x86: Optimize svml_s_tanhf8_core_avx2.S

Optimizations are:
    1. Reduce code size (-81 bytes).
    2. Remove redundant move instructions.
    3. Slightly improve instruction selection/scheduling where
       possible.
    4. Prefer registers which get short instruction encoding.
    5. Reduce rodata size (-32 bytes).

Result is roughly a 17-18% speedup:

       Function, New Time, Old Time, New / Old
_ZGVdN8v_tanhf,     1.977,    2.402,     0.823

1 files changed, 171 insertions, 741 deletions

diff --git a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf8_core_avx2.S b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf8_core_avx2.S
index c5c87bf5b0..55df346a00 100644
--- a/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf8_core_avx2.S
+++ b/sysdeps/x86_64/fpu/multiarch/svml_s_tanhf8_core_avx2.S
@@ -70,773 +70,203 @@
  *
  */
 
-/* Offsets for data table __svml_stanh_data_internal
- */
-#define _dbP				0
-#define _sSignMask			4288
-#define _sAbsMask			4320
-#define _iExpMantMask			4352
-#define _iExpMask			4384
-#define _iMinIdxOfsMask			4416
-#define _iMaxIdxMask			4448
-
 #include <sysdep.h>
 
+/* tanhf data tables for avx2 and sse4 implementatins defined here.
+ */
+#include "svml_s_tanhf_rodata.S"
+
 	.section .text.avx2, "ax", @progbits
 ENTRY(_ZGVdN8v_tanhf_avx2)
-	pushq	%rbp
-	cfi_def_cfa_offset(16)
-	movq	%rsp, %rbp
-	cfi_def_cfa(6, 16)
-	cfi_offset(6, -16)
-	andq	$-32, %rsp
-	pushq	%r12
-	subq	$120, %rsp
-	lea	_dbP+16+__svml_stanh_data_internal(%rip), %r10
-	vmovaps	%ymm0, %ymm12
-
 	/* Here huge arguments, INF and NaNs are filtered out to callout. */
-	vpand	_iExpMantMask+__svml_stanh_data_internal(%rip), %ymm12, %ymm14
+	vpand	TANHF_DATA(_iExpMantMask)(%rip), %ymm0, %ymm4
+	vpsubd	TANHF_DATA(_iMinIdxOfsMask)(%rip), %ymm4, %ymm2
+
+	/* Selection of arguments between [0, 0x04280000] into ymm2.  */
+	vpxor	%ymm3, %ymm3, %ymm3
+	vpmaxsd	%ymm3, %ymm2, %ymm2
+	vpminsd	TANHF_DATA(_iMaxIdxMask)(%rip), %ymm2, %ymm2
 
