x86-64: Add vector erf/erff implementation to libmvec

Implement vectorized erf/erff containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI.  It also contains
accuracy and ABI tests for vector erf/erff with regenerated ulps.

Reviewed-by: H.J. Lu <hjl.tools@gmail.com>

1 files changed, 664 insertions, 0 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_erff4_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_s_erff4_core_sse4.S
new file mode 100644
index 0000000000..5c052f5921
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_erff4_core_sse4.S
@@ -0,0 +1,664 @@
+/* Function erff vectorized with SSE4.
+   Copyright (C) 2021 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C 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.
+
+   The GNU C 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 the GNU C Library; if not, see
+   https://www.gnu.org/licenses/.  */
+
+/*
+ * ALGORITHM DESCRIPTION:
+ *
+ *   Basic formula is
+ *    erf(x) ~ erf(x0) +
+ *              + exp(-x0*x0)*D*(1+c0+T*P1(T)+D^2*P3(T)+D^4*p5)
+ *   where D=x-x0, T=x0*D
+ *   x0 is x rounded to a specified number of fractional bits (in this case 8),
+ *    except that x0=0 for |x|<3.5/256.0 (using x0=0 for first 4 table entries)
+ *
+ *   Data table packs both erf(x0)_high and a few bits of erf(x0)_low in one
+ *   entry (in place of redundant exponent bits)
+ *
+ */
+
+/* Offsets for data table __svml_serf_data_internal
+ */
+#define _erf_tbl                      	0
+#define _AbsMask                      	4032
+#define _MaxThreshold                 	4048
+#define _SRound                       	4064
+#define _U2Threshold                  	4080
+#define _poly3_0                      	4096
+
+/* Lookup bias for data table __svml_serf_data_internal.  */
+#define Table_Lookup_Bias               -0x3c000000
+
+#include <sysdep.h>
+
+        .text
+	.section .text.sse4,"ax",@progbits
+ENTRY(_ZGVbN4v_erff_sse4)
+        lea       Table_Lookup_Bias+__svml_serf_data_internal(%rip), %rdi
+        movups    _AbsMask+__svml_serf_data_internal(%rip), %xmm9
+        andps     %xmm0, %xmm9
+
+/*
+ * erf(x) rounds to 1.0 for x>_MaxThreshold (3.9375)
+ * can compute all results in the main path
+ */
+        movaps    %xmm9, %xmm12
+
+/* save sign */
+        pxor      %xmm9, %xmm0
+        minps     _MaxThreshold+__svml_serf_data_internal(%rip), %xmm12
+
+/*
+ * vector gather:
+ * erf(x0), exp(-x0*x0)*2.0/sqrt(pi)
+ */
+        movups    _SRound+__svml_serf_data_internal(%rip), %xmm1
+        movaps    %xmm1, %xmm4
+        movups    _U2Threshold+__svml_serf_data_internal(%rip), %xmm11
+        addps     %xmm12, %xmm4
+        cmpltps   %xmm12, %xmm11
+        movaps    %xmm4, %xmm10
+        pslld     $3, %xmm4
+        pshufd    $1, %xmm4, %xmm2
+        subps     %xmm1, %xmm10
+        movd      %xmm4, %eax
+        movd      %xmm2, %edx
+        pshufd    $2, %xmm4, %xmm3
+        subps     %xmm10, %xmm12
+        movd      %xmm3, %ecx
+        andps     %xmm12, %xmm11
+
+/* D2 = Diff^2 */
+        mulps     %xmm11, %xmm11
