```/* Apple Copyright 2009
CoreOS - vector & Numerics, cclee 10-22-09

This following source code implements a vectorized version of adler32 computation that is defined in zlib.
The target architectures are x86_64 and i386.

Given 2 unsigned 32-bit alder and sum2 (both pre-modulo by BASE=65521) and a sequence of input bytes x[0],...x[N-1].
The adler-sum2 pair is updated according to

for (i=0;i<N;i++) {
}

To reduce/save the modulo operations, it can be shown that, if initial alder and sum2 are less than BASE(=65521),
adler and sum2 (in 32-bit representation), will never overflow for the next NMAX=5552 bytes. This simplifies the
algorithm to

for (i=0;i<N;i+=NMAX) {
for (k=0;k<NMAX;k++) {
}
sum2%=BASE;
}

The hand optimization of this function is now reduced to

for (k=0;k<NMAX;k++) {
}

This subtask turns out to be very vecterizable. Suppose we perform the adler/sum2 update once per K bytes,

for (k=0;k<K;k++) {
}

It can be shown that the sum2-adler pair can be updated according to

adler += (x[0] + x[1] + ... + x[K-1]);
sum2 += (x[0]*K + x[1]*(K-1) + ... + x[K-1]*1);

The last 2 equations obviously show that the adler-sum2 pair update can be speeded up using vector processor.
The input vector [ x[0] x[1] ... x[K-1] ]. And we need two coefficient vectors
[ 1 1 1 ... 1 ] for adler update.
[ K K-1 ... 1 ] for sum2 update.

The implementation below reads vector (K=16,32,48,64) into xmm registers, and sets up coefficient vectors in xmm
registers. It then uses SSE instructions to perform the aforementioned vector computation.

For i386, NMAX/16 = 347, whenever possible (NMAX-bytes block), it calls 173 times of macro code DO32 (K=32),
followed by a single DO16 (K=16), before calling a modulo operation for adler and sum2.

For x86_64 (where more xmm registers are available), NMAX/64 = 86, whenever possible (NMAX-bytes block),
it calls 86 times of macro code DO64 (K=64), followed by a single DO48 (K=48),
before calling a modulo operation for adler and sum2.

*/

/* added cpu_capability to detect kHasSupplementalSSE3 to branch into code w or wo SupplementalSSE3

Previously, ssse3 code was intentionally turned off, because Yonah does not support ssse3
add code here to probe cpu_capabilities for ssse3 support
if ssse3 is supported, branch to ssse3-based code, otherwise use the original code

cclee 5-3-10
*/

#define BASE 65521  /* largest prime smaller than 65536 */
#define NMAX 5552 	/* NMAX is the largest n such that 255n(n+1)/2 + (n+1)(BASE-1) <= 2^32-1 */

// uLong	adler32_vec(unsigned int adler, unsigned int sum2, const Bytef *buf, int len) {
//    unsigned n;
//    while (len >= NMAX) {
//        len -= NMAX;
//        n = NMAX / 16;          /* NMAX is divisible by 16 */
//        do {
//            DO16(buf);          /* 16 sums unrolled */
//            buf += 16;
//        } while (--n);
//        MOD(sum2);
//    }
//    if (len) {                  /* avoid modulos if none remaining */
//        while (len >= 16) {
//            len -= 16;
//            DO16(buf);
//            buf += 16;
//        }
//        while (len--) {
//        }
//        MOD(sum2);
//    }
//    return adler | (sum2 << 16);
// }

#if (defined __i386__ || defined __x86_64__)

#include <i386/cpu_capabilities.h>

.text
.align 4,0x90

#if (defined __i386__)

pushl	%ebp
movl	%esp, %ebp

pushl	%ebx
pushl	%edi
pushl	%esi

#ifdef	KERNEL 						// if this is for kernel, need to save xmm registers
subl	\$140, %esp				// to save %xmm0-%xmm7 into stack, extra 12 to align %esp to 16-byte boundary
