X-Git-Url: https://git.distorted.org.uk/~mdw/catacomb/blobdiff_plain/6d2bd7f11dcd292461bbd66e487e4367f05f9fe8..HEAD:/symm/gcm-x86ish-pclmul.S

diff --git a/symm/gcm-x86ish-pclmul.S b/symm/gcm-x86ish-pclmul.S
index 5edf56e1..fadeca58 100644
--- a/symm/gcm-x86ish-pclmul.S
+++ b/symm/gcm-x86ish-pclmul.S
@@ -73,14 +73,21 @@
 	//	u v = SUM_{0<=i,j<n} u_i v_j t^{i+j}
 	//
 	// Suppose instead that we're given Å© = SUM_{0<=i<n} u_{n-i-1} t^i
-	// and ṽ = SUM_{0<=j<n} v_{n-j-1} t^j, so the bits are backwards.
+	// and á¹½ = SUM_{0<=j<n} v_{n-j-1} t^j, so the bits are backwards.
 	// Then
 	//
-	//	ũ ṽ = SUM_{0<=i,j<n} u_{n-i-1} v_{n-j-1} t^{i+j}
+	//	Å© á¹½ = SUM_{0<=i,j<n} u_{n-i-1} v_{n-j-1} t^{i+j}
 	//	    = SUM_{0<=i,j<n} u_i v_j t^{2n-2-(i+j)}
 	//
 	// which is almost the bit-reversal of u v, only it's shifted right
-	// by one place.  Oh, well: we'll have to shift it back later.
+	// by one place.  Putting this another way, what we have is actually
+	// the bit reversal of the product u v t.  We could get the correct
+	// answer (modulo p(t)) if we'd sneakily divided one of the operands
+	// by t before we started.  Conveniently, v is actually the secret
+	// value k set up by the GCM `mktable' function, so we can arrange to
+	// actually store k/t (mod p(t)) and then the product will come out
+	// correct (modulo p(t)) and we won't have anything more to worry
+	// about here.
 	//
 	// That was important to think about, but there's not a great deal to
 	// do about it yet other than to convert what we've got from the
@@ -106,110 +113,25 @@
 	// use Karatsuba's identity here, but I suspect that loses more in
 	// the shifting, bit-twiddling, and dependency chains that it gains
 	// in saving a multiplication which otherwise pipelines well.
-	// xmm0 =			// (u_1; u_0)
-	// xmm1 =			// (v_1; v_0)
-	movdqa	xmm2, xmm1		// (v_1; v_0) again
-	movdqa	xmm3, xmm0		// (u_1; u_0) again
-	movdqa	xmm4, xmm0		// (u_1; u_0) yet again
+	// xmm0 =			// (u_0; u_1)
+	// xmm1 =			// (v_0; v_1)
+	movdqa	xmm2, xmm1		// (v_0; v_1) again
+	movdqa	xmm3, xmm0		// (u_0; u_1) again
+	movdqa	xmm4, xmm0		// (u_0; u_1) yet again
 	pclmulhqlqdq xmm2, xmm0		// u_1 v_0
 	pclmullqlqdq xmm0, xmm1		// u_1 v_1
 	pclmulhqlqdq xmm3, xmm1		// u_0 v_1
 	pclmulhqhqdq xmm4, xmm1		// u_0 v_0
 
