Fix spurious underflows from pow with results close to 1 (bug 14811).

4 files changed, 50 insertions, 4 deletions

diff --git a/sysdeps/i386/fpu/e_powl.S b/sysdeps/i386/fpu/e_powl.S
index 933418c..ac4842c 100644
--- a/sysdeps/i386/fpu/e_powl.S
+++ b/sysdeps/i386/fpu/e_powl.S
@@ -38,6 +38,9 @@ p64:	.byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43
 	.type p78,@object
 p78:	.byte 0, 0, 0, 0, 0, 0, 0xd0, 0x44
 	ASM_SIZE_DIRECTIVE(p78)
+	.type pm79,@object
+pm79:	.byte 0, 0, 0, 0, 0, 0, 0, 0x3b
+	ASM_SIZE_DIRECTIVE(pm79)
 
 	.section .rodata.cst16,"aM",@progbits,16
 
@@ -120,9 +123,25 @@ ENTRY(__ieee754_powl)
 	fucomp	%st(1)		// y : x
 	fnstsw
 	sahf
-	jne	3f
+	je	9f
 
-	/* OK, we have an integer value for y.  */
+	// If y has absolute value at most 0x1p-79, then any finite
+	// nonzero x will result in 1.  Saturate y to those bounds to
+	// avoid underflow in the calculation of y*log2(x).
+	fld	%st		// y : y : x
+	fabs			// |y| : y : x
+	fcompl	MO(pm79)	// y : x
+	fnstsw
+	sahf
+	jnc	3f
+	fstp	%st(0)		// pop y
+	fldl	MO(pm79)	// 0x1p-79 : x
+	testb	$2, %dl
+	jnz	3f		// y > 0
+	fchs			// -0x1p-79 : x
+	jmp	3f
+
+9:	/* OK, we have an integer value for y.  */
 	popl	%eax
 	cfi_adjust_cfa_offset (-4)
 	popl	%edx
diff --git a/sysdeps/ieee754/dbl-64/e_pow.c b/sysdeps/ieee754/dbl-64/e_pow.c
index 3fd5e65..5131718 100644
--- a/sysdeps/ieee754/dbl-64/e_pow.c
+++ b/sysdeps/ieee754/dbl-64/e_pow.c
@@ -90,6 +90,10 @@ __ieee754_pow(double x, double y) {
 
     SET_RESTORE_ROUND (FE_TONEAREST);
 
+    /* Avoid internal underflow for tiny y.  The exact value of y does
+       not matter if |y| <= 2**-64.  */
+    if (ABS (y) < 0x1p-64)
+      y = y < 0 ? -0x1p-64 : 0x1p-64;
     z = log1(x,&aa,&error);                                 /* x^y  =e^(y log (X)) */
     t = y*134217729.0;
     y1 = t - (t-y);
diff --git a/sysdeps/ieee754/flt-32/e_powf.c b/sysdeps/ieee754/flt-32/e_powf.c
index 4306947..12c408f 100644
--- a/sysdeps/ieee754/flt-32/e_powf.c
+++ b/sysdeps/ieee754/flt-32/e_powf.c
@@ -141,6 +141,10 @@ __ieee754_powf(float x, float y)
 	    t2 = v-(t1-u);
 	} else {
 	    float s2,s_h,s_l,t_h,t_l;
+	    /* Avoid internal underflow for tiny y.  The exact value
+	       of y does not matter if |y| <= 2**-32.  */
+	    if (iy < 0x2f800000)
+	      SET_FLOAT_WORD (y, (hy & 0x80000000) | 0x2f800000);
 	    n = 0;
 	/* take care subnormal number */
 	    if(ix<0x00800000)
diff --git a/sysdeps/x86_64/fpu/e_powl.S b/sysdeps/x86_64/fpu/e_powl.S
index 4fe23c0..1b37185 100644
--- a/sysdeps/x86_64/fpu/e_powl.S
+++ b/sysdeps/x86_64/fpu/e_powl.S
@@ -38,6 +38,9 @@ p64:	.byte 0, 0, 0, 0, 0, 0, 0xf0, 0x43
 	.type p78,@object
 p78:	.byte 0, 0, 0, 0, 0, 0, 0xd0, 0x44
 	ASM_SIZE_DIRECTIVE(p78)
+	.type pm79,@object
+pm79:	.byte 0, 0, 0, 0, 0, 0, 0, 0x3b
+	ASM_SIZE_DIRECTIVE(pm79)
 
 	.section .rodata.cst16,"aM",@progbits,16
 
@@ -110,9 +113,25 @@ ENTRY(__ieee754_powl)
 	fistpll	-8(%rsp)	// y : x
 	fildll	-8(%rsp)	// int(y) : y : x
 	fucomip	%st(1),%st	// y : x
-	jne	3f
+	je	9f
+
+	// If y has absolute value at most 0x1p-79, then any finite
+	// nonzero x will result in 1.  Saturate y to those bounds to
+	// avoid underflow in the calculation of y*log2(x).
+	fldl	MO(pm79)	// 0x1p-79 : y : x
+	fld	%st(1)		// y : 0x1p-79 : y : x
+	fabs			// |y| : 0x1p-79 : y : x
+	fcomip	%st(1), %st	// 0x1p-79 : y : x
+	fstp	%st(0)		// y : x
+	jnc	3f
+	fstp	%st(0)		// pop y
+	fldl	MO(pm79)	// 0x1p-79 : x
+	testb	$2, %dl
+	jnz	3f		// y > 0
+	fchs			// -0x1p-79 : x
+	jmp	3f
 
-	/* OK, we have an integer value for y.  */
+9:	/* OK, we have an integer value for y.  */
 	mov	-8(%rsp),%eax
 	mov	-4(%rsp),%edx
 	orl	$0, %edx