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[PATCH][BZ 4997] Fix erroneous corner cases in PowerPC lround implementations
- From: "Ryan S. Arnold" <rsa at us dot ibm dot com>
- To: GNU libc devel <libc-alpha at sources dot redhat dot com>
- Date: Thu, 29 Nov 2007 14:48:52 -0600
- Subject: [PATCH][BZ 4997] Fix erroneous corner cases in PowerPC lround implementations
- Reply-to: rsa at us dot ibm dot com
Regarding Bugzilla 4997:
http://sourceware.org/bugzilla/show_bug.cgi?id=4997
The following patch fixes erroneous corner cases in the PowerPC
implementations of lround and llround for generic PowerPC, POWER4,
POWER5 and PowerPC 970.
The POWER5+ and POWER6[x] architectures are not affected by the bug due
to their use of the newly available 'frin' instruction).
I added a few new test cases to libm-test.inc and I've tested the patch
on POWER5, PowerPC 970, and POWER6 with success.
Ryan S. Arnold
IBM Linux Technology Center
Linux Toolchain Development
2007-11-29 Ryan S. Arnold <rsa@us.ibm.com>
[BZ4997]
* sysdeps/powerpc/powerpc32/fpu/s_lround.S (__lround): Fixed erroneous
result when x is +/-nextafter(+/-0.5,-/+1) i.e. all 1's in the
mantissa.
* sysdeps/powerpc/powerpc32/power4/fpu/s_llround.S (__llround): Same
as above and also accounts for when x is an odd number between 2^52
and 2^53-1.
* sysdeps/powerpc/powerpc64/fpu/s_llround.S (__llround): Same as
previous.
* sysdeps/powerpc/powerpc64/fpu/s_llroundf.S (__llroundf): Same as
previous.
* math/libm-test.inc: (lround_test, llround_test): Added test cases to
detect aforementioned erroneous conditions.
diff -uNr libc.orig/math/libm-test.inc libc/math/libm-test.inc
--- libc.orig/math/libm-test.inc 2007-10-27 18:14:25.000000000 -0700
+++ libc/math/libm-test.inc 2007-11-29 09:21:48.000000000 -0800
@@ -4300,6 +4300,17 @@
# endif
TEST_f_l (lround, 2097152.5, 2097153);
TEST_f_l (lround, -2097152.5, -2097153);
+ /* nextafter(0.5,-1) */
+ TEST_f_l (lround, 0x1.fffffffffffffp-2, 0);
+ /* nextafter(-0.5,1) */
+ TEST_f_l (lround, -0x1.fffffffffffffp-2, 0);
+#else
+ /* nextafter(0.5,-1) */
+ TEST_f_l (lround, 0x1.fffffp-2, 0);
+ /* nextafter(-0.5,1) */
+ TEST_f_l (lround, -0x1.fffffp-2, 0);
+ TEST_f_l (lround, 0x1.fffffep+23, 16777215);
+ TEST_f_l (lround, -0x1.fffffep+23, -16777215);
#endif
END (lround);
}
@@ -4359,8 +4370,40 @@
TEST_f_L (llround, 4294967295.5, 4294967296LL);
/* 0x200000000 */
TEST_f_L (llround, 8589934591.5, 8589934592LL);
+
+ /* nextafter(0.5,-1) */
+ TEST_f_L (llround, 0x1.fffffffffffffp-2, 0);
+ /* nextafter(-0.5,1) */
+ TEST_f_L (llround, -0x1.fffffffffffffp-2, 0);
+ /* On PowerPC an exponent of '52' is the largest incrementally
+ * representable sequence of whole-numbers in the 'double' range. We test
+ * lround to make sure that a guard bit set during the lround operation
+ * hasn't forced an erroneous shift giving us an incorrect result. The odd
+ * numbers between +-(2^52+1 and 2^53-1) are affected since they have the
+ * rightmost bit set. */
+ /* +-(2^52+1) */
+ TEST_f_L (llround, 0x1.0000000000001p+52,4503599627370497LL);
+ TEST_f_L (llround, -0x1.0000000000001p+52,-4503599627370497LL);
+ /* +-(2^53-1): Input is the last (positive and negative) incrementally
+ * representable whole-number in the 'double' range that might round
+ * erroneously. */
+ TEST_f_L (llround, 0x1.fffffffffffffp+52, 9007199254740991LL);
+ TEST_f_L (llround, -0x1.fffffffffffffp+52, -9007199254740991LL);
+#else
+ /* nextafter(0.5,-1) */
+ TEST_f_L (llround, 0x1.fffffep-2, 0);
+ /* nextafter(-0.5,1) */
+ TEST_f_L (llround, -0x1.fffffep-2, 0);
+ /* As above, on PowerPC an exponent of '23' is the largest incrementally
+ * representable sequence of whole-numbers in the 'float' range.
