Merge parts of L001-AVRCurrentControl

linear_pendulum_2009/avr/Makefile

+PROJECT=current_control
+CHIP=atmega16
+
+ARCH=avr
+AVRSOURCE=
+AVRAUTO=compiled/$(ARCH)/
+AVRARCH=compiled/$(ARCH)/
+LIB_TARGET=$(AVRARCH)lib$(TARGET).a
+
+CC=$(ARCH)-gcc
+CXX=$(ARCH)-gcc
+CCFLAGS=-mmcu=$(CHIP) -O5 -I. -I$(AVRAUTO) 
+AS=$(ARCH)-as
+ASFLAGS=-mmcu=$(CHIP)
+AR=$(ARCH)-ar
+LD=$(ARCH)-ld
+OBJDUMP=$(ARCH)-objdump
+LDFLAGS= -T $(CHIP).link
+
+all: $(AVRARCH)$(PROJECT)
+
+$(LIB_TARGET)(%.o):     $(AVRSOURCE)%.c Makefile
+	$(CC) $(CCFLAGS) -c -o $(AVRARCH)$(%) -I$(AVRSOURCE) -I$(AVRAUTO) $(<) 
+	$(AR) r $(@) $(AVRARCH)$(%)
+	rm $(AVRARCH)$(%)
+
+$(LIB_TARGET)(%.o):     $(AVRSOURCE)%.cc Makefile
+	$(CXX) $(CCFLAGS) -c -o $(AVRARCH)$(%) -I$(AVRSOURCE) -I$(AVRAUTO) $(<) 
+	$(AR) r $(@) $(AVRARCH)$(%)
+	rm $(AVRARCH)$(%)
+
+$(LIB_TARGET)(%.o):     $(AVRSOURCE)%.s Makefile
+	$(AS) $(ASFLAGS) -o $(AVRARCH)$(%) $(AVRSOURCE)$(*).s
+	$(AR) r $(@) $(AVRARCH)$(%)
+	rm $(AVRARCH)$(%)
+
+$(AVRARCH)%.o:           $(AVRSOURCE)%.s Makefile
+	$(AS) $(ASFLAGS) -o $@ $(AVRSOURCE)$(*).s
+
+$(AVRARCH)%.o:           $(AVRSOURCE)%.c Makefile
+	$(CC) $(CCFLAGS) -c -o $@ -I. -I$(AVRAUTO) $< 
+
+
+$(AVRARCH)%:           $(AVRARCH)%.o Makefile
+	$(CC) $(CCFLAGS) -o $@ $<  -lm
+
+$(AVRARCH)%.sr:	all $(AVRARCH)%
+	avr-objcopy -O srec $(AVRARCH)/$(*) $@ 
+
+%.sr:	$(AVRARCH)%.sr
+	@/bin/true
+
+%.load:	compiled/avr/%.sr
+#	/work/andersb/atmel/uisp/uisp-0.2b/src/uisp \
+#	 	-dno-poll -dstk200 --erase --upload if=$(AVRARCH)/$(*).sr
+	uisp \
+		-dprog=stk200 \
+		--erase \
+		--upload if=compiled/avr/$*.sr
+
+%.load.stk500:	compiled/avr/%.sr
+	uisp \
+		-dprog=stk500 \
+		--erase \
+		--upload if=compiled/avr/$*.sr
+
+%.dump:	all $(AVRARCH)/%
+	$(OBJDUMP) -D $(AVRARCH)/$(*)
+
+$(AVRARCH)fuse.sr:	fuse.s
+	avr-gcc -o $(AVRARCH)fuse.o -c fuse.s 
+	avr-objcopy -O srec $(AVRARCH)fuse.o $(AVRARCH)fuse.sr
+
+fuse.load:	$(AVRARCH)fuse.sr
+	uisp \
+		-dprog=stk200 \
+		--erase \
+		--segment=fuse \
+		--upload if=compiled/avr/fuse.sr
+
+load.stk500:	$(PROJECT).load.stk500
\ No newline at end of file

linear_pendulum_2009/avr/compileUploadCurrentControl.sh

+avr-gcc -mmcu=atmega16 -g -Wall -o current_control current_control.c
+avr-objcopy -Osrec current_control current_control.sr
+uisp -dprog=stk200 --erase --upload if=current_control.sr
\ No newline at end of file

