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Minor cleanups and optimizations:

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- Remove dead code that I forgot to remove in the previous commit.

- Calculate the sum of the lower terms of the polynomial (divided by
  x**5) in a single expression (sum of odd terms) + (sum of even terms)
  with parentheses to control grouping.  This is clearer and happens to
  give better instruction scheduling for a tiny optimization (an
  average of about ~0.5 cycles/call on Athlons).

- Calculate the final sum in a single expression with parentheses to
  control grouping too.  Change the grouping from
  first_term + (second_term + sum_of_lower_terms) to
  (first_term + second_term) + sum_of_lower_terms.  Normally the first
  grouping must be used for accuracy, but extra precision makes any
  grouping give a correct result so we can group for efficiency.  This
  is a larger optimization (average 3-4 cycles/call or 5%).

- Use parentheses to indicate that the C order of left to right evaluation
  is what is wanted (for efficiency) in a multiplication too.

The old fdlibm code has several optimizations related to these.  2
involve doing an extra operation that can be done almost in parallel
on some superscalar machines but are pessimizations on sequential
machines.  Others involve statement ordering or expression grouping.
All of these except the ordering for the combining the sums of the odd
and even terms seem to be ideal for Athlons, but parallelism is still
limited so all of these optimizations combined together with the ones
in this commit save only ~6-8 cycles (~10%).

On an AXP, tanf() on uniformly distributed args in [-2pi, 2pi] now
takes 39-59 cycles.  I don't know of any more optimizations for tanf()
short of writing it all in asm with very MD instruction scheduling.
Hardware fsin takes 122-138 cycles.  Most of the optimizations for
tanf() don't work very well for tan[l]().  fdlibm tan() now takes
145-365 cycles.
This commit is contained in:
Bruce Evans 2005-11-24 13:48:40 +00:00
parent 34c96b563e
commit 833f0e1a4a
1 changed files with 5 additions and 11 deletions
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16
lib/msun/src/k_tanf.c
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@ -38,23 +38,17 @@ extern inline
float
__kernel_tandf(double x, int iy)
{
double z,r,v,w,s;
int32_t ix,hx;
double z,r,w,s;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
z = x*x;
w = z*z;
/* Break x^5*(T[1]+x^2*T[2]+...) into
* x^5*(T[1]+x^4*T[3]+x^8*T[5]) +
* x^5*(x^2*(T[2]+x^4*T[4]))
*/
r = T[1]+w*(T[3]+w*T[5]);
v = z*(T[2]+w*T[4]);
r = T[1]+w*(T[3]+w*T[5]) + z*(T[2]+w*T[4]);
s = z*x;
r = z*s*(r+v);
r += T[0]*s;
w = x+r;
if(iy==1) return w;
else return -1.0/w;
r = (x+s*T[0])+(s*z)*r;
if(iy==1) return r;
else return -1.0/r;
}