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| /*
| 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
| //
| // If |x| < SNN (SNN meaning the smallest normal number), we
| // simply perform 0.1111111 cdots 1111 * x. For SNN <= |x|, we
| // do 2^-55 * (2^55 * x - x).
| //
| // Special cases:
| // sin(NaN) = quiet NaN, and raise invalid exception
| // sin(INF) = NaN and raise invalid exception
| // sin(+/-0) = +/-0
| //
| /******************************************************************************/
|
| #include <private/bionic_asm.h>
| # -- Begin static_func
| .text
| .align __bionic_asm_align
| .type static_func, @function
| static_func:
| ..B1.1:
| call ..L2
| ..L2:
| popl %eax
| lea _GLOBAL_OFFSET_TABLE_+[. - ..L2](%eax), %eax
| lea static_const_table@GOTOFF(%eax), %eax
| ret
| .size static_func,.-static_func
| # -- End static_func
|
| # -- Begin sin
| ENTRY(sin)
| # parameter 1: 8 + %ebp
| ..B2.1:
| ..B2.2:
| pushl %ebp
| movl %esp, %ebp
| subl $120, %esp
| movl %ebx, 56(%esp)
| call static_func
| movl %eax, %ebx
| movsd 128(%esp), %xmm0
| pextrw $3, %xmm0, %eax
| andl $32767, %eax
| subl $12336, %eax
| cmpl $4293, %eax
| ja .L_2TAG_PACKET_0.0.2
| movsd 2160(%ebx), %xmm1
| mulsd %xmm0, %xmm1
| movsd 2272(%ebx), %xmm5
| movapd 2256(%ebx), %xmm4
| andpd %xmm0, %xmm4
| orps %xmm4, %xmm5
| movsd 2128(%ebx), %xmm3
| movapd 2112(%ebx), %xmm2
| addpd %xmm5, %xmm1
| cvttsd2si %xmm1, %edx
| cvtsi2sdl %edx, %xmm1
| mulsd %xmm1, %xmm3
| unpcklpd %xmm1, %xmm1
| addl $1865216, %edx
| movapd %xmm0, %xmm4
| andl $63, %edx
| movapd 2096(%ebx), %xmm5
| lea (%ebx), %eax
| shll $5, %edx
| addl %edx, %eax
| mulpd %xmm1, %xmm2
| subsd %xmm3, %xmm0
| mulsd 2144(%ebx), %xmm1
| subsd %xmm3, %xmm4
| movsd 8(%eax), %xmm7
| unpcklpd %xmm0, %xmm0
| movapd %xmm4, %xmm3
| subsd %xmm2, %xmm4
| mulpd %xmm0, %xmm5
| subpd %xmm2, %xmm0
| movapd 2064(%ebx), %xmm6
| mulsd %xmm4, %xmm7
| subsd %xmm4, %xmm3
| mulpd %xmm0, %xmm5
| mulpd %xmm0, %xmm0
| subsd %xmm2, %xmm3
| movapd (%eax), %xmm2
| subsd %xmm3, %xmm1
| movsd 24(%eax), %xmm3
| addsd %xmm3, %xmm2
| subsd %xmm2, %xmm7
| mulsd %xmm4, %xmm2
| mulpd %xmm0, %xmm6
| mulsd %xmm4, %xmm3
| mulpd %xmm0, %xmm2
| mulpd %xmm0, %xmm0
| addpd 2080(%ebx), %xmm5
| mulsd (%eax), %xmm4
| addpd 2048(%ebx), %xmm6
| mulpd %xmm0, %xmm5
| movapd %xmm3, %xmm0
| addsd 8(%eax), %xmm3
| mulpd %xmm7, %xmm1
| movapd %xmm4, %xmm7
| addsd %xmm3, %xmm4
| addpd %xmm5, %xmm6
| movsd 8(%eax), %xmm5
| subsd %xmm3, %xmm5
| subsd %xmm4, %xmm3
| addsd 16(%eax), %xmm1
| mulpd %xmm2, %xmm6
| addsd %xmm0, %xmm5
| addsd %xmm7, %xmm3
| addsd %xmm5, %xmm1
| addsd %xmm3, %xmm1
| addsd %xmm6, %xmm1
| unpckhpd %xmm6, %xmm6
| addsd %xmm6, %xmm1
| addsd %xmm1, %xmm4
| movsd %xmm4, (%esp)
| fldl (%esp)
| jmp .L_2TAG_PACKET_1.0.2
| .L_2TAG_PACKET_0.0.2:
| jg .L_2TAG_PACKET_2.0.2
| shrl $4, %eax
| cmpl $268434685, %eax
| jne .L_2TAG_PACKET_3.0.2
| movsd %xmm0, (%esp)
| fldl (%esp)
| jmp .L_2TAG_PACKET_1.0.2
| .L_2TAG_PACKET_3.0.2:
| movsd 2192(%ebx), %xmm3
| mulsd %xmm0, %xmm3
| subsd %xmm0, %xmm3
| mulsd 2208(%ebx), %xmm3
| movsd %xmm0, (%esp)
| fldl (%esp)
| jmp .L_2TAG_PACKET_1.0.2
| .L_2TAG_PACKET_2.0.2:
| movl 132(%esp), %eax
| andl $2146435072, %eax
| cmpl $2146435072, %eax
| je .L_2TAG_PACKET_4.0.2
| subl $32, %esp
| movsd %xmm0, (%esp)
| lea 40(%esp), %eax
| movl %eax, 8(%esp)
