Gcc46 and 128 Bit Floating Point

[Steve Kargl]

On Wed, Feb 29, 2012 at 07:23:36PM +1100, Bruce Evans wrote:
> On Tue, 28 Feb 2012, Thomas D. Dean wrote:
> 
> >On 02/28/12 22:03, Bruce Evans wrote:
> >>
> >>>#include <quadmath.h>
> >>>#include <stdio.h>
> >>>int main() {
> >>>char buf[128];
> >>>__float128 x = sqrtq(2.0Q);
> >>>quadmath_snprintf(buf, sizeof buf, "%.45Qf",x);
> >>>printf("sin(%s) = ",buf);
> >>>quadmath_snprintf(buf, sizeof buf, "%.45Qf",sinq(x));
> >>>printf("%s\n",buf);
> >>>return 0;
> >>>}
> >>>
> >>>gcc46 math.c -o math /usr/local/lib/gcc46/libquadmath.a /usr/lib/libm.a
> >
> >>objdump -d math | grep fsqrt
> > 4014fd:       d9 fa                   fsqrt
> > 407bb4:       d9 fa                   fsqrt
> >
> >Comes from the libs.
> 
> It's not unreasonable in the libraries.  A lower-precision sqrt gives
> a good place to start for a Newton approximation method.  I wouldn't
> have expected fsqrt to be a better place to start that a 64-bit sqrt
> using SSE though.  SSE also provides 32-bit sqrt and an even
> lower-precision but much faster reciprocal square root to start from.
> 

>From libquadmath/math/sqrtq.c

  if (x <= DBL_MAX && x >= DBL_MIN)
  {
    /* Use double result as starting point.  */
    y = sqrt ((double) x);

    /* Two Newton iterations.  */
    y -= 0.5q * (y - x / y);
    y -= 0.5q * (y - x / y);
    return y;
  }

This probably explains the presences of fsqrt.  There's
a similar block for LDBL_MAX and LDBL_MIN.

-- 
Steve