I hate floating point operations
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In VS2003 the float.h header has the following definitions :
#define DBL_EPSILON 2.2204460492503131e-016 /* smallest such that 1.0+DBL_EPSILON != 1.0 */This is a very handy value to use when comparing floating point values. A tactic similar to this can be used :double value = ComputeValue(); double delta = fabs( value - expectedValue ); if( delta <= DBL_EPSILON ) TRACE( "values are considered to be equal\n" );Rick York wrote:
if( delta <= DBL_EPSILON )
This is still not foolproof, as the floating point round-off errors can accumulate, depending on your calculations. If there is enough error in your calculations (try using log() or tan() near their "blow up" values, if you want really bad results, really quickly) then DBL_EPSILON will not be sufficient. Unfortunately (having seen this problem in action for many years) there is no one-line solution to this problem. The proper comparison will depend on your calculations, the input values, and what you are using your results for.
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Rick York wrote:
if( delta <= DBL_EPSILON )
This is still not foolproof, as the floating point round-off errors can accumulate, depending on your calculations. If there is enough error in your calculations (try using log() or tan() near their "blow up" values, if you want really bad results, really quickly) then DBL_EPSILON will not be sufficient. Unfortunately (having seen this problem in action for many years) there is no one-line solution to this problem. The proper comparison will depend on your calculations, the input values, and what you are using your results for.
www.IconsReview.com <-- Huge list of stock icon collections (both free and commercial)
Very true and that's why I said, "A tactic similar to this can be used." Personally I always compare to a "tolerance" value and that works well. The big issue is - what do you use for a tolerance value ? That varies according to the circumstances as you said.
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I may have oversimplified. The case was more like the following: double dTime = 0.; double dT = atof(<some value read in a file>); double dFinal = atof(<some value read in a file>); do{ ... dTime += dT; ... while(dTime < dFinal); A loop was missing because of the 'epsilon' induced by atof.
Where do you expect us to go when the bombs fall?
Ravi's statement still holds. Floating point addition is bad, multiplication is good. What is 20.0 + 0.000000000000000000000000000001? 20 There isn't enough mantissa to hold all the digits. Then you add in the fact that floating point is basically base 2 while our math is base 10, floating point doesn't have much hope of representing numbers exactly. That is why banks used such things as scaled integers.
Tim Smith I'm going to patent thought. I have yet to see any prior art.
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Very true and that's why I said, "A tactic similar to this can be used." Personally I always compare to a "tolerance" value and that works well. The big issue is - what do you use for a tolerance value ? That varies according to the circumstances as you said.
Rick York wrote:
Very true and that's why I said, "A tactic similar to this can be used."
Don't take any offense - I wasn't trying to be pedantic (or bust your chops on the subject) I just wanted any newbie readers to be clear that there isn't a one-liner fix to the problem; after all this is the subtle bugs board.
Rick York wrote:
The big issue is - what do you use for a tolerance value ?
Yes! :sigh: the million dollar question...
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Very true and that's why I said, "A tactic similar to this can be used." Personally I always compare to a "tolerance" value and that works well. The big issue is - what do you use for a tolerance value ? That varies according to the circumstances as you said.
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Very true and that's why I said, "A tactic similar to this can be used." Personally I always compare to a "tolerance" value and that works well. The big issue is - what do you use for a tolerance value ? That varies according to the circumstances as you said.
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Ravi's statement still holds. Floating point addition is bad, multiplication is good. What is 20.0 + 0.000000000000000000000000000001? 20 There isn't enough mantissa to hold all the digits. Then you add in the fact that floating point is basically base 2 while our math is base 10, floating point doesn't have much hope of representing numbers exactly. That is why banks used such things as scaled integers.
Tim Smith I'm going to patent thought. I have yet to see any prior art.
Tim Smith wrote:
Ravi's statement still holds. Floating point addition is bad, multiplication is good.
Mine still holds too, beware atof. I believe you could get the same result without any addition or multiplication (whose I doubt it is good). Introduction of an epsilon by atof is not indicated in the documentation[^]. Some might be fooled.
Tim Smith wrote:
scaled integers
Replacing a double by a structure of an integer and a floating point position?
Where do you expect us to go when the bombs fall?
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I really do think the compiler should throw an error when you try to compare floating point values for equality.
cheers, Chris Maunder
CodeProject.com : C++ MVP
A warning may be sufficient, like the ';' after a 'if'. In my case, that would not have been enough. Guys who made that code didn't believe in warnings. When I reactivated the compiler option, over 1,400 warnings popped up at the first rebuild. Yeepee.