| movl $2, %eax
| movl %eax, 12(%esp)
| call __libm_sincos_huge
| addl $32, %esp
| fldl 16(%esp)
| jmp .L_2TAG_PACKET_1.0.2
| .L_2TAG_PACKET_4.0.2:
| fldl 128(%esp)
| fmull 2240(%ebx)
| .L_2TAG_PACKET_1.0.2:
| movl 56(%esp), %ebx
| movl %ebp, %esp
| popl %ebp
| ret
| ..B2.3:
| END(sin)
| # -- End sin
|
| # Start file scope ASM
| ALIAS_SYMBOL(sinl, sin);
| # End file scope ASM
| .section .rodata, "a"
| .align 16
| .align 16
| static_const_table:
| .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
| .long 1070765062
| .long 2684354560
| .long 3161838221
| .long 0
| .long 1072693248
| .long 2255197647
| .long 3216211105
| .long 2796464483
| .long 1071152610
| .long 3758096384
| .long 3160878317
| .long 0
| .long 1072693248
| .long 1945768569
| .long 3216915048
| .long 939980347
| .long 1071524701
| .long 536870912
| .long 1012796809
| .long 0
| .long 1072693248
| .long 1539668340
| .long 3217396327
| .long 967731400
| .long 1071761211
| .long 536870912
| .long 1015752157
| .long 0
| .long 1072693248
| .long 1403757309
| .long 3217886718
| .long 621354454
| .long 1071926515
| .long 536870912
| .long 1013450602
| .long 0
| .long 1072693248
| .long 2583490354
| .long 1070236281
| .long 1719614413
| .long 1072079006
| .long 536870912
| .long 3163282740
| .long 0
| .long 1071644672
| .long 2485417816
| .long 1069626316
| .long 1796544321
| .long 1072217216
| .long 536870912
| .long 3162686945
| .long 0
| .long 1071644672
| .long 2598800519
| .long 1068266419
| .long 688824739
| .long 1072339814
| .long 3758096384
| .long 1010431536
| .long 0
| .long 1071644672
| .long 2140183630
| .long 3214756396
| .long 4051746225
| .long 1072445618
| .long 2147483648
| .long 3161907377
| .long 0
| .long 1071644672
| .long 1699043957
| .long 3216902261
| .long 3476196678
| .long 1072533611
| .long 536870912
| .long 1014257638
| .long 0
| .long 1071644672
| .long 1991047213
| .long 1067753521
| .long 1455828442
| .long 1072602945
| .long 3758096384
| .long 1015505073
| .long 0
| .long 1070596096
| .long 240740309
| .long 3215727903
| .long 3489094832
| .long 1072652951
| .long 536870912
| .long 1014325783
| .long 0
| .long 1070596096
| .long 257503056
| .long 3214647653
| .long 2748392742
| .long 1072683149
| .long 1073741824
| .long 3163061750
| .long 0
| .long 1069547520
| .long 0
| .long 0
| .long 0
| .long 1072693248
| .long 0
| .long 0
| .long 0
| .long 0
| .long 257503056
| .long 1067164005
| .long 2748392742
| .long 1072683149
| .long 1073741824
| .long 3163061750
| .long 0
| .long 3217031168
| .long 240740309
| .long 1068244255
| .long 3489094832
| .long 1072652951
| .long 536870912
| .long 1014325783
| .long 0
| .long 3218079744
| .long 1991047213
| .long 3215237169
| .long 1455828442
| .long 1072602945
| .long 3758096384
| .long 1015505073
| .long 0
| .long 3218079744
| .long 1699043957
| .long 1069418613
| .long 3476196678
| .long 1072533611
| .long 536870912
| .long 1014257638
| .long 0
| .long 3219128320
| .long 2140183630
| .long 1067272748
| .long 4051746225
| .long 1072445618
| .long 2147483648
| .long 3161907377
| .long 0
| .long 3219128320
| .long 2598800519
| .long 3215750067
| .long 688824739
| .long 1072339814
| .long 3758096384
| .long 1010431536
| .long 0
| .long 3219128320
| .long 2485417816
| .long 3217109964
| .long 1796544321
| .long 1072217216
| .long 536870912
