WiringPi/wiringPi/wiringPi.c

/*
 * wiringPi:
 *	Arduino compatable (ish) Wiring library for the Raspberry Pi
 *	Copyright (c) 2012 Gordon Henderson
 *
 *	Thanks to code samples from Gert Jan van Loo and the
 *	BCM2835 ARM Peripherals manual, however it's missing
 *	the clock section /grr/mutter/
 ***********************************************************************
 * This file is part of wiringPi:
 *	https://projects.drogon.net/raspberry-pi/wiringpi/
 *
 *    wiringPi is free software: you can redistribute it and/or modify
 *    it under the terms of the GNU General Public License as published by
 *    the Free Software Foundation, either version 3 of the License, or
 *    (at your option) any later version.
 *
 *    wiringPi is distributed in the hope that it will be useful,
 *    but WITHOUT ANY WARRANTY; without even the implied warranty of
 *    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 *    GNU General Public License for more details.
 *
 *    You should have received a copy of the GNU General Public License
 *    along with wiringPi.  If not, see <http://www.gnu.org/licenses/>.
 ***********************************************************************
 */

// Revisions:
//	 2 Jul 2012:
//		Fixed a few more bugs to do with range-checking when in GPIO mode.
//	11 Jun 2012:
//		Fixed some typos.
//		Added c++ support for the .h file
//		Added a new function to allow for using my "pin" numbers, or native
//			GPIO pin numbers.
//		Removed my busy-loop delay and replaced it with a call to delayMicroseconds
//
//	02 May 2012:
//		Added in the 2 UART pins
//		Change maxPins to numPins to more accurately reflect purpose

// Pad drive current fiddling

#undef	DEBUG_PADS

#include <stdio.h>
#include <stdint.h>
#include <unistd.h>
#include <errno.h>
#include <string.h>
#include <time.h>
#include <fcntl.h>
#include <sys/time.h>
#include <sys/mman.h>
#include <sys/types.h>
#include <sys/stat.h>



#include "wiringPi.h"

#ifndef	TRUE
#define	TRUE	(1==1)
#define	FALSE	(1==2)
#endif

// Port function select bits

#define	FSEL_INPT		0b000
#define	FSEL_OUTP		0b001
#define	FSEL_ALT0		0b100
#define	FSEL_ALT0		0b100
#define	FSEL_ALT1		0b101
#define	FSEL_ALT2		0b110
#define	FSEL_ALT3		0b111
#define	FSEL_ALT4		0b011
#define	FSEL_ALT5		0b010

// Access from ARM Running Linux
//	Take from Gerts code. Some of this is not in the manual
//	that I can find )-:

#define BCM2708_PERI_BASE	0x20000000
#define GPIO_PADS		(BCM2708_PERI_BASE + 0x100000)
#define CLOCK_BASE		(BCM2708_PERI_BASE + 0x101000)
#define GPIO_BASE		(BCM2708_PERI_BASE + 0x200000)
#define GPIO_PWM		(BCM2708_PERI_BASE + 0x20C000)

#define	PAGE_SIZE		(4*1024)
#define	BLOCK_SIZE		(4*1024)

// PWM

#define	PWM_CONTROL 0
#define	PWM_STATUS  1
#define	PWM0_RANGE  4
#define	PWM0_DATA   5
#define	PWM1_RANGE  8
#define	PWM1_DATA   9

#define	PWMCLK_CNTL	40
#define	PWMCLK_DIV	41

#define	PWM1_MS_MODE    0x8000  // Run in MS mode
#define	PWM1_USEFIFO    0x2000  // Data from FIFO
#define	PWM1_REVPOLAR   0x1000  // Reverse polarity
#define	PWM1_OFFSTATE   0x0800  // Ouput Off state
#define	PWM1_REPEATFF   0x0400  // Repeat last value if FIFO empty
#define	PWM1_SERIAL     0x0200  // Run in serial mode
#define	PWM1_ENABLE     0x0100  // Channel Enable

