I don't have much experience working with these low level bytes and numbers, so I've come here for help. I'm connecting to a bluetooth thermometer in my Flutter app, and I get an array of numbers formatted like this according to their documentation. I'm attempting to convert these numbers to a plain temperature double, but can't figure out how. This is the "example" the company gives me. However when I get a reading of 98.5 on the thermometer I get a response as an array of [113, 14, 0, 254]
Thanks for any help!
IEEE-11073 is a commonly used format in medical devices. The table you quoted has everything in it for you to decode the numbers, though might be hard to decipher at first.
Let's take the first example you have: 0xFF00016C. This is a 32-bit number and the first byte is the exponent, and the last three bytes are the mantissa. Both are encoded in 2s complement representation:
Exponent, 0xFF, in 2's complement this is the number -1
Mantissa, 0x00016C, in 2's complement this is the number 364
(If you're not quite sure how numbers are encoded in 2's complement, please ask that as a separate question.)
The next thing we do is to make sure it's not a "special" value, as dictated in your table. Since the exponent you have is not 0 (it is -1), we know that you're OK. So, no special processing is needed.
Since the value is not special, its numeric value is simply: mantissa * 10^exponent. So, we have: 364*10^-1 = 36.4, as your example shows.
Your second example is similar. The exponent is 0xFE, and that's the number -2 in 2's complement. The mantissa is 0x000D97, which is 3479 in decimal. Again, the exponent isn't 0, so no special processing is needed. So you have: 3479*10^-2 = 34.79.
You say for the 98.5 value, you get the byte-array [113, 14, 0, 254]. Let's see if we can make sense of that. Your byte array, written in hex is: [0x71, 0x0E, 0x00, 0xFE]. I'm guessing you receive these bytes in the "reverse" order, so as a 32-bit hexadecimal this is actually 0xFE000E71.
We proceed similarly: Exponent is again -2, since 0xFE is how you write -2 in 2's complement using 8-bits. (See above.) Mantissa is 0xE71 which equals 3697. So, the number is 3697*10^-2 = 36.97.
You are claiming that this is actually 98.5. My best guess is that you are reading it in Fahrenheit, and your device is reporting in Celcius. If you do the math, you'll find that 36.97C = 98.55F, which is close enough. I'm not sure how you got the 98.5 number, but with devices like this, this outcome seems to be within the precision you can about expect.
Hope this helps!
Here is something that I used to convert sfloat16 to double in dart for our flutter app.
double sfloat2double(ieee11073) {
var reservedValues = {
0x07FE: 'PositiveInfinity',
0x07FF: 'NaN',
0x0800: 'NaN',
0x0801: 'NaN',
0x0802: 'NegativeInfinity'
};
var mantissa = ieee11073 & 0x0FFF;
if (reservedValues.containsKey(mantissa)){
return 0.0; // basically error
}
if ((ieee11073 & 0x0800) != 0){
mantissa = -((ieee11073 & 0x0FFF) + 1 );
}else{
mantissa = (ieee11073 & 0x0FFF);
}
var exponent = ieee11073 >> 12;
if (((ieee11073 >> 12) & 0x8) != 0){
exponent = -((~(ieee11073 >> 12) & 0x0F) + 1 );
}else{
exponent = ((ieee11073 >> 12) & 0x0F);
}
var magnitude = pow(10, exponent);
return (mantissa * magnitude);
}
Related
I don't have much experience working with these low level bytes and numbers, so I've come here for help. I'm connecting to a bluetooth thermometer in my Flutter app, and I get an array of numbers formatted like this according to their documentation. I'm attempting to convert these numbers to a plain temperature double, but can't figure out how. This is the "example" the company gives me. However when I get a reading of 98.5 on the thermometer I get a response as an array of [113, 14, 0, 254]
Thanks for any help!
IEEE-11073 is a commonly used format in medical devices. The table you quoted has everything in it for you to decode the numbers, though might be hard to decipher at first.
Let's take the first example you have: 0xFF00016C. This is a 32-bit number and the first byte is the exponent, and the last three bytes are the mantissa. Both are encoded in 2s complement representation:
Exponent, 0xFF, in 2's complement this is the number -1
Mantissa, 0x00016C, in 2's complement this is the number 364
(If you're not quite sure how numbers are encoded in 2's complement, please ask that as a separate question.)
The next thing we do is to make sure it's not a "special" value, as dictated in your table. Since the exponent you have is not 0 (it is -1), we know that you're OK. So, no special processing is needed.
