892 lines
19 KiB
ArmAsm
892 lines
19 KiB
ArmAsm
/*
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Copyright (c) 2014, Intel Corporation
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All rights reserved.
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Redistribution and use in source and binary forms, with or without
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modification, are permitted provided that the following conditions are met:
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* Redistributions of source code must retain the above copyright notice,
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* this list of conditions and the following disclaimer.
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* Redistributions in binary form must reproduce the above copyright notice,
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* this list of conditions and the following disclaimer in the documentation
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* and/or other materials provided with the distribution.
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* Neither the name of Intel Corporation nor the names of its contributors
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* may be used to endorse or promote products derived from this software
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* without specific prior written permission.
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THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
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ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
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WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
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ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
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(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON
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ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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/******************************************************************************/
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// ALGORITHM DESCRIPTION
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// ---------------------
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//
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// 1. RANGE REDUCTION
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//
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// We perform an initial range reduction from X to r with
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//
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// X =~= N * pi/32 + r
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//
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// so that |r| <= pi/64 + epsilon. We restrict inputs to those
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// where |N| <= 932560. Beyond this, the range reduction is
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// insufficiently accurate. For extremely small inputs,
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// denormalization can occur internally, impacting performance.
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// This means that the main path is actually only taken for
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// 2^-252 <= |X| < 90112.
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//
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// To avoid branches, we perform the range reduction to full
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// accuracy each time.
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//
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// X - N * (P_1 + P_2 + P_3)
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//
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// where P_1 and P_2 are 32-bit numbers (so multiplication by N
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// is exact) and P_3 is a 53-bit number. Together, these
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// approximate pi well enough for all cases in the restricted
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// range.
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//
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// The main reduction sequence is:
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//
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// y = 32/pi * x
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// N = integer(y)
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// (computed by adding and subtracting off SHIFTER)
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//
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// m_1 = N * P_1
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// m_2 = N * P_2
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// r_1 = x - m_1
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// r = r_1 - m_2
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// (this r can be used for most of the calculation)
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//
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// c_1 = r_1 - r
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// m_3 = N * P_3
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// c_2 = c_1 - m_2
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// c = c_2 - m_3
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//
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// 2. MAIN ALGORITHM
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//
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// The algorithm uses a table lookup based on B = M * pi / 32
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// where M = N mod 64. The stored values are:
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// sigma closest power of 2 to cos(B)
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// C_hl 53-bit cos(B) - sigma
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// S_hi + S_lo 2 * 53-bit sin(B)
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//
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// The computation is organized as follows:
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//
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// sin(B + r + c) = [sin(B) + sigma * r] +
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// r * (cos(B) - sigma) +
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// sin(B) * [cos(r + c) - 1] +
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// cos(B) * [sin(r + c) - r]
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//
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// which is approximately:
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//
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// [S_hi + sigma * r] +
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// C_hl * r +
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// S_lo + S_hi * [(cos(r) - 1) - r * c] +
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// (C_hl + sigma) * [(sin(r) - r) + c]
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//
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// and this is what is actually computed. We separate this sum
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// into four parts:
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//
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// hi + med + pols + corr
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//
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// where
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//
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// hi = S_hi + sigma r
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// med = C_hl * r
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// pols = S_hi * (cos(r) - 1) + (C_hl + sigma) * (sin(r) - r)
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// corr = S_lo + c * ((C_hl + sigma) - S_hi * r)
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//
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// 3. POLYNOMIAL
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//
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// The polynomial S_hi * (cos(r) - 1) + (C_hl + sigma) *
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// (sin(r) - r) can be rearranged freely, since it is quite
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// small, so we exploit parallelism to the fullest.
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//
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// psc4 = SC_4 * r_1
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// msc4 = psc4 * r
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// r2 = r * r
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// msc2 = SC_2 * r2
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// r4 = r2 * r2
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// psc3 = SC_3 + msc4
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// psc1 = SC_1 + msc2
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// msc3 = r4 * psc3
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// sincospols = psc1 + msc3
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// pols = sincospols *
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// <S_hi * r^2 | (C_hl + sigma) * r^3>
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//
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// 4. CORRECTION TERM
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//
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// This is where the "c" component of the range reduction is
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// taken into account; recall that just "r" is used for most of
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// the calculation.
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//
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// -c = m_3 - c_2
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// -d = S_hi * r - (C_hl + sigma)
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// corr = -c * -d + S_lo
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//
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// 5. COMPENSATED SUMMATIONS
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//
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// The two successive compensated summations add up the high
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// and medium parts, leaving just the low parts to add up at
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// the end.
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//
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// rs = sigma * r
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// res_int = S_hi + rs
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// k_0 = S_hi - res_int
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// k_2 = k_0 + rs
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// med = C_hl * r
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// res_hi = res_int + med
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// k_1 = res_int - res_hi
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// k_3 = k_1 + med
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//
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// 6. FINAL SUMMATION
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//
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// We now add up all the small parts:
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//
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// res_lo = pols(hi) + pols(lo) + corr + k_1 + k_3
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//
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// Now the overall result is just:
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//
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// res_hi + res_lo
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//
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// 7. SMALL ARGUMENTS
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//
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// Inputs with |X| < 2^-252 are treated specially as
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// 1 - |x|.
