Floating Point
-
@hek @Yveaux
Let me see if I am understanding.The payload types would be enhanced.
typedef enum { P_STRING, P_BYTE, P_INT16, P_UINT16, P_LONG32, P_ULONG32, P_CUSTOM } payload;to add an 8:8 and/or 16:16 fixed point formats, eg: P_FIX8P8 or P_FIX16P16. I'm guessing only signed fixed point, no unsigned?
And to add a 4 byte binary floating point P_FLOAT32?
One small suggestion: put P_CUSTOM first, so its numeric code doesn't change when you add additional formats. Or if it's too late for that, we can skip over P_CUSTOM for these new formats.
And also the payload setters:
MyMessage& set(const char* value); MyMessage& set(uint8_t value); MyMessage& set(double value, uint8_t decimals); MyMessage& set(unsigned long value); MyMessage& set(long value); MyMessage& set(unsigned int value); MyMessage& set(int value);would be enhanced to support these types.
MyMessage& set(double value, uint8_t decimals);could be unchanged as seen by the user even if the underlying OTA representation became binary. But we might add something like:
MyMessage& set(fix8p8 value, uint8_t: decimals); MyMessage& set(fix16p16 value, uint8_t: decimals);(the decimals parameter is needed for this like for floats, as described earlier)
This implies creating new C++ types, in this example "fix8p8", which is basically a int16_t with an implicit radix point in the middle.
Adding is simple. Multiply of fix8p8 is easy because you can use a long as temp before renormalizing, but multiply of fix16p16 gets trickier, of course.
Another discussion to have before it's set in stone...
Adding fixed point support both OTA and within library code has value, so I'm not against it. Getting the library right and educating users is going to be some work, tho. I use fixed point math fairly often, but it definitely has some gotchas that we are biting off.
The concept of having a scaling factor (see a few messages back) may be an easier step to implement and educate. It's an easy concept: every integer step represents X units, so the integer value must be multiplied by the scaling factor to get the real value in units. Default = 1.0 with both the same, as now.
The simplest version just scales by factors of 10, and could be implemented by adding a second integer to the set() function. In this version to send -12.5 you use set(-125,1), or to send 0.14 you use set(14,2). This can be interpreted into a string without even using floating point math, you just adjust where to insert a decimal point in a printed integer.
(The slightly more complex version would use an arbitrary floating point factor as the scale, so you could use 0.1 or 3.56 or whatever).
(Aside: from the viewpoint of the gateway, the fixed point enhancement is equivalent to having a fixed scaling factor of 2*-8 or 2^-16)
These enhancements are not mutually exclusive, but I would think that one of the scaled integer version might be easier to implement and understand as a first step.
@Zeph said:
The payload types would be enhanced.
typedef enum { P_STRING, P_BYTE, P_INT16, P_UINT16, P_LONG32, P_ULONG32, P_CUSTOM } payload;Darn, just realized we only got 3 bits to describe payload type. We need another one to fit the new ones.
MyMessage& set(double value, uint8_t decimals);Shouldn't this be set(float, uint8_t). Wouldn't it be confusing to have double-argument when only sending 32-bit float?
-
@Zeph said:
The payload types would be enhanced.
typedef enum { P_STRING, P_BYTE, P_INT16, P_UINT16, P_LONG32, P_ULONG32, P_CUSTOM } payload;Darn, just realized we only got 3 bits to describe payload type. We need another one to fit the new ones.
MyMessage& set(double value, uint8_t decimals);Shouldn't this be set(float, uint8_t). Wouldn't it be confusing to have double-argument when only sending 32-bit float?
-
@Zeph said:
The payload types would be enhanced.
typedef enum { P_STRING, P_BYTE, P_INT16, P_UINT16, P_LONG32, P_ULONG32, P_CUSTOM } payload;Darn, just realized we only got 3 bits to describe payload type. We need another one to fit the new ones.
MyMessage& set(double value, uint8_t decimals);Shouldn't this be set(float, uint8_t). Wouldn't it be confusing to have double-argument when only sending 32-bit float?
