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authorElliott Hughes <enh@google.com>2014-09-12 14:00:02 -0700
committerElliott Hughes <enh@google.com>2014-09-12 14:00:02 -0700
commit460ad7454a281470a1938103f099a1e3192fb3d6 (patch)
treea7427b2e2bde312e596fccd00af1c427667c915e /libm
parente39e47c6b377170d696c6b9b5b523a28c1382ca4 (diff)
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Sync libm with upstream.
Change-Id: I8ac8ee52122ee19a2e423c3211092023cb4896eb
Diffstat (limited to 'libm')
-rw-r--r--libm/Android.mk1
-rw-r--r--libm/upstream-freebsd/lib/msun/ld128/e_rem_pio2l.h18
-rw-r--r--libm/upstream-freebsd/lib/msun/ld128/invtrig.c4
-rw-r--r--libm/upstream-freebsd/lib/msun/ld128/k_cosl.c2
-rw-r--r--libm/upstream-freebsd/lib/msun/ld128/k_expl.h328
-rw-r--r--libm/upstream-freebsd/lib/msun/ld128/k_sinl.c2
-rw-r--r--libm/upstream-freebsd/lib/msun/ld128/s_erfl.c329
-rw-r--r--libm/upstream-freebsd/lib/msun/ld128/s_exp2l.c2
-rw-r--r--libm/upstream-freebsd/lib/msun/ld128/s_expl.c298
-rw-r--r--libm/upstream-freebsd/lib/msun/src/e_cosh.c6
-rw-r--r--libm/upstream-freebsd/lib/msun/src/e_lgamma_r.c64
-rw-r--r--libm/upstream-freebsd/lib/msun/src/e_lgammaf_r.c57
-rw-r--r--libm/upstream-freebsd/lib/msun/src/e_pow.c8
-rw-r--r--libm/upstream-freebsd/lib/msun/src/e_sinh.c6
-rw-r--r--libm/upstream-freebsd/lib/msun/src/imprecise.c2
-rw-r--r--libm/upstream-freebsd/lib/msun/src/s_erf.c64
-rw-r--r--libm/upstream-freebsd/lib/msun/src/s_erff.c127
-rw-r--r--libm/upstream-freebsd/lib/msun/src/s_rintl.c1
-rw-r--r--libm/upstream-freebsd/lib/msun/src/s_tanh.c9
-rw-r--r--libm/upstream-freebsd/lib/msun/src/s_tanhf.c4
20 files changed, 919 insertions, 413 deletions
diff --git a/libm/Android.mk b/libm/Android.mk
index f59b71f..7c0ff81 100644
--- a/libm/Android.mk
+++ b/libm/Android.mk
@@ -224,6 +224,7 @@ libm_ld_src_files += \
upstream-freebsd/lib/msun/ld128/k_cosl.c \
upstream-freebsd/lib/msun/ld128/k_sinl.c \
upstream-freebsd/lib/msun/ld128/k_tanl.c \
+ upstream-freebsd/lib/msun/ld128/s_erfl.c \
upstream-freebsd/lib/msun/ld128/s_exp2l.c \
upstream-freebsd/lib/msun/ld128/s_expl.c \
upstream-freebsd/lib/msun/ld128/s_logl.c \
diff --git a/libm/upstream-freebsd/lib/msun/ld128/e_rem_pio2l.h b/libm/upstream-freebsd/lib/msun/ld128/e_rem_pio2l.h
index 078d0c3..5d78c4d 100644
--- a/libm/upstream-freebsd/lib/msun/ld128/e_rem_pio2l.h
+++ b/libm/upstream-freebsd/lib/msun/ld128/e_rem_pio2l.h
@@ -6,7 +6,7 @@
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
+ * software is freely granted, provided that this notice
* is preserved.
* ====================================================
*
@@ -17,8 +17,8 @@
__FBSDID("$FreeBSD$");
/* ld128 version of __ieee754_rem_pio2l(x,y)
- *
- * return the remainder of x rem pi/2 in y[0]+y[1]
+ *
+ * return the remainder of x rem pi/2 in y[0]+y[1]
* use __kernel_rem_pio2()
*/
@@ -88,24 +88,24 @@ __ieee754_rem_pio2l(long double x, long double *y)
union IEEEl2bits u2;
int ex1;
j = ex;
- y[0] = r-w;
+ y[0] = r-w;
u2.e = y[0];
ex1 = u2.xbits.expsign & 0x7fff;
i = j-ex1;
if(i>51) { /* 2nd iteration needed, good to 248 */
t = r;
- w = fn*pio2_2;
+ w = fn*pio2_2;
r = t-w;
- w = fn*pio2_2t-((t-r)-w);
+ w = fn*pio2_2t-((t-r)-w);
y[0] = r-w;
u2.e = y[0];
ex1 = u2.xbits.expsign & 0x7fff;
i = j-ex1;
if(i>119) { /* 3rd iteration need, 316 bits acc */
t = r; /* will cover all possible cases */
- w = fn*pio2_3;
+ w = fn*pio2_3;
r = t-w;
- w = fn*pio2_3t-((t-r)-w);
+ w = fn*pio2_3t-((t-r)-w);
y[0] = r-w;
}
}
@@ -113,7 +113,7 @@ __ieee754_rem_pio2l(long double x, long double *y)
y[1] = (r-y[0])-w;
return n;
}
- /*
+ /*
* all other (large) arguments
*/
if(ex==0x7fff) { /* x is inf or NaN */
diff --git a/libm/upstream-freebsd/lib/msun/ld128/invtrig.c b/libm/upstream-freebsd/lib/msun/ld128/invtrig.c
index df67d16..4ceca8a 100644
--- a/libm/upstream-freebsd/lib/msun/ld128/invtrig.c
+++ b/libm/upstream-freebsd/lib/msun/ld128/invtrig.c
@@ -58,8 +58,8 @@ qS9 = -1.99407384882605586705979504567947007e-04L;
*/
const long double atanhi[] = {
4.63647609000806116214256231461214397e-01L,
- 7.85398163397448309615660845819875699e-01L,
- 9.82793723247329067985710611014666038e-01L,
+ 7.85398163397448309615660845819875699e-01L,
+ 9.82793723247329067985710611014666038e-01L,
1.57079632679489661923132169163975140e+00L,
};
diff --git a/libm/upstream-freebsd/lib/msun/ld128/k_cosl.c b/libm/upstream-freebsd/lib/msun/ld128/k_cosl.c
index 5f4aa37..fe57773 100644
--- a/libm/upstream-freebsd/lib/msun/ld128/k_cosl.c
+++ b/libm/upstream-freebsd/lib/msun/ld128/k_cosl.c
@@ -6,7 +6,7 @@
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
+ * software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
diff --git a/libm/upstream-freebsd/lib/msun/ld128/k_expl.h b/libm/upstream-freebsd/lib/msun/ld128/k_expl.h
new file mode 100644
index 0000000..a5668fd
--- /dev/null
+++ b/libm/upstream-freebsd/lib/msun/ld128/k_expl.h
@@ -0,0 +1,328 @@
+/* from: FreeBSD: head/lib/msun/ld128/s_expl.c 251345 2013-06-03 20:09:22Z kargl */
+
+/*-
+ * Copyright (c) 2009-2013 Steven G. Kargl
+ * All rights reserved.
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ * 1. Redistributions of source code must retain the above copyright
+ * notice unmodified, this list of conditions, and the following
+ * disclaimer.
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in the
+ * documentation and/or other materials provided with the distribution.
+ *
+ * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
+ * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
+ * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
+ * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
+ * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
+ * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+ * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+ * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+ * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
+ * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+ *
+ * Optimized by Bruce D. Evans.
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * ld128 version of k_expl.h. See ../ld80/s_expl.c for most comments.
+ *
+ * See ../src/e_exp.c and ../src/k_exp.h for precision-independent comments
+ * about the secondary kernels.
+ */
+
+#define INTERVALS 128
+#define LOG2_INTERVALS 7
+#define BIAS (LDBL_MAX_EXP - 1)
+
+static const double
+/*
+ * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must
+ * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest
+ * bits zero so that multiplication of it by n is exact.
+ */
+INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
+L2 = -1.0253670638894731e-29; /* -0x1.9ff0342542fc3p-97 */
+static const long double
+/* 0x1.62e42fefa39ef35793c768000000p-8 */
+L1 = 5.41521234812457272982212595914567508e-3L;
+
+/*
+ * XXX values in hex in comments have been lost (or were never present)
+ * from here.
+ */
+static const long double
+/*
+ * Domain [-0.002708, 0.002708], range ~[-2.4021e-38, 2.4234e-38]:
+ * |exp(x) - p(x)| < 2**-124.9
+ * (0.002708 is ln2/(2*INTERVALS) rounded up a little).
+ *
+ * XXX the coeffs aren't very carefully rounded, and I get 3.6 more bits.
+ */
+A2 = 0.5,
+A3 = 1.66666666666666666666666666651085500e-1L,
+A4 = 4.16666666666666666666666666425885320e-2L,
+A5 = 8.33333333333333333334522877160175842e-3L,
+A6 = 1.38888888888888888889971139751596836e-3L;
+
+static const double
+A7 = 1.9841269841269470e-4, /* 0x1.a01a01a019f91p-13 */
+A8 = 2.4801587301585286e-5, /* 0x1.71de3ec75a967p-19 */
+A9 = 2.7557324277411235e-6, /* 0x1.71de3ec75a967p-19 */
+A10 = 2.7557333722375069e-7; /* 0x1.27e505ab56259p-22 */
+
+static const struct {
+ /*
+ * hi must be rounded to at most 106 bits so that multiplication
+ * by r1 in expm1l() is exact, but it is rounded to 88 bits due to
+ * historical accidents.
+ *
+ * XXX it is wasteful to use long double for both hi and lo. ld128
+ * exp2l() uses only float for lo (in a very differently organized
+ * table; ld80 exp2l() is different again. It uses 2 doubles in a
+ * table organized like this one. 1 double and 1 float would
+ * suffice). There are different packing/locality/alignment/caching
+ * problems with these methods.
+ *
+ * XXX C's bad %a format makes the bits unreadable. They happen
+ * to all line up for the hi values 1 before the point and 88
+ * in 22 nybbles, but for the low values the nybbles are shifted
+ * randomly.
+ */
+ long double hi;
+ long double lo;
+} tbl[INTERVALS] = {
+ 0x1p0L, 0x0p0L,
+ 0x1.0163da9fb33356d84a66aep0L, 0x3.36dcdfa4003ec04c360be2404078p-92L,
+ 0x1.02c9a3e778060ee6f7cacap0L, 0x4.f7a29bde93d70a2cabc5cb89ba10p-92L,
+ 0x1.04315e86e7f84bd738f9a2p0L, 0xd.a47e6ed040bb4bfc05af6455e9b8p-96L,
+ 0x1.059b0d31585743ae7c548ep0L, 0xb.68ca417fe53e3495f7df4baf84a0p-92L,
+ 0x1.0706b29ddf6ddc6dc403a8p0L, 0x1.d87b27ed07cb8b092ac75e311753p-88L,
+ 0x1.0874518759bc808c35f25cp0L, 0x1.9427fa2b041b2d6829d8993a0d01p-88L,
+ 0x1.09e3ecac6f3834521e060cp0L, 0x5.84d6b74ba2e023da730e7fccb758p-92L,
+ 0x1.0b5586cf9890f6298b92b6p0L, 0x1.1842a98364291408b3ceb0a2a2bbp-88L,
+ 0x1.0cc922b7247f7407b705b8p0L, 0x9.3dc5e8aac564e6fe2ef1d431fd98p-92L,
+ 0x1.0e3ec32d3d1a2020742e4ep0L, 0x1.8af6a552ac4b358b1129e9f966a4p-88L,
+ 0x1.0fb66affed31af232091dcp0L, 0x1.8a1426514e0b627bda694a400a27p-88L,
+ 0x1.11301d0125b50a4ebbf1aep0L, 0xd.9318ceac5cc47ab166ee57427178p-92L,
+ 0x1.12abdc06c31cbfb92bad32p0L, 0x4.d68e2f7270bdf7cedf94eb1cb818p-92L,
+ 0x1.1429aaea92ddfb34101942p0L, 0x1.b2586d01844b389bea7aedd221d4p-88L,
+ 0x1.15a98c8a58e512480d573cp0L, 0x1.d5613bf92a2b618ee31b376c2689p-88L,
+ 0x1.172b83c7d517adcdf7c8c4p0L, 0x1.0eb14a792035509ff7d758693f24p-88L,
+ 0x1.18af9388c8de9bbbf70b9ap0L, 0x3.c2505c97c0102e5f1211941d2840p-92L,
+ 0x1.1a35beb6fcb753cb698f68p0L, 0x1.2d1c835a6c30724d5cfae31b84e5p-88L,
+ 0x1.1bbe084045cd39ab1e72b4p0L, 0x4.27e35f9acb57e473915519a1b448p-92L,