linear_pendulum_2009/avr/compileUploadVelControl.sh

+avr-gcc -mmcu=atmega16 -O -g -Wall -o vel_control.o vel_control.c pccom.c
+avr-objcopy -Osrec vel_control.o vel_control.sr
+uisp -dprog=stk200 --erase --upload if=vel_control.sr
\ No newline at end of file

linear_pendulum_2009/avr/current_control.c

+/*
+***************************************************************
+
+ Current regulation - Pontus Giselsson, Per-Ola Larsson 18/02/09
+           for LTH - reglerteknik
+
+***************************************************************
+*/
+#include <avr/twi.h>
+#include <avr/io.h>
+#include <avr/signal.h>
+#include <avr/interrupt.h>
+#include <inttypes.h>
+
+
+// control variables
+volatile int16_t ref=0;        // reference value (from velocity controller)
+volatile int16_t y;            // measurement, 9 frac bits
+volatile uint16_t low, high;   // when reading AD-conversion
+volatile int16_t e = 0;        // control error, 9 frac bits
+volatile int16_t v = 0;        // temporary ctrl signal, 9 frac bits
+volatile int16_t vSat = 0;     // saturated temporary ctrl signal, 9 frac bits
+volatile int16_t I = 0;        // integral part of ctrl, 13 frac bits
+volatile int16_t u = 0;        // ctrl signal = pwm high time (8 bits)
+volatile int16_t K = 111;      // 7 frac bits
+volatile int16_t Ke = 38;      // 7 frac bits, K*h/Ti
+volatile int8_t intCond = 0;   // flag for conditional integration
+
+#define V_MAX 508              //max/min for saturation
+#define V_MIN -508
+
+// twi variable
+volatile int16_t status;
+
+// logging variables
+/*
+#define log_len 100
+volatile int16_t ctrl_log[log_len];
+volatile int16_t error_log[log_len];
+volatile int32_t I_log[log_len];
+volatile int16_t skipSamples = 1000;
+volatile int16_t countSamples = 0;
+volatile int16_t jj=0;
+volatile int8_t stop = 0;
+*/
+
+/* Routine used to transmit bytes on the serial port */
+/*
+static void putchar(unsigned char ch)
+{
+	while ((inp(UCSRA) & 0x20) == 0) {};
+	outp(ch, UDR);
+	while ((inp(UCSRA) & 0x20) == 0) {};
+}
+*/
+
+/* Send logged data over Serial connection */
+/*
+static inline void sendData() {
+  int16_t ii = 0;
+  while (ii < log_len) {
+
+    putchar((unsigned char) ((ctrl_log[ii]&0xff00)>>8));
+    putchar((unsigned char) (ctrl_log[ii]&0x00ff));
+
+    putchar((unsigned char) ((error_log[ii]&0xff00)>>8));
+    putchar((unsigned char) (error_log[ii]&0x00ff));
+
+    putchar((unsigned char) ((I_log[ii]&0xff000000)>>24));
+    putchar((unsigned char) ((I_log[ii]&0x00ff0000)>>16));
+
+    putchar((unsigned char) ((I_log[ii]&0x0000ff00)>>8));
+    putchar((unsigned char) (I_log[ii]&0x000000ff));
+
+    ii++;
+  }
+}
+*/
+
+
+
+/* Timer 2 compare match interupt, 28.8 kHz, syncronized with pwm-period */
+SIGNAL(SIG_OUTPUT_COMPARE2) {
+
+  // Start AD conversion
+  ADCSRA |= BV(ADSC);
+  
+  // Read previous AD-conversion result
+  low = inp(ADCL);
+  high = inp(ADCH);
+  y = ((int16_t)((high<<8) | low)) - 512; // y 9 frac bits
+
+  // control error
+  e = ref-y; // e 9 frac bits
+  
+  // temporary ctrl-signal
+  v = (((K*e+64)>>7)+((I+8)>>4));
+
+  // variable that decides if I-part should be updated
+  intCond = 1;
+
+  // saturation and update integral part of ctrl with antiwindup
