Refactor code forcing underflow exceptions.

Various floating-point functions have code to force underflow
exceptions if a tiny result was computed in a way that might not have
resulted in such exceptions even though the result is inexact.  This
typically uses math_force_eval to ensure that the underflowing
expression is evaluated, but sometimes uses volatile.

This patch refactors such code to use three new macros
math_check_force_underflow, math_check_force_underflow_nonneg and
math_check_force_underflow_complex (which in turn use
math_force_eval).  In the limited number of cases not suited to a
simple conversion to these macros, existing uses of volatile are
changed to use math_force_eval instead.  The converted code does not
always execute exactly the same sequence of operations as the original
code, but the overall effects should be the same.

Tested for x86_64, x86, mips64 and powerpc.

	* sysdeps/generic/math_private.h (fabs_tg): New macro.
	(min_of_type): Likewise.
	(math_check_force_underflow): Likewise.
	(math_check_force_underflow_nonneg): Likewise.
	(math_check_force_underflow_complex): Likewise.
	* math/e_exp2l.c (__ieee754_exp2l): Use
	math_check_force_underflow_nonneg.
	* math/k_casinh.c (__kernel_casinh): Likewise.
	* math/k_casinhf.c (__kernel_casinhf): Likewise.
	* math/k_casinhl.c (__kernel_casinhl): Likewise.
	* math/s_catan.c (__catan): Use
	math_check_force_underflow_complex.
	* math/s_catanf.c (__catanf): Likewise.
	* math/s_catanh.c (__catanh): Likewise.
	* math/s_catanhf.c (__catanhf): Likewise.
	* math/s_catanhl.c (__catanhl): Likewise.
	* math/s_catanl.c (__catanl): Likewise.
	* math/s_ccosh.c (__ccosh): Likewise.
	* math/s_ccoshf.c (__ccoshf): Likewise.
	* math/s_ccoshl.c (__ccoshl): Likewise.
	* math/s_cexp.c (__cexp): Likewise.
	* math/s_cexpf.c (__cexpf): Likewise.
	* math/s_cexpl.c (__cexpl): Likewise.
	* math/s_clog.c (__clog): Use math_check_force_underflow_nonneg.
	* math/s_clog10.c (__clog10): Likewise.
	* math/s_clog10f.c (__clog10f): Likewise.
	* math/s_clog10l.c (__clog10l): Likewise.
	* math/s_clogf.c (__clogf): Likewise.
	* math/s_clogl.c (__clogl): Likewise.
	* math/s_csin.c (__csin): Use math_check_force_underflow_complex.
	* math/s_csinf.c (__csinf): Likewise.
	* math/s_csinh.c (__csinh): Likewise.
	* math/s_csinhf.c (__csinhf): Likewise.
	* math/s_csinhl.c (__csinhl): Likewise.
	* math/s_csinl.c (__csinl): Likewise.
	* math/s_csqrt.c (__csqrt): Use math_check_force_underflow.
	* math/s_csqrtf.c (__csqrtf): Likewise.
	* math/s_csqrtl.c (__csqrtl): Likewise.
	* math/s_ctan.c (__ctan): Use math_check_force_underflow_complex.
	* math/s_ctanf.c (__ctanf): Likewise.
	* math/s_ctanh.c (__ctanh): Likewise.
	* math/s_ctanhf.c (__ctanhf): Likewise.
	* math/s_ctanhl.c (__ctanhl): Likewise.
	* math/s_ctanl.c (__ctanl): Likewise.
	* stdlib/strtod_l.c (round_and_return): Use math_force_eval
	instead of volatile.
	* sysdeps/ieee754/dbl-64/e_asin.c (__ieee754_asin): Use
	math_check_force_underflow.
	* sysdeps/ieee754/dbl-64/e_atanh.c (__ieee754_atanh): Likewise.
	* sysdeps/ieee754/dbl-64/e_exp.c (__ieee754_exp): Do not use
	volatile when forcing underflow.
	* sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Use
	math_check_force_underflow_nonneg.
	* sysdeps/ieee754/dbl-64/e_gamma_r.c (__ieee754_gamma_r):
	Likewise.
