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.

12 files changed, 14 insertions, 57 deletions

diff --git a/sysdeps/ieee754/ldbl-96/e_asinl.c b/sysdeps/ieee754/ldbl-96/e_asinl.c
index 2973bf0..f52b931 100644
--- a/sysdeps/ieee754/ldbl-96/e_asinl.c
+++ b/sysdeps/ieee754/ldbl-96/e_asinl.c
@@ -112,11 +112,7 @@ __ieee754_asinl (long double x)
     {				/* |x|<0.5 */
       if (ix < 0x3fde8000)
 	{			/* if |x| < 2**-33 */
-	  if (fabsl (x) < LDBL_MIN)
-	    {
-	      long double force_underflow = x * x;
-	      math_force_eval (force_underflow);
-	    }
+	  math_check_force_underflow (x);
 	  if (huge + x > one)
 	    return x;		/* return x with inexact if x!=0 */
 	}
diff --git a/sysdeps/ieee754/ldbl-96/e_atanhl.c b/sysdeps/ieee754/ldbl-96/e_atanhl.c
index 9a957c9..b99a83c 100644
--- a/sysdeps/ieee754/ldbl-96/e_atanhl.c
+++ b/sysdeps/ieee754/ldbl-96/e_atanhl.c
@@ -55,11 +55,7 @@ __ieee754_atanhl(long double x)
 	    return x/zero;
 	if(ix<0x3fdf) {
 	    math_force_eval(huge+x);
-	    if (fabsl (x) < LDBL_MIN)
-	      {
-		long double force_underflow = x * x;
-		math_force_eval (force_underflow);
-	      }
+	    math_check_force_underflow (x);
 	    return x;	/* x<2**-32 */
 	}
 	SET_LDOUBLE_EXP(x,ix);
diff --git a/sysdeps/ieee754/ldbl-96/e_gammal_r.c b/sysdeps/ieee754/ldbl-96/e_gammal_r.c
index a5767e7..78495d1 100644
--- a/sysdeps/ieee754/ldbl-96/e_gammal_r.c
+++ b/sysdeps/ieee754/ldbl-96/e_gammal_r.c
@@ -186,11 +186,7 @@ __ieee754_gammal_r (long double x, int *signgamp)
 	      ret = M_PIl / (-x * sinpix
 			     * gammal_positive (-x, &exp2_adj));
 	      ret = __scalbnl (ret, -exp2_adj);
-	      if (ret < LDBL_MIN)
-		{
-		  long double force_underflow = ret * ret;
-		  math_force_eval (force_underflow);
-		}
+	      math_check_force_underflow_nonneg (ret);
 	    }
 	}
     }
diff --git a/sysdeps/ieee754/ldbl-96/e_j1l.c b/sysdeps/ieee754/ldbl-96/e_j1l.c
index 46e28df..1bca949 100644
--- a/sysdeps/ieee754/ldbl-96/e_j1l.c
+++ b/sysdeps/ieee754/ldbl-96/e_j1l.c
@@ -154,11 +154,7 @@ __ieee754_j1l (long double x)
       if (huge + x > one)		/* inexact if x!=0 necessary */
 	{
 	  long double ret = 0.5 * x;
-	  if (fabsl (ret) < LDBL_MIN)
-	    {
-	      long double force_underflow = ret * ret;
-	      math_force_eval (force_underflow);
-	    }
+	  math_check_force_underflow (ret);
 	  return ret;
 	}
     }
diff --git a/sysdeps/ieee754/ldbl-96/e_jnl.c b/sysdeps/ieee754/ldbl-96/e_jnl.c
index 2f3a452..ed2068b 100644
--- a/sysdeps/ieee754/ldbl-96/e_jnl.c
+++ b/sysdeps/ieee754/ldbl-96/e_jnl.c
@@ -290,11 +290,8 @@ __ieee754_jnl (int n, long double x)
   }
   if (ret == 0)
     ret = __copysignl (LDBL_MIN, ret) * LDBL_MIN;
-  else if (fabsl (ret) < LDBL_MIN)
-    {
-      long double force_underflow = ret * ret;
-      math_force_eval (force_underflow);
-    }
+  else
+    math_check_force_underflow (ret);
   return ret;
 }
 strong_alias (__ieee754_jnl, __jnl_finite)
diff --git a/sysdeps/ieee754/ldbl-96/e_sinhl.c b/sysdeps/ieee754/ldbl-96/e_sinhl.c
index de6dff6..095b142 100644
--- a/sysdeps/ieee754/ldbl-96/e_sinhl.c
+++ b/sysdeps/ieee754/ldbl-96/e_sinhl.c
@@ -60,11 +60,7 @@ __ieee754_sinhl(long double x)
     /* |x| in [0,25], return sign(x)*0.5*(E+E/(E+1))) */
 	if (ix < 0x4003 || (ix == 0x4003 && i0 <= 0xc8000000)) { /* |x|<25 */
 	    if (ix<0x3fdf) {		/* |x|<2**-32 */