 	// Arrange the pieces to form a double-precision polynomial.
-	pxor	xmm2, xmm3		// (m_1; m_0) = u_1 v_0 + u_0 v_1
-	movdqa	xmm1, xmm2		// (m_1; m_0) again
-	pslldq	xmm2, 8			// (0; m_1)
-	psrldq	xmm1, 8			// (m_0; 0)
-	pxor	xmm0, xmm2		// x_1 = u_1 v_1 + m_1
-	pxor	xmm1, xmm4		// x_0 = u_0 v_0 + t^64 m_0
-
-	// Two problems remain.  The first is that this product is shifted
-	// left (from GCM's backwards perspective) by one place, which is
-	// annoying.  Let's take care of that now.  Once this is done, we'll
-	// be properly in GCM's backwards bit-ordering, so xmm1 will hold the
-	// low half of the product and xmm0 the high half.  (The following
-	// diagrams show bit 0 consistently on the right.)
-	//
-	//				 xmm1
-	//    ,-------------.-------------.-------------.-------------.
-	//    | 0  x_0-x_30 |  x_31-x_62  |  x_63-x_94  |  x_95-x_126 |
-	//    `-------------^-------------^-------------^-------------'
-	//
-	//				 xmm0
-	//    ,-------------.-------------.-------------.-------------.
-	//    | x_127-x_158 | x_159-x_190 | x_191-x_222 | x_223-x_254 |
-	//    `-------------^-------------^-------------^-------------'
-	//
-	// We start by shifting each 32-bit lane right (from GCM's point of
-	// view -- physically, left) by one place, which gives us this:
-	//
-	//			     low (xmm3)
-	//    ,-------------.-------------.-------------.-------------.
-	//    | x_0-x_30  0 | x_32-x_62 0 | x_64-x_94 0 | x_96-x_126 0|
-	//    `-------------^-------------^-------------^-------------'
-	//
-	//			     high (xmm2)
-	//    ,-------------.-------------.-------------.-------------.
-	//    |x_128-x_158 0|x_160-x_190 0|x_192-x_222 0|x_224-x_254 0|
-	//    `-------------^-------------^-------------^-------------'
-	//
-	// but we've lost a bunch of bits.  We separately shift each lane
-	// left by 31 places to give us the bits we lost.
-	//
-	//			     low (xmm1)
-	//    ,-------------.-------------.-------------.-------------.
-	//    |    0...0    | 0...0  x_31 | 0...0  x_63 | 0...0  x_95 |
-	//    `-------------^-------------^-------------^-------------'
-	//
-	//			     high (xmm0)
-	//    ,-------------.-------------.-------------.-------------.
-	//    | 0...0 x_127 | 0...0 x_159 | 0...0 x_191 | 0...0 x_223 |
-	//    `-------------^-------------^-------------^-------------'
-	//
-	// Which is close, but we don't get a cigar yet.  To get the missing
-	// bits into position, we shift each of these right by a lane, but,
-	// alas, the x_127 falls off, so, separately, we shift the high
-	// register left by three lanes, so that everything is lined up
-	// properly when we OR them all together:
-	//
-	//			     low (xmm1)
-	//    ,-------------.-------------.-------------.-------------.
-	//    ? 0...0  x_31 | 0...0  x_63 | 0...0  x_95 |    0...0    |
-	//    `-------------^-------------^-------------^-------------'
-	//
-	//			     wrap (xmm4)
-	//    ,-------------.-------------.-------------.-------------.
-	//    |    0...0    |    0...0    |    0...0    | 0...0 x_127 |
-	//    `-------------^-------------^-------------^-------------'
-	//
-	//			     high (xmm0)
-	//    ,-------------.-------------.-------------.-------------.
-	//    | 0...0 x_159 | 0...0 x_191 | 0...0 x_223 |    0...0    |
-	//    `-------------^-------------^-------------^-------------'
-	//
-	// The `low' and `wrap' registers (xmm1, xmm3, xmm4) then collect the
-	// low 128 coefficients, while the `high' registers (xmm0, xmm2)
-	// collect the high 127 registers, leaving a zero bit at the most
-	// significant end as we expect.
-
-	// xmm0 =			// (x_7, x_6; x_5, x_4)
-	// xmm1 =			// (x_3, x_2; x_1, x_0)
-	movdqa	xmm3, xmm1		// (x_3, x_2; x_1, x_0) again
-	movdqa	xmm2, xmm0		// (x_7, x_6; x_5, x_4) again
-	psrld	xmm1, 31		// shifted left; just the carries
-	psrld	xmm0, 31
-	pslld	xmm3, 1			// shifted right, but dropped carries
-	pslld	xmm2, 1
-	movdqa	xmm4, xmm0		// another copy for the carry around
-	pslldq	xmm1, 4			// move carries over
-	pslldq	xmm0, 4
-	psrldq	xmm4, 12		// the big carry wraps around
-	por	xmm1, xmm3
-	por	xmm0, xmm2		// (y_7, y_6; y_5, y_4)
-	por	xmm1, xmm4		// (y_3, y_2; y_1, y_0)
-
-	// And the other problem is that the result needs to be reduced
+	pxor	xmm2, xmm3		// (m_0; m_1) = u_1 v_0 + u_0 v_1
+	movdqa	xmm1, xmm2		// (m_0; m_1) again
+	pslldq	xmm2, 8			// (m_1; 0)
+	psrldq	xmm1, 8			// (0; m_0)
+	pxor	xmm0, xmm2		// z_1 = u_1 v_1 + m_1
+	pxor	xmm1, xmm4		// z_0 = u_0 v_0 + t^64 m_0
+
+	// The remaining problem is that the result needs to be reduced
 	// modulo p(t) = t^128 + t^7 + t^2 + t + 1.  Let R = t^128 = t^7 +
 	// t^2 + t + 1 in our field.  So far, we've calculated z_0 and z_1
 	// such that z_0 + z_1 R = u v using the identity R = t^128: now we
@@ -217,28 +139,28 @@
 	// identity R = t^7 + t^2 + t + 1.
 	//
 	// We do this by working on each 32-bit word of the high half of z
-	// separately, so consider y_i, for some 4 <= i < 8.  Certainly, y_i
-	// t^{32i} = y_i R t^{32(i-4)} = (t^7 + t^2 + t + 1) y_i t^{32(i-4)},
+	// separately, so consider x_i, for some 4 <= i < 8.  Certainly, x_i
+	// t^{32i} = x_i R t^{32(i-4)} = (t^7 + t^2 + t + 1) x_i t^{32(i-4)},
 	// but we can't use that directly without breaking up the 32-bit word
-	// structure.  Instead, we start by considering just y_i t^7
-	// t^{32(i-4)}, which again looks tricky.  Now, split y_i = a_i +
+	// structure.  Instead, we start by considering just x_i t^7
+	// t^{32(i-4)}, which again looks tricky.  Now, split x_i = a_i +
 	// t^25 b_i, with deg a_i < 25; then
 	//
-	//	y_i t^7 t^{32(i-4)} = a_i t^7 t^{32(i-4)} + b_i t^{32(i-3)}
+	//	x_i t^7 t^{32(i-4)} = a_i t^7 t^{32(i-4)} + b_i t^{32(i-3)}
 	//
-	// We can similarly decompose y_i t^2 and y_i t into a pair of 32-bit
+	// We can similarly decompose x_i t^2 and x_i t into a pair of 32-bit
 	// contributions to the t^{32(i-4)} and t^{32(i-3)} words, but the
 	// splits are different.  This is lovely, with one small snag: when
-	// we do this to y_7, we end up with a contribution back into the
+	// we do this to x_7, we end up with a contribution back into the
 	// t^128 coefficient word.  But notice that only the low seven bits
 	// of this word are affected, so there's no knock-on contribution
 	// into the t^32 word.  Therefore, if we handle the high bits of each
 	// word together, and then the low bits, everything will be fine.
 
