm_shuffle_epi32(s0, _MM_SHUFFLE(3,3,1,1)), sse2_bot32bitmask.v);
    c1 = _mm_srli_epi32(r0, 26);
    c2 = _mm_srli_epi32(r1, 25);
    r0 = _mm_and_si128(r0, packedmask26.v);
    r1 = _mm_and_si128(r1, packedmask25.v);
    r0 = _mm_add_epi32(r0, _mm_slli_si128(c2, 8));
    r1 = _mm_add_epi32(r1, c1);
    s0 = _mm_unpacklo_epi64(_mm_unpacklo_epi32(r0, r1), _mm_unpackhi_epi32(r0, r1));
    s1 = _mm_add_epi32(s1, _mm_srli_si128(c2, 8));
    nq[0].v = _mm_unpacklo_epi64(a0, s0);
    nq[2].v = _mm_unpackhi_epi64(a0, s0);
    nq[4].v = _mm_unpacklo_epi64(a1, s1);
    nq[6].v = _mm_unpackhi_epi64(a1, s1);
    nq[8].v = _mm_unpacklo_epi64(a2, s2);
    nq[1].v = _mm_shuffle_epi32(nq[0].v, _MM_SHUFFLE(3,3,1,1));
    nq[3].v = _mm_shuffle_epi32(nq[2].v, _MM_SHUFFLE(3,3,1,1));
    nq[5].v = _mm_shuffle_epi32(nq[4].v, _MM_SHUFFLE(3,3,1,1));
    nq[7].v = _mm_shuffle_epi32(nq[6].v, _MM_SHUFFLE(3,3,1,1));
    nq[9].v = _mm_shuffle_epi32(nq[8].v, _MM_SHUFFLE(3,3,1,1));
}


/* compute [x+z,x-z] from [x,z] */
inline void
curve25519_addsub_packed64(packedelem64 *r)  {
    packed32bignum25519 x,z,add,sub;

    x[0].v = _mm_unpacklo_epi64(r[0].v, r[1].v);
    z[0].v = _mm_unpackhi_epi64(r[0].v, r[1].v);
    x[1].v = _mm_unpacklo_epi64(r[2].v, r[3].v);
    z[1].v = _mm_unpackhi_epi64(r[2].v, r[3].v);
    x[2].v = _mm_unpacklo_epi64(r[4].v, r[5].v);
    z[2].v = _mm_unpackhi_epi64(r[4].v, r[5].v);
    x[3].v = _mm_unpacklo_epi64(r[6].v, r[7].v);
    z[3].v = _mm_unpackhi_epi64(r[6].v, r[7].v);
    x[4].v = _mm_unpacklo_epi64(r[8].v, r[9].v);
    z[4].v = _mm_unpackhi_epi64(r[8].v, r[9].v);

    curve25519_add_packed32(add, x, z);
    curve25519_sub_packed32(sub, x, z);

    r[0].v = _mm_unpacklo_epi64(add[0].v, sub[0].v);
    r[1].v = _mm_unpackhi_epi64(add[0].v, sub[0].v);
    r[2].v = _mm_unpacklo_epi64(add[1].v, sub[1].v);
    r[3].v = _mm_unpackhi_epi64(add[1].v, sub[1].v);
    r[4].v = _mm_unpacklo_epi64(add[2].v, sub[2].v);
    r[5].v = _mm_unpackhi_epi64(add[2].v, sub[2].v);
    r[6].v = _mm_unpacklo_epi64(add[3].v, sub[3].v);
    r[7].v = _mm_unpackhi_epi64(add[3].v, sub[3].v);
    r[8].v = _mm_unpacklo_epi64(add[4].v, sub[4].v);
    r[9].v = _mm_unpackhi_epi64(add[4].v, sub[4].v);
}