+        mulps     %xmm12, %xmm10
+
+/* NaN fixup */
+        minps     %xmm9, %xmm12
+
+/*
+ * Start polynomial evaluation
+ * P1
+ */
+        mulps     _poly3_0+__svml_serf_data_internal(%rip), %xmm11
+        pshufd    $3, %xmm4, %xmm5
+        subps     %xmm10, %xmm11
+        movd      %xmm5, %esi
+
+/*
+ * branch-free
+ * (exp_h(x0) * Diff) * (poly + 1.0)
+ */
+        mulps     %xmm12, %xmm11
+        movslq    %eax, %rax
+        addps     %xmm11, %xmm12
+        movslq    %edx, %rdx
+        movslq    %ecx, %rcx
+        movslq    %esi, %rsi
+        movq      (%rdi,%rax), %xmm13
+        movq      (%rdi,%rdx), %xmm6
+        movq      (%rdi,%rcx), %xmm8
+        movq      (%rdi,%rsi), %xmm7
+        unpcklps  %xmm6, %xmm13
+        unpcklps  %xmm7, %xmm8
+        movaps    %xmm13, %xmm14
+        shufps    $238, %xmm8, %xmm13
+
+/* Final result */
+        mulps     %xmm12, %xmm13
+        movlhps   %xmm8, %xmm14
+        addps     %xmm13, %xmm14
+
+/* set sign */
+        orps      %xmm14, %xmm0
+        ret
+
+END(_ZGVbN4v_erff_sse4)
+
+        .section .rodata, "a"
+        .align 16
+
+#ifdef __svml_serf_data_internal_typedef
+typedef unsigned int VUINT32;
+typedef struct
+{
+        __declspec(align(16)) VUINT32 _erf_tbl[1008][1];
+        __declspec(align(16)) VUINT32 _AbsMask[4][1];
+        __declspec(align(16)) VUINT32 _MaxThreshold[4][1];
+        __declspec(align(16)) VUINT32 _SRound[4][1];
+        __declspec(align(16)) VUINT32 _U2Threshold[4][1];
+        __declspec(align(16)) VUINT32 _poly3_0[4][1];
+} __svml_serf_data_internal;
+#endif
+__svml_serf_data_internal:
+        /*== _erf_tbl ==*/
+        .long 0x00000000, 0x3f906ebb
+        .long 0x3c106dfa, 0x3f906c79
+        .long 0x3c906bb8, 0x3f9065b4
+        .long 0x3cd89bf0, 0x3f905a6c
+        .long 0x3d1062b2, 0x3f904aa3
+        .long 0x3d3472ea, 0x3f90365a
+        .long 0x3d587d7f, 0x3f901d93
+        .long 0x3d7c8154, 0x3f900050
+        .long 0x3d903ea4, 0x3f8fde94
+        .long 0x3da2381f, 0x3f8fb862
+        .long 0x3db42c8d, 0x3f8f8dbd
+        .long 0x3dc61b5f, 0x3f8f5eab
+        .long 0x3dd80409, 0x3f8f2b2e
+        .long 0x3de9e5fc, 0x3f8ef34c
+        .long 0x3dfbc0ad, 0x3f8eb70a
+        .long 0x3e06c9c8, 0x3f8e766e
+        .long 0x3e0faf0d, 0x3f8e317d
+        .long 0x3e188fe1, 0x3f8de83e
+        .long 0x3e216bfe, 0x3f8d9ab9
+        .long 0x3e2a4321, 0x3f8d48f3
+        .long 0x3e331506, 0x3f8cf2f5
+        .long 0x3e3be169, 0x3f8c98c6
+        .long 0x3e44a808, 0x3f8c3a6f
+        .long 0x3e4d68a1, 0x3f8bd7f8
+        .long 0x3e5622f2, 0x3f8b716c
+        .long 0x3e5ed6b9, 0x3f8b06d2
+        .long 0x3e6783b7, 0x3f8a9834
+        .long 0x3e7029aa, 0x3f8a259e
+        .long 0x3e78c855, 0x3f89af18
+        .long 0x3e80afbc, 0x3f8934af
+        .long 0x3e84f76b, 0x3f88b66c
+        .long 0x3e893b19, 0x3f88345d
+        .long 0x3e8d7aa7, 0x3f87ae8b
+        .long 0x3e91b5f8, 0x3f872504
+        .long 0x3e95ecee, 0x3f8697d3
+        .long 0x3e9a1f6b, 0x3f860705
+        .long 0x3e9e4d54, 0x3f8572a8