movaps	%xmm0, 0(%esp)		// save xmm0, offset -12 for ebx/edi/esi
movaps	%xmm1, 16(%esp)		// save xmm1
movaps	%xmm2, 32(%esp)		// save xmm2
movaps	%xmm3, 48(%esp)		// save xmm3
movaps	%xmm4, 64(%esp)		// save xmm4
movaps	%xmm5, 80(%esp)		// save xmm5
movaps	%xmm6, 96(%esp)		// save xmm6
movaps	%xmm7, 112(%esp)		// save xmm7, if this is for SSSE3 or above
#endif

#define	sum2	%esi				// 12(%ebp)
#define	buf		%ecx				// 16(%ebp)
#define	len		%ebx				// 20(%ebp)
#define	zero	%xmm0
#define ones	%xmm5

movl	12(%ebp), sum2
movl	16(%ebp), buf			// use ecx as buf pointer
movl	20(%ebp), len

.macro		modulo_BASE
movl		\$\$-2146992015, %eax		// 1/BASE in Q47
shrl		\$\$15, %edx				// edx is now the floor integer of adler and BASE
imull		\$\$BASE, %edx, %edx		// edx * BASE
movl		\$\$-2146992015, %eax		// 1/BASE in Q47
mull		sum2					// edx:eax = sum2 divided by BASE in Q47
shrl		\$\$15, %edx				// edx is now the floor integer of sum2 and BASE
imull		\$\$BASE, %edx, %eax		// eax = edx * BASE
subl		%eax, sum2				// sum2 -= sdx*BASE
.endmacro

// update adler/sum2 according to a new 16-byte vector
.macro		DO16
movaps		(buf), %xmm1			// 16 bytes vector, in xmm1
movaps		%xmm1, %xmm3			// a copy of the vector, used for unsigned byte in the destination of pmaddubsw
addl		\$\$16, buf				// buf -> next vector
pmaddubsw	%xmm4, %xmm3			// 8 16-bit words to be added for sum2 in xmm3
movhlps		%xmm1, %xmm2			// higher 16-bit word (for adler) in xmm2
pmaddwd		ones, %xmm3				// 4 32-bit elements to be added for sum2 in xmm3
movhlps		%xmm3, %xmm2			// 2 higher 32-bit elements of xmm3 to be added to lower 2 32-bit elements
paddd		%xmm2, %xmm3			// 2 32-bits elements in xmm3 to be added to sum2
movd		%xmm3, %edx				// to be added to sum2
psrlq		\$\$32, %xmm3				// another 32-bit to be added to sum2
addl		%edx, sum2				// sum2 += 1st half of update
movd		%xmm3, %edx				// to be added to sum2
addl		%edx, sum2				// sum2 += 2nd half of update
.endm

// update adler/sum2 according to a new 32-byte vector
.macro		DO32
movaps		(buf), %xmm1			// 1st 16 bytes vector
movaps		16(buf), %xmm7			// 2nd 16 bytes vector
movaps		%xmm1, %xmm3			// a copy of 1st vector, used for unsigned byte in the destination of pmaddubsw
movaps		%xmm7, %xmm2			// a copy of 2nd vector, used for unsigned byte in the destination of pmaddubsw
pmaddubsw	%xmm6, %xmm3			// 8 16-bit words to be added for sum2 in xmm3
pmaddubsw	%xmm4, %xmm2			// 8 16-bit words to be added for sum2 in xmm2
paddd		%xmm2, %xmm3			// 8 16-bit words to be added for sum2 in xmm3
addl		\$\$32, buf				// buf -> vector for next iteration
movhlps		%xmm1, %xmm2			// higher 16-bit word (for adler) in xmm2
pmaddwd		ones, %xmm3				// 4 32-bit elements to be added for sum2 in xmm3
movhlps		%xmm3, %xmm2			// 2 higher 32-bit elements of xmm3 to be added to lower 2 32-bit elements
paddd		%xmm2, %xmm3			// 2 32-bits elements in xmm3 to be added to sum2
movd		%xmm3, %edx				// to be added to sum2
psrlq		\$\$32, %xmm3				// another 32-bit to be added to sum2
addl		%edx, sum2				// sum2 += 1st half of update
movd		%xmm3, %edx				// to be added to sum2
addl		%edx, sum2				// sum2 += 2nd half of update
.endm

// this defines the macro DO16 for SSSE3 not supported
.macro      DO16_nossse3
movaps      (buf), %xmm1            // 16 bytes vector
movaps      %xmm1, %xmm3            // a copy of the vector, the lower 8 bytes to be shuffled into 8 words
movaps      %xmm1, %xmm2            // a copy of the vector, the higher 8 bytes to be shuffled into 8 words