/* compute [x,z] * [121666,121665] */
inline void
curve25519_121665_packed64(packedelem64 *out, const packedelem64 *in) {
    xmmi c1,c2;

    out[0].v = _mm_mul_epu32(in[0].v, packed121666121665.v);
    out[1].v = _mm_mul_epu32(in[1].v, packed121666121665.v);
    out[2].v = _mm_mul_epu32(in[2].v, packed121666121665.v);
    out[3].v = _mm_mul_epu32(in[3].v, packed121666121665.v);
    out[4].v = _mm_mul_epu32(in[4].v, packed121666121665.v);
    out[5].v = _mm_mul_epu32(in[5].v, packed121666121665.v);
    out[6].v = _mm_mul_epu32(in[6].v, packed121666121665.v);
    out[7].v = _mm_mul_epu32(in[7].v, packed121666121665.v);
    out[8].v = _mm_mul_epu32(in[8].v, packed121666121665.v);
    out[9].v = _mm_mul_epu32(in[9].v, packed121666121665.v);

    c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
    c1 = _mm_srli_epi64(out[1].v, 25); c2 = _mm_srli_epi64(out[5].v, 25); out[1].v = _mm_and_si128(out[1].v, packedmask25.v); out[5].v = _mm_and_si128(out[5].v, packedmask25.v); out[2].v = _mm_add_epi64(out[2].v, c1); out[6].v = _mm_add_epi64(out[6].v, c2);
    c1 = _mm_srli_epi64(out[2].v, 26); c2 = _mm_srli_epi64(out[6].v, 26); out[2].v = _mm_and_si128(out[2].v, packedmask26.v); out[6].v = _mm_and_si128(out[6].v, packedmask26.v); out[3].v = _mm_add_epi64(out[3].v, c1); out[7].v = _mm_add_epi64(out[7].v, c2);
    c1 = _mm_srli_epi64(out[3].v, 25); c2 = _mm_srli_epi64(out[7].v, 25); out[3].v = _mm_and_si128(out[3].v, packedmask25.v); out[7].v = _mm_and_si128(out[7].v, packedmask25.v); out[4].v = _mm_add_epi64(out[4].v, c1); out[8].v = _mm_add_epi64(out[8].v, c2);
                                       c2 = _mm_srli_epi64(out[8].v, 26);                                                     out[8].v = _mm_and_si128(out[8].v, packedmask26.v);                                         out[9].v = _mm_add_epi64(out[9].v, c2);
                                       c2 = _mm_srli_epi64(out[9].v, 25);                                                     out[9].v = _mm_and_si128(out[9].v, packedmask25.v);                                         out[0].v = _mm_add_epi64(out[0].v, _mm_mul_epu32(c2, packednineteen.v));
    c1 = _mm_srli_epi64(out[0].v, 26); c2 = _mm_srli_epi64(out[4].v, 26); out[0].v = _mm_and_si128(out[0].v, packedmask26.v); out[4].v = _mm_and_si128(out[4].v, packedmask26.v); out[1].v = _mm_add_epi64(out[1].v, c1); out[5].v = _mm_add_epi64(out[5].v, c2);
}

/* compute [sq.x,sqscalar.x-sqscalar.z] * [sq.z,sq.x-sq.z] */
inline void
curve25519_final_nq(packedelem64 *nq, const packedelem64 *sq, const packedelem64 *sq121665) {
    packed32bignum25519 x, z, sub;
    packed64bignum25519 t, nqa, nqb;

