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author | Ulrich Drepper <drepper@redhat.com> | 2001-10-14 22:33:08 +0000 |
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committer | Ulrich Drepper <drepper@redhat.com> | 2001-10-14 22:33:08 +0000 |
commit | 1f5649f86b7de5aec990e03f2700df36a01c2752 (patch) | |
tree | c6126aff7f80434c64f21dd6033215864afd57cd /sysdeps/ieee754/ldbl-128/s_cbrtl.c | |
parent | 459a31635e9fe474c05e995312fde318d7c4a5b0 (diff) | |
download | glibc-1f5649f86b7de5aec990e03f2700df36a01c2752.tar.gz glibc-1f5649f86b7de5aec990e03f2700df36a01c2752.tar.xz glibc-1f5649f86b7de5aec990e03f2700df36a01c2752.zip |
Update.
2001-10-14 Ulrich Drepper <drepper@redhat.com> * locale/programs/ld-collate.c (handle_ellipsis): Use %lX not %lx to generate hexadecimal identifier. Patch by Jungshik Shin <jungshik.shin@yale.edu>. 2001-10-09 Stephen L Moshier <moshier@mediaone.net> * sysdeps/ieee754/ldbl-96/s_cbrtl.c (__cbrtl): Fix algorithm. 2001-10-14 Ulrich Drepper <drepper@redhat.com> * sysdeps/ieee754/ldbl-128/e_powl.c: New file. * sysdeps/ieee754/ldbl-128/s_cbrtl.c: New file. Contributed by Stephen L Moshier <moshier@mediaone.net>. * sysdeps/ieee754/ldbl-128/e_j0l.c: Constify float variables. * sysdeps/ieee754/ldbl-128/e_j1l.c: Likewise. * sysdeps/ieee754/ldbl-128/e_lgammal_r.c: Likewise * sysdeps/ieee754/ldbl-128/s_erfl.c: Likewise * sysdeps/ieee754/ldbl-128/s_expm1l.c: Likewise * sysdeps/ieee754/ldbl-128/s_log1pl.c: Likewise * timezone/africa: Update from tzdata2001d. * timezone/asia: Likewise. * timezone/australasia: Likewise. * timezone/backward: Likewise. * timezone/europe: Likewise. * timezone/leapseconds: Likewise. * timezone/northamerica: Likewise. * timezone/southamerica: Likewise. * timezone/zone.tab: Likewise. 2001-10-09 Martin Schwidefsky <schwidefsky@de.ibm.com> * sysdeps/s390/s390-32/sys/ucontext.h: Correct __psw_t typedef. * sysdeps/s390/s390-64/sys/ucontext.h: Likewise.
Diffstat (limited to 'sysdeps/ieee754/ldbl-128/s_cbrtl.c')
-rw-r--r-- | sysdeps/ieee754/ldbl-128/s_cbrtl.c | 121 |
1 files changed, 121 insertions, 0 deletions
diff --git a/sysdeps/ieee754/ldbl-128/s_cbrtl.c b/sysdeps/ieee754/ldbl-128/s_cbrtl.c new file mode 100644 index 0000000000..298754ea74 --- /dev/null +++ b/sysdeps/ieee754/ldbl-128/s_cbrtl.c @@ -0,0 +1,121 @@ +/* cbrtl.c + * + * Cube root, long double precision + * + * + * + * SYNOPSIS: + * + * long double x, y, cbrtl(); + * + * y = cbrtl( x ); + * + * + * + * DESCRIPTION: + * + * Returns the cube root of the argument, which may be negative. + * + * Range reduction involves determining the power of 2 of + * the argument. A polynomial of degree 2 applied to the + * mantissa, and multiplication by the cube root of 1, 2, or 4 + * approximates the root to within about 0.1%. Then Newton's + * iteration is used three times to converge to an accurate + * result. + * + * + * + * ACCURACY: + * + * Relative error: + * arithmetic domain # trials peak rms + * IEEE -8,8 100000 1.3e-34 3.9e-35 + * IEEE exp(+-707) 100000 1.3e-34 4.3e-35 + * + */ + +/* +Cephes Math Library Release 2.2: January, 1991 +Copyright 1984, 1991 by Stephen L. Moshier +Adapted for glibc October, 2001. +*/ + +#include "math.h" +#include "math_private.h" + +static const long double CBRT2 = 1.259921049894873164767210607278228350570251L; +static const long double CBRT4 = 1.587401051968199474751705639272308260391493L; +static const long double CBRT2I = 0.7937005259840997373758528196361541301957467L; +static const long double CBRT4I = 0.6299605249474365823836053036391141752851257L; + + +long double +__cbrtl (long double x) +{ + int e, rem, sign; + long double z; + + if (!__finitel (x)) + return x + x; + + if (x == 0) + return (x); + + if (x > 0) + sign = 1; + else + { + sign = -1; + x = -x; + } + + z = x; + /* extract power of 2, leaving mantissa between 0.5 and 1 */ + x = __frexpl (x, &e); + + /* Approximate cube root of number between .5 and 1, + peak relative error = 1.2e-6 */ + x = ((((1.3584464340920900529734e-1L * x + - 6.3986917220457538402318e-1L) * x + + 1.2875551670318751538055e0L) * x + - 1.4897083391357284957891e0L) * x + + 1.3304961236013647092521e0L) * x + 3.7568280825958912391243e-1L; + + /* exponent divided by 3 */ + if (e >= 0) + { + rem = e; + e /= 3; + rem -= 3 * e; + if (rem == 1) + x *= CBRT2; + else if (rem == 2) + x *= CBRT4; + } + else + { /* argument less than 1 */ + e = -e; + rem = e; + e /= 3; + rem -= 3 * e; + if (rem == 1) + x *= CBRT2I; + else if (rem == 2) + x *= CBRT4I; + e = -e; + } + + /* multiply by power of 2 */ + x = __ldexpl (x, e); + + /* Newton iteration */ + x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L; + x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L; + x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L; + + if (sign < 0) + x = -x; + return (x); +} + +weak_alias (__cbrtl, cbrtl) |