Since the value is not special, its numeric value is simply: mantissa * 10^exponent. So, we have: 364*10^-1 = 36.4, as your example shows.
Your second example is similar. The exponent is 0xFE, and that's the number -2 in 2's complement. The mantissa is 0x000D97, which is 3479 in decimal. Again, the exponent isn't 0, so no special processing is needed. So you have: 3479*10^-2 = 34.79.
You say for the 98.5 value, you get the byte-array [113, 14, 0, 254]. Let's see if we can make sense of that. Your byte array, written in hex is: [0x71, 0x0E, 0x00, 0xFE]. I'm guessing you receive these bytes in the "reverse" order, so as a 32-bit hexadecimal this is actually 0xFE000E71.
We proceed similarly: Exponent is again -2, since 0xFE is how you write -2 in 2's complement using 8-bits. (See above.) Mantissa is 0xE71 which equals 3697. So, the number is 3697*10^-2 = 36.97.
You are claiming that this is actually 98.5. My best guess is that you are reading it in Fahrenheit, and your device is reporting in Celcius. If you do the math, you'll find that 36.97C = 98.55F, which is close enough. I'm not sure how you got the 98.5 number, but with devices like this, this outcome seems to be within the precision you can about expect.
Hope this helps!
Here is something that I used to convert sfloat16 to double in dart for our flutter app.
double sfloat2double(ieee11073) {
var reservedValues = {
0x07FE: 'PositiveInfinity',
0x07FF: 'NaN',
0x0800: 'NaN',
0x0801: 'NaN',
0x0802: 'NegativeInfinity'
};
var mantissa = ieee11073 & 0x0FFF;
if (reservedValues.containsKey(mantissa)){
return 0.0; // basically error
}
if ((ieee11073 & 0x0800) != 0){
mantissa = -((ieee11073 & 0x0FFF) + 1 );
}else{
mantissa = (ieee11073 & 0x0FFF);
}
var exponent = ieee11073 >> 12;
if (((ieee11073 >> 12) & 0x8) != 0){
exponent = -((~(ieee11073 >> 12) & 0x0F) + 1 );
}else{
exponent = ((ieee11073 >> 12) & 0x0F);
}
var magnitude = pow(10, exponent);
return (mantissa * magnitude);
}
I observed something really strange. If you run this code in Swift:
Int(Float(Int.max))
It crashes with the error message:
fatal error: Float value cannot be converted to Int because the result would be greater than Int.max
This is really counter-intuitive, so I expanded the expression into 3 lines and tried to see what happens in each step in a playground:
let a = Int.max
let b = Float(a)
let c = Int(b)
It crashes with the same message. This time, I see that a is 9223372036854775807 and b is 9.223372e+18. It is obvious that a is greater than b by 36854775807. I also understand that floating points are inaccurate, so I expected something less than Int.max, with the last few digits being 0.
I also tried this with Double, it crashes too.
Then I thought, maybe this is just how floating point numbers behave, so I tested the same thing in Java:
long a = Long.MAX_VALUE;
float b = (float)a;
long c = (long)b;
System.out.println(c);
It prints the expected 9223372036854775807!
What is wrong with swift?
There aren't enough bits in the mantissa of a Double or Float to accurately represent 19 significant digits, so you are getting a rounded result.
If you print the Float using String(format:) you can see a more accurate representation of the value of the Float:
let a = Int.max
print(a) // 9223372036854775807
let b = Float(a)
print(String(format: "%.1f", b)) // 9223372036854775808.0
So the value represented by the Float is 1 larger than Int.max.
Many values will be converted to the same Float value. The question becomes, how much would you have to reduce Int.max before it results in a different Double or Float value.
Starting with Double:
var y = Int.max
while Double(y) == Double(Int.max) {
y -= 1
}
print(Int.max - y) // 512
So with Double, the last 512 Ints all convert to the same Double.
Float has fewer bits to represent the value, so there are more values that all map to the same Float. Switching to - 1000 so that it runs in reasonable time:
var y = Int.max
while Float(y) == Float(Int.max) {
y -= 1000
}
print(Int.max - y) // 274877907000
So, your expectation that a Float could accurately represent a specific Int was misplaced.
Follow up question from the comments:
If float does not have enough bits to represent Int.max, how is it
able to represent a number one larger than that?
Floating point numbers are represented as two parts: mantissa and exponent. The mantissa represents the significant digits (in binary) and the exponent represents the power of 2. As a result, a floating point number can accurately express an even power of 2 by having a mantissa of 1 with an exponent that represents the power.
