8152907: Update for x86 tan and log10 in the math lib
Summary: Optimize Math.tan() and log10() for 64 and 32 bit X86 architecture using Intel LIBM implementation.
Reviewed-by: kvn, twisti
Contributed-by: shravya.rukmannagari@intel.com
/*
* Copyright (c) 2016, Intel Corporation.
* Intel Math Library (LIBM) Source Code
*
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
*
* This code is free software; you can redistribute it and/or modify it
* under the terms of the GNU General Public License version 2 only, as
* published by the Free Software Foundation.
*
* This code is distributed in the hope that it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
* version 2 for more details (a copy is included in the LICENSE file that
* accompanied this code).
*
* You should have received a copy of the GNU General Public License version
* 2 along with this work; if not, write to the Free Software Foundation,
* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
*
* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
* or visit www.oracle.com if you need additional information or have any
* questions.
*
*/
#include "precompiled.hpp"
#include "asm/assembler.hpp"
#include "asm/assembler.inline.hpp"
#include "runtime/stubRoutines.hpp"
#include "macroAssembler_x86.hpp"
#ifdef _MSC_VER
#define ALIGNED_(x) __declspec(align(x))
#else
#define ALIGNED_(x) __attribute__ ((aligned(x)))
#endif
/******************************************************************************/
// ALGORITHM DESCRIPTION - COS()
// ---------------------
//
// 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
//
/******************************************************************************/
#ifdef _LP64
// The 64 bit code is at most SSE2 compliant
ALIGNED_(8) juint _ONE[] =
{
0x00000000UL, 0x3ff00000UL
};
void MacroAssembler::fast_cos(XMMRegister xmm0, XMMRegister xmm1, XMMRegister xmm2, XMMRegister xmm3, XMMRegister xmm4, XMMRegister xmm5, XMMRegister xmm6, XMMRegister xmm7, Register eax, Register ecx, Register edx, Register r8, Register r9, Register r10, Register r11) {
Label L_2TAG_PACKET_0_0_1, L_2TAG_PACKET_1_0_1, L_2TAG_PACKET_2_0_1, L_2TAG_PACKET_3_0_1;
Label L_2TAG_PACKET_4_0_1, L_2TAG_PACKET_5_0_1, L_2TAG_PACKET_6_0_1, L_2TAG_PACKET_7_0_1;
Label L_2TAG_PACKET_8_0_1, L_2TAG_PACKET_9_0_1, L_2TAG_PACKET_10_0_1, L_2TAG_PACKET_11_0_1;
Label L_2TAG_PACKET_12_0_1, L_2TAG_PACKET_13_0_1, B1_2, B1_3, B1_4, B1_5, start;
