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authorRoland McGrath <roland@gnu.org>2006-01-28 00:15:15 +0000
committerRoland McGrath <roland@gnu.org>2006-01-28 00:15:15 +0000
commitf964490f3c4f094fd684960c2e98885b23e31376 (patch)
treee10f697bd55240b9be7a9c1a5109ee07893d3136 /sysdeps/ieee754/ldbl-128ibm/s_log1pl.c
parentd421a7801d1bdfd8175e53a79068833ae4de56b1 (diff)
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2006-01-27 Dwayne Grant McConnell <decimal@us.ibm.com>cvs/fedora-glibc-20060130T0922
Jakub Jelinek <jakub@redhat.com> Roland McGrath <roland@redhat.com> Steven Munroe <sjmunroe@us.ibm.com> Alan Modra <amodra@bigpond.net.au> * sysdeps/powerpc/powerpc64/fpu/s_truncf.S: Comment fix. * sysdeps/powerpc/powerpc32/fpu/s_truncf.S: Likewise. * sysdeps/powerpc/powerpc64/fpu/s_llroundf.S: Likewise. * sysdeps/powerpc/fpu/libm-test-ulps: Update. * math/libm-test.inc (check_float_internal): Allow ulp <= 0.5. (erfc_test): Don't run erfcl (27.0L) test if erfcl (27.0L) is denormal. [TEST_LDOUBLE] (ceil_test, floor_test, llrint_test, llround_test, rint_test, round_test, trunc_test): Add new tests. * sysdeps/powerpc/powerpc32/fpu/s_copysignl.S: New file. * sysdeps/powerpc/powerpc32/fpu/s_fabs.S: New file. * sysdeps/powerpc/powerpc32/fpu/s_fabsl.S: New file. * sysdeps/powerpc/powerpc32/fpu/s_fdim.c: New file. * sysdeps/powerpc/powerpc32/fpu/s_fmax.S: New file. * sysdeps/powerpc/powerpc32/fpu/s_fmin.S: New file. * sysdeps/powerpc/powerpc32/fpu/s_isnan.c: New file. * sysdeps/powerpc/powerpc64/fpu/s_ceill.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_copysignl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_fabs.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_fabsl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_fdim.c: New file. * sysdeps/powerpc/powerpc64/fpu/s_floorl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_fmax.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_fmin.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_isnan.c: New file. * sysdeps/powerpc/powerpc64/fpu/s_llrintl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_llroundl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_lrintl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_lroundl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_nearbyintl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_rintl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_roundl.S: New file. * sysdeps/powerpc/powerpc64/fpu/s_truncl.S: New file. * sysdeps/unix/sysv/linux/powerpc/Implies: New file. * sysdeps/unix/sysv/linux/powerpc/powerpc64/fpu/Implies: New file. * sysdeps/unix/sysv/linux/powerpc/powerpc32/fpu/Implies: New file. * sysdeps/unix/sysv/linux/powerpc/configure.in: New file. * sysdeps/unix/sysv/linux/powerpc/configure: New file. * sysdeps/unix/sysv/linux/powerpc/bits/wordsize.h (__LONG_DOUBLE_MATH_OPTIONAL): Define. (__NO_LONG_DOUBLE_MATH): Define. * sysdeps/unix/sysv/linux/powerpc/nldbl-abi.h: New file. * sysdeps/powerpc/fpu/s_isnan.c: Include math_ldbl_opt.h. * sysdeps/powerpc/powerpc64/fpu/s_ceil.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (ceill): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_copysign.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (copysignl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_floor.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (floorl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_llrint.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (llrintl, lrintl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_llround.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (llroundl, lroundl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_rint.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (rintl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_round.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (roundl): Add compatibility symbols. * sysdeps/powerpc/powerpc64/fpu/s_trunc.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (truncl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_ceil.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (ceill): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_copysign.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (copysignl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_floor.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (floorl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_lrint.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (lrintl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_llrint.c: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (llrintl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_lround.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (lroundl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_rint.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (rintl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_round.