 	/*
 	 *  small table specific variables *
 	 *  Constant loading
 	 */
-	vmovups	_iMaxIdxMask+__svml_stanh_data_internal(%rip), %ymm8
-	vpsubd	_iMinIdxOfsMask+__svml_stanh_data_internal(%rip), %ymm14, %ymm9
-
-	/* if VMIN, VMAX is defined for I type */
-	vxorps	%ymm15, %ymm15, %ymm15
-	vpcmpgtd %ymm15, %ymm9, %ymm0
-	vpand	%ymm0, %ymm9, %ymm7
-	vpcmpgtd %ymm8, %ymm9, %ymm6
-	vblendvps %ymm6, %ymm8, %ymm7, %ymm3
-	vpsrld	$14, %ymm3, %ymm1
-	vpcmpgtd _iExpMask+__svml_stanh_data_internal(%rip), %ymm14, %ymm13
-	vmovmskps %ymm13, %r11d
-	vandps	_sAbsMask+__svml_stanh_data_internal(%rip), %ymm12, %ymm10
-	vandps	_sSignMask+__svml_stanh_data_internal(%rip), %ymm12, %ymm11
-	vextractf128 $1, %ymm1, %xmm2
-	vmovd	%xmm1, %r9d
-	vmovd	%xmm2, %ecx
-	vpextrd	$1, %xmm2, %edx
-	vpextrd	$1, %xmm1, %r8d
-	movslq	%r9d, %r9
-	movslq	%edx, %rdx
-	movslq	%r8d, %r8
-	vpextrd	$2, %xmm1, %edi
-	movslq	%ecx, %rcx
-	/*  DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -8; DW_OP_plus)  */
-	.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xf8, 0xff, 0xff, 0xff, 0x22
-	vpextrd	$3, %xmm2, %r12d
-	vpextrd	$3, %xmm1, %esi
-	vpextrd	$2, %xmm2, %eax
-	movslq	%edi, %rdi
-	movslq	%r12d, %r12
-	movslq	%esi, %rsi
-	movslq	%eax, %rax
-	vmovupd	-16(%r9, %r10), %xmm5
-	vmovupd	-16(%rdx, %r10), %xmm14
-	vmovupd	-16(%rcx, %r10), %xmm13
-	vmovupd	(%r9, %r10), %xmm1
-	vmovupd	(%r8, %r10), %xmm2
-	vmovupd	-16(%r8, %r10), %xmm4
-	vinsertf128 $1, -16(%rdi, %r10), %ymm5, %ymm15
-	vinsertf128 $1, -16(%r12, %r10), %ymm14, %ymm3
-	vinsertf128 $1, -16(%rax, %r10), %ymm13, %ymm6
-	vinsertf128 $1, (%rdi, %r10), %ymm1, %ymm5
-	vinsertf128 $1, (%rsi, %r10), %ymm2, %ymm14
-	vunpcklpd %ymm3, %ymm6, %ymm8
+	vpsrld	$14, %ymm2, %ymm1
+
+	/* We are splitting xmm1 into 8 GPRs. This may be faster to do with
+	   store/load as we can take advantage of store-forwarding.  */
+	vmovq	%xmm1, %r8
+	/* We have eliminated all negative values for ymm1 so no need to sign
+	   extend.  */
+	movl	%r8d, %r9d
+	shrq	$32, %r8
+
+	/* Store base of lookup table in rax.  */
+	leaq	TANHF_DATA(_lookupTable)(%rip), %rax
+
+	/* Instead of using cross-lane permutes on ymm vectors, use vpinsertf128
+	   with memory operand. This helps alleviate bottleneck on p5.  */
+	vmovupd	16(%r9, %rax), %xmm5
+
+	vpextrq	$1, %xmm1, %rsi
+	movl	%esi, %edi
+	shrq	$32, %rsi
+
+	vinsertf128 $1, 16(%rdi, %rax), %ymm5, %ymm5
+
+	vextracti128 $1, %ymm1, %xmm2
+	vmovq	%xmm2, %rdx
+	movl	%edx, %ecx
+	shrq	$32, %rdx
+
+	vmovupd	(%rcx, %rax), %xmm6
+
+	vpextrq	$1, %xmm2, %r10
+	movl	%r10d, %r11d
+	shrq	$32, %r10
+
+	vinsertf128 $1, (%r11, %rax), %ymm6, %ymm6
+
+	vmovupd	16(%r8, %rax), %xmm1
+	vinsertf128 $1, 16(%rsi, %rax), %ymm1, %ymm1
+	vmovupd	(%rdx, %rax), %xmm3
+	vinsertf128 $1, (%r10, %rax), %ymm3, %ymm3
+
+	vunpcklpd %ymm3, %ymm6, %ymm7
 	vunpckhpd %ymm3, %ymm6, %ymm6
-	vunpcklpd %ymm14, %ymm5, %ymm3
-	vunpckhpd %ymm14, %ymm5, %ymm2
-	vmovupd	(%rcx, %r10), %xmm13
-	vcvtps2pd %xmm10, %ymm5
-	vextractf128 $1, %ymm10, %xmm10
-	vfmadd213pd %ymm3, %ymm5, %ymm2
-	vinsertf128 $1, -16(%rsi, %r10), %ymm4, %ymm0
-	vmovupd	(%rdx, %r10), %xmm4
-	vunpcklpd %ymm0, %ymm15, %ymm9
-	vunpckhpd %ymm0, %ymm15, %ymm7
-	vfmadd213pd %ymm7, %ymm5, %ymm2
-	vfmadd213pd %ymm9, %ymm5, %ymm2
-	vinsertf128 $1, (%r12, %r10), %ymm4, %ymm0
-	vcvtps2pd %xmm10, %ymm4
-	vinsertf128 $1, (%rax, %r10), %ymm13, %ymm15
-	vunpcklpd %ymm0, %ymm15, %ymm1
-	vunpckhpd %ymm0, %ymm15, %ymm0
-	vfmadd213pd %ymm1, %ymm4, %ymm0
-	vcvtpd2ps %ymm2, %xmm1
-	vfmadd213pd %ymm6, %ymm4, %ymm0
-	vfmadd213pd %ymm8, %ymm4, %ymm0
-	vcvtpd2ps %ymm0, %xmm0
-	vinsertf128 $1, %xmm0, %ymm1, %ymm2
-	vorps	%ymm11, %ymm2, %ymm0
-	testl	%r11d, %r11d
 
-	/* Go to special inputs processing branch */
-	jne	L(SPECIAL_VALUES_BRANCH)
-	# LOE rbx r13 r14 r15 r11d ymm0 ymm12
+	vunpcklpd %ymm1, %ymm5, %ymm3
+	vunpckhpd %ymm1, %ymm5, %ymm1
 
-	/* Restore registers
-	 * and exit the function
-	 */
+	vmovaps	TANHF_DATA(_sAbsMask)(%rip), %ymm11
+	/* Store special cases in ymm15.  */
+	vpcmpgtd TANHF_DATA(_iExpMask)(%rip), %ymm4, %ymm15
 
-L(EXIT):
-	addq	$120, %rsp
-	cfi_restore(12)
-	popq	%r12
-	movq	%rbp, %rsp
-	popq	%rbp
-	cfi_def_cfa(7, 8)
-	cfi_restore(6)
-	ret
-	cfi_def_cfa(6, 16)
-	cfi_offset(6, -16)
-	/*  DW_CFA_expression: r12 (r12) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -8; DW_OP_plus)  */
-	.cfi_escape 0x10, 0x0c, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0xf8, 0xff, 0xff, 0xff, 0x22
+	vandps	%ymm11, %ymm0, %ymm4
 
