Add sample zipf distribution randomizer

Instead of just doing purely random IO where each block is
touched exactly (or close to, depending on random map) once,
add a zipf distribution scheme where a selectable theta
defines the spread and frequency of blocks read/written.

Committing this so I don't lose it. Needs a few changes,
for instance we need to hash the zipf output so that
the spread doesn't always just favor the lower LBA range.

Signed-off-by: Jens Axboe <axboe@kernel.dk>
diff --git a/Makefile b/Makefile
index ccfa802..94856e0 100644
--- a/Makefile
+++ b/Makefile
@@ -15,7 +15,7 @@
 		lib/num2str.c lib/ieee754.c $(wildcard crc/*.c) engines/cpu.c \
 		engines/mmap.c engines/sync.c engines/null.c engines/net.c \
 		memalign.c server.c client.c iolog.c backend.c libfio.c flow.c \
-		json.c
+		json.c lib/zipf.c
 
 ifeq ($(UNAME), Linux)
   SOURCE += diskutil.c fifo.c blktrace.c helpers.c cgroup.c trim.c \
diff --git a/examples/zipf b/examples/zipf
new file mode 100644
index 0000000..fcfa38d
--- /dev/null
+++ b/examples/zipf
@@ -0,0 +1,10 @@
+# Example job file for using a zipf distribution instead
+# of a purely random workload where each block is read
+# or written once.
+[job]
+ioengine=null
+rw=randread
+norandommap
+size=1280m
+bs=4k
+random_distribution=zipf:0.5
diff --git a/fio.h b/fio.h
index 139b938..15ab308 100644
--- a/fio.h
+++ b/fio.h
@@ -39,6 +39,7 @@
 #include "server.h"
 #include "stat.h"
 #include "flow.h"
+#include "lib/zipf.h"
 
 #ifdef FIO_HAVE_GUASI
 #include <guasi.h>
@@ -177,6 +178,9 @@
 	unsigned int bs_unaligned;
 	unsigned int fsync_on_close;
 
+	unsigned int random_distribution;
+	double zipf_theta;
+
 	unsigned int hugepage_size;
 	unsigned int rw_min_bs;
 	unsigned int thinktime;
@@ -452,6 +456,11 @@
 		struct frand_state __random_state;
 	};
 
+	/*
+	 * Used for zipf random distribution
+	 */
+	struct zipf_state zipf;
+
 	struct timeval start;	/* start of this loop */
 	struct timeval epoch;	/* time job was started */
 	struct timeval last_issue;
@@ -815,4 +824,9 @@
 	FIO_OUTPUT_NORMAL,
 };
 
+enum {
+	FIO_RAND_DIST_RANDOM	= 0,
+	FIO_RAND_DIST_ZIPF,
+};
+
 #endif
diff --git a/init.c b/init.c
index 23be863..1cee096 100644
--- a/init.c
+++ b/init.c
@@ -382,6 +382,20 @@
 		o->min_bs[DDIR_READ] == o->min_bs[DDIR_TRIM];
 }
 
+static void init_rand_distribution(struct thread_data *td)
+{
+	unsigned int range_size;
+	unsigned long nranges;
+
+	if (td->o.random_distribution == FIO_RAND_DIST_RANDOM)
+		return;
+
+	range_size = min(td->o.min_bs[DDIR_READ], td->o.min_bs[DDIR_WRITE]);
+
+	nranges = (td->o.size + range_size - 1) / range_size;
+	zipf_init(&td->zipf, nranges, td->o.zipf_theta);
+}
+
 /*
  * Lazy way of fixing up options that depend on each other. We could also
  * define option callback handlers, but this is easier.
@@ -592,6 +606,8 @@
 		td->o.compress_percentage = 0;
 	}
 
+	init_rand_distribution(td);
+
 	return ret;
 }
 
diff --git a/io_u.c b/io_u.c
index b049b61..8f2ce30 100644
--- a/io_u.c
+++ b/io_u.c
@@ -157,8 +157,8 @@
 	return 1;
 }
 
-static int get_next_rand_offset(struct thread_data *td, struct fio_file *f,
-				enum fio_ddir ddir, unsigned long long *b)
+static int __get_next_rand_offset(struct thread_data *td, struct fio_file *f,
+				  enum fio_ddir ddir, unsigned long long *b)
 {
 	unsigned long long rmax, r, lastb;
 	int loops = 5;
@@ -234,6 +234,25 @@
 	return 0;
 }
 
