devices.c revision 32f51664c8c44b8a4ab357e34590deb62c582c7c 
1/*
2 * Copyright (C) 2007 The Android Open Source Project
3 *
4 * Licensed under the Apache License, Version 2.0 (the "License");
5 * you may not use this file except in compliance with the License.
6 * You may obtain a copy of the License at
7 *
8 *      http://www.apache.org/licenses/LICENSE-2.0
9 *
10 * Unless required by applicable law or agreed to in writing, software
11 * distributed under the License is distributed on an "AS IS" BASIS,
12 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
13 * See the License for the specific language governing permissions and
14 * limitations under the License.
15 */
16
17#include <errno.h>
18#include <stdio.h>
19#include <stdlib.h>
20#include <sys/stat.h>
21#include <sys/types.h>
22
23#include <fcntl.h>
24#include <dirent.h>
25#include <unistd.h>
26#include <string.h>
27
28#include <sys/socket.h>
29#include <sys/un.h>
30#include <linux/netlink.h>
31#include <private/android_filesystem_config.h>
32#include <sys/time.h>
33#include <asm/page.h>
34
35#include "init.h"
36#include "devices.h"
37
38#define CMDLINE_PREFIX  "/dev"
39#define SYSFS_PREFIX    "/sys"
40#define FIRMWARE_DIR    "/etc/firmware"
41#define MAX_QEMU_PERM 6
42
43struct uevent {
44    const char *action;
45    const char *path;
46    const char *subsystem;
47    const char *firmware;
48    int major;
49    int minor;
50};
51
52static int open_uevent_socket(void)
53{
54    struct sockaddr_nl addr;
55    int sz = 64*1024; // XXX larger? udev uses 16MB!
56    int s;
57
58    memset(&addr, 0, sizeof(addr));
59    addr.nl_family = AF_NETLINK;
60    addr.nl_pid = getpid();
61    addr.nl_groups = 0xffffffff;
62
63    s = socket(PF_NETLINK, SOCK_DGRAM, NETLINK_KOBJECT_UEVENT);
64    if(s < 0)
65        return -1;
66
67    setsockopt(s, SOL_SOCKET, SO_RCVBUFFORCE, &sz, sizeof(sz));
68
69    if(bind(s, (struct sockaddr *) &addr, sizeof(addr)) < 0) {
70        close(s);
71        return -1;
72    }
73
74    return s;
75}
76
77struct perms_ {
78    char *name;
79    mode_t perm;
80    unsigned int uid;
81    unsigned int gid;
82    unsigned short prefix;
83};
84static struct perms_ devperms[] = {
85    { "/dev/null",          0666,   AID_ROOT,       AID_ROOT,       0 },
86    { "/dev/zero",          0666,   AID_ROOT,       AID_ROOT,       0 },
87    { "/dev/full",          0666,   AID_ROOT,       AID_ROOT,       0 },
88    { "/dev/ptmx",          0666,   AID_ROOT,       AID_ROOT,       0 },
89    { "/dev/tty",           0666,   AID_ROOT,       AID_ROOT,       0 },
90    { "/dev/random",        0666,   AID_ROOT,       AID_ROOT,       0 },
91    { "/dev/urandom",       0666,   AID_ROOT,       AID_ROOT,       0 },
92    { "/dev/ashmem",        0666,   AID_ROOT,       AID_ROOT,       0 },
93    { "/dev/binder",        0666,   AID_ROOT,       AID_ROOT,       0 },
94
95	    /* logger should be world writable (for logging) but not readable */
96    { "/dev/log/",          0662,   AID_ROOT,       AID_LOG,        1 },
97
98    /* the msm hw3d client device node is world writable/readable. */
99    { "/dev/msm_hw3dc",     0666,   AID_ROOT,       AID_ROOT,       0 },
100
101    /* gpu driver for adreno200 is globally accessible */
102    { "/dev/kgsl",          0666,   AID_ROOT,       AID_ROOT,       0 },
103
104        /* these should not be world writable */
105    { "/dev/diag",          0660,   AID_RADIO,      AID_RADIO,        0 },
106    { "/dev/diag_arm9",     0660,   AID_RADIO,      AID_RADIO,        0 },
107    { "/dev/android_adb",   0660,   AID_ADB,        AID_ADB,        0 },
108    { "/dev/android_adb_enable",   0660,   AID_ADB,        AID_ADB,        0 },