-	/* Branch to process
-	 * special inputs
-	 */
+	vcvtps2pd %xmm4, %ymm5
 
-L(SPECIAL_VALUES_BRANCH):
-	vmovups	%ymm12, 32(%rsp)
-	vmovups	%ymm0, 64(%rsp)
-	# LOE rbx r13 r14 r15 r11d ymm0
+	vextractf128 $1, %ymm4, %xmm4
+	vcvtps2pd %xmm4, %ymm4
 
-	xorl	%r12d, %r12d
-	# LOE rbx r13 r14 r15 r11d r12d
+	vmovupd	16(%rcx, %rax), %xmm2
+	vinsertf128 $1, 16(%r11, %rax), %ymm2, %ymm2
 
-	vzeroupper
-	movq	%r13, 8(%rsp)
-	/*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -120; DW_OP_plus)  */
-	.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22
-	movl	%r11d, %r13d
-	movq	%r14, (%rsp)
-	/*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -128; DW_OP_plus)  */
-	.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 0xff, 0xff, 0xff, 0x22
-	# LOE rbx r15 r12d r13d
-
-	/* Range mask
-	 * bits check
-	 */
+	vfmadd213pd %ymm3, %ymm5, %ymm1
+
+	vmovupd	16(%rdx, %rax), %xmm3
+	vinsertf128 $1, 16(%r10, %rax), %ymm3, %ymm3
+
+	vunpcklpd %ymm3, %ymm2, %ymm10
+	vunpckhpd %ymm3, %ymm2, %ymm2
+
+	vfmadd213pd %ymm10, %ymm4, %ymm2
+	vfmadd213pd %ymm6, %ymm4, %ymm2
+	vfmadd213pd %ymm7, %ymm4, %ymm2
+	vcvtpd2ps %ymm2, %xmm2
+
+	vmovupd	(%r9, %rax), %xmm7
+	vinsertf128 $1, (%rdi, %rax), %ymm7, %ymm7
+
+	vmovupd	(%r8, %rax), %xmm3
+	vinsertf128 $1, (%rsi, %rax), %ymm3, %ymm3
+
+	vunpckhpd %ymm3, %ymm7, %ymm4
+	vunpcklpd %ymm3, %ymm7, %ymm7
 
-L(RANGEMASK_CHECK):
-	btl	%r12d, %r13d
+	vfmadd213pd %ymm4, %ymm5, %ymm1
+	vfmadd213pd %ymm7, %ymm5, %ymm1
+
+
+	vcvtpd2ps %ymm1, %xmm1
+	vinsertf128 $1, %xmm2, %ymm1, %ymm1
+
+	vmovmskps %ymm15, %edx
+	vandnps	%ymm0, %ymm11, %ymm2
+	testl	%edx, %edx
+	/* Go to special inputs processing branch */
+	jne	L(SPECIAL_VALUES_BRANCH)
+	# LOE rbx r12 r13 r14 r15 ymm0 ymm1 ymm2
+	/* Wait until after branch of write over ymm0.  */
+	vorps	%ymm2, %ymm1, %ymm0
+	/* No stack restoration on the fastpath.  */
+	ret
 
-	/* Call scalar math function */
-	jc	L(SCALAR_MATH_CALL)
-	# LOE rbx r15 r12d r13d
 
-	/* Special inputs
-	 * processing loop
+	/* Cold case. edx has 1s where there was a special value that
+	   needs to be handled by a tanhf call. Optimize for code size
+	   more so than speed here. */
+L(SPECIAL_VALUES_BRANCH):
+	# LOE rbx rdx r12 r13 r14 r15 ymm0 ymm1 ymm2
+    /* Use r13 to save/restore the stack. This allows us to use rbp as
+       callee save register saving code size. */
+	pushq	%r13
+	cfi_adjust_cfa_offset(8)
+	cfi_offset(r13, -16)
+	/* Need to callee save registers to preserve state across tanhf calls.
 	 */
+	pushq	%rbx
+	cfi_adjust_cfa_offset(8)
+	cfi_offset(rbx, -24)
+	pushq	%rbp
+	cfi_adjust_cfa_offset(8)
+	cfi_offset(rbp, -32)
+	movq	%rsp, %r13
+	cfi_def_cfa_register(r13)
+
+	/* Align stack and make room for 2x ymm vectors.  */
+	andq	$-32, %rsp
+	addq	$-64, %rsp
+
+	/* Save all already computed inputs.  */
+	vorps	%ymm2, %ymm1, %ymm1
+	vmovaps	%ymm1, (%rsp)
+	/* Save original input (ymm0 unchanged up to this point).  */
+	vmovaps	%ymm0, 32(%rsp)
+
+	vzeroupper
 