	* sysdeps/ieee754/dbl-64/e_j1.c (__ieee754_j1): Use
	math_check_force_underflow.
	* sysdeps/ieee754/dbl-64/e_jn.c (__ieee754_jn): Likewise.
	* sysdeps/ieee754/dbl-64/e_sinh.c (__ieee754_sinh): Likewise.
	* sysdeps/ieee754/dbl-64/s_asinh.c (__asinh): Likewise.
	* sysdeps/ieee754/dbl-64/s_atan.c (atan): Use
	math_check_force_underflow_nonneg.
	* sysdeps/ieee754/dbl-64/s_erf.c (__erf): Use
	math_check_force_underflow.
	* sysdeps/ieee754/dbl-64/s_expm1.c (__expm1): Likewise.
	* sysdeps/ieee754/dbl-64/s_fma.c (__fma): Use math_force_eval
	instead of volatile.
	* sysdeps/ieee754/dbl-64/s_log1p.c (__log1p): Use
	math_check_force_underflow.
	* sysdeps/ieee754/dbl-64/s_sin.c (__sin): Likewise.
	* sysdeps/ieee754/dbl-64/s_tan.c (tan): Use
	math_check_force_underflow_nonneg.
	* sysdeps/ieee754/dbl-64/s_tanh.c (__tanh): Use
	math_check_force_underflow.
	* sysdeps/ieee754/flt-32/e_asinf.c (__ieee754_asinf): Likewise.
	* sysdeps/ieee754/flt-32/e_atanhf.c (__ieee754_atanhf): Likewise.
	* sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Use
	math_check_force_underflow_nonneg.
	* sysdeps/ieee754/flt-32/e_gammaf_r.c (__ieee754_gammaf_r):
	Likewise.
	* sysdeps/ieee754/flt-32/e_j1f.c (__ieee754_j1f): Use
	math_check_force_underflow.
	* sysdeps/ieee754/flt-32/e_jnf.c (__ieee754_jnf): Likewise.
	* sysdeps/ieee754/flt-32/e_sinhf.c (__ieee754_sinhf): Likewise.
	* sysdeps/ieee754/flt-32/k_sinf.c (__kernel_sinf): Likewise.
	* sysdeps/ieee754/flt-32/k_tanf.c (__kernel_tanf): Likewise.
	* sysdeps/ieee754/flt-32/s_asinhf.c (__asinhf): Likewise.
	* sysdeps/ieee754/flt-32/s_atanf.c (__atanf): Likewise.
	* sysdeps/ieee754/flt-32/s_erff.c (__erff): Likewise.
	* sysdeps/ieee754/flt-32/s_expm1f.c (__expm1f): Likewise.
	* sysdeps/ieee754/flt-32/s_log1pf.c (__log1pf): Likewise.
	* sysdeps/ieee754/flt-32/s_tanhf.c (__tanhf): Likewise.
	* sysdeps/ieee754/ldbl-128/e_asinl.c (__ieee754_asinl): Likewise.
	* sysdeps/ieee754/ldbl-128/e_atanhl.c (__ieee754_atanhl):
	Likewise.
	* sysdeps/ieee754/ldbl-128/e_expl.c (__ieee754_expl): Use
	math_check_force_underflow_nonneg.
	* sysdeps/ieee754/ldbl-128/e_gammal_r.c (__ieee754_gammal_r):
	Likewise.
	* sysdeps/ieee754/ldbl-128/e_j1l.c (__ieee754_j1l): Use
	math_check_force_underflow.
	* sysdeps/ieee754/ldbl-128/e_jnl.c (__ieee754_jnl): Likewise.
	* sysdeps/ieee754/ldbl-128/e_sinhl.c (__ieee754_sinhl): Likewise.
	* sysdeps/ieee754/ldbl-128/k_sincosl.c (__kernel_sincosl):
	Likewise.
	* sysdeps/ieee754/ldbl-128/k_sinl.c (__kernel_sinl): Likewise.
	* sysdeps/ieee754/ldbl-128/k_tanl.c (__kernel_tanl): Likewise.
	* sysdeps/ieee754/ldbl-128/s_asinhl.c (__asinhl): Likewise.