+static int __get_next_rand_offset_zipf(struct thread_data *td, struct fio_file *f,
+				  enum fio_ddir ddir, unsigned long long *b)
+{
+	*b = zipf_next(&td->zipf);
+	return 0;
+}
+
+static int get_next_rand_offset(struct thread_data *td, struct fio_file *f,
+				enum fio_ddir ddir, unsigned long long *b)
+{
+	if (td->o.random_distribution == FIO_RAND_DIST_RANDOM)
+		return __get_next_rand_offset(td, f, ddir, b);
+	else if (td->o.random_distribution == FIO_RAND_DIST_ZIPF)
+		return __get_next_rand_offset_zipf(td, f, ddir, b);
+
+	log_err("fio: unknown random distribution: %d\n", td->o.random_distribution);
+	return 1;
+}
+
 static int get_next_rand_block(struct thread_data *td, struct fio_file *f,
 			       enum fio_ddir ddir, unsigned long long *b)
 {
diff --git a/lib/zipf.c b/lib/zipf.c
new file mode 100644
index 0000000..34f2877
--- /dev/null
+++ b/lib/zipf.c
@@ -0,0 +1,128 @@
+#include <math.h>
+#include <string.h>
+#include <inttypes.h>
+#include <stdio.h>
+#include <unistd.h>
+#include <sys/types.h>
+#include <fcntl.h>
+#include "ieee754.h"
+#include "../log.h"
+#include "zipf.h"
+#include "../minmax.h"
+#include "../os/os.h"
+
+struct fio_zipf_disk {
+	uint64_t ver_magic;
+	uint64_t nranges;
+	uint64_t zetan;
+};
+
+#define FIO_ZIPF_DISK_MAGIC	0x7a697066
+#define FIO_ZIPF_DISK_VER	1
+#define FIO_ZIPF_MAGIC		((FIO_ZIPF_DISK_MAGIC << 16) | FIO_ZIPF_DISK_VER)
+
+static void write_zipf(struct zipf_state *zs)
+{
+	struct fio_zipf_disk f;
+	char tmp[80];
+	int fd;
+
+	sprintf(tmp, "fio.zipf.%f.%llu", zs->theta, (unsigned long long) zs->nranges);
+	fd = open(tmp, O_CREAT | O_WRONLY, 0644);
+	if (fd == -1)
+		return;
+
+	f.ver_magic = __cpu_to_le64(FIO_ZIPF_MAGIC);
+	f.nranges = __cpu_to_le64(zs->nranges);
+	f.zetan = __cpu_to_le64(fio_double_to_uint64(zs->zetan));
+	if (write(fd, &f, sizeof(f)) != sizeof(f))
+		unlink(tmp);
+
+	close(fd);
+}
+
+static void zipf_update(struct zipf_state *zs)
+{
+	unsigned int i;
+
+	log_info("fio: generating zetan for theta=%f, ranges=%lu\n", zs->theta, zs->nranges);
+
+	for (i = 0; i < zs->nranges; i++)
+		zs->zetan += pow(1.0 / (double) (i + 1), zs->theta);
+
+	write_zipf(zs);
+}
+
+static void zipf_load_gen_zeta(struct zipf_state *zs)
+{
+	struct fio_zipf_disk f;
+	char tmp[80];
+	int fd;
+
+	sprintf(tmp, "fio.zipf.%f.%llu", zs->theta, (unsigned long long) zs->nranges);
+	fd = open(tmp, O_RDONLY);
+	if (fd == -1) {
+punt:
+		zipf_update(zs);
+		return;
+	}
+
+	if (read(fd, &f, sizeof(f)) != sizeof(f)) {
+		close(fd);
+		goto punt;
+	}
+
+	close(fd);
+
+	f.ver_magic = le64_to_cpu(f.ver_magic);
+	f.nranges = le64_to_cpu(f.nranges);
+	f.zetan = le64_to_cpu(f.zetan);
+
+	if (f.ver_magic != FIO_ZIPF_MAGIC) {
+		unlink(tmp);
+		goto punt;
+	}
+
+	zs->zetan = fio_uint64_to_double(f.zetan);
+	zs->nranges = f.nranges;
+}
+
+void zipf_init(struct zipf_state *zs, unsigned long nranges, double theta)
+{
+	unsigned int i;
+
+	memset(zs, 0, sizeof(*zs));
+
+	zs->nranges = nranges;
+	zs->theta = theta;
+
+	for (i = 1; i <= 2; i++)
+		zs->zeta2 += pow(1.0 / (double) i, zs->theta);
+
+	init_rand(&zs->rand);
+
+	zipf_load_gen_zeta(zs);
+}
+
+unsigned long long zipf_next(struct zipf_state *zs)
+{
+
+	double alpha, eta, rand_uni, rand_z;
+	unsigned long long n = zs->nranges;
+	unsigned long long val;
+
+	alpha = 1.0 / (1.0 - zs->theta);
+	eta = (1.0 - pow(2.0 / n, 1.0 - zs->theta)) / (1.0 - zs->zeta2 / zs->zetan);
+
+	rand_uni = (double) __rand(&zs->rand) / (double) FRAND_MAX;
+	rand_z = rand_uni * zs->zetan;
+
+	if (rand_z < 1.0)
+		val = 1;
+	else if (rand_z < (1.0 + pow(0.5, zs->theta)))
+		val = 2;
+	else
+		val = 1 + (unsigned long long)(n * pow(eta*rand_uni - eta + 1.0, alpha));
+
+	return val - 1;
+}
diff --git a/lib/zipf.h b/lib/zipf.h
new file mode 100644
index 0000000..6578ef1
--- /dev/null
+++ b/lib/zipf.h
@@ -0,0 +1,17 @@
+#ifndef FIO_ZIPF_H
+#define FIO_ZIPF_H
+
+#include "rand.h"
+
+struct zipf_state {
+	uint64_t nranges;
+	double theta;
+	double zeta2;
+	double zetan;
+	struct frand_state rand;
+};
+
+void zipf_init(struct zipf_state *zs, unsigned long nranges, double theta);
+unsigned long long zipf_next(struct zipf_state *zs);
+
+#endif
diff --git a/options.c b/options.c
index 380df36..05a6a50 100644
--- a/options.c
+++ b/options.c
@@ -728,6 +728,29 @@
 }
 #endif
 