 	// First, shift the high bits down.
-	movdqa	xmm2, xmm0		// (y_7, y_6; y_5, y_4) again
-	movdqa	xmm3, xmm0		// (y_7, y_6; y_5, y_4) yet again
-	movdqa	xmm4, xmm0		// (y_7, y_6; y_5, y_4) again again
+	movdqa	xmm2, xmm0		// (x_4, x_5; x_6, x_7) again
+	movdqa	xmm3, xmm0		// (x_4, x_5; x_6, x_7) yet again
+	movdqa	xmm4, xmm0		// (x_4, x_5; x_6, x_7) again again
 	pslld	xmm2, 31		// the b_i for t
 	pslld	xmm3, 30		// the b_i for t^2
 	pslld	xmm4, 25		// the b_i for t^7
@@ -267,28 +189,20 @@
 	// respectively; leave with z = u v in xmm0.  Clobbers xmm1--xmm4.
 
 	// The multiplication is thankfully easy.
-	pclmullqlqdq xmm0, xmm1		// u v
-
-	// Shift the product up by one place.  After this, we're in GCM
-	// bizarro-world.
-	movdqa	xmm1, xmm0		// u v again
-	psrld	xmm0, 31		// shifted left; just the carries
-	pslld	xmm1, 1			// shifted right, but dropped carries
-	pslldq	xmm0, 4			// move carries over
-	por	xmm1, xmm0		// (y_3, y_2; y_1, y_0)
+	pclmullqlqdq xmm1, xmm0		// u v
 
 	// Now we must reduce.  This is essentially the same as the 128-bit
 	// case above, but mostly simpler because everything is smaller.  The
 	// polynomial this time is p(t) = t^64 + t^4 + t^3 + t + 1.
 
 	// First, we must detach the top (`low'!) half of the result.
-	movdqa	xmm0, xmm1		// (y_3, y_2; y_1, y_0) again
-	psrldq	xmm1, 8			// (y_1, y_0; 0, 0)
+	movdqa	xmm0, xmm1		// (x_0, x_1; x_2, x_3) again
+	psrldq	xmm1, 8			// (0, 0; x_0, x_1)
 
 	// Next, shift the high bits down.
-	movdqa	xmm2, xmm0		// (y_3, y_2; ?, ?) again
-	movdqa	xmm3, xmm0		// (y_3, y_2; ?, ?) yet again
-	movdqa	xmm4, xmm0		// (y_3, y_2; ?, ?) again again
+	movdqa	xmm2, xmm0		// (?, ?; x_2, x_3) again
+	movdqa	xmm3, xmm0		// (?, ?; x_2, x_3) yet again
+	movdqa	xmm4, xmm0		// (?, ?; x_2, x_3) again again
 	pslld	xmm2, 31		// b_i for t
 	pslld	xmm3, 29		// b_i for t^3
 	pslld	xmm4, 28		// b_i for t^4
@@ -325,11 +239,11 @@
 	// shift both of them up by four bytes before we start.  This will
 	// mean that the high 64 bits of the result (from GCM's viewpoint)
 	// will be zero.
-	// xmm0 =			// (0, u_2; u_1, u_0)
-	// xmm1 =			// (0, v_2; v_1, v_0)
-	movdqa	xmm2, xmm1		// (0, v_2; v_1, v_0) again
-	movdqa	xmm3, xmm0		// (0, u_2; u_1, u_0) again
-	movdqa	xmm4, xmm0		// (0, u_2; u_1, u_0) yet again
+	// xmm0 =			// (u_0, u_1; u_2, 0)
+	// xmm1 =			// (v_0, v_1; v_2, 0)
+	movdqa	xmm2, xmm1		// (v_0, v_1; v_2, 0) again
+	movdqa	xmm3, xmm0		// (u_0, u_1; u_2, 0) again
+	movdqa	xmm4, xmm0		// (u_0, u_1; u_2, 0) yet again
 	pclmulhqlqdq xmm2, xmm0		// u_2 (v_1 t^32 + v_0) = e_0
 	pclmullqlqdq xmm0, xmm1		// u_2 v_2 = d = (0; d)
 	pclmulhqlqdq xmm3, xmm1		// v_2 (u_1 t^32 + u_0) = e_1
@@ -341,37 +255,20 @@
 	// registers.  The answer we want is d t^128 + e t^64 + f, where e =
 	// e_0 + e_1.
 	//
-	// The place values for the two halves are (t^160, t^128; t^96, ?)
-	// and (?, t^64; t^32, 1).
-	psrldq	xmm0, 8			// (d; 0) = d t^128
+	// The place values for the two halves are (?, t^96; t^128, t^160)
+	// and (1, t^32; t^64, ?).  But we also want to shift the high part
+	// left by a word, for symmetry's sake.
+	psrldq	xmm0, 8			// (0; d) = d t^128
 	pxor	xmm2, xmm3		// e = (e_0 + e_1)
 	movdqa	xmm1, xmm4		// f again
 	pxor	xmm0, xmm2		// d t^128 + e t^64
 	psrldq	xmm2, 12		// e[31..0] t^64
 	psrldq	xmm1, 4			// f[95..0]
-	pslldq	xmm4, 8			// f[127..96]
+	pslldq	xmm4, 12		// f[127..96], shifted
+	pslldq	xmm0, 4			// shift high 96 bits
 	pxor	xmm1, xmm2		// low 96 bits of result
 	pxor	xmm0, xmm4		// high 96 bits of result
 