+        .long 0x3ea2768c, 0x3f84dac8
+        .long 0x3ea69af8, 0x3f843f72
+        .long 0x3eaaba7a, 0x3f83a0b6
+        .long 0x3eaed4fa, 0x3f82fe9f
+        .long 0x3eb2ea5c, 0x3f82593e
+        .long 0x3eb6fa85, 0x3f81b0a0
+        .long 0x3ebb055d, 0x3f8104d3
+        .long 0x3ebf0aca, 0x3f8055e8
+        .long 0x3ec30ab3, 0x3f7f47d8
+        .long 0x3ec70501, 0x3f7ddddf
+        .long 0x3ecaf99b, 0x3f7c6e05
+        .long 0x3ecee869, 0x3f7af867
+        .long 0x3ed2d156, 0x3f797d26
+        .long 0x3ed6b44b, 0x3f77fc62
+        .long 0x3eda9132, 0x3f76763c
+        .long 0x3ede67f6, 0x3f74ead4
+        .long 0x3ee23882, 0x3f735a4c
+        .long 0x3ee602c2, 0x3f71c4c4
+        .long 0x3ee9c6a2, 0x3f702a5f
+        .long 0x3eed840e, 0x3f6e8b3e
+        .long 0x3ef13af5, 0x3f6ce783
+        .long 0x3ef4eb45, 0x3f6b3f51
+        .long 0x3ef894ea, 0x3f6992c9
+        .long 0x3efc37d5, 0x3f67e20f
+        .long 0x3effd3f5, 0x3f662d45
+        .long 0x3f01b49d, 0x3f64748e
+        .long 0x3f037bca, 0x3f62b80d
+        .long 0x3f053f7b, 0x3f60f7e5
+        .long 0x3f06ffa8, 0x3f5f3439
+        .long 0x3f08bc4a, 0x3f5d6d2d
+        .long 0x3f0a755a, 0x3f5ba2e3
+        .long 0x3f0c2ad3, 0x3f59d57e
+        .long 0x3f0ddcae, 0x3f580523
+        .long 0x3f0f8ae6, 0x3f5631f4
+        .long 0x3f113574, 0x3f545c14
+        .long 0x3f12dc54, 0x3f5283a7
+        .long 0x3f147f81, 0x3f50a8cf
+        .long 0x3f161ef6, 0x3f4ecbb1
+        .long 0x3f17baae, 0x3f4cec6d
+        .long 0x3f1952a6, 0x3f4b0b28
+        .long 0x3f1ae6da, 0x3f492804
+        .long 0x3f1c7745, 0x3f474323
+        .long 0x3f1e03e5, 0x3f455ca8
+        .long 0x3f1f8cb7, 0x3f4374b5
+        .long 0x3f2111b7, 0x3f418b6b
+        .long 0x3f2292e4, 0x3f3fa0ee
+        .long 0x3f24103a, 0x3f3db55e
+        .long 0x3f2589b9, 0x3f3bc8dc
+        .long 0x3f26ff5d, 0x3f39db8a
+        .long 0x3f287126, 0x3f37ed89
+        .long 0x3f29df13, 0x3f35fef8
+        .long 0x3f2b4922, 0x3f340ff9
+        .long 0x3f2caf53, 0x3f3220ab
+        .long 0x3f2e11a4, 0x3f30312e
+        .long 0x3f2f7017, 0x3f2e41a1
+        .long 0x3f30caab, 0x3f2c5223
+        .long 0x3f322160, 0x3f2a62d3
+        .long 0x3f337437, 0x3f2873cf
+        .long 0x3f34c32f, 0x3f268534
+        .long 0x3f360e4c, 0x3f249721
+        .long 0x3f37558c, 0x3f22a9b3
+        .long 0x3f3898f3, 0x3f20bd06
+        .long 0x3f39d881, 0x3f1ed137
+        .long 0x3f3b1438, 0x3f1ce661
+        .long 0x3f3c4c1b, 0x3f1afca0
+        .long 0x3f3d802c, 0x3f19140f
+        .long 0x3f3eb06c, 0x3f172cc9
+        .long 0x3f3fdce0, 0x3f1546e7
+        .long 0x3f410589, 0x3f136284
+        .long 0x3f422a6b, 0x3f117fb9
+        .long 0x3f434b89, 0x3f0f9e9e
+        .long 0x3f4468e7, 0x3f0dbf4c
+        .long 0x3f458287, 0x3f0be1db
+        .long 0x3f46986f, 0x3f0a0662
+        .long 0x3f47aaa2, 0x3f082cf7
+        .long 0x3f48b925, 0x3f0655b1
+        .long 0x3f49c3fb, 0x3f0480a6
+        .long 0x3f4acb29, 0x3f02adeb
+        .long 0x3f4bceb4, 0x3f00dd96
+        .long 0x3f4ccea1, 0x3efe1f73
+        .long 0x3f4dcaf4, 0x3efa88d5