psrldq      \$\$8, %xmm2              // shift down 8 bytes, to reuse the shuffle vector
punpcklbw   zero, %xmm3             // convert lower 8 bytes into 8 words
punpcklbw   zero, %xmm2             // convert higher 8 bytes into 8 words
pmullw      %xmm6, %xmm3            // lower 8 words * 16:9
pmullw      %xmm4, %xmm2            // higher 8 words * 8:1
addl        \$\$16, buf               // buf -> next vector
paddw       %xmm2, %xmm3            // 8 16-bit words to be added for sum2 in xmm3
movhlps     %xmm1, %xmm2            // higher 16-bit word (for adler) in xmm2
pmaddwd     ones, %xmm3             // 4 32-bit elements to be added for sum2 in xmm3
movhlps     %xmm3, %xmm2            // 2 higher 32-bit elements of xmm3 to be added to lower 2 32-bit elements
paddd       %xmm2, %xmm3            // 2 32-bits elements in xmm3 to be added to sum2
movd        %xmm3, %edx             // to be added to sum2
psrlq       \$\$32, %xmm3             // another 32-bit to be added to sum2
addl        %edx, sum2              // sum2 += 1st half of update
movd        %xmm3, %edx             // to be added to sum2
addl        %edx, sum2              // sum2 += 2nd half of update
.endm

#ifdef  KERNEL
leal    __cpu_capabilities, %eax                        // %eax -> __cpu_capabilities
mov     (%eax), %eax                                    // %eax = __cpu_capabilities
#else
mov    _COMM_PAGE_CPU_CAPABILITIES, %eax
#endif
test    \$(kHasSupplementalSSE3), %eax 					// __cpu_capabilities & kHasAES
je		L_no_ssse3

// need to fill up xmm4/xmm5/xmm6 only if len>=16
cmpl	\$16, len

// set up table starting address to %eax
leal	sum2_coefficients, %eax

pxor	zero, zero
movaps	(%eax), %xmm6			// coefficients for computing sum2 : pmaddubsw 32:17
movaps	16(%eax), %xmm4			// coefficients for computing sum2 : pmaddubsw 16:1
movaps	32(%eax), ones			// coefficients for computing sum2 : pmaddwd 1,1,...,1

cmpl	\$NMAX, len				// len vs NMAX
jl		len_lessthan_NMAX		// if (len < NMAX), skip the following NMAX batches processing

len_ge_NMAX_loop:					// while (len>=NMAX) {

subl	\$NMAX, len				// 		len -= NMAX
movl	\$(NMAX/32), %eax		// 		n = NMAX/32

n_loop:								// 		do {
DO32							// 			update adler/sum2 for a 32-byte input
decl 	%eax					// 			n--;
jg		n_loop					//  	} while (n);
DO16							//  	update adler/sum2 for a 16-byte input
cmpl	\$NMAX, len				//
jge		len_ge_NMAX_loop		// }	/* len>=NMAX */

len_lessthan_NMAX:

subl	\$32, len				// pre-decrement len by 32
jl		len_lessthan_32			// if len < 32, skip the 32-vector code
len32_loop:							// while (len>=32) {
DO32							//   update adler/sum2 for a 32-byte input
subl	\$32, len				//   len -= 32;
jge		len32_loop				// }

len_lessthan_32:

addl	\$(32-16), len			// post-increment by 32 + pre-decrement by 16 on len
jl		L_len_lessthan_16			// if len < 16, skip the 16-vector code
DO16							// update adler/sum2 for a 16-byte input
subl	\$16, len				// len -= 16;

L_len_lessthan_16:
addl	\$16, len				// post-increment len by 16
jz		len_is_zero				// if len==0, branch over scalar processing

0:									// while (len) {
movzbl	(buf), %edx				// 	new input byte
incl	buf						// 	buf++
subl	\$1, len					// 	len--
jg		0b						// }

len_is_zero:

// construct 32-bit (sum2<<16 | adler) to be returned

sall	\$16, sum2				// sum2 <<16
orl		sum2, %eax				// sum2<<16 | adler

#ifdef	KERNEL 					// if this is for kernel code, need to restore xmm registers
movaps	(%esp), %xmm0		// restore xmm0, offset -12 for ebx/edi/esi
movaps	16(%esp), %xmm1		// restore xmm1