#define	PWM0_MS_MODE    0x0080  // Run in MS mode
#define	PWM0_USEFIFO    0x0020  // Data from FIFO
#define	PWM0_REVPOLAR   0x0010  // Reverse polarity
#define	PWM0_OFFSTATE   0x0008  // Ouput Off state
#define	PWM0_REPEATFF   0x0004  // Repeat last value if FIFO empty
#define	PWM0_SERIAL     0x0002  // Run in serial mode
#define	PWM0_ENABLE     0x0001  // Channel Enable


// Locals to hold pointers to the hardware

static volatile uint32_t *gpio ;
static volatile uint32_t *pwm ;
static volatile uint32_t *clk ;

// The BCM2835 has 54 GPIO pins.
//	BCM2835 data sheet, Page 90 onwards.
//	There are 6 control registers, each control the functions of a block
//	of 10 pins.
//	Each control register has 10 sets of 3 bits per GPIO pin:
//
//	000 = GPIO Pin X is an input
//	001 = GPIO Pin X is an output
//	100 = GPIO Pin X takes alternate function 0
//	101 = GPIO Pin X takes alternate function 1
//	110 = GPIO Pin X takes alternate function 2
//	111 = GPIO Pin X takes alternate function 3
//	011 = GPIO Pin X takes alternate function 4
//	010 = GPIO Pin X takes alternate function 5
//
// So the 3 bits for port X are:
//	X / 10 + ((X % 10) * 3)

// sysFds:
//	Map a file descriptor from the /sys/class/gpio/gpioX/value file

static int sysFds [64] ;

// Mode

static int gpioPinMode ;

// Doing it the Arduino way with lookup tables...
//	Yes, it's probably more innefficient than all the bit-twidling, but it
//	does tend to make it all a bit clearer. At least to me!

// pinToGpio:
//	Take a Wiring pin (0 through X) and re-map it to the BCM_GPIO pin

static int pinToGpio [] =
{
  17, 18, 21, 22, 23, 24, 25, 4,	// From the Original Wiki - GPIO 0 through 7
   0,  1,				// I2C  - SDA0, SCL0
   8,  7,				// SPI  - CE1, CE0
  10,  9, 11, 				// SPI  - MOSI, MISO, SCLK
  14, 15,				// UART - Tx, Rx
} ;

// gpioToGPFSEL:
//	Map a BCM_GPIO pin to it's control port. (GPFSEL 0-5)

static uint8_t gpioToGPFSEL [] =
{
  0,0,0,0,0,0,0,0,0,0,
  1,1,1,1,1,1,1,1,1,1,
  2,2,2,2,2,2,2,2,2,2,
  3,3,3,3,3,3,3,3,3,3,
  4,4,4,4,4,4,4,4,4,4,
  5,5,5,5,5,5,5,5,5,5,
} ;

// gpioToShift
//	Define the shift up for the 3 bits per pin in each GPFSEL port

static uint8_t gpioToShift [] =
{
  0,3,6,9,12,15,18,21,24,27,
  0,3,6,9,12,15,18,21,24,27,
  0,3,6,9,12,15,18,21,24,27,
  0,3,6,9,12,15,18,21,24,27,
  0,3,6,9,12,15,18,21,24,27,
} ;

// gpioToGPSET:
//	(Word) offset to the GPIO Set registers for each GPIO pin

static uint8_t gpioToGPSET [] =
{
   7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7,
   8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
} ;

// gpioToGPCLR:
//	(Word) offset to the GPIO Clear registers for each GPIO pin

static uint8_t gpioToGPCLR [] =
{
  10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,
  11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,
} ;

// gpioToGPLEV:
//	(Word) offset to the GPIO Input level registers for each GPIO pin

static uint8_t gpioToGPLEV [] =
{
  13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,
  14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,
} ;

// gpioToPUDCLK
//	(Word) offset to the Pull Up Down Clock regsiter

static uint8_t gpioToPUDCLK [] =
{
  38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,38,
  39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,39,
} ;