+ 0x1.1d4873168b9aa7805b8028p0L, 0x9.90f07a98b42206e46166cf051d70p-92L,
+ 0x1.1ed5022fcd91cb8819ff60p0L, 0x1.121d1e504d36c47474c9b7de6067p-88L,
+ 0x1.2063b88628cd63b8eeb028p0L, 0x1.50929d0fc487d21c2b84004264dep-88L,
+ 0x1.21f49917ddc962552fd292p0L, 0x9.4bdb4b61ea62477caa1dce823ba0p-92L,
+ 0x1.2387a6e75623866c1fadb0p0L, 0x1.c15cb593b0328566902df69e4de2p-88L,
+ 0x1.251ce4fb2a63f3582ab7dep0L, 0x9.e94811a9c8afdcf796934bc652d0p-92L,
+ 0x1.26b4565e27cdd257a67328p0L, 0x1.d3b249dce4e9186ddd5ff44e6b08p-92L,
+ 0x1.284dfe1f5638096cf15cf0p0L, 0x3.ca0967fdaa2e52d7c8106f2e262cp-92L,
+ 0x1.29e9df51fdee12c25d15f4p0L, 0x1.a24aa3bca890ac08d203fed80a07p-88L,
+ 0x1.2b87fd0dad98ffddea4652p0L, 0x1.8fcab88442fdc3cb6de4519165edp-88L,
+ 0x1.2d285a6e4030b40091d536p0L, 0xd.075384589c1cd1b3e4018a6b1348p-92L,
+ 0x1.2ecafa93e2f5611ca0f45cp0L, 0x1.523833af611bdcda253c554cf278p-88L,
+ 0x1.306fe0a31b7152de8d5a46p0L, 0x3.05c85edecbc27343629f502f1af2p-92L,
+ 0x1.32170fc4cd8313539cf1c2p0L, 0x1.008f86dde3220ae17a005b6412bep-88L,
+ 0x1.33c08b26416ff4c9c8610cp0L, 0x1.96696bf95d1593039539d94d662bp-88L,
+ 0x1.356c55f929ff0c94623476p0L, 0x3.73af38d6d8d6f9506c9bbc93cbc0p-92L,
+ 0x1.371a7373aa9caa7145502ep0L, 0x1.4547987e3e12516bf9c699be432fp-88L,
+ 0x1.38cae6d05d86585a9cb0d8p0L, 0x1.bed0c853bd30a02790931eb2e8f0p-88L,
+ 0x1.3a7db34e59ff6ea1bc9298p0L, 0x1.e0a1d336163fe2f852ceeb134067p-88L,
+ 0x1.3c32dc313a8e484001f228p0L, 0xb.58f3775e06ab66353001fae9fca0p-92L,
+ 0x1.3dea64c12342235b41223ep0L, 0x1.3d773fba2cb82b8244267c54443fp-92L,
+ 0x1.3fa4504ac801ba0bf701aap0L, 0x4.1832fb8c1c8dbdff2c49909e6c60p-92L,
+ 0x1.4160a21f72e29f84325b8ep0L, 0x1.3db61fb352f0540e6ba05634413ep-88L,
+ 0x1.431f5d950a896dc7044394p0L, 0x1.0ccec81e24b0caff7581ef4127f7p-92L,
+ 0x1.44e086061892d03136f408p0L, 0x1.df019fbd4f3b48709b78591d5cb5p-88L,
+ 0x1.46a41ed1d005772512f458p0L, 0x1.229d97df404ff21f39c1b594d3a8p-88L,
+ 0x1.486a2b5c13cd013c1a3b68p0L, 0x1.062f03c3dd75ce8757f780e6ec99p-88L,
+ 0x1.4a32af0d7d3de672d8bcf4p0L, 0x6.f9586461db1d878b1d148bd3ccb8p-92L,
+ 0x1.4bfdad5362a271d4397afep0L, 0xc.42e20e0363ba2e159c579f82e4b0p-92L,
+ 0x1.4dcb299fddd0d63b36ef1ap0L, 0x9.e0cc484b25a5566d0bd5f58ad238p-92L,
+ 0x1.4f9b2769d2ca6ad33d8b68p0L, 0x1.aa073ee55e028497a329a7333dbap-88L,
+ 0x1.516daa2cf6641c112f52c8p0L, 0x4.d822190e718226177d7608d20038p-92L,
+ 0x1.5342b569d4f81df0a83c48p0L, 0x1.d86a63f4e672a3e429805b049465p-88L,
+ 0x1.551a4ca5d920ec52ec6202p0L, 0x4.34ca672645dc6c124d6619a87574p-92L,
+ 0x1.56f4736b527da66ecb0046p0L, 0x1.64eb3c00f2f5ab3d801d7cc7272dp-88L,
+ 0x1.58d12d497c7fd252bc2b72p0L, 0x1.43bcf2ec936a970d9cc266f0072fp-88L,
+ 0x1.5ab07dd48542958c930150p0L, 0x1.91eb345d88d7c81280e069fbdb63p-88L,
+ 0x1.5c9268a5946b701c4b1b80p0L, 0x1.6986a203d84e6a4a92f179e71889p-88L,
+ 0x1.5e76f15ad21486e9be4c20p0L, 0x3.99766a06548a05829e853bdb2b52p-92L,
+ 0x1.605e1b976dc08b076f592ap0L, 0x4.86e3b34ead1b4769df867b9c89ccp-92L,
+ 0x1.6247eb03a5584b1f0fa06ep0L, 0x1.d2da42bb1ceaf9f732275b8aef30p-88L,
+ 0x1.6434634ccc31fc76f8714cp0L, 0x4.ed9a4e41000307103a18cf7a6e08p-92L,
+ 0x1.66238825522249127d9e28p0L, 0x1.b8f314a337f4dc0a3adf1787ff74p-88L,
+ 0x1.68155d44ca973081c57226p0L, 0x1.b9f32706bfe4e627d809a85dcc66p-88L,
+ 0x1.6a09e667f3bcc908b2fb12p0L, 0x1.66ea957d3e3adec17512775099dap-88L,
+ 0x1.6c012750bdabeed76a9980p0L, 0xf.4f33fdeb8b0ecd831106f57b3d00p-96L,
+ 0x1.6dfb23c651a2ef220e2cbep0L, 0x1.bbaa834b3f11577ceefbe6c1c411p-92L,
+ 0x1.6ff7df9519483cf87e1b4ep0L, 0x1.3e213bff9b702d5aa477c12523cep-88L,
+ 0x1.71f75e8ec5f73dd2370f2ep0L, 0xf.0acd6cb434b562d9e8a20adda648p-92L,
+ 0x1.73f9a48a58173bd5c9a4e6p0L, 0x8.ab1182ae217f3a7681759553e840p-92L,
+ 0x1.75feb564267c8bf6e9aa32p0L, 0x1.a48b27071805e61a17b954a2dad8p-88L,
+ 0x1.780694fde5d3f619ae0280p0L, 0x8.58b2bb2bdcf86cd08e35fb04c0f0p-92L,
+ 0x1.7a11473eb0186d7d51023ep0L, 0x1.6cda1f5ef42b66977960531e821bp-88L,
+ 0x1.7c1ed0130c1327c4933444p0L, 0x1.937562b2dc933d44fc828efd4c9cp-88L,
+ 0x1.7e2f336cf4e62105d02ba0p0L, 0x1.5797e170a1427f8fcdf5f3906108p-88L,
+ 0x1.80427543e1a11b60de6764p0L, 0x9.a354ea706b8e4d8b718a672bf7c8p-92L,
+ 0x1.82589994cce128acf88afap0L, 0xb.34a010f6ad65cbbac0f532d39be0p-92L,
+ 0x1.8471a4623c7acce52f6b96p0L, 0x1.c64095370f51f48817914dd78665p-88L,
+ 0x1.868d99b4492ec80e41d90ap0L, 0xc.251707484d73f136fb5779656b70p-92L,
+ 0x1.88ac7d98a669966530bcdep0L, 0x1.2d4e9d61283ef385de170ab20f96p-88L,
+ 0x1.8ace5422aa0db5ba7c55a0p0L, 0x1.92c9bb3e6ed61f2733304a346d8fp-88L,
+ 0x1.8cf3216b5448bef2aa1cd0p0L, 0x1.61c55d84a9848f8c453b3ca8c946p-88L,
+ 0x1.8f1ae991577362b982745cp0L, 0x7.2ed804efc9b4ae1458ae946099d4p-92L,
+ 0x1.9145b0b91ffc588a61b468p0L, 0x1.f6b70e01c2a90229a4c4309ea719p-88L,
+ 0x1.93737b0cdc5e4f4501c3f2p0L, 0x5.40a22d2fc4af581b63e8326efe9cp-92L,
+ 0x1.95a44cbc8520ee9b483694p0L, 0x1.a0fc6f7c7d61b2b3a22a0eab2cadp-88L,
+ 0x1.97d829fde4e4f8b9e920f8p0L, 0x1.1e8bd7edb9d7144b6f6818084cc7p-88L,
+ 0x1.9a0f170ca07b9ba3109b8cp0L, 0x4.6737beb19e1eada6825d3c557428p-92L,
+ 0x1.9c49182a3f0901c7c46b06p0L, 0x1.1f2be58ddade50c217186c90b457p-88L,
+ 0x1.9e86319e323231824ca78ep0L, 0x6.4c6e010f92c082bbadfaf605cfd4p-92L,
+ 0x1.a0c667b5de564b29ada8b8p0L, 0xc.ab349aa0422a8da7d4512edac548p-92L,
+ 0x1.a309bec4a2d3358c171f76p0L, 0x1.0daad547fa22c26d168ea762d854p-88L,
+ 0x1.a5503b23e255c8b424491cp0L, 0xa.f87bc8050a405381703ef7caff50p-92L,
+ 0x1.a799e1330b3586f2dfb2b0p0L, 0x1.58f1a98796ce8908ae852236ca94p-88L,
+ 0x1.a9e6b5579fdbf43eb243bcp0L, 0x1.ff4c4c58b571cf465caf07b4b9f5p-88L,
+ 0x1.ac36bbfd3f379c0db966a2p0L, 0x1.1265fc73e480712d20f8597a8e7bp-88L,
+ 0x1.ae89f995ad3ad5e8734d16p0L, 0x1.73205a7fbc3ae675ea440b162d6cp-88L,
+ 0x1.b0e07298db66590842acdep0L, 0x1.c6f6ca0e5dcae2aafffa7a0554cbp-88L,
+ 0x1.b33a2b84f15faf6bfd0e7ap0L, 0x1.d947c2575781dbb49b1237c87b6ep-88L,
+ 0x1.b59728de559398e3881110p0L, 0x1.64873c7171fefc410416be0a6525p-88L,
+ 0x1.b7f76f2fb5e46eaa7b081ap0L, 0xb.53c5354c8903c356e4b625aacc28p-92L,
+ 0x1.ba5b030a10649840cb3c6ap0L, 0xf.5b47f297203757e1cc6eadc8bad0p-92L,
+ 0x1.bcc1e904bc1d2247ba0f44p0L, 0x1.b3d08cd0b20287092bd59be4ad98p-88L,
+ 0x1.bf2c25bd71e088408d7024p0L, 0x1.18e3449fa073b356766dfb568ff4p-88L,
+ 0x1.c199bdd85529c2220cb12ap0L, 0x9.1ba6679444964a36661240043970p-96L,
+ 0x1.c40ab5fffd07a6d14df820p0L, 0xf.1828a5366fd387a7bdd54cdf7300p-92L,
+ 0x1.c67f12e57d14b4a2137fd2p0L, 0xf.2b301dd9e6b151a6d1f9d5d5f520p-96L,
+ 0x1.c8f6d9406e7b511acbc488p0L, 0x5.c442ddb55820171f319d9e5076a8p-96L,
+ 0x1.cb720dcef90691503cbd1ep0L, 0x9.49db761d9559ac0cb6dd3ed599e0p-92L,
+ 0x1.cdf0b555dc3f9c44f8958ep0L, 0x1.ac51be515f8c58bdfb6f5740a3a4p-88L,
+ 0x1.d072d4a07897b8d0f22f20p0L, 0x1.a158e18fbbfc625f09f4cca40874p-88L,
+ 0x1.d2f87080d89f18ade12398p0L, 0x9.ea2025b4c56553f5cdee4c924728p-92L,
+ 0x1.d5818dcfba48725da05aeap0L, 0x1.66e0dca9f589f559c0876ff23830p-88L,
+ 0x1.d80e316c98397bb84f9d04p0L, 0x8.805f84bec614de269900ddf98d28p-92L,
+ 0x1.da9e603db3285708c01a5ap0L, 0x1.6d4c97f6246f0ec614ec95c99392p-88L,
+ 0x1.dd321f301b4604b695de3cp0L, 0x6.30a393215299e30d4fb73503c348p-96L,
+ 0x1.dfc97337b9b5eb968cac38p0L, 0x1.ed291b7225a944efd5bb5524b927p-88L,
+ 0x1.e264614f5a128a12761fa0p0L, 0x1.7ada6467e77f73bf65e04c95e29dp-88L,
+ 0x1.e502ee78b3ff6273d13014p0L, 0x1.3991e8f49659e1693be17ae1d2f9p-88L,
+ 0x1.e7a51fbc74c834b548b282p0L, 0x1.23786758a84f4956354634a416cep-88L,
+ 0x1.ea4afa2a490d9858f73a18p0L, 0xf.5db301f86dea20610ceee13eb7b8p-92L,
+ 0x1.ecf482d8e67f08db0312fap0L, 0x1.949cef462010bb4bc4ce72a900dfp-88L,
+ 0x1.efa1bee615a27771fd21a8p0L, 0x1.2dac1f6dd5d229ff68e46f27e3dfp-88L,
+ 0x1.f252b376bba974e8696fc2p0L, 0x1.6390d4c6ad5476b5162f40e1d9a9p-88L,
+ 0x1.f50765b6e4540674f84b76p0L, 0x2.862baff99000dfc4352ba29b8908p-92L,
+ 0x1.f7bfdad9cbe138913b4bfep0L, 0x7.2bd95c5ce7280fa4d2344a3f5618p-92L,
+ 0x1.fa7c1819e90d82e90a7e74p0L, 0xb.263c1dc060c36f7650b4c0f233a8p-92L,
+ 0x1.fd3c22b8f71f10975ba4b2p0L, 0x1.2bcf3a5e12d269d8ad7c1a4a8875p-88L
+};
+
+/*
+ * Kernel for expl(x). x must be finite and not tiny or huge.
+ * "tiny" is anything that would make us underflow (|A6*x^6| < ~LDBL_MIN).
+ * "huge" is anything that would make fn*L1 inexact (|x| > ~2**17*ln2).
+ */
+static inline void
+__k_expl(long double x, long double *hip, long double *lop, int *kp)
+{
+ long double q, r, r1, t;
+ double dr, fn, r2;
+ int n, n2;
+
+ /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
+ /* Use a specialized rint() to get fn. Assume round-to-nearest. */
+ /* XXX assume no extra precision for the additions, as for trig fns. */
+ /* XXX this set of comments is now quadruplicated. */
+ /* XXX but see ../src/e_exp.c for a fix using double_t. */
+ fn = (double)x * INV_L + 0x1.8p52 - 0x1.8p52;
+#if defined(HAVE_EFFICIENT_IRINT)
+ n = irint(fn);
+#else
+ n = (int)fn;
+#endif
+ n2 = (unsigned)n % INTERVALS;
+ /* Depend on the sign bit being propagated: */
+ *kp = n >> LOG2_INTERVALS;
+ r1 = x - fn * L1;
+ r2 = fn * -L2;
+ r = r1 + r2;
+
+ /* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */
+ dr = r;
+ q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 +
+ dr * (A7 + dr * (A8 + dr * (A9 + dr * A10))))))));
+ t = tbl[n2].lo + tbl[n2].hi;
+ *hip = tbl[n2].hi;
+ *lop = tbl[n2].lo + t * (q + r1);
+}
+
+/*
+ * XXX: the rest of the functions are identical for ld80 and ld128.
+ * However, we should use scalbnl() for ld128, since long double
+ * multiplication is very slow on the only supported ld128 arch (sparc64).
+ */
+
+static inline void
+k_hexpl(long double x, long double *hip, long double *lop)
+{
+ float twopkm1;
+ int k;
+
+ __k_expl(x, hip, lop, &k);
+ SET_FLOAT_WORD(twopkm1, 0x3f800000 + ((k - 1) << 23));
+ *hip *= twopkm1;
+ *lop *= twopkm1;
+}
+
+static inline long double
+hexpl(long double x)
+{
+ long double hi, lo, twopkm2;
+ int k;
+
+ twopkm2 = 1;
+ __k_expl(x, &hi, &lo, &k);
+ SET_LDBL_EXPSIGN(twopkm2, BIAS + k - 2);
+ return (lo + hi) * 2 * twopkm2;
+}
+
+#ifdef _COMPLEX_H
+/*
+ * See ../src/k_exp.c for details.