+static int str_random_distribution_cb(void *data, const char *str)
+{
+	struct thread_data *td = data;
+	double val;
+	char *nr;
+
+	if (td->o.random_distribution == FIO_RAND_DIST_RANDOM)
+		return 0;
+
+	nr = get_opt_postfix(str);
+	if (!nr)
+		val = 0.6;
+	else if (!str_to_float(nr, &val)) {
+		log_err("fio: random postfix parsing failed\n");
+		free(nr);
+		return 1;
+	}
+
+	td->o.zipf_theta = val;
+	free(nr);
+	return 0;
+}
+
 static int check_dir(struct thread_data *td, char *fname)
 {
 #if 0
@@ -1473,6 +1496,24 @@
 		.def	= "0",
 	},
 	{
+		.name	= "random_distribution",
+		.type	= FIO_OPT_STR,
+		.off1	= td_var_offset(random_distribution),
+		.cb	= str_random_distribution_cb,
+		.help	= "Random offset distribution generator",
+		.def	= "random",
+		.posval	= {
+			  { .ival = "random",
+			    .oval = FIO_RAND_DIST_RANDOM,
+			    .help = "Completely random",
+			  },
+			  { .ival = "zipf",
+			    .oval = FIO_RAND_DIST_ZIPF,
+			    .help = "Zipf distribution",
+			  },
+		},
+	},
+	{
 		.name	= "nrfiles",
 		.alias	= "nr_files",
 		.type	= FIO_OPT_INT,
diff --git a/parse.c b/parse.c
index 1a686e4..0bbb0b3 100644
--- a/parse.c
+++ b/parse.c
@@ -14,6 +14,7 @@
 #include "parse.h"
 #include "debug.h"
 #include "options.h"
+#include "minmax.h"
 
 static struct fio_option *fio_options;
 extern unsigned int fio_get_kb_base(void *);
@@ -220,7 +221,7 @@
 /*
  * Convert string into a floating number. Return 1 for success and 0 otherwise.
  */
-static int str_to_float(const char *str, double *val)
+int str_to_float(const char *str, double *val)
 {
 	return (1 == sscanf(str, "%lf", val));
 }
@@ -505,7 +506,7 @@
 					o->maxlen);
 			return 1;
 		}
-		if(!str_to_float(ptr, &uf)){
+		if (!str_to_float(ptr, &uf)){
 			log_err("not a floating point value: %s\n", ptr);
 			return 1;
 		}
diff --git a/parse.h b/parse.h
index 71190ea..b2f9e5a 100644
--- a/parse.h
+++ b/parse.h
@@ -79,6 +79,7 @@
 extern void strip_blank_front(char **);
 extern void strip_blank_end(char *);
 extern int str_to_decimal(const char *, long long *, int, void *);
+extern int str_to_float(const char *str, double *val);
 
 /*
  * Handlers for the options
@@ -90,13 +91,6 @@
 
 #define td_var(start, offset)	((void *) start + (offset))
 
-#ifndef min
-#define min(a, b)	((a) < (b) ? (a) : (b))
-#endif
-#ifndef max
-#define max(a, b)	((a) > (b) ? (a) : (b))
-#endif
-
 static inline int parse_is_percent(unsigned long long val)
 {
 	return val <= -1ULL && val >= (-1ULL - 100ULL);