| .long 3162686945
| .long 0
| .long 3219128320
| .long 2583490354
| .long 3217719929
| .long 1719614413
| .long 1072079006
| .long 536870912
| .long 3163282740
| .long 0
| .long 3219128320
| .long 1403757309
| .long 1070403070
| .long 621354454
| .long 1071926515
| .long 536870912
| .long 1013450602
| .long 0
| .long 3220176896
| .long 1539668340
| .long 1069912679
| .long 967731400
| .long 1071761211
| .long 536870912
| .long 1015752157
| .long 0
| .long 3220176896
| .long 1945768569
| .long 1069431400
| .long 939980347
| .long 1071524701
| .long 536870912
| .long 1012796809
| .long 0
| .long 3220176896
| .long 2255197647
| .long 1068727457
| .long 2796464483
| .long 1071152610
| .long 3758096384
| .long 3160878317
| .long 0
| .long 3220176896
| .long 2476548698
| .long 1067846634
| .long 785751814
| .long 1070765062
| .long 2684354560
| .long 3161838221
| .long 0
| .long 3220176896
| .long 18115067
| .long 1066642694
| .long 1013556747
| .long 1070135480
| .long 3221225472
| .long 3160567065
| .long 0
| .long 3220176896
| .long 393047345
| .long 1064548654
| .long 3156849708
| .long 1069094822
| .long 3758096384
| .long 3158189848
| .long 0
| .long 3220176896
| .long 0
| .long 0
| .long 0
| .long 0
| .long 0
| .long 0
| .long 0
| .long 3220176896
| .long 393047345
| .long 1064548654
| .long 3156849708
| .long 3216578470
| .long 3758096384
| .long 1010706200
| .long 0
| .long 3220176896
| .long 18115067
| .long 1066642694
| .long 1013556747
| .long 3217619128
| .long 3221225472
| .long 1013083417
| .long 0
| .long 3220176896
| .long 2476548698
| .long 1067846634
| .long 785751814
| .long 3218248710
| .long 2684354560
| .long 1014354573
| .long 0
| .long 3220176896
| .long 2255197647
| .long 1068727457
| .long 2796464483
| .long 3218636258
| .long 3758096384
| .long 1013394669
| .long 0
| .long 3220176896
| .long 1945768569
| .long 1069431400
| .long 939980347
| .long 3219008349
| .long 536870912
| .long 3160280457
| .long 0
| .long 3220176896
| .long 1539668340
| .long 1069912679
| .long 967731400
| .long 3219244859
| .long 536870912
| .long 3163235805
| .long 0
| .long 3220176896
| .long 1403757309
| .long 1070403070
| .long 621354454
| .long 3219410163
| .long 536870912
| .long 3160934250
| .long 0
| .long 3220176896
| .long 2583490354
| .long 3217719929
| .long 1719614413
| .long 3219562654
| .long 536870912
| .long 1015799092
| .long 0
| .long 3219128320
| .long 2485417816
| .long 3217109964
| .long 1796544321
| .long 3219700864
| .long 536870912
| .long 1015203297
| .long 0
| .long 3219128320
| .long 2598800519
| .long 3215750067
| .long 688824739
| .long 3219823462
| .long 3758096384
| .long 3157915184
| .long 0
| .long 3219128320
| .long 2140183630
| .long 1067272748
| .long 4051746225
| .long 3219929266
| .long 2147483648
| .long 1014423729
| .long 0
| .long 3219128320
| .long 1699043957
| .long 1069418613
| .long 3476196678
| .long 3220017259
| .long 536870912
| .long 3161741286
| .long 0
| .long 3219128320
| .long 1991047213
| .long 3215237169
| .long 1455828442
| .long 3220086593
| .long 3758096384
| .long 3162988721
| .long 0
| .long 3218079744
| .long 240740309
| .long 1068244255
| .long 3489094832
| .long 3220136599
| .long 536870912
| .long 3161809431
| .long 0
| .long 3218079744
| .long 257503056
| .long 1067164005
| .long 2748392742
| .long 3220166797
