Re: RFC: Improve hypot performance

["Paul A. Clarke" <pc@us.ibm.com>]

On Wed, Nov 17, 2021 at 03:58:53PM +0000, Wilco Dijkstra via Libc-alpha wrote:
> Hi Adhemerval,
> 
> Here is an early version of a much faster hypot implementation. It uses fma
> to significantly outperform the powerpc version both in throughput and
> latency. It has a worst-case ULP of ~0.949 and passes the testsuite. The
> powerpc version has a worst-case ULP of ~1.21 and several test failures.
> 
> It applies on top of your hypot patch series. I didn't optimize the non-fma
> case since modern targets have fma. It'll be interesting to compare it on
> Power. You'll need to correctly set FAST_FMINMAX to indicate support for
> inlined fmin/fmax instructions (this will be added to math_private.h for
> targets that have it), without it the code tries to use a conditional move
> since using a branch here is really bad for performance.

On Power10, this implementation is still has a large delta compared to the
current implementation:

current on Power10:
  "hypot": {
   "workload-random": {
    "duration": 5.27306e+08,
    "iterations": 4.8e+07,
    "reciprocal-throughput": 8.26834,
    "latency": 13.7027,
    "max-throughput": 1.20943e+08,
    "min-throughput": 7.29781e+07
   }
  }

with Adhemerval's patches and this patch:
  "hypot": {
   "workload-random": {
    "duration": 5.34629e+08,
    "iterations": 3.6e+07,
    "reciprocal-throughput": 12.5006,
    "latency": 17.201,
    "max-throughput": 7.99959e+07,
    "min-throughput": 5.81362e+07
   }
  }

