path: root/libm/x86_64/s_cos.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
//                     ---------------------
//
//     1. RANGE REDUCTION
//
//     We perform an initial range reduction from X to r with
//
//          X =~= N * pi/32 + r
//
//     so that |r| <= pi/64 + epsilon. We restrict inputs to those
//     where |N| <= 932560. Beyond this, the range reduction is
//     insufficiently accurate. For extremely small inputs, 
//     denormalization can occur internally, impacting performance.
//     This means that the main path is actually only taken for
//     2^-252 <= |X| < 90112.
//
//     To avoid branches, we perform the range reduction to full
//     accuracy each time.
//
//          X - N * (P_1 + P_2 + P_3)
//
//     where P_1 and P_2 are 32-bit numbers (so multiplication by N
//     is exact) and P_3 is a 53-bit number. Together, these
//     approximate pi well enough for all cases in the restricted
//     range.
//
//     The main reduction sequence is:
//
//             y = 32/pi * x
//             N = integer(y)
//     (computed by adding and subtracting off SHIFTER)
//
//             m_1 = N * P_1
//             m_2 = N * P_2
//             r_1 = x - m_1
//             r = r_1 - m_2
//     (this r can be used for most of the calculation)
//
//             c_1 = r_1 - r
//             m_3 = N * P_3
//             c_2 = c_1 - m_2
//             c = c_2 - m_3
//
//     2. MAIN ALGORITHM
//
//     The algorithm uses a table lookup based on B = M * pi / 32
//     where M = N mod 64. The stored values are:
//       sigma             closest power of 2 to cos(B)
//       C_hl              53-bit cos(B) - sigma
//       S_hi + S_lo       2 * 53-bit sin(B)
//
//     The computation is organized as follows:
//
//          sin(B + r + c) = [sin(B) + sigma * r] +
//                           r * (cos(B) - sigma) +
//                           sin(B) * [cos(r + c) - 1] +
//                           cos(B) * [sin(r + c) - r]
//
//     which is approximately:
//
//          [S_hi + sigma * r] +
//          C_hl * r +
//          S_lo + S_hi * [(cos(r) - 1) - r * c] +
//          (C_hl + sigma) * [(sin(r) - r) + c]
//
//     and this is what is actually computed. We separate this sum
//     into four parts:
//
//          hi + med + pols + corr
//
//     where
//
//          hi       = S_hi + sigma r
//          med      = C_hl * r
//          pols     = S_hi * (cos(r) - 1) + (C_hl + sigma) * (sin(r) - r)
//          corr     = S_lo + c * ((C_hl + sigma) - S_hi * r)
//
//     3. POLYNOMIAL
//
//     The polynomial S_hi * (cos(r) - 1) + (C_hl + sigma) *
//     (sin(r) - r) can be rearranged freely, since it is quite
//     small, so we exploit parallelism to the fullest.
//
//          psc4       =   SC_4 * r_1
//          msc4       =   psc4 * r
//          r2         =   r * r
//          msc2       =   SC_2 * r2
//          r4         =   r2 * r2
//          psc3       =   SC_3 + msc4
//          psc1       =   SC_1 + msc2
//          msc3       =   r4 * psc3
//          sincospols =   psc1 + msc3
//          pols       =   sincospols *
//                         <S_hi * r^2 | (C_hl + sigma) * r^3>
//
//     4. CORRECTION TERM
//
//     This is where the "c" component of the range reduction is
//     taken into account; recall that just "r" is used for most of
//     the calculation.
//
//          -c   = m_3 - c_2
//          -d   = S_hi * r - (C_hl + sigma)
//          corr = -c * -d + S_lo
//
//     5. COMPENSATED SUMMATIONS
//
//     The two successive compensated summations add up the high
//     and medium parts, leaving just the low parts to add up at
//     the end.