movaps	32(%esp), %xmm2		// restore xmm2
movaps	48(%esp), %xmm3		// restore xmm3
movaps	64(%esp), %xmm4		// restore xmm4
movaps	80(%esp), %xmm5		// restore xmm5
movaps	96(%esp), %xmm6		// restore xmm6
movaps	112(%esp), %xmm7	// restore xmm7, if this is for SSSE3 or above
#endif

popl   %esi
popl   %edi
popl   %ebx
leave						// pop ebp out from stack
ret

L_no_ssse3:

// need to fill up xmm4/xmm5/xmm6 only if len>=16
cmpl	\$16, len
jl		2f

// set up table starting address to %eax
leal	sum2_coefficients, %eax

pxor	zero, zero
movaps  48(%eax), %xmm6         // coefficients for computing sum2 : pmaddubsw 16:9
movaps  64(%eax), %xmm4         // coefficients for computing sum2 : pmaddubsw 8:1
movaps  80(%eax), ones          // coefficients for computing sum2 : pmaddwd 1,1,...,1

2:

cmpl	\$NMAX, len				// len vs NMAX
jl		3f						// if (len < NMAX), skip the following NMAX batches processing

0:									// while (len>=NMAX) {

subl	\$NMAX, len				// 		len -= NMAX
movl	\$(NMAX/16), %eax		// 		n = NMAX/16

1:									// 		do {
DO16_nossse3					//			update adler/sum2 for a 16-byte input
decl 	%eax					// 			n--;
jg		1b						//  	} while (n);

cmpl	\$NMAX, len				//
jge		0b						// }	/* len>=NMAX */

3:

subl	\$16, len				// pre-decrement len by 16
jl		L_len_lessthan_16		// if len < 16, skip the 16-vector code
DO16_nossse3					// update adler/sum2 for a 16-byte input
subl	\$16, len				// len -= 16;
jmp		L_len_lessthan_16

.const
.align	4
sum2_coefficients:	// used for vectorizing adler32 computation

.byte	32
.byte	31
.byte	30
.byte	29
.byte	28
.byte	27
.byte	26
.byte	25
.byte	24
.byte	23
.byte	22
.byte	21
.byte	20
.byte	19
.byte	18
.byte	17
.byte	16
.byte	15
.byte	14
.byte	13
.byte	12
.byte	11
.byte	10
.byte	9
.byte	8
.byte	7
.byte	6
.byte	5
.byte	4
.byte	3
.byte	2
.byte	1

// coefficients for pmaddwd, to combine into 4 32-bit elements for sum2
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1

// data for without ssse3

.word   16
.word   15
.word   14
.word   13
.word   12
.word   11
.word   10
.word   9
.word   8
.word   7
.word   6
.word   5
.word   4
.word   3
.word   2
.word   1

// coefficients for pmaddwd, to combine into 4 32-bit elements for sum2
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1

#else	// (defined __x86_64__)

movq    __cpu_capabilities@GOTPCREL(%rip), %rax         // %rax -> __cpu_capabilities
mov     (%rax), %eax                                    // %eax = __cpu_capabilities
test    \$(kHasSupplementalSSE3), %eax                   // __cpu_capabilities & kHasSupplementalSSE3
jne      L_has_ssse3

// ----------------------------------------------------------------------------------
// the following is added for x86_64 without SSSE3 support
// it is essentially a translated copy of the i386 code without SSSE3 code
// ----------------------------------------------------------------------------------

// input :
//		 sum2  : rsi
// 		 buf   : rdx
//		 len   : rcx

pushq	%rbp
movq	%rsp, %rbp
pushq	%rbx

#ifdef	KERNEL			// if for kernel, save %xmm0-%xmm11
subq	\$200, %rsp	// allocate for %xmm0-%xmm11 (192 bytes), extra 8 to align %rsp to 16-byte boundary
movaps	%xmm0, -32(%rbp)
movaps	%xmm1, -48(%rbp)
movaps	%xmm2, -64(%rbp)
movaps	%xmm3, -80(%rbp)
movaps	%xmm4, -96(%rbp)
movaps	%xmm5, -112(%rbp)
movaps	%xmm6, -128(%rbp)
#endif

#define	sum2	%rsi				// 24(%ebp)
#define	buf		%rcx				// 32(%ebp)
#define	len		%rbx				// 40(%ebp)
#define	zero	%xmm0
#define ones	%xmm5

movq	%rcx, len
movq	%rdx, buf

.macro		modulo_BASE
movl		\$\$-2146992015, %eax		// 1/BASE in Q47