// gpioToPwmALT
//	the ALT value to put a GPIO pin into PWM mode

static uint8_t gpioToPwmALT [] =
{
          0,         0,         0,         0,         0,         0,         0,         0,	//  0 ->  7
          0,         0,         0,         0, FSEL_ALT0, FSEL_ALT0,         0,         0, 	//  8 -> 15
          0,         0, FSEL_ALT5, FSEL_ALT5,         0,         0,         0,         0, 	// 16 -> 23
          0,         0,         0,         0,         0,         0,         0,         0,	// 24 -> 31
          0,         0,         0,         0,         0,         0,         0,         0,	// 32 -> 39
  FSEL_ALT0, FSEL_ALT0,         0,         0,         0, FSEL_ALT0,         0,         0,	// 40 -> 47
          0,         0,         0,         0,         0,         0,         0,         0,	// 48 -> 55
          0,         0,         0,         0,         0,         0,         0,         0,	// 56 -> 63
} ;

static uint8_t gpioToPwmPort [] =
{
          0,         0,         0,         0,         0,         0,         0,         0,	//  0 ->  7
          0,         0,         0,         0, PWM0_DATA, PWM1_DATA,         0,         0, 	//  8 -> 15
          0,         0, PWM0_DATA, PWM1_DATA,         0,         0,         0,         0, 	// 16 -> 23
          0,         0,         0,         0,         0,         0,         0,         0,	// 24 -> 31
          0,         0,         0,         0,         0,         0,         0,         0,	// 32 -> 39
  PWM0_DATA, PWM1_DATA,         0,         0,         0, PWM1_DATA,         0,         0,	// 40 -> 47
          0,         0,         0,         0,         0,         0,         0,         0,	// 48 -> 55
          0,         0,         0,         0,         0,         0,         0,         0,	// 56 -> 63

} ;


// Time for easy calculations

static unsigned long long epoch ;

//////////////////////////////////////////////////////////////////////////////////


/*
 * wiringPiGpioMode:
 *	Set the mode - use Pin numbers (0-16) or GPIO number (seemingly random)
 *********************************************************************************
 */

void wiringPiGpioMode (int mode)
{
  gpioPinMode = mode ;
}


/*
 * wiringPiSetup:
 *	Must be called once at the start of your program execution.
 *
 * Default setup: Initialises the system into wiringPi Pin mode and uses the
 *	memory mapped hardware directly.
 *********************************************************************************
 */

int wiringPiSetup (void)
{
  int      fd ;
  uint8_t *gpioMem, *pwmMem, *clkMem ;
  struct timeval tv ;

#ifdef	DEBUG_PADS
  uint8_t *gpioMem, *padsMem, *pwmMem, *clkMem ;
  uint32_t *pads ;
#endif

// Set Pin mode by default

  wiringPiGpioMode (WPI_MODE_PINS) ;
  
// Open the master /dev/memory device

  if ((fd = open ("/dev/mem", O_RDWR | O_SYNC) ) < 0)
  {
    fprintf (stderr, "wiringPiSetup: Unable to open /dev/mem: %s\n", strerror (errno)) ;
    return -1 ;
  }

// GPIO:

// Allocate 2 pages - 1 ...

  if ((gpioMem = malloc (BLOCK_SIZE + (PAGE_SIZE-1))) == NULL)
  {
    fprintf (stderr, "wiringPiSetup: malloc failed: %s\n", strerror (errno)) ;
    return -1 ;
  }

// ... presumably to make sure we can round it up to a whole page size

  if (((uint32_t)gpioMem % PAGE_SIZE) != 0)
    gpioMem += PAGE_SIZE - ((uint32_t)gpioMem % PAGE_SIZE) ;

  gpio = (uint32_t *)mmap((caddr_t)gpioMem, BLOCK_SIZE, PROT_READ|PROT_WRITE, MAP_SHARED|MAP_FIXED, fd, GPIO_BASE) ;

  if ((int32_t)gpio < 0)
  {
    fprintf (stderr, "wiringPiSetup: mmap failed: %s\n", strerror (errno)) ;
    return -1 ;
  }

