Fix x86_64 / x86 powl inaccuracy for integer exponents (bug 19848).

Bug 19848 reports cases where powl on x86 / x86_64 has error
accumulation, for small integer exponents, larger than permitted by
glibc's accuracy goals, at least in some rounding modes.  This patch
further restricts the exponent range for which the
small-integer-exponent logic is used to limit the possible error
accumulation.

Tested for x86_64 and x86 and ulps updated accordingly.

	[BZ #19848]
	* sysdeps/i386/fpu/e_powl.S (p3): Rename to p2 and change value
	from 8 to 4.
	(__ieee754_powl): Compare integer exponent against 4 not 8.
	* sysdeps/x86_64/fpu/e_powl.S (p3): Rename to p2 and change value
	from 8 to 4.
	(__ieee754_powl): Compare integer exponent against 4 not 8.
	* math/auto-libm-test-in: Add more tests of pow.
	* math/auto-libm-test-out: Regenerated.
	* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Update.
	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.

ChangeLog

@@ -1,3 +1,17 @@
+2016-03-24  Joseph Myers  <joseph@codesourcery.com>
+
+	[BZ #19848]
+	* sysdeps/i386/fpu/e_powl.S (p3): Rename to p2 and change value
+	from 8 to 4.
+	(__ieee754_powl): Compare integer exponent against 4 not 8.
+	* sysdeps/x86_64/fpu/e_powl.S (p3): Rename to p2 and change value
+	from 8 to 4.
+	(__ieee754_powl): Compare integer exponent against 4 not 8.
+	* math/auto-libm-test-in: Add more tests of pow.
+	* math/auto-libm-test-out: Regenerated.
+	* sysdeps/i386/i686/fpu/multiarch/libm-test-ulps: Update.
+	* sysdeps/x86_64/fpu/libm-test-ulps: Likewise.
+
 2016-03-23  Aurelien Jarno  <aurelien@aurel32.net>
 
 	* sysdeps/unix/sysv/linux/futimens.c (futimens) [__NR_utimensat]:

math/auto-libm-test-in

@@ -3717,6 +3717,44 @@ pow 0x2.000582p0 -1022
 pow 2 -0x3.fe513p+8
 pow 2 -0x3.fe4e8p+8
 
+pow 10 -1
+pow 10 -2
+pow 10 -3
+pow 10 -4
+pow 10 -5
+pow 10 -6
+pow 10 -7
+
+pow 0x0.ffffffffffffffffp0 1
+pow 0x0.ffffffffffffffffp0 2
+pow 0x0.ffffffffffffffffp0 3
+pow 0x0.ffffffffffffffffp0 4
+pow 0x0.ffffffffffffffffp0 5
+pow 0x0.ffffffffffffffffp0 6
+pow 0x0.ffffffffffffffffp0 7
+pow 0x0.ffffffffffffffffp0 -1
+pow 0x0.ffffffffffffffffp0 -2
+pow 0x0.ffffffffffffffffp0 -3
+pow 0x0.ffffffffffffffffp0 -4
+pow 0x0.ffffffffffffffffp0 -5
+pow 0x0.ffffffffffffffffp0 -6
+pow 0x0.ffffffffffffffffp0 -7
+
+pow 0x1.0000000000000002p0 1
+pow 0x1.0000000000000002p0 2
+pow 0x1.0000000000000002p0 3
+pow 0x1.0000000000000002p0 4
+pow 0x1.0000000000000002p0 5
+pow 0x1.0000000000000002p0 6
+pow 0x1.0000000000000002p0 7
+pow 0x1.0000000000000002p0 -1
+pow 0x1.0000000000000002p0 -2
+pow 0x1.0000000000000002p0 -3
+pow 0x1.0000000000000002p0 -4
+pow 0x1.0000000000000002p0 -5
+pow 0x1.0000000000000002p0 -6
+pow 0x1.0000000000000002p0 -7
+
 pow 1.0625 1.125
 pow 1.5 1.03125
 pow 0x1.7d1a0a6f2p+681 1.5