-	// Next, shift everything one bit to the left to compensate for GCM's
-	// strange ordering.  This will be easier if we shift up the high
-	// half by a word before we start.  After this we're in GCM bizarro-
-	// world.
-	movdqa	xmm3, xmm1		// low half again
-	pslldq	xmm0, 4			// shift high half
-	psrld	xmm1, 31		// shift low half down: just carries
-	movdqa	xmm2, xmm0		// copy high half
-	pslld	xmm3, 1			// shift low half down: drop carries
-	psrld	xmm0, 31		// shift high half up: just carries
-	pslld	xmm2, 1			// shift high half down: drop carries
-	movdqa	xmm4, xmm0		// copy high carries for carry-around
-	pslldq	xmm0, 4			// shift carries down
-	pslldq	xmm1, 4
-	psrldq	xmm4, 12		// the big carry wraps around
-	por	xmm1, xmm3
-	por	xmm0, xmm2
-	por	xmm1, xmm4
-
 	// Finally, the reduction.  This is essentially the same as the
 	// 128-bit case, except that the polynomial is p(t) = t^96 + t^10 +
 	// t^9 + t^6 + 1.  The degrees are larger but not enough to cause
@@ -411,101 +308,76 @@
 	// are unimportant.  Clobbers xmm2--xmm7.
 
 	// Start multiplying and accumulating pieces of product.
-	// xmm0 =			// (u_2; u_1)
-	// xmm1 =			// (u_0; ?)
-	// xmm2 =			// (v_2; v_1)
-	// xmm3 =			// (v_0; ?)
-	movdqa	xmm4, xmm0		// (u_2; u_1) again
-	movdqa	xmm5, xmm0		// (u_2; u_1) yet again
-	movdqa	xmm6, xmm0		// (u_2; u_1) again again
-	movdqa	xmm7, xmm1		// (u_0; ?) again
-	punpcklqdq xmm1, xmm3		// (u_0; v_0)
+	// xmm0 =			// (u_1; u_2)
+	// xmm1 =			// (?; u_0)
+	// xmm2 =			// (v_1; v_2)
+	// xmm3 =			// (?; v_0)
+	movdqa	xmm4, xmm0		// (u_1; u_2) again
+	movdqa	xmm5, xmm0		// (u_1; u_2) yet again
+	movdqa	xmm6, xmm0		// (u_1; u_2) again again
+	movdqa	xmm7, xmm3		// (?; v_0) again
+	punpcklqdq xmm3, xmm1		// (u_0; v_0)
 	pclmulhqhqdq xmm4, xmm2		// u_1 v_1
-	pclmullqlqdq xmm3, xmm0		// u_2 v_0
+	pclmullqlqdq xmm1, xmm2		// u_0 v_2
 	pclmullqhqdq xmm5, xmm2		// u_2 v_1
 	pclmulhqlqdq xmm6, xmm2		// u_1 v_2
-	pxor	xmm4, xmm3		// u_2 v_0 + u_1 v_1
-	pclmullqlqdq xmm7, xmm2		// u_0 v_2
+	pxor	xmm1, xmm4		// u_0 v_2 + u_1 v_1
+	pclmullqlqdq xmm7, xmm0		// u_2 v_0
 	pxor	xmm5, xmm6		// b = u_2 v_1 + u_1 v_2
-	movdqa	xmm6, xmm0		// (u_2; u_1) like a bad penny
-	pxor	xmm4, xmm7		// c = u_0 v_2 + u_1 v_1 + u_2 v_0
+	movdqa	xmm6, xmm0		// (u_1; u_2) like a bad penny
+	pxor	xmm1, xmm7		// c = u_0 v_2 + u_1 v_1 + u_2 v_0
 	pclmullqlqdq xmm0, xmm2		// a = u_2 v_2
-	pclmulhqhqdq xmm6, xmm1		// u_1 v_0
-	pclmulhqlqdq xmm2, xmm1		// u_0 v_1
-	pclmullqhqdq xmm1, xmm1		// e = u_0 v_0
-	pxor	xmm2, xmm6		// d = u_1 v_0 + u_0 v_1
-
-	// Next, the piecing together of the product.
-	// xmm0 =			// (a_1; a_0) = a = u_2 v_2
-	// xmm5 =			// (b_1; b_0) = b = u_1 v_2 + u_2 v_1
-	// xmm4 =			// (c_1; c_0) = c = u_0 v_2 +
+	pclmulhqlqdq xmm6, xmm3		// u_1 v_0
+	pclmulhqhqdq xmm2, xmm3		// u_0 v_1
+	pclmullqhqdq xmm3, xmm3		// e = u_0 v_0
+	pxor	xmm6, xmm2		// d = u_1 v_0 + u_0 v_1
+
+	// Next, the piecing together of the product.  There's significant
+	// work here to leave the completed pieces in sensible registers.
+	// xmm0 =			// (a_0; a_1) = a = u_2 v_2
+	// xmm5 =			// (b_0; b_1) = b = u_1 v_2 + u_2 v_1
+	// xmm1 =			// (c_0; c_1) = c = u_0 v_2 +
 					//	u_1 v_1 + u_2 v_0
-	// xmm2 =			// (d_1; d_0) = d = u_0 v_1 + u_1 v_0
-	// xmm1 =			// (e_1; e_0) = e = u_0 v_0
-	// xmm3, xmm6, xmm7 spare
-	movdqa	xmm3, xmm2		// (d_1; d_0) again
-	movdqa	xmm6, xmm5		// (b_1; b_0) again
-	pslldq	xmm2, 8			// (0; d_1)
-	psrldq	xmm5, 8			// (b_0; 0)
-	psrldq	xmm3, 8			// (d_0; 0)
-	pslldq	xmm6, 8			// (0; b_1)
-	pxor	xmm5, xmm2		// (b_0; d_1)
-	pxor	xmm0, xmm6		// x_2 = (a_1; a_0 + b_1)
-	pxor	xmm3, xmm1		// x_0 = (e_1 + d_0; e_0)
-	pxor	xmm4, xmm5		// x_1 = (b_0 + c_1; c_0 + d_1)
-
-	// Now, shift it right (from GCM's point of view) by one bit, and try
-	// to leave the result in less random registers.  After this, we'll
-	// be in GCM bizarro-world.
-	// xmm1, xmm2, xmm5, xmm6, xmm7 spare
-	movdqa	xmm5, xmm0		// copy x_2
-	movdqa	xmm1, xmm4		// copy x_1
-	movdqa	xmm2, xmm3		// copy x_0
-	psrld	xmm0, 31		// x_2 carries
-	psrld	xmm4, 31		// x_1 carries
-	psrld	xmm3, 31		// x_0 carries
-	pslld	xmm5, 1			// x_2 shifted
-	pslld	xmm1, 1			// x_1 shifted
-	pslld	xmm2, 1			// x_0 shifted
-	movdqa	xmm6, xmm0		// x_2 carry copy
-	movdqa	xmm7, xmm4		// x_1 carry copy
-	pslldq	xmm0, 4			// x_2 carry shifted
-	pslldq	xmm4, 4			// x_1 carry shifted
-	pslldq	xmm3, 4			// x_0 carry shifted
-	psrldq	xmm6, 12		// x_2 carry out
-	psrldq	xmm7, 12		// x_1 carry out
-	por	xmm0, xmm5		// (y_5; y_4)
-	por	xmm1, xmm4
-	por	xmm2, xmm3
-	por	xmm1, xmm6		// (y_3; y_2)
-	por	xmm2, xmm7		// (y_1; y_0)
+	// xmm6 =			// (d_0; d_1) = d = u_0 v_1 + u_1 v_0
+	// xmm3 =			// (e_0; e_1) = e = u_0 v_0
+	// xmm2, xmm4, xmm7 spare
+	movdqa	xmm2, xmm6		// (d_0; d_1) again
+	movdqa	xmm4, xmm5		// (b_0; b_1) again
+	pslldq	xmm6, 8			// (d_1; 0)
+	psrldq	xmm5, 8			// (0; b_0)
+	psrldq	xmm2, 8			// (0; d_0)
+	pslldq	xmm4, 8			// (b_1; 0)
+	pxor	xmm5, xmm6		// (d_1; b_0)
+	pxor	xmm0, xmm4		// (x_4; x_5) = (a_0 + b_1; a_1)
+	pxor	xmm2, xmm3		// (x_0; x_1) = (e_0; e_1 + d_0)
+	pxor	xmm1, xmm5	       // (x_2; x_3) = (c_0 + d_1; b_0 + c_1)
 