Shouldn't this be set(float, uint8_t). Wouldn't it be confusing to have double-argument when only sending 32-bit float?
Also the Atmega based boards do not support double, well they do in naming but are float precisions
My Domotica project: http://www.pidome.org
-
Shouldn't this be set(float, uint8_t). Wouldn't it be confusing to have double-argument when only sending 32-bit float?
Also the Atmega based boards do not support double, well they do in naming but are float precisions
-
Just pushed the float changes.
To free up some bits in header for the new fixed point types (and simplify things) I'm considering reducing the commandTypes to just 3 values (SET, REQ, INTERNAL) the rest (PRESENTATION, STREAM) will be moved to be INTERNAL messages.
I could make serial interface unaffected by this change. But I'd rather remove it there as well.@Yveaux . Regarding remove the unsigned variant (e.g. ULONG). It is actually good to keep this. As there actually are some sensors reporting large numbers like meter-ticks which can be huge.
-
Just pushed the float changes.
To free up some bits in header for the new fixed point types (and simplify things) I'm considering reducing the commandTypes to just 3 values (SET, REQ, INTERNAL) the rest (PRESENTATION, STREAM) will be moved to be INTERNAL messages.
I could make serial interface unaffected by this change. But I'd rather remove it there as well.@Yveaux . Regarding remove the unsigned variant (e.g. ULONG). It is actually good to keep this. As there actually are some sensors reporting large numbers like meter-ticks which can be huge.
@hek Maybe not for 1.4, but you should consider removing a lot of the data from the header and leave only the routing info & message type in.
Depending on message type you then get a 'nested' header which tells you about the message-type specifics.
This also will help in the struggle to store data format types, for which you've now reserved 3 bits. They are always sent, also when there's no SET/GET data present in the message. Then you simply reserve e.g. a byte which will go a long way...http://yveaux.blogspot.nl
-
@hek Maybe not for 1.4, but you should consider removing a lot of the data from the header and leave only the routing info & message type in.
Depending on message type you then get a 'nested' header which tells you about the message-type specifics.
This also will help in the struggle to store data format types, for which you've now reserved 3 bits. They are always sent, also when there's no SET/GET data present in the message. Then you simply reserve e.g. a byte which will go a long way...@Yveaux said:
This also will help in the struggle to store data format types, for which you've now reserved 3 bits. They are always sent, also when there's no SET/GET data present in the message. Then you simply reserve e.g. a byte which will go a long way...
Darn... you are so right..
-
@Yveaux said:
This also will help in the struggle to store data format types, for which you've now reserved 3 bits. They are always sent, also when there's no SET/GET data present in the message. Then you simply reserve e.g. a byte which will go a long way...
Darn... you are so right..
-
@Zeph said:
(the decimals parameter is needed for this like for floats, as described earlier)
I don't see why the decimals parameter is needed. Currently it is used for the amount of decimals converted to textual presentation. This is not required for fixed point presentation (unless you want a scaling factor).
IMHO scaling just complicates things too much -- you also need to exchange the scaling factor with the gateway.This implies creating new C++ types, in this example "fix8p8", which is basically a int16_t with an implicit radix point in the middle.
Adding is simple. Multiply of fix8p8 is easy because you can use a long as temp before renormalizing, but multiply of fix16p16 gets trickier, of course.
My idea is to just wrap the new types in a class library, which allows for easy conversion and maths with these new fixedpt types.
Getting the library right and educating users is going to be some work, tho. I use fixed point math fairly often, but it definitely has some gotchas that we are biting off.
The library should shield regular users from the internals and pitfalls of fixed point. Most sketches just get a value from a sensor library and pass it on to MySensors, without modifying the value.
As part of this exercise we also have to modify these libraries which return their values in float-format, as it doesn't make sense to keeps floats in partly...@Yveaux said:
@Zeph said:
(the decimals parameter is needed for this like for floats, as described earlier)
I don't see why the decimals parameter is needed. Currently it is used for the amount of decimals converted to textual presentation.