+  if (v > V_MAX) {
+    vSat = V_MAX;
+    if (e > 0)
+      intCond = 0;
+  } else if (v < V_MIN) {
+    vSat = V_MIN;
+    if (e < 0)
+      intCond = 0; 
+  } else {
+    vSat = v;
+  }
+
+  if (intCond)
+    I = I + (((Ke*e)+(1<<2))>>3);
+
+  // ctrl signal, 7 bits + direction
+  u = ((vSat+2)>>2); //7 frac bits to pwm 
+
+  // set pwm switching time
+  if (u < 0) {
+    PORTC |= 0x80;  // set direction of motion
+    OCR1BL = ((unsigned char) (-u)); // set length of pwm-high
+  } else {
+    PORTC &= 0x7f; // set direction of motion
+    OCR1BL = ((unsigned char) (u)); // set length of pwm-high
+  }
+
+  
+  // TWI-communication, recieve reference from velocity controller
+  if ((BV(TWINT)&inp(TWCR))) {
+    status = (inp(TWSR)&0xf8);
+    // status 0x80 means data recieved
+    if (status == 0x80) {
+      ref = (int16_t)((int8_t)inp(TWDR)); // read 8 bit reference
+      ref = (ref<<2);  // shift up 2 steps for 10 bits reference in loop
+    } 
+    else {
+    }
+    outp(BV(TWINT)|BV(TWEN)|BV(TWEA),TWCR);
+  }
+
+  // For logging purposes
+  /*
+  countSamples++;
+  if (countSamples == skipSamples) {
+    ctrl_log[jj] = u;
+    I_log[jj] = I;
+    error_log[jj] = e;
+    jj++;
+    countSamples = 0;
+    
+    // Stop after a while
+    if ((jj == (log_len-1)) & !stop) {
+	outp(0x7f,OCR1BL);
+	stop = 1;
+	sendData();
+    }
+  }
+  */
+  
+}
+
+
+int main()
+{
+  // clear interrupts (might not be needed)
+  cli();
+  
+  //Port directions
+  outp(0x08,PORTC); // pull up on overtemperature signals
+  outp(0xa0,DDRC);  // output on direction and brake
+  outp(0x10,DDRD);  // output on pwm-signal
+  outp(0x40,DDRB);  // temp pwm output
+
+  /* Timer section */
+  // Timer 1, fast PWM no prescaling (non-inverting mode (start high, switch to low))
+  outp(BV(COM1B1)|BV(WGM11)|BV(WGM10),TCCR1A);
+  outp(BV(CS10)|BV(WGM13)|BV(WGM12),TCCR1B);
+  
+  // Reset Timer1 and set TOP-value to 128 (means 7-bit pwm-signal-> 115.2 kHz)
+  outp(0x00,OCR1AH);
+  outp(0x7f,OCR1AL);
+  outp(0x00,TCNT1H);
+  outp(0x00,TCNT1L);
+  outp(0x00,OCR1BH);
+  outp(0x7f,OCR1BL); // to not start motor-rotation before control
+
+
+  
+  /* Timer 2, 4 times pwm-period, for control sampling, prescaler 8, 28.8 kHz */
+  outp(BV(WGM21)|BV(CS21),TCCR2);
+  outp(0x3f,OCR2);
+  /* Reset timer 2 */
+  outp(0,TCNT2);
+
+  // Enable timer2 compare match interrupts
+  outp(BV(OCIE2),TIMSK);
+
+  //Serial communication
+  outp(0x00, UCSRA);	// USART:
+  outp(0x18, UCSRB);	// USART: RxEnable|TxEnable
+  outp(0x86, UCSRC);	// USART: 8bit, no parity
+  outp(0x00, UBRRH);	// USART: 115200 @ 14.7456MHz
+  outp(7,UBRRL);	// USART: 115200 @ 14.7456MHz
+  
+  /* AREF (AREF is 5V) pin external capacitor, MUX0 for current measurement */
+  outp(BV(REFS0)|BV(MUX0),ADMUX); 	
+  
+  // Enable ADC, start first conversion, prescaler 32, not free running mode
+  outp(BV(ADEN)|BV(ADSC)|BV(ADPS2)|BV(ADPS0),ADCSRA);
+
+
+  // Initialize TWI
+  outp(0x02,TWBR);  // set SCL-frequency CPU-freq/(16+2*2)
+  outp(0x02,TWAR);  // slave address
+  outp(BV(TWEA)|BV(TWEN),TWCR); // enable TWI, enable ACK
+
+  //Enable interrupts
+  sei();
+
+  // loop
+  while (1) {}
+}

