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.

15 files changed, 16 insertions, 73 deletions

diff --git a/sysdeps/ieee754/flt-32/e_asinf.c b/sysdeps/ieee754/flt-32/e_asinf.c
index 00bad4239b..2ca2dbcb28 100644
--- a/sysdeps/ieee754/flt-32/e_asinf.c
+++ b/sysdeps/ieee754/flt-32/e_asinf.c
@@ -73,11 +73,7 @@ float __ieee754_asinf(float x)
 	    return (x-x)/(x-x);		/* asin(|x|>1) is NaN */
 	} else if (ix<0x3f000000) {	/* |x|<0.5 */
 	    if(ix<0x32000000) {		/* if |x| < 2**-27 */
-		if (fabsf (x) < FLT_MIN)
-		  {
-		    float 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*/
 	    } else {
 		t = x*x;
diff --git a/sysdeps/ieee754/flt-32/e_atanhf.c b/sysdeps/ieee754/flt-32/e_atanhf.c
index bc74960e16..77e4b03c75 100644
--- a/sysdeps/ieee754/flt-32/e_atanhf.c
+++ b/sysdeps/ieee754/flt-32/e_atanhf.c
@@ -52,11 +52,7 @@ __ieee754_atanhf (float x)
       if (__glibc_unlikely (xa < 0x1.0p-28f))
 	{
 	  math_force_eval (huge + x);
-	  if (fabsf (x) < FLT_MIN)
-	    {
-	      float force_underflow = x * x;
-	      math_force_eval (force_underflow);
-	    }
+	  math_check_force_underflow (x);
 	  return x;
 	}
 