	* sysdeps/ieee754/ldbl-128/s_atanl.c (__atanl): Likewise.
	* sysdeps/ieee754/ldbl-128/s_erfl.c (__erfl): Likewise.
	* sysdeps/ieee754/ldbl-128/s_expm1l.c (__expm1l): Likewise.
	* sysdeps/ieee754/ldbl-128/s_fmal.c (__fmal): Use math_force_eval
	instead of volatile.
	* sysdeps/ieee754/ldbl-128/s_log1pl.c (__log1pl): Use
	math_check_force_underflow.
	* sysdeps/ieee754/ldbl-128/s_tanhl.c (__tanhl): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/e_asinl.c (__ieee754_asinl): Use
	math_check_force_underflow.
	* sysdeps/ieee754/ldbl-128ibm/e_atanhl.c (__ieee754_atanhl):
	Likewise.
	* sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c (__ieee754_gammal_r):
	Use math_check_force_underflow_nonneg.
	* sysdeps/ieee754/ldbl-128ibm/e_jnl.c (__ieee754_jnl): Use
	math_check_force_underflow.
	* sysdeps/ieee754/ldbl-128ibm/e_sinhl.c (__ieee754_sinhl):
	Likewise.
	* sysdeps/ieee754/ldbl-128ibm/k_sincosl.c (__kernel_sincosl):
	Likewise.
	* sysdeps/ieee754/ldbl-128ibm/k_sinl.c (__kernel_sinl): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/k_tanl.c (__kernel_tanl): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_asinhl.c (__asinhl): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_atanl.c (__atanl): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_erfl.c (__erfl): Likewise.
	* sysdeps/ieee754/ldbl-128ibm/s_tanhl.c (__tanhl): Likewise.
	* sysdeps/ieee754/ldbl-96/e_asinl.c (__ieee754_asinl): Likewise.
	* sysdeps/ieee754/ldbl-96/e_atanhl.c (__ieee754_atanhl): Likewise.
	* sysdeps/ieee754/ldbl-96/e_gammal_r.c (__ieee754_gammal_r): Use
	math_check_force_underflow_nonneg.
	* sysdeps/ieee754/ldbl-96/e_j1l.c (__ieee754_j1l): Use
	math_check_force_underflow.
	* sysdeps/ieee754/ldbl-96/e_jnl.c (__ieee754_jnl): Likewise.
	* sysdeps/ieee754/ldbl-96/e_sinhl.c (__ieee754_sinhl): Likewise.
	* sysdeps/ieee754/ldbl-96/k_sinl.c (__kernel_sinl): Likewise.
	* sysdeps/ieee754/ldbl-96/k_tanl.c (__kernel_tanl): Use
	math_check_force_underflow_nonneg.
	* sysdeps/ieee754/ldbl-96/s_asinhl.c (__asinhl): Use
	math_check_force_underflow.
	* sysdeps/ieee754/ldbl-96/s_erfl.c (__erfl): Likewise.
	* sysdeps/ieee754/ldbl-96/s_fmal.c (__fmal): Use math_force_eval
	instead of volatile.
	* sysdeps/ieee754/ldbl-96/s_tanhl.c (__tanhl): Use
	math_check_force_underflow.

