Comparison with the Fletcher checksum
The difference between the two algorithms is that Adler-32 sums are calculated modulo a prime number, whereas Fletcher sums are calculated modulo 24, 28, or 216 (depending on the number of bits used), which are all composite numbers. Using a prime number makes it possible for Adler-32 to catch differences in certain combinations of bytes that Fletcher is unable to detect.

Fletcher is faster for this reason; the operation X modulo 2n is equal to extracting the n least significant bits of X (or calculating X (binary and
2^n-1). This is possible in a single step on almost any processor, whereas calculating X modulo 65521 requires time-consuming integer division.

2 NMAX怎么来的?我不明白

3 那两个宏能提高多少效率?

* For conditions of distribution and use, see copyright notice in zlib.h
*/

/* @(#) \$Id\$ */

#define ZLIB_INTERNAL
#include "zlib.h"

#define BASE 65521UL /* 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 */

#define DO1(buf,i) {s1 += buf[i]; s2 += s1;}
#define DO2(buf,i) DO1(buf,i); DO1(buf,i+1);
#define DO4(buf,i) DO2(buf,i); DO2(buf,i+2);
#define DO8(buf,i) DO4(buf,i); DO4(buf,i+4);
#define DO16(buf) DO8(buf,0); DO8(buf,8);

#ifdef NO_DIVIDE
# define MOD(a) \
do { \
if (a >= (BASE << 16)) a -= (BASE << 16); \
if (a >= (BASE << 15)) a -= (BASE << 15); \
if (a >= (BASE << 14)) a -= (BASE << 14); \
if (a >= (BASE << 13)) a -= (BASE << 13); \
if (a >= (BASE << 12)) a -= (BASE << 12); \
if (a >= (BASE << 11)) a -= (BASE << 11); \
if (a >= (BASE << 10)) a -= (BASE << 10); \
if (a >= (BASE << 9)) a -= (BASE << 9); \
if (a >= (BASE << 8)) a -= (BASE << 8); \
if (a >= (BASE << 7)) a -= (BASE << 7); \
if (a >= (BASE << 6)) a -= (BASE << 6); \
if (a >= (BASE << 5)) a -= (BASE << 5); \
if (a >= (BASE << 4)) a -= (BASE << 4); \
if (a >= (BASE << 3)) a -= (BASE << 3); \
if (a >= (BASE << 2)) a -= (BASE << 2); \
if (a >= (BASE << 1)) a -= (BASE << 1); \
if (a >= BASE) a -= BASE; \
} while (0)
#else
# define MOD(a) a %= BASE
#endif

/* ========================================================================= */
const Bytef *buf;
uInt len;
{
unsigned long s1 = adler & 0xffff;
unsigned long s2 = (adler >> 16) & 0xffff;
int k;

if (buf == Z_NULL) return 1L;

while (len > 0) {
k = len < NMAX ? (int)len : NMAX;
len -= k;
while (k >= 16) {
DO16(buf);
buf += 16;
k -= 16;
}
if (k != 0) do {
s1 += *buf++;
s2 += s1;
} while (--k);
MOD(s1);
MOD(s2);
}
return (s2 << 16) | s1;
}
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