diff mbox series

[39/42] x86-64: Add vector tan/tanf implementation to libmvec

Message ID 20211124193807.2093208-40-skpgkp2@gmail.com
State Changes Requested
Headers show
Series x86-64: Add vector math functions to libmvec | expand

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Commit Message

Sunil Pandey Nov. 24, 2021, 7:38 p.m. UTC
Implement vectorized tan/tanf containing SSE, AVX, AVX2 and
AVX512 versions for libmvec as per vector ABI.  It also contains
accuracy and ABI tests for vector tan/tanf with regenerated ulps.
---
 bits/libm-simd-decl-stubs.h                   |    11 +
 math/bits/mathcalls.h                         |     2 +-
 .../unix/sysv/linux/x86_64/libmvec.abilist    |     8 +
 sysdeps/x86/fpu/bits/math-vector.h            |     4 +
 sysdeps/x86_64/fpu/Makeconfig                 |     1 +
 sysdeps/x86_64/fpu/Versions                   |     2 +
 sysdeps/x86_64/fpu/libm-test-ulps             |    20 +
 .../fpu/multiarch/svml_d_tan2_core-sse2.S     |    20 +
 .../x86_64/fpu/multiarch/svml_d_tan2_core.c   |    27 +
 .../fpu/multiarch/svml_d_tan2_core_sse4.S     | 21778 ++++++++++++++++
 .../fpu/multiarch/svml_d_tan4_core-sse.S      |    20 +
 .../x86_64/fpu/multiarch/svml_d_tan4_core.c   |    27 +
 .../fpu/multiarch/svml_d_tan4_core_avx2.S     | 21275 +++++++++++++++
 .../fpu/multiarch/svml_d_tan8_core-avx2.S     |    20 +
 .../x86_64/fpu/multiarch/svml_d_tan8_core.c   |    27 +
 .../fpu/multiarch/svml_d_tan8_core_avx512.S   | 20210 ++++++++++++++
 .../fpu/multiarch/svml_s_tanf16_core-avx2.S   |    20 +
 .../x86_64/fpu/multiarch/svml_s_tanf16_core.c |    28 +
 .../fpu/multiarch/svml_s_tanf16_core_avx512.S |  3168 +++
 .../fpu/multiarch/svml_s_tanf4_core-sse2.S    |    20 +
 .../x86_64/fpu/multiarch/svml_s_tanf4_core.c  |    28 +
 .../fpu/multiarch/svml_s_tanf4_core_sse4.S    |  4562 ++++
 .../fpu/multiarch/svml_s_tanf8_core-sse.S     |    20 +
 .../x86_64/fpu/multiarch/svml_s_tanf8_core.c  |    28 +
 .../fpu/multiarch/svml_s_tanf8_core_avx2.S    |  4192 +++
 sysdeps/x86_64/fpu/svml_d_tan2_core.S         |    29 +
 sysdeps/x86_64/fpu/svml_d_tan4_core.S         |    29 +
 sysdeps/x86_64/fpu/svml_d_tan4_core_avx.S     |    25 +
 sysdeps/x86_64/fpu/svml_d_tan8_core.S         |    25 +
 sysdeps/x86_64/fpu/svml_s_tanf16_core.S       |    25 +
 sysdeps/x86_64/fpu/svml_s_tanf4_core.S        |    29 +
 sysdeps/x86_64/fpu/svml_s_tanf8_core.S        |    29 +
 sysdeps/x86_64/fpu/svml_s_tanf8_core_avx.S    |    25 +
 .../x86_64/fpu/test-double-libmvec-tan-avx.c  |     1 +
 .../x86_64/fpu/test-double-libmvec-tan-avx2.c |     1 +
 .../fpu/test-double-libmvec-tan-avx512f.c     |     1 +
 sysdeps/x86_64/fpu/test-double-libmvec-tan.c  |     3 +
 .../x86_64/fpu/test-double-vlen2-wrappers.c   |     1 +
 .../fpu/test-double-vlen4-avx2-wrappers.c     |     1 +
 .../x86_64/fpu/test-double-vlen4-wrappers.c   |     1 +
 .../x86_64/fpu/test-double-vlen8-wrappers.c   |     1 +
 .../x86_64/fpu/test-float-libmvec-tanf-avx.c  |     1 +
 .../x86_64/fpu/test-float-libmvec-tanf-avx2.c |     1 +
 .../fpu/test-float-libmvec-tanf-avx512f.c     |     1 +
 sysdeps/x86_64/fpu/test-float-libmvec-tanf.c  |     3 +
 .../x86_64/fpu/test-float-vlen16-wrappers.c   |     1 +
 .../x86_64/fpu/test-float-vlen4-wrappers.c    |     1 +
 .../fpu/test-float-vlen8-avx2-wrappers.c      |     1 +
 .../x86_64/fpu/test-float-vlen8-wrappers.c    |     1 +
 49 files changed, 75753 insertions(+), 1 deletion(-)
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core-sse2.S
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core.c
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core_sse4.S
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_d_tan4_core-sse.S
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_d_tan4_core.c
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_d_tan4_core_avx2.S
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_d_tan8_core-avx2.S
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_d_tan8_core.c
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_d_tan8_core_avx512.S
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanf16_core-avx2.S
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanf16_core.c
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanf16_core_avx512.S
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanf4_core-sse2.S
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanf4_core.c
