From: sgk@REMOVEtroutmask.apl.washington.edu   
      
   On Thu, 24 Oct 2024 05:22:53 +0000, Lawrence D'Oliveiro wrote:   
      
   > On Thu, 24 Oct 2024 05:06:37 -0000 (UTC), Steven G. Kargl wrote:   
   >   
   >> For sin(x), argument reduction will give sin(0) = 0, exactly. That's one   
   >> angle.   
   >   
   > More generally, it gives sin(x) ≃ x, for uncountably many angles.   
   >   
   >> For sind(x), argument reduction will give sind(x) = 0, exactly,   
   >> for countable many angles.   
   >   
   > But it never gives sind(x) anywhere close to x.   
      
   Never claimed sind(x) for x near 0 was exact.   
      
   It is, however, for floatin point arithmetic,   
   correct to less than or equal to 0.5 ULP.  Now,   
   got read Goldberg.   
      
   --   
   steve   
      
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