sysdeps/i386/fpu/e_powl.S

@@ -26,9 +26,9 @@
 	.type one,@object
 one:	.double 1.0
 	ASM_SIZE_DIRECTIVE(one)
-	.type p3,@object
-p3:	.byte 0, 0, 0, 0, 0, 0, 0x20, 0x40
-	ASM_SIZE_DIRECTIVE(p3)
+	.type p2,@object
+p2:	.byte 0, 0, 0, 0, 0, 0, 0x10, 0x40
+	ASM_SIZE_DIRECTIVE(p2)
 	.type p63,@object
 p63:	.byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
 	ASM_SIZE_DIRECTIVE(p63)
@@ -146,11 +146,11 @@ ENTRY(__ieee754_powl)
 	jmp	3f
 
 9:	/* OK, we have an integer value for y.  Unless very small
-	   (we use < 8), use the algorithm for real exponent to avoid
+	   (we use < 4), use the algorithm for real exponent to avoid
 	   accumulation of errors.  */
 	fld	%st		// y : y : x
 	fabs			// |y| : y : x
-	fcompl	MO(p3)		// y : x
+	fcompl	MO(p2)		// y : x
 	fnstsw
 	sahf
 	jnc	3f

sysdeps/i386/i686/fpu/multiarch/libm-test-ulps

@@ -1903,14 +1903,14 @@ ldouble: 4
 Function: "pow_towardzero":
 double: 1
 idouble: 1
-ildouble: 1
-ldouble: 1
+ildouble: 4
+ldouble: 4
 
 Function: "pow_upward":
 double: 1
 idouble: 1
-ildouble: 2
-ldouble: 2
+ildouble: 4
+ldouble: 4
 
 Function: "sin":
 ildouble: 1

sysdeps/x86_64/fpu/e_powl.S

@@ -26,9 +26,9 @@
 	.type one,@object
 one:	.double 1.0
 	ASM_SIZE_DIRECTIVE(one)
-	.type p3,@object
-p3:	.byte 0, 0, 0, 0, 0, 0, 0x20, 0x40
-	ASM_SIZE_DIRECTIVE(p3)
+	.type p2,@object
+p2:	.byte 0, 0, 0, 0, 0, 0, 0x10, 0x40
+	ASM_SIZE_DIRECTIVE(p2)
 	.type p63,@object
 p63:	.byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
 	ASM_SIZE_DIRECTIVE(p63)
@@ -136,12 +136,12 @@ ENTRY(__ieee754_powl)
 	jmp	3f
 
 9:	/* OK, we have an integer value for y.  Unless very small
-	   (we use < 8), use the algorithm for real exponent to avoid
+	   (we use < 4), use the algorithm for real exponent to avoid
 	   accumulation of errors.  */
-	fldl	MO(p3)		// 8 : y : x
-	fld	%st(1)		// y : 8 : y : x
-	fabs			// |y| : 8 : y : x
-	fcomip	%st(1), %st	// 8 : y : x
+	fldl	MO(p2)		// 4 : y : x
+	fld	%st(1)		// y : 4 : y : x
+	fabs			// |y| : 4 : y : x
+	fcomip	%st(1), %st	// 4 : y : x
 	fstp	%st(0)		// y : x
 	jnc	3f
 	mov	-8(%rsp),%eax

sysdeps/x86_64/fpu/libm-test-ulps

@@ -2016,16 +2016,16 @@ double: 1
 float: 1
 idouble: 1
 ifloat: 1
-ildouble: 1
-ldouble: 1
+ildouble: 4
+ldouble: 4
 
 Function: "pow_upward":
 double: 1
 float: 1
 idouble: 1
 ifloat: 1
-ildouble: 2
-ldouble: 2
+ildouble: 4
+ldouble: 4
 
 Function: "pow_vlen16":
 float: 3