+ */
+static inline long double complex
+__ldexp_cexpl(long double complex z, int expt)
+{
+ long double exp_x, hi, lo;
+ long double x, y, scale1, scale2;
+ int half_expt, k;
+
+ x = creall(z);
+ y = cimagl(z);
+ __k_expl(x, &hi, &lo, &k);
+
+ exp_x = (lo + hi) * 0x1p16382;
+ expt += k - 16382;
+
+ scale1 = 1;
+ half_expt = expt / 2;
+ SET_LDBL_EXPSIGN(scale1, BIAS + half_expt);
+ scale2 = 1;
+ SET_LDBL_EXPSIGN(scale1, BIAS + expt - half_expt);
+
+ return (cpackl(cos(y) * exp_x * scale1 * scale2,
+ sinl(y) * exp_x * scale1 * scale2));
+}
+#endif /* _COMPLEX_H */
diff --git a/libm/upstream-freebsd/lib/msun/ld128/k_sinl.c b/libm/upstream-freebsd/lib/msun/ld128/k_sinl.c
index bd415c0..09472d6 100644
--- a/libm/upstream-freebsd/lib/msun/ld128/k_sinl.c
+++ b/libm/upstream-freebsd/lib/msun/ld128/k_sinl.c
@@ -6,7 +6,7 @@
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
- * software is freely granted, provided that this notice
+ * software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/
diff --git a/libm/upstream-freebsd/lib/msun/ld128/s_erfl.c b/libm/upstream-freebsd/lib/msun/ld128/s_erfl.c
new file mode 100644
index 0000000..e29c969
--- /dev/null
+++ b/libm/upstream-freebsd/lib/msun/ld128/s_erfl.c
@@ -0,0 +1,329 @@
+/* @(#)s_erf.c 5.1 93/09/24 */
+/*
+ * ====================================================
+ * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
+ *
+ * Developed at SunPro, a Sun Microsystems, Inc. business.
+ * Permission to use, copy, modify, and distribute this
+ * software is freely granted, provided that this notice
+ * is preserved.
+ * ====================================================
+ */
+
+#include <sys/cdefs.h>
+__FBSDID("$FreeBSD$");
+
+/*
+ * See s_erf.c for complete comments.
+ *
+ * Converted to long double by Steven G. Kargl.
+ */
+#include <float.h>
+
+#include "fpmath.h"
+#include "math.h"
+#include "math_private.h"
+
+/* XXX Prevent compilers from erroneously constant folding these: */
+static const volatile long double tiny = 0x1p-10000L;
+
+static const double
+half= 0.5,
+one = 1,
+two = 2;
+/*
+ * In the domain [0, 2**-40], only the first term in the power series
+ * expansion of erf(x) is used. The magnitude of the first neglected
+ * terms is less than 2**-120.
+ */
+static const long double
+efx = 1.28379167095512573896158903121545167e-01L, /* 0xecbff6a7, 0x481dd788, 0xb64d21a8, 0xeb06fc3f */
+efx8 = 1.02703333676410059116927122497236133e+00L, /* 0xecbff6a7, 0x481dd788, 0xb64d21a8, 0xeb06ff3f */
+/*
+ * Domain [0, 0.84375], range ~[-1.919e-38, 1.919e-38]:
+ * |(erf(x) - x)/x - pp(x)/qq(x)| < 2**-125.29
+ */
+pp0 = 1.28379167095512573896158903121545167e-01L, /* 0x3ffc06eb, 0xa8214db6, 0x88d71d48, 0xa7f6bfec */
+pp1 = -3.14931554396568573802046931159683404e-01L, /* 0xbffd427d, 0x6ada7263, 0x547eb096, 0x95f37463 */
+pp2 = -5.27514920282183487103576956956725309e-02L, /* 0xbffab023, 0xe5a271e3, 0xb0e79b01, 0x2f7ac962 */
+pp3 = -1.13202828509005281355609495523452713e-02L, /* 0xbff872f1, 0x6a5023a1, 0xe08b3884, 0x326af20f */
+pp4 = -9.18626155872522453865998391206048506e-04L, /* 0xbff4e19f, 0xea5fb024, 0x43247a37, 0xe430b06c */
+pp5 = -7.87518862406176274922506447157284230e-05L, /* 0xbff14a4f, 0x31a85fe0, 0x7fff2204, 0x09c49b37 */
+pp6 = -3.42357944472240436548115331090560881e-06L, /* 0xbfeccb81, 0x4b43c336, 0xcd2eb6c2, 0x903f2d87 */
+pp7 = -1.37317432573890412634717890726745428e-07L, /* 0xbfe826e3, 0x0e915eb6, 0x42aee414, 0xf7e36805 */
+pp8 = -2.71115170113861755855049008732113726e-09L, /* 0xbfe2749e, 0x2b94fd00, 0xecb4d166, 0x0efb91f8 */
+pp9 = -3.37925756196555959454018189718117864e-11L, /* 0xbfdc293e, 0x1d9060cb, 0xd043204a, 0x314cd7f0 */
+qq1 = 4.76672625471551170489978555182449450e-01L, /* 0x3ffde81c, 0xde6531f0, 0x76803bee, 0x526e29e9 */
+qq2 = 1.06713144672281502058807525850732240e-01L, /* 0x3ffbb518, 0xd7a6bb74, 0xcd9bdd33, 0x7601eee5 */
+qq3 = 1.47747613127513761102189201923147490e-02L, /* 0x3ff8e423, 0xae527e18, 0xf12cb447, 0x723b4749 */
+qq4 = 1.39939377672028671891148770908874816e-03L, /* 0x3ff56ed7, 0xba055d84, 0xc21b45c4, 0x388d1812 */
+qq5 = 9.44302939359455241271983309378738276e-05L, /* 0x3ff18c11, 0xc18c99a4, 0x86d0fe09, 0x46387b4c */
+qq6 = 4.56199342312522842161301671745365650e-06L, /* 0x3fed3226, 0x73421d05, 0x08875300, 0x32fa1432 */
+qq7 = 1.53019260483764773845294600092361197e-07L, /* 0x3fe8489b, 0x3a63f627, 0x2b9ad2ce, 0x26516e57 */
+qq8 = 3.25542691121324805094777901250005508e-09L, /* 0x3fe2bf6c, 0x26d93a29, 0x9142be7c, 0x9f1dd043 */
+qq9 = 3.37405581964478060434410167262684979e-11L; /* 0x3fdc28c8, 0xfb8fa1be, 0x10e57eec, 0xaa19e49f */
+
+static const long double
+erx = 8.42700792949714894142232424201210961e-01L, /* 0x3ffeaf76, 0x7a741088, 0xb0000000, 0x00000000 */
+/*
+ * Domain [0.84375, 1.25], range ~[-2.521e-36, 2.523e-36]:
+ * |(erf(x) - erx) - pa(x)/qa(x)| < 2**-120.15
+ */
+pa0 = -2.48010117891186017024438233323795897e-17L, /* 0xbfc7c97f, 0x77812279, 0x6c877f22, 0xef4bfb2e */
+pa1 = 4.15107497420594680894327969504526489e-01L, /* 0x3ffda911, 0xf096fbc2, 0x55662005, 0x2337fa64 */
+pa2 = -3.94180628087084846724448515851892609e-02L, /* 0xbffa42e9, 0xab54528c, 0xad529da1, 0x6efc2af3 */
+pa3 = 4.48897599625192107295954790681677462e-02L, /* 0x3ffa6fbc, 0xa65edba1, 0x0e4cbcea, 0x73ef9a31 */
+pa4 = 8.02069252143016600110972019232995528e-02L, /* 0x3ffb4887, 0x0e8b548e, 0x3230b417, 0x11b553b3 */
+pa5 = -1.02729816533435279443621120242391295e-02L, /* 0xbff850a0, 0x041de3ee, 0xd5bca6c9, 0x4ef5f9f2 */
+pa6 = 5.70777694530755634864821094419982095e-03L, /* 0x3ff77610, 0x9b501e10, 0x4c978382, 0x742df68f */
+pa7 = 1.22635150233075521018231779267077071e-03L, /* 0x3ff5417b, 0x0e623682, 0x60327da0, 0x96b9219e */
+pa8 = 5.36100234820204569428412542856666503e-04L, /* 0x3ff41912, 0x27ceb4c1, 0x1d3298ec, 0x84ced627 */
+pa9 = -1.97753571846365167177187858667583165e-04L, /* 0xbff29eb8, 0x23f5bcf3, 0x15c83c46, 0xe4fda98b */
+pa10 = 6.19333039900846970674794789568415105e-05L, /* 0x3ff103c4, 0x60f88e46, 0xc0c9fb02, 0x13cc7fc1 */
+pa11 = -5.40531400436645861492290270311751349e-06L, /* 0xbfed6abe, 0x9665f8a8, 0xdd0ad3ba, 0xe5dc0ee3 */
+qa1 = 9.05041313265490487793231810291907851e-01L, /* 0x3ffecf61, 0x93340222, 0xe9930620, 0xc4e61168 */
+qa2 = 6.79848064708886864767240880834868092e-01L, /* 0x3ffe5c15, 0x0ba858dc, 0xf7900ae9, 0xfea1e09a */
+qa3 = 4.04720609926471677581066689316516445e-01L, /* 0x3ffd9e6f, 0x145e9b00, 0x6d8c1749, 0xd2928623 */
+qa4 = 1.69183273898369996364661075664302225e-01L, /* 0x3ffc5a7c, 0xc2a363c1, 0xd6c19097, 0xef9b4063 */
+qa5 = 7.44476185988067992342479750486764248e-02L, /* 0x3ffb30ef, 0xfc7259ef, 0x1bcbb089, 0x686dd62d */
+qa6 = 2.02981172725892407200420389604788573e-02L, /* 0x3ff94c90, 0x7976cb0e, 0x21e1d36b, 0x0f09ca2b */
+qa7 = 6.94281866271607668268269403102277234e-03L, /* 0x3ff7c701, 0x2b193250, 0xc5d46ecc, 0x374843d8 */
+qa8 = 1.12952275469171559611651594706820034e-03L, /* 0x3ff52818, 0xfd2a7c06, 0xd13e38fd, 0xda4b34f5 */
+qa9 = 3.13736683241992737197226578597710179e-04L, /* 0x3ff348fa, 0x0cb48d18, 0x051f849b, 0x135ccf74 */
+qa10 = 1.17037675204033225470121134087771410e-05L, /* 0x3fee88b6, 0x98f47704, 0xa5d8f8f2, 0xc6422e11 */
+qa11 = 4.61312518293853991439362806880973592e-06L, /* 0x3fed3594, 0xe31db94f, 0x3592b693, 0xed4386b4 */
+qa12 = -1.02158572037456893687737553657431771e-06L; /* 0xbfeb123a, 0xd60d9b1e, 0x1f6fdeb9, 0x7dc8410a */
+/*
+ * Domain [1.25,2.85715], range ~[-2.922e-37,2.922e-37]:
+ * |log(x*erfc(x)) + x**2 + 0.5625 - ra(x)/sa(x)| < 2**-121.36
+ */
+static const long double
+ra0 = -9.86494292470069009555706994426014461e-03L, /* 0xbff84341, 0x239e8709, 0xe941b06a, 0xcb4b6ec5 */
+ra1 = -1.13580436992565640457579040117568870e+00L, /* 0xbfff22c4, 0x133f7c0d, 0x72d5e231, 0x2eb1ee3f */
+ra2 = -4.89744330295291950661185707066921755e+01L, /* 0xc00487cb, 0xa38b4fc2, 0xc136695b, 0xc1df8047 */
+ra3 = -1.10766149300215937173768072715352140e+03L, /* 0xc00914ea, 0x55e6beb3, 0xabc50e07, 0xb6e5664d */
+ra4 = -1.49991031232170934967642795601952100e+04L, /* 0xc00cd4b8, 0xd33243e6, 0xffbf6545, 0x3c57ef6e */
+ra5 = -1.29805749738318462882524181556996692e+05L, /* 0xc00ffb0d, 0xbfeed9b6, 0x5b2a3ff4, 0xe245bd3c */
+ra6 = -7.42828497044940065828871976644647850e+05L, /* 0xc0126ab5, 0x8fe7caca, 0x473352d9, 0xcd4e0c90 */
+ra7 = -2.85637299581890734287995171242421106e+06L, /* 0xc0145cad, 0xa7f76fe7, 0x3e358051, 0x1799f927 */
+ra8 = -7.40674797129824999383748865571026084e+06L, /* 0xc015c412, 0x6fe29c02, 0x298ad158, 0x7d24e45c */
+ra9 = -1.28653420911930973914078724204151759e+07L, /* 0xc016889e, 0x7c2eb0dc, 0x95d5863b, 0x0aa34dc3 */
+ra10 = -1.47198163599330179552932489109452638e+07L, /* 0xc016c136, 0x90b84923, 0xf9bcb497, 0x19bbd0f5 */
+ra11 = -1.07812992258382800318665248311522624e+07L, /* 0xc0164904, 0xe673a113, 0x35d7f079, 0xe13701f3 */
+ra12 = -4.83545565681708642630419905537756076e+06L, /* 0xc0152721, 0xfea094a8, 0x869eb39d, 0x413d6f13 */
+ra13 = -1.23956521201673964822976917356685286e+06L, /* 0xc0132ea0, 0xd3646baa, 0x2fe62b0d, 0xbae5ce85 */
+ra14 = -1.62289333553652417591275333240371812e+05L, /* 0xc0103cf8, 0xaab1e2d6, 0x4c25e014, 0x248d76ab */
+ra15 = -8.82890392601176969729168894389833110e+03L, /* 0xc00c13e7, 0x3b3d8f94, 0x6fbda6f6, 0xe7049a82 */
+ra16 = -1.22591866337261720023681535568334619e+02L, /* 0xc005ea5e, 0x12358891, 0xcfa712c5, 0x77f050d4 */
+sa1 = 6.44508918884710829371852723353794047e+01L, /* 0x400501cd, 0xb69a6c0f, 0x5716de14, 0x47161af6 */
+sa2 = 1.76118475473171481523704824327358534e+03L, /* 0x4009b84b, 0xd305829f, 0xc4c771b0, 0xbf1f7f9b */
+sa3 = 2.69448346969488374857087646131950188e+04L, /* 0x400da503, 0x56bacc05, 0x4fdba68d, 0x2cca27e6 */
+sa4 = 2.56826633369941456778326497384543763e+05L, /* 0x4010f59d, 0x51124428, 0x69c41de6, 0xbd0d5753 */
+sa5 = 1.60647413092257206847700054645905859e+06L, /* 0x40138834, 0xa2184244, 0x557a1bed, 0x68c9d556 */
+sa6 = 6.76963075165099718574753447122393797e+06L, /* 0x40159d2f, 0x7b01b0cc, 0x8bac9e95, 0x5d35d56e */
+sa7 = 1.94295690905361884290986932493647741e+07L, /* 0x40172878, 0xc1172d61, 0x3068501e, 0x2f3c71da */
+sa8 = 3.79774781017759149060839255547073541e+07L, /* 0x401821be, 0xc30d06fe, 0x410563d7, 0x032111fd */
+sa9 = 5.00659831846029484248302236457727397e+07L, /* 0x40187df9, 0x1f97a111, 0xc51d6ac2, 0x4b389793 */
+sa10 = 4.36486287620506484276130525941972541e+07L, /* 0x40184d03, 0x3a618ae0, 0x2a723357, 0xfa45c60a */
+sa11 = 2.43779678791333894255510508253951934e+07L, /* 0x401773fa, 0x6fe10ee2, 0xc467850d, 0xc6b7ff30 */
+sa12 = 8.30732360384443202039372372212966542e+06L, /* 0x4015fb09, 0xee6a5631, 0xdd98de7e, 0x8b00461a */
+sa13 = 1.60160846942050515734192397495105693e+06L, /* 0x40138704, 0x8782bf13, 0x5b8fb315, 0xa898abe5 */
+sa14 = 1.54255505242533291014555153757001825e+05L, /* 0x40102d47, 0xc0abc98e, 0x843c9490, 0xb4352440 */
+sa15 = 5.87949220002375547561467275493888824e+03L, /* 0x400b6f77, 0xe00d21d1, 0xec4d41e8, 0x2f8e1673 */
+sa16 = 4.97272976346793193860385983372237710e+01L; /* 0x40048dd1, 0x816c1b3f, 0x24f540a6, 0x4cfe03cc */