+	/* edx has 1s where there was a special value that needs to be handled
+	   by a tanhf call.  */
+	movl	%edx, %ebx
 L(SPECIAL_VALUES_LOOP):
-	incl	%r12d
-	cmpl	$8, %r12d
-
-	/* Check bits in range mask */
-	jl	L(RANGEMASK_CHECK)
-	# LOE rbx r15 r12d r13d
-
-	movq	8(%rsp), %r13
-	cfi_restore(13)
-	movq	(%rsp), %r14
-	cfi_restore(14)
-	vmovups	64(%rsp), %ymm0
-
-	/* Go to exit */
-	jmp	L(EXIT)
-	/*  DW_CFA_expression: r13 (r13) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -120; DW_OP_plus)  */
-	.cfi_escape 0x10, 0x0d, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x88, 0xff, 0xff, 0xff, 0x22
-	/*  DW_CFA_expression: r14 (r14) (DW_OP_lit8; DW_OP_minus; DW_OP_const4s: -32; DW_OP_and; DW_OP_const4s: -128; DW_OP_plus)  */
-	.cfi_escape 0x10, 0x0e, 0x0e, 0x38, 0x1c, 0x0d, 0xe0, 0xff, 0xff, 0xff, 0x1a, 0x0d, 0x80, 0xff, 0xff, 0xff, 0x22
-	# LOE rbx r13 r14 r15 ymm0
-
-	/* Scalar math fucntion call
-	 * to process special input
-	 */
+	# LOE rbx rbp r12 r13 r14 r15
+	/* use rbp as index for special value that is saved across calls to
+	   tanhf. We technically don't need a callee save register here as offset
+	   to rsp is always [0, 28] so we can restore rsp by realigning to 64.
+	   Essentially the tradeoff is 1 extra save/restore vs 2 extra instructions
+	   in the loop. Realigning also costs more code size.  */
+	xorl	%ebp, %ebp
+	tzcntl	%ebx, %ebp
 
-L(SCALAR_MATH_CALL):
-	movl	%r12d, %r14d
-	movss	32(%rsp, %r14, 4), %xmm0
+	/* Scalar math function call to process special input.  */
+	movss	32(%rsp, %rbp, 4), %xmm0
 	call	tanhf@PLT
-	# LOE rbx r14 r15 r12d r13d xmm0
 
-	movss	%xmm0, 64(%rsp, %r14, 4)
+	/* No good way to avoid the store-forwarding fault this will cause on
+	   return. `lfence` avoids the SF fault but at greater cost as it
+	   serialized stack/callee save restoration.  */
+	movss	%xmm0, (%rsp, %rbp, 4)
+
+	blsrl   %ebx, %ebx
+	jnz	L(SPECIAL_VALUES_LOOP)
+	# LOE r12 r13 r14 r15
 
-	/* Process special inputs in loop */
-	jmp	L(SPECIAL_VALUES_LOOP)
-	# LOE rbx r15 r12d r13d
-END(_ZGVdN8v_tanhf_avx2)
 