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//
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// Special cases:
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// cos(NaN) = quiet NaN, and raise invalid exception
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// cos(INF) = NaN and raise invalid exception
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// cos(0) = 1
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//
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/******************************************************************************/
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#include <private/bionic_asm.h>
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# -- Begin static_func
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.text
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.align __bionic_asm_align
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.type static_func, @function
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static_func:
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..B1.1:
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call ..L2
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..L2:
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popl %eax
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lea _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
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lea static_const_table@GOTOFF(%eax), %eax
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ret
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.size static_func,.-static_func
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# -- End static_func
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# -- Begin cos
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ENTRY(cos)
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# parameter 1: 8 + %ebp
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..B2.1:
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..B2.2:
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pushl %ebp
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movl %esp, %ebp
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subl $120, %esp
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movl %ebx, 56(%esp)
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call static_func
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movl %eax, %ebx
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movsd 128(%esp), %xmm0
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pextrw $3, %xmm0, %eax
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andl $32767, %eax
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subl $12336, %eax
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cmpl $4293, %eax
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ja .L_2TAG_PACKET_0.0.2
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movsd 2160(%ebx), %xmm1
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mulsd %xmm0, %xmm1
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movapd 2240(%ebx), %xmm5
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movsd 2224(%ebx), %xmm4
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andpd %xmm0, %xmm4
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orps %xmm4, %xmm5
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movsd 2128(%ebx), %xmm3
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movapd 2112(%ebx), %xmm2
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addpd %xmm5, %xmm1
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cvttsd2si %xmm1, %edx
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cvtsi2sdl %edx, %xmm1
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mulsd %xmm1, %xmm3
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unpcklpd %xmm1, %xmm1
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addl $1865232, %edx
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movapd %xmm0, %xmm4
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andl $63, %edx
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movapd 2096(%ebx), %xmm5
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lea (%ebx), %eax
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shll $5, %edx
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addl %edx, %eax
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mulpd %xmm1, %xmm2
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subsd %xmm3, %xmm0
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mulsd 2144(%ebx), %xmm1
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subsd %xmm3, %xmm4
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movsd 8(%eax), %xmm7
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unpcklpd %xmm0, %xmm0
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movapd %xmm4, %xmm3
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subsd %xmm2, %xmm4
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mulpd %xmm0, %xmm5
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subpd %xmm2, %xmm0
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movapd 2064(%ebx), %xmm6
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mulsd %xmm4, %xmm7
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subsd %xmm4, %xmm3
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mulpd %xmm0, %xmm5
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mulpd %xmm0, %xmm0
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subsd %xmm2, %xmm3
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movapd (%eax), %xmm2
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subsd %xmm3, %xmm1
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movsd 24(%eax), %xmm3
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addsd %xmm3, %xmm2
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subsd %xmm2, %xmm7
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mulsd %xmm4, %xmm2
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mulpd %xmm0, %xmm6
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mulsd %xmm4, %xmm3
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mulpd %xmm0, %xmm2
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mulpd %xmm0, %xmm0
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addpd 2080(%ebx), %xmm5
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mulsd (%eax), %xmm4
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addpd 2048(%ebx), %xmm6
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mulpd %xmm0, %xmm5
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movapd %xmm3, %xmm0
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addsd 8(%eax), %xmm3
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mulpd %xmm7, %xmm1
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movapd %xmm4, %xmm7
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addsd %xmm3, %xmm4
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addpd %xmm5, %xmm6
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movsd 8(%eax), %xmm5
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subsd %xmm3, %xmm5
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subsd %xmm4, %xmm3
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addsd 16(%eax), %xmm1
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mulpd %xmm2, %xmm6
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addsd %xmm0, %xmm5
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addsd %xmm7, %xmm3
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addsd %xmm5, %xmm1
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addsd %xmm3, %xmm1
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addsd %xmm6, %xmm1
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unpckhpd %xmm6, %xmm6
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addsd %xmm6, %xmm1
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addsd %xmm1, %xmm4
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movsd %xmm4, (%esp)
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fldl (%esp)
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jmp .L_2TAG_PACKET_1.0.2
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.L_2TAG_PACKET_0.0.2:
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jg .L_2TAG_PACKET_2.0.2
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pextrw $3, %xmm0, %eax
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andl $32767, %eax
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pinsrw $3, %eax, %xmm0
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movsd 2192(%ebx), %xmm1
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subsd %xmm0, %xmm1
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movsd %xmm1, (%esp)
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fldl (%esp)
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jmp .L_2TAG_PACKET_1.0.2
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.L_2TAG_PACKET_2.0.2:
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movl 132(%esp), %eax
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andl $2146435072, %eax
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cmpl $2146435072, %eax
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je .L_2TAG_PACKET_3.0.2
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subl $32, %esp
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movsd %xmm0, (%esp)
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lea 40(%esp), %eax
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movl %eax, 8(%esp)
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movl $1, %eax
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movl %eax, 12(%esp)
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call __libm_sincos_huge
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addl $32, %esp
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fldl 8(%esp)
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jmp .L_2TAG_PACKET_1.0.2
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.L_2TAG_PACKET_3.0.2:
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fldl 128(%esp)
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fmull 2208(%ebx)
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.L_2TAG_PACKET_1.0.2:
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movl 56(%esp), %ebx
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movl %ebp, %esp
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popl %ebp
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ret
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..B2.3:
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END(cos)
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# -- End cos
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# Start file scope ASM
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ALIAS_SYMBOL(cosl, cos);
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# End file scope ASM
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.section .rodata, "a"
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.align 16
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.align 16
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static_const_table:
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.long 0
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.long 0
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.long 0
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.long 0
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.long 0
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.long 0
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.long 0
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.long 1072693248
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.long 393047345
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.long 3212032302
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.long 3156849708
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.long 1069094822
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.long 3758096384
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.long 3158189848
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.long 0
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.long 1072693248
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.long 18115067
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.long 3214126342
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.long 1013556747
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.long 1070135480
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.long 3221225472