| .long 1073741824
| .long 1015578102
| .long 0
| .long 3217031168
| .long 0
| .long 0
| .long 0
| .long 3220176896
| .long 0
| .long 0
| .long 0
| .long 0
| .long 257503056
| .long 3214647653
| .long 2748392742
| .long 3220166797
| .long 1073741824
| .long 1015578102
| .long 0
| .long 1069547520
| .long 240740309
| .long 3215727903
| .long 3489094832
| .long 3220136599
| .long 536870912
| .long 3161809431
| .long 0
| .long 1070596096
| .long 1991047213
| .long 1067753521
| .long 1455828442
| .long 3220086593
| .long 3758096384
| .long 3162988721
| .long 0
| .long 1070596096
| .long 1699043957
| .long 3216902261
| .long 3476196678
| .long 3220017259
| .long 536870912
| .long 3161741286
| .long 0
| .long 1071644672
| .long 2140183630
| .long 3214756396
| .long 4051746225
| .long 3219929266
| .long 2147483648
| .long 1014423729
| .long 0
| .long 1071644672
| .long 2598800519
| .long 1068266419
| .long 688824739
| .long 3219823462
| .long 3758096384
| .long 3157915184
| .long 0
| .long 1071644672
| .long 2485417816
| .long 1069626316
| .long 1796544321
| .long 3219700864
| .long 536870912
| .long 1015203297
| .long 0
| .long 1071644672
| .long 2583490354
| .long 1070236281
| .long 1719614413
| .long 3219562654
| .long 536870912
| .long 1015799092
| .long 0
| .long 1071644672
| .long 1403757309
| .long 3217886718
| .long 621354454
| .long 3219410163
| .long 536870912
| .long 3160934250
| .long 0
| .long 1072693248
| .long 1539668340
| .long 3217396327
| .long 967731400
| .long 3219244859
| .long 536870912
| .long 3163235805
| .long 0
| .long 1072693248
| .long 1945768569
| .long 3216915048
| .long 939980347
| .long 3219008349
| .long 536870912
| .long 3160280457
| .long 0
| .long 1072693248
| .long 2255197647
| .long 3216211105
| .long 2796464483
| .long 3218636258
| .long 3758096384
| .long 1013394669
| .long 0
| .long 1072693248
| .long 2476548698
| .long 3215330282
| .long 785751814
| .long 3218248710
| .long 2684354560
| .long 1014354573
| .long 0
| .long 1072693248
| .long 18115067
| .long 3214126342
| .long 1013556747
| .long 3217619128
| .long 3221225472
| .long 1013083417
| .long 0
| .long 1072693248
| .long 393047345
| .long 3212032302
| .long 3156849708
| .long 3216578470
| .long 3758096384
| .long 1010706200
| .long 0
| .long 1072693248
| .long 1431655765
| .long 3217380693
| .long 0
| .long 3219128320
| .long 286331153
| .long 1065423121
| .long 1431655765
| .long 1067799893
| .long 436314138
| .long 3207201184
| .long 381774871
| .long 3210133868
| .long 2773927732
| .long 1053236707
| .long 436314138
| .long 1056571808
| .long 442499072
| .long 1032893537
| .long 442499072
| .long 1032893537
| .long 1413480448
| .long 1069097467
| .long 0
| .long 0
| .long 771977331
| .long 996350346
| .long 0
| .long 0
| .long 1841940611
| .long 1076125488
| .long 0
| .long 0
| .long 0
| .long 1127743488
| .long 0
| .long 0
| .long 0
| .long 1130364928
| .long 0
| .long 0
| .long 0
| .long 1015021568
| .long 0
| .long 0
| .long 4294967295
| .long 1072693247
| .long 0
| .long 0
| .long 0
| .long 2147483648
| .long 0
| .long 0
| .long 0
| .long 2147483648
| .long 0
| .long 2147483648
| .long 0
| .long 1071644672
| .long 0
| .long 1071644672
| .type static_const_table,@object
| .size static_const_table,2288
| .data
| .hidden __libm_sincos_huge
| .section .note.GNU-stack, ""
| # End
|
|
