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From: bart <bc@freeuk.com>
Newsgroups: comp.lang.c,comp.arch
Subject: Re: Radians Or Degrees?
Date: Sun, 17 Mar 2024 00:00:00 +0000
Organization: A noiseless patient Spider
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On 16/03/2024 23:19, Keith Thompson wrote:
> mitchalsup@aol.com (MitchAlsup1) writes:

>> Say you are a programmer and you receive a value like 2^53 from an
>> Input read and you wan the most accurate possible SIN( of that ).
> 
> I can't think of a scenario where that would be useful (other than just
> doing it for the sake of doing it).
> 
> If 2^53 represents a physical quantity, how likely is the actual value
> to be known within ±π (+/i pi for those who prefer ASCII)?
> 
> If you can get better precision without too much extra cost, that's
> great.  I don't know enough to have an opinion about what the best
> tradeoff is, but I presume it's going to be different depending on the
> application.
> 
> Here's a C program that shows how precise sin(2^53) can be for types
> float, double, and long double (I used gcc and glibc).  The nextafter
> functions are used to compute the nearest representable number.  For
> long double, the value of sin() changes by about 1 part in 1600, which
> seems decent, but it's not nearly as precise as for values around 1.0.
> For float and double, the imprecision of the argument is enough to make
> the result practically meaningless.
> 
 > ...
> Output:
> 
> float (32 bits, 24 mantissa bits)
> 9007199254740992.00000000 -0.84892595
> 9007200328482816.00000000 -0.34159181
> 
> double (64 bits, 53 mantissa bits)
> 9007199254740992.00000000 -0.84892596
> 9007199254740994.00000000 -0.12729655
> 
> long double (128 bits, 64 mantissa bits)
> 9007199254740992.00000000 -0.84892596
> 9007199254740992.00097656 -0.84944168


Is this output supposed to be different between gcc -O0 and gcc -O3?