+ * Likewise, numbers between +-(2^23+1 and 2^24-1) are affected. */
+ TEST_f_L (llround, 0x1.000002p+23,8388609);
+ TEST_f_L (llround, -0x1.000002p+23,-8388609);
+ TEST_f_L (llround, 0x1.fffffep+23, 16777215);
+ TEST_f_L (llround, -0x1.fffffep+23, -16777215);
#endif
+
#ifdef TEST_LDOUBLE
/* The input can only be represented in long double. */
TEST_f_L (llround, 4503599627370495.5L, 4503599627370496LL);
diff -uNr libc.orig/sysdeps/powerpc/powerpc32/fpu/s_lround.S libc/sysdeps/powerpc/powerpc32/fpu/s_lround.S
--- libc.orig/sysdeps/powerpc/powerpc32/fpu/s_lround.S 2006-01-27 16:07:39.000000000 -0800
+++ libc/sysdeps/powerpc/powerpc32/fpu/s_lround.S 2007-11-29 09:21:48.000000000 -0800
@@ -1,5 +1,5 @@
/* lround function. PowerPC32 version.
- Copyright (C) 2004, 2006 Free Software Foundation, Inc.
+ Copyright (C) 2004, 2006, 2007 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
@@ -20,13 +20,10 @@
#include <sysdep.h>
#include <math_ldbl_opt.h>
- .section .rodata.cst8,"aM",@progbits,8
+ .section .rodata.cst4,"aM",@progbits,4
.align 2
-.LC0: /* 0.0 */
- .long 0x00000000
-.LC1: /* 0.5 */
+.LC0: /* 0.5 */
.long 0x3f000000
-
.section ".text"
/* long [r3] lround (float x [fp1])
@@ -37,7 +34,10 @@
tie, choose the one that is even (least significant bit o).".
So we can't use the PowerPC "round to Nearest" mode. Instead we set
"round toward Zero" mode and round by adding +-0.5 before rounding
- to the integer value. */
+ to the integer value. It is necessary to detect when x is
+ (+-)0x1.fffffffffffffp-2 because adding +-0.5 in this case will
+ cause an erroneous shift, carry and round. We simply return 0 if
+ 0.5 > x > -0.5. */
ENTRY (__lround)
stwu r1,-16(r1)
@@ -49,40 +49,40 @@
bcl 20,31,1f
1: mflr r9
addis r9,r9,.LC0-1b@ha
- addi r9,r9,.LC0-1b@l
+ lfs fp10,.LC0-1b@l(r9)
# else
bl _GLOBAL_OFFSET_TABLE_@local-4
mflr r10
lwz r9,.LC0@got(10)
+ lfs fp10,0(r9)
# endif
mtlr r11
cfi_same_value (lr)
- lfs fp12,0(r9)
#else
lis r9,.LC0@ha
- lfs fp12,.LC0@l(r9)
-#endif
-#ifdef SHARED
- lfs fp10,.LC1-.LC0(r9)
-#else
- lis r9,.LC1@ha
- lfs fp10,.LC1@l(r9)
+ lfs fp10,.LC0@l(r9)
#endif
- fcmpu cr6,fp1,fp12 /* if (x > 0.0) */
- ble- cr6,.L4
- fadd fp1,fp1,fp10 /* x+= 0.5; */
-.L9:
- fctiwz fp2,fp1 /* Convert To Integer DW lround toward 0. */
- stfd fp2,8(r1)
+ fabs fp2, fp1 /* Get the absolute value of x. */
+ fsub fp12,fp10,fp10 /* Compute 0.0. */
+ fcmpu cr6, fp2, fp10 /* if |x| < 0.5 */
+ fcmpu cr3, fp1, fp12 /* x is negative? x < 0.0 */
+ blt- cr6,.Lretzero
+ fadd fp3,fp2,fp10 /* |x|+=0.5 bias to prepare to round. */
+ bge cr3,.Lconvert /* x is positive so don't negate x. */
+ fnabs fp3,fp3 /* -(|x|+=0.5) */
+.Lconvert:
+ fctiwz fp4,fp3 /* Convert to Integer word lround toward 0. */
+ stfd fp4,8(r1)
nop /* Ensure the following load is in a different dispatch */
nop /* group to avoid pipe stall on POWER4&5. */
nop
- lwz r3,12(r1)
+ lwz r3,12(r1) /* Load return as integer. */
+.Lout:
addi r1,r1,16
blr
-.L4:
- fsub fp1,fp1,fp10 /* x-= 0.5; */
- b .L9
+.Lretzero: /* when 0.5 > x > -0.5 */
+ li r3,0 /* return 0. */
+ b .Lout
END (__lround)
weak_alias (__lround, lround)
diff -uNr libc.orig/sysdeps/powerpc/powerpc32/power4/fpu/s_llround.S libc/sysdeps/powerpc/powerpc32/power4/fpu/s_llround.S
--- libc.orig/sysdeps/powerpc/powerpc32/power4/fpu/s_llround.S 2007-06-03 13:50:48.000000000 -0700
+++ libc/sysdeps/powerpc/powerpc32/power4/fpu/s_llround.S 2007-11-29 09:21:48.000000000 -0800
@@ -1,5 +1,5 @@
/* llround function. PowerPC32 on PowerPC64 version.