//
//          rs        =  sigma * r
//          res_int   =  S_hi + rs
//          k_0       =  S_hi - res_int
//          k_2       =  k_0 + rs
//          med       =  C_hl * r
//          res_hi    =  res_int + med
//          k_1       =  res_int - res_hi
//          k_3       =  k_1 + med
//
//     6. FINAL SUMMATION
//
//     We now add up all the small parts:
//
//          res_lo = pols(hi) + pols(lo) + corr + k_1 + k_3
//
//     Now the overall result is just:
//
//          res_hi + res_lo
//
//     7. SMALL ARGUMENTS
//
//     Inputs with |X| < 2^-252 are treated specially as
//     1 - |x|.
//
// Special cases:
//  cos(NaN) = quiet NaN, and raise invalid exception
//  cos(INF) = NaN and raise invalid exception
//  cos(0) = 1
//
/******************************************************************************/

#include <private/bionic_asm.h>
# -- Begin  cos
ENTRY(cos)
# parameter 1: %xmm0
..B1.1:
..___tag_value_cos.1:
        pushq     %rbx
..___tag_value_cos.3:
        subq      $16, %rsp
..___tag_value_cos.5:
        movsd     %xmm0, 8(%rsp)
..B1.2:
        movl      12(%rsp), %eax
        movq      PI32INV(%rip), %xmm1
        andl      $2147418112, %eax
        subl      $808452096, %eax
        cmpl      $281346048, %eax
        ja        .L_2TAG_PACKET_0.0.1
        mulsd     %xmm0, %xmm1
        movapd    ONEHALF(%rip), %xmm5
        movq      SIGN_MASK(%rip), %xmm4
        andpd     %xmm0, %xmm4
        orps      %xmm4, %xmm5
        addpd     %xmm5, %xmm1
        cvttsd2si %xmm1, %edx
        cvtsi2sd  %edx, %xmm1
        movapd    P_2(%rip), %xmm2
        movq      P_1(%rip), %xmm3
        mulsd     %xmm1, %xmm3
        unpcklpd  %xmm1, %xmm1
        addq      $1865232, %rdx
        movq      %xmm0, %xmm4
        andq      $63, %rdx
        movapd    SC_4(%rip), %xmm5
        lea       Ctable(%rip), %rax
        shlq      $5, %rdx
        addq      %rdx, %rax
        mulpd     %xmm1, %xmm2
        subsd     %xmm3, %xmm0
        mulsd     P_3(%rip), %xmm1
        subsd     %xmm3, %xmm4
        movq      8(%rax), %xmm7
        unpcklpd  %xmm0, %xmm0
        movq      %xmm4, %xmm3
        subsd     %xmm2, %xmm4
        mulpd     %xmm0, %xmm5
        subpd     %xmm2, %xmm0
        movapd    SC_2(%rip), %xmm6
        mulsd     %xmm4, %xmm7
        subsd     %xmm4, %xmm3
        mulpd     %xmm0, %xmm5
        mulpd     %xmm0, %xmm0
        subsd     %xmm2, %xmm3
        movapd    (%rax), %xmm2
        subsd     %xmm3, %xmm1
        movq      24(%rax), %xmm3
        addsd     %xmm3, %xmm2
        subsd     %xmm2, %xmm7
        mulsd     %xmm4, %xmm2
        mulpd     %xmm0, %xmm6
        mulsd     %xmm4, %xmm3
        mulpd     %xmm0, %xmm2
        mulpd     %xmm0, %xmm0
        addpd     SC_3(%rip), %xmm5
        mulsd     (%rax), %xmm4
        addpd     SC_1(%rip), %xmm6
        mulpd     %xmm0, %xmm5
        movq      %xmm3, %xmm0
        addsd     8(%rax), %xmm3
        mulpd     %xmm7, %xmm1
        movq      %xmm4, %xmm7
        addsd     %xmm3, %xmm4
        addpd     %xmm5, %xmm6
        movq      8(%rax), %xmm5
        subsd     %xmm3, %xmm5