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (roundl): Add compatibility symbols. * sysdeps/powerpc/powerpc32/fpu/s_trunc.S: Include math_ldbl_opt.h. [LONG_DOUBLE_COMPAT] (truncl): Add compatibility symbols. * misc/qefgcvt_r.c [LDBL_MIN_10_EXP == -291] (FLOAT_MIN_10_NORM): New. * sysdeps/powerpc/fpu/bits/mathdef.h (__NO_LONG_DOUBLE_MATH): Remove. * sysdeps/powerpc/Implies: Add ieee754/ldbl-128ibm. * sysdeps/powerpc/powerpc32/Implies: Remove powerpc/soft-fp. * sysdeps/ieee754/ldbl-128ibm/Makefile: New file. * sysdeps/ieee754/ldbl-128ibm/e_acoshl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_acosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_asinl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_atan2l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_atanhl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_coshl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_expl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_fmodl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_gammal_r.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_hypotl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_j0l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_j1l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_jnl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_lgammal_r.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_log10l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_log2l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_logl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_powl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_rem_pio2l.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_remainderl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_sinhl.c: New file. * sysdeps/ieee754/ldbl-128ibm/e_sqrtl.c: New file. * sysdeps/ieee754/ldbl-128ibm/ieee754.h: New file. * sysdeps/ieee754/ldbl-128ibm/k_cosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/k_sincosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/k_sinl.c: New file. * sysdeps/ieee754/ldbl-128ibm/k_tanl.c: New file. * sysdeps/ieee754/ldbl-128ibm/ldbl2mpn.c: New file. * sysdeps/ieee754/ldbl-128ibm/math_ldbl.h: New file. * sysdeps/ieee754/ldbl-128ibm/mpn2ldbl.c: New file. * sysdeps/ieee754/ldbl-128ibm/printf_fphex.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_asinhl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_atanl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_cbrtl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_cosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_erfl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_expm1l.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_fabsl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_finitel.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_fpclassifyl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_frexpl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_ilogbl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_isinfl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_isnanl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_log1pl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_logbl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_modfl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_nextafterl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_nexttoward.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_nexttowardf.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_remquol.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_rintl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_scalblnl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_scalbnl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_signbitl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_sincosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_sinl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_tanhl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_tanl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_truncl.c: New file. * sysdeps/ieee754/ldbl-128ibm/strtold_l.c: New file. * sysdeps/ieee754/ldbl-128ibm/t_sincosl.c: New file. * sysdeps/ieee754/ldbl-128ibm/w_expl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_copysignl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_floorl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_llrintl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_llroundl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_roundl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_ceill.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_nearbyintl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_lrintl.c: New file. * sysdeps/ieee754/ldbl-128ibm/s_lroundl.c: New file. * sysdeps/ieee754/ldbl-128/e_powl.c: Fix old comment.
Diffstat (limited to 'sysdeps/ieee754/ldbl-128ibm/s_log1pl.c')
-rw-r--r--sysdeps/ieee754/ldbl-128ibm/s_log1pl.c257
1 files changed, 257 insertions, 0 deletions
diff --git a/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c b/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c
new file mode 100644
index 0000000..f1863fb
--- /dev/null
+++ b/sysdeps/ieee754/ldbl-128ibm/s_log1pl.c
@@ -0,0 +1,257 @@
+/* log1pl.c
+ *
+ * Relative error logarithm
+ * Natural logarithm of 1+x, 128-bit long double precision
+ *
+ *
+ *
+ * SYNOPSIS:
+ *
+ * long double x, y, log1pl();
+ *
+ * y = log1pl( x );
+ *
+ *
+ *
+ * DESCRIPTION:
+ *
+ * Returns the base e (2.718...) logarithm of 1+x.
+ *
+ * The argument 1+x is separated into its exponent and fractional
+ * parts. If the exponent is between -1 and +1, the logarithm
+ * of the fraction is approximated by
+ *
+ * log(1+x) = x - 0.5 x^2 + x^3 P(x)/Q(x).
+ *
+ * Otherwise, setting z = 2(w-1)/(w+1),
+ *
+ * log(w) = z + z^3 P(z)/Q(z).