I was think of when packets are converted to the comma separated textual representation for the API.
Convert 25.7 degrees to fixed point at the node, then at the gateway convert the fixed point it to a text string, and you'll see what I mean. It's not for the scaling option.
IMHO scaling just complicates things too much -- you also need to exchange the scaling factor with the gateway.
There are tradeoffs either way. In the current architecture, to support scaling you'd need to at least tell the gateway the scaling factor as part of the one-time presentation configuration. (Alternately, the gateway could retrieve the scaling factor along with type and name from local configuration, rather than receiving all of those OTA, but that's another discussion)
Beyond that there's no need for new libraries, and it's easy to explain.
However, I understand that you are excited by the fixed point functionality (which could be useful for more than just OTA encoding). I don't want to discourage that exploration. I look forward to some examples of encoding at the node end, and decoding at the gateway end, for some sensors like the DHT-22 or 18B20.
This implies creating new C++ types, in this example "fix8p8", which is basically a int16_t with an implicit radix point in the middle.
Adding is simple. Multiply of fix8p8 is easy because you can use a long as temp before renormalizing, but multiply of fix16p16 gets trickier, of course.
My idea is to just wrap the new types in a class library, which allows for easy conversion and maths with these new fixedpt types.
Yes, that was what I was guessing. Go for it!
As part of this exercise we also have to modify these libraries which return their values in float-format, as it doesn't make sense to keeps floats in partly...
Agreed. It would be nice if we rarely needed to even link the floating point library in nodes. (And it would make an ATtiny based node more feasible someday).
-
@Zeph said:
The payload types would be enhanced.
typedef enum { P_STRING, P_BYTE, P_INT16, P_UINT16, P_LONG32, P_ULONG32, P_CUSTOM } payload;Darn, just realized we only got 3 bits to describe payload type. We need another one to fit the new ones.
MyMessage& set(double value, uint8_t decimals);Shouldn't this be set(float, uint8_t). Wouldn't it be confusing to have double-argument when only sending 32-bit float?
@hek said:
MyMessage& set(double value, uint8_t decimals);Shouldn't this be set(float, uint8_t). Wouldn't it be confusing to have double-argument when only sending 32-bit float?
I was quoting an excerpt of the current system. I would tend to agree with changing that to float, just for clarity of intent, even though they are the same in GCC for the AVR
-
@Yveaux said:
@Zeph said:
(the decimals parameter is needed for this like for floats, as described earlier)
I don't see why the decimals parameter is needed. Currently it is used for the amount of decimals converted to textual presentation.
I was think of when packets are converted to the comma separated textual representation for the API.
Convert 25.7 degrees to fixed point at the node, then at the gateway convert the fixed point it to a text string, and you'll see what I mean. It's not for the scaling option.
IMHO scaling just complicates things too much -- you also need to exchange the scaling factor with the gateway.
There are tradeoffs either way. In the current architecture, to support scaling you'd need to at least tell the gateway the scaling factor as part of the one-time presentation configuration. (Alternately, the gateway could retrieve the scaling factor along with type and name from local configuration, rather than receiving all of those OTA, but that's another discussion)
Beyond that there's no need for new libraries, and it's easy to explain.
However, I understand that you are excited by the fixed point functionality (which could be useful for more than just OTA encoding). I don't want to discourage that exploration. I look forward to some examples of encoding at the node end, and decoding at the gateway end, for some sensors like the DHT-22 or 18B20.
This implies creating new C++ types, in this example "fix8p8", which is basically a int16_t with an implicit radix point in the middle.
Adding is simple. Multiply of fix8p8 is easy because you can use a long as temp before renormalizing, but multiply of fix16p16 gets trickier, of course.
My idea is to just wrap the new types in a class library, which allows for easy conversion and maths with these new fixedpt types.
Yes, that was what I was guessing. Go for it!
As part of this exercise we also have to modify these libraries which return their values in float-format, as it doesn't make sense to keeps floats in partly...
Agreed. It would be nice if we rarely needed to even link the floating point library in nodes. (And it would make an ATtiny based node more feasible someday).