assert_different_registers(r8, r9, r10, r11, eax, ecx, edx);
address ONEHALF = StubRoutines::x86::_ONEHALF_addr();
address P_2 = StubRoutines::x86::_P_2_addr();
address SC_4 = StubRoutines::x86::_SC_4_addr();
address Ctable = StubRoutines::x86::_Ctable_addr();
address SC_2 = StubRoutines::x86::_SC_2_addr();
address SC_3 = StubRoutines::x86::_SC_3_addr();
address SC_1 = StubRoutines::x86::_SC_1_addr();
address PI_INV_TABLE = StubRoutines::x86::_PI_INV_TABLE_addr();
address PI_4 = (address)StubRoutines::x86::_PI_4_addr();
address PI32INV = (address)StubRoutines::x86::_PI32INV_addr();
address SIGN_MASK = (address)StubRoutines::x86::_SIGN_MASK_addr();
address P_1 = (address)StubRoutines::x86::_P_1_addr();
address P_3 = (address)StubRoutines::x86::_P_3_addr();
address ONE = (address)_ONE;
address NEG_ZERO = (address)StubRoutines::x86::_NEG_ZERO_addr();
bind(start);
push(rbx);
subq(rsp, 16);
movsd(Address(rsp, 8), xmm0);
bind(B1_2);
movl(eax, Address(rsp, 12));
movq(xmm1, ExternalAddress(PI32INV)); //0x6dc9c883UL, 0x40245f30UL
andl(eax, 2147418112);
subl(eax, 808452096);
cmpl(eax, 281346048);
jcc(Assembler::above, L_2TAG_PACKET_0_0_1);
mulsd(xmm1, xmm0);
movdqu(xmm5, ExternalAddress(ONEHALF)); //0x00000000UL, 0x3fe00000UL, 0x00000000UL, 0x3fe00000UL
movq(xmm4, ExternalAddress(SIGN_MASK)); //0x00000000UL, 0x80000000UL
pand(xmm4, xmm0);
por(xmm5, xmm4);
addpd(xmm1, xmm5);
cvttsd2sil(edx, xmm1);
cvtsi2sdl(xmm1, edx);
movdqu(xmm2, ExternalAddress(P_2)); //0x1a600000UL, 0x3d90b461UL, 0x1a600000UL, 0x3d90b461UL
movq(xmm3, ExternalAddress(P_1)); //0x54400000UL, 0x3fb921fbUL
mulsd(xmm3, xmm1);
unpcklpd(xmm1, xmm1);
addq(rdx, 1865232);
movdqu(xmm4, xmm0);
andq(rdx, 63);
movdqu(xmm5, ExternalAddress(SC_4)); //0xa556c734UL, 0x3ec71de3UL, 0x1a01a01aUL, 0x3efa01a0UL
lea(rax, ExternalAddress(Ctable));
shlq(rdx, 5);
addq(rax, rdx);
mulpd(xmm2, xmm1);
subsd(xmm0, xmm3);
mulsd(xmm1, ExternalAddress(P_3)); //0x2e037073UL, 0x3b63198aUL
subsd(xmm4, xmm3);
movq(xmm7, Address(rax, 8));
unpcklpd(xmm0, xmm0);
movdqu(xmm3, xmm4);
subsd(xmm4, xmm2);
mulpd(xmm5, xmm0);
subpd(xmm0, xmm2);
movdqu(xmm6, ExternalAddress(SC_2)); //0x11111111UL, 0x3f811111UL, 0x55555555UL, 0x3fa55555UL
mulsd(xmm7, xmm4);
subsd(xmm3, xmm4);
mulpd(xmm5, xmm0);
mulpd(xmm0, xmm0);
subsd(xmm3, xmm2);
movdqu(xmm2, Address(rax, 0));
subsd(xmm1, xmm3);
movq(xmm3, Address(rax, 24));
addsd(xmm2, xmm3);
subsd(xmm7, xmm2);
mulsd(xmm2, xmm4);
mulpd(xmm6, xmm0);
mulsd(xmm3, xmm4);
mulpd(xmm2, xmm0);