linear_pendulum_2009/avr/pccom.c

+// pccom.c: Communication interface to PC via serialio_core.
+
+#include "pccom.h"
+#include "serialio_core.h"
+#include "vel_control.h"
+
+/*
+ * Serial I/O assignments
+ *
+ *   AO 0 -- Axis 1  motor voltage
+ *   A0 1 -- Axis 1  velocity reference !
+ *
+ *   EI 0 -- Axis 1  position !
+ *   EI 1 -- Axis 1  filtered velocity !
+ *   EI 5 -- Axis 1  position with predicted fraction
+ *   EI 6 -- Axis 1  position unquantized
+ *
+ *   AI 2 -- Axis 1  current
+ *   AI 3 -- Pendulum angle !
+ *
+ *   AI 4 -- Axis 1  motor voltage (actual)
+ *
+ *   DI 0 -- Axis 1  endpoint sensor
+ */
+
+#define POLL_AXIS1_POSITION      0x0001
+#define POLL_AXIS1_VELOCITY      0x0002
+#define POLL_PEND_ANGLE          0x0004
+#define POLL_CURRENT_REFERENCE   0x0008
+//#define POLL_AXIS1_RESET         0x0008
+#define POLL_CONFIG              0x8000
+
+static volatile uint16_t pccom_poll=0;
+
+
+// ---------------------------------- Receiver --------------------------------
+
+// only call from UART receive interrupt
+static inline void addPoll(uint16_t flags) {
+  pccom_poll |= flags;
+}
+
+
+void pccom_receiveByte(char ch)
+{
+  switch (serialio_RXC(ch)) {
+  case serialio_clearbit: {
+    switch (serialio_channel) {
+    }
+  } break;
+  case serialio_setbit: {
+    switch (serialio_channel) {
+    }
+  } break;
+  case serialio_pollbit: {
+    switch (serialio_channel) {
+      //case 0: { addPoll(POLL_AXIS1_RESET); } break;
+    }
+  } break;
+  case serialio_pollchannel: {
+    switch (serialio_channel) {
+    case 0:  { addPoll(POLL_AXIS1_POSITION); } break;
+    case 1:  { addPoll(POLL_AXIS1_VELOCITY); } break;
+    case 2:  { addPoll(POLL_PEND_ANGLE); } break;
+    case 3:  { addPoll(POLL_CURRENT_REFERENCE); } break;
+    case 31: { addPoll(POLL_CONFIG); } break;
+    }
+  } break;
+  case serialio_setchannel: {
+    switch (serialio_channel) {
+    case 0: { 
+      setRef(serialio_value - (1L<<12));
+    } break;
+    }
+  } break;
+  case serialio_more: {
+  } break;
+    
+  case serialio_error: {
+  } break;
+  }
+}
+
+
+// ----------------------------------- Sender ------------------------------
+// return true if more to send
+static uint8_t sendConfigPacket(uint8_t position)
+{
+  switch (position) {
+    case 0: CONF_ANALOG_IN(0, CONF_RESOLUTION(16)); break;     // Position (now reference)
+    case 1: CONF_ANALOG_IN(0, CONF_MIN(CONF_NEGATIVE_VOLT(1))); break;
+    case 2: CONF_ANALOG_IN(0, CONF_MAX(CONF_POSITIVE_VOLT(1))); break;
+
+    case 3: CONF_ANALOG_IN(1, CONF_RESOLUTION(18)); break;     // Velocity estimate
+    case 4: CONF_ANALOG_IN(1, CONF_MIN(CONF_NEGATIVE_VOLT(1))); break;
+    case 5: CONF_ANALOG_IN(1, CONF_MAX(CONF_POSITIVE_VOLT(1))); break;
+
+    case 6: CONF_ANALOG_IN(2, CONF_RESOLUTION(11)); break;     // Pend angle measurement
+    case 7: CONF_ANALOG_IN(2, CONF_MIN(CONF_NEGATIVE_VOLT(1))); break;
+    case 8: CONF_ANALOG_IN(2, CONF_MAX(CONF_POSITIVE_VOLT(1))); break;
+
+    case 9: CONF_ANALOG_IN(3, CONF_RESOLUTION(8)); break;     // Current reference
+    case 10: CONF_ANALOG_IN(3, CONF_MIN(CONF_NEGATIVE_VOLT(1))); break;
