ENTC-489 Embedded Real Time Software Development Embedded Real Time Software Development Week 5 Mail Boxes / Binary Semaphores Fixed Point Arithmetic

ENTC-489 Embedded Real Time Software Development

Embedded Real Time Software Development

Week 5Mail Boxes / Binary Semaphores

Fixed Point Arithmetic


Today’s Agenda

• Homework• Mail Boxes• Mail Boxes as Binary Semaphores• Fixed Point Arithmetic


Mail Boxes

• Mechanism to send a single value (usually pointer sized) to a task

• Receiving task can pend on the posting of a value

• Can not post 0


Mailbox Functions

• OSMboxCreate()– Creates a new mailbox

• OSMboxPost()– Posts a value to a mailbox

• OSMboxPend()– Waits on a value to be placed in a mailbox, then

empties the mailbox• OSMboxAccept()– Same as Pend, but does not wait


OSMboxCreate()

• OS_EVENT *OSMboxCreate(void *msg)– msg is the initial value to go in the box, usually 0– Returns a pointer to the created mailbox or 0 if

there are no more available Event Control BlocksOS_EVENT *my_mbox_ptr;…my_mbox_ptr = OSMboxCreate((void *)0);…


OSMboxPost()• INT8U OSMboxPost(OS_EVENT *pevent, void *msg);

– *pevent – pointer to the mailbox TCB– *msg – value to be posted, 0 doesn’t post anything– returns the following error codes:

OS_ERR_NONE, OS_ERR_FULL, OS_MBOX_FULL, OS_ERR_EVENT_TYPE, OS_ERR_PEVENT_NULL, OS_ERR_POST_NULL_PTR

OS_EVENT *my_mbox_ptr;uint8_t recvd_data[100]…if (index == new_index){ … err = OSMboxPost(my_mbox_ptr,(void *)&recvd_data[index]); …}


OSMboxPend()• void *OSMboxPend(OS_EVENT *pevent, INT16U timeout, INT8U *err);

– *pevent – Pointer to the mailbox TCB– timeout – Max time, in ticks, to pend. 0 waits forever– *err – Pointer to location that will hold the return code from the function

OS_ERR_NONE, OS_ERR_TIMEOUT, OS_ERR_EVENT_TYPE, OS_ERR_PEND_ISR, OS_ERR_PEVENT_NULL

– Returns the value in the mailbox, (void *)0, if the mailbox is empty

OS_EVENT *my_mbox_ptr;UINT8 error_code;uint16_t *next_value;…next_value = OSMboxPend(my_mbox_ptr,0,&error_code);switch (error_code){case OS_ERR_NONE: return *next_value;…}…


OSMboxAccept()

• void *OSMboxAccept(OS_EVENT *pevent)– *pevent – Pointer to the mailbox TCB– Returns the value in the mailbox, (void *)0, if the mailbox is empty

…OS_EVENT *my_mbox_ptr;uint16_t *next_value;…next_value = OSMboxAccept(my_mbox_ptr);if (next_value != 0){ … return *next_value; …}…


Mail Boxes as Binary Semaphores

• You do not have to post a pointer, you can post any variable or constant that is the same size or smaller than a pointer.

• If you “Post” a constant, the behavior of a mailbox is exactly the same as a binary semaphore would be.


Break


Fixed Point Arithmetic

• The Problem– Floating point math is slower than integer math

(even with a Floating Point Unit)– Use of floating point math slows multi-threaded /

multi-tasked systems even more (lots of BIG registers to push to save context)

– We still need to deal with fractional values• The Solution– Fixed point arithmetic


What is a Fixed Point Number?

• The meaning of an N-bit binary word depends entirely on its interpretation. For example, if I have the 8 bit binary value 01000011– Traditionally it could be interpreted as

Hex 43, Octal 103, Decimal 67, ASCII ‘C’– But what if I decided to interpret the value as 1/16th of the

signed, binary count. We the value could then be interpreted as:Binary 0100.0011, Hex 4.3, Octal 4.14, Decimal 4.1875

– The notation describing the interpretation of this number is Q4.3, meaning 3 integer bits and 4 fractional bits (the high order bit is the sign).

– We say that the “Scale” of our numbers is:


Whoa! What?

• Assuming Q4.3 notation (scale = 16)….– Decimal 4.0 = 01000000 = 0x40… how?

– Decimal 1.62= 25.9, (25)=00011001converting back =1.56

– Decimal -2.13=-34.08, (-34)=11011110=-2.125

• Note the precision is


Huh?

• Let’s think about this in decimal…• I tell you that every number I give you is 100 times

the value I “mean” (scale=) then if I say:– 25, you interpret 0.25– 314, you interpret 3.14– -7, you interpret – 0.07– 3,583,771, you interpret 35,837.71


Why is this better, I understand floating point?

• You only think you understand floating point• The math is faster than floating point because you

can use integer arithmetic for everything– Addition and subtraction just work… using a scale of :

7.16-3.05=4.11 and 716-305=411– Multiplication and Division require us to think about

the scale:3.71*0.4=1.484,

– If our Scale is an even power of two the division above can be accomplished with shifts, which are cheap!


Facts to Ponder• Word size: • Range of values: • Resolution of values: for • Accuracy of values: for • Addition and subtraction require both operands to be the same scale• The result for addition and subtraction will always be the same scale• Multiplication and division the scale of the operands may be different• Multiplication, the scale of the result is the scale of the first operand

multiplied by the scale of the second operand• Division, the scale of the result is the scale of the dividend divided by the

scale of the divisor• “Saturation” is when a Fixed point number reaches the highest or lowest

value in its range.


Tivaware IQMath Library• Based on 32 bit values• Supports Q30.1 to Q1.30

– Type for Q30.1 is _iq30– Type for Q29.2 is _iq29– …– Type for Q1.30 is _iq1

• Conversion– To String– To _iq?? From _iq??– Do not use floating point

conversions

• Multiplication / Division• Trig, Sqrt, Exponents, etc.• #include “IQmath/IQmathlib.h”


Tivaware IQ Functions• Division - _IQNdiv()

_iq16 numerator, denominator, result;…result = _IQ16div(numerator,denominator);

• Multiplication - _IQNmpy()_iq16 mpy1, mpy2, result;…result = _IQ16mpy(mpy1,mpy2);

• Addition and subtraction_iq16 op1, op2, op3, result;…result = (op1 + op2) – op3;

• Output Format_iq16 op1;char outstr[16];…_IQ16toa(op1,”%2.05f”,outstr);

• Convert from IQn to IQm#define IQtoIQ(Q1,Q2,A) ((_iq ##Q1)(A) >> (Q1 – Q2))_iq16 val1;_iq24 val2;…val1 = IQtoIQ(16,24,val2);


Creating a Constant

• π as Q24.7– Range is -8 to 7.999999996– Scale is 16,777,216– π = 3.141592653 * Scale =52707178 (calculator)– #define Q24_SCALE ((int64_t)16777216)– #define PI_9DIGITS ((int64_t)3141592653)– #define TEN_EXP9 ((int64_t)1000000000)– #define PI_Q24 ((_iq24)((PI_9DIGITS*Q24_SCALE)/TEN_EXP9))


You have to design before writing code

• Working with fixed point numbers you have to think about– Range– Precision– Order of evaluation

Documents

ENTC-489 Embedded Real Time Software Development Embedded Real Time Software Development Week 5 Mail Boxes / Binary Semaphores Fixed Point Arithmetic