path: root/libm/x86_64/s_tan.S

/*
Copyright (c) 2014, Intel Corporation
All rights reserved.

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

    * Redistributions of source code must retain the above copyright notice,
    * this list of conditions and the following disclaimer.

    * Redistributions in binary form must reproduce the above copyright notice,
    * this list of conditions and the following disclaimer in the documentation
    * and/or other materials provided with the distribution.

    * Neither the name of Intel Corporation nor the names of its contributors
    * may be used to endorse or promote products derived from this software
    * without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/

/******************************************************************************/
//                     ALGORITHM DESCRIPTION
//                     ---------------------
//
// Polynomials coefficients and other constants.
//
// Note that in this algorithm, there is a different polynomial for
// each breakpoint, so there are 32 sets of polynomial coefficients
// as well as 32 instances of the other constants.
//
// The polynomial coefficients and constants are offset from the start
// of the main block as follows:
//
//   0:  c8 | c0
//  16:  c9 | c1
//  32: c10 | c2
//  48: c11 | c3
//  64: c12 | c4
//  80: c13 | c5
//  96: c14 | c6
// 112: c15 | c7
// 128: T_hi
// 136: T_lo
// 144: Sigma
// 152: T_hl
// 160: Tau
// 168: Mask
// 176: (end of block)
//
// The total table size is therefore 5632 bytes.
//
// Note that c0 and c1 are always zero. We could try storing
// other constants here, and just loading the low part of the
// SIMD register in these cases, after ensuring the high part
// is zero.
//
// The higher terms of the polynomial are computed in the *low*
// part of the SIMD register. This is so we can overlap the
// multiplication by r^8 and the unpacking of the other part.
//
// The constants are:
// T_hi + T_lo = accurate constant term in power series
// Sigma + T_hl = accurate coefficient of r in power series (Sigma=1 bit)
// Tau = multiplier for the reciprocal, always -1 or 0
//
// The basic reconstruction formula using these constants is:
//
// High = tau * recip_hi + t_hi
// Med = (sgn * r + t_hl * r)_hi
// Low = (sgn * r + t_hl * r)_lo +
//       tau * recip_lo + T_lo + (T_hl + sigma) * c + pol
//
// where pol = c0 + c1 * r + c2 * r^2 + ... + c15 * r^15
//
// (c0 = c1 = 0, but using them keeps SIMD regularity)
//
// We then do a compensated sum High + Med, add the low parts together
// and then do the final sum.
//
// Here recip_hi + recip_lo is an accurate reciprocal of the remainder
// modulo pi/2
//
// Special cases:
//  tan(NaN) = quiet NaN, and raise invalid exception
//  tan(INF) = NaN and raise invalid exception
//  tan(+/-0) = +/-0
//
/******************************************************************************/

#include <private/bionic_asm.h>
# -- Begin  tan
ENTRY(tan)
# parameter 1: %xmm0
..B1.1:
..___tag_value_tan.1:
        pushq     %rbx
..___tag_value_tan.3:
        subq      $16, %rsp
..___tag_value_tan.5:
        movsd     %xmm0, 8(%rsp)
..B1.2:
        pextrw    $3, %xmm0, %eax
        andl      $32767, %eax
        subl      $16314, %eax
        cmpl      $270, %eax
        ja        .L_2TAG_PACKET_0.0.1
        movapd    ONEHALF(%rip), %xmm5
        movapd    MUL16(%rip), %xmm6
        unpcklpd  %xmm0, %xmm0
        movapd    sign_mask(%rip), %xmm4
        andpd     %xmm0, %xmm4
        movapd    PI32INV(%rip), %xmm1
        mulpd     %xmm0, %xmm1