// PWM

  if ((pwmMem = malloc (BLOCK_SIZE + (PAGE_SIZE-1))) == NULL)
  {
    fprintf (stderr, "wiringPiSetup: pwmMem malloc failed: %s\n", strerror (errno)) ;
    return -1 ;
  }

  if (((uint32_t)pwmMem % PAGE_SIZE) != 0)
    pwmMem += PAGE_SIZE - ((uint32_t)pwmMem % PAGE_SIZE) ;

  pwm = (uint32_t *)mmap(pwmMem, BLOCK_SIZE, PROT_READ|PROT_WRITE, MAP_SHARED|MAP_FIXED, fd, GPIO_PWM) ;

  if ((int32_t)pwm < 0)
  {
    fprintf (stderr, "wiringPiSetup: mmap failed (pwm): %s\n", strerror (errno)) ;
    return -1 ;
  }
 
// Clock control (needed for PWM)

  if ((clkMem = malloc (BLOCK_SIZE + (PAGE_SIZE-1))) == NULL)
  {
    fprintf (stderr, "wiringPiSetup: clkMem malloc failed: %s\n", strerror (errno)) ;
    return -1 ;
  }

  if (((uint32_t)clkMem % PAGE_SIZE) != 0)
    clkMem += PAGE_SIZE - ((uint32_t)clkMem % PAGE_SIZE) ;

  clk = (uint32_t *)mmap(clkMem, BLOCK_SIZE, PROT_READ|PROT_WRITE, MAP_SHARED|MAP_FIXED, fd, CLOCK_BASE) ;

  if ((int32_t)clk < 0)
  {
    fprintf (stderr, "wiringPiSetup: mmap failed (clk): %s\n", strerror (errno)) ;
    return -1 ;
  }
 
#ifdef	DEBUG_PADS
  if ((padsMem = malloc (BLOCK_SIZE + (PAGE_SIZE-1))) == NULL)
  {
    fprintf (stderr, "wiringPiSetup: padsMem malloc failed: %s\n", strerror (errno)) ;
    return -1 ;
  }

  if (((uint32_t)padsMem % PAGE_SIZE) != 0)
    padsMem += PAGE_SIZE - ((uint32_t)padsMem % PAGE_SIZE) ;

  pads = (uint32_t *)mmap(padsMem, BLOCK_SIZE, PROT_READ|PROT_WRITE, MAP_SHARED|MAP_FIXED, fd, GPIO_PADS) ;

  if ((int32_t)pads < 0)
  {
    fprintf (stderr, "wiringPiSetup: mmap failed (pads): %s\n", strerror (errno)) ;
    return -1 ;
  }
 
  printf ("Checking pads @ 0x%08X\n", (unsigned int)pads) ;

  printf ("%08X %08X %08X\n", *(pads + 11), *(pads + 12), *(pads + 13)) ;
//  *(pads + 11) = 0x1F ;
  printf ("%08X %08X %08X\n", *(pads + 11), *(pads + 12), *(pads + 13)) ;
#endif

  gettimeofday (&tv, NULL) ;
  epoch = (tv.tv_sec * 1000000 + tv.tv_usec) / 1000 ;

  return 0 ;
}


/*
 * wiringPiSetupGpio:
 *	Must be called once at the start of your program execution.
 *
 * GPIO setup: Initialises the system into GPIO Pin mode and uses the
 *	memory mapped hardware directly.
 *********************************************************************************
 */

int wiringPiSetupGpio (void)
{
  int x = wiringPiSetup () ;

  if (x != 0)
    return x ;

  wiringPiGpioMode (WPI_MODE_GPIO) ;
  return 0 ;
}


/*
 * wiringPiSetupSys:
 *	Must be called once at the start of your program execution.
 *
 * Initialisation (again), however this time we are using the /sys/class/gpio
 *	interface to the GPIO systems - slightly slower, but always usable as
 *	a non-root user, assuming the devices are already exported and setup correctly.
 */

int wiringPiSetupSys (void)
{
  int fd, pin ;
  struct timeval tv ;
  char fName [128] ;

// Set GPIO_SYS mode by default

  wiringPiGpioMode (WPI_MODE_GPIO_SYS) ;

