Fix exp2 missing underflows (bug 16521).

Various exp2 implementations in glibc can miss underflow exceptions
when the scaling down part of the calculation is exact (or, in the x86
case, when the conversion from extended precision to the target
precision is exact).  This patch forces the exception in a similar way
to previous fixes.

The x86 exp2f changes may in fact not be needed for this purpose -
it's likely to be the case that no argument of type float has an exp2
result so close to an exact subnormal float value that it equals that
value when rounded to 64 bits (even taking account of variation
between different x86 implementations).  However, they are included
for consistency with the changes to exp2 and so as to fix the exp2f
part of bug 18875 by ensuring that excess range and precision is
removed from underflowing return values.

Tested for x86_64, x86 and mips64.

	[BZ #16521]
	[BZ #18875]
	* math/e_exp2l.c (__ieee754_exp2l): Force underflow exception for
	small results.
	* sysdeps/i386/fpu/e_exp2.S (dbl_min): New object.
	(MO): New macro.
	(__ieee754_exp2): For small results, force underflow exception and
	remove excess range and precision from return value.
	* sysdeps/i386/fpu/e_exp2f.S (flt_min): New object.
	(MO): New macro.
	(__ieee754_exp2f): For small results, force underflow exception
	and remove excess range and precision from return value.
	* sysdeps/i386/fpu/e_exp2l.S (ldbl_min): New object.
	(MO): New macro.
	(__ieee754_exp2l): Force underflow exception for small results.
	* sysdeps/ieee754/dbl-64/e_exp2.c (__ieee754_exp2): Likewise.
	* sysdeps/ieee754/flt-32/e_exp2f.c (__ieee754_exp2f): Likewise.
	* sysdeps/x86_64/fpu/e_exp2l.S (ldbl_min): New object.
	(MO): New macro.
	(__ieee754_exp2l): Force underflow exception for small results.
	* math/auto-libm-test-in: Add more tests or exp2.
	* math/auto-libm-test-out: Regenerated.

6 files changed, 136 insertions, 6 deletions

diff --git a/sysdeps/i386/fpu/e_exp2.S b/sysdeps/i386/fpu/e_exp2.S
index f802cf8b98..b75a63a0b3 100644
--- a/sysdeps/i386/fpu/e_exp2.S
+++ b/sysdeps/i386/fpu/e_exp2.S
@@ -6,7 +6,24 @@
 
 #include <machine/asm.h>
 
+	.section .rodata.cst8,"aM",@progbits,8
+
+	.p2align 3
+	.type dbl_min,@object
+dbl_min:	.byte 0, 0, 0, 0, 0, 0, 0x10, 0
+	ASM_SIZE_DIRECTIVE(dbl_min)
+
+#ifdef PIC
+# define MO(op) op##@GOTOFF(%ecx)
+#else
+# define MO(op) op
+#endif
+
+	.text
 ENTRY(__ieee754_exp2)
+#ifdef  PIC
+	LOAD_PIC_REG (cx)
+#endif
 	fldl	4(%esp)
 /* I added the following ugly construct because exp(+-Inf) resulted
    in NaN.  The ugliness results from the bright minds at Intel.
@@ -27,7 +44,22 @@ ENTRY(__ieee754_exp2)
 	faddp				/* 2^(fract(x)) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	ret
+	fldl	MO(dbl_min)
+	fld	%st(1)
+	fucompp
+	fnstsw
+	sahf
+	jnc 3f
+	subl	$8, %esp
+	cfi_adjust_cfa_offset (8)
+	fld	%st(0)
+	fmul	%st(0)
+	fstpl	(%esp)
+	fstpl	(%esp)
+	fldl	(%esp)
+	addl	$8, %esp
+	cfi_adjust_cfa_offset (-8)
+3:	ret
 
 1:	testl	$0x200, %eax		/* Test sign.  */
 	jz	2f			/* If positive, jump.  */
diff --git a/sysdeps/i386/fpu/e_exp2f.S b/sysdeps/i386/fpu/e_exp2f.S
index f867d0d472..042c83b1ef 100644
--- a/sysdeps/i386/fpu/e_exp2f.S
+++ b/sysdeps/i386/fpu/e_exp2f.S
@@ -6,7 +6,24 @@
 
 #include <machine/asm.h>
 
+	.section .rodata.cst4,"aM",@progbits,4
+
+	.p2align 2
+	.type flt_min,@object
+flt_min:	.byte 0, 0, 0x80, 0
+	ASM_SIZE_DIRECTIVE(flt_min)
+
+#ifdef PIC
+# define MO(op) op##@GOTOFF(%ecx)
+#else
+# define MO(op) op
+#endif
+
+	.text
 ENTRY(__ieee754_exp2f)
+#ifdef  PIC
+	LOAD_PIC_REG (cx)
+#endif
 	flds	4(%esp)
 /* I added the following ugly construct because exp(+-Inf) resulted
    in NaN.  The ugliness results from the bright minds at Intel.
@@ -27,7 +44,22 @@ ENTRY(__ieee754_exp2f)
 	faddp				/* 2^(fract(x)) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	ret
+	flds	MO(flt_min)
+	fld	%st(1)
+	fucompp
+	fnstsw
+	sahf
+	jnc 3f
+	subl	$4, %esp
+	cfi_adjust_cfa_offset (4)
+	fld	%st(0)
+	fmul	%st(0)
+	fstps	(%esp)
+	fstps	(%esp)
+	flds	(%esp)
+	addl	$4, %esp
+	cfi_adjust_cfa_offset (-4)
+3:	ret
 