        subsd     %xmm4, %xmm3
        addsd     16(%rax), %xmm1
        mulpd     %xmm2, %xmm6
        addsd     %xmm5, %xmm0
        addsd     %xmm7, %xmm3
        addsd     %xmm1, %xmm0
        addsd     %xmm3, %xmm0
        addsd     %xmm6, %xmm0
        unpckhpd  %xmm6, %xmm6
        addsd     %xmm6, %xmm0
        addsd     %xmm4, %xmm0
        jmp       ..B1.4
.L_2TAG_PACKET_0.0.1:
        jg        .L_2TAG_PACKET_1.0.1
        pextrw    $3, %xmm0, %eax
        andw      $32767, %ax
        pinsrw    $3, %eax, %xmm0
        movq      ONE(%rip), %xmm1
        subsd     %xmm0, %xmm1
        movq      %xmm1, %xmm0
        jmp       ..B1.4
.L_2TAG_PACKET_1.0.1:
        pextrw    $3, %xmm0, %eax
        andl      $32752, %eax
        cmpl      $32752, %eax
        je        .L_2TAG_PACKET_2.0.1
        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      $1, %ecx
        jl        .L_2TAG_PACKET_3.0.1
        negl      %ecx
        addl      $29, %ecx
        shll      %cl, %r9d
        movl      %r9d, %edi
        andl      $536870911, %r9d
        testl     $268435456, %r9d
        jne       .L_2TAG_PACKET_4.0.1
        shrl      %cl, %r9d
        movl      $0, %ebx
        shlq      $32, %r9
        orq       %r11, %r9
.L_2TAG_PACKET_5.0.1:
.L_2TAG_PACKET_6.0.1:
        cmpq      $0, %r9
        je        .L_2TAG_PACKET_7.0.1
.L_2TAG_PACKET_8.0.1:
        bsr       %r9, %r11
        movl      $29, %ecx
        subl      %r11d, %ecx
        jle       .L_2TAG_PACKET_9.0.1
        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_10.0.1:
        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), %xmm6
        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      $29, %edi
        addsd     %xmm3, %xmm1
        mulsd     %xmm2, %xmm3
        addl      %esi, %edi
        xorl      %esi, %edi
        mulsd     %xmm1, %xmm6
        movl      %edi, %eax
        addsd     %xmm3, %xmm6
        movq      %xmm0, %xmm2
        addsd     %xmm6, %xmm0
        subsd     %xmm0, %xmm2
        addsd     %xmm2, %xmm6
.L_2TAG_PACKET_11.0.1:
        movq      PI32INV(%rip), %xmm1
        mulsd     %xmm0, %xmm1
        movq      ONEHALF(%rip), %xmm5
        movq      SIGN_MASK(%rip), %xmm4
        andpd     %xmm0, %xmm4
        orps      %xmm4, %xmm5
        addpd     %xmm5, %xmm1
        cvttsd2si %xmm1, %rdx
        cvtsi2sdq %rdx, %xmm1
        movq      P_1(%rip), %xmm3
        movapd    P_2(%rip), %xmm2
        mulsd     %xmm1, %xmm3
        unpcklpd  %xmm1, %xmm1
        shll      $3, %eax
        addl      $1865232, %edx
        movq      %xmm0, %xmm4
        addl      %eax, %edx
        andl      $63, %edx
        movapd    SC_4(%rip), %xmm5
        lea       Ctable(%rip), %rax
        shll      $5, %edx
        addq      %rdx, %rax
        mulpd     %xmm1, %xmm2
        subsd     %xmm3, %xmm0
        mulsd     P_3(%rip), %xmm1
        subsd     %xmm3, %xmm4
        movq      8(%rax), %xmm7
        unpcklpd  %xmm0, %xmm0
        movq      %xmm4, %xmm3
        subsd     %xmm2, %xmm4
        mulpd     %xmm0, %xmm5
        subpd     %xmm2, %xmm0
        mulsd     %xmm4, %xmm7