+/*
+ * Domain [2.85715,9], range ~[-7.886e-37,7.918e-37]:
+ * |log(x*erfc(x)) + x**2 + 0.5625 - rb(x)/sb(x)| < 2**-120
+ */
+static const long double
+rb0 = -9.86494292470008707171371994479162369e-3L, /* 0xbff84341, 0x239e86f4, 0x2f57e561, 0xf4469360 */
+rb1 = -1.57047326624110727986326503729442830L, /* 0xbfff920a, 0x8935bf73, 0x8803b894, 0x4656482d */
+rb2 = -1.03228196364885474342132255440317065e2L, /* 0xc0059ce9, 0xac4ed0ff, 0x2cff0ff7, 0x5e70d1ab */
+rb3 = -3.74000570653418227179358710865224376e3L, /* 0xc00ad380, 0x2ebf7835, 0xf6b07ed2, 0x861242f7 */
+rb4 = -8.35435477739098044190860390632813956e4L, /* 0xc00f4657, 0x8c3ae934, 0x3647d7b3, 0x80e76fb7 */
+rb5 = -1.21398672055223642118716640216747152e6L, /* 0xc0132862, 0x2b8761c8, 0x27d18c0f, 0x137c9463 */
+rb6 = -1.17669175877248796101665344873273970e7L, /* 0xc0166719, 0x0b2cea46, 0x81f14174, 0x11602ea5 */
+rb7 = -7.66108006086998253606773064264599615e7L, /* 0xc019243f, 0x3c26f4f0, 0x1cc05241, 0x3b953728 */
+rb8 = -3.32547117558141845968704725353130804e8L, /* 0xc01b3d24, 0x42d8ee26, 0x24ef6f3b, 0x604a8c65 */
+rb9 = -9.41561252426350696802167711221739746e8L, /* 0xc01cc0f8, 0xad23692a, 0x8ddb2310, 0xe9937145 */
+rb10 = -1.67157110805390944549427329626281063e9L, /* 0xc01d8e88, 0x9a903734, 0x09a55fa3, 0xd205c903 */
+rb11 = -1.74339631004410841337645931421427373e9L, /* 0xc01d9fa8, 0x77582d2a, 0xc183b8ab, 0x7e00cb05 */
+rb12 = -9.57655233596934915727573141357471703e8L, /* 0xc01cc8a5, 0x460cc685, 0xd0271fa0, 0x6a70e3da */
+rb13 = -2.26320062731339353035254704082495066e8L, /* 0xc01aafab, 0xd7d76721, 0xc9720e11, 0x6a8bd489 */
+rb14 = -1.42777302996263256686002973851837039e7L, /* 0xc016b3b8, 0xc499689f, 0x2b88d965, 0xc32414f9 */
+sb1 = 1.08512869705594540211033733976348506e2L, /* 0x4005b20d, 0x2db7528d, 0x00d20dcb, 0x858f6191 */
+sb2 = 5.02757713761390460534494530537572834e3L, /* 0x400b3a39, 0x3bf4a690, 0x3025d28d, 0xfd40a891 */
+sb3 = 1.31019107205412870059331647078328430e5L, /* 0x400fffcb, 0x1b71d05e, 0x3b28361d, 0x2a3c3690 */
+sb4 = 2.13021555152296846166736757455018030e6L, /* 0x40140409, 0x3c6984df, 0xc4491d7c, 0xb04aa08d */
+sb5 = 2.26649105281820861953868568619768286e7L, /* 0x401759d6, 0xce8736f0, 0xf28ad037, 0x2a901e0c */
+sb6 = 1.61071939490875921812318684143076081e8L, /* 0x401a3338, 0x686fb541, 0x6bd27d06, 0x4f95c9ac */
+sb7 = 7.66895673844301852676056750497991966e8L, /* 0x401c6daf, 0x31cec121, 0x54699126, 0x4bd9bf9e */
+sb8 = 2.41884450436101936436023058196042526e9L, /* 0x401e2059, 0x46b0b8d7, 0x87b64cbf, 0x78bc296d */
+sb9 = 4.92403055884071695093305291535107666e9L, /* 0x401f257e, 0xbe5ed739, 0x39e17346, 0xcadd2e55 */
+sb10 = 6.18627786365587486459633615573786416e9L, /* 0x401f70bb, 0x1be7a7e7, 0x6a45b5ae, 0x607c70f0 */
+sb11 = 4.45898013426501378097430226324743199e9L, /* 0x401f09c6, 0xa32643d7, 0xf1724620, 0x9ea46c32 */
+sb12 = 1.63006115763329848117160344854224975e9L, /* 0x401d84a3, 0x0996887f, 0x65a4f43b, 0x978c1d74 */
+sb13 = 2.39216717012421697446304015847567721e8L, /* 0x401ac845, 0x09a065c2, 0x30095da7, 0x9d72d6ae */
+sb14 = 7.84837329009278694937250358810225609e6L; /* 0x4015df06, 0xd5290e15, 0x63031fac, 0x4d9c894c */
+/*
+ * Domain [9,108], range ~[-5.324e-38,5.340e-38]:
+ * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-124
+ */
+static const long double
+rc0 = -9.86494292470008707171367567652935673e-3L, /* 0xbff84341, 0x239e86f4, 0x2f57e55b, 0x1aa10fd3 */
+rc1 = -1.26229447747315096406518846411562266L, /* 0xbfff4325, 0xbb1aab28, 0xda395cd9, 0xfb861c15 */
+rc2 = -6.13742634438922591780742637728666162e1L, /* 0xc004eafe, 0x7dd51cd8, 0x3c7c5928, 0x751e50cf */
+rc3 = -1.50455835478908280402912854338421517e3L, /* 0xc0097823, 0xbc15b9ab, 0x3d60745c, 0x523e80a5 */
+rc4 = -2.04415631865861549920184039902945685e4L, /* 0xc00d3f66, 0x40b3fc04, 0x5388f2ec, 0xb009e1f0 */
+rc5 = -1.57625662981714582753490610560037638e5L, /* 0xc01033dc, 0xd4dc95b6, 0xfd4da93b, 0xf355b4a9 */
+rc6 = -6.73473451616752528402917538033283794e5L, /* 0xc01248d8, 0x2e73a4f9, 0xcded49c5, 0xfa3bfeb7 */
+rc7 = -1.47433165421387483167186683764364857e6L, /* 0xc01367f1, 0xba77a8f7, 0xcfdd0dbb, 0x25d554b3 */
+rc8 = -1.38811981807868828563794929997744139e6L, /* 0xc01352e5, 0x7d16d9ad, 0xbbdcbf38, 0x38fbc5ea */
+rc9 = -3.59659700530831825640766479698155060e5L, /* 0xc0115f3a, 0xecd57f45, 0x21f8ad6c, 0x910a5958 */
+sc1 = 7.72730753022908298637508998072635696e1L, /* 0x40053517, 0xa10d52bc, 0xdabb55b6, 0xbd0328cd */
+sc2 = 2.36825757341694050500333261769082182e3L, /* 0x400a2808, 0x3e0a9b42, 0x82977842, 0x9c5de29e */
+sc3 = 3.72210540173034735352888847134073099e4L, /* 0x400e22ca, 0x1ba827ef, 0xac8390d7, 0x1fc39a41 */
+sc4 = 3.24136032646418336712461033591393412e5L, /* 0x40113c8a, 0x0216e100, 0xc59d1e44, 0xf0e68d9d */
+sc5 = 1.57836135851134393802505823370009175e6L, /* 0x40138157, 0x95bc7664, 0x17575961, 0xdbe58eeb */
+sc6 = 4.12881981392063738026679089714182355e6L, /* 0x4014f801, 0x9e82e8d2, 0xb8b3a70e, 0xfd84185d */
+sc7 = 5.24438427289213488410596395361544142e6L, /* 0x40154017, 0x81177109, 0x2aa6c3b0, 0x1f106625 */
+sc8 = 2.59909544563616121735963429710382149e6L, /* 0x40143d45, 0xbb90a9b1, 0x12bf9390, 0xa827a700 */
+sc9 = 2.80930665169282501639651995082335693e5L; /* 0x40111258, 0xaa92222e, 0xa97e3216, 0xa237fa6c */
+
+long double
+erfl(long double x)
+{
+ long double ax,R,S,P,Q,s,y,z,r;
+ uint64_t lx, llx;
+ int32_t i;
+ uint16_t hx;
+
+ EXTRACT_LDBL128_WORDS(hx, lx, llx, x);
+
+ if((hx & 0x7fff) == 0x7fff) { /* erfl(nan)=nan */
+ i = (hx>>15)<<1;
+ return (1-i)+one/x; /* erfl(+-inf)=+-1 */
+ }
+
+ ax = fabsl(x);
+ if(ax < 0.84375) {
+ if(ax < 0x1p-40L) {
+ if(ax < 0x1p-16373L)
+ return (8*x+efx8*x)/8; /* avoid spurious underflow */
+ return x + efx*x;
+ }
+ z = x*x;
+ r = pp0+z*(pp1+z*(pp2+z*(pp3+z*(pp4+z*(pp5+z*(pp6+z*(pp7+
+ z*(pp8+z*pp9))))))));
+ s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*(qq5+z*(qq6+z*(qq7+
+ z*(qq8+z*qq9))))))));
+ y = r/s;
+ return x + x*y;
+ }
+ if(ax < 1.25) {
+ s = ax-one;
+ P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*(pa6+s*(pa7+
+ s*(pa8+s*(pa9+s*(pa10+s*pa11))))))))));
+ Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*(qa6+s*(qa7+
+ s*(qa8+s*(qa9+s*(qa10+s*(qa11+s*qa12)))))))))));
+ if(x>=0) return (erx + P/Q); else return (-erx - P/Q);
+ }
+ if (ax >= 9) { /* inf>|x|>= 9 */
+ if(x>=0) return (one-tiny); else return (tiny-one);
+ }
+ s = one/(ax*ax);
+ if(ax < 2.85715) { /* |x| < 2.85715 */
+ R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*(ra7+
+ s*(ra8+s*(ra9+s*(ra10+s*(ra11+s*(ra12+s*(ra13+s*(ra14+
+ s*(ra15+s*ra16)))))))))))))));
+ S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+
+ s*(sa8+s*(sa9+s*(sa10+s*(sa11+s*(sa12+s*(sa13+s*(sa14+
+ s*(sa15+s*sa16)))))))))))))));
+ } else { /* |x| >= 2.85715 */
+ R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*(rb6+s*(rb7+
+ s*(rb8+s*(rb9+s*(rb10+s*(rb11+s*(rb12+s*(rb13+
+ s*rb14)))))))))))));
+ S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*(sb7+
+ s*(sb8+s*(sb9+s*(sb10+s*(sb11+s*(sb12+s*(sb13+
+ s*sb14)))))))))))));
+ }
+ z = (float)ax;
+ r = expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S);
+ if(x>=0) return (one-r/ax); else return (r/ax-one);
+}
+
+long double
+erfcl(long double x)
+{
+ long double ax,R,S,P,Q,s,y,z,r;
+ uint64_t lx, llx;
+ uint16_t hx;
+
+ EXTRACT_LDBL128_WORDS(hx, lx, llx, x);
+
+ if((hx & 0x7fff) == 0x7fff) { /* erfcl(nan)=nan */
+ /* erfcl(+-inf)=0,2 */
+ return ((hx>>15)<<1)+one/x;
+ }
+
+ ax = fabsl(x);
+ if(ax < 0.84375L) {
+ if(ax < 0x1p-34L)
+ return one-x;
+ z = x*x;
+ r = pp0+z*(pp1+z*(pp2+z*(pp3+z*(pp4+z*(pp5+z*(pp6+z*(pp7+
+ z*(pp8+z*pp9))))))));
+ s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*(qq5+z*(qq6+z*(qq7+
+ z*(qq8+z*qq9))))))));
+ y = r/s;
+ if(ax < 0.25L) { /* x<1/4 */
+ return one-(x+x*y);
+ } else {
+ r = x*y;
+ r += (x-half);
+ return half - r;
+ }
+ }
+ if(ax < 1.25L) {
+ s = ax-one;
+ P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*(pa6+s*(pa7+
+ s*(pa8+s*(pa9+s*(pa10+s*pa11))))))))));
+ Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*(qa6+s*(qa7+
+ s*(qa8+s*(qa9+s*(qa10+s*(qa11+s*qa12)))))))))));
+ if(x>=0) {
+ z = one-erx; return z - P/Q;
+ } else {
+ z = erx+P/Q; return one+z;
+ }
+ }
+
+ if(ax < 108) { /* |x| < 108 */
+ s = one/(ax*ax);
+ if(ax < 2.85715) { /* |x| < 2.85715 */
+ R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*(ra7+
+ s*(ra8+s*(ra9+s*(ra10+s*(ra11+s*(ra12+s*(ra13+s*(ra14+
+ s*(ra15+s*ra16)))))))))))))));
+ S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+
+ s*(sa8+s*(sa9+s*(sa10+s*(sa11+s*(sa12+s*(sa13+s*(sa14+
+ s*(sa15+s*sa16)))))))))))))));
+ } else if(ax < 9) {
+ R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*(rb6+s*(rb7+
+ s*(rb8+s*(rb9+s*(rb10+s*(rb11+s*(rb12+s*(rb13+
+ s*rb14)))))))))))));
+ S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*(sb7+
+ s*(sb8+s*(sb9+s*(sb10+s*(sb11+s*(sb12+s*(sb13+
+ s*sb14)))))))))))));
+ } else {
+ if(x < -9) return two-tiny; /* x < -9 */
+ R=rc0+s*(rc1+s*(rc2+s*(rc3+s*(rc4+s*(rc5+s*(rc6+s*(rc7+
+ s*(rc8+s*rc9))))))));
+ S=one+s*(sc1+s*(sc2+s*(sc3+s*(sc4+s*(sc5+s*(sc6+s*(sc7+
+ s*(sc8+s*sc9))))))));
+ }
+ z = (float)ax;
+ r = expl(-z*z-0.5625)*expl((z-ax)*(z+ax)+R/S);
+ if(x>0) return r/ax; else return two-r/ax;
+ } else {
+ if(x>0) return tiny*tiny; else return two-tiny;
+ }
+}
diff --git a/libm/upstream-freebsd/lib/msun/ld128/s_exp2l.c b/libm/upstream-freebsd/lib/msun/ld128/s_exp2l.c
index 5ed514c..5afa37e 100644
--- a/libm/upstream-freebsd/lib/msun/ld128/s_exp2l.c
+++ b/libm/upstream-freebsd/lib/msun/ld128/s_exp2l.c
@@ -369,7 +369,7 @@ exp2l(long double x)
|| u.xbits.manl != 0
|| (hx & 0x8000) == 0)
return (x + x); /* x is NaN or +Inf */
- else
+ else
return (0.0); /* x is -Inf */
}
if (x >= 16384)
diff --git a/libm/upstream-freebsd/lib/msun/ld128/s_expl.c b/libm/upstream-freebsd/lib/msun/ld128/s_expl.c
index 176c932..a6a9676 100644
--- a/libm/upstream-freebsd/lib/msun/ld128/s_expl.c
+++ b/libm/upstream-freebsd/lib/msun/ld128/s_expl.c
@@ -38,16 +38,15 @@ __FBSDID("$FreeBSD$");
#include "fpmath.h"
#include "math.h"
#include "math_private.h"
+#include "k_expl.h"
-#define INTERVALS 128
-#define LOG2_INTERVALS 7
-#define BIAS (LDBL_MAX_EXP - 1)
+/* XXX Prevent compilers from erroneously constant folding these: */
+static const volatile long double
+huge = 0x1p10000L,
+tiny = 0x1p-10000L;
static const long double
-huge = 0x1p10000L,
twom10000 = 0x1p-10000L;
-/* XXX Prevent gcc from erroneously constant folding this: */
-static volatile const long double tiny = 0x1p-10000L;
static const long double
/* log(2**16384 - 0.5) rounded towards zero: */
@@ -56,184 +55,16 @@ o_threshold = 11356.523406294143949491931077970763428L,
/* log(2**(-16381-64-1)) rounded towards zero: */
u_threshold = -11433.462743336297878837243843452621503L;
-static const double
-/*
- * ln2/INTERVALS = L1+L2 (hi+lo decomposition for multiplication). L1 must
- * have at least 22 (= log2(|LDBL_MIN_EXP-extras|) + log2(INTERVALS)) lowest
- * bits zero so that multiplication of it by n is exact.