mulpd(xmm0, xmm0);
addpd(xmm5, ExternalAddress(SC_3)); //0x1a01a01aUL, 0xbf2a01a0UL, 0x16c16c17UL, 0xbf56c16cUL
mulsd(xmm4, Address(rax, 0));
addpd(xmm6, ExternalAddress(SC_1)); //0x55555555UL, 0xbfc55555UL, 0x00000000UL, 0xbfe00000UL
mulpd(xmm5, xmm0);
movdqu(xmm0, xmm3);
addsd(xmm3, Address(rax, 8));
mulpd(xmm1, xmm7);
movdqu(xmm7, xmm4);
addsd(xmm4, xmm3);
addpd(xmm6, xmm5);
movq(xmm5, Address(rax, 8));
subsd(xmm5, xmm3);
subsd(xmm3, xmm4);
addsd(xmm1, Address(rax, 16));
mulpd(xmm6, xmm2);
addsd(xmm0, xmm5);
addsd(xmm3, xmm7);
addsd(xmm0, xmm1);
addsd(xmm0, xmm3);
addsd(xmm0, xmm6);
unpckhpd(xmm6, xmm6);
addsd(xmm0, xmm6);
addsd(xmm0, xmm4);
jmp(B1_4);
bind(L_2TAG_PACKET_0_0_1);
jcc(Assembler::greater, L_2TAG_PACKET_1_0_1);
pextrw(eax, xmm0, 3);
andl(eax, 32767);
pinsrw(xmm0, eax, 3);
movq(xmm1, ExternalAddress(ONE)); //0x00000000UL, 0x3ff00000UL
subsd(xmm1, xmm0);
movdqu(xmm0, xmm1);
jmp(B1_4);
bind(L_2TAG_PACKET_1_0_1);
pextrw(eax, xmm0, 3);
andl(eax, 32752);
cmpl(eax, 32752);
jcc(Assembler::equal, L_2TAG_PACKET_2_0_1);
pextrw(ecx, xmm0, 3);
andl(ecx, 32752);
subl(ecx, 16224);
shrl(ecx, 7);
andl(ecx, 65532);
lea(r11, ExternalAddress(PI_INV_TABLE));
addq(rcx, r11);
movdq(rax, xmm0);
movl(r10, Address(rcx, 20));
movl(r8, Address(rcx, 24));
movl(edx, eax);
shrq(rax, 21);
orl(eax, INT_MIN);
shrl(eax, 11);
movl(r9, r10);
imulq(r10, rdx);
imulq(r9, rax);
imulq(r8, rax);
movl(rsi, Address(rcx, 16));
movl(rdi, Address(rcx, 12));
movl(r11, r10);
shrq(r10, 32);
addq(r9, r10);
addq(r11, r8);
movl(r8, r11);
shrq(r11, 32);
addq(r9, r11);
movl(r10, rsi);
imulq(rsi, rdx);
imulq(r10, rax);
movl(r11, rdi);
imulq(rdi, rdx);
movl(rbx, rsi);
shrq(rsi, 32);
addq(r9, rbx);
movl(rbx, r9);
shrq(r9, 32);
addq(r10, rsi);
addq(r10, r9);
shlq(rbx, 32);
orq(r8, rbx);
imulq(r11, rax);
movl(r9, Address(rcx, 8));
movl(rsi, Address(rcx, 4));
movl(rbx, rdi);
shrq(rdi, 32);
addq(r10, rbx);
movl(rbx, r10);
shrq(r10, 32);
addq(r11, rdi);
addq(r11, r10);
movq(rdi, r9);
imulq(r9, rdx);
imulq(rdi, rax);
movl(r10, r9);
shrq(r9, 32);
addq(r11, r10);
movl(r10, r11);
shrq(r11, 32);
addq(rdi, r9);
addq(rdi, r11);
movq(r9, rsi);
imulq(rsi, rdx);
imulq(r9, rax);
shlq(r10, 32);
orq(r10, rbx);
movl(eax, Address(rcx, 0));
movl(r11, rsi);
shrq(rsi, 32);
addq(rdi, r11);
movl(r11, rdi);
shrq(rdi, 32);
addq(r9, rsi);
addq(r9, rdi);
imulq(rdx, rax);
pextrw(rbx, xmm0, 3);
lea(rdi, ExternalAddress(PI_INV_TABLE));
subq(rcx, rdi);
addl(ecx, ecx);
addl(ecx, ecx);