109    { "/dev/ttyMSM0",       0600,   AID_BLUETOOTH,  AID_BLUETOOTH,  0 },
110    { "/dev/ttyHS0",        0600,   AID_BLUETOOTH,  AID_BLUETOOTH,  0 },
111    { "/dev/uinput",        0660,   AID_SYSTEM,     AID_BLUETOOTH,  0 },
112    { "/dev/alarm",         0664,   AID_SYSTEM,     AID_RADIO,      0 },
113    { "/dev/tty0",          0660,   AID_ROOT,       AID_SYSTEM,     0 },
114    { "/dev/graphics/",     0660,   AID_ROOT,       AID_GRAPHICS,   1 },
115    { "/dev/msm_hw3dm",     0660,   AID_SYSTEM,     AID_GRAPHICS,   0 },
116    { "/dev/input/",        0660,   AID_ROOT,       AID_INPUT,      1 },
117    { "/dev/eac",           0660,   AID_ROOT,       AID_AUDIO,      0 },
118    { "/dev/cam",           0660,   AID_ROOT,       AID_CAMERA,     0 },
119    { "/dev/pmem",          0660,   AID_SYSTEM,     AID_GRAPHICS,   0 },
120    { "/dev/pmem_adsp",     0660,   AID_SYSTEM,     AID_AUDIO,      1 },
121    { "/dev/pmem_camera",   0660,   AID_SYSTEM,     AID_CAMERA,     1 },
122    { "/dev/oncrpc/",       0660,   AID_ROOT,       AID_SYSTEM,     1 },
123    { "/dev/adsp/",         0660,   AID_SYSTEM,     AID_AUDIO,      1 },
124    { "/dev/snd/",          0660,   AID_SYSTEM,     AID_AUDIO,      1 },
125    { "/dev/mt9t013",       0660,   AID_SYSTEM,     AID_SYSTEM,     0 },
126    { "/dev/msm_camera/",   0660,   AID_SYSTEM,     AID_SYSTEM,     1 },
127    { "/dev/akm8976_daemon",0640,   AID_COMPASS,    AID_SYSTEM,     0 },
128    { "/dev/akm8976_aot",   0640,   AID_COMPASS,    AID_SYSTEM,     0 },
129    { "/dev/akm8973_daemon",0640,   AID_COMPASS,    AID_SYSTEM,     0 },
130    { "/dev/akm8973_aot",   0640,   AID_COMPASS,    AID_SYSTEM,     0 },
131    { "/dev/bma150",        0640,   AID_COMPASS,    AID_SYSTEM,     0 },
132    { "/dev/cm3602",        0640,   AID_COMPASS,    AID_SYSTEM,     0 },
133    { "/dev/akm8976_pffd",  0640,   AID_COMPASS,    AID_SYSTEM,     0 },
134    { "/dev/lightsensor",   0640,   AID_SYSTEM,     AID_SYSTEM,     0 },
135    { "/dev/msm_pcm_out",   0660,   AID_SYSTEM,     AID_AUDIO,      1 },
136    { "/dev/msm_pcm_in",    0660,   AID_SYSTEM,     AID_AUDIO,      1 },
137    { "/dev/msm_pcm_ctl",   0660,   AID_SYSTEM,     AID_AUDIO,      1 },
138    { "/dev/msm_snd",       0660,   AID_SYSTEM,     AID_AUDIO,      1 },
139    { "/dev/msm_mp3",       0660,   AID_SYSTEM,     AID_AUDIO,      1 },
140    { "/dev/audience_a1026", 0660,   AID_SYSTEM,     AID_AUDIO,      1 },
141    { "/dev/tpa2018d1",     0660,   AID_SYSTEM,     AID_AUDIO,      1 },
142    { "/dev/msm_audpre",    0660,   AID_SYSTEM,     AID_AUDIO,      0 },
143    { "/dev/msm_audio_ctl", 0660,   AID_SYSTEM,     AID_AUDIO,      0 },
144    { "/dev/htc-acoustic",  0660,   AID_SYSTEM,     AID_AUDIO,      0 },
145    { "/dev/vdec",          0660,   AID_SYSTEM,     AID_AUDIO,      0 },
146    { "/dev/q6venc",        0660,   AID_SYSTEM,     AID_AUDIO,      0 },
147    { "/dev/snd/dsp",       0660,   AID_SYSTEM,     AID_AUDIO,      0 },
148    { "/dev/snd/dsp1",      0660,   AID_SYSTEM,     AID_AUDIO,      0 },
149    { "/dev/snd/mixer",     0660,   AID_SYSTEM,     AID_AUDIO,      0 },
150    { "/dev/smd0",          0640,   AID_RADIO,      AID_RADIO,      0 },
151    { "/dev/qemu_trace",    0666,   AID_SYSTEM,     AID_SYSTEM,     0 },
152    { "/dev/qmi",           0640,   AID_RADIO,      AID_RADIO,      0 },
153    { "/dev/qmi0",          0640,   AID_RADIO,      AID_RADIO,      0 },
154    { "/dev/qmi1",          0640,   AID_RADIO,      AID_RADIO,      0 },
155    { "/dev/qmi2",          0640,   AID_RADIO,      AID_RADIO,      0 },
156        /* CDMA radio interface MUX */
157    { "/dev/ts0710mux",     0640,   AID_RADIO,      AID_RADIO,      1 },