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanf4_core_sse4.S
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanf8_core-sse.S
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanf8_core.c
 create mode 100644 sysdeps/x86_64/fpu/multiarch/svml_s_tanf8_core_avx2.S
 create mode 100644 sysdeps/x86_64/fpu/svml_d_tan2_core.S
 create mode 100644 sysdeps/x86_64/fpu/svml_d_tan4_core.S
 create mode 100644 sysdeps/x86_64/fpu/svml_d_tan4_core_avx.S
 create mode 100644 sysdeps/x86_64/fpu/svml_d_tan8_core.S
 create mode 100644 sysdeps/x86_64/fpu/svml_s_tanf16_core.S
 create mode 100644 sysdeps/x86_64/fpu/svml_s_tanf4_core.S
 create mode 100644 sysdeps/x86_64/fpu/svml_s_tanf8_core.S
 create mode 100644 sysdeps/x86_64/fpu/svml_s_tanf8_core_avx.S
 create mode 100644 sysdeps/x86_64/fpu/test-double-libmvec-tan-avx.c
 create mode 100644 sysdeps/x86_64/fpu/test-double-libmvec-tan-avx2.c
 create mode 100644 sysdeps/x86_64/fpu/test-double-libmvec-tan-avx512f.c
 create mode 100644 sysdeps/x86_64/fpu/test-double-libmvec-tan.c
 create mode 100644 sysdeps/x86_64/fpu/test-float-libmvec-tanf-avx.c
 create mode 100644 sysdeps/x86_64/fpu/test-float-libmvec-tanf-avx2.c
 create mode 100644 sysdeps/x86_64/fpu/test-float-libmvec-tanf-avx512f.c
 create mode 100644 sysdeps/x86_64/fpu/test-float-libmvec-tanf.c
diff mbox series

Patch

diff --git a/bits/libm-simd-decl-stubs.h b/bits/libm-simd-decl-stubs.h
index 9ed3c17389..3968f2935b 100644
--- a/bits/libm-simd-decl-stubs.h
+++ b/bits/libm-simd-decl-stubs.h
@@ -307,4 +307,15 @@ 
 #define __DECL_SIMD_sinhf32x
 #define __DECL_SIMD_sinhf64x
 #define __DECL_SIMD_sinhf128x
+
+#define __DECL_SIMD_tan
+#define __DECL_SIMD_tanf
+#define __DECL_SIMD_tanl
+#define __DECL_SIMD_tanf16
+#define __DECL_SIMD_tanf32
+#define __DECL_SIMD_tanf64
+#define __DECL_SIMD_tanf128
+#define __DECL_SIMD_tanf32x
+#define __DECL_SIMD_tanf64x
+#define __DECL_SIMD_tanf128x
 #endif
diff --git a/math/bits/mathcalls.h b/math/bits/mathcalls.h
index cb733b3773..48a525234e 100644
--- a/math/bits/mathcalls.h
+++ b/math/bits/mathcalls.h
@@ -63,7 +63,7 @@  __MATHCALL_VEC (cos,, (_Mdouble_ __x));
 /* Sine of X.  */
 __MATHCALL_VEC (sin,, (_Mdouble_ __x));
 /* Tangent of X.  */
-__MATHCALL (tan,, (_Mdouble_ __x));
+__MATHCALL_VEC (tan,, (_Mdouble_ __x));
 
 /* Hyperbolic functions.  */
 
diff --git a/sysdeps/unix/sysv/linux/x86_64/libmvec.abilist b/sysdeps/unix/sysv/linux/x86_64/libmvec.abilist
index 19f5e2edf2..f8280539f6 100644
--- a/sysdeps/unix/sysv/linux/x86_64/libmvec.abilist
+++ b/sysdeps/unix/sysv/linux/x86_64/libmvec.abilist
@@ -63,6 +63,7 @@  GLIBC_2.35 _ZGVbN2v_log10 F
 GLIBC_2.35 _ZGVbN2v_log1p F
 GLIBC_2.35 _ZGVbN2v_log2 F
 GLIBC_2.35 _ZGVbN2v_sinh F
+GLIBC_2.35 _ZGVbN2v_tan F
 GLIBC_2.35 _ZGVbN2vv_atan2 F
 GLIBC_2.35 _ZGVbN2vv_hypot F
 GLIBC_2.35 _ZGVbN4v_acosf F
@@ -82,6 +83,7 @@  GLIBC_2.35 _ZGVbN4v_log10f F
 GLIBC_2.35 _ZGVbN4v_log1pf F
 GLIBC_2.35 _ZGVbN4v_log2f F
 GLIBC_2.35 _ZGVbN4v_sinhf F
+GLIBC_2.35 _ZGVbN4v_tanf F
 GLIBC_2.35 _ZGVbN4vv_atan2f F
 GLIBC_2.35 _ZGVbN4vv_hypotf F
 GLIBC_2.35 _ZGVcN4v_acos F
@@ -101,6 +103,7 @@  GLIBC_2.35 _ZGVcN4v_log10 F
 GLIBC_2.35 _ZGVcN4v_log1p F
 GLIBC_2.35 _ZGVcN4v_log2 F
 GLIBC_2.35 _ZGVcN4v_sinh F
+GLIBC_2.35 _ZGVcN4v_tan F
 GLIBC_2.35 _ZGVcN4vv_atan2 F
 GLIBC_2.35 _ZGVcN4vv_hypot F
 GLIBC_2.35 _ZGVcN8v_acosf F
@@ -120,6 +123,7 @@  GLIBC_2.35 _ZGVcN8v_log10f F
 GLIBC_2.35 _ZGVcN8v_log1pf F
 GLIBC_2.35 _ZGVcN8v_log2f F
 GLIBC_2.35 _ZGVcN8v_sinhf F
+GLIBC_2.35 _ZGVcN8v_tanf F
 GLIBC_2.35 _ZGVcN8vv_atan2f F
 GLIBC_2.35 _ZGVcN8vv_hypotf F
 GLIBC_2.35 _ZGVdN4v_acos F
@@ -139,6 +143,7 @@  GLIBC_2.35 _ZGVdN4v_log10 F
 GLIBC_2.35 _ZGVdN4v_log1p F
 GLIBC_2.35 _ZGVdN4v_log2 F
 GLIBC_2.35 _ZGVdN4v_sinh F
+GLIBC_2.35 _ZGVdN4v_tan F
 GLIBC_2.35 _ZGVdN4vv_atan2 F
 GLIBC_2.35 _ZGVdN4vv_hypot F
 GLIBC_2.35 _ZGVdN8v_acosf F
@@ -158,6 +163,7 @@  GLIBC_2.35 _ZGVdN8v_log10f F
 GLIBC_2.35 _ZGVdN8v_log1pf F
 GLIBC_2.35 _ZGVdN8v_log2f F
 GLIBC_2.35 _ZGVdN8v_sinhf F
+GLIBC_2.35 _ZGVdN8v_tanf F
 GLIBC_2.35 _ZGVdN8vv_atan2f F
 GLIBC_2.35 _ZGVdN8vv_hypotf F
 GLIBC_2.35 _ZGVeN16v_acosf F
@@ -177,6 +183,7 @@  GLIBC_2.35 _ZGVeN16v_log10f F
 GLIBC_2.35 _ZGVeN16v_log1pf F
 GLIBC_2.35 _ZGVeN16v_log2f F
 GLIBC_2.35 _ZGVeN16v_sinhf F
+GLIBC_2.35 _ZGVeN16v_tanf F
 GLIBC_2.35 _ZGVeN16vv_atan2f F
 GLIBC_2.35 _ZGVeN16vv_hypotf F
 GLIBC_2.35 _ZGVeN8v_acos F