 	// Next, the reduction.  Our polynomial this time is p(x) = t^192 +
 	// t^7 + t^2 + t + 1.  Yes, the magic numbers are the same as the
 	// 128-bit case.  I don't know why.
 
 	// First, shift the high bits down.
-	// xmm0 =			// (y_5; y_4)
-	// xmm1 =			// (y_3; y_2)
-	// xmm2 =			// (y_1; y_0)
+	// xmm0 =			// (x_4; x_5)
+	// xmm1 =			// (x_2; x_3)
+	// xmm2 =			// (x_0; x_1)
 	// xmm3--xmm7 spare
-	movdqa	xmm3, xmm0		// (y_5; y_4) copy
-	movdqa	xmm4, xmm0		// (y_5; y_4) copy
-	movdqa	xmm5, xmm0		// (y_5; y_4) copy
-	pslld	xmm3, 31		// (y_5; y_4) b_i for t
-	pslld	xmm4, 30		// (y_5; y_4) b_i for t^2
-	pslld	xmm5, 25		// (y_5; y_4) b_i for t^7
-	 movq	xmm6, xmm1		// (y_3; 0) copy
+	movdqa	xmm3, xmm0		// (x_4; x_5) copy
+	movdqa	xmm4, xmm0		// (x_4; x_5) copy
+	movdqa	xmm5, xmm0		// (x_4; x_5) copy
+	pslld	xmm3, 31		// (x_4; x_5) b_i for t
+	pslld	xmm4, 30		// (x_4; x_5) b_i for t^2
+	pslld	xmm5, 25		// (x_4; x_5) b_i for t^7
+	 movq	xmm6, xmm1		// (0; x_3) copy
 	pxor	xmm3, xmm4
-	 movq	xmm7, xmm1		// (y_3; 0) copy
+	 movq	xmm7, xmm1		// (0; x_3) copy
 	pxor	xmm3, xmm5
-	 movq	xmm5, xmm1		// (y_3; 0) copy
-	movdqa	xmm4, xmm3		// (y_5; y_4) b_i combined
-	 pslld	xmm6, 31		// (y_3; 0) b_i for t
-	 pslld	xmm7, 30		// (y_3; 0) b_i for t^2
-	 pslld	xmm5, 25		// (y_3; 0) b_i for t^7
-	psrldq	xmm3, 12		// (y_5; y_4) low contrib
-	pslldq	xmm4, 4			// (y_5; y_4) high contrib
+	 movq	xmm5, xmm1		// (0; x_3) copy
+	movdqa	xmm4, xmm3		// (x_4; x_5) b_i combined
+	 pslld	xmm6, 31		// (0; x_3) b_i for t
+	 pslld	xmm7, 30		// (0; x_3) b_i for t^2
+	 pslld	xmm5, 25		// (0; x_3) b_i for t^7
+	psrldq	xmm3, 12		// (x_4; x_5) low contrib
+	pslldq	xmm4, 4			// (x_4; x_5) high contrib
 	 pxor	xmm6, xmm7
 	pxor	xmm2, xmm3
 	 pxor	xmm6, xmm5
@@ -515,17 +387,17 @@
 