158    { "/dev/ppp",           0660,   AID_RADIO,      AID_VPN,        0 },
159    { "/dev/tun",           0640,   AID_VPN,        AID_VPN,        0 },
160    { NULL, 0, 0, 0, 0 },
161};
162
163/* devperms_partners list and perm_node are for hardware specific /dev entries */
164struct perm_node {
165    struct perms_ dp;
166    struct listnode plist;
167};
168list_declare(devperms_partners);
169
170/*
171 * Permission override when in emulator mode, must be parsed before
172 * system properties is initalized.
173 */
174static int qemu_perm_count;
175static struct perms_ qemu_perms[MAX_QEMU_PERM + 1];
176
177int add_devperms_partners(const char *name, mode_t perm, unsigned int uid,
178                        unsigned int gid, unsigned short prefix) {
179    int size;
180    struct perm_node *node = malloc(sizeof (struct perm_node));
181    if (!node)
182        return -ENOMEM;
183
184    size = strlen(name) + 1;
185    if ((node->dp.name = malloc(size)) == NULL)
186        return -ENOMEM;
187
188    memcpy(node->dp.name, name, size);
189    node->dp.perm = perm;
190    node->dp.uid = uid;
191    node->dp.gid = gid;
192    node->dp.prefix = prefix;
193
194    list_add_tail(&devperms_partners, &node->plist);
195    return 0;
196}
197
198void qemu_init(void) {
199    qemu_perm_count = 0;
200    memset(&qemu_perms, 0, sizeof(qemu_perms));
201}
202
203static int qemu_perm(const char* name, mode_t perm, unsigned int uid,
204                         unsigned int gid, unsigned short prefix)
205{
206    char *buf;
207    if (qemu_perm_count == MAX_QEMU_PERM)
208        return -ENOSPC;
209
210    buf = malloc(strlen(name) + 1);
211    if (!buf)
212        return -errno;
213
214    strlcpy(buf, name, strlen(name) + 1);
215    qemu_perms[qemu_perm_count].name = buf;
216    qemu_perms[qemu_perm_count].perm = perm;
217    qemu_perms[qemu_perm_count].uid = uid;
218    qemu_perms[qemu_perm_count].gid = gid;
219    qemu_perms[qemu_perm_count].prefix = prefix;
220
221    qemu_perm_count++;
222    return 0;
223}
224
225/* Permission overrides for emulator that are parsed from /proc/cmdline. */
226void qemu_cmdline(const char* name, const char *value)
227{
228    char *buf;
229    if (!strcmp(name, "android.ril")) {
230        /* cmd line params currently assume /dev/ prefix */
231        if (asprintf(&buf, CMDLINE_PREFIX"/%s", value) == -1) {
232            return;
233        }
234        INFO("nani- buf:: %s\n", buf);
235        qemu_perm(buf, 0660, AID_RADIO, AID_ROOT, 0);
236    }
237}
238
239static int get_device_perm_inner(struct perms_ *perms, const char *path,
240                                    unsigned *uid, unsigned *gid, mode_t *perm)
241{
242    int i;
243    for(i = 0; perms[i].name; i++) {
244
245        if(perms[i].prefix) {
246            if(strncmp(path, perms[i].name, strlen(perms[i].name)))
247                continue;
248        } else {
249            if(strcmp(path, perms[i].name))
250                continue;
251        }
252        *uid = perms[i].uid;
253        *gid = perms[i].gid;
254        *perm = perms[i].perm;
255        return 0;
256    }
257    return -1;
258}
259
260/* First checks for emulator specific permissions specified in /proc/cmdline. */
261static mode_t get_device_perm(const char *path, unsigned *uid, unsigned *gid)
262{
263    mode_t perm;
264
265    if (get_device_perm_inner(qemu_perms, path, uid, gid, &perm) == 0) {
266        return perm;
267    } else if (get_device_perm_inner(devperms, path, uid, gid, &perm) == 0) {
268        return perm;
269    } else {
270        struct listnode *node;
271        struct perm_node *perm_node;
272        struct perms_ *dp;