        orps      %xmm4, %xmm5
        addpd     %xmm5, %xmm1
        movapd    %xmm1, %xmm7
        unpckhpd  %xmm7, %xmm7
        cvttsd2si %xmm7, %edx
        cvttpd2dq %xmm1, %xmm1
        cvtdq2pd  %xmm1, %xmm1
        mulpd     %xmm6, %xmm1
        movapd    P_1(%rip), %xmm3
        movq      QQ_2(%rip), %xmm5
        addq      $469248, %rdx
        movapd    P_2(%rip), %xmm4
        mulpd     %xmm1, %xmm3
        andq      $31, %rdx
        mulsd     %xmm1, %xmm5
        movq      %rdx, %rcx
        mulpd     %xmm1, %xmm4
        shlq      $1, %rcx
        subpd     %xmm3, %xmm0
        mulpd     P_3(%rip), %xmm1
        addq      %rcx, %rdx
        shlq      $2, %rcx
        addq      %rcx, %rdx
        addsd     %xmm0, %xmm5
        movapd    %xmm0, %xmm2
        subpd     %xmm4, %xmm0
        movq      ONE(%rip), %xmm6
        shlq      $4, %rdx
        lea       Ctable(%rip), %rax
        andpd     MASK_35(%rip), %xmm5
        movapd    %xmm0, %xmm3
        addq      %rdx, %rax
        subpd     %xmm0, %xmm2
        unpckhpd  %xmm0, %xmm0
        divsd     %xmm5, %xmm6
        subpd     %xmm4, %xmm2
        movapd    16(%rax), %xmm7
        subsd     %xmm5, %xmm3
        mulpd     %xmm0, %xmm7
        subpd     %xmm1, %xmm2
        movapd    48(%rax), %xmm1
        mulpd     %xmm0, %xmm1
        movapd    96(%rax), %xmm4
        mulpd     %xmm0, %xmm4
        addsd     %xmm3, %xmm2
        movapd    %xmm0, %xmm3
        mulpd     %xmm0, %xmm0
        addpd     (%rax), %xmm7
        addpd     32(%rax), %xmm1
        mulpd     %xmm0, %xmm1
        addpd     80(%rax), %xmm4
        addpd     %xmm1, %xmm7
        movapd    112(%rax), %xmm1
        mulpd     %xmm0, %xmm1
        mulpd     %xmm0, %xmm0
        addpd     %xmm1, %xmm4
        movapd    64(%rax), %xmm1
        mulpd     %xmm0, %xmm1
        addpd     %xmm1, %xmm7
        movapd    %xmm3, %xmm1
        mulpd     %xmm0, %xmm3
        mulsd     %xmm0, %xmm0
        mulpd     144(%rax), %xmm1
        mulpd     %xmm3, %xmm4
        movq      %xmm1, %xmm3
        addpd     %xmm4, %xmm7
        movq      %xmm1, %xmm4
        mulsd     %xmm7, %xmm0
        unpckhpd  %xmm7, %xmm7
        addsd     %xmm7, %xmm0
        unpckhpd  %xmm1, %xmm1
        addsd     %xmm1, %xmm3
        subsd     %xmm3, %xmm4
        addsd     %xmm4, %xmm1
        movq      %xmm2, %xmm4
        movq      144(%rax), %xmm7
        unpckhpd  %xmm2, %xmm2
        addsd     152(%rax), %xmm7
        mulsd     %xmm2, %xmm7
        addsd     136(%rax), %xmm7
        addsd     %xmm1, %xmm7
        addsd     %xmm7, %xmm0
        movq      ONE(%rip), %xmm7
        mulsd     %xmm6, %xmm4
        movq      168(%rax), %xmm2
        andpd     %xmm6, %xmm2
        mulsd     %xmm2, %xmm5
        mulsd     160(%rax), %xmm6
        subsd     %xmm5, %xmm7
        subsd     128(%rax), %xmm2
        subsd     %xmm4, %xmm7
        mulsd     %xmm6, %xmm7
        movq      %xmm3, %xmm4
        subsd     %xmm2, %xmm3
        addsd     %xmm3, %xmm2
        subsd     %xmm2, %xmm4
        addsd     %xmm4, %xmm0
        subsd     %xmm7, %xmm0
        addsd     %xmm3, %xmm0
        jmp       ..B1.4
.L_2TAG_PACKET_0.0.1:
        jg        .L_2TAG_PACKET_1.0.1
        pextrw    $3, %xmm0, %eax
        movl      %eax, %edx
        andl      $32752, %eax
        je        .L_2TAG_PACKET_2.0.1
        andl      $32767, %edx
        cmpl      $15904, %edx
        jb        .L_2TAG_PACKET_3.0.1
        movq      %xmm0, %xmm2
        movq      %xmm0, %xmm3
        movq      Q_11(%rip), %xmm1
        mulsd     %xmm0, %xmm2