    x[0].v = _mm_or_si128(_mm_unpacklo_epi64(sq[0].v, sq[1].v), _mm_slli_si128(_mm_unpacklo_epi64(sq121665[0].v, sq121665[1].v), 4));
    z[0].v = _mm_or_si128(_mm_unpackhi_epi64(sq[0].v, sq[1].v), _mm_slli_si128(_mm_unpackhi_epi64(sq121665[0].v, sq121665[1].v), 4));
    x[1].v = _mm_or_si128(_mm_unpacklo_epi64(sq[2].v, sq[3].v), _mm_slli_si128(_mm_unpacklo_epi64(sq121665[2].v, sq121665[3].v), 4));
    z[1].v = _mm_or_si128(_mm_unpackhi_epi64(sq[2].v, sq[3].v), _mm_slli_si128(_mm_unpackhi_epi64(sq121665[2].v, sq121665[3].v), 4));
    x[2].v = _mm_or_si128(_mm_unpacklo_epi64(sq[4].v, sq[5].v), _mm_slli_si128(_mm_unpacklo_epi64(sq121665[4].v, sq121665[5].v), 4));
    z[2].v = _mm_or_si128(_mm_unpackhi_epi64(sq[4].v, sq[5].v), _mm_slli_si128(_mm_unpackhi_epi64(sq121665[4].v, sq121665[5].v), 4));
    x[3].v = _mm_or_si128(_mm_unpacklo_epi64(sq[6].v, sq[7].v), _mm_slli_si128(_mm_unpacklo_epi64(sq121665[6].v, sq121665[7].v), 4));
    z[3].v = _mm_or_si128(_mm_unpackhi_epi64(sq[6].v, sq[7].v), _mm_slli_si128(_mm_unpackhi_epi64(sq121665[6].v, sq121665[7].v), 4));
    x[4].v = _mm_or_si128(_mm_unpacklo_epi64(sq[8].v, sq[9].v), _mm_slli_si128(_mm_unpacklo_epi64(sq121665[8].v, sq121665[9].v), 4));
    z[4].v = _mm_or_si128(_mm_unpackhi_epi64(sq[8].v, sq[9].v), _mm_slli_si128(_mm_unpackhi_epi64(sq121665[8].v, sq121665[9].v), 4));

    curve25519_sub_packed32(sub, x, z);

    t[0].v = _mm_shuffle_epi32(sub[0].v, _MM_SHUFFLE(1,1,0,0));
    t[1].v = _mm_shuffle_epi32(sub[0].v, _MM_SHUFFLE(3,3,2,2));
    t[2].v = _mm_shuffle_epi32(sub[1].v, _MM_SHUFFLE(1,1,0,0));
    t[3].v = _mm_shuffle_epi32(sub[1].v, _MM_SHUFFLE(3,3,2,2));
    t[4].v = _mm_shuffle_epi32(sub[2].v, _MM_SHUFFLE(1,1,0,0));
    t[5].v = _mm_shuffle_epi32(sub[2].v, _MM_SHUFFLE(3,3,2,2));
    t[6].v = _mm_shuffle_epi32(sub[3].v, _MM_SHUFFLE(1,1,0,0));
    t[7].v = _mm_shuffle_epi32(sub[3].v, _MM_SHUFFLE(3,3,2,2));
    t[8].v = _mm_shuffle_epi32(sub[4].v, _MM_SHUFFLE(1,1,0,0));
    t[9].v = _mm_shuffle_epi32(sub[4].v, _MM_SHUFFLE(3,3,2,2));

    nqa[0].v = _mm_unpacklo_epi64(sq[0].v, t[0].v);
    nqb[0].v = _mm_unpackhi_epi64(sq[0].v, t[0].v);
    nqa[1].v = _mm_unpacklo_epi64(sq[1].v, t[1].v);
    nqb[1].v = _mm_unpackhi_epi64(sq[1].v, t[1].v);
    nqa[2].v = _mm_unpacklo_epi64(sq[2].v, t[2].v);
    nqb[2].v = _mm_unpackhi_epi64(sq[2].v, t[2].v);
    nqa[3].v = _mm_unpacklo_epi64(sq[3].v, t[3].v);
    nqb[3].v = _mm_unpackhi_epi64(sq[3].v, t[3].v);
    nqa[4].v = _mm_unpacklo_epi64(sq[4].v, t[4].v);
    nqb[4].v = _mm_unpackhi_epi64(sq[4].v, t[4].v);
    nqa[5].v = _mm_unpacklo_epi64(sq[5].v, t[5].v);
    nqb[5].v = _mm_unpackhi_epi64(sq[5].v, t[5].v);
    nqa[6].v = _mm_unpacklo_epi64(sq[6].v, t[6].v);
    nqb[6].v = _mm_unpackhi_epi64(sq[6].v, t[6].v);
    nqa[7].v = _mm_unpacklo_epi64(sq[7].v, t[7].v);
    nqb[7].v = _mm_unpackhi_epi64(sq[7].v, t[7].v);
    nqa[8].v = _mm_unpacklo_epi64(sq[8].v, t[8].v);
    nqb[8].v = _mm_unpackhi_epi64(sq[8].v, t[8].v);
    nqa[9].v = _mm_unpacklo_epi64(sq[9].v, t[9].v);
    nqb[9].v = _mm_unpackhi_epi64(sq[9].v, t[9].v);