@@ -196,5 +203,6 @@  GLIBC_2.35 _ZGVeN8v_log10 F
 GLIBC_2.35 _ZGVeN8v_log1p F
 GLIBC_2.35 _ZGVeN8v_log2 F
 GLIBC_2.35 _ZGVeN8v_sinh F
+GLIBC_2.35 _ZGVeN8v_tan F
 GLIBC_2.35 _ZGVeN8vv_atan2 F
 GLIBC_2.35 _ZGVeN8vv_hypot F
diff --git a/sysdeps/x86/fpu/bits/math-vector.h b/sysdeps/x86/fpu/bits/math-vector.h
index 3fab52e942..618a30cdc1 100644
--- a/sysdeps/x86/fpu/bits/math-vector.h
+++ b/sysdeps/x86/fpu/bits/math-vector.h
@@ -134,6 +134,10 @@ 
 #  define __DECL_SIMD_sinh __DECL_SIMD_x86_64
 #  undef __DECL_SIMD_sinhf
 #  define __DECL_SIMD_sinhf __DECL_SIMD_x86_64
+#  undef __DECL_SIMD_tan
+#  define __DECL_SIMD_tan __DECL_SIMD_x86_64
+#  undef __DECL_SIMD_tanf
+#  define __DECL_SIMD_tanf __DECL_SIMD_x86_64
 
 # endif
 #endif
diff --git a/sysdeps/x86_64/fpu/Makeconfig b/sysdeps/x86_64/fpu/Makeconfig
index c23bc47f3c..8e2272e1eb 100644
--- a/sysdeps/x86_64/fpu/Makeconfig
+++ b/sysdeps/x86_64/fpu/Makeconfig
@@ -47,6 +47,7 @@  libmvec-funcs = \
   sin \
   sincos \
   sinh \
+  tan \
 
 # Define libmvec function for benchtests directory.
 libmvec-bench-funcs = \
diff --git a/sysdeps/x86_64/fpu/Versions b/sysdeps/x86_64/fpu/Versions
index 626142bd6b..6cb335cf94 100644
--- a/sysdeps/x86_64/fpu/Versions
+++ b/sysdeps/x86_64/fpu/Versions
@@ -31,6 +31,7 @@  libmvec {
     _ZGVbN2v_log1p; _ZGVcN4v_log1p; _ZGVdN4v_log1p; _ZGVeN8v_log1p;
     _ZGVbN2v_log2; _ZGVcN4v_log2; _ZGVdN4v_log2; _ZGVeN8v_log2;
     _ZGVbN2v_sinh; _ZGVcN4v_sinh; _ZGVdN4v_sinh; _ZGVeN8v_sinh;
+    _ZGVbN2v_tan; _ZGVcN4v_tan; _ZGVdN4v_tan; _ZGVeN8v_tan;
     _ZGVbN2vv_atan2; _ZGVcN4vv_atan2; _ZGVdN4vv_atan2; _ZGVeN8vv_atan2;
     _ZGVbN2vv_hypot; _ZGVcN4vv_hypot; _ZGVdN4vv_hypot; _ZGVeN8vv_hypot;
     _ZGVbN4v_acosf; _ZGVcN8v_acosf; _ZGVdN8v_acosf; _ZGVeN16v_acosf;
@@ -50,6 +51,7 @@  libmvec {
     _ZGVbN4v_log1pf; _ZGVcN8v_log1pf; _ZGVdN8v_log1pf; _ZGVeN16v_log1pf;
     _ZGVbN4v_log2f; _ZGVcN8v_log2f; _ZGVdN8v_log2f; _ZGVeN16v_log2f;
     _ZGVbN4v_sinhf; _ZGVcN8v_sinhf; _ZGVdN8v_sinhf; _ZGVeN16v_sinhf;
+    _ZGVbN4v_tanf; _ZGVcN8v_tanf; _ZGVdN8v_tanf; _ZGVeN16v_tanf;
     _ZGVbN4vv_atan2f; _ZGVcN8vv_atan2f; _ZGVdN8vv_atan2f; _ZGVeN16vv_atan2f;
     _ZGVbN4vv_hypotf; _ZGVcN8vv_hypotf; _ZGVdN8vv_hypotf; _ZGVeN16vv_hypotf;
   }
diff --git a/sysdeps/x86_64/fpu/libm-test-ulps b/sysdeps/x86_64/fpu/libm-test-ulps
index 67126a5c2b..4a6b224b5d 100644
--- a/sysdeps/x86_64/fpu/libm-test-ulps
+++ b/sysdeps/x86_64/fpu/libm-test-ulps
@@ -2080,6 +2080,26 @@  float: 1
 float128: 1
 ldouble: 2
 
+Function: "tan_vlen16":
+float: 1
+
+Function: "tan_vlen2":
+double: 2
+
+Function: "tan_vlen4":
+double: 2
+float: 2
+
+Function: "tan_vlen4_avx2":
+double: 1
+
+Function: "tan_vlen8":
+double: 2
+float: 2
+
+Function: "tan_vlen8_avx2":
+float: 2
+
 Function: "tanh":
 double: 2
 float: 2
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core-sse2.S b/sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core-sse2.S
new file mode 100644
index 0000000000..a8f5a390cd
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core-sse2.S
@@ -0,0 +1,20 @@ 
+/* SSE2 version of vectorized tan, vector length is 2.
+   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/>.  */
+
+#define _ZGVbN2v_tan _ZGVbN2v_tan_sse2
+#include "../svml_d_tan2_core.S"
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core.c b/sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core.c
new file mode 100644
index 0000000000..4c41025a23
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core.c
@@ -0,0 +1,27 @@ 
+/* Multiple versions of vectorized tan, vector length is 2.
+   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/>.  */
+
+#define SYMBOL_NAME _ZGVbN2v_tan
+#include "ifunc-mathvec-sse4_1.h"
+
+libc_ifunc_redirected (REDIRECT_NAME, SYMBOL_NAME, IFUNC_SELECTOR ());
+
+#ifdef SHARED
+__hidden_ver1 (_ZGVbN2v_tan, __GI__ZGVbN2v_tan, __redirect__ZGVbN2v_tan)
+  __attribute__ ((visibility ("hidden")));
+#endif
diff --git a/sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core_sse4.S b/sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core_sse4.S
new file mode 100644
index 0000000000..16b77fc132
--- /dev/null
+++ b/sysdeps/x86_64/fpu/multiarch/svml_d_tan2_core_sse4.S
@@ -0,0 +1,21778 @@ 
+/* Function tan 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:
+ *
+ *      1) Range reduction to [-Pi/4; +Pi/4] interval
+ *       a) Grab sign from source argument and save it.