-	.section .rodata, "a"
-	.align	32
-
-#ifdef __svml_stanh_data_internal_typedef
-typedef unsigned int VUINT32;
-typedef struct {
-	__declspec(align(32)) VUINT32 _dbP[(134*4)][2];
-	__declspec(align(32)) VUINT32 _sSignMask[8][1];
-	__declspec(align(32)) VUINT32 _sAbsMask[8][1];
-	__declspec(align(32)) VUINT32 _iExpMantMask[8][1];
-	__declspec(align(32)) VUINT32 _iExpMask[8][1];
-	__declspec(align(32)) VUINT32 _iMinIdxOfsMask[8][1];
-	__declspec(align(32)) VUINT32 _iMaxIdxMask[8][1];
-} __svml_stanh_data_internal;
-#endif
-__svml_stanh_data_internal:
-	/* Pol_000:  err=7.93e-09, x in [0.0000000; 0.0312500]. */
-	.quad	0x0000000000000000 /* A00 = +0.000000000000000000000e-01 */
-	.quad	0x3FF00000022C70EB /* A01 = +1.000000008097283510367e+00 */
-	.quad	0xBED00E878CFFA194 /* A02 = -3.828228912518614443549e-06 */
-	.quad	0xBFD551766D0607A9 /* A03 = -3.330970825846813476723e-01 */
-	.quad	0xBE53D60CE3E4C297 /* A00 = -1.847383956330407336230e-08 */
-	.quad	0x3FF000024177CF5C /* A01 = +1.000002151235967140508e+00 */
-	.quad	0xBF1758BC94A51A25 /* A02 = -8.906031613262943753568e-05 */
-	.quad	0xBFD53EAE67E0D4F0 /* A03 = -3.319507612644221339337e-01 */
-	.quad	0xBE5A9E47EF32D6FE /* A00 = -2.479020984039698285657e-08 */
-	.quad	0x3FF00002DA983057 /* A01 = +1.000002721676556793895e+00 */
-	.quad	0xBF1BD953509E94AA /* A02 = -1.062352277175377670507e-04 */
-	.quad	0xBFD53BDB562EEDD5 /* A03 = -3.317783681520414806876e-01 */
-	.quad	0xBE6191BBE496D294 /* A00 = -3.272532162914017685901e-08 */
-	.quad	0x3FF0000390492017 /* A01 = +1.000003398528866105366e+00 */
-	.quad	0xBF20727E814A57CE /* A02 = -1.254825043772153972919e-04 */
-	.quad	0xBFD538DE060A6F22 /* A03 = -3.315959033004550748913e-01 */
-	.quad	0xBE66DAFA2A893A25 /* A00 = -4.257146219278012568149e-08 */
-	.quad	0x3FF0000465E08CD1 /* A01 = +1.000004194219219266770e+00 */
-	.quad	0xBF2341C765EF91B6 /* A02 = -1.469188600530365522261e-04 */
-	.quad	0xBFD535B6841FAF9E /* A03 = -3.314033785124993469751e-01 */
-	.quad	0xBE6D5794E361E964 /* A00 = -5.465394929765249413434e-08 */
-	.quad	0x3FF000055EE2A0CB /* A01 = +1.000005121846742950353e+00 */
-	.quad	0xBF265E6C77E66C8B /* A02 = -1.706607253709506650304e-04 */
-	.quad	0xBFD53264DDCCEDA6 /* A03 = -3.312008062382240103361e-01 */
-	.quad	0xBE729C844D374A6E /* A00 = -6.933284462462096107184e-08 */
-	.quad	0x3FF000067F019093 /* A01 = +1.000006195180536350264e+00 */
-	.quad	0xBF29CC5348D6DCE5 /* A02 = -1.968242326435338705130e-04 */
-	.quad	0xBFD52EE92121ED35 /* A03 = -3.309881995734998416658e-01 */
-	.quad	0xBE775AEA17EAA872 /* A00 = -8.700465590574974405858e-08 */
-	.quad	0x3FF00007CA1D66B8 /* A01 = +1.000007428656699559610e+00 */
-	.quad	0xBF2D8F5EB98A2637 /* A02 = -2.255252009216044881395e-04 */
-	.quad	0xBFD52B435CDF9128 /* A03 = -3.307655722585587376727e-01 */
-	.quad	0xBE7D04DA28C343F0 /* A00 = -1.081040272327705484794e-07 */
-	.quad	0x3FF000094443CCF5 /* A01 = +1.000008837375216730337e+00 */
-	.quad	0xBF30D5B76C947AE5 /* A02 = -2.568791210978817814332e-04 */
-	.quad	0xBFD52773A0776FAD /* A03 = -3.305329386764651045105e-01 */
-	.quad	0xBE81DD77A12C51C7 /* A00 = -1.331054169875768625701e-07 */
-	.quad	0x3FF0000AF1AFD2DA /* A01 = +1.000010437096696680470e+00 */
-	.quad	0xBF331230624C1680 /* A02 = -2.910011410651516805537e-04 */
-	.quad	0xBFD52379FC0B61DF /* A03 = -3.302903138515186909352e-01 */
-	.quad	0xBE85D04EEEB3C435 /* A00 = -1.625247628488202841012e-07 */
-	.quad	0x3FF0000CD6C9B1F2 /* A01 = +1.000012244238970726684e+00 */
-	.quad	0xBF357F0742FADDD4 /* A02 = -3.280060509313874068243e-04 */
-	.quad	0xBFD51F56806D0E81 /* A03 = -3.300377134475880880338e-01 */
-	.quad	0xBE8A6E289B59681B /* A00 = -1.969211333326924655065e-07 */