- Copyright (C) 2004, 2006 Free Software Foundation, Inc.
+ Copyright (C) 2004, 2006, 2007 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
@@ -20,15 +20,15 @@
#include <sysdep.h>
#include <math_ldbl_opt.h>
- .section .rodata.cst8,"aM",@progbits,8
- .align 2
-.LC0: /* 0.0 */
+ .section .rodata.cst12,"aM",@progbits,12
+ .align 3
+ .LC0: /* 0x1.0000000000000p+52 == 2^52 */
+ .long 0x43300000
.long 0x00000000
-.LC1: /* 0.5 */
- .long 0x3f000000
+ .long 0x3f000000 /* Use this for 0.5 */
.section ".text"
-
+
/* long [r3] lround (float x [fp1])
IEEE 1003.1 lround function. IEEE specifies "round to the nearest
integer value, rounding halfway cases away from zero, regardless of
@@ -37,7 +37,15 @@
tie, choose the one that is even (least significant bit o).".
So we can't use the PowerPC "round to Nearest" mode. Instead we set
"round toward Zero" mode and round by adding +-0.5 before rounding
- to the integer value. */
+ to the integer value.
+
+ It is necessary to detect when x is (+-)0x1.fffffffffffffp-2
+ because adding +-0.5 in this case will cause an erroneous shift,
+ carry and round. We simply return 0 if 0.5 > x > -0.5. Likewise
+ if x is and odd number between +-(2^52 and 2^53-1) a shift and
+ carry will erroneously round if biased with +-0.5. Therefore if x
+ is greater/less than +-2^52 we don't need to bias the number with
+ +-0.5. */
ENTRY (__llround)
stwu r1,-16(r1)
@@ -57,30 +65,41 @@
# endif
mtlr r11
cfi_same_value (lr)
- lfs fp12,0(r9)
- lfs fp10,.LC1-.LC0(r9)
+ lfd fp9,0(r9)
+ lfs fp10,8(r9)
#else
- lis r9,.LC0@ha
- lis r10,.LC1@ha
- lfs fp12,.LC0@l(r9)
- lfs fp10,.LC1@l(r10)
+ lis r9,.LC0@ha
+ lfd fp9,.LC0@l(r9) /* Load 2^52 into fpr9. */
+ lfs fp10,.LC0@l+8(r9) /* Load 0.5 into fpr10. */
#endif
- fcmpu cr6,fp1,fp12 /* if (x > 0.0) */
- ble- cr6,.L4
- fadd fp1,fp1,fp10 /* x+= 0.5; */
-.L9:
- fctidz fp2,fp1 /* Convert To Integer DW round toward 0. */
- stfd fp2,8(r1)
- nop /* Ensure the following load is in a different dispatch */
- nop /* group to avoid pipe stall on POWER4&5. */
+ fabs fp2,fp1 /* Get the absolute value of x. */
+ fsub fp12,fp10,fp10 /* Compute 0.0 into fpr12. */
+ fcmpu cr6,fp2,fp10 /* if |x| < 0.5 */
+ fcmpu cr4,fp2,fp9 /* if |x| >= 2^52 */
+ fcmpu cr3,fp1,fp12 /* x is negative? x < 0.0 */
+ blt- cr6,.Lretzero /* 0.5 > x < -0.5 so just return 0. */
+ bge- cr4,.Lnobias /* 2^52 > x < -2^52 just convert with no bias. */
+ fadd fp3,fp2,fp10 /* |x|+=0.5 bias to prepare to round. */
+ bge cr3,.Lconvert /* x is positive so don't negate x. */
+ fnabs fp3,fp3 /* -(|x|+=0.5) */
+.Lconvert:
+ fctidz fp4,fp3 /* Convert to Integer double word round toward 0. */
+ stfd fp4,8(r1)
+ nop
+ nop
nop
- lwz r4,12(r1)
+ lwz r4,12(r1) /* Load return as integer. */
lwz r3,8(r1)
+.Lout:
addi r1,r1,16
blr
-.L4:
- fsub fp1,fp1,fp10 /* x-= 0.5; */
- b .L9
+.Lretzero: /* 0.5 > x > -0.5 */
+ li r3,0 /* return 0. */
+ li r4,0
+ b .Lout
+.Lnobias:
+ fmr fp3,fp1
+ b .Lconvert
END (__llround)
weak_alias (__llround, llround)
diff -uNr libc.orig/sysdeps/powerpc/powerpc64/fpu/s_llround.S libc/sysdeps/powerpc/powerpc64/fpu/s_llround.S
--- libc.orig/sysdeps/powerpc/powerpc64/fpu/s_llround.S 2006-01-27 16:07:40.000000000 -0800
+++ libc/sysdeps/powerpc/powerpc64/fpu/s_llround.S 2007-11-29 09:21:48.000000000 -0800
@@ -1,5 +1,5 @@
/* llround function. PowerPC64 version.