+ *       b) Remove sign using AND 0x7fffffffffffffff operation
+ *       c) Getting octant Y by 2/Pi multiplication
+ *       d) Add "Right Shifter" (0x4330000000000000) value
+ *       e) Treat obtained value as integer for destination sign setting.
+ *          Shift first bit of this value to the last (sign) position (S << 63)
+ *       f) Change destination sign if source sign is negative
+ *          using XOR operation.
+ *       g) Subtract "Right Shifter" (0x4330000000000000) value
+ *       h) Subtract Y*(PI/2) from X argument, where PI/2 divided to 4 parts:
+ *          X = X - Y*PI1 - Y*PI2 - Y*PI3 - Y*PI4;
+ *      2) Rational polynomial approximation ( at [-Pi/4; +Pi/4] interval)
+ *       a) Calculate X^2 = X * X
+ *       b) Calculate 2 polynomials:
+ *          P = X * (P0 + X^2 * (P1 + x^2 * (P2 + x^2 * (P3))));
+ *          Q = Q0 + X^2 * (Q1 + x^2 * (Q2 + x^2 * (Q3)));
+ *       c) Swap P and Q if first bit of obtained value after
+ *          Right Shifting is set to 1. Using And, Andnot & Or operations.
+ *       d) Divide R = P / Q;
+ *      3) Destination sign setting
+ *       a) Set shifted destination sign using XOR operation:
+ *          R = XOR( R, S );
+ *
+ */
+
+#include <sysdep.h>
+
+        .text
+ENTRY(_ZGVbN2v_tan_sse4)
+        pushq     %rbp
+        cfi_def_cfa_offset(16)
+        movq      %rsp, %rbp
+        cfi_def_cfa(6, 16)
+        cfi_offset(6, -16)
+        andq      $-64, %rsp
+        subq      $192, %rsp
+        movaps    %xmm0, %xmm1
+        movups    1024+__svml_dtan_data_internal(%rip), %xmm4
+
+/* Legacy Code */
+        xorl      %eax, %eax
+
+/* b) Remove sign using AND 0x7fffffffffffffff operation */
+        movaps    %xmm4, %xmm5
+
+/* a) Grab sign from source argument and save it. */
+        andnps    %xmm1, %xmm4
+
+/*
+ * c) Getting octant Y by 2/Pi multiplication
+ * d) Add "Right Shifter" (0x4330000000000000) value
+ */
+        movups    28288+__svml_dtan_data_internal(%rip), %xmm3
+        andps     %xmm1, %xmm5
+        mulpd     %xmm5, %xmm3
+        movups    1152+__svml_dtan_data_internal(%rip), %xmm6
+
+/*
+ * Range reduction
+ * X = X - Y*PI1 - Y*PI2 - Y*PI3 - Y*PI4;
+ */
+        movaps    %xmm5, %xmm2
+        addpd     %xmm6, %xmm3
+
+/* g) Subtract "Right Shifter" (0x4330000000000000) value */
+        movaps    %xmm3, %xmm0
+        subpd     %xmm6, %xmm0
+        movups    28352+__svml_dtan_data_internal(%rip), %xmm7
+        mulpd     %xmm0, %xmm7
+        movups    28416+__svml_dtan_data_internal(%rip), %xmm6
+        mulpd     %xmm0, %xmm6
+        subpd     %xmm7, %xmm2
+        movups    %xmm8, 176(%rsp)
+        .cfi_escape 0x10, 0x19, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xf0, 0xff, 0xff, 0xff, 0x22
+        movups    28480+__svml_dtan_data_internal(%rip), %xmm8
+        mulpd     %xmm0, %xmm8
+        subpd     %xmm6, %xmm2
+        subpd     %xmm8, %xmm2
+        movups    %xmm13, 80(%rsp)
+        .cfi_escape 0x10, 0x1e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 0xff, 0xff, 0xff, 0x22
+
+/* a) Calculate X^2 = X * X */
+        movaps    %xmm2, %xmm13
+        mulpd     %xmm2, %xmm13
+        movups    %xmm11, 112(%rsp)
+        .cfi_escape 0x10, 0x1c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
+
+/*
+ * b) Calculate 2 polynomials:
+ * P = X * (P0 + X^2 * (P1 + x^2 * (P2 + x^2 * (P3))));
+ * Q = Q0 + X^2 * (Q1 + x^2 * (Q2 + x^2 * (Q3)));
+ * Assume P0 = 1
+ */
+        movups    28928+__svml_dtan_data_internal(%rip), %xmm11
+        mulpd     %xmm13, %xmm11
+        movups    %xmm10, 144(%rsp)
+        .cfi_escape 0x10, 0x1b, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xd0, 0xff, 0xff, 0xff, 0x22
+        movups    29184+__svml_dtan_data_internal(%rip), %xmm10
+        addpd     28864+__svml_dtan_data_internal(%rip), %xmm11
+        mulpd     %xmm13, %xmm10
+        mulpd     %xmm13, %xmm11
+        addpd     29120+__svml_dtan_data_internal(%rip), %xmm10
+        addpd     28800+__svml_dtan_data_internal(%rip), %xmm11
+        mulpd     %xmm13, %xmm10
+        mulpd     %xmm13, %xmm11
+        addpd     29056+__svml_dtan_data_internal(%rip), %xmm10
+        mulpd     %xmm2, %xmm11
+        mulpd     %xmm10, %xmm13
+        addpd     %xmm11, %xmm2
+        addpd     28992+__svml_dtan_data_internal(%rip), %xmm13
+        movups    %xmm9, 160(%rsp)
+        movups    %xmm14, 48(%rsp)
+        .cfi_escape 0x10, 0x1a, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x1f, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x70, 0xff, 0xff, 0xff, 0x22
+
+/* 1) Range reduction to [-Pi/4; +Pi/4] interval */
+        pxor      %xmm9, %xmm9
+
+/*
+ * e) Treat obtained value as integer for destination sign setting.
+ * Shift first bit of this value to the last (sign) position (S << 63)
+ * f) Change destination sign if source sign is negative
+ * using XOR operation.