+        .long 0x3f4ec3b4, 0x3ef6f777
+        .long 0x3f4fb8e5, 0x3ef36b80
+        .long 0x3f50aa8d, 0x3eefe513
+        .long 0x3f5198b1, 0x3eec6455
+        .long 0x3f528358, 0x3ee8e968
+        .long 0x3f536a86, 0x3ee5746d
+        .long 0x3f544e43, 0x3ee20584
+        .long 0x3f552e93, 0x3ede9ccc
+        .long 0x3f560b7e, 0x3edb3a64
+        .long 0x3f56e50a, 0x3ed7de6a
+        .long 0x3f57bb3d, 0x3ed488f8
+        .long 0x3f588e1e, 0x3ed13a2b
+        .long 0x3f595db4, 0x3ecdf21c
+        .long 0x3f5a2a05, 0x3ecab0e4
+        .long 0x3f5af318, 0x3ec7769b
+        .long 0x3f5bb8f4, 0x3ec44359
+        .long 0x3f5c7ba1, 0x3ec11733
+        .long 0x3f5d3b25, 0x3ebdf23d
+        .long 0x3f5df788, 0x3ebad48d
+        .long 0x3f5eb0d1, 0x3eb7be35
+        .long 0x3f5f6707, 0x3eb4af46
+        .long 0x3f601a32, 0x3eb1a7d3
+        .long 0x3f60ca59, 0x3eaea7ea
+        .long 0x3f617784, 0x3eabaf9a
+        .long 0x3f6221bb, 0x3ea8bef3
+        .long 0x3f62c905, 0x3ea5d600
+        .long 0x3f636d69, 0x3ea2f4ce
+        .long 0x3f640ef1, 0x3ea01b68
+        .long 0x3f64ada3, 0x3e9d49d9
+        .long 0x3f654987, 0x3e9a8029
+        .long 0x3f65e2a6, 0x3e97be62
+        .long 0x3f667906, 0x3e95048b
+        .long 0x3f670cb1, 0x3e9252aa
+        .long 0x3f679dae, 0x3e8fa8c5
+        .long 0x3f682c06, 0x3e8d06e3
+        .long 0x3f68b7bf, 0x3e8a6d05
+        .long 0x3f6940e2, 0x3e87db31
+        .long 0x3f69c778, 0x3e855168
+        .long 0x3f6a4b88, 0x3e82cfad
+        .long 0x3f6acd1a, 0x3e805600
+        .long 0x3f6b4c36, 0x3e7bc8c2
+        .long 0x3f6bc8e5, 0x3e76f5a0
+        .long 0x3f6c432f, 0x3e723298
+        .long 0x3f6cbb1b, 0x3e6d7fa5
+        .long 0x3f6d30b1, 0x3e68dcc1
+        .long 0x3f6da3fa, 0x3e6449e7
+        .long 0x3f6e14fe, 0x3e5fc70e
+        .long 0x3f6e83c4, 0x3e5b542b
+        .long 0x3f6ef055, 0x3e56f136
+        .long 0x3f6f5ab8, 0x3e529e21
+        .long 0x3f6fc2f5, 0x3e4e5adf
+        .long 0x3f702915, 0x3e4a2761
+        .long 0x3f708d1f, 0x3e460399
+        .long 0x3f70ef1b, 0x3e41ef75
+        .long 0x3f714f11, 0x3e3deae4
+        .long 0x3f71ad09, 0x3e39f5d2
+        .long 0x3f72090a, 0x3e36102b
+        .long 0x3f72631c, 0x3e3239db
+        .long 0x3f72bb46, 0x3e2e72cb
+        .long 0x3f731191, 0x3e2abae4
+        .long 0x3f736604, 0x3e27120f
+        .long 0x3f73b8a5, 0x3e237833
+        .long 0x3f74097e, 0x3e1fed36
+        .long 0x3f745895, 0x3e1c70fd
+        .long 0x3f74a5f2, 0x3e19036e
+        .long 0x3f74f19b, 0x3e15a46d
+        .long 0x3f753b98, 0x3e1253dc
+        .long 0x3f7583f1, 0x3e0f119f
+        .long 0x3f75caac, 0x3e0bdd96
+        .long 0x3f760fd1, 0x3e08b7a4
+        .long 0x3f765366, 0x3e059fa9
+        .long 0x3f769573, 0x3e029586
+        .long 0x3f76d5fe, 0x3dff3230
+        .long 0x3f77150f, 0x3df95481
+        .long 0x3f7752ab, 0x3df391b9
+        .long 0x3f778eda, 0x3dede995
+        .long 0x3f77c9a2, 0x3de85bd0
+        .long 0x3f78030a, 0x3de2e825
+        .long 0x3f783b18, 0x3ddd8e4c
+        .long 0x3f7871d3, 0x3dd84dfe