Where do you expect us to go when the bombs fall?
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A warning may be sufficient, like the ';' after a 'if'. In my case, that would not have been enough. Guys who made that code didn't believe in warnings. When I reactivated the compiler option, over 1,400 warnings popped up at the first rebuild. Yeepee.
Where do you expect us to go when the bombs fall?
K(arl) wrote:
over 1,400 warnings popped up at the first rebuild
:omg: A cardinal sin. Everything we do here is warning level 3 or higher, with "warning as errors" on release builds.
Kicking squealing Gucci little piggy.
The Rob Blog -
Tim Smith wrote:
Ravi's statement still holds. Floating point addition is bad, multiplication is good.
Mine still holds too, beware atof. I believe you could get the same result without any addition or multiplication (whose I doubt it is good). Introduction of an epsilon by atof is not indicated in the documentation[^]. Some might be fooled.
Tim Smith wrote:
scaled integers
Replacing a double by a structure of an integer and a floating point position?
Where do you expect us to go when the bombs fall?
K(arl) wrote:
Tim Smith wrote: scaled integers Replacing a double by a structure of an integer and a floating point position?
Possible I suppose, but storing the value in cents, not dollars would be a simpler method.
-- Rules of thumb should not be taken for the whole hand.
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<Using MFC>
double dValue = atof("0.1"); ASSERT(dValue == 0.1); double dSecondValue = (1 + dValue + dValue + dValue + dValue); ASSERT(dSecondValue == 1.4); // Crash
Where do you expect us to go when the bombs fall?
Try this, this is what I use in every of my code :
double dValue = atof("0.1");
double dTest = 0.1;
ASSERT
(
((*((LONGLONG*)&dValue))&0xFFFFFFFFFFFFFF00)
== ((*((LONGLONG*)&dTest)) &0xFFFFFFFFFFFFFF00)
);double dSecondValue = (1 + dValue + dValue + dValue + dValue);
double dTest2 = 1.4;
ASSERT
(
(*((LONGLONG*)&dSecondValue)&0xFFFFFFFFFFFFFF00)
== (*((LONGLONG*)&dTest2) &0xFFFFFFFFFFFFFF00)
); // *NO* CrashBy reducing mantissa's complexity (skiping lasting bits) by an interger cast (mostly like an union over a double), you can do some pretty decent comparison with no headache... By using float (4 bytes) instead, you could simply things to :
float dValue = atof("0.1");
float dTest = 0.1;
ASSERT
(
((*((int*)&dValue))&0xFFFFFFF0)
== ((*((int*)&dTest)) &0xFFFFFFF0)
);float dSecondValue = (1 + dValue + dValue + dValue + dValue);
float dTest2 = 1.4;
ASSERT
(
(*((int*)&dSecondValue)&0xFFFFFFF0)
== (*((int*)&dTest2) &0xFFFFFFF0)
); // *NO* CrashThe problem comes mostly because the preprocessor code which convert
double dTest = 0.1is *NOT* the same than the code within ATOF which convertdouble dValue = atof("0.1"). So you don't get a bitwise exact match of the value, only a close approximation. By using the cast technique, you : 1- can control over how many bits how want to perform the comparison 2- do a full integer comparison, which is faster by far than loading floating point registers to do the same 3- etc... So define the following macros :#define DCMP(x,y) ((*((LONGLONG*)&x))&0xFFFFFFFFFFFFFF00)==((*((LONGLONG*)&y))&0xFFFFFFFFFFFFFF00)
#define FCMP(x,y) (*((int*)&x)&0xFFFFFFF0)==(*((int*)&y)&0xFFFFFFF0)Use
DCMPon double, andFCMPon float... But beware, you cannot do that :ASSERT(DCMP(atof("0.1"),0.1)); // atof returns a value which have to be stored...
The following code works :
#define FCMP(x,y) (*((int*)&x)&0xFFFFF000)==(*((int*)&y)&0xFFFFF000)
float dSecondValue = atof("1.4"); // RAW : 0x3FB332DF
float dTest2 = 1.39999; // RAW : 0x3FB33333, last 12 bits are differents, so don't compare them
ASSERT(FCMP(dSecondValue,dTest2)); // *NO* CrashKochise EDIT : you may have used a
memcmpapproach, which is similar in functionality, but you can only test on byte boundaries (base of lenght of comparison is byte) and x86 is little endian, so you start comparing the different bytes first, -
Tim Smith wrote:
Ravi's statement still holds. Floating point addition is bad, multiplication is good.