- */
-INV_L = 1.8466496523378731e+2, /* 0x171547652b82fe.0p-45 */
-L2 = -1.0253670638894731e-29; /* -0x1.9ff0342542fc3p-97 */
-static const long double
-/* 0x1.62e42fefa39ef35793c768000000p-8 */
-L1 = 5.41521234812457272982212595914567508e-3L;
-
-static const long double
-/*
- * Domain [-0.002708, 0.002708], range ~[-2.4021e-38, 2.4234e-38]:
- * |exp(x) - p(x)| < 2**-124.9
- * (0.002708 is ln2/(2*INTERVALS) rounded up a little).
- */
-A2 = 0.5,
-A3 = 1.66666666666666666666666666651085500e-1L,
-A4 = 4.16666666666666666666666666425885320e-2L,
-A5 = 8.33333333333333333334522877160175842e-3L,
-A6 = 1.38888888888888888889971139751596836e-3L;
-
-static const double
-A7 = 1.9841269841269471e-4,
-A8 = 2.4801587301585284e-5,
-A9 = 2.7557324277411234e-6,
-A10 = 2.7557333722375072e-7;
-
-static const struct {
- /*
- * hi must be rounded to at most 106 bits so that multiplication
- * by r1 in expm1l() is exact, but it is rounded to 88 bits due to
- * historical accidents.
- */
- long double hi;
- long double lo;
-} tbl[INTERVALS] = {
- 0x1p0L, 0x0p0L,
- 0x1.0163da9fb33356d84a66aep0L, 0x3.36dcdfa4003ec04c360be2404078p-92L,
- 0x1.02c9a3e778060ee6f7cacap0L, 0x4.f7a29bde93d70a2cabc5cb89ba10p-92L,
- 0x1.04315e86e7f84bd738f9a2p0L, 0xd.a47e6ed040bb4bfc05af6455e9b8p-96L,
- 0x1.059b0d31585743ae7c548ep0L, 0xb.68ca417fe53e3495f7df4baf84a0p-92L,
- 0x1.0706b29ddf6ddc6dc403a8p0L, 0x1.d87b27ed07cb8b092ac75e311753p-88L,
- 0x1.0874518759bc808c35f25cp0L, 0x1.9427fa2b041b2d6829d8993a0d01p-88L,
- 0x1.09e3ecac6f3834521e060cp0L, 0x5.84d6b74ba2e023da730e7fccb758p-92L,
- 0x1.0b5586cf9890f6298b92b6p0L, 0x1.1842a98364291408b3ceb0a2a2bbp-88L,
- 0x1.0cc922b7247f7407b705b8p0L, 0x9.3dc5e8aac564e6fe2ef1d431fd98p-92L,
- 0x1.0e3ec32d3d1a2020742e4ep0L, 0x1.8af6a552ac4b358b1129e9f966a4p-88L,
- 0x1.0fb66affed31af232091dcp0L, 0x1.8a1426514e0b627bda694a400a27p-88L,
- 0x1.11301d0125b50a4ebbf1aep0L, 0xd.9318ceac5cc47ab166ee57427178p-92L,
- 0x1.12abdc06c31cbfb92bad32p0L, 0x4.d68e2f7270bdf7cedf94eb1cb818p-92L,
- 0x1.1429aaea92ddfb34101942p0L, 0x1.b2586d01844b389bea7aedd221d4p-88L,
- 0x1.15a98c8a58e512480d573cp0L, 0x1.d5613bf92a2b618ee31b376c2689p-88L,
- 0x1.172b83c7d517adcdf7c8c4p0L, 0x1.0eb14a792035509ff7d758693f24p-88L,
- 0x1.18af9388c8de9bbbf70b9ap0L, 0x3.c2505c97c0102e5f1211941d2840p-92L,
- 0x1.1a35beb6fcb753cb698f68p0L, 0x1.2d1c835a6c30724d5cfae31b84e5p-88L,
- 0x1.1bbe084045cd39ab1e72b4p0L, 0x4.27e35f9acb57e473915519a1b448p-92L,
- 0x1.1d4873168b9aa7805b8028p0L, 0x9.90f07a98b42206e46166cf051d70p-92L,
- 0x1.1ed5022fcd91cb8819ff60p0L, 0x1.121d1e504d36c47474c9b7de6067p-88L,
- 0x1.2063b88628cd63b8eeb028p0L, 0x1.50929d0fc487d21c2b84004264dep-88L,
- 0x1.21f49917ddc962552fd292p0L, 0x9.4bdb4b61ea62477caa1dce823ba0p-92L,
- 0x1.2387a6e75623866c1fadb0p0L, 0x1.c15cb593b0328566902df69e4de2p-88L,
- 0x1.251ce4fb2a63f3582ab7dep0L, 0x9.e94811a9c8afdcf796934bc652d0p-92L,
- 0x1.26b4565e27cdd257a67328p0L, 0x1.d3b249dce4e9186ddd5ff44e6b08p-92L,
- 0x1.284dfe1f5638096cf15cf0p0L, 0x3.ca0967fdaa2e52d7c8106f2e262cp-92L,
- 0x1.29e9df51fdee12c25d15f4p0L, 0x1.a24aa3bca890ac08d203fed80a07p-88L,
- 0x1.2b87fd0dad98ffddea4652p0L, 0x1.8fcab88442fdc3cb6de4519165edp-88L,
- 0x1.2d285a6e4030b40091d536p0L, 0xd.075384589c1cd1b3e4018a6b1348p-92L,
- 0x1.2ecafa93e2f5611ca0f45cp0L, 0x1.523833af611bdcda253c554cf278p-88L,
- 0x1.306fe0a31b7152de8d5a46p0L, 0x3.05c85edecbc27343629f502f1af2p-92L,
- 0x1.32170fc4cd8313539cf1c2p0L, 0x1.008f86dde3220ae17a005b6412bep-88L,
- 0x1.33c08b26416ff4c9c8610cp0L, 0x1.96696bf95d1593039539d94d662bp-88L,
- 0x1.356c55f929ff0c94623476p0L, 0x3.73af38d6d8d6f9506c9bbc93cbc0p-92L,
- 0x1.371a7373aa9caa7145502ep0L, 0x1.4547987e3e12516bf9c699be432fp-88L,
- 0x1.38cae6d05d86585a9cb0d8p0L, 0x1.bed0c853bd30a02790931eb2e8f0p-88L,
- 0x1.3a7db34e59ff6ea1bc9298p0L, 0x1.e0a1d336163fe2f852ceeb134067p-88L,
- 0x1.3c32dc313a8e484001f228p0L, 0xb.58f3775e06ab66353001fae9fca0p-92L,
- 0x1.3dea64c12342235b41223ep0L, 0x1.3d773fba2cb82b8244267c54443fp-92L,
- 0x1.3fa4504ac801ba0bf701aap0L, 0x4.1832fb8c1c8dbdff2c49909e6c60p-92L,
- 0x1.4160a21f72e29f84325b8ep0L, 0x1.3db61fb352f0540e6ba05634413ep-88L,
- 0x1.431f5d950a896dc7044394p0L, 0x1.0ccec81e24b0caff7581ef4127f7p-92L,
- 0x1.44e086061892d03136f408p0L, 0x1.df019fbd4f3b48709b78591d5cb5p-88L,
- 0x1.46a41ed1d005772512f458p0L, 0x1.229d97df404ff21f39c1b594d3a8p-88L,
- 0x1.486a2b5c13cd013c1a3b68p0L, 0x1.062f03c3dd75ce8757f780e6ec99p-88L,
- 0x1.4a32af0d7d3de672d8bcf4p0L, 0x6.f9586461db1d878b1d148bd3ccb8p-92L,
- 0x1.4bfdad5362a271d4397afep0L, 0xc.42e20e0363ba2e159c579f82e4b0p-92L,
- 0x1.4dcb299fddd0d63b36ef1ap0L, 0x9.e0cc484b25a5566d0bd5f58ad238p-92L,
- 0x1.4f9b2769d2ca6ad33d8b68p0L, 0x1.aa073ee55e028497a329a7333dbap-88L,
- 0x1.516daa2cf6641c112f52c8p0L, 0x4.d822190e718226177d7608d20038p-92L,
- 0x1.5342b569d4f81df0a83c48p0L, 0x1.d86a63f4e672a3e429805b049465p-88L,
- 0x1.551a4ca5d920ec52ec6202p0L, 0x4.34ca672645dc6c124d6619a87574p-92L,
- 0x1.56f4736b527da66ecb0046p0L, 0x1.64eb3c00f2f5ab3d801d7cc7272dp-88L,
- 0x1.58d12d497c7fd252bc2b72p0L, 0x1.43bcf2ec936a970d9cc266f0072fp-88L,
- 0x1.5ab07dd48542958c930150p0L, 0x1.91eb345d88d7c81280e069fbdb63p-88L,
- 0x1.5c9268a5946b701c4b1b80p0L, 0x1.6986a203d84e6a4a92f179e71889p-88L,
- 0x1.5e76f15ad21486e9be4c20p0L, 0x3.99766a06548a05829e853bdb2b52p-92L,
- 0x1.605e1b976dc08b076f592ap0L, 0x4.86e3b34ead1b4769df867b9c89ccp-92L,
- 0x1.6247eb03a5584b1f0fa06ep0L, 0x1.d2da42bb1ceaf9f732275b8aef30p-88L,
- 0x1.6434634ccc31fc76f8714cp0L, 0x4.ed9a4e41000307103a18cf7a6e08p-92L,
- 0x1.66238825522249127d9e28p0L, 0x1.b8f314a337f4dc0a3adf1787ff74p-88L,
- 0x1.68155d44ca973081c57226p0L, 0x1.b9f32706bfe4e627d809a85dcc66p-88L,
- 0x1.6a09e667f3bcc908b2fb12p0L, 0x1.66ea957d3e3adec17512775099dap-88L,
- 0x1.6c012750bdabeed76a9980p0L, 0xf.4f33fdeb8b0ecd831106f57b3d00p-96L,
- 0x1.6dfb23c651a2ef220e2cbep0L, 0x1.bbaa834b3f11577ceefbe6c1c411p-92L,
- 0x1.6ff7df9519483cf87e1b4ep0L, 0x1.3e213bff9b702d5aa477c12523cep-88L,
- 0x1.71f75e8ec5f73dd2370f2ep0L, 0xf.0acd6cb434b562d9e8a20adda648p-92L,
- 0x1.73f9a48a58173bd5c9a4e6p0L, 0x8.ab1182ae217f3a7681759553e840p-92L,
- 0x1.75feb564267c8bf6e9aa32p0L, 0x1.a48b27071805e61a17b954a2dad8p-88L,
- 0x1.780694fde5d3f619ae0280p0L, 0x8.58b2bb2bdcf86cd08e35fb04c0f0p-92L,
- 0x1.7a11473eb0186d7d51023ep0L, 0x1.6cda1f5ef42b66977960531e821bp-88L,
- 0x1.7c1ed0130c1327c4933444p0L, 0x1.937562b2dc933d44fc828efd4c9cp-88L,
- 0x1.7e2f336cf4e62105d02ba0p0L, 0x1.5797e170a1427f8fcdf5f3906108p-88L,
- 0x1.80427543e1a11b60de6764p0L, 0x9.a354ea706b8e4d8b718a672bf7c8p-92L,
- 0x1.82589994cce128acf88afap0L, 0xb.34a010f6ad65cbbac0f532d39be0p-92L,
- 0x1.8471a4623c7acce52f6b96p0L, 0x1.c64095370f51f48817914dd78665p-88L,
- 0x1.868d99b4492ec80e41d90ap0L, 0xc.251707484d73f136fb5779656b70p-92L,
- 0x1.88ac7d98a669966530bcdep0L, 0x1.2d4e9d61283ef385de170ab20f96p-88L,
- 0x1.8ace5422aa0db5ba7c55a0p0L, 0x1.92c9bb3e6ed61f2733304a346d8fp-88L,
- 0x1.8cf3216b5448bef2aa1cd0p0L, 0x1.61c55d84a9848f8c453b3ca8c946p-88L,
- 0x1.8f1ae991577362b982745cp0L, 0x7.2ed804efc9b4ae1458ae946099d4p-92L,
- 0x1.9145b0b91ffc588a61b468p0L, 0x1.f6b70e01c2a90229a4c4309ea719p-88L,
- 0x1.93737b0cdc5e4f4501c3f2p0L, 0x5.40a22d2fc4af581b63e8326efe9cp-92L,
- 0x1.95a44cbc8520ee9b483694p0L, 0x1.a0fc6f7c7d61b2b3a22a0eab2cadp-88L,
- 0x1.97d829fde4e4f8b9e920f8p0L, 0x1.1e8bd7edb9d7144b6f6818084cc7p-88L,
- 0x1.9a0f170ca07b9ba3109b8cp0L, 0x4.6737beb19e1eada6825d3c557428p-92L,
- 0x1.9c49182a3f0901c7c46b06p0L, 0x1.1f2be58ddade50c217186c90b457p-88L,
- 0x1.9e86319e323231824ca78ep0L, 0x6.4c6e010f92c082bbadfaf605cfd4p-92L,
- 0x1.a0c667b5de564b29ada8b8p0L, 0xc.ab349aa0422a8da7d4512edac548p-92L,
- 0x1.a309bec4a2d3358c171f76p0L, 0x1.0daad547fa22c26d168ea762d854p-88L,
- 0x1.a5503b23e255c8b424491cp0L, 0xa.f87bc8050a405381703ef7caff50p-92L,
- 0x1.a799e1330b3586f2dfb2b0p0L, 0x1.58f1a98796ce8908ae852236ca94p-88L,
- 0x1.a9e6b5579fdbf43eb243bcp0L, 0x1.ff4c4c58b571cf465caf07b4b9f5p-88L,
- 0x1.ac36bbfd3f379c0db966a2p0L, 0x1.1265fc73e480712d20f8597a8e7bp-88L,
- 0x1.ae89f995ad3ad5e8734d16p0L, 0x1.73205a7fbc3ae675ea440b162d6cp-88L,
- 0x1.b0e07298db66590842acdep0L, 0x1.c6f6ca0e5dcae2aafffa7a0554cbp-88L,
- 0x1.b33a2b84f15faf6bfd0e7ap0L, 0x1.d947c2575781dbb49b1237c87b6ep-88L,
- 0x1.b59728de559398e3881110p0L, 0x1.64873c7171fefc410416be0a6525p-88L,
- 0x1.b7f76f2fb5e46eaa7b081ap0L, 0xb.53c5354c8903c356e4b625aacc28p-92L,
- 0x1.ba5b030a10649840cb3c6ap0L, 0xf.5b47f297203757e1cc6eadc8bad0p-92L,
- 0x1.bcc1e904bc1d2247ba0f44p0L, 0x1.b3d08cd0b20287092bd59be4ad98p-88L,
- 0x1.bf2c25bd71e088408d7024p0L, 0x1.18e3449fa073b356766dfb568ff4p-88L,
- 0x1.c199bdd85529c2220cb12ap0L, 0x9.1ba6679444964a36661240043970p-96L,
- 0x1.c40ab5fffd07a6d14df820p0L, 0xf.1828a5366fd387a7bdd54cdf7300p-92L,
- 0x1.c67f12e57d14b4a2137fd2p0L, 0xf.2b301dd9e6b151a6d1f9d5d5f520p-96L,
- 0x1.c8f6d9406e7b511acbc488p0L, 0x5.c442ddb55820171f319d9e5076a8p-96L,
- 0x1.cb720dcef90691503cbd1ep0L, 0x9.49db761d9559ac0cb6dd3ed599e0p-92L,
- 0x1.cdf0b555dc3f9c44f8958ep0L, 0x1.ac51be515f8c58bdfb6f5740a3a4p-88L,
