# commit 4cf69995e26e16005d4e3843ad4d18c75cf21a04
# Author: Alan Modra <amodra@gmail.com>
# Date: Sat Aug 17 18:19:44 2013 +0930
#
# Fix for [BZ #15680] IBM long double inaccuracy
# http://sourceware.org/ml/libc-alpha/2013-06/msg00919.html
#
# I discovered a number of places where denormals and other corner cases
# were being handled wrongly.
#
# - printf_fphex.c: Testing for the low double exponent being zero is
# unnecessary. If the difference in exponents is less than 53 then the
# high double exponent must be nearing the low end of its range, and the
# low double exponent hit rock bottom.
#
# - ldbl2mpn.c: A denormal (ie. exponent of zero) value is treated as
# if the exponent was one, so shift mantissa left by one. Code handling
# normalisation of the low double mantissa lacked a test for shift count
# greater than bits in type being shifted, and lacked anything to handle
# the case where the difference in exponents is less than 53 as in
# printf_fphex.c.
#
# - math_ldbl.h (ldbl_extract_mantissa): Same as above, but worse, with
# code testing for exponent > 1 for some reason, probably a typo for >= 1.
#
# - math_ldbl.h (ldbl_insert_mantissa): Round the high double as per
# mpn2ldbl.c (hi is odd or explicit mantissas non-zero) so that the
# number we return won't change when applying ldbl_canonicalize().
# Add missing overflow checks and normalisation of high mantissa.
# Correct misleading comment: "The hidden bit of the lo mantissa is
# zero" is not always true as can be seen from the code rounding the hi
# mantissa. Also by inspection, lzcount can never be less than zero so
# remove that test. Lastly, masking bitfields to their widths can be
# left to the compiler.
#
# - mpn2ldbl.c: The overflow checks here on rounding of high double were
# just plain wrong. Incrementing the exponent must be accompanied by a
# shift right of the mantissa to keep the value unchanged. Above notes
# for ldbl_insert_mantissa are also relevant.
#
# [BZ #15680]
# * sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c: Comment fix.
# * sysdeps/ieee754/ldbl-128ibm/printf_fphex.c
# (PRINT_FPHEX_LONG_DOUBLE): Tidy code by moving -53 into ediff
# calculation. Remove unnecessary test for denormal exponent.
# * sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c (__mpn_extract_long_double):
# Correct handling of denormals. Avoid undefined shift behaviour.
# Correct normalisation of low mantissa when low double is denormal.
# * sysdeps/ieee754/ldbl-128ibm/math_ldbl.h
# (ldbl_extract_mantissa): Likewise. Comment. Use uint64_t* for hi64.
# (ldbl_insert_mantissa): Make both hi64 and lo64 parms uint64_t.
# Correct normalisation of low mantissa. Test for overflow of high
# mantissa and normalise.
# (ldbl_nearbyint): Use more readable constant for two52.
# * sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c
# (__mpn_construct_long_double): Fix test for overflow of high
# mantissa and correct normalisation. Avoid undefined shift.
#
diff -urN glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c
--- glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c 2014-05-27 19:13:56.000000000 -0500
+++ glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c 2014-05-27 19:14:45.000000000 -0500
@@ -243,7 +243,7 @@
We split the 113 bits of the mantissa into 5 24bit integers
stored in a double array. */
/* Make the IBM extended format 105 bit mantissa look like the ieee854 112
- bit mantissa so the next operatation will give the correct result. */
+ bit mantissa so the next operation will give the correct result. */
ldbl_extract_mantissa (&ixd, &lxd, &exp, x);
exp = exp - 23;
/* This is faster than doing this in floating point, because we
diff -urN glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c
--- glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c 2014-05-27 19:13:56.000000000 -0500
+++ glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c 2014-05-27 19:14:45.000000000 -0500
@@ -36,6 +36,7 @@
union ibm_extended_long_double u;
unsigned long long hi, lo;
int ediff;
+
u.ld = value;
*is_neg = u.d[0].ieee.negative;
@@ -43,27 +44,36 @@
lo = ((long long) u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1;
hi = ((long long) u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1;
- /* If the lower double is not a denomal or zero then set the hidden
+
+ /* If the lower double is not a denormal or zero then set the hidden
53rd bit. */
- if (u.d[1].ieee.exponent > 0)
- {
- lo |= 1LL << 52;
+ if (u.d[1].ieee.exponent != 0)
+ lo |= 1ULL << 52;
+ else
+ lo = lo << 1;
- /* The lower double is normalized separately from the upper. We may
- need to adjust the lower manitissa to reflect this. */
- ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent;
- if (ediff > 53)
- lo = lo >> (ediff-53);
+ /* The lower double is normalized separately from the upper. We may
+ need to adjust the lower manitissa to reflect this. */
+ ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53;
+ if (ediff > 0)
+ {
+ if (ediff < 64)
+ lo = lo >> ediff;
+ else
+ lo = 0;
}
+ else if (ediff < 0)
+ lo = lo << -ediff;
+
/* The high double may be rounded and the low double reflects the
difference between the long double and the rounded high double
value. This is indicated by a differnce between the signs of the
high and low doubles. */
- if ((u.d[0].ieee.negative != u.d[1].ieee.negative)
- && ((u.d[1].ieee.exponent != 0) && (lo != 0L)))
+ if (u.d[0].ieee.negative != u.d[1].ieee.negative
+ && lo != 0)
{
lo = (1ULL << 53) - lo;
- if (hi == 0LL)
+ if (hi == 0)
{
/* we have a borrow from the hidden bit, so shift left 1. */
hi = 0x0ffffffffffffeLL | (lo >> 51);
diff -urN glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h
--- glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h 2014-05-27 19:13:56.000000000 -0500
+++ glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/math_ldbl.h 2014-05-27 19:51:13.000000000 -0500
@@ -13,77 +13,118 @@
the number before the decimal point and the second implicit bit
as bit 53 of the mantissa. */
uint64_t hi, lo;
- int ediff;
union ibm_extended_long_double u;
+
u.ld = x;
*exp = u.d[0].ieee.exponent - IEEE754_DOUBLE_BIAS;
lo = ((uint64_t)u.d[1].ieee.mantissa0 << 32) | u.d[1].ieee.mantissa1;
hi = ((uint64_t)u.d[0].ieee.mantissa0 << 32) | u.d[0].ieee.mantissa1;
- /* If the lower double is not a denomal or zero then set the hidden
- 53rd bit. */
- if (u.d[1].ieee.exponent > 0x001)
- {
- lo |= (1ULL << 52);
- lo = lo << 7; /* pre-shift lo to match ieee854. */
- /* The lower double is normalized separately from the upper. We
- may need to adjust the lower manitissa to reflect this. */
- ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent;
- if (ediff > 53)
- lo = lo >> (ediff-53);
- hi |= (1ULL << 52);
- }
- if ((u.d[0].ieee.negative != u.d[1].ieee.negative)
- && ((u.d[1].ieee.exponent != 0) && (lo != 0LL)))
+ if (u.d[0].ieee.exponent != 0)
{
- hi--;
- lo = (1ULL << 60) - lo;
- if (hi < (1ULL << 52))
+ int ediff;
+
+ /* If not a denormal or zero then we have an implicit 53rd bit. */
+ hi |= (uint64_t) 1 << 52;
+
+ if (u.d[1].ieee.exponent != 0)
+ lo |= (uint64_t) 1 << 52;
+ else
+ /* A denormal is to be interpreted as having a biased exponent
+ of 1. */
+ lo = lo << 1;
+
+ /* We are going to shift 4 bits out of hi later, because we only
+ want 48 bits in *hi64. That means we want 60 bits in lo, but
+ we currently only have 53. Shift the value up. */
+ lo = lo << 7;
+
+ /* The lower double is normalized separately from the upper.
