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Diffstat (limited to 'libm/x86/s_cos.S')
| -rw-r--r-- | libm/x86/s_cos.S | 893 |
1 files changed, 893 insertions, 0 deletions
diff --git a/libm/x86/s_cos.S b/libm/x86/s_cos.S new file mode 100644 index 0000000..0f5d570 --- /dev/null +++ b/libm/x86/s_cos.S @@ -0,0 +1,893 @@ +/* +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 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 cos +ENTRY(cos) +# 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 + movapd 2240(%ebx), %xmm5 + movsd 2224(%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 $1865232, %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 + pextrw $3, %xmm0, %eax + andl $32767, %eax + pinsrw $3, %eax, %xmm0 + movsd 2192(%ebx), %xmm1 + subsd %xmm0, %xmm1 + movsd %xmm1, (%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_3.0.2 + subl $32, %esp + movsd %xmm0, (%esp) + lea 40(%esp), %eax + movl %eax, 8(%esp) + movl $1, %eax + movl %eax, 12(%esp) + call __libm_sincos_huge + addl $32, %esp + fldl 8(%esp) + jmp .L_2TAG_PACKET_1.0.2 +.L_2TAG_PACKET_3.0.2: + fldl 128(%esp) + fmull 2208(%ebx) +.L_2TAG_PACKET_1.0.2: + movl 56(%esp), %ebx + movl %ebp, %esp + popl %ebp + ret +..B2.3: +END(cos) +# -- End cos + +# Start file scope ASM +.weak cosl +.equ cosl, cos +# 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 1072693248 + .long 0 + .long 0 + .long 0 + .long 2147483648 + .long 0 + .long 0 + .long 0 + .long 2147483648 + .long 0 + .long 0 + .long 0 + .long 1071644672 + .long 0 + .long 1071644672 + .type static_const_table,@object + .size static_const_table,2256 + .data + .hidden __libm_sincos_huge + .section .note.GNU-stack, "" +# End |