- 0x1.d072d4a07897b8d0f22f20p0L, 0x1.a158e18fbbfc625f09f4cca40874p-88L,
- 0x1.d2f87080d89f18ade12398p0L, 0x9.ea2025b4c56553f5cdee4c924728p-92L,
- 0x1.d5818dcfba48725da05aeap0L, 0x1.66e0dca9f589f559c0876ff23830p-88L,
- 0x1.d80e316c98397bb84f9d04p0L, 0x8.805f84bec614de269900ddf98d28p-92L,
- 0x1.da9e603db3285708c01a5ap0L, 0x1.6d4c97f6246f0ec614ec95c99392p-88L,
- 0x1.dd321f301b4604b695de3cp0L, 0x6.30a393215299e30d4fb73503c348p-96L,
- 0x1.dfc97337b9b5eb968cac38p0L, 0x1.ed291b7225a944efd5bb5524b927p-88L,
- 0x1.e264614f5a128a12761fa0p0L, 0x1.7ada6467e77f73bf65e04c95e29dp-88L,
- 0x1.e502ee78b3ff6273d13014p0L, 0x1.3991e8f49659e1693be17ae1d2f9p-88L,
- 0x1.e7a51fbc74c834b548b282p0L, 0x1.23786758a84f4956354634a416cep-88L,
- 0x1.ea4afa2a490d9858f73a18p0L, 0xf.5db301f86dea20610ceee13eb7b8p-92L,
- 0x1.ecf482d8e67f08db0312fap0L, 0x1.949cef462010bb4bc4ce72a900dfp-88L,
- 0x1.efa1bee615a27771fd21a8p0L, 0x1.2dac1f6dd5d229ff68e46f27e3dfp-88L,
- 0x1.f252b376bba974e8696fc2p0L, 0x1.6390d4c6ad5476b5162f40e1d9a9p-88L,
- 0x1.f50765b6e4540674f84b76p0L, 0x2.862baff99000dfc4352ba29b8908p-92L,
- 0x1.f7bfdad9cbe138913b4bfep0L, 0x7.2bd95c5ce7280fa4d2344a3f5618p-92L,
- 0x1.fa7c1819e90d82e90a7e74p0L, 0xb.263c1dc060c36f7650b4c0f233a8p-92L,
- 0x1.fd3c22b8f71f10975ba4b2p0L, 0x1.2bcf3a5e12d269d8ad7c1a4a8875p-88L
-};
-
long double
expl(long double x)
{
- union IEEEl2bits u, v;
- long double q, r, r1, t, twopk, twopkp10000;
- double dr, fn, r2;
- int k, n, n2;
+ union IEEEl2bits u;
+ long double hi, lo, t, twopk;
+ int k;
uint16_t hx, ix;
+ DOPRINT_START(&x);
+
/* Filter out exceptional cases. */
u.e = x;
hx = u.xbits.expsign;
@@ -241,60 +72,33 @@ expl(long double x)
if (ix >= BIAS + 13) { /* |x| >= 8192 or x is NaN */
if (ix == BIAS + LDBL_MAX_EXP) {
if (hx & 0x8000) /* x is -Inf or -NaN */
- return (-1 / x);
- return (x + x); /* x is +Inf or +NaN */
+ RETURNP(-1 / x);
+ RETURNP(x + x); /* x is +Inf or +NaN */
}
if (x > o_threshold)
- return (huge * huge);
+ RETURNP(huge * huge);
if (x < u_threshold)
- return (tiny * tiny);
+ RETURNP(tiny * tiny);
} else if (ix < BIAS - 114) { /* |x| < 0x1p-114 */
- return (1 + x); /* 1 with inexact iff x != 0 */
+ RETURN2P(1, x); /* 1 with inexact iff x != 0 */
}
ENTERI();
- /* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
- /* Use a specialized rint() to get fn. Assume round-to-nearest. */
- /* XXX assume no extra precision for the additions, as for trig fns. */
- /* XXX this set of comments is now quadruplicated. */
- fn = (double)x * INV_L + 0x1.8p52 - 0x1.8p52;
-#if defined(HAVE_EFFICIENT_IRINT)
- n = irint(fn);
-#else
- n = (int)fn;
-#endif
- n2 = (unsigned)n % INTERVALS;
- k = n >> LOG2_INTERVALS;
- r1 = x - fn * L1;
- r2 = fn * -L2;
- r = r1 + r2;
-
- /* Prepare scale factors. */
- /* XXX sparc64 multiplication is so slow that scalbnl() is faster. */
- v.e = 1;
- if (k >= LDBL_MIN_EXP) {
- v.xbits.expsign = BIAS + k;
- twopk = v.e;
- } else {
- v.xbits.expsign = BIAS + k + 10000;
- twopkp10000 = v.e;
- }
-
- /* Evaluate expl(endpoint[n2] + r1 + r2) = tbl[n2] * expl(r1 + r2). */
- dr = r;
- q = r2 + r * r * (A2 + r * (A3 + r * (A4 + r * (A5 + r * (A6 +
- dr * (A7 + dr * (A8 + dr * (A9 + dr * A10))))))));
- t = tbl[n2].lo + tbl[n2].hi;
- t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
+ twopk = 1;
+ __k_expl(x, &hi, &lo, &k);
+ t = SUM2P(hi, lo);
/* Scale by 2**k. */
+ /* XXX sparc64 multiplication is so slow that scalbnl() is faster. */
if (k >= LDBL_MIN_EXP) {
if (k == LDBL_MAX_EXP)
RETURNI(t * 2 * 0x1p16383L);
+ SET_LDBL_EXPSIGN(twopk, BIAS + k);
RETURNI(t * twopk);
} else {
- RETURNI(t * twopkp10000 * twom10000);
+ SET_LDBL_EXPSIGN(twopk, BIAS + k + 10000);
+ RETURNI(t * twopk * twom10000);
}
}
@@ -312,6 +116,12 @@ expl(long double x)
* Setting T3 to 0 would require the |x| < 0x1p-113 condition to appear
* in both subintervals, so set T3 = 2**-5, which places the condition
* into the [T1, T3] interval.
+ *
+ * XXX we now do this more to (partially) balance the number of terms
+ * in the C and D polys than to avoid checking the condition in both
+ * intervals.
+ *
+ * XXX these micro-optimizations are excessive.
*/
static const double
T1 = -0.1659, /* ~-30.625/128 * log(2) */
@@ -321,6 +131,12 @@ T3 = 0.03125;
/*
* Domain [-0.1659, 0.03125], range ~[2.9134e-44, 1.8404e-37]:
* |(exp(x)-1-x-x**2/2)/x - p(x)| < 2**-122.03
+ *
+ * XXX none of the long double C or D coeffs except C10 is correctly printed.
+ * If you re-print their values in %.35Le format, the result is always
+ * different. For example, the last 2 digits in C3 should be 59, not 67.
+ * 67 is apparently from rounding an extra-precision value to 36 decimal
+ * places.
*/
static const long double
C3 = 1.66666666666666666666666666666666667e-1L,
@@ -335,6 +151,13 @@ C11 = 2.50521083854417203619031960151253944e-8L,
C12 = 2.08767569878679576457272282566520649e-9L,
C13 = 1.60590438367252471783548748824255707e-10L;
+/*
+ * XXX this has 1 more coeff than needed.
+ * XXX can start the double coeffs but not the double mults at C10.
+ * With my coeffs (C10-C17 double; s = best_s):
+ * Domain [-0.1659, 0.03125], range ~[-1.1976e-37, 1.1976e-37]:
+ * |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65
+ */
static const double
C14 = 1.1470745580491932e-11, /* 0x1.93974a81dae30p-37 */
C15 = 7.6471620181090468e-13, /* 0x1.ae7f3820adab1p-41 */
@@ -359,6 +182,13 @@ D11 = 2.50521083855084570046480450935267433e-8L,
D12 = 2.08767569819738524488686318024854942e-9L,
D13 = 1.60590442297008495301927448122499313e-10L;
+/*
+ * XXX this has 1 more coeff than needed.
+ * XXX can start the double coeffs but not the double mults at D11.
+ * With my coeffs (D11-D16 double):
+ * Domain [0.03125, 0.1659], range ~[-1.1980e-37, 1.1980e-37]:
+ * |(exp(x)-1-x-x**2/2)/x - p(x)| ~< 2**-122.65
+ */
static const double
D14 = 1.1470726176204336e-11, /* 0x1.93971dc395d9ep-37 */
D15 = 7.6478532249581686e-13, /* 0x1.ae892e3D16fcep-41 */
@@ -375,6 +205,8 @@ expm1l(long double x)
int k, n, n2;
uint16_t hx, ix;
+ DOPRINT_START(&x);
+
/* Filter out exceptional cases. */
u.e = x;
hx = u.xbits.expsign;
@@ -382,11 +214,11 @@ expm1l(long double x)
if (ix >= BIAS + 7) { /* |x| >= 128 or x is NaN */
if (ix == BIAS + LDBL_MAX_EXP) {
if (hx & 0x8000) /* x is -Inf or -NaN */
- return (-1 / x - 1);
- return (x + x); /* x is +Inf or +NaN */
+ RETURNP(-1 / x - 1);
+ RETURNP(x + x); /* x is +Inf or +NaN */
}
if (x > o_threshold)
- return (huge * huge);
+ RETURNP(huge * huge);
/*
* expm1l() never underflows, but it must avoid
* unrepresentable large negative exponents. We used a
@@ -395,7 +227,7 @@ expm1l(long double x)
* in the same way as large ones here.
*/
if (hx & 0x8000) /* x <= -128 */
- return (tiny - 1); /* good for x < -114ln2 - eps */
+ RETURN2P(tiny, -1); /* good for x < -114ln2 - eps */
}
ENTERI();
@@ -407,7 +239,7 @@ expm1l(long double x)
if (x < T3) {
if (ix < BIAS - 113) { /* |x| < 0x1p-113 */
/* x (rounded) with inexact if x != 0: */
- RETURNI(x == 0 ? x :
+ RETURNPI(x == 0 ? x :
(0x1p200 * x + fabsl(x)) * 0x1p-200);
}
q = x * x2 * C3 + x2 * x2 * (C4 + x * (C5 + x * (C6 +
@@ -428,9 +260,9 @@ expm1l(long double x)
hx2_hi = x_hi * x_hi / 2;
hx2_lo = x_lo * (x + x_hi) / 2;
if (ix >= BIAS - 7)
- RETURNI(hx2_lo + x_lo + q + (hx2_hi + x_hi));
+ RETURN2PI(hx2_hi + x_hi, hx2_lo + x_lo + q);
else
- RETURNI(hx2_lo + q + hx2_hi + x);
+ RETURN2PI(x, hx2_lo + q + hx2_hi);
}
/* Reduce x to (k*ln2 + endpoint[n2] + r1 + r2). */
@@ -463,21 +295,21 @@ expm1l(long double x)
t = tbl[n2].lo + tbl[n2].hi;
if (k == 0) {
- t = tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1 +
- (tbl[n2].hi - 1);
+ t = SUM2P(tbl[n2].hi - 1, tbl[n2].lo * (r1 + 1) + t * q +
+ tbl[n2].hi * r1);
RETURNI(t);
}
if (k == -1) {
- t = tbl[n2].lo * (r1 + 1) + t * q + tbl[n2].hi * r1 +
- (tbl[n2].hi - 2);
+ t = SUM2P(tbl[n2].hi - 2, tbl[n2].lo * (r1 + 1) + t * q +
+ tbl[n2].hi * r1);
RETURNI(t / 2);
}
if (k < -7) {
- t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
+ t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1));
RETURNI(t * twopk - 1);
}
if (k > 2 * LDBL_MANT_DIG - 1) {
- t = tbl[n2].lo + t * (q + r1) + tbl[n2].hi;
+ t = SUM2P(tbl[n2].hi, tbl[n2].lo + t * (q + r1));
if (k == LDBL_MAX_EXP)
RETURNI(t * 2 * 0x1p16383L - 1);
RETURNI(t * twopk - 1);
@@ -487,8 +319,8 @@ expm1l(long double x)
twomk = v.e;
if (k > LDBL_MANT_DIG - 1)
- t = tbl[n2].lo - twomk + t * (q + r1) + tbl[n2].hi;
+ t = SUM2P(tbl[n2].hi, tbl[n2].lo - twomk + t * (q + r1));
else
- t = tbl[n2].lo + t * (q + r1) + (tbl[n2].hi - twomk);
+ t = SUM2P(tbl[n2].hi - twomk, tbl[n2].lo + t * (q + r1));
RETURNI(t * twopk);
}
diff --git a/libm/upstream-freebsd/lib/msun/src/e_cosh.c b/libm/upstream-freebsd/lib/msun/src/e_cosh.c
index a363695..246b5fb 100644
--- a/libm/upstream-freebsd/lib/msun/src/e_cosh.c
+++ b/libm/upstream-freebsd/lib/msun/src/e_cosh.c
@@ -35,6 +35,8 @@ __FBSDID("$FreeBSD$");
* only cosh(0)=1 is exact for finite x.