+ *
+ *
+ *
+ * ACCURACY:
+ *
+ * Relative error:
+ * arithmetic domain # trials peak rms
+ * IEEE -1, 8 100000 1.9e-34 4.3e-35
+ */
+
+/* Copyright 2001 by Stephen L. Moshier
+
+ This library is free software; you can redistribute it and/or
+ modify it under the terms of the GNU Lesser General Public
+ License as published by the Free Software Foundation; either
+ version 2.1 of the License, or (at your option) any later version.
+
+ This library is distributed in the hope that it will be useful,
+ but WITHOUT ANY WARRANTY; without even the implied warranty of
+ MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ Lesser General Public License for more details.
+
+ You should have received a copy of the GNU Lesser General Public
+ License along with this library; if not, write to the Free Software
+ Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
+
+
+#include "math.h"
+#include "math_private.h"
+#include <math_ldbl_opt.h>
+
+/* Coefficients for log(1+x) = x - x^2 / 2 + x^3 P(x)/Q(x)
+ * 1/sqrt(2) <= 1+x < sqrt(2)
+ * Theoretical peak relative error = 5.3e-37,
+ * relative peak error spread = 2.3e-14
+ */
+static const long double
+ P12 = 1.538612243596254322971797716843006400388E-6L,
+ P11 = 4.998469661968096229986658302195402690910E-1L,
+ P10 = 2.321125933898420063925789532045674660756E1L,
+ P9 = 4.114517881637811823002128927449878962058E2L,
+ P8 = 3.824952356185897735160588078446136783779E3L,
+ P7 = 2.128857716871515081352991964243375186031E4L,
+ P6 = 7.594356839258970405033155585486712125861E4L,
+ P5 = 1.797628303815655343403735250238293741397E5L,
+ P4 = 2.854829159639697837788887080758954924001E5L,
+ P3 = 3.007007295140399532324943111654767187848E5L,
+ P2 = 2.014652742082537582487669938141683759923E5L,
+ P1 = 7.771154681358524243729929227226708890930E4L,
+ P0 = 1.313572404063446165910279910527789794488E4L,
+ /* Q12 = 1.000000000000000000000000000000000000000E0L, */
+ Q11 = 4.839208193348159620282142911143429644326E1L,
+ Q10 = 9.104928120962988414618126155557301584078E2L,
+ Q9 = 9.147150349299596453976674231612674085381E3L,
+ Q8 = 5.605842085972455027590989944010492125825E4L,
+ Q7 = 2.248234257620569139969141618556349415120E5L,
+ Q6 = 6.132189329546557743179177159925690841200E5L,
+ Q5 = 1.158019977462989115839826904108208787040E6L,
+ Q4 = 1.514882452993549494932585972882995548426E6L,
+ Q3 = 1.347518538384329112529391120390701166528E6L,
+ Q2 = 7.777690340007566932935753241556479363645E5L,
+ Q1 = 2.626900195321832660448791748036714883242E5L,
+ Q0 = 3.940717212190338497730839731583397586124E4L;
+
+/* Coefficients for log(x) = z + z^3 P(z^2)/Q(z^2),
+ * where z = 2(x-1)/(x+1)
+ * 1/sqrt(2) <= x < sqrt(2)
+ * Theoretical peak relative error = 1.1e-35,
+ * relative peak error spread 1.1e-9
+ */
+static const long double
+ R5 = -8.828896441624934385266096344596648080902E-1L,
+ R4 = 8.057002716646055371965756206836056074715E1L,
+ R3 = -2.024301798136027039250415126250455056397E3L,
+ R2 = 2.048819892795278657810231591630928516206E4L,
+ R1 = -8.977257995689735303686582344659576526998E4L,