+        .long 0x3f78a741, 0x3dd326f3
+        .long 0x3f78db68, 0x3dce18e3
+        .long 0x3f790e50, 0x3dc92385
+        .long 0x3f793ffc, 0x3dc4468f
+        .long 0x3f797075, 0x3dbf81b6
+        .long 0x3f799fbf, 0x3dbad4b0
+        .long 0x3f79cde1, 0x3db63f32
+        .long 0x3f79fae1, 0x3db1c0f1
+        .long 0x3f7a26c4, 0x3dad59a1
+        .long 0x3f7a518f, 0x3da908f6
+        .long 0x3f7a7b4a, 0x3da4cea4
+        .long 0x3f7aa3f9, 0x3da0aa5e
+        .long 0x3f7acba1, 0x3d9c9bd9
+        .long 0x3f7af248, 0x3d98a2c7
+        .long 0x3f7b17f4, 0x3d94bedd
+        .long 0x3f7b3ca9, 0x3d90efcd
+        .long 0x3f7b606e, 0x3d8d354b
+        .long 0x3f7b8346, 0x3d898f0a
+        .long 0x3f7ba537, 0x3d85fcbf
+        .long 0x3f7bc646, 0x3d827e1d
+        .long 0x3f7be677, 0x3d7e25af
+        .long 0x3f7c05d1, 0x3d777546
+        .long 0x3f7c2456, 0x3d70ea68
+        .long 0x3f7c420d, 0x3d6a847d
+        .long 0x3f7c5ef9, 0x3d6442f0
+        .long 0x3f7c7b1f, 0x3d5e252a
+        .long 0x3f7c9684, 0x3d582a98
+        .long 0x3f7cb12b, 0x3d5252a5
+        .long 0x3f7ccb1a, 0x3d4c9cbd
+        .long 0x3f7ce454, 0x3d47084e
+        .long 0x3f7cfcdd, 0x3d4194c7
+        .long 0x3f7d14ba, 0x3d3c4196
+        .long 0x3f7d2bef, 0x3d370e2c
+        .long 0x3f7d427f, 0x3d31f9fb
+        .long 0x3f7d586f, 0x3d2d0474
+        .long 0x3f7d6dc2, 0x3d282d0c
+        .long 0x3f7d827b, 0x3d237336
+        .long 0x3f7d96a0, 0x3d1ed669
+        .long 0x3f7daa32, 0x3d1a561b
+        .long 0x3f7dbd36, 0x3d15f1c6
+        .long 0x3f7dcfb0, 0x3d11a8e1
+        .long 0x3f7de1a2, 0x3d0d7ae9
+        .long 0x3f7df30f, 0x3d09675a
+        .long 0x3f7e03fd, 0x3d056db0
+        .long 0x3f7e146c, 0x3d018d6b
+        .long 0x3f7e2461, 0x3cfb8c15
+        .long 0x3f7e33de, 0x3cf42e22
+        .long 0x3f7e42e8, 0x3ced0003
+        .long 0x3f7e517f, 0x3ce600c0
+        .long 0x3f7e5fa9, 0x3cdf2f67
+        .long 0x3f7e6d66, 0x3cd88b05
+        .long 0x3f7e7abb, 0x3cd212ad
+        .long 0x3f7e87aa, 0x3ccbc574
+        .long 0x3f7e9435, 0x3cc5a273
+        .long 0x3f7ea05f, 0x3cbfa8c4
+        .long 0x3f7eac2b, 0x3cb9d786
+        .long 0x3f7eb79a, 0x3cb42ddb
+        .long 0x3f7ec2b1, 0x3caeaae6
+        .long 0x3f7ecd71, 0x3ca94dcf
+        .long 0x3f7ed7dc, 0x3ca415c2
+        .long 0x3f7ee1f4, 0x3c9f01ec
+        .long 0x3f7eebbd, 0x3c9a117f
+        .long 0x3f7ef537, 0x3c9543ae
+        .long 0x3f7efe66, 0x3c9097b1
+        .long 0x3f7f074b, 0x3c8c0cc2
+        .long 0x3f7f0fe8, 0x3c87a21f
+        .long 0x3f7f1840, 0x3c83570a
+        .long 0x3f7f2053, 0x3c7e558a
+        .long 0x3f7f2826, 0x3c763931
+        .long 0x3f7f2fb8, 0x3c6e579b
+        .long 0x3f7f370c, 0x3c66af65
+        .long 0x3f7f3e23, 0x3c5f3f2d
+        .long 0x3f7f4500, 0x3c58059c
+        .long 0x3f7f4ba4, 0x3c51015f
+        .long 0x3f7f5211, 0x3c4a3127
+        .long 0x3f7f5848, 0x3c4393af
+        .long 0x3f7f5e4b, 0x3c3d27b5
+        .long 0x3f7f641b, 0x3c36ebff
+        .long 0x3f7f69ba, 0x3c30df57
+        .long 0x3f7f6f29, 0x3c2b008e
+        .long 0x3f7f746a, 0x3c254e7b