@Zeph said:
to support scaling you'd need to at least tell the gateway the scaling factor as part of the one-time presentation configuration
This method (and the same holds for the decimals-parameter) seems attrictive, but has a few drawbacks:
- The presentation message currently has no 'guaranteed' delivery; we would need to change that as without this info the gateway cannot interpret the incoming data
- It also has to be sent to the sensor (actuator actually) nodes from the gateway when data goes the other way. No 'presentation' mechanism from gateway to sensor currently exists.
- It places an administration burden on the gateway, and possibly on actuators
Beyond that there's no need for new libraries, and it's easy to explain.
Possibly, but when you start mixing up values with different scaling factors or want to do (simple) maths on them the story changes completely...
-
I've been google'ing around looking for existing fixed point c++ libraries which fit the ATMega and tend to try out the following: https://code.google.com/p/libfixmath
It has regular updates, a unit test suite, impressive performance advantages (especially addition/substract, see https://code.google.com/p/libfixmath/wiki/Benchmarks), has been tested on ATMega and uses an MIT license.
It only supports 16.16, but other derivates like 8.8 seems doable.Rolling my own from start is too much work for me, as implementation is tricky at some points (unit tests are a requirement IMHO)
Anyone has a better suggestion?
http://yveaux.blogspot.nl
-
I've been google'ing around looking for existing fixed point c++ libraries which fit the ATMega and tend to try out the following: https://code.google.com/p/libfixmath
It has regular updates, a unit test suite, impressive performance advantages (especially addition/substract, see https://code.google.com/p/libfixmath/wiki/Benchmarks), has been tested on ATMega and uses an MIT license.
It only supports 16.16, but other derivates like 8.8 seems doable.Rolling my own from start is too much work for me, as implementation is tricky at some points (unit tests are a requirement IMHO)
Anyone has a better suggestion?
-
Just pushed the float changes.
To free up some bits in header for the new fixed point types (and simplify things) I'm considering reducing the commandTypes to just 3 values (SET, REQ, INTERNAL) the rest (PRESENTATION, STREAM) will be moved to be INTERNAL messages.
I could make serial interface unaffected by this change. But I'd rather remove it there as well.@Yveaux . Regarding remove the unsigned variant (e.g. ULONG). It is actually good to keep this. As there actually are some sensors reporting large numbers like meter-ticks which can be huge.
-
I 'ported' libfixmath to the Arduino (see https://github.com/Yveaux/Arduino_fixpt)
Ran into a lot of internal compiler error issues and had to convert the unittests to C++ variants (no need to test C-implementation only) which revealed some issues in the C++ wrapper.Anyway, stuff is running now and I have some preliminary benchmark results.
I create a benchmark sketch which runs a number of multiplications/divisions/additions/subtractions/sqrt.Code size results:
Bare (no float/fix16) 450 double 2514 fix16 2956So code size slightly increases with fixed point calculations.
Calculation performance results:
with overflow detection and rounding:
Op double fixpt speed improvement fixpt over double Mult 870448 1708304 50.95% Div 2303348 2986484 77.13% Add 858280 296760 289.22% Sub 858108 296644 289.27% Sqrt 13164 15444 85.24%without overflow detection and rounding (FIXMATH_NO_OVERFLOW & FIXMATH_NO_ROUNDING defined)
Op double fixpt speed improvement fixpt over double Mult 870452 1699392 51.22% Div 2303348 4794636 48.04% Add 858280 82568 1039.48% Sub 858108 72776 1179.11% Sqrt 13168 15528 84.80%So additions & subtractions are significantly faster using Fix16 (we can probably live without overflow detection & rounding) and mul/div/sqrt are slower...
First conclusion: we don't gain in flash code space and don't gain (on average) in code execution speed. Maybe very specific applications can benefit from Fix16 implementation on AVR, but I seriously doubt if it's worth all the effort....
Seems like the AVR floating point library is very efficient, both in code size and execution speed.