*/
+#include <float.h>
+
#include "math.h"
#include "math_private.h"
@@ -77,3 +79,7 @@ __ieee754_cosh(double x)
/* |x| > overflowthresold, cosh(x) overflow */
return huge*huge;
}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(cosh, coshl);
+#endif
diff --git a/libm/upstream-freebsd/lib/msun/src/e_lgamma_r.c b/libm/upstream-freebsd/lib/msun/src/e_lgamma_r.c
index 1cff592..7a95ea4 100644
--- a/libm/upstream-freebsd/lib/msun/src/e_lgamma_r.c
+++ b/libm/upstream-freebsd/lib/msun/src/e_lgamma_r.c
@@ -86,8 +86,10 @@ __FBSDID("$FreeBSD$");
#include "math.h"
#include "math_private.h"
+static const volatile double vzero = 0;
+
static const double
-two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */
+zero= 0.00000000000000000000e+00,
half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */
@@ -154,39 +156,35 @@ w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */
w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */
w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */
-static const double zero= 0.00000000000000000000e+00;
-
- static double sin_pi(double x)
+/*
+ * Compute sin(pi*x) without actually doing the pi*x multiplication.
+ * sin_pi(x) is only called for x < 0 and |x| < 2**(p-1) where p is
+ * the precision of x.
+ */
+static double
+sin_pi(double x)
{
+ volatile double vz;
double y,z;
- int n,ix;
+ int n;
+
+ y = -x;
- GET_HIGH_WORD(ix,x);
- ix &= 0x7fffffff;
+ vz = y+0x1p52; /* depend on 0 <= y < 0x1p52 */
+ z = vz-0x1p52; /* rint(y) for the above range */
+ if (z == y)
+ return zero;
- if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0);
- y = -x; /* x is assume negative */
+ vz = y+0x1p50;
+ GET_LOW_WORD(n,vz); /* bits for rounded y (units 0.25) */
+ z = vz-0x1p50; /* y rounded to a multiple of 0.25 */
+ if (z > y) {
+ z -= 0.25; /* adjust to round down */
+ n--;
+ }
+ n &= 7; /* octant of y mod 2 */
+ y = y - z + n * 0.25; /* y mod 2 */
- /*
- * argument reduction, make sure inexact flag not raised if input
- * is an integer
- */
- z = floor(y);
- if(z!=y) { /* inexact anyway */
- y *= 0.5;
- y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */
- n = (int) (y*4.0);
- } else {
- if(ix>=0x43400000) {
- y = zero; n = 0; /* y must be even */
- } else {
- if(ix<0x43300000) z = y+two52; /* exact */
- GET_LOW_WORD(n,z);
- n &= 1;
- y = n;
- n<<= 2;
- }
- }
switch (n) {
case 0: y = __kernel_sin(pi*y,zero,0); break;
case 1:
@@ -206,7 +204,7 @@ __ieee754_lgamma_r(double x, int *signgamp)
{
double t,y,z,nadj,p,p1,p2,p3,q,r,w;
int32_t hx;
- int i,lx,ix;
+ int i,ix,lx;
EXTRACT_WORDS(hx,lx,x);
@@ -214,7 +212,7 @@ __ieee754_lgamma_r(double x, int *signgamp)
*signgamp = 1;
ix = hx&0x7fffffff;
if(ix>=0x7ff00000) return x*x;
- if((ix|lx)==0) return one/zero;
+ if((ix|lx)==0) return one/vzero;
if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */
if(hx<0) {
*signgamp = -1;
@@ -223,9 +221,9 @@ __ieee754_lgamma_r(double x, int *signgamp)
}
if(hx<0) {
if(ix>=0x43300000) /* |x|>=2**52, must be -integer */
- return one/zero;
+ return one/vzero;
t = sin_pi(x);
- if(t==zero) return one/zero; /* -integer */
+ if(t==zero) return one/vzero; /* -integer */
nadj = __ieee754_log(pi/fabs(t*x));
if(t<zero) *signgamp = -1;
x = -x;
diff --git a/libm/upstream-freebsd/lib/msun/src/e_lgammaf_r.c b/libm/upstream-freebsd/lib/msun/src/e_lgammaf_r.c
index e2d90ef..9a7ab39 100644
--- a/libm/upstream-freebsd/lib/msun/src/e_lgammaf_r.c
+++ b/libm/upstream-freebsd/lib/msun/src/e_lgammaf_r.c
@@ -19,8 +19,10 @@ __FBSDID("$FreeBSD$");
#include "math.h"
#include "math_private.h"
+static const volatile float vzero = 0;
+
static const float
-two23= 8.3886080000e+06, /* 0x4b000000 */
+zero= 0.0000000000e+00,
half= 5.0000000000e-01, /* 0x3f000000 */
one = 1.0000000000e+00, /* 0x3f800000 */
pi = 3.1415927410e+00, /* 0x40490fdb */
@@ -87,39 +89,30 @@ w4 = -5.9518753551e-04, /* 0xba1c065c */
w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */
w6 = -1.6309292987e-03; /* 0xbad5c4e8 */
-static const float zero= 0.0000000000e+00;
-
- static float sin_pif(float x)
+static float
+sin_pif(float x)
{
+ volatile float vz;
float y,z;
- int n,ix;
+ int n;
- GET_FLOAT_WORD(ix,x);
- ix &= 0x7fffffff;
+ y = -x;
- if(ix<0x3e800000) return __kernel_sindf(pi*x);
- y = -x; /* x is assume negative */
+ vz = y+0x1p23F; /* depend on 0 <= y < 0x1p23 */
+ z = vz-0x1p23F; /* rintf(y) for the above range */
+ if (z == y)
+ return zero;
+
+ vz = y+0x1p21F;
+ GET_FLOAT_WORD(n,vz); /* bits for rounded y (units 0.25) */
+ z = vz-0x1p21F; /* y rounded to a multiple of 0.25 */
+ if (z > y) {
+ z -= 0.25F; /* adjust to round down */
+ n--;
+ }
+ n &= 7; /* octant of y mod 2 */
+ y = y - z + n * 0.25F; /* y mod 2 */
- /*
- * argument reduction, make sure inexact flag not raised if input
- * is an integer
- */
- z = floorf(y);
- if(z!=y) { /* inexact anyway */
- y *= (float)0.5;
- y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */
- n = (int) (y*(float)4.0);
- } else {
- if(ix>=0x4b800000) {
- y = zero; n = 0; /* y must be even */
- } else {
- if(ix<0x4b000000) z = y+two23; /* exact */
- GET_FLOAT_WORD(n,z);
- n &= 1;
- y = n;
- n<<= 2;
- }
- }
switch (n) {
case 0: y = __kernel_sindf(pi*y); break;
case 1:
@@ -147,7 +140,7 @@ __ieee754_lgammaf_r(float x, int *signgamp)
*signgamp = 1;
ix = hx&0x7fffffff;
if(ix>=0x7f800000) return x*x;
- if(ix==0) return one/zero;
+ if(ix==0) return one/vzero;
if(ix<0x35000000) { /* |x|<2**-21, return -log(|x|) */
if(hx<0) {
*signgamp = -1;
@@ -156,9 +149,9 @@ __ieee754_lgammaf_r(float x, int *signgamp)
}
if(hx<0) {
if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */
- return one/zero;
+ return one/vzero;
t = sin_pif(x);
- if(t==zero) return one/zero; /* -integer */
+ if(t==zero) return one/vzero; /* -integer */
nadj = __ieee754_logf(pi/fabsf(t*x));
if(t<zero) *signgamp = -1;
x = -x;
diff --git a/libm/upstream-freebsd/lib/msun/src/e_pow.c b/libm/upstream-freebsd/lib/msun/src/e_pow.c
index 7607a4a..d54af9d 100644
--- a/libm/upstream-freebsd/lib/msun/src/e_pow.c
+++ b/libm/upstream-freebsd/lib/msun/src/e_pow.c
@@ -19,20 +19,20 @@ __FBSDID("$FreeBSD$");
* 1. Compute and return log2(x) in two pieces:
* log2(x) = w1 + w2,
* where w1 has 53-24 = 29 bit trailing zeros.
- * 2. Perform y*log2(x) = n+y' by simulating muti-precision
+ * 2. Perform y*log2(x) = n+y' by simulating multi-precision
* arithmetic, where |y'|<=0.5.
* 3. Return x**y = 2**n*exp(y'*log2)
*
* Special cases:
* 1. (anything) ** 0 is 1
* 2. (anything) ** 1 is itself
- * 3. (anything) ** NAN is NAN
+ * 3. (anything) ** NAN is NAN except 1 ** NAN = 1
* 4. NAN ** (anything except 0) is NAN
* 5. +-(|x| > 1) ** +INF is +INF
* 6. +-(|x| > 1) ** -INF is +0
* 7. +-(|x| < 1) ** +INF is +0
* 8. +-(|x| < 1) ** -INF is +INF
- * 9. +-1 ** +-INF is NAN
+ * 9. +-1 ** +-INF is 1
* 10. +0 ** (+anything except 0, NAN) is +0
* 11. -0 ** (+anything except 0, NAN, odd integer) is +0
* 12. +0 ** (-anything except 0, NAN) is +INF
@@ -141,7 +141,7 @@ __ieee754_pow(double x, double y)
if(ly==0) {
if (iy==0x7ff00000) { /* y is +-inf */
if(((ix-0x3ff00000)|lx)==0)
- return one; /* (-1)**+-inf is NaN */
+ return one; /* (-1)**+-inf is 1 */
else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */
return (hy>=0)? y: zero;
else /* (|x|<1)**-,+inf = inf,0 */
diff --git a/libm/upstream-freebsd/lib/msun/src/e_sinh.c b/libm/upstream-freebsd/lib/msun/src/e_sinh.c
index 17442d0..6c01f4a 100644
--- a/libm/upstream-freebsd/lib/msun/src/e_sinh.c
+++ b/libm/upstream-freebsd/lib/msun/src/e_sinh.c
@@ -32,6 +32,8 @@ __FBSDID("$FreeBSD$");
* only sinh(0)=0 is exact for finite x.
*/
+#include <float.h>
+
#include "math.h"
#include "math_private.h"
@@ -71,3 +73,7 @@ __ieee754_sinh(double x)
/* |x| > overflowthresold, sinh(x) overflow */
return x*shuge;
}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(sinh, sinhl);
+#endif
diff --git a/libm/upstream-freebsd/lib/msun/src/imprecise.c b/libm/upstream-freebsd/lib/msun/src/imprecise.c
index a7503bf..e0ad103 100644
--- a/libm/upstream-freebsd/lib/msun/src/imprecise.c
+++ b/libm/upstream-freebsd/lib/msun/src/imprecise.c
@@ -61,8 +61,6 @@ DECLARE_WEAK(powl);
DECLARE_WEAK(f ## l)
DECLARE_IMPRECISE(cosh);
-DECLARE_IMPRECISE(erfc);
-DECLARE_IMPRECISE(erf);
DECLARE_IMPRECISE(lgamma);
DECLARE_IMPRECISE(sinh);
DECLARE_IMPRECISE(tanh);
diff --git a/libm/upstream-freebsd/lib/msun/src/s_erf.c b/libm/upstream-freebsd/lib/msun/src/s_erf.c
index 0886e5e..e1d63bc 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_erf.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_erf.c
@@ -111,18 +111,25 @@ __FBSDID("$FreeBSD$");
#include "math.h"
#include "math_private.h"
+/* XXX Prevent compilers from erroneously constant folding: */
+static const volatile double tiny= 1e-300;
+
static const double
-tiny = 1e-300,
-half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
-one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
-two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */
- /* c = (float)0.84506291151 */
+half= 0.5,
+one = 1,
+two = 2,
+/* c = (float)0.84506291151 */
erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */
/*
- * Coefficients for approximation to erf on [0,0.84375]
+ * In the domain [0, 2**-28], only the first term in the power series
+ * expansion of erf(x) is used. The magnitude of the first neglected
+ * terms is less than 2**-84.
