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Re: Range Reduction Using Big Number Arithmetic

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On 8/28/26 10:39, Krishna Myneni wrote:
> On 8/20/26 22:01, Krishna Myneni wrote:
>> On 8/15/26 07:32, Krishna Myneni wrote:
>>> A simple Forth implementation for reducing large angles (|x| > 500000 
>>> rad) for accurate evaluation by the x87 native fpu trig instructions 
>>> FSIN FCOS FSINCOS FTAN is given below. The Forth code relies on the 
>>> Forth Scientific Library (FSL #47) big number arithmetic module.
>> ...
>>>
>>> FREDUCE-RANGE ( F: x -- x' )
>>>
>>> With the present implementation, the argument x is limited to a range,
>>>
>>> |x| < 9.2e18 ( radians )
>>>
>>> Test results of the effect of range reduction implementation on the 
>>> accuracy of the native FSIN instruction are provided. Shown is the 
>>> rapid loss of accuracy for |x| > 10^6 rad when providing x as the 
>>> argument to the native FSIN fpu instruction (only 3 significant 
>>> digits at x = 1e18 rad). In contrast, the reduced-range angle, x', 
>>> computed by FREDUCE- RANGE maintains 14 to 15 significant digits in 
>>> the result of FSIN over the range of x stated above. A vertical 
>>> separator "|" shows the decimal place where the native FSIN result 
>>> deviates from the range-reduced result. Note how quickly the 
>>> separator moves to the left as the angle argument is increased by 
>>> factors of 10.
>>>
>> ...
>>> If you are using a C-based Forth, the libc function may or may not 
>>> provide range-reduction. Comparison with the GNU library function
>>>
>>> sin( x ),
>>>
>>> which does perform range-reduction is shown in the test results.
>>>
> ...
> One can examine the glibc code for double precision sin(x) at the link 
> below.
> 
> https://github.com/bminor/glibc/ 
> blob/6059938728a98270b9706488887f43baa0471eba/sysdeps/ieee754/dbl-64/ 
> s_sin.c
> 
> === clip from above file ===
> ...
> /*******************************************************************/
> /* An ultimate sin routine. Given an IEEE double machine number x  */
> /* it computes the rounded value of sin(x).               */
> /*******************************************************************/
> #ifndef IN_SINCOS
> double
> SECTION
> __sin (double x)
> {
> ...
> === end of clip ===
> 
> There are several ranges of the input parameter x, each of which are 
> handled differently:
> 
...
> V. 105414350 < |x| < 2^1024; set error condition
> 
> 

Copy and paste error:

V. |x| > 2^1024;  set error condition

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Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-15 07:32 -0500
  Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-15 07:48 -0500
  Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-20 22:01 -0500
    Re: Range Reduction Using Big Number Arithmetic albert@spenarnc.xs4all.nl - 2026-08-22 19:31 +0200
      Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-31 08:49 -0500
    Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-28 10:39 -0500
      Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-28 10:42 -0500
      Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-03 18:03 -0500
        Re: Range Reduction Using Big Number Arithmetic marcel hendrix <mhx@iae.nl> - 2026-09-04 07:29 +0200
          Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-04 07:45 -0500
            Re: Range Reduction Using Big Number Arithmetic marcel hendrix <mhx@iae.nl> - 2026-09-04 15:29 +0200
              Re: Range Reduction Using Big Number Arithmetic albert@spenarnc.xs4all.nl - 2026-09-05 12:27 +0200
                Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-05 08:39 -0500
        Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-09 07:37 -0500
          Re: Range Reduction Using Big Number Arithmetic peter <peter.noreply@tin.it> - 2026-09-09 18:49 +0200
            Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-09 15:06 -0500
            Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-10 19:03 -0500
              Re: Range Reduction Using Big Number Arithmetic peter <peter.noreply@tin.it> - 2026-09-11 14:56 +0200
                Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-11 09:17 -0500
                Re: Range Reduction Using Big Number Arithmetic peter <peter.noreply@tin.it> - 2026-09-11 17:04 +0200
                Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-11 10:46 -0500
                Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-11 13:24 -0500
                Re: Range Reduction Using Big Number Arithmetic peter <peter.noreply@tin.it> - 2026-09-11 23:21 +0200
                Re: Range Reduction Using Big Number Arithmetic peter <peter.noreply@tin.it> - 2026-09-12 00:42 +0200
                Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-11 18:33 -0500
                Re: Range Reduction Using Big Number Arithmetic peter <peter.noreply@tin.it> - 2026-09-12 11:04 +0200
                Re: Range Reduction Using Big Number Arithmetic Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-12 10:33 -0500

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