+ */
+        movaps    %xmm3, %xmm14
+        psllq     $62, %xmm3
+        cmpneqpd  %xmm9, %xmm3
+        movups    %xmm12, 96(%rsp)
+
+/*
+ * c) Swap P and Q if first bit of obtained value after
+ * Right Shifting is set to 1. Using And, Andnot & Or operations.
+ */
+        movaps    %xmm3, %xmm0
+        .cfi_escape 0x10, 0x1d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
+        movaps    %xmm3, %xmm12
+        andnps    %xmm2, %xmm0
+        andps     %xmm13, %xmm12
+        andps     %xmm3, %xmm2
+        andnps    %xmm13, %xmm3
+        orps      %xmm12, %xmm0
+        orps      %xmm3, %xmm2
+        psllq     $63, %xmm14
+
+/* d) Divide R = P / Q; */
+        divpd     %xmm2, %xmm0
+        pxor      %xmm4, %xmm14
+
+/* Large values check */
+        movaps    %xmm5, %xmm4
+        cmpnlepd  28160+__svml_dtan_data_internal(%rip), %xmm4
+        movmskpd  %xmm4, %edx
+
+/*
+ * 3) Destination sign setting
+ * a) Set shifted destination sign using XOR operation:
+ * R = XOR( R, S );
+ */
+        pxor      %xmm14, %xmm0
+        movups    %xmm15, 32(%rsp)
+        testl     %edx, %edx
+        jne       .LBL_1_12
+        .cfi_escape 0x10, 0x20, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x60, 0xff, 0xff, 0xff, 0x22
+
+.LBL_1_2:
+        testl     %eax, %eax
+        jne       .LBL_1_4
+
+.LBL_1_3:
+        movups    176(%rsp), %xmm8
+        cfi_restore(25)
+        movups    160(%rsp), %xmm9
+        cfi_restore(26)
+        movups    144(%rsp), %xmm10
+        cfi_restore(27)
+        movups    112(%rsp), %xmm11
+        cfi_restore(28)
+        movups    96(%rsp), %xmm12
+        cfi_restore(29)
+        movups    80(%rsp), %xmm13
+        cfi_restore(30)
+        movups    48(%rsp), %xmm14
+        cfi_restore(31)
+        movups    32(%rsp), %xmm15
+        cfi_restore(32)
+        movq      %rbp, %rsp
+        popq      %rbp
+        cfi_def_cfa(7, 8)
+        cfi_restore(6)
+        ret
+        cfi_def_cfa(6, 16)
+        cfi_offset(6, -16)
+        .cfi_escape 0x10, 0x19, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xf0, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x1a, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x1b, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xd0, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x1c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xb0, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x1d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xa0, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x1e, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x90, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x1f, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x70, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x20, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x60, 0xff, 0xff, 0xff, 0x22
+
+.LBL_1_4:
+        movups    %xmm1, 64(%rsp)
+        movups    %xmm0, 128(%rsp)
+        je        .LBL_1_3
+        xorl      %edx, %edx
+        movq      %rsi, 8(%rsp)
+        movq      %rdi, (%rsp)
+        movq      %r12, 24(%rsp)
+        .cfi_escape 0x10, 0x04, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x05, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x58, 0xff, 0xff, 0xff, 0x22
+        movl      %edx, %r12d
+        movq      %r13, 16(%rsp)
+        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
+        movl      %eax, %r13d
+
+.LBL_1_8:
+        btl       %r12d, %r13d
+        jc        .LBL_1_11
+
+.LBL_1_9:
+        incl      %r12d
+        cmpl      $2, %r12d
+        jl        .LBL_1_8
+        movq      8(%rsp), %rsi
+        cfi_restore(4)
+        movq      (%rsp), %rdi
+        cfi_restore(5)
+        movq      24(%rsp), %r12
+        cfi_restore(12)
+        movq      16(%rsp), %r13
+        cfi_restore(13)
+        movups    128(%rsp), %xmm0
+        jmp       .LBL_1_3
+        .cfi_escape 0x10, 0x04, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x48, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x05, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x40, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x58, 0xff, 0xff, 0xff, 0x22
+        .cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xc0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x50, 0xff, 0xff, 0xff, 0x22
+
+.LBL_1_11:
+        lea       64(%rsp,%r12,8), %rdi
+        lea       128(%rsp,%r12,8), %rsi
+        call      __svml_dtan_cout_rare_internal
+        jmp       .LBL_1_9
+        cfi_restore(4)
+        cfi_restore(5)
+        cfi_restore(12)
+        cfi_restore(13)
+
+.LBL_1_12:
+        movdqu    .FLT_20(%rip), %xmm3
+
+/*
+ * Get the (2^a / 2pi) mod 1 values from the table.
+ * Because VLANG doesn't have L-type gather, we need a trivial cast
+ */
+        lea       __svml_dtan_reduction_data_internal(%rip), %r10
+        pand      %xmm1, %xmm3
+        psrlq     $52, %xmm3
+
+/*
+ * Also get the significand as an integer
+ * NB: adding in the integer bit is wrong for denorms!