    curve25519_mul_packed64(nq, nqa, nqb);
}

/*
 * In:  b =   2^5 - 2^0
 * Out: b = 2^250 - 2^0
 */
void
curve25519_pow_two5mtwo0_two250mtwo0(bignum25519 b) {
    ALIGN(16) bignum25519 t0,c;

    /* 2^5  - 2^0 */ /* b */
    /* 2^10 - 2^5 */ curve25519_square_times(t0, b, 5);
    /* 2^10 - 2^0 */ curve25519_mul(b, t0, b);
    /* 2^20 - 2^10 */ curve25519_square_times(t0, b, 10);
    /* 2^20 - 2^0 */ curve25519_mul(c, t0, b);
    /* 2^40 - 2^20 */ curve25519_square_times(t0, c, 20);
    /* 2^40 - 2^0 */ curve25519_mul(t0, t0, c);
    /* 2^50 - 2^10 */ curve25519_square_times(t0, t0, 10);
    /* 2^50 - 2^0 */ curve25519_mul(b, t0, b);
    /* 2^100 - 2^50 */ curve25519_square_times(t0, b, 50);
    /* 2^100 - 2^0 */ curve25519_mul(c, t0, b);
    /* 2^200 - 2^100 */ curve25519_square_times(t0, c, 100);
    /* 2^200 - 2^0 */ curve25519_mul(t0, t0, c);
    /* 2^250 - 2^50 */ curve25519_square_times(t0, t0, 50);
    /* 2^250 - 2^0 */ curve25519_mul(b, t0, b);
}

/*
 * z^(p - 2) = z(2^255 - 21)
 */
void
curve25519_recip(bignum25519 out, const bignum25519 z) {
    ALIGN(16) bignum25519 a, t0, b;

    /* 2 */ curve25519_square(a, z); /* a = 2 */
    /* 8 */ curve25519_square_times(t0, a, 2);
    /* 9 */ curve25519_mul(b, t0, z); /* b = 9 */
    /* 11 */ curve25519_mul(a, b, a); /* a = 11 */
    /* 22 */ curve25519_square(t0, a);
    /* 2^5 - 2^0 = 31 */ curve25519_mul(b, t0, b);
    /* 2^250 - 2^0 */ curve25519_pow_two5mtwo0_two250mtwo0(b);
    /* 2^255 - 2^5 */ curve25519_square_times(b, b, 5);
    /* 2^255 - 21 */  curve25519_mul(out, b, a);
}

ANONYMOUS_NAMESPACE_END

NAMESPACE_BEGIN(CryptoPP)
NAMESPACE_BEGIN(Donna)

int curve25519_mult_SSE2(byte sharedKey[32], const byte secretKey[32], const byte othersKey[32])
{
    FixedSizeSecBlock<byte, 32> e;
    for (size_t i = 0;i < 32;++i)
        e[i] = secretKey[i];
    e[0] &= 0xf8; e[31] &= 0x7f; e[31] |= 0x40;