 	// And finally shift the low bits up.  Unfortunately, we also have to
 	// split the low bits out.
-	// xmm0 =			// (y'_5; y'_4)
-	// xmm1 =			// (y'_3; y'_2)
-	// xmm2 =			// (y'_1; y'_0)
-	 movdqa xmm5, xmm1		// copies of (y'_3; y'_2)
+	// xmm0 =			// (x'_4; x'_5)
+	// xmm1 =			// (x'_2; x'_3)
+	// xmm2 =			// (x'_0; x'_1)
+	 movdqa xmm5, xmm1		// copies of (x'_2; x'_3)
 	 movdqa	xmm6, xmm1
 	 movdqa	xmm7, xmm1
-	  psrldq xmm1, 8		// bring down (y'_2; ?)
-	movdqa	xmm3, xmm0		// copies of (y'_5; y'_4)
+	  psrldq xmm1, 8		// bring down (?; x'_2)
+	movdqa	xmm3, xmm0		// copies of (x'_4; x'_5)
 	movdqa	xmm4, xmm0
-	  punpcklqdq  xmm1, xmm2	// (y'_2; y'_1)
-	  psrldq xmm2, 8		// (y'_0; ?)
+	  punpcklqdq  xmm1, xmm2	// (x'_1; x'_2)
+	  psrldq xmm2, 8		// (?; x'_0)
 	 pxor	xmm2, xmm5		// low half and unit contrib
 	pxor	xmm1, xmm0
 	 psrld	xmm5, 1
@@ -540,7 +412,7 @@
 	pxor	xmm0, xmm4
 	 pxor	xmm5, xmm2		// mix everything together
 	pxor	xmm0, xmm1
-	 movq	xmm1, xmm5		// shunt (z_0; ?) into proper place
+	 movq	xmm1, xmm5		// shunt (?; z_0) into proper place
 .endm
 
 .macro	mul256
@@ -559,7 +431,7 @@
 	//
 	//	q = r s = (u_0 + u_1) (v_0 + v_1)
 	//	  = (u_0 v_0) + (u1 v_1) + (u_0 v_1 + u_1 v_0)
-	//	  = a + d + c
+	//	  = a + c + b
 	//
 	// The first two terms we've already calculated; the last is the
 	// remaining one we want.  We'll set B = t^128.  We know how to do
@@ -570,10 +442,10 @@
 	// On x86, there aren't quite enough registers, so spill one for a
 	// bit.  On AMD64, we can keep on going, so it's all good.
 
-	// xmm0 =			// u_1 = (u_11; u_10)
-	// xmm1 =			// u_0 = (u_01; u_00)
-	// xmm2 =			// v_1 = (v_11; v_10)
-	// xmm3 =			// v_0 = (v_01; v_00)
+	// xmm0 =			// u_1 = (u_10; u_11)
+	// xmm1 =			// u_0 = (u_00; u_01)
+	// xmm2 =			// v_1 = (v_10; v_11)
+	// xmm3 =			// v_0 = (v_00; v_01)
 	movdqa	xmm4, xmm0		// u_1 again
 #if CPUFAM_X86
 	movdqa	[SP + 0], xmm3
@@ -581,8 +453,8 @@
 	movdqa	xmm8, xmm3
 #  define V0 xmm8
 #endif
-	pxor	xmm4, xmm1		// u_* = (u_01 + u_11; u_00 + u_10)
-	pxor	xmm3, xmm2		// v_* = (v_01 + v_11; v_00 + v_10)
+	pxor	xmm4, xmm1		// u_* = (u_00 + u_10; u_01 + u_11)
+	pxor	xmm3, xmm2		// v_* = (v_00 + v_10; v_01 + v_11)
 
 	// Start by building the cross product, q = u_* v_*.
 	movdqa	xmm7, xmm4		// more copies of u_*
@@ -615,7 +487,7 @@
 	movdqa	xmm3, xmm0
 	pslldq	xmm0, 8
 	psrldq	xmm3, 8
-	pxor	xmm4, xmm0		// x_1 = a_1
+	pxor	xmm4, xmm0		// x_3 = a_1
 	pxor	xmm7, xmm3		// a_0
 