        subsd     %xmm4, %xmm3
        mulpd     %xmm0, %xmm5
        mulpd     %xmm0, %xmm0
        subsd     %xmm2, %xmm3
        movapd    (%rax), %xmm2
        subsd     %xmm3, %xmm1
        movq      24(%rax), %xmm3
        addsd     %xmm3, %xmm2
        subsd     %xmm2, %xmm7
        subsd     %xmm6, %xmm1
        movapd    SC_2(%rip), %xmm6
        mulsd     %xmm4, %xmm2
        mulpd     %xmm0, %xmm6
        mulsd     %xmm4, %xmm3
        mulpd     %xmm0, %xmm2
        mulpd     %xmm0, %xmm0
        addpd     SC_3(%rip), %xmm5
        mulsd     (%rax), %xmm4
        addpd     SC_1(%rip), %xmm6
        mulpd     %xmm0, %xmm5
        movq      %xmm3, %xmm0
        addsd     8(%rax), %xmm3
        mulpd     %xmm7, %xmm1
        movq      %xmm4, %xmm7
        addsd     %xmm3, %xmm4
        addpd     %xmm5, %xmm6
        movq      8(%rax), %xmm5
        subsd     %xmm3, %xmm5
        subsd     %xmm4, %xmm3
        addsd     16(%rax), %xmm1
        mulpd     %xmm2, %xmm6
        addsd     %xmm0, %xmm5
        addsd     %xmm7, %xmm3
        addsd     %xmm5, %xmm1
        addsd     %xmm3, %xmm1
        addsd     %xmm6, %xmm1
        unpckhpd  %xmm6, %xmm6
        movq      %xmm4, %xmm0
        addsd     %xmm6, %xmm1
        addsd     %xmm1, %xmm0
        jmp       ..B1.4
.L_2TAG_PACKET_7.0.1:
        addl      $64, %edx
        movq      %r10, %r9
        movq      %r8, %r10
        movq      $0, %r8
        cmpq      $0, %r9
        jne       .L_2TAG_PACKET_8.0.1
        addl      $64, %edx
        movq      %r10, %r9
        movq      %r8, %r10
        cmpq      $0, %r9
        jne       .L_2TAG_PACKET_8.0.1
        xorpd     %xmm0, %xmm0
        xorpd     %xmm6, %xmm6
        jmp       .L_2TAG_PACKET_11.0.1
.L_2TAG_PACKET_9.0.1:
        je        .L_2TAG_PACKET_10.0.1
        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_10.0.1
.L_2TAG_PACKET_3.0.1:
        negl      %ecx
        shlq      $32, %r9
        orq       %r11, %r9
        shlq      %cl, %r9
        movq      %r9, %rdi
        testl     $-2147483648, %r9d
        jne       .L_2TAG_PACKET_12.0.1
        shrl      %cl, %r9d
        movl      $0, %ebx
        shrq      $3, %rdi
        jmp       .L_2TAG_PACKET_6.0.1
.L_2TAG_PACKET_4.0.1:
        shrl      %cl, %r9d
        movl      $536870912, %ebx
        shrl      %cl, %ebx
        shlq      $32, %r9
        orq       %r11, %r9
        shlq      $32, %rbx
        addl      $536870912, %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_5.0.1
.L_2TAG_PACKET_12.0.1:
        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      $3, %rdi
        addl      $536870912, %edi
        jmp       .L_2TAG_PACKET_6.0.1
.L_2TAG_PACKET_2.0.1:
        movsd     8(%rsp), %xmm0
        mulsd     NEG_ZERO(%rip), %xmm0
        movq      %xmm0, (%rsp)
.L_2TAG_PACKET_13.0.1:
..B1.4:
        addq      $16, %rsp
..___tag_value_cos.6:
        popq      %rbx
..___tag_value_cos.8:
        ret       
..___tag_value_cos.9:
END(cos)
# -- End  cos
	.section .rodata, "a"
	.align 16
	.align 16
ONEHALF:
	.long	0
	.long	1071644672
	.long	0
	.long	1071644672