17 files changed, 19 insertions, 81 deletions

diff --git a/sysdeps/ieee754/dbl-64/e_asin.c b/sysdeps/ieee754/dbl-64/e_asin.c
index a7684d1078..214a61211a 100644
--- a/sysdeps/ieee754/dbl-64/e_asin.c
+++ b/sysdeps/ieee754/dbl-64/e_asin.c
@@ -71,11 +71,7 @@ __ieee754_asin(double x){
 
   if (k < 0x3e500000)
     {
-      if (fabs (x) < DBL_MIN)
-	{
-	  double force_underflow = x * x;
-	  math_force_eval (force_underflow);
-	}
+      math_check_force_underflow (x);
       return x;  /* for x->0 => sin(x)=x */
     }
   /*----------------------2^-26 <= |x| < 2^ -3    -----------------*/
diff --git a/sysdeps/ieee754/dbl-64/e_atanh.c b/sysdeps/ieee754/dbl-64/e_atanh.c
index 6b00b800f2..f011e4c4eb 100644
--- a/sysdeps/ieee754/dbl-64/e_atanh.c
+++ b/sysdeps/ieee754/dbl-64/e_atanh.c
@@ -52,11 +52,7 @@ __ieee754_atanh (double x)
       if (__glibc_unlikely (xa < 0x1.0p-28))
 	{
 	  math_force_eval (huge + x);
-	  if (fabs (x) < DBL_MIN)
-	    {
-	      double force_underflow = x * x;
-	      math_force_eval (force_underflow);
-	    }
+	  math_check_force_underflow (x);
 	  return x;
 	}
 
diff --git a/sysdeps/ieee754/dbl-64/e_exp.c b/sysdeps/ieee754/dbl-64/e_exp.c
index bb76907f74..db7626844a 100644
--- a/sysdeps/ieee754/dbl-64/e_exp.c
+++ b/sysdeps/ieee754/dbl-64/e_exp.c
@@ -200,10 +200,7 @@ __ieee754_exp (double x)
       check_uflow_ret:
 	if (retval < DBL_MIN)
 	  {
-#if FLT_EVAL_METHOD != 0
-	    volatile
-#endif
-	      double force_underflow = tiny * tiny;
+	    double force_underflow = tiny * tiny;
 	    math_force_eval (force_underflow);
 	  }
 	if (retval == 0)
diff --git a/sysdeps/ieee754/dbl-64/e_exp2.c b/sysdeps/ieee754/dbl-64/e_exp2.c
index 01df62150d..48a7254086 100644
--- a/sysdeps/ieee754/dbl-64/e_exp2.c
+++ b/sysdeps/ieee754/dbl-64/e_exp2.c
@@ -122,11 +122,7 @@ __ieee754_exp2 (double x)
       else
 	{
 	  result *= scale_u.d;
-	  if (result < DBL_MIN)
-	    {
-	      double force_underflow = result * result;
-	      math_force_eval (force_underflow);
-	    }
+	  math_check_force_underflow_nonneg (result);
 	  return result;
 	}
     }
diff --git a/sysdeps/ieee754/dbl-64/e_gamma_r.c b/sysdeps/ieee754/dbl-64/e_gamma_r.c
index d3fb8af97e..a09a3fc1f2 100644
--- a/sysdeps/ieee754/dbl-64/e_gamma_r.c
+++ b/sysdeps/ieee754/dbl-64/e_gamma_r.c
@@ -187,11 +187,7 @@ __ieee754_gamma_r (double x, int *signgamp)
 	      double tret = M_PI / (-x * sinpix
 				    * gamma_positive (-x, &exp2_adj));
 	      ret = __scalbn (tret, -exp2_adj);
-	      if (ret < DBL_MIN)
-		{
-		  double force_underflow = ret * ret;
-		  math_force_eval (force_underflow);
-		}
+	      math_check_force_underflow_nonneg (ret);
 	    }
 	}
       ret = math_narrow_eval (ret);
diff --git a/sysdeps/ieee754/dbl-64/e_j1.c b/sysdeps/ieee754/dbl-64/e_j1.c
index 26ffdfe282..7f80b3ced0 100644
--- a/sysdeps/ieee754/dbl-64/e_j1.c
+++ b/sysdeps/ieee754/dbl-64/e_j1.c
@@ -128,11 +128,7 @@ __ieee754_j1 (double x)
       if (huge + x > one)                 /* inexact if x!=0 necessary */
 	{
 	  double ret = 0.5 * x;
-	  if (fabs (ret) < DBL_MIN)
-	    {
-	      double force_underflow = ret * ret;