273
274        /* Check partners list. */
275        list_for_each(node, &devperms_partners) {
276            perm_node = node_to_item(node, struct perm_node, plist);
277            dp = &perm_node->dp;
278
279            if (dp->prefix) {
280                if (strncmp(path, dp->name, strlen(dp->name)))
281                    continue;
282            } else {
283                if (strcmp(path, dp->name))
284                    continue;
285            }
286            /* Found perm in partner list. */
287            *uid = dp->uid;
288            *gid = dp->gid;
289            return dp->perm;
290        }
291        /* Default if nothing found. */
292        *uid = 0;
293        *gid = 0;
294        return 0600;
295    }
296}
297
298static void make_device(const char *path, int block, int major, int minor)
299{
300    unsigned uid;
301    unsigned gid;
302    mode_t mode;
303    dev_t dev;
304
305    if(major > 255 || minor > 255)
306        return;
307
308    mode = get_device_perm(path, &uid, &gid) | (block ? S_IFBLK : S_IFCHR);
309    dev = (major << 8) | minor;
310    /* Temporarily change egid to avoid race condition setting the gid of the
311     * device node. Unforunately changing the euid would prevent creation of
312     * some device nodes, so the uid has to be set with chown() and is still
313     * racy. Fixing the gid race at least fixed the issue with system_server
314     * opening dynamic input devices under the AID_INPUT gid. */
315    setegid(gid);
316    mknod(path, mode, dev);
317    chown(path, uid, -1);
318    setegid(AID_ROOT);
319}
320
321#if LOG_UEVENTS
322
323static inline suseconds_t get_usecs(void)
324{
325    struct timeval tv;
326    gettimeofday(&tv, 0);
327    return tv.tv_sec * (suseconds_t) 1000000 + tv.tv_usec;
328}
329
330#define log_event_print(x...) INFO(x)
331
332#else
333
334#define log_event_print(fmt, args...)   do { } while (0)
335#define get_usecs()                     0
336
337#endif
338
339static void parse_event(const char *msg, struct uevent *uevent)
340{
341    uevent->action = "";
342    uevent->path = "";
343    uevent->subsystem = "";
344    uevent->firmware = "";
345    uevent->major = -1;
346    uevent->minor = -1;
347
348        /* currently ignoring SEQNUM */
349    while(*msg) {
350        if(!strncmp(msg, "ACTION=", 7)) {
351            msg += 7;
352            uevent->action = msg;
353        } else if(!strncmp(msg, "DEVPATH=", 8)) {
354            msg += 8;
355            uevent->path = msg;
356        } else if(!strncmp(msg, "SUBSYSTEM=", 10)) {
357            msg += 10;
358            uevent->subsystem = msg;
359        } else if(!strncmp(msg, "FIRMWARE=", 9)) {
360            msg += 9;
361            uevent->firmware = msg;
362        } else if(!strncmp(msg, "MAJOR=", 6)) {
363            msg += 6;
364            uevent->major = atoi(msg);
365        } else if(!strncmp(msg, "MINOR=", 6)) {
366            msg += 6;
367            uevent->minor = atoi(msg);
368        }
369
370            /* advance to after the next \0 */
371        while(*msg++)
372            ;
373    }
374
375    log_event_print("event { '%s', '%s', '%s', '%s', %d, %d }\n",
376                    uevent->action, uevent->path, uevent->subsystem,
377                    uevent->firmware, uevent->major, uevent->minor);
378}
379
380static void handle_device_event(struct uevent *uevent)
381{
382    char devpath[96];
383    char *base, *name;
384    int block;
385
386        /* if it's not a /dev device, nothing to do */
387    if((uevent->major < 0) || (uevent->minor < 0))
388        return;
389
390        /* do we have a name? */
391    name = strrchr(uevent->path, '/');