        mulsd     %xmm2, %xmm3
        mulsd     %xmm2, %xmm1
        addsd     Q_9(%rip), %xmm1
        mulsd     %xmm2, %xmm1
        addsd     Q_7(%rip), %xmm1
        mulsd     %xmm2, %xmm1
        addsd     Q_5(%rip), %xmm1
        mulsd     %xmm2, %xmm1
        addsd     Q_3(%rip), %xmm1
        mulsd     %xmm3, %xmm1
        addsd     %xmm1, %xmm0
        jmp       ..B1.4
.L_2TAG_PACKET_3.0.1:
        movq      TWO_POW_55(%rip), %xmm3
        mulsd     %xmm0, %xmm3
        addsd     %xmm3, %xmm0
        mulsd     TWO_POW_M55(%rip), %xmm0
        jmp       ..B1.4
.L_2TAG_PACKET_2.0.1:
        movq      %xmm0, %xmm1
        mulsd     %xmm1, %xmm1
        jmp       ..B1.4
.L_2TAG_PACKET_1.0.1:
        pextrw    $3, %xmm0, %eax
        andl      $32752, %eax
        cmpl      $32752, %eax
        je        .L_2TAG_PACKET_4.0.1
        pextrw    $3, %xmm0, %ecx
        andl      $32752, %ecx
        subl      $16224, %ecx
        shrl      $7, %ecx
        andl      $65532, %ecx
        lea       PI_INV_TABLE(%rip), %r11
        addq      %r11, %rcx
        movd      %xmm0, %rax
        movl      20(%rcx), %r10d
        movl      24(%rcx), %r8d
        movl      %eax, %edx
        shrq      $21, %rax
        orl       $-2147483648, %eax
        shrl      $11, %eax
        movl      %r10d, %r9d
        imulq     %rdx, %r10
        imulq     %rax, %r9
        imulq     %rax, %r8
        movl      16(%rcx), %esi
        movl      12(%rcx), %edi
        movl      %r10d, %r11d
        shrq      $32, %r10
        addq      %r10, %r9
        addq      %r8, %r11
        movl      %r11d, %r8d
        shrq      $32, %r11
        addq      %r11, %r9
        movl      %esi, %r10d
        imulq     %rdx, %rsi
        imulq     %rax, %r10
        movl      %edi, %r11d
        imulq     %rdx, %rdi
        movl      %esi, %ebx
        shrq      $32, %rsi
        addq      %rbx, %r9
        movl      %r9d, %ebx
        shrq      $32, %r9
        addq      %rsi, %r10
        addq      %r9, %r10
        shlq      $32, %rbx
        orq       %rbx, %r8
        imulq     %rax, %r11
        movl      8(%rcx), %r9d
        movl      4(%rcx), %esi
        movl      %edi, %ebx
        shrq      $32, %rdi
        addq      %rbx, %r10
        movl      %r10d, %ebx
        shrq      $32, %r10
        addq      %rdi, %r11
        addq      %r10, %r11
        movq      %r9, %rdi
        imulq     %rdx, %r9
        imulq     %rax, %rdi
        movl      %r9d, %r10d
        shrq      $32, %r9
        addq      %r10, %r11
        movl      %r11d, %r10d
        shrq      $32, %r11
        addq      %r9, %rdi
        addq      %r11, %rdi
        movq      %rsi, %r9
        imulq     %rdx, %rsi
        imulq     %rax, %r9
        shlq      $32, %r10
        orq       %rbx, %r10
        movl      (%rcx), %eax
        movl      %esi, %r11d
        shrq      $32, %rsi
        addq      %r11, %rdi
        movl      %edi, %r11d
        shrq      $32, %rdi
        addq      %rsi, %r9
        addq      %rdi, %r9
        imulq     %rax, %rdx
        pextrw    $3, %xmm0, %ebx
        lea       PI_INV_TABLE(%rip), %rdi
        subq      %rdi, %rcx
        addl      %ecx, %ecx
        addl      %ecx, %ecx
        addl      %ecx, %ecx
        addl      $19, %ecx
        movl      $32768, %esi
        andl      %ebx, %esi
        shrl      $4, %ebx
        andl      $2047, %ebx
        subl      $1023, %ebx
        subl      %ebx, %ecx
        addq      %rdx, %r9
        movl      %ecx, %edx
        addl      $32, %edx
        cmpl      $0, %ecx