	.type	ONEHALF,@object
	.size	ONEHALF,16
	.align 16
P_2:
	.long	442499072
	.long	1032893537
	.long	442499072
	.long	1032893537
	.type	P_2,@object
	.size	P_2,16
	.align 16
SC_4:
	.long	2773927732
	.long	1053236707
	.long	436314138
	.long	1056571808
	.type	SC_4,@object
	.size	SC_4,16
	.align 16
Ctable:
	.long	0
	.long	0
	.long	0
	.long	0
	.long	0
	.long	0
	.long	0
	.long	1072693248
	.long	393047345
	.long	3212032302
	.long	3156849708
	.long	1069094822
	.long	3758096384
	.long	3158189848
	.long	0
	.long	1072693248
	.long	18115067
	.long	3214126342
	.long	1013556747
	.long	1070135480
	.long	3221225472
	.long	3160567065
	.long	0
	.long	1072693248
	.long	2476548698
	.long	3215330282
	.long	785751814
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	.long	0
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	.type	Ctable,@object
	.size	Ctable,2048
	.align 16
SC_2:
	.long	286331153
	.long	1065423121
	.long	1431655765
	.long	1067799893
	.type	SC_2,@object
	.size	SC_2,16
	.align 16
SC_3:
	.long	436314138
	.long	3207201184
	.long	381774871
	.long	3210133868
	.type	SC_3,@object
	.size	SC_3,16
	.align 16
SC_1:
	.long	1431655765
	.long	3217380693
	.long	0
	.long	3219128320
	.type	SC_1,@object
	.size	SC_1,16
	.align 16
PI_INV_TABLE:
	.long	0
	.long	0
	.long	2734261102
	.long	1313084713
	.long	4230436817
	.long	4113882560
	.long	3680671129
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	.long	3072618042
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	.long	2972297022
	.long	3900847605
	.long	784024708
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	.long	3026157121
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	.long	2625920907
	.long	3187222587
	.long	536385535
	.long	3724908559
	.long	4012839307
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	.long	1832287951
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	.long	1965537991
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	.long	2320667370
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	.long	529358088
	.long	1443049542
	.long	4235946923
	.long	4040145953
	.type	PI_INV_TABLE,@object
	.size	PI_INV_TABLE,164
	.space 12, 0x00 	# pad
	.align 16
PI_4:
	.long	1073741824
	.long	1072243195
	.long	407279769
	.long	1046758445
	.type	PI_4,@object
	.size	PI_4,16
	.align 8
PI32INV:
	.long	1841940611
	.long	1076125488
	.type	PI32INV,@object
	.size	PI32INV,8
	.align 8
SIGN_MASK:
	.long	0
	.long	2147483648
	.type	SIGN_MASK,@object
	.size	SIGN_MASK,8
	.align 8
P_1:
	.long	1413480448
	.long	1069097467
	.type	P_1,@object
	.size	P_1,8
	.align 8
P_3:
	.long	771977331
	.long	996350346
	.type	P_3,@object
	.size	P_3,8
	.align 8
ONE:
	.long	0
	.long	1072693248
	.type	ONE,@object
	.size	ONE,8
	.align 8
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_cos.1-.
	.4byte ..___tag_value_cos.9-..___tag_value_cos.1
	.2byte 0x0400
	.4byte ..___tag_value_cos.3-..___tag_value_cos.1
	.4byte 0x0283100e
	.byte 0x04
	.4byte ..___tag_value_cos.5-..___tag_value_cos.3
	.2byte 0x200e
	.byte 0x04
	.4byte ..___tag_value_cos.6-..___tag_value_cos.5
	.4byte 0x04c3100e
	.4byte ..___tag_value_cos.8-..___tag_value_cos.6
	.2byte 0x080e
# End