-	.quad	0x3FF0000EF8268F72 /* A01 = +1.000014275873550406715e+00 */
-	.quad	0xBF381E277A1B747A /* A02 = -3.680082682942575423093e-04 */
-	.quad	0xBFD51B093F1D6FD4 /* A03 = -3.297751537663746734808e-01 */
-	.quad	0xBE8FCBC40EE9ABD5 /* A00 = -2.368983653301529373887e-07 */
-	.quad	0x3FF000115A883B6C /* A01 = +1.000016549721943981410e+00 */
-	.quad	0xBF3AF17AC974B3D9 /* A02 = -4.111218235774406434303e-04 */
-	.quad	0xBFD516924A4C549C /* A03 = -3.295026517456081105450e-01 */
-	.quad	0xBE92FFBC60A3F956 /* A00 = -2.831066871072026054144e-07 */
-	.quad	0x3FF0001402DCED8A /* A01 = +1.000019084151832604590e+00 */
-	.quad	0xBF3DFAE9390C4801 /* A02 = -4.574603454311488280083e-04 */
-	.quad	0xBFD511F1B4D7DC3A /* A03 = -3.292202249571719585575e-01 */
-	.quad	0xBE9690A22F96D5AD /* A00 = -3.362443262393081632612e-07 */
-	.quad	0x3FF00016F63EFF5D /* A01 = +1.000021898173108825247e+00 */
-	.quad	0xBF409E2C839605BB /* A02 = -5.071370461992499986334e-04 */
-	.quad	0xBFD50D27924BEE00 /* A03 = -3.289278916051614487515e-01 */
-	.quad	0xBE9AA56C65E72A73 /* A00 = -3.970591019557469835586e-07 */
-	.quad	0x3FF0001A39F4A43E /* A01 = +1.000025011433776978009e+00 */
-	.quad	0xBF425BD74C3D6667 /* A02 = -5.602647074553602319844e-04 */
-	.quad	0xBFD50833F6E1ABA2 /* A03 = -3.286256705238718156536e-01 */
-	.quad	0xBE9F4BD4FF1A83B0 /* A00 = -4.663500013744687071912e-07 */
-	.quad	0x3FF0001DD36F9EC2 /* A01 = +1.000028444215715683896e+00 */
-	.quad	0xBF44376634149405 /* A02 = -6.169556656102642569831e-04 */
-	.quad	0xBFD50316F77EDEE5 /* A03 = -3.283135811757190158922e-01 */
-	.quad	0xBEA3B625387BB079 /* A00 = -5.874486399249461304297e-07 */
-	.quad	0x3FF00023E14CFBA9 /* A01 = +1.000034217911642153709e+00 */
-	.quad	0xBF47392F923218D2 /* A02 = -7.087213783883111826306e-04 */
-	.quad	0xBFD4FB1FACDEB938 /* A03 = -3.278273761924483942209e-01 */
-	.quad	0xBEAA6E24F543500A /* A00 = -7.876828740601738750574e-07 */
-	.quad	0x3FF0002D5C6E8412 /* A01 = +1.000043259679163742959e+00 */
-	.quad	0xBF4BAF02BD7FDD70 /* A02 = -8.448375110664940040861e-04 */
-	.quad	0xBFD4EFEE6527A7DE /* A03 = -3.271442401734229177279e-01 */
-	.quad	0xBEB16E3EBE2157D0 /* A00 = -1.038947396133402500647e-06 */
-	.quad	0x3FF00038990FEE2F /* A01 = +1.000053975962952312884e+00 */
-	.quad	0xBF50569481C574CB /* A02 = -9.972048056490652716971e-04 */
-	.quad	0xBFD4E419278DA2B4 /* A03 = -3.264220129263251113372e-01 */
-	.quad	0xBEB6A7B6723165D4 /* A00 = -1.350350836279403750524e-06 */
-	.quad	0x3FF00045CAB4158E /* A01 = +1.000066558657042303793e+00 */
-	.quad	0xBF531D7C9C849108 /* A02 = -1.166698160951775212202e-03 */
-	.quad	0xBFD4D7A0BB33B152 /* A03 = -3.256608799117844954552e-01 */
-	.quad	0xBEBD0EE2A8654AFD /* A00 = -1.732000471561702711532e-06 */
-	.quad	0x3FF00055276F18D6 /* A01 = +1.000081209219890521211e+00 */
-	.quad	0xBF562FDBA3FB6C6C /* A02 = -1.354183666925102939860e-03 */
-	.quad	0xBFD4CA85F1B93DB2 /* A03 = -3.248610363561638125773e-01 */
-	.quad	0xBEC269D4036A207E /* A00 = -2.195047297096822741730e-06 */
-	.quad	0x3FF00066E7DA6E4E /* A01 = +1.000098138500919997540e+00 */
-	.quad	0xBF5991499FC36B3A /* A02 = -1.560518167983372759405e-03 */
-	.quad	0xBFD4BCC9A72283D6 /* A03 = -3.240226871658341556426e-01 */
-	.quad	0xBEC7154B6C09CFE1 /* A00 = -2.751729738565190291276e-06 */
-	.quad	0x3FF0007B47086B80 /* A01 = +1.000117566559055148900e+00 */
-	.quad	0xBF5D455433B4F8F4 /* A02 = -1.786548832412968197680e-03 */
-	.quad	0xBFD4AE6CC1BFE145 /* A03 = -3.231460468373550942722e-01 */
-	.quad	0xBECCA68CC64A0F8A /* A00 = -3.415415948561670285790e-06 */
-	.quad	0x3FF00092827742F7 /* A01 = +1.000139722473418535387e+00 */
-	.quad	0xBF60A7BF15A527AF /* A02 = -2.033112728132522705610e-03 */