 	// Mix that into the product now forming in xmm4--xmm7.
@@ -645,91 +517,55 @@
 
 #undef V0
 
-	// Now we need to shift that whole lot one bit to the left.  This
-	// will also give us an opportunity to put the product back in
-	// xmm0--xmm3.  This is a slightly merry dance because it's nearly
-	// pipelined but we don't have enough registers.
-	//
-	// After this, we'll be in GCM bizarro-world.
-	movdqa	xmm0, xmm4		// x_3 again
-	psrld	xmm4, 31		// x_3 carries
-	pslld	xmm0, 1			// x_3 shifted left
-	movdqa	xmm3, xmm4		// x_3 copy carries
-	 movdqa	xmm1, xmm5		// x_2 again
-	pslldq	xmm4, 4			// x_3 carries shifted up
-	 psrld	xmm5, 31		// x_2 carries
-	psrldq	xmm3, 12		// x_3 big carry out
-	 pslld	xmm1, 1			// x_2 shifted left
-	por	xmm0, xmm4		// x_3 mixed together
-	 movdqa	xmm4, xmm5		// x_2 copy carries
-	  movdqa xmm2, xmm6		// x_1 again
-	 pslldq	xmm5, 4			// x_2 carries shifted up
-	  psrld	xmm6, 31		// x_1 carries
-	 psrldq	xmm4, 12		// x_2 big carry out
-	  pslld	xmm2, 1			// x_1 shifted
-	 por	xmm1, xmm5		// x_2 mixed together
-	  movdqa xmm5, xmm6		// x_1 copy carries
-	 por	xmm1, xmm3		// x_2 with carry from x_3
-	   movdqa xmm3, xmm7		// x_0 again
-	  pslldq xmm6, 4		// x_1 carries shifted up
-	   psrld xmm7, 31		// x_2 carries
-	  psrldq xmm5, 12		// x_1 big carry out
-	   pslld xmm3, 1		// x_0 shifted
-	  por	xmm2, xmm6		// x_1 mixed together
-	   pslldq xmm7, 4		// x_0 carries shifted up
-	  por	xmm2, xmm4		// x_1 with carry from x_2
-	   por	xmm3, xmm7		// x_0 mixed together
-	   por	xmm3, xmm5		// x_0 with carry from x_1
-
 	// Now we must reduce.  This is essentially the same as the 128-bit
 	// case above, but more complicated because everything is bigger.
 	// The polynomial this time is p(t) = t^256 + t^10 + t^5 + t^2 + 1.
 
 	// First, shift the high bits down.
-	movdqa	xmm4, xmm0		// y_3 again
-	movdqa	xmm5, xmm0		// y_3 yet again
-	movdqa	xmm6, xmm0		// y_3 again again
-	pslld	xmm4, 30		// y_3: b_i for t^2
-	pslld	xmm5, 27		// y_3: b_i for t^5
-	pslld	xmm6, 22		// y_3: b_i for t^10
-	 movdqa	xmm7, xmm1		// y_2 again
-	pxor	xmm4, xmm5
-	 movdqa	xmm5, xmm1		// y_2 again
-	pxor	xmm4, xmm6
-	 movdqa	xmm6, xmm1		// y_2 again
-	 pslld	xmm7, 30		// y_2: b_i for t^2
-	 pslld	xmm5, 27		// y_2: b_i for t^5
-	 pslld	xmm6, 22		// y_2: b_i for t^10
-	 pxor	xmm7, xmm5
-	movdqa	xmm5, xmm4
-	 pxor	xmm7, xmm6
-	psrldq	xmm4, 4
-	 movdqa	xmm6, xmm7
-	pslldq	xmm5, 12
-	 psrldq	xmm7, 4
-	pxor	xmm2, xmm4
-	 pslldq	xmm6, 12
-	 pxor	xmm3, xmm7
-	pxor	xmm1, xmm5
-	 pxor	xmm2, xmm6
+	movdqa	xmm0, xmm4		// x_3 again
+	movdqa	xmm1, xmm4		// x_3 yet again
+	movdqa	xmm2, xmm4		// x_3 again again
+	pslld	xmm0, 30		// x_3: b_i for t^2
+	pslld	xmm1, 27		// x_3: b_i for t^5
+	pslld	xmm2, 22		// x_3: b_i for t^10
+	 movdqa	xmm3, xmm5		// x_2 again
+	pxor	xmm0, xmm1
+	 movdqa	xmm1, xmm5		// x_2 again
+	pxor	xmm0, xmm2		// b_3
+	 movdqa	xmm2, xmm5		// x_2 again
+	 pslld	xmm3, 30		// x_2: b_i for t^2
+	 pslld	xmm1, 27		// x_2: b_i for t^5
+	 pslld	xmm2, 22		// x_2: b_i for t^10
+	 pxor	xmm3, xmm1
+	movdqa	xmm1, xmm0
+	 pxor	xmm3, xmm2		// b_2
+	psrldq	xmm0, 4
+	 movdqa	xmm2, xmm3
+	pslldq	xmm1, 12
+	 psrldq	xmm3, 4
+	pxor	xmm6, xmm0
+	 pslldq	xmm2, 12
+	 pxor	xmm7, xmm3
+	pxor	xmm5, xmm1
+	 pxor	xmm6, xmm2
 