+        .long 0x3f7f797f, 0x3c1fc7fb
+        .long 0x3f7f7e67, 0x3c1a6bee
+        .long 0x3f7f8326, 0x3c15393d
+        .long 0x3f7f87bb, 0x3c102ed6
+        .long 0x3f7f8c29, 0x3c0b4bab
+        .long 0x3f7f9070, 0x3c068eb5
+        .long 0x3f7f9492, 0x3c01f6f1
+        .long 0x3f7f9890, 0x3bfb06c5
+        .long 0x3f7f9c6b, 0x3bf26625
+        .long 0x3f7fa024, 0x3bea0a1d
+        .long 0x3f7fa3bc, 0x3be1f0d3
+        .long 0x3f7fa734, 0x3bda1876
+        .long 0x3f7faa8d, 0x3bd27f42
+        .long 0x3f7fadc8, 0x3bcb237a
+        .long 0x3f7fb0e6, 0x3bc4036c
+        .long 0x3f7fb3e8, 0x3bbd1d6f
+        .long 0x3f7fb6cf, 0x3bb66fe6
+        .long 0x3f7fb99c, 0x3baff93b
+        .long 0x3f7fbc4f, 0x3ba9b7e1
+        .long 0x3f7fbeea, 0x3ba3aa56
+        .long 0x3f7fc16d, 0x3b9dcf20
+        .long 0x3f7fc3d9, 0x3b9824ce
+        .long 0x3f7fc62e, 0x3b92a9f7
+        .long 0x3f7fc86e, 0x3b8d5d3c
+        .long 0x3f7fca99, 0x3b883d46
+        .long 0x3f7fccb0, 0x3b8348c6
+        .long 0x3f7fceb4, 0x3b7cfce8
+        .long 0x3f7fd0a5, 0x3b73ba24
+        .long 0x3f7fd283, 0x3b6ac6d3
+        .long 0x3f7fd450, 0x3b622096
+        .long 0x3f7fd60c, 0x3b59c51d
+        .long 0x3f7fd7b7, 0x3b51b22a
+        .long 0x3f7fd953, 0x3b49e589
+        .long 0x3f7fdadf, 0x3b425d18
+        .long 0x3f7fdc5c, 0x3b3b16c2
+        .long 0x3f7fddcc, 0x3b341080
+        .long 0x3f7fdf2d, 0x3b2d4858
+        .long 0x3f7fe081, 0x3b26bc5e
+        .long 0x3f7fe1c8, 0x3b206ab2
+        .long 0x3f7fe303, 0x3b1a5183
+        .long 0x3f7fe431, 0x3b146f09
+        .long 0x3f7fe554, 0x3b0ec18c
+        .long 0x3f7fe66c, 0x3b09475d
+        .long 0x3f7fe77a, 0x3b03feda
+        .long 0x3f7fe87d, 0x3afdccdc
+        .long 0x3f7fe975, 0x3af3f919
+        .long 0x3f7fea65, 0x3aea7f6c
+        .long 0x3f7feb4b, 0x3ae15ce8
+        .long 0x3f7fec27, 0x3ad88eb8
+        .long 0x3f7fecfc, 0x3ad0121b
+        .long 0x3f7fedc8, 0x3ac7e464
+        .long 0x3f7fee8c, 0x3ac002f8
+        .long 0x3f7fef48, 0x3ab86b52
+        .long 0x3f7feffd, 0x3ab11afe
+        .long 0x3f7ff0aa, 0x3aaa0f9a
+        .long 0x3f7ff151, 0x3aa346d7
+        .long 0x3f7ff1f1, 0x3a9cbe77
+        .long 0x3f7ff28a, 0x3a96744c
+        .long 0x3f7ff31e, 0x3a90663b
+        .long 0x3f7ff3ab, 0x3a8a9237
+        .long 0x3f7ff433, 0x3a84f643
+        .long 0x3f7ff4b5, 0x3a7f20e7
+        .long 0x3f7ff532, 0x3a74bdd2
+        .long 0x3f7ff5aa, 0x3a6abfa9
+        .long 0x3f7ff61d, 0x3a6122ea
+        .long 0x3f7ff68b, 0x3a57e42f
+        .long 0x3f7ff6f5, 0x3a4f002c
+        .long 0x3f7ff75a, 0x3a4673af
+        .long 0x3f7ff7bb, 0x3a3e3ba2
+        .long 0x3f7ff819, 0x3a365507
+        .long 0x3f7ff872, 0x3a2ebcf6
+        .long 0x3f7ff8c7, 0x3a2770a1
+        .long 0x3f7ff919, 0x3a206d52
+        .long 0x3f7ff968, 0x3a19b066
+        .long 0x3f7ff9b3, 0x3a133754
+        .long 0x3f7ff9fb, 0x3a0cffa3
+        .long 0x3f7ffa40, 0x3a0706f4
+        .long 0x3f7ffa82, 0x3a014af8
+        .long 0x3f7ffac1, 0x39f792ea
+        .long 0x3f7ffafe, 0x39ed0088
+        .long 0x3f7ffb38, 0x39e2daa1
