32-bit and 64-bit FloatIng Point Maths
The Positron16 compiler performs single precision (32-bit) IEEE754 FloatIng Point calculations and double precision (64-bit) IEEE754 FloatIng Point calculations.
Declaring a variable as Float or Double will enable 32-bit or 64-bit floating point calculations on that variable.
Dim MyFloat as Float
Dim MyDouble as DoubleTo create a floating point constant, add a decimal point. Especially if the value is a whole number.
Symbol PI = 3.14 ' Create an obvious floating point constant
Symbol FlNum = 5.0 ' Create a floating point value of a whole numberNote.
It is important to remember that floating point arithmetic is not the ultimate in accuracy, it is merely a means of compressing a complex or large value into a small space (4 bytes in the case of 32-bit Floats, and 8 bytes in the case of 64-bit Doubles), in essence, it is an approximation of a value. Perfectly adequate results can usually be obtained from correct scaling of integer variables, with an increase in speed and a saving of RAM and code space. 32-bit and 64-bit floating point math is quite microcontroller intensive since the microcontroller is only a 16-bit processor. It also consumes quite large amounts of RAM, and code space for its operation, therefore always use floating point sparingly, and only when strictly necessary.
Unlike Positron8 for 8-bit microcontrollers, which uses a modified floating point format, Positron16 uses the IEEE754 standard.
An IEEE754 single precision float variable has three components: a sign bit telling whether the number is positive or negative, an exponent giving its order of magnitude, and a mantissa specifying the actual digits of the number. Below is the bit layout:
For 32-bit Float:
seeeeeeeemmmmmmmmmmmmmmmmmmmmmmm meaning
31 0 bit numberFor 64-bit Double:
seeeeeeeeeeeeeeeemmmmmmmmmmmmmmmmmmmmmmm.... meaning
63 0 bit numbers = sign bit, e = exponent, m = mantissa
32-bit FloatIng Point Example Programs.
' Multiply two floating point values
Device = 24FJ64GA002 ' Select the device to compile for
Declare Xtal = 16 ' Tell the compiler the device will be operating at 16MHz
Declare Hserial_Baud = 9600 ' USART1 Baud rate
Declare Hrsout1_Pin = PORTB.14 ' Select the pin for TX with USART1
Dim MyFloat as Float
Symbol cFlNum = 1.234 ' Create a floating point constant value
RPOR7 = 3 ' Make PPS Pin RP14 U1TX
MyFloat = cFlNum * 10
HrsoutLn Dec MyFloat
' Add two floating point variables
Device = 24FJ64GA002 ' Select the device to compile for
Declare Xtal = 16 ' Tell the compiler the device will be operating at 16MHz
Declare Hserial_Baud = 9600 ' USART1 Baud rate
Declare Hrsout1_Pin = PORTB.14 ' Select the pin for TX with USART1
Dim MyFloat as Float
Dim MyFloat1 as Float
Dim MyFloat2 as Float
RPOR7 = 3 ' Make PPS Pin RP14 U1TX
MyFloat1 = 1.23
MyFloat2 = 1000.1
MyFloat = MyFloat1 + MyFloat2
HrsoutLn Dec MyFloat
' A digital volt meter, using the on-board 10-bit ADC
Device = 24FJ64GA002 ' Select the device to compile for
Declare Xtal = 16 ' Tell the compiler the device will be operating at 16MHz
Declare Hserial_Baud = 9600 ' USART1 Baud rate
Declare Hrsout1_Pin = PORTB.14 ' Select the pin for TX with USART1
Declare Adin_Tad = cFRC ' RC OSC chosen
Declare Adin_Delay = 10 ' Allow 10us sample time
Dim wRaw as Word
Dim fVolts as Float
Symbol cQuanta = 3.3 / 1024 ' Calculate the quantising value for 10-bits
RPOR7 = 3 ' Make PPS Pin RP14 U1TX
AD1CON2 = 0 ' +Vref = AVdd, -Vref = AVss
AD1PCFGbits_PCFG0 = 0 ' Analogue input on AN0
Do
wRaw = ADin 0
fVolts = wRaw * cQuanta
HrsoutLn Dec2 fVolts, "V"
DelayMs 300
Loop
64-bit FloatIng Point Example Programs.
' Multiply two 64-bit floating point values
Device = 24FJ64GA002 ' Select the device to compile for
Declare Xtal = 16 ' Tell the compiler the device will be operating at 16MHz
Declare Hserial_Baud = 9600 ' USART1 Baud rate
Declare Hrsout1_Pin = PORTB.14 ' Select the pin for TX with USART1
Dim MyDouble as Double
Symbol cFlNum = 1.234 ' Create a floating point constant value
RPOR7 = 3 ' Make PPS Pin RP14 U1TX
MyDouble = cFlNum * 10
HrsoutLn Dec MyDouble
' Add two 64-bit floating point variables
Device = 24FJ64GA002 ' Select the device to compile for
Declare Xtal = 16 ' Tell the compiler the device will be operating at 16MHz
Declare Hserial_Baud = 9600 ' USART1 Baud rate
Declare Hrsout1_Pin = PORTB.14 ' Select the pin for TX with USART1
Dim MyDouble as Double
Dim MyDouble 1 as Double
Dim MyDouble 2 as Double
RPOR7 = 3 ' Make PPS Pin RP14 U1TX
MyDouble1 = 1.23
MyDouble2 = 1000.1
MyDouble = MyDouble1 + MyDouble2
HrsoutLn Dec MyDouble
' A digital volt meter, using the on-board 10-bit ADC
Device = 24FJ64GA002 ' Select the device to compile for
Declare Xtal = 16 ' Tell the compiler the device will be operating at 16MHz
Declare Hserial_Baud = 9600 ' USART1 Baud rate
Declare Hrsout1_Pin = PORTB.14 ' Select the pin for TX with USART1
Declare Adin_Tad = cFRC ' RC OSC chosen
Declare Adin_Delay = 10 ' Allow 10us sample time
Dim wRaw as Word
Dim fVolts as Double
Symbol cQuanta = 3.3 / 1024 ' Calculate the quantising value for 10-bits
RPOR7 = 3 ' Make PPS Pin RP14 U1TX
AD1CON2 = 0 ' +Vref = AVdd, -Vref = AVss
AD1PCFGbits_PCFG0 = 0 ' Analogue input on AN0
Do
wRaw = ADin 0
fVolts = wRaw * cQuanta
HrsoutLn Dec2 fVolts, "V"
DelayMs 300
Loop
Notes.
Any expression that contains a floating point variable or constant will always be calculated as a floating point, even if the expression also contains integer constants or variables. The same applies for Doubles. If an expression has a mix of 32-bit floats and 64-bit doubles, the it will be carried out as 64-bit Double.
If the assignment variable is an integer variable, but the expression is of a floating point nature, then the floating point result will be converted into an integer.
Device = 24FJ64GA002 ' Select the device to compile for
Declare Xtal = 16 ' Tell the compiler the device will be operating at 16MHz
Declare Hserial_Baud = 9600 ' USART1 Baud rate
Declare Hrsout1_Pin = PORTB.14 ' Select the pin for TX with USART1
Dim MyDword as Dword
Dim MyFloat as Float
Symbol cPI = 3.14
RPOR7 = 3 ' Make PPS Pin RP14 U1TX
MyFloat = 10
'
' Float calculation with result 13.14, reduced to integer 13
'
MyDword = MyFloat + cPI
HrsoutLn Dec MyDword ' Display the integer result 13