392    if(!name)
393        return;
394    name++;
395
396        /* too-long names would overrun our buffer */
397    if(strlen(name) > 64)
398        return;
399
400        /* are we block or char? where should we live? */
401    if(!strncmp(uevent->subsystem, "block", 5)) {
402        block = 1;
403        base = "/dev/block/";
404        mkdir(base, 0755);
405    } else {
406        block = 0;
407            /* this should probably be configurable somehow */
408        if(!strncmp(uevent->subsystem, "graphics", 8)) {
409            base = "/dev/graphics/";
410            mkdir(base, 0755);
411        } else if (!strncmp(uevent->subsystem, "oncrpc", 6)) {
412            base = "/dev/oncrpc/";
413            mkdir(base, 0755);
414        } else if (!strncmp(uevent->subsystem, "adsp", 4)) {
415            base = "/dev/adsp/";
416            mkdir(base, 0755);
417        } else if (!strncmp(uevent->subsystem, "msm_camera", 10)) {
418            base = "/dev/msm_camera/";
419            mkdir(base, 0755);
420        } else if(!strncmp(uevent->subsystem, "input", 5)) {
421            base = "/dev/input/";
422            mkdir(base, 0755);
423        } else if(!strncmp(uevent->subsystem, "mtd", 3)) {
424            base = "/dev/mtd/";
425            mkdir(base, 0755);
426        } else if(!strncmp(uevent->subsystem, "sound", 5)) {
427            base = "/dev/snd/";
428            mkdir(base, 0755);
429        } else if(!strncmp(uevent->subsystem, "misc", 4) &&
430                    !strncmp(name, "log_", 4)) {
431            base = "/dev/log/";
432            mkdir(base, 0755);
433            name += 4;
434        } else
435            base = "/dev/";
436    }
437
438    snprintf(devpath, sizeof(devpath), "%s%s", base, name);
439
440    if(!strcmp(uevent->action, "add")) {
441        make_device(devpath, block, uevent->major, uevent->minor);
442        return;
443    }
444
445    if(!strcmp(uevent->action, "remove")) {
446        unlink(devpath);
447        return;
448    }
449}
450
451static int load_firmware(int fw_fd, int loading_fd, int data_fd)
452{
453    struct stat st;
454    long len_to_copy;
455    int ret = 0;
456
457    if(fstat(fw_fd, &st) < 0)
458        return -1;
459    len_to_copy = st.st_size;
460
461    write(loading_fd, "1", 1);  /* start transfer */
462
463    while (len_to_copy > 0) {
464        char buf[PAGE_SIZE];
465        ssize_t nr;
466
467        nr = read(fw_fd, buf, sizeof(buf));
468        if(!nr)
469            break;
470        if(nr < 0) {
471            ret = -1;
472            break;
473        }
474
475        len_to_copy -= nr;
476        while (nr > 0) {
477            ssize_t nw = 0;
478
479            nw = write(data_fd, buf + nw, nr);
480            if(nw <= 0) {
481                ret = -1;
482                goto out;
483            }
484            nr -= nw;
485        }
486    }
487
488out:
489    if(!ret)
490        write(loading_fd, "0", 1);  /* successful end of transfer */
491    else
492        write(loading_fd, "-1", 2); /* abort transfer */
493
494    return ret;
495}
496
497static void process_firmware_event(struct uevent *uevent)
498{
499    char *root, *loading, *data, *file;
500    int l, loading_fd, data_fd, fw_fd;
501
502    log_event_print("firmware event { '%s', '%s' }\n",
503                    uevent->path, uevent->firmware);
504
505    l = asprintf(&root, SYSFS_PREFIX"%s/", uevent->path);
506    if (l == -1)
507        return;
508
509    l = asprintf(&loading, "%sloading", root);
510    if (l == -1)
511        goto root_free_out;
512
513    l = asprintf(&data, "%sdata", root);
514    if (l == -1)
515        goto loading_free_out;
516
