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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 01:57:22 +0000
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On 17/03/2024 01:38, Keith Thompson wrote:
> bart <bc@freeuk.com> writes:
>> 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?
> 
> No, why do you ask?
> 
> On my system, the output is identical with gcc and clang, and tcc at all
> optimization levels, with both glibc and musl.  I do get slightly
> different results for long double on Cygwin vs. Ubuntu (Cygwin uses
> newlib, not glibc).


Because I get the results shown below. Even if the library is different 
from yours, I would have assumed matching results.


------------------------------

C:\c>gcc c.c -O3

C:\c>a
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

C:\c>gcc c.c -O0

C:\c>a
float (32 bits, 24 mantissa bits)
9007199254740992.00000000 -0.84893209
9007200328482816.00000000 -0.34160271

double (64 bits, 53 mantissa bits)
9007199254740992.00000000 -0.84893209
9007199254740994.00000000 -0.12728505

long double (128 bits, 64 mantissa bits)
9007199254740992.00000000 -0.84893209
9007199254740992.00097656 -0.84944780

C:\c>gcc --version
gcc (tdm64-1) 10.3.0