Re: The joy of type aliasing and C

>>> that claim to adhere to it.  These will give you the min, max,
>>> radix (FLT_RADIX), precision in digits (FLT_DIG), etc.
>>>
>>> I feel so ashamed for knowing this stuff...

Well, maybe you'd feel a little less ashamed if you took a
look at Section 2.1 of Game Programming Gems 2: 
"Floating-Point Tricks: Improving Performance with IEEE
Floating Point" (Yossarian King, Electronic Arts Canada).
It's 14 pages of this stuff!

It begins like this (which is "aliasing" not "punning", right?):

  typedef union
  {
  int   i;
  float f;
  } INTORFLOAT;

The author points out that "(int)f" costs about 60 cycles
on a Pentium II, and then shows the following faster code:

  INTORFLOAT  n;     // floating-point number to convert
  INTORFLOAT  bias;  // "magic" number

  bias.i = (23 + 127) << 23; // bias constant = 1 x 2^23
  n.f = 123.456f;            // some floating-point number

  n.f += bias.f; // add as floating-point
  n.i -= bias.i; // subtract as integer
  // n.i is now 123 - the integer portion of the original n.f

The author says this reduces the conversion time from 60 cycles
to about 5 cycles (assuming everything is in cache).  Wow!

Later in the article the author mentions a fast absolute
value:

  INTORFLOAT  ftmp;
  ftmp.f = f;
  ftmp.i &= 0x7fffffff;
  f = ftmp.f;

But I'm not sure how this compares with the inline __fabs()
instruction.

The author shows an improved version of the old square-root
trick (bit shift followed by add), taking about 16 cycles 
instead of 80 on a Pentium II; five times faster.

The Intel "Software Optimization Cookbook" (2002) has fun items
like this:

  float FastSqrt( float f )   // roughly 5% error
  {
    float RetVal;
    __asm
      {
      mov  eax, f
      sub  eax, 0x3f800000
      sar  eax, 1
      add  eax, 0x3f800000
      mov  RetVal, eax
      }
  return RetVal;
  }

But, check it; they have the following code on p. 157
(taken out of context):

  return (*((int *)&f) - IT_FTOI_MAGIC_NUM) >> 1;

Type punning!  Intel compiler?

--- Colin





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