+        .long 0x3f7ffb6f, 0x39d91d2d
+        .long 0x3f7ffba5, 0x39cfc44a
+        .long 0x3f7ffbd7, 0x39c6cc35
+        .long 0x3f7ffc08, 0x39be314d
+        .long 0x3f7ffc36, 0x39b5f011
+        .long 0x3f7ffc63, 0x39ae051c
+        .long 0x3f7ffc8e, 0x39a66d2a
+        .long 0x3f7ffcb6, 0x399f2512
+        .long 0x3f7ffcdd, 0x399829c8
+        .long 0x3f7ffd02, 0x3991785a
+        .long 0x3f7ffd26, 0x398b0df2
+        .long 0x3f7ffd48, 0x3984e7d2
+        .long 0x3f7ffd68, 0x397e06ab
+        .long 0x3f7ffd87, 0x3972bbde
+        .long 0x3f7ffda5, 0x3967ea53
+        .long 0x3f7ffdc1, 0x395d8d4b
+        .long 0x3f7ffddc, 0x3953a034
+        .long 0x3f7ffdf6, 0x394a1ea5
+        .long 0x3f7ffe0f, 0x3941045e
+        .long 0x3f7ffe27, 0x39384d47
+        .long 0x3f7ffe3d, 0x392ff56d
+        .long 0x3f7ffe53, 0x3927f904
+        .long 0x3f7ffe67, 0x39205461
+        .long 0x3f7ffe7b, 0x391903fe
+        .long 0x3f7ffe8d, 0x39120475
+        .long 0x3f7ffe9f, 0x390b5281
+        .long 0x3f7ffeb0, 0x3904eafc
+        .long 0x3f7ffec0, 0x38fd95bd
+        .long 0x3f7ffed0, 0x38f1de7a
+        .long 0x3f7ffedf, 0x38e6aa94
+        .long 0x3f7ffeed, 0x38dbf4a3
+        .long 0x3f7ffefa, 0x38d1b776
+        .long 0x3f7fff07, 0x38c7ee0e
+        .long 0x3f7fff13, 0x38be939c
+        .long 0x3f7fff1f, 0x38b5a381
+        .long 0x3f7fff2a, 0x38ad194e
+        .long 0x3f7fff34, 0x38a4f0bc
+        .long 0x3f7fff3f, 0x389d25b0
+        .long 0x3f7fff48, 0x3895b43b
+        .long 0x3f7fff51, 0x388e9890
+        .long 0x3f7fff5a, 0x3887cf0e
+        .long 0x3f7fff62, 0x38815434
+        .long 0x3f7fff6a, 0x3876494d
+        .long 0x3f7fff72, 0x386a7a5a
+        .long 0x3f7fff79, 0x385f355e
+        .long 0x3f7fff80, 0x38547466
+        .long 0x3f7fff86, 0x384a31bf
+        .long 0x3f7fff8c, 0x384067ee
+        .long 0x3f7fff92, 0x383711b4
+        .long 0x3f7fff98, 0x382e2a06
+        .long 0x3f7fff9d, 0x3825ac0e
+        .long 0x3f7fffa2, 0x381d9329
+        .long 0x3f7fffa7, 0x3815dae6
+        .long 0x3f7fffab, 0x380e7f01
+        .long 0x3f7fffb0, 0x38077b62
+        .long 0x3f7fffb4, 0x3800cc21
+        .long 0x3f7fffb8, 0x37f4daf4
+        .long 0x3f7fffbc, 0x37e8b7ac
+        .long 0x3f7fffbf, 0x37dd2782
+        .long 0x3f7fffc2, 0x37d223dc
+        .long 0x3f7fffc6, 0x37c7a666
+        .long 0x3f7fffc9, 0x37bda912
+        .long 0x3f7fffcc, 0x37b42611
+        .long 0x3f7fffce, 0x37ab17d6
+        .long 0x3f7fffd1, 0x37a2790f
+        .long 0x3f7fffd3, 0x379a44a5
+        .long 0x3f7fffd6, 0x379275b9
+        .long 0x3f7fffd8, 0x378b07a2
+        .long 0x3f7fffda, 0x3783f5e9
+        .long 0x3f7fffdc, 0x377a7897
+        .long 0x3f7fffde, 0x376dad68
+        .long 0x3f7fffe0, 0x37618278
+        .long 0x3f7fffe2, 0x3755f04f
+        .long 0x3f7fffe3, 0x374aefcc
+        .long 0x3f7fffe5, 0x37407a1d
+        .long 0x3f7fffe6, 0x373688bc
+        .long 0x3f7fffe8, 0x372d1570
+        .long 0x3f7fffe9, 0x37241a44
+        .long 0x3f7fffea, 0x371b9188
+        .long 0x3f7fffeb, 0x371375cf