mull		%edi					// edx:eax = adler divided by BASE in Q47
shrl		\$\$15, %edx				// edx is now the floor integer of adler and BASE
imull		\$\$BASE, %edx, %edx		// edx * BASE
movl		\$\$-2146992015, %eax		// 1/BASE in Q47
mull		%esi					// edx:eax = sum2 divided by BASE in Q47
shrl		\$\$15, %edx				// edx is now the floor integer of sum2 and BASE
imull		\$\$BASE, %edx, %eax		// eax = edx * BASE
subq		%rax, sum2				// sum2 -= sdx*BASE
.endmacro

// update adler/sum2 according to a new 16-byte vector, no ssse3
.macro		DO16_nossse3
movaps      (buf), %xmm1            // 16 bytes vector
movaps      %xmm1, %xmm3            // a copy of the vector, the lower 8 bytes to be shuffled into 8 words
movaps      %xmm1, %xmm2            // a copy of the vector, the higher 8 bytes to be shuffled into 8 words
psrldq      \$\$8, %xmm2              // shift down 8 bytes, to reuse the shuffle vector
punpcklbw   zero, %xmm3             // convert lower 8 bytes into 8 words
punpcklbw   zero, %xmm2             // convert higher 8 bytes into 8 words
pmullw      %xmm6, %xmm3            // lower 8 words * 16:9
pmullw      %xmm4, %xmm2            // higher 8 words * 8:1
add	        \$\$16, buf               // buf -> next vector
paddw       %xmm2, %xmm3            // 8 16-bit words to be added for sum2 in xmm3
movhlps     %xmm1, %xmm2            // higher 16-bit word (for adler) in xmm2
pmaddwd     ones, %xmm3             // 4 32-bit elements to be added for sum2 in xmm3
movhlps     %xmm3, %xmm2            // 2 higher 32-bit elements of xmm3 to be added to lower 2 32-bit elements
paddd       %xmm2, %xmm3            // 2 32-bits elements in xmm3 to be added to sum2
movd        %xmm3, %edx             // to be added to sum2
psrlq       \$\$32, %xmm3             // another 32-bit to be added to sum2
addq        %rdx, sum2              // sum2 += 1st half of update
movd        %xmm3, %edx             // to be added to sum2
addq        %rdx, sum2              // sum2 += 2nd half of update
.endm

// need to fill up xmm4/xmm5/xmm6 only if len>=16
cmpq	\$16, len
jl		0f

// set up table starting address to %eax
leaq    sum2_coefficients_nossse3(%rip), %rax

pxor	zero, zero
movaps  (%rax), %xmm6           // coefficients for computing sum2 : pmaddubsw 16:9
movaps  16(%rax), %xmm4         // coefficients for computing sum2 : pmaddubsw 8:1
movaps  32(%rax), ones          // coefficients for computing sum2 : pmaddwd 1,1,...,1
0:

cmp		\$NMAX, len				// len vs NMAX
jl		3f						// if (len < NMAX), skip the following NMAX batches processing

0:									// while (len>=NMAX) {

sub		\$NMAX, len				// 		len -= NMAX
mov		\$(NMAX/16), %eax		// 		n = NMAX/16

1:									// 		do {
DO16_nossse3					//			update adler/sum2 for a 16-byte input
decl 	%eax					// 			n--;
jg		1b						//  	} while (n);

cmp		\$NMAX, len				//
jge		0b						// }	/* len>=NMAX */

3:

sub		\$16, len				// pre-decrement len by 16
jl		2f						// if len < 16, skip the 16-vector code
DO16_nossse3					// update adler/sum2 for a 16-byte input
sub		\$16, len				// len -= 16;

2:
add		\$16, len				// post-increment len by 16
jz		1f						// if len==0, branch over scalar processing

0:									// while (len) {
movzbq	(buf), %rdx				// 	new input byte
incq	buf						// 	buf++
decq	len						// 	len--
jg		0b						// }

1:

// construct 32-bit (sum2<<16 | adler) to be returned

salq	\$16, sum2				// sum2 <<16
orq		sum2, %rax				// sum2<<16 | adler

#ifdef	KERNEL 					// if this is for kernel code, need to restore xmm registers
movaps	-32(%rbp), %xmm0