    ALIGN(16) bignum25519 nqx = {1}, nqpqz = {1}, nqz = {0}, nqpqx, zmone;
    packed32bignum25519 qx, qz, pqz, pqx;
    packed64bignum25519 nq, sq, sqscalar, prime, primex, primez, nqpq;
    bignum25519mulprecomp preq;
    size_t bit=0;

    curve25519_expand(nqpqx, othersKey);
    curve25519_mul_precompute(&preq, nqpqx);

    /* do bits 254..3 */
    for (size_t i = 254, lastbit=0; i >= 3; i--) {
        bit = (e[i/8] >> (i & 7)) & 1;
        curve25519_swap_conditional(nqx, nqpqx, (word32)(bit ^ lastbit));
        curve25519_swap_conditional(nqz, nqpqz, (word32)(bit ^ lastbit));
        lastbit = bit;

        curve25519_tangle32(qx, nqx, nqpqx); /* qx = [nqx,nqpqx] */
        curve25519_tangle32(qz, nqz, nqpqz); /* qz = [nqz,nqpqz] */

        curve25519_add_packed32(pqx, qx, qz); /* pqx = [nqx+nqz,nqpqx+nqpqz] */
        curve25519_sub_packed32(pqz, qx, qz); /* pqz = [nqx-nqz,nqpqx-nqpqz] */

        curve25519_make_nqpq(primex, primez, pqx, pqz); /* primex = [nqx+nqz,nqpqx+nqpqz], primez = [nqpqx-nqpqz,nqx-nqz] */
        curve25519_mul_packed64(prime, primex, primez); /* prime = [nqx+nqz,nqpqx+nqpqz] * [nqpqx-nqpqz,nqx-nqz] */
        curve25519_addsub_packed64(prime); /* prime = [prime.x+prime.z,prime.x-prime.z] */
        curve25519_square_packed64(nqpq, prime); /* nqpq = prime^2 */
        curve25519_untangle64(nqpqx, nqpqz, nqpq);
        curve25519_mul_precomputed(nqpqz, nqpqz, &preq); /* nqpqz = nqpqz * q */

        /* (((sq.x-sq.z)*121665)+sq.x) * (sq.x-sq.z) is equivalent to (sq.x*121666-sq.z*121665) * (sq.x-sq.z) */
        curve25519_make_nq(nq, pqx, pqz); /* nq = [nqx+nqz,nqx-nqz] */
        curve25519_square_packed64(sq, nq); /* sq = nq^2 */
        curve25519_121665_packed64(sqscalar, sq); /* sqscalar = sq * [121666,121665] */
        curve25519_final_nq(nq, sq, sqscalar); /* nq = [sq.x,sqscalar.x-sqscalar.z] * [sq.z,sq.x-sq.z] */
        curve25519_untangle64(nqx, nqz, nq);
    };

    /* it's possible to get rid of this swap with the swap in the above loop
       at the bottom instead of the top, but compilers seem to optimize better this way */
    curve25519_swap_conditional(nqx, nqpqx, (word32)bit);
    curve25519_swap_conditional(nqz, nqpqz, (word32)bit);

    /* do bits 2..0 */
    for (size_t i = 0; i < 3; i++) {
        curve25519_compute_nq(nq, nqx, nqz);
        curve25519_square_packed64(sq, nq); /* sq = nq^2 */
        curve25519_121665_packed64(sqscalar, sq); /* sqscalar = sq * [121666,121665] */
        curve25519_final_nq(nq, sq, sqscalar); /* nq = [sq.x,sqscalar.x-sqscalar.z] * [sq.z,sq.x-sq.z] */
        curve25519_untangle64(nqx, nqz, nq);
    }

    curve25519_recip(zmone, nqz);
    curve25519_mul(nqz, nqx, zmone);
    curve25519_contract(sharedKey, nqz);

    return 0;
}

NAMESPACE_END  // Donna
NAMESPACE_END  // CryptoPP

#endif  // CRYPTOPP_CURVE25519_SSE2