// Open and scan the directory, looking for exported GPIOs, and pre-open
//	the 'value' part to speed things up for later
  
  for (pin = 0 ; pin < 64 ; ++pin)
  {
    sysFds [pin] = -1 ;
    sprintf (fName, "/sys/class/gpio/gpio%d/value", pin) ;
    if ((fd = open (fName, O_RDWR)) == -1)
      continue ;
    sysFds [pin] = fd ;
  }

  gettimeofday (&tv, NULL) ;
  epoch = (tv.tv_sec * 1000000 + tv.tv_usec) / 1000 ;

  return 0 ;
}


/*
 * pinMode:
 *	Sets the mode of a pin to be input, output or PWM output
 *********************************************************************************
 */

void pinMode (int pin, int mode)
{
  static int pwmRunning  = FALSE ;

  int gpioPin, fSel, shift ;
  int alt ;

// We can't change the mode in GPIO_SYS mode

  if (gpioPinMode == WPI_MODE_GPIO_SYS)
    return ;

  if (gpioPinMode == WPI_MODE_PINS)
  {
    if ((pin < 0) || (pin >= NUM_PINS))
      return ;
    gpioPin = pinToGpio    [pin] ;
  }
  else
    gpioPin = pin ;

  fSel    = gpioToGPFSEL [gpioPin] ;
  shift   = gpioToShift  [gpioPin] ;

  /**/ if (mode == INPUT)
    *(gpio + fSel) = (*(gpio + fSel) & ~(7 << shift)) ; // Sets bits to zero = input
  else if (mode == OUTPUT)
    *(gpio + fSel) = (*(gpio + fSel) & ~(7 << shift)) | (1 << shift) ;
  else if (mode == PWM_OUTPUT)
  {
    if ((alt = gpioToPwmALT [gpioPin]) == 0)	// Not a PWM pin
      return ;

// Set pin to PWM mode

    *(gpio + fSel) = (*(gpio + fSel) & ~(7 << shift)) | (alt << shift) ;

// We didn't initialise the PWM hardware at setup time - because it's possible that
//	something else is using the PWM - e.g. the Audio systems! So if we use PWM
//	here, then we're assuming that nothing else is, otherwise things are going
//	to sound a bit funny...

    if (!pwmRunning)
    {

//	Gert/Doms Values
      *(clk + PWMCLK_DIV)  = 0x5A000000 | (32<<12) ;	// set pwm div to 32 (19.2/3 = 600KHz)
      *(clk + PWMCLK_CNTL) = 0x5A000011 ;		// Source=osc and enable
      digitalWrite (pin, LOW) ;
      *(pwm + PWM_CONTROL) = 0 ;			// Disable PWM
      delayMicroseconds (10) ;
      *(pwm + PWM0_RANGE) = 0x400 ;
      delayMicroseconds (10) ;
      *(pwm + PWM1_RANGE) = 0x400 ;
      delayMicroseconds (10) ;

// Enable PWMs

      *(pwm + PWM0_DATA) = 512 ;
      *(pwm + PWM1_DATA) = 512 ;

      *(pwm + PWM_CONTROL) = PWM0_ENABLE | PWM1_ENABLE ;
    }

  }

// When we change mode of any pin, we remove the pull up/downs

  pullUpDnControl (pin, PUD_OFF) ;
}


/*
 * digitalWrite:
 *	Set an output bit
 *********************************************************************************
 */

void digitalWrite (int pin, int value)
{
  int gpioPin ;

  if (gpioPinMode == WPI_MODE_PINS)
  {
    if ((pin < 0) || (pin >= NUM_PINS))
      return ;
    gpioPin = pinToGpio [pin] ;
  }
  else
    gpioPin = pin ;

  if (gpioPinMode == WPI_MODE_GPIO_SYS)
  {
    if (sysFds [gpioPin] != -1)
    {
      if (value == LOW)
	write (sysFds [gpioPin], "0\n", 2) ;
      else
	write (sysFds [gpioPin], "1\n", 2) ;
    }
  }
  else
  {
    if (value == LOW)
      *(gpio + gpioToGPCLR [gpioPin]) = 1 << gpioPin ;
    else
      *(gpio + gpioToGPSET [gpioPin]) = 1 << gpioPin ;
  }
}