+ We may need to adjust the lower mantissa to reflect this.
+ The difference between the exponents can be larger than 53
+ when the low double is much less than 1ULP of the upper
+ (in which case there are significant bits, all 0's or all
+ 1's, between the two significands). The difference between
+ the exponents can be less than 53 when the upper double
+ exponent is nearing its minimum value (in which case the low
+ double is denormal ie. has an exponent of zero). */
+ ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53;
+ if (ediff > 0)
{
- /* we have a borrow from the hidden bit, so shift left 1. */
- hi = (hi << 1) | (lo >> 59);
- lo = 0xfffffffffffffffLL & (lo << 1);
- *exp = *exp - 1;
+ if (ediff < 64)
+ lo = lo >> ediff;
+ else
+ lo = 0;
+ }
+ else if (ediff < 0)
+ lo = lo << -ediff;
+
+ if (u.d[0].ieee.negative != u.d[1].ieee.negative
+ && lo != 0)
+ {
+ hi--;
+ lo = ((uint64_t) 1 << 60) - lo;
+ if (hi < (uint64_t) 1 << 52)
+ {
+ /* We have a borrow from the hidden bit, so shift left 1. */
+ hi = (hi << 1) | (lo >> 59);
+ lo = (((uint64_t) 1 << 60) - 1) & (lo << 1);
+ *exp = *exp - 1;
+ }
}
}
+ else
+ /* If the larger magnitude double is denormal then the smaller
+ one must be zero. */
+ hi = hi << 1;
+
*lo64 = (hi << 60) | lo;
*hi64 = hi >> 4;
}
static inline long double
-ldbl_insert_mantissa (int sign, int exp, int64_t hi64, u_int64_t lo64)
+ldbl_insert_mantissa (int sign, int exp, int64_t hi64, uint64_t lo64)
{
union ibm_extended_long_double u;
- unsigned long hidden2, lzcount;
- unsigned long long hi, lo;
+ int expnt2;
+ uint64_t hi, lo;
u.d[0].ieee.negative = sign;
u.d[1].ieee.negative = sign;
u.d[0].ieee.exponent = exp + IEEE754_DOUBLE_BIAS;
- u.d[1].ieee.exponent = exp-53 + IEEE754_DOUBLE_BIAS;
+ u.d[1].ieee.exponent = 0;
+ expnt2 = exp - 53 + IEEE754_DOUBLE_BIAS;
+
/* Expect 113 bits (112 bits + hidden) right justified in two longs.
The low order 53 bits (52 + hidden) go into the lower double */
- lo = (lo64 >> 7)& ((1ULL << 53) - 1);
- hidden2 = (lo64 >> 59) & 1ULL;
+ lo = (lo64 >> 7) & (((uint64_t) 1 << 53) - 1);
/* The high order 53 bits (52 + hidden) go into the upper double */
- hi = (lo64 >> 60) & ((1ULL << 11) - 1);
- hi |= (hi64 << 4);
+ hi = lo64 >> 60;
+ hi |= hi64 << 4;
- if (lo != 0LL)
+ if (lo != 0)
{
- /* hidden2 bit of low double controls rounding of the high double.
- If hidden2 is '1' then round up hi and adjust lo (2nd mantissa)
+ int lzcount;
+
+ /* hidden bit of low double controls rounding of the high double.