-	.quad	0xBFD49F703214084C /* A03 = -3.222313393636155876010e-01 */
-	.quad	0xBED19E68676B241B /* A00 = -4.200644630977303616698e-06 */
-	.quad	0x3FF000ACDA037B26 /* A01 = +1.000164844146362863597e+00 */
-	.quad	0xBF62D99F836A02F8 /* A02 = -2.301036405072284102280e-03 */
-	.quad	0xBFD48FD4F2B91B28 /* A03 = -3.212787981359945810311e-01 */
-	.quad	0xBED57CF4B0C7AA54 /* A00 = -5.123164339408145209103e-06 */
-	.quad	0x3FF000CA8FD9E1A1 /* A01 = +1.000193178099017865534e+00 */
-	.quad	0xBF653A014548E686 /* A02 = -2.591135484433962181405e-03 */
-	.quad	0xBFD47F9C0844B38F /* A03 = -3.202886658426046806447e-01 */
-	.quad	0xBEDA012B1B1A41E2 /* A00 = -6.199971197454598722328e-06 */
-	.quad	0x3FF000EBE868FDF4 /* A01 = +1.000224979259539459520e+00 */
-	.quad	0xBF67CA9427E0A544 /* A02 = -2.904214255086275467410e-03 */
-	.quad	0xBFD46EC6812ADB37 /* A03 = -3.192611943626845749655e-01 */
-	.quad	0xBEDF3EAC5BF12194 /* A00 = -7.449344990702664567927e-06 */
-	.quad	0x3FF001112A520784 /* A01 = +1.000260510744255704196e+00 */
-	.quad	0xBF6A8D01ABDA4DC4 /* A02 = -3.241065277345108255891e-03 */
-	.quad	0xBFD45D55759FFA4A /* A03 = -3.181966446572103146551e-01 */
-	.quad	0xBEE2A541BC274267 /* A00 = -8.890883582164319970972e-06 */
-	.quad	0x3FF0013A9E5961F2 /* A01 = +1.000300043631906721231e+00 */
-	.quad	0xBF6D82ECD080C540 /* A02 = -3.602468994380686462264e-03 */
-	.quad	0xBFD44B4A0779C0AD /* A03 = -3.170952866557950611259e-01 */
-	.quad	0xBEE61D97609A27F4 /* A00 = -1.054553560499505625520e-05 */
-	.quad	0x3FF001688F56A3AF /* A01 = +1.000343856731187974773e+00 */
-	.quad	0xBF7056F8EFB683EC /* A02 = -3.989193351487490407647e-03 */
-	.quad	0xBFD438A5620F0F74 /* A03 = -3.159573991399533543500e-01 */
-	.quad	0xBEEA145429EDD370 /* A00 = -1.243563138839952927732e-05 */
-	.quad	0x3FF0019B4A242A67 /* A01 = +1.000392236341804297339e+00 */
-	.quad	0xBF7207D31CA78D9B /* A02 = -4.401993423445739288258e-03 */
-	.quad	0xBFD42568BA16E7CD /* A03 = -3.147832696228050619602e-01 */
-	.quad	0xBEEE96370D52680F /* A00 = -1.458491207477835326165e-05 */
-	.quad	0x3FF001D31D8E4115 /* A01 = +1.000445476009251821736e+00 */
-	.quad	0xBF73D4CC11EDC094 /* A02 = -4.841611050196221316400e-03 */
-	.quad	0xBFD411954D8664E7 /* A03 = -3.135731942252974469021e-01 */
-	.quad	0xBEF338C046215EF8 /* A00 = -1.833122622260562810219e-05 */
-	.quad	0x3FF00230C32C2EC1 /* A01 = +1.000534784691737621998e+00 */
-	.quad	0xBF76BD019BCC5DAF /* A02 = -5.551344188254799492943e-03 */
-	.quad	0xBFD3F2C7156DC21E /* A03 = -3.116929730668135389848e-01 */
-	.quad	0xBEF9B15EAE411EAE /* A00 = -2.450261207822986676092e-05 */
-	.quad	0x3FF002C2DF057A4D /* A01 = +1.000674124886830940184e+00 */
-	.quad	0xBF7B08CCD9AC1E30 /* A02 = -6.600189396301511801646e-03 */
-	.quad	0xBFD3C7A7A114FED8 /* A03 = -3.090609620157755976777e-01 */
-	.quad	0xBF00E36483C373B3 /* A00 = -3.221178528332122595812e-05 */
-	.quad	0x3FF0036F419480D7 /* A01 = +1.000838524028997644777e+00 */
-	.quad	0xBF7FD255D1777007 /* A02 = -7.768950679260206403087e-03 */
-	.quad	0xBFD39A453911D6CE /* A03 = -3.062909180947429588215e-01 */
-	.quad	0xBF05DFA04DD12059 /* A00 = -4.172046622180685472624e-05 */
-	.quad	0x3FF00438B2A03D8D /* A01 = +1.001030633695197069599e+00 */
-	.quad	0xBF828F8DBB4A9D10 /* A02 = -9.062869337255224921890e-03 */
-	.quad	0xBFD36AAB704697D9 /* A03 = -3.033856007044711255993e-01 */
-	.quad	0xBF0BF3E0C647DEFB /* A00 = -5.331544597092331081714e-05 */
-	.quad	0x3FF005221063D36D /* A01 = +1.001253189109060359741e+00 */
-	.quad	0xBF857A2CB3C96102 /* A02 = -1.048693584122917590862e-02 */
-	.quad	0xBFD338E65BBB4FEC /* A03 = -3.003478904549854444639e-01 */
-	.quad	0xBF11A506ED7C9D31 /* A00 = -6.730894835681591541979e-05 */