-		if (fabsl (x) < LDBL_MIN)
-		  {
-		    long 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 */
 	    }
 	    t = __expm1l(fabsl(x));
diff --git a/sysdeps/ieee754/ldbl-96/k_sinl.c b/sysdeps/ieee754/ldbl-96/k_sinl.c
index b7b5ae3..b709740 100644
--- a/sysdeps/ieee754/ldbl-96/k_sinl.c
+++ b/sysdeps/ieee754/ldbl-96/k_sinl.c
@@ -96,11 +96,7 @@ __kernel_sinl(long double x, long double y, int iy)
 	 polynomial of degree 17.  */
       if (absx < 0x1p-33L)
 	{
-	  if (fabsl (x) < LDBL_MIN)
-	    {
-	      long double force_underflow = x * x;
-	      math_force_eval (force_underflow);
-	    }
+	  math_check_force_underflow (x);
 	  if (!((int)x)) return x;	/* generate inexact */
 	}
       z = x * x;
diff --git a/sysdeps/ieee754/ldbl-96/k_tanl.c b/sysdeps/ieee754/ldbl-96/k_tanl.c
index 6276c06..6bee53e 100644
--- a/sysdeps/ieee754/ldbl-96/k_tanl.c
+++ b/sysdeps/ieee754/ldbl-96/k_tanl.c
@@ -98,11 +98,7 @@ __kernel_tanl (long double x, long double y, int iy)
 	    return one / fabsl (x);
 	  else if (iy == 1)
 	    {
-	      if (absx < LDBL_MIN)
-		{
-		  long double force_underflow = x * x;
-		  math_force_eval (force_underflow);
-		}
+	      math_check_force_underflow_nonneg (absx);
 	      return x;
 	    }
 	  else
diff --git a/sysdeps/ieee754/ldbl-96/s_asinhl.c b/sysdeps/ieee754/ldbl-96/s_asinhl.c
index 75e47c7..da49ea5 100644
--- a/sysdeps/ieee754/ldbl-96/s_asinhl.c
+++ b/sysdeps/ieee754/ldbl-96/s_asinhl.c
@@ -45,11 +45,7 @@ long double __asinhl(long double x)
 	GET_LDOUBLE_EXP(hx,x);
 	ix = hx&0x7fff;
 	if(__builtin_expect(ix< 0x3fde, 0)) {	/* |x|<2**-34 */
-	    if (fabsl (x) < LDBL_MIN)
-	      {
-		long 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 */
 	}
 	if(__builtin_expect(ix>0x4020,0)) {		/* |x| > 2**34 */
diff --git a/sysdeps/ieee754/ldbl-96/s_erfl.c b/sysdeps/ieee754/ldbl-96/s_erfl.c
index c27de81..d00adb1 100644
--- a/sysdeps/ieee754/ldbl-96/s_erfl.c
+++ b/sysdeps/ieee754/ldbl-96/s_erfl.c
@@ -274,11 +274,7 @@ __erfl (long double x)
 	    {
 	      /* Avoid spurious underflow.  */
 	      long double ret = 0.0625 * (16.0 * x + (16.0 * efx) * x);
-	      if (fabsl (ret) < LDBL_MIN)
-		{
-		  long 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/ldbl-96/s_fmal.c b/sysdeps/ieee754/ldbl-96/s_fmal.c
index 1232c9e..d11885e 100644
--- a/sysdeps/ieee754/ldbl-96/s_fmal.c
+++ b/sysdeps/ieee754/ldbl-96/s_fmal.c
@@ -92,8 +92,8 @@ __fmal (long double x, long double y, long double z)
 		     && w.ieee.mantissa1 == 0
 		     && w.ieee.mantissa0 == 0x80000000)))
 	    {
-	      volatile long double force_underflow = x * y;
-	      (void) force_underflow;
+	      long double force_underflow = x * y;
+	      math_force_eval (force_underflow);
 	    }
 	  return v.d * 0x1p-65L;
 	}
diff --git a/sysdeps/ieee754/ldbl-96/s_tanhl.c b/sysdeps/ieee754/ldbl-96/s_tanhl.c
index 035037c..38edf9f 100644
--- a/sysdeps/ieee754/ldbl-96/s_tanhl.c
+++ b/sysdeps/ieee754/ldbl-96/s_tanhl.c
@@ -71,11 +71,7 @@ long double __tanhl(long double x)
 		return x;		/* x == +- 0 */
 	    if (ix<0x3fc8)		/* |x|<2**-55 */
 	      {
-		if (fabsl (x) < LDBL_MIN)
-		  {
-		    long double force_underflow = x * x;
-		    math_force_eval (force_underflow);
-		  }
+		math_check_force_underflow (x);
 		return x*(one+tiny);	/* tanh(small) = small */
 	      }
 	    if (ix>=0x3fff) {	/* |x|>=1  */