PC

> ---
> 
> diff --git a/sysdeps/ieee754/dbl-64/e_hypot.c b/sysdeps/ieee754/dbl-64/e_hypot.c
> index d20bc3e3657e350a1103a8f8477db35ee60399e0..3906711788cff5d66725e5879bb4d6c36dd24dc7 100644
> --- a/sysdeps/ieee754/dbl-64/e_hypot.c
> +++ b/sysdeps/ieee754/dbl-64/e_hypot.c
> @@ -37,73 +37,40 @@
>  #include <math-svid-compat.h>
>  #include <errno.h>
>  
> +#define FAST_FMINMAX 1
> +//#undef __FP_FAST_FMA
> +
> +#define SCALE     0x1p-600
> +#define LARGE_VAL 0x1p+511
> +#define TINY_VAL  0x1p-459
> +#define EPS       0x1p-54
> +
> +
>  static inline double
>  handle_errno (double r)
>  {
> +  r = math_narrow_eval (r);
>    if (isinf (r))
>      __set_errno (ERANGE);
>    return r;
>  }
>  
> -/* sqrt (DBL_EPSILON / 2.0)  */
> -#define SQRT_EPS_DIV_2     0x1.6a09e667f3bcdp-27
> -/* DBL_MIN / (sqrt (DBL_EPSILON / 2.0))   */
> -#define DBL_MIN_THRESHOLD  0x1.6a09e667f3bcdp-996
> -/* eps (double) * sqrt (DBL_MIN))  */
> -#define SCALE              0x1p-563
> -/* 1 / eps (sqrt (DBL_MIN)  */
> -#define INV_SCALE          0x1p+563
> -/* sqrt (DBL_MAX)  */
> -#define SQRT_DBL_MAX       0x1.6a09e667f3bccp+511
> -/* sqrt (DBL_MIN)  */
> -#define SQRT_DBL_MIN       0x1p-511
> -
> -double
> -__hypot (double x, double y)
> +static inline double
> +kernel (double ax, double ay)
>  {
> -  if ((isinf (x) || isinf (y))
> -      && !issignaling (x) && !issignaling (y))
> -    return INFINITY;
> -  if (isnan (x) || isnan (y))
> -    return x + y;
> -
> -  double ax = fabs (x);
> -  double ay = fabs (y);
> -  if (ay > ax)
> -    {
> -      double tmp = ax;
> -      ax = ay;
> -      ay = tmp;
> -    }
> -
> -  /* Widely varying operands.  The DBL_MIN_THRESHOLD check is used to avoid
> -     a spurious underflow from the multiplication.  */
> -  if (ax >= DBL_MIN_THRESHOLD && ay <= ax * SQRT_EPS_DIV_2)
> -    return (ay == 0.0)
> -	   ? ax
> -	   : handle_errno (math_narrow_eval (ax + DBL_TRUE_MIN));
> +  double t1, t2;
> +#ifdef __FP_FAST_FMA
> +  t1 = ay + ay;
> +  t2 = ax - ay;
>  
> -  double scale = SCALE;
> -  if (ax > SQRT_DBL_MAX)
> -    {
> -      ax *= scale;
> -      ay *= scale;
> -      scale = INV_SCALE;
> -    }
> -  else if (ay < SQRT_DBL_MIN)
> -    {
> -      ax /= scale;
> -      ay /= scale;
> -    }
> +  if (t1 >= ax)
> +    return sqrt (fma (t1, ax, t2 * t2));
>    else
> -    scale = 1.0;
> -
> +    return sqrt (fma (ax, ax, ay * ay));
> +#else
>    double h = sqrt (ax * ax + ay * ay);
>  
> -  double t1, t2;
> -  if (h == 0.0)
> -    return h;
> -  else if (h <= 2.0 * ay)
> +  if (h <= 2.0 * ay)
>      {
>        double delta = h - ay;
>        t1 = ax * (2.0 * delta - ax);
> @@ -112,14 +79,57 @@ __hypot (double x, double y)
>    else
>      {
>        double delta = h - ax;
> -      t1 = 2.0 * delta * (ax - 2 * ay);
> +      t1 = 2.0 * delta * (ax - 2.0 * ay);
>        t2 = (4.0 * delta - ay) * ay + delta * delta;
>      }
>    h -= (t1 + t2) / (2.0 * h);
> -  h = math_narrow_eval (h * scale);
> -  math_check_force_underflow_nonneg (h);
> -  return handle_errno (h);
> +  return h;
> +#endif
> +}
> +
> +
> +double
> +__hypot (double x, double y)
> +{
> +  if (!isfinite (x) || !isfinite (y))
> +    {
> +      if ((isinf (x) || isinf (y))
> +	  && !issignaling_inline (x) && !issignaling_inline (y))
> +	return INFINITY;
> +      return x + y;
> +    }
> +
> +  x = fabs (x);
> +  y = fabs (y);
> +
> +  double ax = FAST_FMINMAX ? fmax (x, y) : (x < y ? y : x);
> +  double ay = FAST_FMINMAX ? fmin (x, y) : (x < y ? x : y);
> +
> +  if (__glibc_unlikely (ax > LARGE_VAL))
> +    {
> +      if (__glibc_unlikely (ay <= ax * EPS))
> +	return handle_errno (ax + ay);
> +
> +      return handle_errno (kernel (ax * SCALE, ay * SCALE) / SCALE);
> +    }
> +
> +  if (__glibc_unlikely (ay < TINY_VAL))
> +    {
> +      if (__glibc_unlikely (ax >= ay / EPS))
> +	return math_narrow_eval (ax + ay);
> +
> +      ax = math_narrow_eval (kernel (ax / SCALE, ay / SCALE) * SCALE);
> +      math_check_force_underflow_nonneg (ax);
> +      return ax;
> +    }
> +
> +  /* Common case: ax is not huge and ay is not tiny.  */
> +  if (__glibc_unlikely (ay <= ax * EPS))
> +    return math_narrow_eval (ax + ay);
> +
> +  return math_narrow_eval (kernel (ax, ay));
>  }
> +
>  strong_alias (__hypot, __ieee754_hypot)
>  libm_alias_finite (__ieee754_hypot, __hypot)
>  #if LIBM_SVID_COMPAT