-	.quad	0x3FF0062E4D0EA92A /* A01 = +1.001508999829250345925e+00 */
-	.quad	0xBF88AB82C2761AF3 /* A02 = -1.204588085125866091241e-02 */
-	.quad	0xBFD305028D6BD206 /* A03 = -2.971807843271395688234e-01 */
-	.quad	0xBF1607C0922D9BF1 /* A00 = -8.403885708006799337092e-05 */
-	.quad	0x3FF007606C341961 /* A01 = +1.001800940198869449560e+00 */
-	.quad	0xBF8C25E6DA487BCF /* A02 = -1.374416688582682892494e-02 */
-	.quad	0xBFD2CF0D0EE8F7B5 /* A03 = -2.938873906713255768075e-01 */
-	.quad	0xBF1B3A8480A0A16D /* A00 = -1.038688061788578038307e-04 */
-	.quad	0x3FF008BB802D02D6 /* A01 = +1.002131939589323561535e+00 */
-	.quad	0xBF8FEB8AE99FD100 /* A02 = -1.558598065819483124983e-02 */
-	.quad	0xBFD297135BD0911B /* A03 = -2.904709240558688843059e-01 */
-	.quad	0xBF20ABB9BDB75C65 /* A00 = -1.271881327357976163798e-04 */
-	.quad	0x3FF00A42A76D8CD1 /* A01 = +1.002504972472525901495e+00 */
-	.quad	0xBF91FF3D752BB9E6 /* A02 = -1.757522609380570560722e-02 */
-	.quad	0xBFD25D235C1F88B4 /* A03 = -2.869346999779154305799e-01 */
-	.quad	0xBF243D3254425461 /* A00 = -1.544116913733432829448e-04 */
-	.quad	0x3FF00BF909D1795E /* A01 = +1.002923048355647051011e+00 */
-	.quad	0xBF94304E04D44942 /* A02 = -1.971551804042204897316e-02 */
-	.quad	0xBFD2214B5E61CFA6 /* A03 = -2.832821294498394371075e-01 */
-	.quad	0xBF286070011B61CE /* A00 = -1.859795307186510085994e-04 */
-	.quad	0x3FF00DE1D5E1627E /* A01 = +1.003389201612804537689e+00 */
-	.quad	0xBF9689D5F4163F59 /* A02 = -2.201017668045266231780e-02 */
-	.quad	0xBFD1E39A11C3B42C /* A03 = -2.795167134743816728104e-01 */
-	.quad	0xBF2D250B366A79E8 /* A00 = -2.223564326486314902259e-04 */
-	.quad	0x3FF010003E134001 /* A01 = +1.003906481248123094829e+00 */
-	.quad	0xBF990C9FF91F6F81 /* A02 = -2.446222265267250853271e-02 */
-	.quad	0xBFD1A41E80084CDC /* A03 = -2.756420374218586655246e-01 */
-	.quad	0xBF314DB5DDC2A30E /* A00 = -2.640313157465248123865e-04 */
-	.quad	0x3FF012577608921B /* A01 = +1.004477940624503018441e+00 */
-	.quad	0xBF9BB9626875B0C9 /* A02 = -2.707437288829409385849e-02 */
-	.quad	0xBFD162E80768A9D0 /* A03 = -2.716617653228725615122e-01 */
-	.quad	0xBF346A6133808864 /* A00 = -3.115165050094957730625e-04 */
-	.quad	0x3FF014EAAFCC88A3 /* A01 = +1.005106627192198898157e+00 */
-	.quad	0xBF9E90BEF9BF7419 /* A02 = -2.984903716411588595059e-02 */
-	.quad	0xBFD12006545F7FAD /* A03 = -2.675796340899932457269e-01 */
-	.quad	0xBF37F180DC3848EA /* A00 = -3.653468704395550778821e-04 */
-	.quad	0x3FF017BD19147861 /* A01 = +1.005795572250939295955e+00 */
-	.quad	0xBFA0C9A14C702E07 /* A02 = -3.278831537326359207851e-02 */
-	.quad	0xBFD0DB895B650092 /* A03 = -2.633994476818851682154e-01 */
-	.quad	0xBF3BEC6AAC6D7635 /* A00 = -4.260788377246944457107e-04 */
-	.quad	0x3FF01AD1D884E719 /* A01 = +1.006547780778822565040e+00 */
-	.quad	0xBFA260B2A1B1434A /* A02 = -3.589399551186163439542e-02 */
-	.quad	0xBFD09581529E93D6 /* A03 = -2.591250712233067465817e-01 */
-	.quad	0xBF4164E26167882B /* A00 = -5.308251737086202562063e-04 */
-	.quad	0x3FF01FEF14B62B81 /* A01 = +1.007796364693348545316e+00 */
-	.quad	0xBFA4EB014538AA42 /* A02 = -4.085544557559163403315e-02 */
-	.quad	0xBFD029D36FEAF41F /* A03 = -2.525528519580024222613e-01 */
-	.quad	0xBF46F6FFF4E53DC8 /* A00 = -7.008313930700277652464e-04 */
-	.quad	0x3FF027CBB51CBBA0 /* A01 = +1.009715754956893363214e+00 */
-	.quad	0xBFA89DEC9FEC112E /* A02 = -4.807986690687680864098e-02 */
-	.quad	0xBFCF2A99464D0DB4 /* A03 = -2.434875100390009317053e-01 */
-	.quad	0xBF4DCC9C4F66A4D9 /* A00 = -9.094012482836712945103e-04 */
-	.quad	0x3FF030E7CFCCD583 /* A01 = +1.011939822882909068014e+00 */
-	.quad	0xBFACAA3B95814081 /* A02 = -5.598627281199331645611e-02 */
-	.quad	0xBFCDF78F15