+ If hidden is '1' and either the explicit mantissa is non-zero
+ or hi is odd, then round up hi and adjust lo (2nd mantissa)
plus change the sign of the low double to compensate. */
- if (hidden2)
+ if ((lo & ((uint64_t) 1 << 52)) != 0
+ && ((hi & 1) != 0 || (lo & (((uint64_t) 1 << 52) - 1)) != 0))
{
hi++;
+ if ((hi & ((uint64_t) 1 << 53)) != 0)
+ {
+ hi = hi >> 1;
+ u.d[0].ieee.exponent++;
+ }
u.d[1].ieee.negative = !sign;
- lo = (1ULL << 53) - lo;
+ lo = ((uint64_t) 1 << 53) - lo;
}
- /* The hidden bit of the lo mantissa is zero so we need to
- normalize the it for the low double. Shift it left until the
- hidden bit is '1' then adjust the 2nd exponent accordingly. */
+ /* Normalize the low double. Shift the mantissa left until
+ the hidden bit is '1' and adjust the exponent accordingly. */
if (sizeof (lo) == sizeof (long))
lzcount = __builtin_clzl (lo);
@@ -91,34 +132,30 @@
lzcount = __builtin_clzl ((long) (lo >> 32));
else
lzcount = __builtin_clzl ((long) lo) + 32;
- lzcount = lzcount - 11;
- if (lzcount > 0)
+ lzcount = lzcount - (64 - 53);
+ lo <<= lzcount;
+ expnt2 -= lzcount;
+
+ if (expnt2 >= 1)
+ /* Not denormal. */
+ u.d[1].ieee.exponent = expnt2;
+ else
{
- int expnt2 = u.d[1].ieee.exponent - lzcount;
- if (expnt2 >= 1)
- {
- /* Not denormal. Normalize and set low exponent. */
- lo = lo << lzcount;
- u.d[1].ieee.exponent = expnt2;
- }
+ /* Is denormal. Note that biased exponent of 0 is treated
+ as if it was 1, hence the extra shift. */
+ if (expnt2 > -53)
+ lo >>= 1 - expnt2;
else
- {
- /* Is denormal. */
- lo = lo << (lzcount + expnt2);
- u.d[1].ieee.exponent = 0;
- }
+ lo = 0;
}
}
else
- {
- u.d[1].ieee.negative = 0;
- u.d[1].ieee.exponent = 0;
- }
+ u.d[1].ieee.negative = 0;
- u.d[1].ieee.mantissa1 = lo & ((1ULL << 32) - 1);
- u.d[1].ieee.mantissa0 = (lo >> 32) & ((1ULL << 20) - 1);
- u.d[0].ieee.mantissa1 = hi & ((1ULL << 32) - 1);
- u.d[0].ieee.mantissa0 = (hi >> 32) & ((1ULL << 20) - 1);
+ u.d[1].ieee.mantissa1 = lo;
+ u.d[1].ieee.mantissa0 = lo >> 32;
+ u.d[0].ieee.mantissa1 = hi;
+ u.d[0].ieee.mantissa0 = hi >> 32;
return u.ld;
}
@@ -133,6 +170,10 @@
return u.ld;
}
+/* To suit our callers we return *hi64 and *lo64 as if they came from
+ an ieee854 112 bit mantissa, that is, 48 bits in *hi64 (plus one
+ implicit bit) and 64 bits in *lo64. */
+
static inline void
default_ldbl_unpack (long double l, double *a, double *aa)
{
@@ -162,13 +203,13 @@
*aa = xl;
}
-/* Simple inline nearbyint (double) function .
+/* Simple inline nearbyint (double) function.
Only works in the default rounding mode
but is useful in long double rounding functions. */
static inline double
ldbl_nearbyint (double a)
{
- double two52 = 0x10000000000000LL;
+ double two52 = 0x1p52;
if (__builtin_expect ((__builtin_fabs (a) < two52), 1))
{
diff -urN glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c
--- glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c 2014-05-27 19:13:56.000000000 -0500
+++ glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c 2014-05-27 19:14:45.000000000 -0500
@@ -70,9 +70,9 @@
else
lzcount = __builtin_clzl ((long) val) + 32;
if (hi)
- lzcount = lzcount - 11;
+ lzcount = lzcount - (64 - 53);
else
- lzcount = lzcount + 42;
+ lzcount = lzcount + 53 - (64 - 53);
if (lzcount > u.d[0].ieee.exponent)
{
@@ -98,29 +98,27 @@
}
}
- if (lo != 0L)
+ if (lo != 0)
{
- /* hidden2 bit of low double controls rounding of the high double.