Please review my code as I might be missing something...
http://yveaux.blogspot.nl
-
I 'ported' libfixmath to the Arduino (see https://github.com/Yveaux/Arduino_fixpt)
Ran into a lot of internal compiler error issues and had to convert the unittests to C++ variants (no need to test C-implementation only) which revealed some issues in the C++ wrapper.Anyway, stuff is running now and I have some preliminary benchmark results.
I create a benchmark sketch which runs a number of multiplications/divisions/additions/subtractions/sqrt.Code size results:
Bare (no float/fix16) 450 double 2514 fix16 2956So code size slightly increases with fixed point calculations.
Calculation performance results:
with overflow detection and rounding:
Op double fixpt speed improvement fixpt over double Mult 870448 1708304 50.95% Div 2303348 2986484 77.13% Add 858280 296760 289.22% Sub 858108 296644 289.27% Sqrt 13164 15444 85.24%without overflow detection and rounding (FIXMATH_NO_OVERFLOW & FIXMATH_NO_ROUNDING defined)
Op double fixpt speed improvement fixpt over double Mult 870452 1699392 51.22% Div 2303348 4794636 48.04% Add 858280 82568 1039.48% Sub 858108 72776 1179.11% Sqrt 13168 15528 84.80%So additions & subtractions are significantly faster using Fix16 (we can probably live without overflow detection & rounding) and mul/div/sqrt are slower...
First conclusion: we don't gain in flash code space and don't gain (on average) in code execution speed. Maybe very specific applications can benefit from Fix16 implementation on AVR, but I seriously doubt if it's worth all the effort....
Seems like the AVR floating point library is very efficient, both in code size and execution speed.
Please review my code as I might be missing something...
-
@hek I implemented a basic version of the 8.8 fixed point version of the library.
It doesn't pass the unittests completely yet, but here are the first results (sqrt not implemented yet):Code size results:
Bare (no float/fix8) 450 double 1214 fix16 2062So, again code size slightly increases with fixed point calculations.
with overflow detection and rounding:
Op double fixpt speed improvement fixpt over double Mult 840016 291008 288.66% Div 2240552 812044 275.92% Add 792564 133344 594.38% Sub 801984 136676 586.78%without overflow detection and rounding (FIXMATH_NO_OVERFLOW & FIXMATH_NO_ROUNDING defined)
Op double fixpt speed improvement fixpt over double Mult 840012 312440 268.86% Div 2240548 790992 283.26% Add 792564 56204 1410.16% Sub 801972 52960 1514.30%This is a very nice speed increase in all cases, especially when ignoring overflow detection and rounding.
Conclusion: Using 8.8 fixed point can definately bring the calculation time and therefore power consumption down! The use-case for 8.8 values is however limited, but for e.g. a temperature or humidity sensors with limited range & accuracy it seems usable.
Using 16.16 fixed point values has no clear advantage over using floating point values.http://yveaux.blogspot.nl
-
@hek I implemented a basic version of the 8.8 fixed point version of the library.
It doesn't pass the unittests completely yet, but here are the first results (sqrt not implemented yet):Code size results:
Bare (no float/fix8) 450 double 1214 fix16 2062So, again code size slightly increases with fixed point calculations.
with overflow detection and rounding:
Op double fixpt speed improvement fixpt over double Mult 840016 291008 288.66% Div 2240552 812044 275.92% Add 792564 133344 594.38% Sub 801984 136676 586.78%without overflow detection and rounding (FIXMATH_NO_OVERFLOW & FIXMATH_NO_ROUNDING defined)
Op double fixpt speed improvement fixpt over double Mult 840012 312440 268.86% Div 2240548 790992 283.26% Add 792564 56204 1410.16% Sub 801972 52960 1514.30%This is a very nice speed increase in all cases, especially when ignoring overflow detection and rounding.
Conclusion: Using 8.8 fixed point can definately bring the calculation time and therefore power consumption down! The use-case for 8.8 values is however limited, but for e.g. a temperature or humidity sensors with limited range & accuracy it seems usable.
Using 16.16 fixed point values has no clear advantage over using floating point values.