movaps	-48(%rbp), %xmm1
movaps	-64(%rbp), %xmm2
movaps	-80(%rbp), %xmm3
movaps	-96(%rbp), %xmm4
movaps	-112(%rbp), %xmm5
movaps	-128(%rbp), %xmm6
#endif

popq   %rbx
leave
ret

.const
.align	4
sum2_coefficients_nossse3:	// used for vectorizing adler32 computation

// data for without ssse3

.word   16
.word   15
.word   14
.word   13
.word   12
.word   11
.word   10
.word   9
.word   8
.word   7
.word   6
.word   5
.word   4
.word   3
.word   2
.word   1

// coefficients for pmaddwd, to combine into 4 32-bit elements for sum2
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1

.text

// ----------------------------------------------------------------------------------
// the following is the original x86_64 adler32_vec code that uses SSSE3 instructions
// ----------------------------------------------------------------------------------

L_has_ssse3:

// input :
//		 sum2  : rsi
// 		 buf   : rdx
//		 len   : rcx

pushq	%rbp
movq	%rsp, %rbp
pushq	%rbx

#ifdef	KERNEL			// if for kernel, save %xmm0-%xmm11
subq	\$200, %rsp	// allocate for %xmm0-%xmm11 (192 bytes), extra 8 to align %rsp to 16-byte boundary
movaps	%xmm0, -32(%rbp)
movaps	%xmm1, -48(%rbp)
movaps	%xmm2, -64(%rbp)
movaps	%xmm3, -80(%rbp)
movaps	%xmm4, -96(%rbp)
movaps	%xmm5, -112(%rbp)
movaps	%xmm6, -128(%rbp)
movaps	%xmm7, -144(%rbp)
movaps	%xmm8, -160(%rbp)
movaps	%xmm9, -176(%rbp)
movaps	%xmm10, -192(%rbp)
movaps	%xmm11, -208(%rbp)
#endif

#define	sum2	%rsi				// 24(%ebp)
#define	buf		%rcx				// 32(%ebp)
#define	len		%rbx				// 40(%ebp)
#define	zero	%xmm0
#define ones	%xmm5

movq	%rcx, len
movq	%rdx, buf

// update adler/sum2 according to a new 16-byte vector
.macro		DO16
movaps		(buf), %xmm1			// 16 bytes vector
movaps		%xmm1, %xmm3			// a copy of the vector, used for unsigned byte in the destination of pmaddubsw
addq		\$\$16, buf				// buf -> next vector
pmaddubsw	%xmm4, %xmm3			// 8 16-bit words to be added for sum2 in xmm3
movhlps		%xmm1, %xmm2			// higher 16-bit word (for adler) in xmm2
pmaddwd		ones, %xmm3				// 4 32-bit elements to be added for sum2 in xmm3
movhlps		%xmm3, %xmm2			// 2 higher 32-bit elements of xmm3 to be added to lower 2 32-bit elements
paddd		%xmm2, %xmm3			// 2 32-bits elements in xmm3 to be added to sum2
movd		%xmm3, %edx				// to be added to sum2
psrlq		\$\$32, %xmm3				// another 32-bit to be added to sum2
addq		%rdx, sum2				// sum2 += 1st half of update
movd		%xmm3, %edx				// to be added to sum2
addq		%rdx, sum2				// sum2 += 2nd half of update
.endm

// update adler/sum2 according to a new 32-byte vector
.macro		DO32
movaps		(buf), %xmm1			// 1st 16 bytes vector
movaps		16(buf), %xmm7			// 2nd 16 bytes vector
movaps		%xmm1, %xmm3			// a copy of 1st vector, used for unsigned byte in the destination of pmaddubsw
movaps		%xmm7, %xmm2			// a copy of 2nd vector, used for unsigned byte in the destination of pmaddubsw
pmaddubsw	%xmm6, %xmm3			// 8 16-bit words to be added for sum2 in xmm3
pmaddubsw	%xmm4, %xmm2			// 8 16-bit words to be added for sum2 in xmm2
paddw		%xmm2, %xmm3			// 8 16-bit words to be added for sum2 in xmm3
addq		\$\$32, buf				// buf -> vector for next iteration
movhlps		%xmm1, %xmm2			// higher 16-bit word (for adler) in xmm2
pmaddwd		ones, %xmm3				// 4 32-bit elements to be added for sum2 in xmm3
movhlps		%xmm3, %xmm2			// 2 higher 32-bit elements of xmm3 to be added to lower 2 32-bit elements
paddd		%xmm2, %xmm3			// 2 32-bits elements in xmm3 to be added to sum2
movd		%xmm3, %edx				// to be added to sum2