+ * To make this work for denorms we should do something slightly different
+ */
+        movdqu    .FLT_21(%rip), %xmm2
+        movd      %xmm3, %edx
+        pand      %xmm1, %xmm2
+        paddq     .FLT_22(%rip), %xmm2
+        pextrw    $4, %xmm3, %r8d
+        movups    1088+__svml_dtan_data_internal(%rip), %xmm10
+        lea       (%rdx,%rdx,2), %ecx
+        shll      $3, %ecx
+        lea       (%r8,%r8,2), %r9d
+        shll      $3, %r9d
+        movdqa    %xmm2, %xmm6
+        movq      16(%rcx,%r10), %xmm8
+        andps     %xmm10, %xmm5
+        movhpd    16(%r9,%r10), %xmm8
+        psrlq     $32, %xmm6
+        movups    %xmm0, 16(%rsp)
+        movaps    %xmm8, %xmm0
+
+/*
+ * Break the P_xxx and m into 32-bit chunks ready for
+ * the long multiplication via 32x32->64 multiplications
+ */
+        movdqu    .FLT_23(%rip), %xmm15
+        psrlq     $32, %xmm0
+        movq      8(%rcx,%r10), %xmm13
+        pand      %xmm15, %xmm2
+        cmpeqpd   %xmm10, %xmm5
+        movdqa    %xmm6, %xmm10
+        movdqa    %xmm2, %xmm11
+        movhpd    8(%r9,%r10), %xmm13
+        pand      %xmm15, %xmm8
+        pmuludq   %xmm0, %xmm10
+        movaps    %xmm13, %xmm14
+        pmuludq   %xmm2, %xmm0
+        pmuludq   %xmm6, %xmm8
+        movmskpd  %xmm5, %eax
+        pand      %xmm15, %xmm13
+        psrlq     $32, %xmm0
+        pmuludq   %xmm13, %xmm11
+        psrlq     $32, %xmm14
+        pmuludq   %xmm6, %xmm13
+        paddq     %xmm0, %xmm10
+        movdqa    %xmm2, %xmm12
+        movdqa    %xmm15, %xmm3
+        pmuludq   %xmm14, %xmm12
+        pand      %xmm11, %xmm3
+        pmuludq   %xmm6, %xmm14
+        paddq     %xmm10, %xmm3
+        movq      (%rcx,%r10), %xmm7
+        movdqa    %xmm15, %xmm9
+        movhpd    (%r9,%r10), %xmm7
+        psrlq     $32, %xmm8
+        psrlq     $32, %xmm11
+        pand      %xmm7, %xmm9
+        movdqa    %xmm2, %xmm5
+        movdqa    %xmm15, %xmm10
+        paddq     %xmm3, %xmm8
+        paddq     %xmm11, %xmm13
+        pmuludq   %xmm9, %xmm5
+
+/* Now do the big multiplication and carry propagation */
+        pmuludq   %xmm9, %xmm6
+        pand      %xmm12, %xmm10
+        movaps    %xmm8, %xmm0
+        paddq     %xmm13, %xmm10
+        psrlq     $32, %xmm0
+        psrlq     $32, %xmm12
+        psrlq     $32, %xmm7
+        movdqa    %xmm15, %xmm11
+        paddq     %xmm10, %xmm0
+        paddq     %xmm12, %xmm14
+        pmuludq   %xmm7, %xmm2
+        pand      %xmm5, %xmm11
+        movdqa    %xmm0, %xmm13
+        paddq     %xmm14, %xmm11
+        psrlq     $32, %xmm13
+        psrlq     $32, %xmm5
+        paddq     %xmm11, %xmm13
+        paddq     %xmm5, %xmm6
+        pand      %xmm15, %xmm2
+        movdqa    %xmm13, %xmm3
+        paddq     %xmm6, %xmm2
+        psrlq     $32, %xmm3
+        pand      %xmm15, %xmm13
+        paddq     %xmm2, %xmm3
+        psllq     $32, %xmm3
+
+/* Assemble reduced argument from the pieces */
+        pand      %xmm15, %xmm8
+        paddq     %xmm13, %xmm3
+
+/*
+ * We want to incorporate the original sign now too.
+ * Do it here for convenience in getting the right N value,
+ * though we could wait right to the end if we were prepared
+ * to modify the sign of N later too.
+ * So get the appropriate sign mask now (or sooner).
+ */
+        movdqu    .FLT_24(%rip), %xmm9
+        movdqa    %xmm3, %xmm5
+
+/*
+ * Create floating-point high part, implicitly adding integer bit 1
+ * Incorporate overall sign at this stage too.
+ */
+        movdqu    .FLT_25(%rip), %xmm15
+        pand      %xmm1, %xmm9
+
+/*
+ * Now round at the 2^-9 bit position for reduction mod pi/2^8
+ * instead of the original 2pi (but still with the same 2pi scaling).
+ * Use a shifter of 2^43 + 2^42.
+ * The N we get is our final version; it has an offset of
+ * 2^9 because of the implicit integer bit, and anyway for negative
+ * starting value it's a 2s complement thing. But we need to mask
+ * off the exponent part anyway so it's fine.
+ */
+        movups    .FLT_26(%rip), %xmm12
+        psrlq     $12, %xmm5
+        pxor      %xmm9, %xmm15
+        movaps    %xmm12, %xmm10
+        por       %xmm15, %xmm5
+        psllq     $32, %xmm0
+        addpd     %xmm5, %xmm10
+        paddq     %xmm8, %xmm0
+        movaps    %xmm10, %xmm14
+
+/*  Load constants (not all needed at once)  */
+        lea       1632+__svml_dtan_data_internal(%rip), %r9
+        movdqu    .FLT_30(%rip), %xmm6
+        movdqu    .FLT_28(%rip), %xmm7
+        pand      %xmm3, %xmm6
+
+/*
+ * Create floating-point low and medium parts, respectively
+ * lo_23, ... lo_0, 0, ..., 0
+ * hi_11, ... hi_0, lo_63, ..., lo_24
+ * then subtract off the implicitly added integer bits,
+ * 2^-104 and 2^-52, respectively.
+ * Put the original sign into all of them at this stage.
+ */
+        movdqu    .FLT_27(%rip), %xmm8
+        pand      %xmm0, %xmm7
+        subpd     %xmm12, %xmm14
+        psllq     $40, %xmm6
+        psrlq     $24, %xmm0
+        pxor      %xmm9, %xmm8
+        por       %xmm0, %xmm6
+        pxor      .FLT_29(%rip), %xmm9
+        psllq     $28, %xmm7
+        subpd     %xmm14, %xmm5
+        por       %xmm9, %xmm6
+
+/* Now add them up into 2 reasonably aligned pieces */
+        movaps    %xmm5, %xmm11
+        subpd     %xmm9, %xmm6
+        addpd     %xmm6, %xmm11
+        subpd     %xmm11, %xmm5
+        por       %xmm8, %xmm7
+        subpd     %xmm8, %xmm7
+        addpd     %xmm5, %xmm6
+
+/* Split RHi into 26-bit leading part and 27-bit trailing part */
+        movups    .FLT_34(%rip), %xmm2
+        movaps    %xmm2, %xmm15
+        andps     %xmm11, %xmm15
+        addpd     %xmm6, %xmm7
+        subpd     %xmm15, %xmm11
+        mulpd     .FLT_31(%rip), %xmm7
+
+/*
+ * Now multiply those numbers all by 2 pi, reasonably accurately.
+ * The top part uses 2pi = d2pi_lead + d2pi_trail, where
+ * d2pi_lead has 27 significant bits.
+ */
+        movups    .FLT_32(%rip), %xmm0
+        movups    .FLT_33(%rip), %xmm3
+
+/*
+ * Do the multiplication as exact top part and "naive" low part.