+        .long 0x3f7fffec, 0x370bc1e7
+        .long 0x3f7fffee, 0x370470dd
+        .long 0x3f7fffef, 0x36fafbec
+        .long 0x3f7fffef, 0x36edc95b
+        .long 0x3f7ffff0, 0x36e14167
+        .long 0x3f7ffff1, 0x36d55bd6
+        .long 0x3f7ffff2, 0x36ca10ce
+        .long 0x3f7ffff3, 0x36bf58d1
+        .long 0x3f7ffff4, 0x36b52cb9
+        .long 0x3f7ffff4, 0x36ab85b5
+        .long 0x3f7ffff5, 0x36a25d43
+        .long 0x3f7ffff5, 0x3699ad31
+        .long 0x3f7ffff6, 0x36916f95
+        .long 0x3f7ffff7, 0x36899ecb
+        .long 0x3f7ffff7, 0x36823575
+        .long 0x3f7ffff8, 0x36765ce8
+        .long 0x3f7ffff8, 0x366909cc
+        .long 0x3f7ffff9, 0x365c684a
+        .long 0x3f7ffff9, 0x36506f88
+        .long 0x3f7ffff9, 0x36451713
+        .long 0x3f7ffffa, 0x363a56e4
+        .long 0x3f7ffffa, 0x36302754
+        .long 0x3f7ffffa, 0x36268119
+        .long 0x3f7ffffb, 0x361d5d43
+        .long 0x3f7ffffb, 0x3614b538
+        .long 0x3f7ffffb, 0x360c82b1
+        .long 0x3f7ffffc, 0x3604bfb1
+        .long 0x3f7ffffc, 0x35facd10
+        .long 0x3f7ffffc, 0x35ece39b
+        .long 0x3f7ffffc, 0x35dfb8b6
+        .long 0x3f7ffffd, 0x35d34296
+        .long 0x3f7ffffd, 0x35c777ec
+        .long 0x3f7ffffd, 0x35bc4fdc
+        .long 0x3f7ffffd, 0x35b1c1fc
+        .long 0x3f7ffffd, 0x35a7c64b
+        .long 0x3f7ffffd, 0x359e5531
+        .long 0x3f7ffffe, 0x35956771
+        .long 0x3f7ffffe, 0x358cf630
+        .long 0x3f7ffffe, 0x3584fae8
+        .long 0x3f7ffffe, 0x357adecb
+        .long 0x3f7ffffe, 0x356c9b8f
+        .long 0x3f7ffffe, 0x355f20ef
+        .long 0x3f7ffffe, 0x3552644f
+        .long 0x3f7ffffe, 0x35465b9c
+        .long 0x3f7fffff, 0x353afd47
+        .long 0x3f7fffff, 0x3530403c
+        .long 0x3f7fffff, 0x35261be0
+        .long 0x3f7fffff, 0x351c8807
+        .long 0x3f7fffff, 0x35137cf0
+        .long 0x3f7fffff, 0x350af341
+        .long 0x3f7fffff, 0x3502e402
+        .long 0x3f7fffff, 0x34f6912a
+        .long 0x3f7fffff, 0x34e8356b
+        .long 0x3f7fffff, 0x34daa8e4
+        .long 0x3f7fffff, 0x34cde050
+        .long 0x3f7fffff, 0x34c1d100
+        .long 0x3f7fffff, 0x34b670d5
+        .long 0x3f7fffff, 0x34abb639
+        .long 0x3f7fffff, 0x34a19816
+        .long 0x3f7fffff, 0x34980dd1
+        .long 0x3f7fffff, 0x348f0f43
+        .long 0x3f7fffff, 0x348694b3
+        .long 0x3f800000, 0x347d2da8
+        .long 0x3f800000, 0x346e1d72
+        .align 16
+        .long 0x7fffffff, 0x7fffffff, 0x7fffffff, 0x7fffffff  /* _AbsMask */
+        .align 16
+        .long 0x407b8000, 0x407b8000, 0x407b8000, 0x407b8000  /* _MaxThreshold */
+        .align 16
+        .long 0x47800000, 0x47800000, 0x47800000, 0x47800000  /* _SRound */
+        .align 16
+        .long 0x2f800000, 0x2f800000, 0x2f800000, 0x2f800000  /* _U2THreshold  */
+        .align 16
+        .long 0xbeaaaade, 0xbeaaaade, 0xbeaaaade, 0xbeaaaade  /* _poly_3_0 */
+        .align 16
+        .type	__svml_serf_data_internal,@object
+        .size	__svml_serf_data_internal,.-__svml_serf_data_internal