517    l = asprintf(&file, FIRMWARE_DIR"/%s", uevent->firmware);
518    if (l == -1)
519        goto data_free_out;
520
521    loading_fd = open(loading, O_WRONLY);
522    if(loading_fd < 0)
523        goto file_free_out;
524
525    data_fd = open(data, O_WRONLY);
526    if(data_fd < 0)
527        goto loading_close_out;
528
529    fw_fd = open(file, O_RDONLY);
530    if(fw_fd < 0)
531        goto data_close_out;
532
533    if(!load_firmware(fw_fd, loading_fd, data_fd))
534        log_event_print("firmware copy success { '%s', '%s' }\n", root, file);
535    else
536        log_event_print("firmware copy failure { '%s', '%s' }\n", root, file);
537
538    close(fw_fd);
539data_close_out:
540    close(data_fd);
541loading_close_out:
542    close(loading_fd);
543file_free_out:
544    free(file);
545data_free_out:
546    free(data);
547loading_free_out:
548    free(loading);
549root_free_out:
550    free(root);
551}
552
553static void handle_firmware_event(struct uevent *uevent)
554{
555    pid_t pid;
556
557    if(strcmp(uevent->subsystem, "firmware"))
558        return;
559
560    if(strcmp(uevent->action, "add"))
561        return;
562
563    /* we fork, to avoid making large memory allocations in init proper */
564    pid = fork();
565    if (!pid) {
566        process_firmware_event(uevent);
567        exit(EXIT_SUCCESS);
568    }
569}
570
571#define UEVENT_MSG_LEN  1024
572void handle_device_fd(int fd)
573{
574    char msg[UEVENT_MSG_LEN+2];
575    int n;
576
577    while((n = recv(fd, msg, UEVENT_MSG_LEN, 0)) > 0) {
578        struct uevent uevent;
579
580        if(n == UEVENT_MSG_LEN)   /* overflow -- discard */
581            continue;
582
583        msg[n] = '\0';
584        msg[n+1] = '\0';
585
586        parse_event(msg, &uevent);
587
588        handle_device_event(&uevent);
589        handle_firmware_event(&uevent);
590    }
591}
592
593/* Coldboot walks parts of the /sys tree and pokes the uevent files
594** to cause the kernel to regenerate device add events that happened
595** before init's device manager was started
596**
597** We drain any pending events from the netlink socket every time
598** we poke another uevent file to make sure we don't overrun the
599** socket's buffer.
600*/
601
602static void do_coldboot(int event_fd, DIR *d)
603{
604    struct dirent *de;
605    int dfd, fd;
606
607    dfd = dirfd(d);
608
609    fd = openat(dfd, "uevent", O_WRONLY);
610    if(fd >= 0) {
611        write(fd, "add\n", 4);
612        close(fd);
613        handle_device_fd(event_fd);
614    }
615
616    while((de = readdir(d))) {
617        DIR *d2;
618
619        if(de->d_type != DT_DIR || de->d_name[0] == '.')
620            continue;
621
622        fd = openat(dfd, de->d_name, O_RDONLY | O_DIRECTORY);
623        if(fd < 0)
624            continue;
625
626        d2 = fdopendir(fd);
627        if(d2 == 0)
628            close(fd);
629        else {
630            do_coldboot(event_fd, d2);
631            closedir(d2);
632        }
633    }
634}
635
636static void coldboot(int event_fd, const char *path)
637{
638    DIR *d = opendir(path);
639    if(d) {
640        do_coldboot(event_fd, d);
641        closedir(d);
642    }
643}
644
645int device_init(void)
646{
647    suseconds_t t0, t1;
648    int fd;
649
650    fd = open_uevent_socket();
651    if(fd < 0)
652        return -1;
653
654    fcntl(fd, F_SETFD, FD_CLOEXEC);
655    fcntl(fd, F_SETFL, O_NONBLOCK);
656
657    t0 = get_usecs();
658    coldboot(fd, "/sys/class");
659    coldboot(fd, "/sys/block");
660    coldboot(fd, "/sys/devices");
661    t1 = get_usecs();
662
663    log_event_print("coldboot %ld uS\n", ((long) (t1 - t0)));
664
665    return fd;
666}
667