psrlq		\$\$32, %xmm3				// another 32-bit to be added to sum2
addq		%rdx, sum2				// sum2 += 1st half of update
movd		%xmm3, %edx				// to be added to sum2
addq		%rdx, sum2				// sum2 += 2nd half of update
.endm

// update adler/sum2 according to a new 48-byte vector

.macro		DO48

movaps		(buf), %xmm7			// 1st 16 bytes vector
movaps		16(buf), %xmm10			// 2nd 16 bytes vector
movaps		32(buf), %xmm11			// 3rd 16 bytes vector

movaps		%xmm7, %xmm1			// 1st vector
movaps		%xmm10, %xmm2			// 2nd vector
movaps		%xmm11, %xmm3			// 3rd vector

pmaddubsw	%xmm9, %xmm1			// 8 16-bit words to be added for sum2 : 1st vector
pmaddubsw	%xmm6, %xmm2			// 8 16-bit words to be added for sum2 : 2nd vector
pmaddubsw	%xmm4, %xmm3			// 8 16-bit words to be added for sum2 : 3rd vector

pmaddwd		ones, %xmm1				// 4 32-bit elements to be added for sum2 in xmm1
pmaddwd		ones, %xmm2				// 4 32-bit elements to be added for sum2 in xmm2
pmaddwd		ones, %xmm3				// 4 32-bit elements to be added for sum2 in xmm3

paddd		%xmm1, %xmm3			// 4 32-bit elements to be added for sum2
paddd		%xmm2, %xmm3			// 4 32-bit elements to be added for sum2

addq		\$\$48, buf				// buf -> vector for next iteration

movhlps		%xmm7, %xmm2			// higher 16-bit word (for adler) in xmm2

movhlps		%xmm3, %xmm2			// 2 higher 32-bit elements of xmm3 to be added to lower 2 32-bit elements
paddd		%xmm2, %xmm3			// 2 32-bits elements in xmm3 to be added to sum2
movd		%xmm3, %edx				// to be added to sum2
psrlq		\$\$32, %xmm3				// another 32-bit to be added to sum2
addq		%rdx, sum2				// sum2 += 1st half of update
movd		%xmm3, %edx				// to be added to sum2
addq		%rdx, sum2				// sum2 += 2nd half of update
.endm

// update adler/sum2 according to a new 64-byte vector
.macro		DO64

movaps		(buf), %xmm1			// 1st 16 bytes vector
movaps		16(buf), %xmm7			// 2nd 16 bytes vector
movaps		32(buf), %xmm10			// 3rd 16 bytes vector
movaps		48(buf), %xmm11			// 4th 16 bytes vector

movaps		%xmm1, %xmm3			// 1st vector
movaps		%xmm11, %xmm2			// 4th vector

pmaddubsw	%xmm8, %xmm3			// 8 16-bit words to be added for sum2 : 1st vector
pmaddubsw	%xmm4, %xmm2			// 8 16-bit words to be added for sum2 : 4th vector
pmaddwd		ones, %xmm3				// 4 32-bit elements to be added for sum2 in xmm3
pmaddwd		ones, %xmm2				// 4 32-bit elements to be added for sum2 in xmm2

paddd		%xmm2, %xmm3			// 4 32-bit elements to be added for sum2 in xmm3

movaps		%xmm7, %xmm2			// 2nd vector
movaps		%xmm10, %xmm11			// 3rd vector

pmaddubsw	%xmm9, %xmm2			// 8 16-bit words to be added for sum2 : 2nd vector
pmaddubsw	%xmm6, %xmm11			// 8 16-bit words to be added for sum2 : 3rd vector
pmaddwd		ones, %xmm2				// 4 32-bit elements to be added for sum2 in xmm2
pmaddwd		ones, %xmm11			// 4 32-bit elements to be added for sum2 in xmm11

paddd		%xmm2, %xmm3			// 4 32-bit elements to be added for sum2 in xmm3
paddd		%xmm11, %xmm3			// 4 32-bit elements to be added for sum2 in xmm3

addq		\$\$64, buf				// buf -> vector for next iteration

movhlps		%xmm1, %xmm2			// higher 16-bit word (for adler) in xmm2
movhlps		%xmm3, %xmm2			// 2 higher 32-bit elements of xmm3 to be added to lower 2 32-bit elements
paddd		%xmm2, %xmm3			// 2 32-bits elements in xmm3 to be added to sum2
movd		%xmm3, %edx				// to be added to sum2
psrlq		\$\$32, %xmm3				// another 32-bit to be added to sum2
addq		%rdx, sum2				// sum2 += 1st half of update
movd		%xmm3, %edx				// to be added to sum2
addq		%rdx, sum2				// sum2 += 2nd half of update
.endm

// need to fill up xmm4/xmm5/xmm6 only if len>=16
cmpq	\$16, len