        jl        .L_2TAG_PACKET_5.0.1
        negl      %ecx
        addl      $29, %ecx
        shll      %cl, %r9d
        movl      %r9d, %edi
        andl      $1073741823, %r9d
        testl     $536870912, %r9d
        jne       .L_2TAG_PACKET_6.0.1
        shrl      %cl, %r9d
        movl      $0, %ebx
        shlq      $32, %r9
        orq       %r11, %r9
.L_2TAG_PACKET_7.0.1:
.L_2TAG_PACKET_8.0.1:
        cmpq      $0, %r9
        je        .L_2TAG_PACKET_9.0.1
.L_2TAG_PACKET_10.0.1:
        bsr       %r9, %r11
        movl      $29, %ecx
        subl      %r11d, %ecx
        jle       .L_2TAG_PACKET_11.0.1
        shlq      %cl, %r9
        movq      %r10, %rax
        shlq      %cl, %r10
        addl      %ecx, %edx
        negl      %ecx
        addl      $64, %ecx
        shrq      %cl, %rax
        shrq      %cl, %r8
        orq       %rax, %r9
        orq       %r8, %r10
.L_2TAG_PACKET_12.0.1:
        cvtsi2sdq %r9, %xmm0
        shrq      $1, %r10
        cvtsi2sdq %r10, %xmm3
        xorpd     %xmm4, %xmm4
        shll      $4, %edx
        negl      %edx
        addl      $16368, %edx
        orl       %esi, %edx
        xorl      %ebx, %edx
        pinsrw    $3, %edx, %xmm4
        movq      PI_4(%rip), %xmm2
        movq      8+PI_4(%rip), %xmm7
        xorpd     %xmm5, %xmm5
        subl      $1008, %edx
        pinsrw    $3, %edx, %xmm5
        mulsd     %xmm4, %xmm0
        shll      $16, %esi
        sarl      $31, %esi
        mulsd     %xmm5, %xmm3
        movq      %xmm0, %xmm1
        mulsd     %xmm2, %xmm0
        shrl      $30, %edi
        addsd     %xmm3, %xmm1
        mulsd     %xmm2, %xmm3
        addl      %esi, %edi
        xorl      %esi, %edi
        mulsd     %xmm1, %xmm7
        movl      %edi, %eax
        addsd     %xmm3, %xmm7
        movq      %xmm0, %xmm2
        addsd     %xmm7, %xmm0
        subsd     %xmm0, %xmm2
        addsd     %xmm2, %xmm7
        movapd    PI32INV(%rip), %xmm1
        movddup   %xmm0, %xmm0
        movapd    sign_mask(%rip), %xmm4
        andpd     %xmm0, %xmm4
        mulpd     %xmm0, %xmm1
        movddup   %xmm7, %xmm7
        movapd    ONEHALF(%rip), %xmm5
        movapd    MUL16(%rip), %xmm6
        orps      %xmm4, %xmm5
        addpd     %xmm5, %xmm1
        movapd    %xmm1, %xmm5
        unpckhpd  %xmm5, %xmm5
        cvttsd2si %xmm5, %edx
        cvttpd2dq %xmm1, %xmm1
        cvtdq2pd  %xmm1, %xmm1
        mulpd     %xmm6, %xmm1
        movapd    P_1(%rip), %xmm3
        movq      QQ_2(%rip), %xmm5
        shll      $4, %eax
        addl      $469248, %edx
        movapd    P_2(%rip), %xmm4
        mulpd     %xmm1, %xmm3
        addl      %eax, %edx
        andl      $31, %edx
        mulsd     %xmm1, %xmm5
        movl      %edx, %ecx
        mulpd     %xmm1, %xmm4
        shll      $1, %ecx
        subpd     %xmm3, %xmm0
        mulpd     P_3(%rip), %xmm1
        addl      %ecx, %edx
        shll      $2, %ecx
        addl      %ecx, %edx
        addsd     %xmm0, %xmm5
        movapd    %xmm0, %xmm2
        subpd     %xmm4, %xmm0
        movq      ONE(%rip), %xmm6
        shll      $4, %edx
        lea       Ctable(%rip), %rax
        andpd     MASK_35(%rip), %xmm5
        movapd    %xmm0, %xmm3
        addq      %rdx, %rax
        subpd     %xmm0, %xmm2
        unpckhpd  %xmm0, %xmm0
        divsd     %xmm5, %xmm6
        subpd     %xmm4, %xmm2
        subsd     %xmm5, %xmm3
        subpd     %xmm1, %xmm2
        movapd    48(%rax), %xmm1
        addpd     %xmm7, %xmm2
        movapd    16(%rax), %xmm7
        mulpd     %xmm0, %xmm7