diff --git a/sysdeps/ieee754/flt-32/e_exp2f.c b/sysdeps/ieee754/flt-32/e_exp2f.c
index 170c565895..d8e7a9c8bc 100644
--- a/sysdeps/ieee754/flt-32/e_exp2f.c
+++ b/sysdeps/ieee754/flt-32/e_exp2f.c
@@ -111,11 +111,7 @@ __ieee754_exp2f (float x)
       else
 	{
 	  result *= scale_u.f;
-	  if (result < FLT_MIN)
-	    {
-	      float force_underflow = result * result;
-	      math_force_eval (force_underflow);
-	    }
+	  math_check_force_underflow_nonneg (result);
 	  return result;
 	}
     }
diff --git a/sysdeps/ieee754/flt-32/e_gammaf_r.c b/sysdeps/ieee754/flt-32/e_gammaf_r.c
index 183db1e033..f97ca34705 100644
--- a/sysdeps/ieee754/flt-32/e_gammaf_r.c
+++ b/sysdeps/ieee754/flt-32/e_gammaf_r.c
@@ -179,11 +179,7 @@ __ieee754_gammaf_r (float x, int *signgamp)
 	      float tret = (float) M_PI / (-x * sinpix
 					   * gammaf_positive (-x, &exp2_adj));
 	      ret = __scalbnf (tret, -exp2_adj);
-	      if (ret < FLT_MIN)
-		{
-		  float 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/flt-32/e_j1f.c b/sysdeps/ieee754/flt-32/e_j1f.c
index 63de21f609..e24024f22e 100644
--- a/sysdeps/ieee754/flt-32/e_j1f.c
+++ b/sysdeps/ieee754/flt-32/e_j1f.c
@@ -72,10 +72,7 @@ __ieee754_j1f(float x)
 	if(__builtin_expect(ix<0x32000000, 0)) {	/* |x|<2**-27 */
 	    if(huge+x>one) {		/* inexact if x!=0 necessary */
 		float ret = (float) 0.5 * x;
-		if (fabsf (ret) < FLT_MIN) {
-		    float force_underflow = ret * ret;
-		    math_force_eval (force_underflow);
-		}
+		math_check_force_underflow (ret);
 		return ret;
 	    }
 	}
diff --git a/sysdeps/ieee754/flt-32/e_jnf.c b/sysdeps/ieee754/flt-32/e_jnf.c
index 44a3761adb..d18922aa05 100644
--- a/sysdeps/ieee754/flt-32/e_jnf.c
+++ b/sysdeps/ieee754/flt-32/e_jnf.c
@@ -170,10 +170,8 @@ __ieee754_jnf(int n, float x)
     }
     if (ret == 0)
 	ret = __copysignf (FLT_MIN, ret) * FLT_MIN;
-    else if (fabsf (ret) < FLT_MIN) {
-	float force_underflow = ret * ret;
-	math_force_eval (force_underflow);
-    }
+    else
+	math_check_force_underflow (ret);
     return ret;
 }
 strong_alias (__ieee754_jnf, __jnf_finite)
diff --git a/sysdeps/ieee754/flt-32/e_sinhf.c b/sysdeps/ieee754/flt-32/e_sinhf.c
index a24fa0c4bc..6100d95c55 100644
--- a/sysdeps/ieee754/flt-32/e_sinhf.c
+++ b/sysdeps/ieee754/flt-32/e_sinhf.c
@@ -36,11 +36,7 @@ __ieee754_sinhf(float x)
     /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */
 	if (ix < 0x41b00000) {		/* |x|<22 */
 	    if (__builtin_expect(ix<0x31800000, 0)) {	/* |x|<2**-28 */
-		if (fabsf (x) < FLT_MIN)
-		  {
-		    float 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 = __expm1f(fabsf(x));
diff --git a/sysdeps/ieee754/flt-32/k_sinf.c b/sysdeps/ieee754/flt-32/k_sinf.c
index 0c98a2ae91..a195d59466 100644
--- a/sysdeps/ieee754/flt-32/k_sinf.c
+++ b/sysdeps/ieee754/flt-32/k_sinf.c
@@ -38,11 +38,7 @@ float __kernel_sinf(float x, float y, int iy)
 	ix &= 0x7fffffff;			/* high word of x */
 	if(ix<0x32000000)			/* |x| < 2**-27 */
 	  {
-	    if (fabsf (x) < FLT_MIN)
-	      {
-		float force_underflow = x * x;
-		math_force_eval (force_underflow);
-	      }
+	    math_check_force_underflow (x);
 	    if ((int) x == 0)
 	      return x;		/* generate inexact */
 	  }
diff --git a/sysdeps/ieee754/flt-32/k_tanf.c b/sysdeps/ieee754/flt-32/k_tanf.c
index 2f2076d6fe..9f0e55860f 100644
--- a/sysdeps/ieee754/flt-32/k_tanf.c
+++ b/sysdeps/ieee754/flt-32/k_tanf.c
@@ -51,11 +51,7 @@ float __kernel_tanf(float x, float y, int iy)
 		if((ix|(iy+1))==0) return one/fabsf(x);
 		else if (iy == 1)
 		  {
-		    if (fabsf (x) < FLT_MIN)
-		      {
-			float force_underflow = x * x;
-			math_force_eval (force_underflow);
-		      }
+		    math_check_force_underflow (x);
 		    return x;
 		  }
 		else
diff --git a/sysdeps/ieee754/flt-32/s_asinhf.c b/sysdeps/ieee754/flt-32/s_asinhf.c
index 697faa843c..da9cafb600 100644
--- a/sysdeps/ieee754/flt-32/s_asinhf.c
+++ b/sysdeps/ieee754/flt-32/s_asinhf.c
@@ -30,11 +30,7 @@ __asinhf(float x)
 	GET_FLOAT_WORD(hx,x);
 	ix = hx&0x7fffffff;
 	if(__builtin_expect(ix< 0x38000000, 0)) {	/* |x|<2**-14 */
-	    if (fabsf (x) < FLT_MIN)
-	      {
-		float 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>0x47000000, 0)) {	/* |x| > 2**14 */
diff --git a/sysdeps/ieee754/flt-32/s_atanf.c b/sysdeps/ieee754/flt-32/s_atanf.c
index be2addbdff..e322a1d41f 100644
--- a/sysdeps/ieee754/flt-32/s_atanf.c
+++ b/sysdeps/ieee754/flt-32/s_atanf.c
@@ -67,11 +67,7 @@ float __atanf(float x)
 	    else     return -atanhi[3]-atanlo[3];
 	} if (ix < 0x3ee00000) {	/* |x| < 0.4375 */
 	    if (ix < 0x31000000) {	/* |x| < 2^-29 */
-		if (fabsf (x) < FLT_MIN)
-		  {
-		    float force_underflow = x * x;
-		    math_force_eval (force_underflow);
-		  }
+		math_check_force_underflow (x);
 		if(huge+x>one) return x;	/* raise inexact */
 	    }
 	    id = -1;
diff --git a/sysdeps/ieee754/flt-32/s_erff.c b/sysdeps/ieee754/flt-32/s_erff.c
index 1aabce5cb8..3162d81d08 100644
--- a/sysdeps/ieee754/flt-32/s_erff.c
+++ b/sysdeps/ieee754/flt-32/s_erff.c
@@ -113,11 +113,7 @@ float __erff(float x)
 		  {
 		    /* Avoid spurious underflow.  */
 		    float ret = 0.0625f * (16.0f * x + (16.0f * efx) * x);
-		    if (fabsf (ret) < FLT_MIN)
-		      {
-			float 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/flt-32/s_expm1f.c b/sysdeps/ieee754/flt-32/s_expm1f.c
index c81b057f24..c515d25e28 100644
--- a/sysdeps/ieee754/flt-32/s_expm1f.c
+++ b/sysdeps/ieee754/flt-32/s_expm1f.c
@@ -81,11 +81,7 @@ __expm1f(float x)
 	    c  = (hi-x)-lo;
 	}
 	else if(hx < 0x33000000) {	/* when |x|<2**-25, return x */
-	    if (fabsf (x) < FLT_MIN)
-	      {
-		float 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/flt-32/s_log1pf.c b/sysdeps/ieee754/flt-32/s_log1pf.c
index 83a09f1414..ade60a2e27 100644
--- a/sysdeps/ieee754/flt-32/s_log1pf.c
+++ b/sysdeps/ieee754/flt-32/s_log1pf.c
@@ -50,11 +50,7 @@ __log1pf(float x)
 		math_force_eval(two25+x);	/* raise inexact */
 		if (ax<0x24800000)		/* |x| < 2**-54 */
 		  {
-		    if (fabsf (x) < FLT_MIN)
-		      {
-			float force_underflow = x * x;
-			math_force_eval (force_underflow);
-		      }
+		    math_check_force_underflow (x);
 		    return x;
 		  }
 		else
diff --git a/sysdeps/ieee754/flt-32/s_tanhf.c b/sysdeps/ieee754/flt-32/s_tanhf.c
index 5b48fb2e00..f70702b29c 100644
--- a/sysdeps/ieee754/flt-32/s_tanhf.c
+++ b/sysdeps/ieee754/flt-32/s_tanhf.c
@@ -43,11 +43,7 @@ float __tanhf(float x)
 		return x;		/* x == +-0 */
 	    if (ix<0x24000000) 		/* |x|<2**-55 */
 	      {
-		if (fabsf (x) < FLT_MIN)
-		  {
-		    float force_underflow = x * x;
-		    math_force_eval (force_underflow);
-		  }
+		math_check_force_underflow (x);
 		return x*(one+x);    	/* tanh(small) = small */
 	      }
 	    if (ix>=0x3f800000) {	/* |x|>=1  */