Numbers that are not even powers of 2 may have a binary pattern that contains more digits than can be represented in the mantissa. This is the case for Int.max (which is 2^63 - 1) because in binary that is 111111111111111111111111111111111111111111111111111111111111111 (63 1's). A Float which is 32 bits cannot store a mantissa which is 63 bits, so it has to be rounded or truncated. In the case of Int.max, rounding up by 1 results in the value
1000000000000000000000000000000000000000000000000000000000000000. Starting from the left, there is only 1 significant bit to be represented by the mantissa (the trailing 0's come for free), so this number is a mantissa of 1 and an exponent of 64.
See #MartinR's answer for an explanation of what Java is doing.
Swift and Java behave differently when converting a "too large" floating point
number to an integer. Java truncates any floating point value
larger than Long.MAX_VALUE = 2^63-1:
long c = (long)(1.0E+30f);
System.out.println(c);
// 9223372036854775807
Swift expects that the value is in the range of Int, and aborts
with a runtime exception otherwise:
/// Creates a new instance by rounding the given floating-point value toward
/// zero.
///
/// - Parameter other: A floating-point value. When `other` is rounded toward
/// zero, the result must be within the range `Int.min...Int.max`.
public init(_ value: Float)
Example:
let c = Int(Float(1.0E30))
print(c)
// fatal error: Float value cannot be converted to Int because the result would be greater than Int.max
The same happens with your value Float(Int.max), which is the
floating point representable value closest to Int.max and happens
to be larger than Int.max.
I observed something really strange. If you run this code in Swift:
Int(Float(Int.max))
It crashes with the error message:
fatal error: Float value cannot be converted to Int because the result would be greater than Int.max
This is really counter-intuitive, so I expanded the expression into 3 lines and tried to see what happens in each step in a playground:
let a = Int.max
let b = Float(a)
let c = Int(b)
It crashes with the same message. This time, I see that a is 9223372036854775807 and b is 9.223372e+18. It is obvious that a is greater than b by 36854775807. I also understand that floating points are inaccurate, so I expected something less than Int.max, with the last few digits being 0.
I also tried this with Double, it crashes too.
Then I thought, maybe this is just how floating point numbers behave, so I tested the same thing in Java:
long a = Long.MAX_VALUE;
float b = (float)a;
long c = (long)b;
System.out.println(c);
It prints the expected 9223372036854775807!
What is wrong with swift?
There aren't enough bits in the mantissa of a Double or Float to accurately represent 19 significant digits, so you are getting a rounded result.
If you print the Float using String(format:) you can see a more accurate representation of the value of the Float:
let a = Int.max
print(a) // 9223372036854775807
let b = Float(a)
print(String(format: "%.1f", b)) // 9223372036854775808.0
So the value represented by the Float is 1 larger than Int.max.
Many values will be converted to the same Float value. The question becomes, how much would you have to reduce Int.max before it results in a different Double or Float value.
Starting with Double:
var y = Int.max
while Double(y) == Double(Int.max) {
y -= 1
}
print(Int.max - y) // 512
So with Double, the last 512 Ints all convert to the same Double.
Float has fewer bits to represent the value, so there are more values that all map to the same Float. Switching to - 1000 so that it runs in reasonable time:
var y = Int.max
while Float(y) == Float(Int.max) {
y -= 1000
}
print(Int.max - y) // 274877907000
So, your expectation that a Float could accurately represent a specific Int was misplaced.
Follow up question from the comments:
If float does not have enough bits to represent Int.max, how is it
able to represent a number one larger than that?
Floating point numbers are represented as two parts: mantissa and exponent. The mantissa represents the significant digits (in binary) and the exponent represents the power of 2. As a result, a floating point number can accurately express an even power of 2 by having a mantissa of 1 with an exponent that represents the power.
Numbers that are not even powers of 2 may have a binary pattern that contains more digits than can be represented in the mantissa. This is the case for Int.max (which is 2^63 - 1) because in binary that is 111111111111111111111111111111111111111111111111111111111111111 (63 1's). A Float which is 32 bits cannot store a mantissa which is 63 bits, so it has to be rounded or truncated. In the case of Int.max, rounding up by 1 results in the value
1000000000000000000000000000000000000000000000000000000000000000. Starting from the left, there is only 1 significant bit to be represented by the mantissa (the trailing 0's come for free), so this number is a mantissa of 1 and an exponent of 64.
See #MartinR's answer for an explanation of what Java is doing.