-	      math_force_eval (force_underflow);
-	    }
+	  math_check_force_underflow (ret);
 	  return ret;
 	}
     }
diff --git a/sysdeps/ieee754/dbl-64/e_jn.c b/sysdeps/ieee754/dbl-64/e_jn.c
index ccef2dcd80..d6ab0bced5 100644
--- a/sysdeps/ieee754/dbl-64/e_jn.c
+++ b/sysdeps/ieee754/dbl-64/e_jn.c
@@ -246,11 +246,8 @@ __ieee754_jn (int n, double x)
   }
   if (ret == 0)
     ret = __copysign (DBL_MIN, ret) * DBL_MIN;
-  else if (fabs (ret) < DBL_MIN)
-    {
-      double force_underflow = ret * ret;
-      math_force_eval (force_underflow);
-    }
+  else
+    math_check_force_underflow (ret);
   return ret;
 }
 strong_alias (__ieee754_jn, __jn_finite)
diff --git a/sysdeps/ieee754/dbl-64/e_sinh.c b/sysdeps/ieee754/dbl-64/e_sinh.c
index 291bfad0b3..8479bdd9b8 100644
--- a/sysdeps/ieee754/dbl-64/e_sinh.c
+++ b/sysdeps/ieee754/dbl-64/e_sinh.c
@@ -60,11 +60,7 @@ __ieee754_sinh (double x)
   if (ix < 0x40360000)                  /* |x|<22 */
     {
       if (__glibc_unlikely (ix < 0x3e300000)) {            /* |x|<2**-28 */
-	if (fabs (x) < DBL_MIN)
-	  {
-	    double force_underflow = x * x;
-	    math_force_eval (force_underflow);
-	  }
+	math_check_force_underflow (x);
 	if (shuge + x > one)
 	  return x;
 	/* sinh(tiny) = tiny with inexact */
diff --git a/sysdeps/ieee754/dbl-64/s_asinh.c b/sysdeps/ieee754/dbl-64/s_asinh.c
index ebe471015b..9193301b5e 100644
--- a/sysdeps/ieee754/dbl-64/s_asinh.c
+++ b/sysdeps/ieee754/dbl-64/s_asinh.c
@@ -39,11 +39,7 @@ __asinh (double x)
   ix = hx & 0x7fffffff;
   if (__glibc_unlikely (ix < 0x3e300000))                  /* |x|<2**-28 */
     {
-      if (fabs (x) < DBL_MIN)
-	{
-	  double force_underflow = x * x;
-	  math_force_eval (force_underflow);
-	}
+      math_check_force_underflow (x);
       if (huge + x > one)
 	return x;                       /* return x inexact except 0 */
     }
diff --git a/sysdeps/ieee754/dbl-64/s_atan.c b/sysdeps/ieee754/dbl-64/s_atan.c
index 5035ae87bc..5160cd1b66 100644
--- a/sysdeps/ieee754/dbl-64/s_atan.c
+++ b/sysdeps/ieee754/dbl-64/s_atan.c
@@ -90,11 +90,7 @@ atan (double x)
 	{
 	  if (u < A)
 	    {
-	      if (u < DBL_MIN)
-		{
-		  double force_underflow = x * x;
-		  math_force_eval (force_underflow);
-		}
+	      math_check_force_underflow_nonneg (u);
 	      return x;
 	    }
 	  else
diff --git a/sysdeps/ieee754/dbl-64/s_erf.c b/sysdeps/ieee754/dbl-64/s_erf.c
index 77cd50d935..e59f5f33ce 100644
--- a/sysdeps/ieee754/dbl-64/s_erf.c
+++ b/sysdeps/ieee754/dbl-64/s_erf.c
@@ -213,11 +213,7 @@ __erf (double x)
 	    {
 	      /* Avoid spurious underflow.  */
 	      double ret = 0.0625 * (16.0 * x + (16.0 * efx) * x);
-	      if (fabs (ret) < DBL_MIN)
-		{
-		  double force_underflow = ret * ret;
-		  math_force_eval (force_underflow);
-		}
+	      math_check_force_underflow (ret);
 	      return ret;
 	    }
 	  return x + efx * x;
diff --git a/sysdeps/ieee754/dbl-64/s_expm1.c b/sysdeps/ieee754/dbl-64/s_expm1.c
index 41ef63a786..54d771007a 100644
--- a/sysdeps/ieee754/dbl-64/s_expm1.c
+++ b/sysdeps/ieee754/dbl-64/s_expm1.c
@@ -195,11 +195,7 @@ __expm1 (double x)
     }