+ R0 = 1.418134209872192732479751274970992665513E5L,
+ /* S6 = 1.000000000000000000000000000000000000000E0L, */
+ S5 = -1.186359407982897997337150403816839480438E2L,
+ S4 = 3.998526750980007367835804959888064681098E3L,
+ S3 = -5.748542087379434595104154610899551484314E4L,
+ S2 = 4.001557694070773974936904547424676279307E5L,
+ S1 = -1.332535117259762928288745111081235577029E6L,
+ S0 = 1.701761051846631278975701529965589676574E6L;
+
+/* C1 + C2 = ln 2 */
+static const long double C1 = 6.93145751953125E-1L;
+static const long double C2 = 1.428606820309417232121458176568075500134E-6L;
+
+static const long double sqrth = 0.7071067811865475244008443621048490392848L;
+/* ln (2^16384 * (1 - 2^-113)) */
+static const long double maxlog = 1.1356523406294143949491931077970764891253E4L;
+static const long double big = 2e300L;
+static const long double zero = 0.0L;
+
+#if 1
+/* Make sure these are prototyped. */
+long double frexpl (long double, int *);
+long double ldexpl (long double, int);
+#endif
+
+
+long double
+__log1pl (long double xm1)
+{
+ long double x, y, z, r, s;
+ ieee854_long_double_shape_type u;
+ int32_t hx;
+ int e;
+
+ /* Test for NaN or infinity input. */
+ u.value = xm1;
+ hx = u.parts32.w0;
+ if (hx >= 0x7ff00000)
+ return xm1;
+
+ /* log1p(+- 0) = +- 0. */
+ if (((hx & 0x7fffffff) == 0)
+ && (u.parts32.w1 | (u.parts32.w2 & 0x7fffffff) | u.parts32.w3) == 0)
+ return xm1;
+
+ x = xm1 + 1.0L;
+
+ /* log1p(-1) = -inf */
+ if (x <= 0.0L)
+ {
+ if (x == 0.0L)
+ return (-1.0L / (x - x));
+ else
+ return (zero / (x - x));
+ }
+
+ /* Separate mantissa from exponent. */
+
+ /* Use frexp used so that denormal numbers will be handled properly. */
+ x = frexpl (x, &e);
+
+ /* Logarithm using log(x) = z + z^3 P(z^2)/Q(z^2),
+ where z = 2(x-1)/x+1). */
+ if ((e > 2) || (e < -2))
+ {
+ if (x < sqrth)
+ { /* 2( 2x-1 )/( 2x+1 ) */
+ e -= 1;
+ z = x - 0.5L;
+ y = 0.5L * z + 0.5L;
+ }
+ else
+ { /* 2 (x-1)/(x+1) */
+ z = x - 0.5L;
+ z -= 0.5L;
+ y = 0.5L * x + 0.5L;
+ }
+ x = z / y;
+ z = x * x;
+ r = ((((R5 * z
+ + R4) * z
+ + R3) * z
+ + R2) * z
+ + R1) * z
+ + R0;
+ s = (((((z
+ + S5) * z
+ + S4) * z
+ + S3) * z
+ + S2) * z
+ + S1) * z
+ + S0;
+ z = x * (z * r / s);
+ z = z + e * C2;
+ z = z + x;
+ z = z + e * C1;
+ return (z);
+ }
+
+
+ /* Logarithm using log(1+x) = x - .5x^2 + x^3 P(x)/Q(x). */
+
+ if (x < sqrth)
+ {
+ e -= 1;
+ if (e != 0)
+ x = 2.0L * x - 1.0L; /* 2x - 1 */
+ else
+ x = xm1;
+ }
+ else
+ {
+ if (e != 0)
+ x = x - 1.0L;
+ else
+ x = xm1;
+ }
+ z = x * x;
+ r = (((((((((((P12 * x
+ + P11) * x
+ + P10) * x
+ + P9) * x
+ + P8) * x
+ + P7) * x
+ + P6) * x
+ + P5) * x
+ + P4) * x
+ + P3) * x
+ + P2) * x
+ + P1) * x
+ + P0;
+ s = (((((((((((x
+ + Q11) * x
+ + Q10) * x
+ + Q9) * x
+ + Q8) * x
+ + Q7) * x
+ + Q6) * x
+ + Q5) * x
+ + Q4) * x
+ + Q3) * x
+ + Q2) * x
+ + Q1) * x
+ + Q0;
+ y = x * (z * r / s);
+ y = y + e * C2;
+ z = y - 0.5L * z;
+ z = z + x;
+ z = z + e * C1;
+ return (z);
+}
+
+long_double_symbol (libm, __log1pl, log1pl);