+    case 11: CONF_ANALOG_IN(3, CONF_MAX(CONF_POSITIVE_VOLT(1))); break;
+ 
+    case 12: CONF_ANALOG_OUT(0, CONF_RESOLUTION(13)); break;    // Reference to vel-ctrl
+    case 13: CONF_ANALOG_OUT(0, CONF_MIN(CONF_NEGATIVE_VOLT(1))); break;
+    case 14: CONF_ANALOG_OUT(0, CONF_MAX(CONF_POSITIVE_VOLT(1))); break;
+      
+    default: CONF_END(); return 0;
+  }
+  
+  return 1;
+}
+
+static uint8_t sendNextPacket() // returns 1 if a packet was available
+{
+  static int8_t configPosition = -1;
+
+#define toPoll pccom_poll // OK since sender and receiver are mutexed
+
+  // Send _first_ requested item (only one packet!)
+  if (toPoll & POLL_AXIS1_POSITION) { 
+    toPoll &= ~POLL_AXIS1_POSITION;
+    serialio_putchannel(0, getPosition()+(1L<<15)); 
+  }
+  else if (toPoll & POLL_AXIS1_VELOCITY) { 
+    toPoll &= ~POLL_AXIS1_VELOCITY;
+    serialio_putchannel(1, getVelocity()+(1L<<17)); 
+  }
+  else if (toPoll & POLL_PEND_ANGLE) { 
+    toPoll &= ~POLL_PEND_ANGLE;
+    serialio_putchannel(2, getAngle()+(1L<<10)); 
+  }
+  else if (toPoll & POLL_CURRENT_REFERENCE) { 
+    toPoll &= ~POLL_CURRENT_REFERENCE;
+    serialio_putchannel(3, getCurrentRef()+(1L<<7)); 
+  }
+  else if (toPoll & POLL_CONFIG) {
+    if (configPosition < 0) configPosition = 0; // Start sending config?   
+    if (!sendConfigPacket(configPosition)) {    // Last packet?
+      configPosition = -1;
+      toPoll &= ~POLL_CONFIG;
+    }
+    else configPosition++;                      // Advance to next packet
+  }
+  else return 0; // should never happen!
+
+  return 1;
+}
+
+// ---- Send buffering ----
+
+#define PCCOM_SEND_BUFFER_SIZE 6 // just enough for one serialio_putchannel() packet
+
+uint8_t pccom_sendBuffer[PCCOM_SEND_BUFFER_SIZE]; // Updated by serialio_putchar()
+uint8_t pccom_sendBufferPosition = 0;             // Updated by pccom_getNextByteToSend()
+uint8_t pccom_sendBufferUsed = 0;                 // Updated by serialio_putchar(),
+                                                  // and pccom_getNextByteToSend() when
+                                                  // the buffer is empty.
+
+void serialio_putchar(unsigned char ch) {
+  if (pccom_sendBufferUsed < PCCOM_SEND_BUFFER_SIZE) {
+    pccom_sendBuffer[pccom_sendBufferUsed] = ch;
+    pccom_sendBufferUsed++;
+  }
+  else {
+    // Buffer already full -- must never happen!
+    // main_emergencyStop(); // show that something is wrong
+  }
+}
+
+int16_t pccom_getNextByteToSend()
+{
+  if (pccom_sendBufferPosition >= pccom_sendBufferUsed) {
+    // Try to refill buffer
+    pccom_sendBufferPosition = 0;
+    pccom_sendBufferUsed = 0;
+
+    //if (!sendNextPacket()) return -1;
+    sendNextPacket();
+  }
+  
+  if (pccom_sendBufferPosition >= pccom_sendBufferUsed) return -1; // no data
+  else {
+    // Return next byte
+    uint8_t data = pccom_sendBuffer[pccom_sendBufferPosition];
+    pccom_sendBufferPosition++;
+    return data;
+  }  
+}
+
+
+// ------------------------------ Initialization ------------------------------
+
+void pccom_init()
+{
+  serialio_init();
+}