+ * This still maintains almost 30 bits of offset and doesn't drop
+ * the accuracy much below what we already have.
+ */
+        movaps    %xmm0, %xmm12
+        mulpd     %xmm15, %xmm12
+        mulpd     %xmm11, %xmm0
+        mulpd     %xmm3, %xmm15
+        mulpd     %xmm11, %xmm3
+        addpd     %xmm15, %xmm0
+        addpd     %xmm3, %xmm7
+        addpd     %xmm7, %xmm0
+
+/*
+ * Do another stage of compensated summation to get full offset
+ * between the pieces dRedHi + dRedLo.
+ * Depending on the later algorithm, we might avoid this stage.
+ */
+        movaps    %xmm0, %xmm13
+        addpd     %xmm12, %xmm13
+        subpd     %xmm13, %xmm12
+
+/*
+ * If the magnitude of the input is <= 2^-20, then
+ * just pass through the input, since no reduction will be needed and
+ * the main path will only work accurately if the reduced argument is
+ * about >= 2^-70 (which it is for all large pi multiples)
+ */
+        movups    .FLT_36(%rip), %xmm7
+        movups    .FLT_35(%rip), %xmm3
+        movaps    %xmm7, %xmm14
+        andps     %xmm1, %xmm3
+        cmpltpd   %xmm3, %xmm14
+        cmplepd   %xmm7, %xmm3
+        addpd     %xmm12, %xmm0
+
+/* Grab our final N value as an integer, appropriately masked mod 2^9 */
+        pand      .FLT_37(%rip), %xmm10
+        andps     %xmm1, %xmm3
+
+/*
+ * Argument reduction is now finished: x = n * pi/256 + r
+ * where n = lIndex and r = dZ
+ * But we have n modulo 512, needed for sin/cos with period 2pi
+ * but we want it modulo 256 since tan has period pi.
+ */
+        pand      .FLT_38(%rip), %xmm10
+        andps     %xmm14, %xmm13
+        movd      %xmm10, %r11d
+        orps      %xmm13, %xmm3
+        andps     %xmm0, %xmm14
+        movups    %xmm1, (%rsp)
+        pextrw    $4, %xmm10, %ecx
+        imull     $104, %r11d, %edx
+
+/*
+ * The output is _VRES_Z (high) + _VRES_E (low), and the integer part is _VRES_IND
+ * Simply absorb E into Z instead of keeping a 2-part result.
+ */
+        addpd     %xmm14, %xmm3
+        imull     $104, %ecx, %r8d
+        movq      -96(%rdx,%r9), %xmm1
+        movhpd    -96(%r8,%r9), %xmm1
+
+/*
+ *  Compute reciprocal component
+ * Construct a separate reduced argument modulo pi near pi/2 multiples.
+ * i.e. (pi/2 - x) mod pi, simply by subtracting the reduced argument
+ * from an accurate B_hi = (128 - n) pi/256.
+ */
+        subpd     %xmm3, %xmm1
+
+/* Now compute an approximate reciprocal to mix into the computation. */
+        cvtpd2ps  %xmm1, %xmm5
+        movlhps   %xmm5, %xmm5
+
+/*
+ * Now compute the error dEr where dRecip_hi = (1/R_full) * (1 - dEr)
+ * so that we can compensate for it.
+ */
+        andps     %xmm1, %xmm2
+        rcpps     %xmm5, %xmm6
+        subpd     %xmm2, %xmm1
+        cvtps2pd  %xmm6, %xmm6
+        mulpd     %xmm6, %xmm2
+        mulpd     %xmm6, %xmm1
+        movups    .FLT_39(%rip), %xmm5
+        subpd     %xmm2, %xmm5
+        subpd     %xmm1, %xmm5
+
+/*
+ * Get a working-precision reciprocal 1/dR_full
+ * using a fourth-order polynomial approximation
+ * R + (E*R) * (1 + E) * (1 + E^2)
+ */
+        movaps    %xmm5, %xmm1
+
+/*
+ *  Higher polynomial terms
+ * Stage 1 (with unlimited parallelism)
+ * Z2 = Z^2
+ */
+        movaps    %xmm3, %xmm2
+        mulpd     %xmm5, %xmm1
+        mulpd     %xmm3, %xmm2
+        addpd     %xmm1, %xmm5
+        mulpd     %xmm6, %xmm1
+        addpd     %xmm6, %xmm1
+        movq      -24(%rdx,%r9), %xmm13
+        movq      -8(%rdx,%r9), %xmm12
+        movhpd    -24(%r8,%r9), %xmm13
+        movhpd    -8(%r8,%r9), %xmm12
+
+/* P5 = C3 + C4 * Z */
+        mulpd     %xmm3, %xmm13
+
+/* P6 = C5 + C6 * Z */
+        mulpd     %xmm3, %xmm12
+        mulpd     %xmm1, %xmm5
+        movq      (%rdx,%r9), %xmm15
+        movhpd    (%r8,%r9), %xmm15
+
+/* P9 = C5 + C6 * Z + C7 * Z^2 */
+        mulpd     %xmm2, %xmm15
+        addpd     %xmm5, %xmm6
+        movq      -40(%rdx,%r9), %xmm14
+
+/*
+ * Stage 2 (with unlimited parallelism)
+ * Z4 = Z^4
+ */
+        movaps    %xmm2, %xmm5
+        movq      -32(%rdx,%r9), %xmm10
+        movq      -16(%rdx,%r9), %xmm11
+        movhpd    -40(%r8,%r9), %xmm14
+        movhpd    -32(%r8,%r9), %xmm10
+        movhpd    -16(%r8,%r9), %xmm11
+
+/* P4 = C1_lo + C2 * Z */
+        mulpd     %xmm3, %xmm14
+        addpd     %xmm13, %xmm10
+        addpd     %xmm12, %xmm11
+        mulpd     %xmm2, %xmm5
+
+/* P10 = C1_lo + C2 * Z + C3 * Z^2 + C4 * Z^3 */
+        mulpd     %xmm10, %xmm2
+        addpd     %xmm15, %xmm11
+        movq      -48(%rdx,%r9), %xmm0
+        movhpd    -48(%r8,%r9), %xmm0
+        addpd     %xmm14, %xmm0
+
+/*
+ * Stage 3 (with unlimited parallelism)
+ * P12 = C1_lo + C2 * Z + ... + C7 * Z^6
+ */
+        mulpd     %xmm11, %xmm5
+        addpd     %xmm2, %xmm0
+        movq      -56(%rdx,%r9), %xmm8
+        movhpd    -56(%r8,%r9), %xmm8
+
+/*
+ *  Sum of dominant component(s)
+ * Compute C0_hi + C1_hi * Z + Recip_hi = H4
+ * H2 = C0_hi + C1_hi * Z (exact since C1_hi is 1 bit)
+ */
+        mulpd     %xmm3, %xmm8
+        addpd     %xmm5, %xmm0
+        movq      -80(%rdx,%r9), %xmm9
+        movhpd    -80(%r8,%r9), %xmm9
+
+/*
+ * dRecip_hi is only used when dTau is one (cotangent path)
+ * H4 = C0_hi + C1_hi * Z + Recip_hi
+ */
+        mulpd     %xmm6, %xmm9
+
+/* And now the very final summation */
+        mulpd     %xmm0, %xmm3
+        movq      -72(%rdx,%r9), %xmm7
+
+/*
+ *
+ * End of large arguments path
+ *
+ * Merge results from main and large paths:
+ */
+        movaps    %xmm4, %xmm0
+        movhpd    -72(%r8,%r9), %xmm7
+        addpd     %xmm8, %xmm7
+        addpd     %xmm9, %xmm7
+        addpd     %xmm3, %xmm7
+        andnps    16(%rsp), %xmm0
+        andps     %xmm4, %xmm7
+        movups    (%rsp), %xmm1
+        orps      %xmm7, %xmm0
+        jmp       .LBL_1_2
+
+END(_ZGVbN2v_tan_sse4)
+
+        .align    16,0x90
+
+__svml_dtan_cout_rare_internal:
+
+        cfi_startproc
+
+        xorl      %eax, %eax
+        movzwl    6(%rdi), %ecx
+        movsd     (%rdi), %xmm1
+        andl      $32752, %ecx
+        movb      7(%rdi), %dl
+        andb      $127, %dl