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.long 3160567065
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.long 0
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.long 1072693248
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.long 2476548698
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.long 3215330282
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.long 785751814
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.long 1070765062
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.long 2684354560
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.long 3161838221
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.long 0
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.long 1072693248
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.long 2255197647
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.long 3216211105
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.long 2796464483
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.long 1071152610
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.long 3758096384
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.long 3160878317
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.long 0
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.long 1072693248
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.long 1945768569
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.long 3216915048
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.long 939980347
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.long 1071524701
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.long 536870912
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.long 1012796809
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.long 0
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.long 1072693248
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.long 1539668340
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.long 3217396327
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.long 967731400
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.long 1071761211
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.long 536870912
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.long 1015752157
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.long 0
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.long 1072693248
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.long 1403757309
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.long 3217886718
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.long 621354454
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.long 1071926515
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.long 536870912
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.long 1013450602
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.long 0
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.long 1072693248
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.long 2583490354
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.long 1070236281
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.long 1719614413
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.long 1072079006
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.long 536870912
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.long 3163282740
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.long 0
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.long 1071644672
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.long 2485417816
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.long 1069626316
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.long 1796544321
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.long 1072217216
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.long 536870912
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.long 3162686945
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.long 0
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.long 1071644672
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.long 2598800519
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.long 1068266419
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.long 688824739
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.long 1072339814
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.long 3758096384
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.long 1010431536
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.long 0
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.long 1071644672
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.long 2140183630
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.long 3214756396
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.long 4051746225
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.long 1072445618
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.long 2147483648
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.long 3161907377
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.long 0
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.long 1071644672
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.long 1699043957
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.long 3216902261
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.long 3476196678
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.long 1072533611
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.long 536870912
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.long 1014257638
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.long 0
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.long 1071644672
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.long 1991047213
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.long 1067753521
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.long 1455828442
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.long 1072602945
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.long 3758096384
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.long 1015505073
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.long 0
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.long 1070596096
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.long 240740309
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.long 3215727903
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.long 3489094832
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.long 1072652951
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.long 536870912
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.long 1014325783
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.long 0
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.long 1070596096
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.long 257503056
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.long 3214647653
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.long 2748392742
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.long 1072683149
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.long 1073741824
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.long 3163061750
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.long 0
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.long 1069547520
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.long 0
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.long 0
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.long 0
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.long 1072693248
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.long 0
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.long 0
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.long 0
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.long 0
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.long 257503056
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.long 1067164005
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.long 2748392742
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.long 1072683149
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.long 1073741824
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.long 3163061750
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.long 0
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.long 3217031168
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.long 240740309
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.long 1068244255
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.long 3489094832
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.long 1072652951
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.long 536870912
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.long 1014325783
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.long 0
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.long 3218079744
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.long 1991047213
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.long 3215237169
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.long 1455828442
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.long 1072602945
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.long 3758096384
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.long 1015505073
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.long 0
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.long 3218079744
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.long 1699043957
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.long 1069418613
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.long 3476196678
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.long 1072533611
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.long 536870912
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.long 1014257638
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.long 0
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.long 3219128320
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.long 2140183630
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.long 1067272748
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.long 4051746225
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.long 1072445618
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.long 2147483648
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.long 3161907377
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.long 0
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.long 3219128320
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.long 2598800519
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.long 3215750067
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.long 688824739
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.long 1072339814
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.long 3758096384
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.long 1010431536
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.long 0
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.long 3219128320
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.long 2485417816
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.long 3217109964
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.long 1796544321
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.long 1072217216
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.long 536870912
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.long 3162686945
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.long 0
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.long 3219128320
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.long 2583490354
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.long 3217719929
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.long 1719614413
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.long 1072079006
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.long 536870912
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.long 3163282740
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.long 0
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.long 3219128320
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.long 1403757309
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.long 1070403070
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.type static_const_table,@object
|
|
.size static_const_table,2256
|
|
.data
|
|
.hidden __libm_sincos_huge
|
|
.section .note.GNU-stack, ""
|
|
# End
|