linear_pendulum_2009/avr/pccom.h

+// pccom.h: Communication interface to PC via serialio_core.
+
+#ifndef __pccom_h
+#define __pccom_h
+
+#include <inttypes.h>
+#include "vel_control.h"
+
+void pccom_init();
+
+// Concurrency constraints:
+// Receiving and sending are mutually exclusive!
+void pccom_receiveByte(char ch);
+int16_t pccom_getNextByteToSend(); // returns -1 for nothing to send
+
+
+// ------------------------------- Callbacks ----------------------------------
+
+void serialio_putchar(unsigned char ch);
+
+#endif

linear_pendulum_2009/avr/serialio_core.h

+// serialio_core.h: Serialio protocol without the hardware bindings.
+
+#ifndef __serialio_core_h
+#define __serialio_core_h
+/*
+ * Digital in/out and poll commands are sent as one byte:
+ *
+ *   +-+-+-+-+-+-+-+-+
+ *   |0|0 0|  chan   | Bit clear
+ *   +-+-+-+-+-+-+-+-+
+ *
+ *   +-+-+-+-+-+-+-+-+
+ *   |0|0 1|  chan   | Bit set
+ *   +-+-+-+-+-+-+-+-+
+ *
+ *   +-+-+-+-+-+-+-+-+
+ *   |0|1 0|  chan   | Bit get
+ *   +-+-+-+-+-+-+-+-+
+ *
+ *   +-+-+-+-+-+-+-+-+
+ *   |0|1 1|  chan   | Channel get
+ *   +-+-+-+-+-+-+-+-+
+ *
+ *
+ * Channels are sent as 2 to 6 bytes, depending on resolution:
+ *
+ *   +-+-+-+-+-+-+-+-+  +-+-+-+-+-+-+-+-+ 
+ * 2 |1| bit8...bit2 |  |0|bit|  chan   |
+ *   +-+-+-+-+-+-+-+-+  +-+-+-+-+-+-+-+-+ 
+ *
+ *   +-+-+-+-+-+-+-+-+  +-+-+-+-+-+-+-+-+  +-+-+-+-+-+-+-+-+ 
+ * 3 |1|bit15...bit9 |  |1| bit8...bit2 |  |0|bit|  chan   |
+ *   +-+-+-+-+-+-+-+-+  +-+-+-+-+-+-+-+-+  +-+-+-+-+-+-+-+-+ 
+ *
+ *   ...
+ *
+ *   +-+-+-+-+-+-+-+-+  +-+-+-+-+-+-+-+-+     +-+-+-+-+-+-+-+-+ 
+ * 6 |1|bit31...bit30|  |1|bit29...bit23| ... |0|bit|  chan   |
+ *   +-+-+-+-+-+-+-+-+  +-+-+-+-+-+-+-+-+     +-+-+-+-+-+-+-+-+ 
+ *
+ *
+ *
+ * Channel 31 is special, as it serves as the configuration channel. When
+ * reading from it multiple responses are sent with the following layout
+ *
+ * +-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-+
+ * |           command specific data           |cmd|kind |conf chan|
+ * +-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-+
+ *
+ *  kind: 000 == end of configuration
+ *        001 == digital in
+ *        010 == digital out
+ *        011 == analog in
+ *        100 == analog out
+ *        101 == counter in
+ *
+ *cmd == 0 (Resolution)
+ *
+ * +-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-+
+ * |                               | # of bits |0 0|kind |conf chan|
+ * +-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-+
+ *
+ *  # of bits (1..32) 
+ *
+ *cmd == 1 (Minimum value)
+ *
+ * +-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-+
+ * |              minimum              |S| unit|0 1|kind |conf chan|
+ * +-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-|-+-+-+-+-+-+-+-+
+ * 
+ *  S (sign): 0 == +
+ *            1 == -