        movapd    96(%rax), %xmm4
        mulpd     %xmm0, %xmm1
        mulpd     %xmm0, %xmm4
        addsd     %xmm3, %xmm2
        movapd    %xmm0, %xmm3
        mulpd     %xmm0, %xmm0
        addpd     (%rax), %xmm7
        addpd     32(%rax), %xmm1
        mulpd     %xmm0, %xmm1
        addpd     80(%rax), %xmm4
        addpd     %xmm1, %xmm7
        movapd    112(%rax), %xmm1
        mulpd     %xmm0, %xmm1
        mulpd     %xmm0, %xmm0
        addpd     %xmm1, %xmm4
        movapd    64(%rax), %xmm1
        mulpd     %xmm0, %xmm1
        addpd     %xmm1, %xmm7
        movapd    %xmm3, %xmm1
        mulpd     %xmm0, %xmm3
        mulsd     %xmm0, %xmm0
        mulpd     144(%rax), %xmm1
        mulpd     %xmm3, %xmm4
        movq      %xmm1, %xmm3
        addpd     %xmm4, %xmm7
        movq      %xmm1, %xmm4
        mulsd     %xmm7, %xmm0
        unpckhpd  %xmm7, %xmm7
        addsd     %xmm7, %xmm0
        unpckhpd  %xmm1, %xmm1
        addsd     %xmm1, %xmm3
        subsd     %xmm3, %xmm4
        addsd     %xmm4, %xmm1
        movq      %xmm2, %xmm4
        movq      144(%rax), %xmm7
        unpckhpd  %xmm2, %xmm2
        addsd     152(%rax), %xmm7
        mulsd     %xmm2, %xmm7
        addsd     136(%rax), %xmm7
        addsd     %xmm1, %xmm7
        addsd     %xmm7, %xmm0
        movq      ONE(%rip), %xmm7
        mulsd     %xmm6, %xmm4
        movq      168(%rax), %xmm2
        andpd     %xmm6, %xmm2
        mulsd     %xmm2, %xmm5
        mulsd     160(%rax), %xmm6
        subsd     %xmm5, %xmm7
        subsd     128(%rax), %xmm2
        subsd     %xmm4, %xmm7
        mulsd     %xmm6, %xmm7
        movq      %xmm3, %xmm4
        subsd     %xmm2, %xmm3
        addsd     %xmm3, %xmm2
        subsd     %xmm2, %xmm4
        addsd     %xmm4, %xmm0
        subsd     %xmm7, %xmm0
        addsd     %xmm3, %xmm0
        jmp       ..B1.4
.L_2TAG_PACKET_9.0.1:
        addl      $64, %edx
        movq      %r10, %r9
        movq      %r8, %r10
        movq      $0, %r8
        cmpq      $0, %r9
        jne       .L_2TAG_PACKET_10.0.1
        addl      $64, %edx
        movq      %r10, %r9
        movq      %r8, %r10
        cmpq      $0, %r9
        jne       .L_2TAG_PACKET_10.0.1
        jmp       .L_2TAG_PACKET_12.0.1
.L_2TAG_PACKET_11.0.1:
        je        .L_2TAG_PACKET_12.0.1
        negl      %ecx
        shrq      %cl, %r10
        movq      %r9, %rax
        shrq      %cl, %r9
        subl      %ecx, %edx
        negl      %ecx
        addl      $64, %ecx
        shlq      %cl, %rax
        orq       %rax, %r10
        jmp       .L_2TAG_PACKET_12.0.1
.L_2TAG_PACKET_5.0.1:
        notl      %ecx
        shlq      $32, %r9
        orq       %r11, %r9
        shlq      %cl, %r9
        movq      %r9, %rdi
        testl     $-2147483648, %r9d
        jne       .L_2TAG_PACKET_13.0.1
        shrl      %cl, %r9d
        movl      $0, %ebx
        shrq      $2, %rdi
        jmp       .L_2TAG_PACKET_8.0.1
.L_2TAG_PACKET_6.0.1:
        shrl      %cl, %r9d
        movl      $1073741824, %ebx
        shrl      %cl, %ebx
        shlq      $32, %r9
        orq       %r11, %r9
        shlq      $32, %rbx
        addl      $1073741824, %edi
        movq      $0, %rcx
        movq      $0, %r11
        subq      %r8, %rcx
        sbbq      %r10, %r11
        sbbq      %r9, %rbx
        movq      %rcx, %r8
        movq      %r11, %r10
        movq      %rbx, %r9
        movl      $32768, %ebx
        jmp       .L_2TAG_PACKET_7.0.1
.L_2TAG_PACKET_13.0.1:
        shrl      %cl, %r9d
        movq      $0x100000000, %rbx
