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acosh patch
- To: libc-alpha at sources dot redhat dot com
- Subject: acosh patch
- From: Stephen L Moshier <moshier at mediaone dot net>
- Date: Sun, 1 Jul 2001 10:53:26 -0400 (EDT)
- Reply-To: moshier at moshier dot ne dot mediaone dot net
For large x, acosh(x) = log(x) + log(2). The threshold of "large" is
2^28, copied from the double precision routine into the long double
routines. That is somewhat too small for 80-bit long double and
much too small for the 128-bit format.
For example with x = 2^28 = 2.68435456e8,
acosh(x) = 2.010126823623841396963028457033350627e1
log(2x) = 2.010126823623841397309973152228712047e1
which differ by 1.7 parts in 10^19.
* sysdeps/ieee754/ldbl-96/e_acoshl.c (__ieee754_acoshl):
acosh(x) = ln(2x) if x > 2^30.
* sysdeps/ieee754/ldbl-128/e_acoshl.c (__ieee754_acoshl):
acosh(x) = ln(2x) if x > 2^54.
*** sysdeps/ieee754/ldbl-96/e_acoshl.c 1999/07/14 00:11:15 1.1
--- sysdeps/ieee754/ldbl-96/e_acoshl.c 2001/07/01 13:06:11
*************** ln2 = 6.931471805599453094287e-01L; /* 0
*** 55,61 ****
GET_LDOUBLE_WORDS(se,i0,i1,x);
if(se<0x3fff || se & 0x8000) { /* x < 1 */
return (x-x)/(x-x);
! } else if(se >=0x401b) { /* x > 2**28 */
if(se >=0x7fff) { /* x is inf of NaN */
return x+x;
} else
--- 55,61 ----
GET_LDOUBLE_WORDS(se,i0,i1,x);
if(se<0x3fff || se & 0x8000) { /* x < 1 */
return (x-x)/(x-x);
! } else if(se >=0x401d) { /* x > 2**30 */
if(se >=0x7fff) { /* x is inf of NaN */
return x+x;
} else
*** sysdeps/ieee754/ldbl-128/e_acoshl.c 1999/07/14 00:04:46 1.1
--- sysdeps/ieee754/ldbl-128/e_acoshl.c 2001/07/01 13:56:06
*************** ln2 = 0.69314718055994530941723212145817
*** 51,57 ****
GET_LDOUBLE_WORDS64(hx,lx,x);
if(hx<0x3fff000000000000LL) { /* x < 1 */
return (x-x)/(x-x);
! } else if(hx >=0x401b000000000000LL) { /* x > 2**28 */
if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */
return x+x;
} else
--- 51,57 ----
GET_LDOUBLE_WORDS64(hx,lx,x);
if(hx<0x3fff000000000000LL) { /* x < 1 */
return (x-x)/(x-x);
! } else if(hx >=0x4035000000000000LL) { /* x > 2**54 */
if(hx >=0x7fff000000000000LL) { /* x is inf of NaN */
return x+x;
} else