// set up table starting address to %eax
leaq    sum2_coefficients(%rip), %rax

pxor	zero, zero
movaps	(%rax), %xmm8			// coefficients for computing sum2 : pmaddubsw 64:49
movaps	16(%rax), %xmm9			// coefficients for computing sum2 : pmaddubsw 48:33
movaps	32(%rax), %xmm6			// coefficients for computing sum2 : pmaddubsw 32:17
movaps	48(%rax), %xmm4			// coefficients for computing sum2 : pmaddubsw 16:1
movaps	64(%rax), ones			// coefficients for computing sum2 : pmaddwd 1,1,...,1

cmpq	\$NMAX, len				// len vs NMAX
jl		len_lessthan_NMAX		// if (len < NMAX), skip the following NMAX batches processing

len_ge_NMAX_loop:					// while (len>=NMAX) {

subq	\$NMAX, len				// 		len -= NMAX
movq	\$(NMAX/64), %rax		// 		n = NMAX/64

n_loop:								// 		do {
DO64							// 			update adler/sum2 for a 64-byte input
decq 	%rax					// 			n--;
jg		n_loop					//  	} while (n);

DO48							//		update adler/sum2 for a 48-byte input

cmpq	\$NMAX, len				//
jge		len_ge_NMAX_loop		// }	/* len>=NMAX */

len_lessthan_NMAX:

subq	\$64, len				// pre-decrement len by 64
jl		len_lessthan_64			// if len < 64, skip the 64-vector code
len64_loop:							// while (len>=64) {
DO64							//   update adler/sum2 for a 64-byte input
subq	\$64, len				//   len -= 64;
jge		len64_loop				// }

len_lessthan_64:
addq	\$(64-32), len			// post-increment 64 + pre-decrement 32 of len
jl		len_lessthan_32			// if len < 32, skip the 32-vector code
DO32							//   update adler/sum2 for a 32-byte input
subq	\$32, len				//   len -= 32;

len_lessthan_32:

addq	\$(32-16), len			// post-increment by 32 + pre-decrement by 16 on len
jl		len_lessthan_16			// if len < 16, skip the 16-vector code
DO16							// update adler/sum2 for a 16-byte input
subq	\$16, len				// len -= 16;

len_lessthan_16:
addq	\$16, len				// post-increment len by 16
jz		len_is_zero				// if len==0, branch over scalar processing

scalar_loop:						// while (len) {
movzbq	(buf), %rdx				// 	new input byte
incq	buf						// 	buf++
decq	len						// 	len--
jg		scalar_loop				// }

len_is_zero:

// construct 32-bit (sum2<<16 | adler) to be returned

salq	\$16, sum2				// sum2 <<16
orq		sum2, %rax				// sum2<<16 | adler

#ifdef	KERNEL			// if for kernel, restore %xmm0-%xmm11
movaps	-32(%rbp), %xmm0
movaps	-48(%rbp), %xmm1
movaps	-64(%rbp), %xmm2
movaps	-80(%rbp), %xmm3
movaps	-96(%rbp), %xmm4
movaps	-112(%rbp), %xmm5
movaps	-128(%rbp), %xmm6
movaps	-144(%rbp), %xmm7
movaps	-160(%rbp), %xmm8
movaps	-176(%rbp), %xmm9
movaps	-192(%rbp), %xmm10
movaps	-208(%rbp), %xmm11
#endif

popq   %rbx
leave							// pop ebp out from stack
ret

.const
.align	4
sum2_coefficients:	// used for vectorizing adler32 computation

// coefficients for pmaddubsw instruction, used to generate 16-bit elements for sum2

.byte	64
.byte	63
.byte	62
.byte	61
.byte	60
.byte	59
.byte	58
.byte	57
.byte	56
.byte	55
.byte	54
.byte	53
.byte	52
.byte	51
.byte	50
.byte	49
.byte	48
.byte	47
.byte	46
.byte	45
.byte	44
.byte	43
.byte	42
.byte	41
.byte	40
.byte	39
.byte	38
.byte	37
.byte	36
.byte	35
.byte	34
.byte	33
.byte	32
.byte	31
.byte	30
.byte	29
.byte	28
.byte	27
.byte	26
.byte	25
.byte	24
.byte	23
.byte	22
.byte	21
.byte	20
.byte	19
.byte	18
.byte	17
.byte	16
.byte	15
.byte	14
.byte	13
.byte	12
.byte	11
.byte	10
.byte	9
.byte	8
.byte	7
.byte	6
.byte	5
.byte	4
.byte	3
.byte	2
.byte	1

// coefficients for pmaddwd, to combine into 4 32-bit elements for sum2
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1
.word	1

#endif	// (defined __i386__)

#endif	// (defined __i386__ || defined __x86_64__)
```