- Copyright (C) 2004, 2006 Free Software Foundation, Inc.
+ Copyright (C) 2004, 2006, 2007 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
@@ -21,13 +21,13 @@
#include <math_ldbl_opt.h>
.section ".toc","aw"
-.LC0: /* -0.0 */
- .tc FD_00000000_0[TC],0x0000000000000000
+.LC0: /* 2^52 */
+ .tc FD_43300000_0[TC],0x4330000000000000
.LC1: /* 0.5 */
.tc FD_3fe00000_0[TC],0x3fe0000000000000
.section ".text"
-/* long long [r3] llround (float x [fp1])
+/* long long [r3] llround (double x [fp1])
IEEE 1003.1 llround function. IEEE specifies "round to the nearest
integer value, rounding halfway cases away from zero, regardless of
the current rounding mode." However PowerPC Architecture defines
@@ -35,26 +35,45 @@
tie, choose the one that is even (least significant bit o).".
So we can't use the PowerPC "round to Nearest" mode. Instead we set
"round toward Zero" mode and round by adding +-0.5 before rounding
- to the integer value. */
+ to the integer value.
+
+ It is necessary to detect when x is (+-)0x1.fffffffffffffp-2
+ because adding +-0.5 in this case will cause an erroneous shift,
+ carry and round. We simply return 0 if 0.5 > x > -0.5. Likewise
+ if x is and odd number between +-(2^52 and 2^53-1) a shift and
+ carry will erroneously round if biased with +-0.5. Therefore if x
+ is greater/less than +-2^52 we don't need to bias the number with
+ +-0.5. */
ENTRY (__llround)
CALL_MCOUNT 0
- lfd fp12,.LC0@toc(2)
- lfd fp10,.LC1@toc(2)
- fcmpu cr6,fp1,fp12 /* if (x > 0.0) */
- ble- cr6,.L4
- fadd fp1,fp1,fp10 /* x+= 0.5; */
-.L9:
- fctidz fp2,fp1 /* Convert To Integer DW llround toward 0. */
- stfd fp2,-16(r1)
- nop /* Insure the following load is in a different dispatch group */
- nop /* to avoid pipe stall on POWER4&5. */
+ lfd fp9,.LC0@toc(2) /* Load 2^52 into fpr9. */
+ lfd fp10,.LC1@toc(2)/* Load 0.5 into fpr10. */
+ fabs fp2,fp1 /* Get the absolute value of x. */
+ fsub fp12,fp10,fp10 /* Compute 0.0 into fp12. */
+ fcmpu cr6,fp2,fp10 /* if |x| < 0.5 */
+ fcmpu cr4,fp2,fp9 /* if |x| >= 2^52 */
+ fcmpu cr3,fp1,fp12 /* x is negative? x < 0.0 */
+ blt- cr6,.Lretzero /* 0.5 > x < -0.5 so just return 0. */
+ bge- cr4,.Lnobias /* 2^52 > x < -2^52 just convert with no bias. */
+ fadd fp3,fp2,fp10 /* |x|+=0.5 bias to prepare to round. */
+ bge cr3,.Lconvert /* x is positive so don't negate x. */
+ fnabs fp3,fp3 /* -(|x|+=0.5) */
+.Lconvert:
+ fctidz fp4,fp3 /* Convert to Integer double word round toward 0. */
+ stfd fp4,-16(r1)
+ nop
+ nop
nop
- ld r3,-16(r1)
+ ld r3,-16(r1) /* Load return as integer. */
+.Lout:
blr
-.L4:
- fsub fp1,fp1,fp10 /* x-= 0.5; */
- b .L9
+.Lretzero: /* 0.5 > x > -0.5 */
+ li r3,0 /* return 0. */
+ b .Lout
+.Lnobias:
+ fmr fp3,fp1
+ b .Lconvert
END (__llround)
strong_alias (__llround, __lround)
diff -uNr libc.orig/sysdeps/powerpc/powerpc64/fpu/s_llroundf.S libc/sysdeps/powerpc/powerpc64/fpu/s_llroundf.S
--- libc.orig/sysdeps/powerpc/powerpc64/fpu/s_llroundf.S 2006-01-27 16:14:39.000000000 -0800
+++ libc/sysdeps/powerpc/powerpc64/fpu/s_llroundf.S 2007-11-29 09:21:48.000000000 -0800
@@ -1,5 +1,5 @@
/* llroundf function. PowerPC64 version.