- If hidden2 is '1' and either the explicit mantissa is non-zero
+ /* hidden bit of low double controls rounding of the high double.
+ If hidden is '1' and either the explicit mantissa is non-zero
or hi is odd, then round up hi and adjust lo (2nd mantissa)
plus change the sign of the low double to compensate. */
if ((lo & (1LL << 52)) != 0
- && ((hi & 1) != 0 || (lo & ((1LL << 52) - 1))))
+ && ((hi & 1) != 0 || (lo & ((1LL << 52) - 1)) != 0))
{
hi++;
- if ((hi & ((1LL << 52) - 1)) == 0)
+ if ((hi & (1LL << 53)) != 0)
{
- if ((hi & (1LL << 53)) != 0)
- hi -= 1LL << 52;
+ hi >>= 1;
u.d[0].ieee.exponent++;
}
u.d[1].ieee.negative = !sign;
lo = (1LL << 53) - lo;
}
- /* The hidden bit of the lo mantissa is zero so we need to normalize
- it for the low double. Shift it left until the hidden bit is '1'
- then adjust the 2nd exponent accordingly. */
+ /* Normalize the low double. Shift the mantissa left until
+ the hidden bit is '1' and adjust the exponent accordingly. */
if (sizeof (lo) == sizeof (long))
lzcount = __builtin_clzl (lo);
@@ -128,24 +126,24 @@
lzcount = __builtin_clzl ((long) (lo >> 32));
else
lzcount = __builtin_clzl ((long) lo) + 32;
- lzcount = lzcount - 11;
- if (lzcount > 0)
- {
- lo = lo << lzcount;
- exponent2 = exponent2 - lzcount;
- }
+ lzcount = lzcount - (64 - 53);
+ lo <<= lzcount;
+ exponent2 -= lzcount;
+
if (exponent2 > 0)
u.d[1].ieee.exponent = exponent2;
- else
+ else if (exponent2 > -53)
lo >>= 1 - exponent2;
+ else
+ lo = 0;
}
else
u.d[1].ieee.negative = 0;
- u.d[1].ieee.mantissa1 = lo & 0xffffffffLL;
- u.d[1].ieee.mantissa0 = (lo >> 32) & 0xfffff;
- u.d[0].ieee.mantissa1 = hi & 0xffffffffLL;
- u.d[0].ieee.mantissa0 = (hi >> 32) & ((1LL << (LDBL_MANT_DIG - 86)) - 1);
+ u.d[1].ieee.mantissa1 = lo;
+ u.d[1].ieee.mantissa0 = lo >> 32;
+ u.d[0].ieee.mantissa1 = hi;
+ u.d[0].ieee.mantissa0 = hi >> 32;
return u.ld;
}
diff -urN glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c
--- glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c 2014-05-27 19:13:56.000000000 -0500
+++ glibc-2.17-c758a686/sysdeps/ieee754/ldbl-128ibm/printf_fphex.c 2014-05-27 19:14:45.000000000 -0500
@@ -43,15 +43,15 @@
lo <<= 1; \
/* The lower double is normalized separately from the upper. We \
may need to adjust the lower manitissa to reflect this. */ \
- ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent; \
- if (ediff > 53 + 63) \
+ ediff = u.d[0].ieee.exponent - u.d[1].ieee.exponent - 53; \
+ if (ediff > 63) \
lo = 0; \
- else if (ediff > 53) \
- lo = lo >> (ediff - 53); \
- else if (u.d[1].ieee.exponent == 0 && ediff < 53) \
- lo = lo << (53 - ediff); \
+ else if (ediff > 0) \
+ lo = lo >> ediff; \
+ else if (ediff < 0) \
+ lo = lo << -ediff; \
if (u.d[0].ieee.negative != u.d[1].ieee.negative \
- && (u.d[1].ieee.exponent != 0 || lo != 0L)) \
+ && lo != 0) \
{ \
lo = (1ULL << 60) - lo; \
if (hi == 0L) \