 	// And then shift the low bits up.
-	movdqa	xmm4, xmm0		// y_3 again
-	 movdqa	xmm5, xmm1		// y_2 again
-	movdqa	xmm6, xmm0		// y_3 yet again
-	 movdqa	xmm7, xmm1		// y_2 yet again
-	pxor	xmm2, xmm0		// y_1 and unit contrib from y_3
-	 pxor	xmm3, xmm1		// y_0 and unit contrib from y_2
-	psrld	xmm0, 2
-	 psrld	xmm1, 2
-	psrld	xmm4, 5
-	 psrld	xmm5, 5
-	psrld	xmm6, 10
-	 psrld	xmm7, 10
-	pxor	xmm0, xmm2		// y_1, with y_3 units and t^2
-	 pxor	xmm1, xmm3		// y_0, with y_2 units and t^2
-	pxor	xmm4, xmm6		// y_3 t^5 and t^10 contribs
-	 pxor	xmm5, xmm7		// y_2 t^5 and t^10 contribs
+	movdqa	xmm0, xmm4		// x_3 again
+	 movdqa	xmm1, xmm5		// x_2 again
+	movdqa	xmm2, xmm4		// x_3 yet again
+	 movdqa	xmm3, xmm5		// x_2 yet again
+	pxor	xmm6, xmm4		// x_1 and unit contrib from x_3
+	 pxor	xmm7, xmm5		// x_0 and unit contrib from x_2
+	psrld	xmm4, 2
+	 psrld	xmm5, 2
+	psrld	xmm0, 5
+	 psrld	xmm1, 5
+	psrld	xmm2, 10
+	 psrld	xmm3, 10
+	pxor	xmm4, xmm6		// x_1, with x_3 units and t^2
+	 pxor	xmm5, xmm7		// x_0, with x_2 units and t^2
+	pxor	xmm0, xmm2		// x_3 t^5 and t^10 contribs
+	 pxor	xmm1, xmm3		// x_2 t^5 and t^10 contribs
 	pxor	xmm0, xmm4		// high half of reduced result
 	pxor	xmm1, xmm5		// low half; all done
 .endm
@@ -752,7 +588,7 @@
 //     the /last/ byte in the block.  If the block size is not a multiple of
 //     16 bytes, then there must be padding.  96-bit blocks are weird: the
 //     padding is inserted at the /least/ significant end, so the register
-//     holds (0, x_0; x_1, x_2); otherwise, the padding goes at the most
+//     holds (x_2, x_1; x_0, 0); otherwise, the padding goes at the most
 //     significant end.
 //
 //   * The `words' format consists of a sequence of bytes, as in the
@@ -777,9 +613,9 @@ SSEFUNC(gcm_mulk_128b_x86ish_pclmul)
   endprologue
 	movdqu	xmm0, [A]
 	movdqu	xmm1, [K]
-	pshufd	xmm0, xmm0, SHUF(3, 2, 1, 0)
+	pshufd	xmm0, xmm0, SHUF(0, 1, 2, 3)
 	mul128
-	pshufd	xmm0, xmm0, SHUF(3, 2, 1, 0)
+	pshufd	xmm0, xmm0, SHUF(0, 1, 2, 3)
 	movdqu	[A], xmm0
 	ret
 ENDFUNC
@@ -817,9 +653,9 @@ SSEFUNC(gcm_mulk_64b_x86ish_pclmul)
   endprologue
 	movq	xmm0, [A]
 	movq	xmm1, [K]
-	pshufd	xmm0, xmm0, SHUF(1, 0, 3, 3)
+	pshufd	xmm0, xmm0, SHUF(3, 3, 0, 1)
 	mul64
-	pshufd	xmm0, xmm0, SHUF(1, 0, 3, 3)
+	pshufd	xmm0, xmm0, SHUF(3, 3, 0, 1)
 	movq	[A], xmm0
 	ret
 ENDFUNC
@@ -860,9 +696,9 @@ SSEFUNC(gcm_mulk_96b_x86ish_pclmul)
 	movd	xmm2, [A + 8]
 	movdqu	xmm1, [K]
 	punpcklqdq xmm0, xmm2
-	pshufd	xmm0, xmm0, SHUF(3, 2, 1, 0)
+	pshufd	xmm0, xmm0, SHUF(0, 1, 2, 3)
 	mul96
-	pshufd	xmm1, xmm0, SHUF(3, 2, 1, 0)
+	pshufd	xmm1, xmm0, SHUF(0, 1, 2, 3)
 	psrldq	xmm0, 4
 	movq	[A + 0], xmm1
 	movd	[A + 8], xmm0
@@ -914,11 +750,11 @@ SSEFUNC(gcm_mulk_192b_x86ish_pclmul)
 	movq	xmm1, [A + 0]
 	movdqu	xmm2, [K + 0]
 	movq	xmm3, [K + 16]
-	pshufd	xmm0, xmm0, SHUF(3, 2, 1, 0)
-	pshufd	xmm1, xmm1, SHUF(1, 0, 3, 3)
+	pshufd	xmm0, xmm0, SHUF(0, 1, 2, 3)
+	pshufd	xmm1, xmm1, SHUF(3, 3, 0, 1)
 	mul192
-	pshufd	xmm0, xmm0, SHUF(3, 2, 1, 0)
-	pshufd	xmm1, xmm1, SHUF(1, 0, 3, 3)
+	pshufd	xmm0, xmm0, SHUF(0, 1, 2, 3)
+	pshufd	xmm1, xmm1, SHUF(3, 3, 0, 1)
 	movdqu	[A + 8], xmm0
 	movq	[A + 0], xmm1
 #if CPUFAM_AMD64 && ABI_WIN
@@ -988,11 +824,11 @@ SSEFUNC(gcm_mulk_256b_x86ish_pclmul)
 	movdqu	xmm1, [A + 0]
 	movdqu	xmm2, [K + 0]
 	movdqu	xmm3, [K + 16]
-	pshufd	xmm0, xmm0, SHUF(3, 2, 1, 0)
-	pshufd	xmm1, xmm1, SHUF(3, 2, 1, 0)
+	pshufd	xmm0, xmm0, SHUF(0, 1, 2, 3)
+	pshufd	xmm1, xmm1, SHUF(0, 1, 2, 3)
 	mul256
-	pshufd	xmm0, xmm0, SHUF(3, 2, 1, 0)
-	pshufd	xmm1, xmm1, SHUF(3, 2, 1, 0)
+	pshufd	xmm0, xmm0, SHUF(0, 1, 2, 3)
+	pshufd	xmm1, xmm1, SHUF(0, 1, 2, 3)
 	movdqu	[A + 16], xmm0
 	movdqu	[A + 0], xmm1
 #if CPUFAM_X86