        shrq      %cl, %rbx
        movq      $0, %rcx
        movq      $0, %r11
        subq      %r8, %rcx
        sbbq      %r10, %r11
        sbbq      %r9, %rbx
        movq      %rcx, %r8
        movq      %r11, %r10
        movq      %rbx, %r9
        movl      $32768, %ebx
        shrq      $2, %rdi
        addl      $1073741824, %edi
        jmp       .L_2TAG_PACKET_8.0.1
.L_2TAG_PACKET_4.0.1:
        movq      8(%rsp), %xmm0
        mulsd     NEG_ZERO(%rip), %xmm0
        movq      %xmm0, (%rsp)
.L_2TAG_PACKET_14.0.1:
..B1.4:
        addq      $16, %rsp
..___tag_value_tan.6:
        popq      %rbx
..___tag_value_tan.8:
        ret       
..___tag_value_tan.9:
END(tan)
# -- End  tan
	.section .rodata, "a"
	.align 16
	.align 16
ONEHALF:
	.long	0
	.long	1071644672
	.long	0
	.long	1071644672
	.type	ONEHALF,@object
	.size	ONEHALF,16
	.align 16
MUL16:
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	.align 16
sign_mask:
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	.align 16
PI32INV:
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	.align 16
P_1:
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	.align 16
P_2:
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	.align 16
P_3:
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	.align 16
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	.type	Ctable,@object
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	.align 16
MASK_35:
	.long	4294705152
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	.type	MASK_35,@object
	.size	MASK_35,16
	.align 16
Q_11:
	.long	3103673719
	.long	1065509018
	.type	Q_11,@object
	.size	Q_11,8
	.space 8, 0x00 	# pad
	.align 16
Q_9:
	.long	3213130307
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	.type	Q_9,@object
	.size	Q_9,8
	.space 8, 0x00 	# pad
	.align 16
Q_7:
	.long	1388628139
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	.type	Q_7,@object
	.size	Q_7,8
	.space 8, 0x00 	# pad
	.align 16
Q_5:
	.long	285812550
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	.type	Q_5,@object
	.size	Q_5,8
	.space 8, 0x00 	# pad
	.align 16
Q_3:
	.long	1431655954
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	.type	Q_3,@object
	.size	Q_3,8
	.space 8, 0x00 	# pad
	.align 16
PI_INV_TABLE:
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	.align 16
PI_4:
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	.type	PI_4,@object
	.size	PI_4,16
	.align 8
QQ_2:
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	.type	QQ_2,@object
	.size	QQ_2,8
	.align 8
ONE:
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	.type	ONE,@object
	.size	ONE,8
	.align 8
TWO_POW_55:
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	.size	TWO_POW_55,8
	.align 8
TWO_POW_M55:
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	.type	TWO_POW_M55,@object
	.size	TWO_POW_M55,8
	.align 4
NEG_ZERO:
	.long	0
	.long	2147483648
	.type	NEG_ZERO,@object
	.size	NEG_ZERO,8
	.data
	.section .note.GNU-stack, ""
// -- Begin DWARF2 SEGMENT .eh_frame
	.section .eh_frame,"a",@progbits
.eh_frame_seg:
	.align 1
	.4byte 0x00000014
	.8byte 0x00527a0100000000
	.8byte 0x08070c1b01107801
	.4byte 0x00000190
	.4byte 0x0000002c
	.4byte 0x0000001c
	.4byte ..___tag_value_tan.1-.
	.4byte ..___tag_value_tan.9-..___tag_value_tan.1
	.2byte 0x0400
	.4byte ..___tag_value_tan.3-..___tag_value_tan.1
	.4byte 0x0283100e
	.byte 0x04
	.4byte ..___tag_value_tan.5-..___tag_value_tan.3
	.2byte 0x200e
	.byte 0x04
	.4byte ..___tag_value_tan.6-..___tag_value_tan.5
	.4byte 0x04c3100e
	.4byte ..___tag_value_tan.8-..___tag_value_tan.6
	.2byte 0x080e
# End