Swift and Java behave differently when converting a "too large" floating point
number to an integer. Java truncates any floating point value
larger than Long.MAX_VALUE = 2^63-1:
long c = (long)(1.0E+30f);
System.out.println(c);
// 9223372036854775807
Swift expects that the value is in the range of Int, and aborts
with a runtime exception otherwise:
/// Creates a new instance by rounding the given floating-point value toward
/// zero.
///
/// - Parameter other: A floating-point value. When `other` is rounded toward
/// zero, the result must be within the range `Int.min...Int.max`.
public init(_ value: Float)
Example:
let c = Int(Float(1.0E30))
print(c)
// fatal error: Float value cannot be converted to Int because the result would be greater than Int.max
The same happens with your value Float(Int.max), which is the
floating point representable value closest to Int.max and happens
to be larger than Int.max.
As the title states, lldb reports the value of UInt.max to be a UInt of -1, which seems highly illogical. Considering that let uint: UInt = -1 doesn't even compile, how is this even possible? I don't see any way to have a negative value of UInt at runtime because the initializer will crash if given a negative value. I want to know the actual maximum value of UInt.
The Int value of -1 and the UInt value UInt.max have the same bit representation in memory.
You can see that if you do:
let i = Int(bitPattern: UInt.max) // i == -1
and in the opposite direction:
if UInt(bitPattern: Int(-1)) == UInt.max {
print("same")
}
Output:
same
The debugger is incorrectly displaying UInt.max as a signed Int. They have the same bit representation in memory (0xffffffffffffffff on a 64-bit system such as iPhone 6 and 0xffffffff on a 32-bit system such as iPhone 5), and the debugger apparently chooses to show that value as an Int.
You can see the same issue if you do:
print(String(format: "%d", UInt.max)) // prints "-1"
It doesn't mean UInt.max is -1, just that both have the same representation in memory.
To see the maximum value of UInt, do the following in an app or on a Swift Playground:
print(UInt.max)
This will print 18446744073709551615 on a 64-bit system (such as a Macintosh or iPhone 6) and 4294967295 on a 32-bit system (such as an iPhone 5).
In lldb:
(lldb) p String(UInt.max)
(String) $R0 = "18446744073709551615"
(lldb)
This sounds like an instance of transitioning between interpreting a literal value under Two's Complement and Unsigned representations.
In the unsigned world, a binary number is just a binary number, so the more digits that are 1, the bigger the number, since there is no need to encode the sign somehow. In order to represent the largest number of signed values, the Two's Complement encoding scheme encodes positive values as normal provided the most extreme bit is not a 1. If the most extreme bit is a 1, then the bits are reinterpreted as described at https://en.wikipedia.org/wiki/Two%27s_complement.
As shown on Wikipedia, the Two's Complement representation of -1 has all bits set to 1, or the maximal unsigned value.
When the numbers are really small, Matlab automatically shows them formatted in Scientific Notation.
Example:
A = rand(3) / 10000000000000000;
A =
1.0e-016 *
0.6340 0.1077 0.6477
0.3012 0.7984 0.0551
0.5830 0.8751 0.9386
Is there some in-built function which returns the exponent? Something like: getExponent(A) = -16?
I know this is sort of a stupid question, but I need to check hundreds of matrices and I can't seem to figure it out.
Thank you for your help.
Basic math can tell you that:
floor(log10(N))
The log base 10 of a number tells you approximately how many digits before the decimal are in that number.
For instance, 99987123459823754 is 9.998E+016
log10(99987123459823754) is 16.9999441, the floor of which is 16 - which can basically tell you "the exponent in scientific notation is 16, very close to being 17".
Floor always rounds down, so you don't need to worry about small exponents:
0.000000000003754 = 3.754E-012
log10(0.000000000003754) = -11.425
floor(log10(0.000000000003754)) = -12
You can use log10(A). The exponent used to print out will be the largest magnitude exponent in A. If you only care about small numbers (< 1), you can use
min(floor(log10(A)))
but if it is possible for them to be large too, you'd want something like:
a = log10(A);
[v i] = max(ceil(abs(a)));
exponent = v * sign(a(i));
this finds the maximum absolute exponent, and returns that. So if A = [1e-6 1e20], it will return 20.
I'm actually not sure quite how Matlab decides what exponent to use when printing out. Obviously, if A is close to 1 (e.g. A = [100, 203]) then it won't use an exponent at all but this solution will return 2. You'd have to play around with it a bit to work out exactly what the rules for printing matrices are.