+        movsd     %xmm1, -8(%rsp)
+        movb      %dl, -1(%rsp)
+        cmpl      $32752, %ecx
+        je        .LBL_2_3
+        ret
+
+.LBL_2_3:
+        cmpl      $0, -8(%rsp)
+        jne       .LBL_2_6
+        cmpl      $2146435072, -4(%rsp)
+        jne       .LBL_2_6
+        movsd     __dtan_la_Tab(%rip), %xmm0
+        movl      $1, %eax
+        mulsd     %xmm0, %xmm1
+        movsd     %xmm1, (%rsi)
+        ret
+
+.LBL_2_6:
+        mulsd     %xmm1, %xmm1
+        movsd     %xmm1, (%rsi)
+        ret
+
+        cfi_endproc
+
+        .type	__svml_dtan_cout_rare_internal,@function
+        .size	__svml_dtan_cout_rare_internal,.-__svml_dtan_cout_rare_internal
+
+        .section .rodata, "a"
+        .align 64
+
+__svml_dtan_data_internal:
+        .long	1841940611
+        .long	1075076912
+        .long	1841940611
+        .long	1075076912
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .long	1413754136
+        .long	1070146043
+        .long	1413754136
+        .long	1070146043
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
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+        .byte	0
+        .byte	0
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+        .byte	0
+        .byte	0
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+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
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+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
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+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .long	856972294
+        .long	1013032486
+        .long	856972294
+        .long	1013032486
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
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+        .byte	0
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+        .byte	0
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+        .byte	0
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+        .byte	0
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+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .long	688016905
+        .long	958143697
+        .long	688016905
+        .long	958143697
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
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+        .byte	0
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+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .long	855638016
+        .long	1013032486
+        .long	855638016
+        .long	1013032486
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
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+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .long	3773204808
+        .long	979655686
+        .long	3773204808
+        .long	979655686
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
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+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .long	0
+        .long	2147483648
+        .long	3763679576
+        .long	1070167541
+        .long	2583490354
+        .long	1071284857
+        .long	716700048
+        .long	1071997368
+        .long	0
+        .long	1072693248
+        .long	3797578849
+        .long	1073213976
+        .long	859807206
+        .long	1073958991
+        .long	3795994481
+        .long	1075059710
+        .long	4294967295
+        .long	4293918719
+        .long	3795994481
+        .long	3222543358
+        .long	859807206
+        .long	3221442639
+        .long	3797578849
+        .long	3220697624
+        .long	0
+        .long	3220176896
+        .long	716700048
+        .long	3219481016
+        .long	2583490354
+        .long	3218768505
+        .long	3763679576
+        .long	3217651189
+        .long	0
+        .long	2147483648
+        .long	1732516166
+        .long	1009710547
+        .long	2973134505
+        .long	1014008623
+        .long	561165941
+        .long	1015523525
+        .long	0
+        .long	0
+        .long	1767150223
+        .long	1016338938
+        .long	4129738197
+        .long	1017254245
+        .long	4275273486
+        .long	1015088902
+        .long	0
+        .long	4238344192
+        .long	4275273486
+        .long	3162572550
+        .long	4129738197
+        .long	3164737893
+        .long	1767150223
+        .long	3163822586
+        .long	0
+        .long	0
+        .long	561165941
+        .long	3163007173
+        .long	2973134505
+        .long	3161492271
+        .long	1732516166
+        .long	3157194195
+        .long	1431655900
+        .long	1070945621
+        .long	1431655900
+        .long	1070945621
+        .byte	0
+        .byte	0
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+        .byte	0
+        .byte	0
+        .byte	0
+        .long	285935618
+        .long	1069617425
+        .long	285935618
+        .long	1069617425
+        .byte	0
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+        .byte	0
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+        .byte	0
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+        .byte	0
+        .long	1218258378
+        .long	1068212666
+        .long	1218258378
+        .long	1068212666
+        .byte	0
+        .byte	0
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+        .byte	0
+        .long	1716452265
+        .long	1066820779
+        .long	1716452265
+        .long	1066820779
+        .byte	0
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+        .byte	0
+        .byte	0
+        .byte	0
+        .long	3351902813
+        .long	1065508044
+        .long	3351902813
+        .long	1065508044
+        .byte	0
+        .byte	0
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+        .byte	0
+        .long	0
+        .long	1072693248
+        .long	0
+        .long	1072693248
+        .byte	0
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+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .byte	0
+        .long	4294967295
+        .long	2147483647
+        .long	4294967295
+        .long	2147483647
+        .byte	0
+        .byte	0
+        .byte	0
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