Mine still holds too, beware atof. I believe you could get the same result without any addition or multiplication (whose I doubt it is good). Introduction of an epsilon by atof is not indicated in the documentation[^]. Some might be fooled.
Tim Smith wrote:
scaled integers
Replacing a double by a structure of an integer and a floating point position?
Where do you expect us to go when the bombs fall?
Read any book on the issues of floating point math and it will tell you that floating point addition is inherently more imprecise that floating point multiplication. For example, this is bad. You accumulate small error all the time: float x = 10; for (i = 0; i < 1000; i++) x += 0.05; This is much better but can still have a problem with the addition: float x = 10; for (i = 0; i < 1000; i++) float x1 = x + (i * 0.05);
Tim Smith I'm going to patent thought. I have yet to see any prior art.
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Try this, this is what I use in every of my code :
double dValue = atof("0.1");
double dTest = 0.1;
ASSERT
(
((*((LONGLONG*)&dValue))&0xFFFFFFFFFFFFFF00)
== ((*((LONGLONG*)&dTest)) &0xFFFFFFFFFFFFFF00)
);double dSecondValue = (1 + dValue + dValue + dValue + dValue);
double dTest2 = 1.4;
ASSERT
(
(*((LONGLONG*)&dSecondValue)&0xFFFFFFFFFFFFFF00)
== (*((LONGLONG*)&dTest2) &0xFFFFFFFFFFFFFF00)
); // *NO* CrashBy reducing mantissa's complexity (skiping lasting bits) by an interger cast (mostly like an union over a double), you can do some pretty decent comparison with no headache... By using float (4 bytes) instead, you could simply things to :
float dValue = atof("0.1");
float dTest = 0.1;
ASSERT
(
((*((int*)&dValue))&0xFFFFFFF0)
== ((*((int*)&dTest)) &0xFFFFFFF0)
);float dSecondValue = (1 + dValue + dValue + dValue + dValue);
float dTest2 = 1.4;
ASSERT
(
(*((int*)&dSecondValue)&0xFFFFFFF0)
== (*((int*)&dTest2) &0xFFFFFFF0)
); // *NO* CrashThe problem comes mostly because the preprocessor code which convert
double dTest = 0.1is *NOT* the same than the code within ATOF which convertdouble dValue = atof("0.1"). So you don't get a bitwise exact match of the value, only a close approximation. By using the cast technique, you : 1- can control over how many bits how want to perform the comparison 2- do a full integer comparison, which is faster by far than loading floating point registers to do the same 3- etc... So define the following macros :#define DCMP(x,y) ((*((LONGLONG*)&x))&0xFFFFFFFFFFFFFF00)==((*((LONGLONG*)&y))&0xFFFFFFFFFFFFFF00)
#define FCMP(x,y) (*((int*)&x)&0xFFFFFFF0)==(*((int*)&y)&0xFFFFFFF0)Use
DCMPon double, andFCMPon float... But beware, you cannot do that :ASSERT(DCMP(atof("0.1"),0.1)); // atof returns a value which have to be stored...
The following code works :
#define FCMP(x,y) (*((int*)&x)&0xFFFFF000)==(*((int*)&y)&0xFFFFF000)
float dSecondValue = atof("1.4"); // RAW : 0x3FB332DF
float dTest2 = 1.39999; // RAW : 0x3FB33333, last 12 bits are differents, so don't compare them
ASSERT(FCMP(dSecondValue,dTest2)); // *NO* CrashKochise EDIT : you may have used a
memcmpapproach, which is similar in functionality, but you can only test on byte boundaries (base of lenght of comparison is byte) and x86 is little endian, so you start comparing the different bytes first,Your code still doesn't work since it suffers from boundary conditions. For example: 0xFFFFFF00 0xFFFFFEFF These are two very close floating point numbers, but your test will fail. Also, there are problems with -0 and +0. bool CMP (float x, float y, int tol) { int ix = *((int *) &x); int iy = *((int *) &y); if (ix < 0) ix = 0x80000000 - ix; if (iy < 0) iy = 0x80000000 - iy; return abs (ix - iy) <= tol; } This fixes the boundary condition and the +0, -0 issue. However, it still has problems with such things as +inf and -inf being close to +/- MAX_FLT and other issues with special floating point bit patterns.