   else if (hx < 0x3c900000)             /* when |x|<2**-54, return x */
     {
-      if (fabs (x) < DBL_MIN)
-	{
-	  double force_underflow = x * x;
-	  math_force_eval (force_underflow);
-	}
+      math_check_force_underflow (x);
       t = huge + x;     /* return x with inexact flags when x!=0 */
       return x - (t - (huge + x));
     }
diff --git a/sysdeps/ieee754/dbl-64/s_fma.c b/sysdeps/ieee754/dbl-64/s_fma.c
index 278b690f9b..8b4e1331f6 100644
--- a/sysdeps/ieee754/dbl-64/s_fma.c
+++ b/sysdeps/ieee754/dbl-64/s_fma.c
@@ -90,8 +90,8 @@ __fma (double x, double y, double z)
 		     && w.ieee.mantissa1 == 0
 		     && w.ieee.mantissa0 == 0)))
 	    {
-	      volatile double force_underflow = x * y;
-	      (void) force_underflow;
+	      double force_underflow = x * y;
+	      math_force_eval (force_underflow);
 	    }
 	  return v.d * 0x1p-54;
 	}
diff --git a/sysdeps/ieee754/dbl-64/s_log1p.c b/sysdeps/ieee754/dbl-64/s_log1p.c
index cff555b0aa..340f6377f7 100644
--- a/sysdeps/ieee754/dbl-64/s_log1p.c
+++ b/sysdeps/ieee754/dbl-64/s_log1p.c
@@ -120,11 +120,7 @@ __log1p (double x)
 	  math_force_eval (two54 + x);          /* raise inexact */
 	  if (ax < 0x3c900000)                  /* |x| < 2**-54 */
 	    {
-	      if (fabs (x) < DBL_MIN)
-		{
-		  double force_underflow = x * x;
-		  math_force_eval (force_underflow);
-		}
+	      math_check_force_underflow (x);
 	      return x;
 	    }
 	  else
diff --git a/sysdeps/ieee754/dbl-64/s_sin.c b/sysdeps/ieee754/dbl-64/s_sin.c
index eff120e88d..48c924c6b6 100644
--- a/sysdeps/ieee754/dbl-64/s_sin.c
+++ b/sysdeps/ieee754/dbl-64/s_sin.c
@@ -297,11 +297,7 @@ __sin (double x)
   k = 0x7fffffff & m;		/* no sign           */
   if (k < 0x3e500000)		/* if x->0 =>sin(x)=x */
     {
-      if (fabs (x) < DBL_MIN)
-	{
-	  double force_underflow = x * x;
-	  math_force_eval (force_underflow);
-	}
+      math_check_force_underflow (x);
       retval = x;
     }
  /*---------------------------- 2^-26 < |x|< 0.25 ----------------------*/
diff --git a/sysdeps/ieee754/dbl-64/s_tan.c b/sysdeps/ieee754/dbl-64/s_tan.c
index b4e3bd2a31..65d056adec 100644
--- a/sysdeps/ieee754/dbl-64/s_tan.c
+++ b/sysdeps/ieee754/dbl-64/s_tan.c
@@ -92,11 +92,7 @@ tan (double x)
   /* (I) The case abs(x) <= 1.259e-8 */
   if (w <= g1.d)
     {
-      if (w < DBL_MIN)
-	{
-	  double force_underflow = x * x;
-	  math_force_eval (force_underflow);
-	}
+      math_check_force_underflow_nonneg (w);
       retval = x;
       goto ret;
     }
diff --git a/sysdeps/ieee754/dbl-64/s_tanh.c b/sysdeps/ieee754/dbl-64/s_tanh.c
index 4f9fcfd2bd..344a2f0330 100644
--- a/sysdeps/ieee754/dbl-64/s_tanh.c
+++ b/sysdeps/ieee754/dbl-64/s_tanh.c
@@ -70,11 +70,7 @@ __tanh (double x)
 	return x;                       /* x == +-0 */
       if (ix < 0x3c800000)              /* |x|<2**-55 */
 	{
-	  if (fabs (x) < DBL_MIN)
-	    {
-	      double force_underflow = x * x;
-	      math_force_eval (force_underflow);
-	    }
+	  math_check_force_underflow (x);
 	  return x * (one + x);           /* tanh(small) = small */
 	}
       if (ix >= 0x3ff00000)             /* |x|>=1  */