*/
efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */
efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */
+/*
+ * Coefficients for approximation to erf on [0,0.84375]
+ */
pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */
pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */
pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */
@@ -134,7 +141,7 @@ qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */
qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */
qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */
/*
- * Coefficients for approximation to erf in [0.84375,1.25]
+ * Coefficients for approximation to erf in [0.84375,1.25]
*/
pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */
pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */
@@ -150,7 +157,7 @@ qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */
qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */
qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */
/*
- * Coefficients for approximation to erfc in [1.25,1/0.35]
+ * Coefficients for approximation to erfc in [1.25,1/0.35]
*/
ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */
ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */
@@ -169,7 +176,7 @@ sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */
sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */
sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */
/*
- * Coefficients for approximation to erfc in [1/.35,28]
+ * Coefficients for approximation to erfc in [1/.35,28]
*/
rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */
rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */
@@ -201,7 +208,7 @@ erf(double x)
if(ix < 0x3feb0000) { /* |x|<0.84375 */
if(ix < 0x3e300000) { /* |x|<2**-28 */
if (ix < 0x00800000)
- return 0.125*(8.0*x+efx8*x); /*avoid underflow */
+ return (8*x+efx8*x)/8; /* avoid spurious underflow */
return x + efx*x;
}
z = x*x;
@@ -222,15 +229,12 @@ erf(double x)
x = fabs(x);
s = one/(x*x);
if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */
- R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
- ra5+s*(ra6+s*ra7))))));
- S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
- sa5+s*(sa6+s*(sa7+s*sa8)))))));
+ R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*ra7))))));
+ S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+
+ s*sa8)))))));
} else { /* |x| >= 1/0.35 */
- R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
- rb5+s*rb6)))));
- S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
- sb5+s*(sb6+s*sb7))))));
+ R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*rb6)))));
+ S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*sb7))))));
}
z = x;
SET_LOW_WORD(z,0);
@@ -238,6 +242,10 @@ erf(double x)
if(hx>=0) return one-r/x; else return r/x-one;
}
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(erf, erfl);
+#endif
+
double
erfc(double x)
{
@@ -279,23 +287,23 @@ erfc(double x)
x = fabs(x);
s = one/(x*x);
if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/
- R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(
- ra5+s*(ra6+s*ra7))))));
- S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(
- sa5+s*(sa6+s*(sa7+s*sa8)))))));
+ R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*(ra5+s*(ra6+s*ra7))))));
+ S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*(sa5+s*(sa6+s*(sa7+
+ s*sa8)))))));
} else { /* |x| >= 1/.35 ~ 2.857143 */
if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */
- R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(
- rb5+s*rb6)))));
- S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(
- sb5+s*(sb6+s*sb7))))));
+ R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+s*rb6)))));
+ S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*(sb5+s*(sb6+s*sb7))))));
}
z = x;
SET_LOW_WORD(z,0);
- r = __ieee754_exp(-z*z-0.5625)*
- __ieee754_exp((z-x)*(z+x)+R/S);
+ r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S);
if(hx>0) return r/x; else return two-r/x;
} else {
if(hx>0) return tiny*tiny; else return two-tiny;
}
}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(erfc, erfcl);
+#endif
diff --git a/libm/upstream-freebsd/lib/msun/src/s_erff.c b/libm/upstream-freebsd/lib/msun/src/s_erff.c
index a3579f1..d6cfbd2 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_erff.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_erff.c
@@ -19,64 +19,63 @@ __FBSDID("$FreeBSD$");
#include "math.h"
#include "math_private.h"
+/* XXX Prevent compilers from erroneously constant folding: */
+static const volatile float tiny = 1e-30;
+
static const float
-tiny = 1e-30,
-half= 5.0000000000e-01, /* 0x3F000000 */
-one = 1.0000000000e+00, /* 0x3F800000 */
-two = 2.0000000000e+00, /* 0x40000000 */
+half= 0.5,
+one = 1,
+two = 2,
+erx = 8.42697144e-01, /* 0x3f57bb00 */
/*
- * Coefficients for approximation to erf on [0,0.84375]
+ * In the domain [0, 2**-14], only the first term in the power series
+ * expansion of erf(x) is used. The magnitude of the first neglected
+ * terms is less than 2**-42.
*/
-efx = 1.2837916613e-01, /* 0x3e0375d4 */
-efx8= 1.0270333290e+00, /* 0x3f8375d4 */
+efx = 1.28379166e-01, /* 0x3e0375d4 */
+efx8= 1.02703333e+00, /* 0x3f8375d4 */
/*
- * Domain [0, 0.84375], range ~[-5.4446e-10,5.5197e-10]:
- * |(erf(x) - x)/x - p(x)/q(x)| < 2**-31.
+ * Domain [0, 0.84375], range ~[-5.4419e-10, 5.5179e-10]:
+ * |(erf(x) - x)/x - pp(x)/qq(x)| < 2**-31
*/
-pp0 = 1.28379166e-01F, /* 0x1.06eba8p-3 */
-pp1 = -3.36030394e-01F, /* -0x1.58185ap-2 */
-pp2 = -1.86260219e-03F, /* -0x1.e8451ep-10 */
-qq1 = 3.12324286e-01F, /* 0x1.3fd1f0p-2 */
-qq2 = 2.16070302e-02F, /* 0x1.620274p-6 */
-qq3 = -1.98859419e-03F, /* -0x1.04a626p-9 */
+pp0 = 1.28379166e-01, /* 0x3e0375d4 */
+pp1 = -3.36030394e-01, /* 0xbeac0c2d */
+pp2 = -1.86261395e-03, /* 0xbaf422f4 */
+qq1 = 3.12324315e-01, /* 0x3e9fe8f9 */
+qq2 = 2.16070414e-02, /* 0x3cb10140 */
+qq3 = -1.98859372e-03, /* 0xbb025311 */
/*
- * Domain [0.84375, 1.25], range ~[-1.953e-11,1.940e-11]:
- * |(erf(x) - erx) - p(x)/q(x)| < 2**-36.
+ * Domain [0.84375, 1.25], range ~[-1.023e-9, 1.023e-9]:
+ * |(erf(x) - erx) - pa(x)/qa(x)| < 2**-31
*/
-erx = 8.42697144e-01F, /* 0x1.af7600p-1. erf(1) rounded to 16 bits. */
-pa0 = 3.64939137e-06F, /* 0x1.e9d022p-19 */
-pa1 = 4.15109694e-01F, /* 0x1.a91284p-2 */
-pa2 = -1.65179938e-01F, /* -0x1.5249dcp-3 */
-pa3 = 1.10914491e-01F, /* 0x1.c64e46p-4 */
-qa1 = 6.02074385e-01F, /* 0x1.344318p-1 */
-qa2 = 5.35934687e-01F, /* 0x1.126608p-1 */
-qa3 = 1.68576106e-01F, /* 0x1.593e6ep-3 */
-qa4 = 5.62181212e-02F, /* 0x1.cc89f2p-5 */
+pa0 = 3.65041046e-06, /* 0x3674f993 */
+pa1 = 4.15109307e-01, /* 0x3ed48935 */
+pa2 = -2.09395722e-01, /* 0xbe566bd5 */
+pa3 = 8.67677554e-02, /* 0x3db1b34b */
+qa1 = 4.95560974e-01, /* 0x3efdba2b */
+qa2 = 3.71248513e-01, /* 0x3ebe1449 */
+qa3 = 3.92478965e-02, /* 0x3d20c267 */
/*
- * Domain [1.25,1/0.35], range ~[-7.043e-10,7.457e-10]:
- * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-30
+ * Domain [1.25,1/0.35], range ~[-4.821e-9, 4.927e-9]:
+ * |log(x*erfc(x)) + x**2 + 0.5625 - ra(x)/sa(x)| < 2**-28
*/
-ra0 = -9.87132732e-03F, /* -0x1.4376b2p-7 */
-ra1 = -5.53605914e-01F, /* -0x1.1b723cp-1 */
-ra2 = -2.17589188e+00F, /* -0x1.1683a0p+1 */
-ra3 = -1.43268085e+00F, /* -0x1.6ec42cp+0 */
-sa1 = 5.45995426e+00F, /* 0x1.5d6fe4p+2 */
-sa2 = 6.69798088e+00F, /* 0x1.acabb8p+2 */
-sa3 = 1.43113089e+00F, /* 0x1.6e5e98p+0 */
-sa4 = -5.77397496e-02F, /* -0x1.d90108p-5 */
+ra0 = -9.88156721e-03, /* 0xbc21e64c */
+ra1 = -5.43658376e-01, /* 0xbf0b2d32 */
+ra2 = -1.66828310e+00, /* 0xbfd58a4d */
+ra3 = -6.91554189e-01, /* 0xbf3109b2 */
+sa1 = 4.48581553e+00, /* 0x408f8bcd */
+sa2 = 4.10799170e+00, /* 0x408374ab */
+sa3 = 5.53855181e-01, /* 0x3f0dc974 */
/*
- * Domain [1/0.35, 11], range ~[-2.264e-13,2.336e-13]:
- * |log(x*erfc(x)) + x**2 + 0.5625 - r(x)/s(x)| < 2**-42
+ * Domain [2.85715, 11], range ~[-1.484e-9, 1.505e-9]:
+ * |log(x*erfc(x)) + x**2 + 0.5625 - rb(x)/sb(x)| < 2**-30
*/
-rb0 = -9.86494310e-03F, /* -0x1.434124p-7 */
-rb1 = -6.25171244e-01F, /* -0x1.401672p-1 */
-rb2 = -6.16498327e+00F, /* -0x1.8a8f16p+2 */
-rb3 = -1.66696873e+01F, /* -0x1.0ab70ap+4 */
-rb4 = -9.53764343e+00F, /* -0x1.313460p+3 */
-sb1 = 1.26884899e+01F, /* 0x1.96081cp+3 */
-sb2 = 4.51839523e+01F, /* 0x1.6978bcp+5 */
-sb3 = 4.72810211e+01F, /* 0x1.7a3f88p+5 */
-sb4 = 8.93033314e+00F; /* 0x1.1dc54ap+3 */
+rb0 = -9.86496918e-03, /* 0xbc21a0ae */
+rb1 = -5.48049808e-01, /* 0xbf0c4cfe */
+rb2 = -1.84115684e+00, /* 0xbfebab07 */
+sb1 = 4.87132740e+00, /* 0x409be1ea */
+sb2 = 3.04982710e+00, /* 0x4043305e */
+sb3 = -7.61900663e-01; /* 0xbf430bec */
float
erff(float x)
@@ -85,9 +84,9 @@ erff(float x)
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
- if(ix>=0x7f800000) { /* erf(nan)=nan */
+ if(ix>=0x7f800000) { /* erff(nan)=nan */
i = ((u_int32_t)hx>>31)<<1;
- return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */
+ return (float)(1-i)+one/x; /* erff(+-inf)=+-1 */
}
if(ix < 0x3f580000) { /* |x|<0.84375 */
@@ -105,7 +104,7 @@ erff(float x)
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
s = fabsf(x)-one;
P = pa0+s*(pa1+s*(pa2+s*pa3));
- Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4)));
+ Q = one+s*(qa1+s*(qa2+s*qa3));
if(hx>=0) return erx + P/Q; else return -erx - P/Q;
}
if (ix >= 0x40800000) { /* inf>|x|>=4 */
@@ -113,12 +112,12 @@ erff(float x)
}
x = fabsf(x);
s = one/(x*x);
- if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */
+ if(ix< 0x4036db8c) { /* |x| < 2.85715 ~ 1/0.35 */
R=ra0+s*(ra1+s*(ra2+s*ra3));
- S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4)));
- } else { /* |x| >= 1/0.35 */
- R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4)));
- S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4)));
+ S=one+s*(sa1+s*(sa2+s*sa3));
+ } else { /* |x| >= 2.85715 ~ 1/0.35 */
+ R=rb0+s*(rb1+s*rb2);
+ S=one+s*(sb1+s*(sb2+s*sb3));
}
SET_FLOAT_WORD(z,hx&0xffffe000);
r = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S);
@@ -132,8 +131,8 @@ erfcf(float x)
float R,S,P,Q,s,y,z,r;
GET_FLOAT_WORD(hx,x);
ix = hx&0x7fffffff;
- if(ix>=0x7f800000) { /* erfc(nan)=nan */
- /* erfc(+-inf)=0,2 */
+ if(ix>=0x7f800000) { /* erfcf(nan)=nan */
+ /* erfcf(+-inf)=0,2 */
return (float)(((u_int32_t)hx>>31)<<1)+one/x;
}
@@ -155,7 +154,7 @@ erfcf(float x)
if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */
s = fabsf(x)-one;
P = pa0+s*(pa1+s*(pa2+s*pa3));
- Q = one+s*(qa1+s*(qa2+s*(qa3+s*qa4)));
+ Q = one+s*(qa1+s*(qa2+s*qa3));
if(hx>=0) {
z = one-erx; return z - P/Q;
} else {
@@ -165,13 +164,13 @@ erfcf(float x)
if (ix < 0x41300000) { /* |x|<11 */
x = fabsf(x);
s = one/(x*x);
- if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/
- R=ra0+s*(ra1+s*(ra2+s*ra3));
- S=one+s*(sa1+s*(sa2+s*(sa3+s*sa4)));
- } else { /* |x| >= 1/.35 ~ 2.857143 */
+ if(ix< 0x4036db8c) { /* |x| < 2.85715 ~ 1/.35 */
+ R=ra0+s*(ra1+s*(ra2+s*ra3));
+ S=one+s*(sa1+s*(sa2+s*sa3));
+ } else { /* |x| >= 2.85715 ~ 1/.35 */
if(hx<0&&ix>=0x40a00000) return two-tiny;/* x < -5 */
- R=rb0+s*(rb1+s*(rb2+s*(rb3+s*rb4)));
- S=one+s*(sb1+s*(sb2+s*(sb3+s*sb4)));
+ R=rb0+s*(rb1+s*rb2);
+ S=one+s*(sb1+s*(sb2+s*sb3));
}
SET_FLOAT_WORD(z,hx&0xffffe000);
r = expf(-z*z-0.5625F)*expf((z-x)*(z+x)+R/S);
diff --git a/libm/upstream-freebsd/lib/msun/src/s_rintl.c b/libm/upstream-freebsd/lib/msun/src/s_rintl.c
index e55b40e..b43df89 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_rintl.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_rintl.c
@@ -29,7 +29,6 @@ __FBSDID("$FreeBSD$");
#include <float.h>
#include <math.h>
-#include <stdint.h>
#include "fpmath.h"
diff --git a/libm/upstream-freebsd/lib/msun/src/s_tanh.c b/libm/upstream-freebsd/lib/msun/src/s_tanh.c
index 96e3565..6d26c69 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_tanh.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_tanh.c
@@ -37,10 +37,13 @@ __FBSDID("$FreeBSD$");
* only tanh(0)=0 is exact for finite argument.
*/
+#include <float.h>
+
#include "math.h"
#include "math_private.h"
-static const double one = 1.0, two = 2.0, tiny = 1.0e-300, huge = 1.0e300;
+static const volatile double tiny = 1.0e-300;
+static const double one = 1.0, two = 2.0, huge = 1.0e300;
double
tanh(double x)
@@ -75,3 +78,7 @@ tanh(double x)
}
return (jx>=0)? z: -z;
}
+
+#if (LDBL_MANT_DIG == 53)
+__weak_reference(tanh, tanhl);
+#endif
diff --git a/libm/upstream-freebsd/lib/msun/src/s_tanhf.c b/libm/upstream-freebsd/lib/msun/src/s_tanhf.c
index 04f09c6..f537be4 100644
--- a/libm/upstream-freebsd/lib/msun/src/s_tanhf.c
+++ b/libm/upstream-freebsd/lib/msun/src/s_tanhf.c
@@ -19,7 +19,9 @@ __FBSDID("$FreeBSD$");
#include "math.h"
#include "math_private.h"
-static const float one=1.0, two=2.0, tiny = 1.0e-30, huge = 1.0e30;
+static const volatile float tiny = 1.0e-30;
+static const float one=1.0, two=2.0, huge = 1.0e30;
+
float
tanhf(float x)
{