Tim Smith I'm going to patent thought. I have yet to see any prior art.
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Your code still doesn't work since it suffers from boundary conditions. For example: 0xFFFFFF00 0xFFFFFEFF These are two very close floating point numbers, but your test will fail. Also, there are problems with -0 and +0. bool CMP (float x, float y, int tol) { int ix = *((int *) &x); int iy = *((int *) &y); if (ix < 0) ix = 0x80000000 - ix; if (iy < 0) iy = 0x80000000 - iy; return abs (ix - iy) <= tol; } This fixes the boundary condition and the +0, -0 issue. However, it still has problems with such things as +inf and -inf being close to +/- MAX_FLT and other issues with special floating point bit patterns.
Tim Smith I'm going to patent thought. I have yet to see any prior art.
My macro can be of great help if you know where you put your foot. Eg when dealing with strict positive numbers set, or strict negative numbers set, without mixing the two. However the test case only works with 0xFF... values padded with 0, not like your 0xFFFFFEFF example. I think you wanted to say 0xFFFFFE00 which is correct :) Kochise PS : If I remember right, there is a 'magical trick' explained in a raticle on CP which explain how to cast double to float and the way back only using integer operations, and it works pretty well and fast, and also deals with the sign...
In Code we trust !
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Read any book on the issues of floating point math and it will tell you that floating point addition is inherently more imprecise that floating point multiplication. For example, this is bad. You accumulate small error all the time: float x = 10; for (i = 0; i < 1000; i++) x += 0.05; This is much better but can still have a problem with the addition: float x = 10; for (i = 0; i < 1000; i++) float x1 = x + (i * 0.05);
Tim Smith I'm going to patent thought. I have yet to see any prior art.
Tim Smith wrote:
it will tell you that floating point addition is inherently more imprecise that floating point multiplication
It works only if one of the term of the multiplication is an integer. :~ I understand it's like incertitude calculation, for addition you sum absolute incertitudes, for multiplication you sum relative ones.
Where do you expect us to go when the bombs fall?
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<Using MFC>
double dValue = atof("0.1"); ASSERT(dValue == 0.1); double dSecondValue = (1 + dValue + dValue + dValue + dValue); ASSERT(dSecondValue == 1.4); // Crash
Where do you expect us to go when the bombs fall?
If you've ever studied the harmonic series (1 + 1/2 + 1/3 + ...), you'll know that it diverges very slowly. However, if you use any calculator to sum it up, you'll think that it converges. When I was still a pre-engineering student, before I switched to Math, we were taught to start any summand from the lower end and add up the bigger numbers so that the round-off error is minimized. In this case, you need to add the 1 last, but not after subtracting the integer part, multiplying the decimal part by a power of ten and rounding it to see if it is still zero or one depending on what the value is exactly and then doing the compare. Since everybody here has been pulling your leg and giving you grief, I'll keep my jokes to myself. Yeah, I don't have any anyway. :) It's annoying as a developer that you actually have to write a check to make sure your numbers are what they should be. Makes you wonder why we use machines for calculations and why cororations aren't going broke because of them. Hmmm, maybe they round to their benefit and that's why people are going broke and they're doing very well. :rolleyes: I'm in the wrong business.
"This perpetual motion machine she made is a joke. It just keeps going faster and faster. Lisa, get in here! In this house, we obey the laws of thermodynamics!" - Homer Simpson Web - Blog - RSS - Math - LinkedIn - BM
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A) Never hate B) Don't expect them to do what they can't
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I really do think the compiler should throw an error when you try to compare floating point values for equality.
cheers, Chris Maunder
CodeProject.com : C++ MVP
Chris Maunder wrote:
I really do think the compiler should throw an error when you try to compare floating point values for equality.
It seems to me that a data type where the concept of equal values is either undefined or can't be practically determined is clearly "half-baked".
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<Using MFC>
double dValue = atof("0.1"); ASSERT(dValue == 0.1); double dSecondValue = (1 + dValue + dValue + dValue + dValue); ASSERT(dSecondValue == 1.4); // Crash
Where do you expect us to go when the bombs fall?
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Chris Maunder wrote:
I really do think the compiler should throw an error when you try to compare floating point values for equality.
It seems to me that a data type where the concept of equal values is either undefined or can't be practically determined is clearly "half-baked".
You think maybe we should instead store the value as "one-point-five"? Or even "three-point-one-four-one-five-nine..."?
cheers, Chris Maunder
CodeProject.com : C++ MVP