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authorJoseph Myers <joseph@codesourcery.com>2012-11-28 13:40:54 +0000
committerJoseph Myers <joseph@codesourcery.com>2012-11-28 13:40:54 +0000
commit1bead169c32a3a688de863709b863207b7aafddd (patch)
tree7c3dcf66e7b4d92a9bcc5e3bb67f2cbbb19172f3 /sysdeps/x86_64
parentFix hashtable size calculation when database has exactly one record (diff)
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Fix powl inaccuracy for x86_64 and x86 (bug 13881).
Diffstat (limited to 'sysdeps/x86_64')
-rw-r--r--sysdeps/x86_64/fpu/e_powl.S52
-rw-r--r--sysdeps/x86_64/fpu/libm-test-ulps4
2 files changed, 26 insertions, 30 deletions
diff --git a/sysdeps/x86_64/fpu/e_powl.S b/sysdeps/x86_64/fpu/e_powl.S
index 1b3718522d..ff96cec68a 100644
--- a/sysdeps/x86_64/fpu/e_powl.S
+++ b/sysdeps/x86_64/fpu/e_powl.S
@@ -26,9 +26,9 @@
.type one,@object
one: .double 1.0
ASM_SIZE_DIRECTIVE(one)
- .type limit,@object
-limit: .double 0.29
- ASM_SIZE_DIRECTIVE(limit)
+ .type p3,@object
+p3: .byte 0, 0, 0, 0, 0, 0, 0x20, 0x40
+ ASM_SIZE_DIRECTIVE(p3)
.type p63,@object
p63: .byte 0, 0, 0, 0, 0, 0, 0xe0, 0x43
ASM_SIZE_DIRECTIVE(p63)
@@ -131,7 +131,15 @@ ENTRY(__ieee754_powl)
fchs // -0x1p-79 : x
jmp 3f
-9: /* OK, we have an integer value for y. */
+9: /* OK, we have an integer value for y. Unless very small
+ (we use < 8), 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
+ fstp %st(0) // y : x
+ jnc 2f
mov -8(%rsp),%eax
mov -4(%rsp),%edx
orl $0, %edx
@@ -167,7 +175,7 @@ ENTRY(__ieee754_powl)
ret
.align ALIGNARG(4)
-2: // y is a large integer (absolute value at least 1L<<63), but
+2: // y is a large integer (absolute value at least 8), but
// may be odd unless at least 1L<<64. So it may be necessary
// to adjust the sign of a negative result afterwards.
fxch // x : y
@@ -190,31 +198,15 @@ ENTRY(__ieee754_powl)
fchs // -(1L<<78) : |x|
.align ALIGNARG(4)
3: /* y is a real number. */
- fxch // x : y
- fldl MO(one) // 1.0 : x : y
- fldl MO(limit) // 0.29 : 1.0 : x : y
- fld %st(2) // x : 0.29 : 1.0 : x : y
- fsub %st(2) // x-1 : 0.29 : 1.0 : x : y
- fabs // |x-1| : 0.29 : 1.0 : x : y
- fucompp // 1.0 : x : y
- fnstsw
- fxch // x : 1.0 : y
- test $0x4500,%eax
- jz 7f
- fsub %st(1) // x-1 : 1.0 : y
- fyl2xp1 // log2(x) : y
- jmp 8f
-
-7: fyl2x // log2(x) : y
-8: fmul %st(1) // y*log2(x) : y
- fst %st(1) // y*log2(x) : y*log2(x)
- frndint // int(y*log2(x)) : y*log2(x)
- fsubr %st, %st(1) // int(y*log2(x)) : fract(y*log2(x))
- fxch // fract(y*log2(x)) : int(y*log2(x))
- f2xm1 // 2^fract(y*log2(x))-1 : int(y*log2(x))
- faddl MO(one) // 2^fract(y*log2(x)) : int(y*log2(x))
- fscale // 2^fract(y*log2(x))*2^int(y*log2(x)) : int(y*log2(x))
- fstp %st(1) // 2^fract(y*log2(x))*2^int(y*log2(x))
+ subq $40, %rsp
+ cfi_adjust_cfa_offset (40)
+ fstpt 16(%rsp) // x
+ fstpt (%rsp) // <empty>
+ mov %edx, 32(%rsp)
+ call HIDDEN_JUMPTARGET (__powl_helper) // <result>
+ mov 32(%rsp), %edx
+ addq $40, %rsp
+ cfi_adjust_cfa_offset (-40)
testb $2, %dh
jz 292f
// x is negative. If y is an odd integer, negate the result.
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index f33dfed3df..9e7a8adac3 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -2398,6 +2398,8 @@ ifloat: 1
Test "pow (0x0.ffffffp0, -0x1p24) == 2.7182819094701610539628664526874952929416":
float: 1
ifloat: 1
+ildouble: 1
+ldouble: 1
Test "pow (0x0.ffffffp0, 0x1p24) == 0.3678794302077803437135155590023422899744":
float: 1
ifloat: 1
@@ -3575,6 +3577,8 @@ ifloat: 1
Function: "pow":
float: 1
ifloat: 1
+ildouble: 1
+ldouble: 1
Function: "pow_downward":
float: 1