/*
 * pwnWrite:
 *	Set an output PWM value
 *********************************************************************************
 */

void pwmWrite (int pin, int value)
{
  int port, gpioPin ;

// We can't do this in GPIO_SYS mode

  if (gpioPinMode == WPI_MODE_GPIO_SYS)
    return ;

  if (gpioPinMode == WPI_MODE_PINS)
  {
    if ((pin < 0) || (pin >= NUM_PINS))
      return ;
    gpioPin = pinToGpio [pin] ;
  }
  else
    gpioPin = pin ;

  port = gpioToPwmPort [gpioPin] ;

  *(pwm + port) = value & ~0x400 ;
}


/*
 * digitalRead:
 *	Read the value of a given Pin, returning HIGH or LOW
 *********************************************************************************
 */

int digitalRead (int pin)
{
  int gpioPin ;
  char c ;

  if (gpioPinMode == WPI_MODE_PINS)
  {
    if ((pin < 0) || (pin >= NUM_PINS))
      return 0 ;
    gpioPin = pinToGpio [pin] ;
  }
  else
    gpioPin = pin ;

  if (gpioPinMode == WPI_MODE_GPIO_SYS)
  {
    if (sysFds [gpioPin] == -1)
      return 0 ;
    else
    {
      lseek (sysFds [gpioPin], 0L, SEEK_SET) ;
      read  (sysFds [gpioPin], &c, 1) ;
      return (c == '0') ? 0 : 1 ;
    }
  }
  else
  {
    if ((*(gpio + gpioToGPLEV [gpioPin]) & (1 << gpioPin)) != 0)
      return HIGH ;
    else
      return LOW ;
  }
}

/*
 * pullUpDownCtrl:
 *	Control the internal pull-up/down resistors on a GPIO pin
 *	The Arduino only has pull-ups and these are enabled by writing 1
 *	to a port when in input mode - this paradigm doesn't quite apply
 *	here though.
 *********************************************************************************
 */

void pullUpDnControl (int pin, int pud)
{
  int gpioPin ;

// We can't do this in GPIO_SYS mode

  if (gpioPinMode == WPI_MODE_GPIO_SYS)
    return ;

  if (gpioPinMode == WPI_MODE_PINS)
  {
    if ((pin < 0) || (pin >= NUM_PINS))
      return ;
    gpioPin = pinToGpio [pin] ;
  }
  else
    gpioPin = pin ;

  *(gpio + 37) = pud ;
  delayMicroseconds (10) ;
  *(gpio + gpioToPUDCLK [gpioPin]) = 1 << gpioPin ;
  delayMicroseconds (10) ;
  
  *(gpio + 37) = 0 ;
  *(gpio + gpioToPUDCLK [gpioPin]) = 0 ;
}


/*
 * delay: delayMicroseconds
 *	Wait for some number of milli/micro seconds
 *********************************************************************************
 */

void delay (unsigned int howLong)
{
  struct timespec sleeper, dummy ;

  sleeper.tv_sec  = (time_t)(howLong / 1000) ;
  sleeper.tv_nsec = (long)(howLong % 1000) * 1000000 ;

  nanosleep (&sleeper, &dummy) ;
}

void delayMicroseconds (unsigned int howLong)
{
  struct timespec sleeper, dummy ;

  sleeper.tv_sec  = 0 ;
  sleeper.tv_nsec = (long)(howLong * 1000) ;

  nanosleep (&sleeper, &dummy) ;
}

/*
 * millis:
 *	Return a number of milliseconds as an unsigned int.
 *********************************************************************************
 */

unsigned int millis (void)
{
  struct timeval tv ;
  unsigned long long t1 ;

  gettimeofday (&tv, NULL) ;

  t1 = (tv.tv_sec * 1000000 + tv.tv_usec) / 1000 ;

  return (uint32_t)(t1 - epoch) ;
}