- Copyright (C) 2004, 2006 Free Software Foundation, Inc.
+ Copyright (C) 2004, 2006, 2007 Free Software Foundation, Inc.
This file is part of the GNU C Library.
The GNU C Library is free software; you can redistribute it and/or
@@ -20,8 +20,8 @@
#include <sysdep.h>
.section ".toc","aw"
-.LC0: /* -0.0 */
- .tc FD_00000000_0[TC],0x0000000000000000
+.LC0: /* 2^23 */
+ .tc FD_41600000_0[TC],0x4160000000000000
.LC1: /* 0.5 */
.tc FD_3fe00000_0[TC],0x3fe0000000000000
.section ".text"
@@ -34,24 +34,45 @@
tie, choose the one that is even (least significant bit o).".
So we can't use the PowerPC "round to Nearest" mode. Instead we set
"round toward Zero" mode and round by adding +-0.5 before rounding
- to the integer value. */
+ to the integer value.
+
+ It is necessary to detect when x is (+-)0x1.fffffffffffffp-2
+ because adding +-0.5 in this case will cause an erroneous shift,
+ carry and round. We simply return 0 if 0.5 > x > -0.5. Likewise
+ if x is and odd number between +-(2^23 and 2^24-1) a shift and
+ carry will erroneously round if biased with +-0.5. Therefore if x
+ is greater/less than +-2^23 we don't need to bias the number with
+ +-0.5. */
ENTRY (__llroundf)
CALL_MCOUNT 0
- lfd fp12,.LC0@toc(2)
- lfd fp10,.LC1@toc(2)
- fcmpu cr6,fp1,fp12 /* if (x < 0.0) */
- fsubs fp3,fp1,fp10 /* x-= 0.5; */
- ble- cr6,.L9
- fadds fp3,fp1,fp10 /* x+= 0.5; */
-.L9:
- fctidz fp2,fp3 /* Convert To Integer DW round toward 0. */
- stfd fp2,-16(r1)
- nop /* Insure the following load is in a different dispatch group */
- nop /* to avoid pipe stall on POWER4&5. */
+ lfd fp9,.LC0@toc(2) /* Load 2^23 into fpr9. */
+ lfd fp10,.LC1@toc(2)/* Load 0.5 into fpr10. */
+ fabs fp2,fp1 /* Get the absolute value of x. */
+ fsub fp12,fp10,fp10 /* Compute 0.0 into fp12. */
+ fcmpu cr6,fp2,fp10 /* if |x| < 0.5 */
+ fcmpu cr4,fp2,fp9 /* if |x| >= 2^23 */
+ fcmpu cr3,fp1,fp12 /* x is negative? x < 0.0 */
+ blt- cr6,.Lretzero /* 0.5 > x < -0.5 so just return 0. */
+ bge- cr4,.Lnobias /* 2^23 > x < -2^23 just convert with no bias. */
+ fadd fp3,fp2,fp10 /* |x|+=0.5 bias to prepare to round. */
+ bge cr3,.Lconvert /* x is positive so don't negate x. */
+ fnabs fp3,fp3 /* -(|x|+=0.5) */
+.Lconvert:
+ fctidz fp4,fp3 /* Convert to Integer double word round toward 0. */
+ stfd fp4,-16(r1)
+ nop
+ nop
nop
- ld r3,-16(r1)
+ ld r3,-16(r1) /* Load return as integer. */
+.Lout:
blr
+.Lretzero: /* 0.5 > x > -0.5 */
+ li r3,0 /* return 0. */
+ b .Lout
+.Lnobias:
+ fmr fp3,fp1
+ b .Lconvert
END (__llroundf)
strong_alias (__llroundf, __lroundf)