 1:	testl	$0x200, %eax		/* Test sign.  */
 	jz	2f			/* If positive, jump.  */
diff --git a/sysdeps/i386/fpu/e_exp2l.S b/sysdeps/i386/fpu/e_exp2l.S
index 2bf9a25727..9a5ff95a6c 100644
--- a/sysdeps/i386/fpu/e_exp2l.S
+++ b/sysdeps/i386/fpu/e_exp2l.S
@@ -6,7 +6,24 @@
 
 #include <machine/asm.h>
 
+	.section .rodata.cst16,"aM",@progbits,16
+	.p2align 4
+	.type ldbl_min,@object
+ldbl_min:	.byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x1, 0
+	.byte 0, 0, 0, 0, 0, 0
+	ASM_SIZE_DIRECTIVE(ldbl_min)
+
+#ifdef PIC
+# define MO(op) op##@GOTOFF(%ecx)
+#else
+# define MO(op) op
+#endif
+
+	.text
 ENTRY(__ieee754_exp2l)
+#ifdef PIC
+	LOAD_PIC_REG (cx)
+#endif
 	fldt	4(%esp)
 /* I added the following ugly construct because exp(+-Inf) resulted
    in NaN.  The ugliness results from the bright minds at Intel.
@@ -35,7 +52,17 @@ ENTRY(__ieee754_exp2l)
 	faddp				/* 2^(fract(x)) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	ret
+	/* Ensure underflow for tiny result.  */
+	fldt	MO(ldbl_min)
+	fld	%st(1)
+	fucompp
+	fnstsw
+	sahf
+	jnc	4f
+	fld	%st
+	fmul	%st
+	fstp	%st
+4:	ret
 
 1:	testl	$0x200, %eax		/* Test sign.  */
 	jz	2f			/* If positive, jump.  */
diff --git a/sysdeps/ieee754/dbl-64/e_exp2.c b/sysdeps/ieee754/dbl-64/e_exp2.c
index 30f0a8f529..01df62150d 100644
--- a/sysdeps/ieee754/dbl-64/e_exp2.c
+++ b/sysdeps/ieee754/dbl-64/e_exp2.c
@@ -120,7 +120,15 @@ __ieee754_exp2 (double x)
       if (!unsafe)
 	return result;
       else
-	return result * scale_u.d;
+	{
+	  result *= scale_u.d;
+	  if (result < DBL_MIN)
+	    {
+	      double force_underflow = result * result;
+	      math_force_eval (force_underflow);
+	    }
+	  return result;
+	}
     }
   else
     /* Return x, if x is a NaN or Inf; or overflow, otherwise.  */
diff --git a/sysdeps/ieee754/flt-32/e_exp2f.c b/sysdeps/ieee754/flt-32/e_exp2f.c
index 0b75a7ea2a..bc62042966 100644
--- a/sysdeps/ieee754/flt-32/e_exp2f.c
+++ b/sysdeps/ieee754/flt-32/e_exp2f.c
@@ -109,7 +109,15 @@ __ieee754_exp2f (float x)
       if (!unsafe)
 	return result;
       else
-	return result * scale_u.f;
+	{
+	  result *= scale_u.f;
+	  if (result < FLT_MIN)
+	    {
+	      float force_underflow = result * result;
+	      math_force_eval (force_underflow);
+	    }
+	  return result;
+	}
     }
   /* Exceptional cases:  */
   else if (isless (x, himark))
diff --git a/sysdeps/x86_64/fpu/e_exp2l.S b/sysdeps/x86_64/fpu/e_exp2l.S
index 7d42a932db..d634ad38f8 100644
--- a/sysdeps/x86_64/fpu/e_exp2l.S
+++ b/sysdeps/x86_64/fpu/e_exp2l.S
@@ -7,6 +7,20 @@
 
 #include <machine/asm.h>
 
+	.section .rodata.cst16,"aM",@progbits,16
+	.p2align 4
+	.type ldbl_min,@object
+ldbl_min:	.byte 0, 0, 0, 0, 0, 0, 0, 0x80, 0x1, 0
+	.byte 0, 0, 0, 0, 0, 0
+	ASM_SIZE_DIRECTIVE(ldbl_min)
+
+#ifdef PIC
+# define MO(op) op##(%rip)
+#else
+# define MO(op) op
+#endif
+
+	.text
 ENTRY(__ieee754_exp2l)
 	fldt	8(%rsp)
 /* I added the following ugly construct because exp(+-Inf) resulted
@@ -36,7 +50,16 @@ ENTRY(__ieee754_exp2l)
 	faddp				/* 2^(fract(x)) */
 	fscale				/* e^x */
 	fstp	%st(1)
-	ret
+	/* Ensure underflow for tiny result.  */
+	fldt	MO(ldbl_min)
+	fld	%st(1)
+	fucomip	%st(1), %st
+	fstp	%st
+	jnc	4f
+	fld	%st
+	fmul	%st
+	fstp	%st
+4:	ret
 
 1:	testl	$0x200, %eax		/* Test sign.  */
 	jz	2f			/* If positive, jump.  */