addl(ecx, ecx);
addl(ecx, 19);
movl(rsi, 32768);
andl(rsi, rbx);
shrl(rbx, 4);
andl(rbx, 2047);
subl(rbx, 1023);
subl(ecx, rbx);
addq(r9, rdx);
movl(edx, ecx);
addl(edx, 32);
cmpl(ecx, 1);
jcc(Assembler::less, L_2TAG_PACKET_3_0_1);
negl(ecx);
addl(ecx, 29);
shll(r9);
movl(rdi, r9);
andl(r9, 536870911);
testl(r9, 268435456);
jcc(Assembler::notEqual, L_2TAG_PACKET_4_0_1);
shrl(r9);
movl(rbx, 0);
shlq(r9, 32);
orq(r9, r11);
bind(L_2TAG_PACKET_5_0_1);
bind(L_2TAG_PACKET_6_0_1);
cmpq(r9, 0);
jcc(Assembler::equal, L_2TAG_PACKET_7_0_1);
bind(L_2TAG_PACKET_8_0_1);
bsrq(r11, r9);
movl(ecx, 29);
subl(ecx, r11);
jcc(Assembler::lessEqual, L_2TAG_PACKET_9_0_1);
shlq(r9);
movq(rax, r10);
shlq(r10);
addl(edx, ecx);
negl(ecx);
addl(ecx, 64);
shrq(rax);
shrq(r8);
orq(r9, rax);
orq(r10, r8);
bind(L_2TAG_PACKET_10_0_1);
cvtsi2sdq(xmm0, r9);
shrq(r10, 1);
cvtsi2sdq(xmm3, r10);
xorpd(xmm4, xmm4);
shll(edx, 4);
negl(edx);
addl(edx, 16368);
orl(edx, rsi);
xorl(edx, rbx);
pinsrw(xmm4, edx, 3);
movq(xmm2, ExternalAddress(PI_4)); //0x40000000UL, 0x3fe921fbUL, 0x18469899UL, 0x3e64442dUL
movq(xmm6, ExternalAddress(8 + PI_4)); //0x3fe921fbUL, 0x18469899UL, 0x3e64442dUL
xorpd(xmm5, xmm5);
subl(edx, 1008);
pinsrw(xmm5, edx, 3);
mulsd(xmm0, xmm4);
shll(rsi, 16);
sarl(rsi, 31);
mulsd(xmm3, xmm5);
movdqu(xmm1, xmm0);
mulsd(xmm0, xmm2);
shrl(rdi, 29);
addsd(xmm1, xmm3);
mulsd(xmm3, xmm2);
addl(rdi, rsi);
xorl(rdi, rsi);
mulsd(xmm6, xmm1);
movl(eax, rdi);
addsd(xmm6, xmm3);
movdqu(xmm2, xmm0);
addsd(xmm0, xmm6);
subsd(xmm2, xmm0);
addsd(xmm6, xmm2);
bind(L_2TAG_PACKET_11_0_1);
movq(xmm1, ExternalAddress(PI32INV)); //0x6dc9c883UL, 0x40245f30UL
mulsd(xmm1, xmm0);
movq(xmm5, ExternalAddress(ONEHALF)); //0x00000000UL, 0x3fe00000UL, 0x00000000UL, 0x3fe00000UL
movq(xmm4, ExternalAddress(SIGN_MASK)); //0x00000000UL, 0x80000000UL
pand(xmm4, xmm0);
por(xmm5, xmm4);
addpd(xmm1, xmm5);
cvttsd2siq(rdx, xmm1);
cvtsi2sdq(xmm1, rdx);
movq(xmm3, ExternalAddress(P_1)); //0x54400000UL, 0x3fb921fbUL
movdqu(xmm2, ExternalAddress(P_2)); //0x1a600000UL, 0x3d90b461UL, 0x1a600000UL, 0x3d90b461UL
mulsd(xmm3, xmm1);
unpcklpd(xmm1, xmm1);
shll(eax, 3);
addl(edx, 1865232);
movdqu(xmm4, xmm0);
addl(edx, eax);
andl(edx, 63);
movdqu(xmm5, ExternalAddress(SC_4)); //0xa556c734UL, 0x3ec71de3UL, 0x1a01a01aUL, 0x3efa01a0UL
lea(rax, ExternalAddress(Ctable));
shll(edx, 5);
addq(rax, rdx);
mulpd(xmm2, xmm1);
subsd(xmm0, xmm3);
mulsd(xmm1, ExternalAddress(P_3)); //0x2e037073UL, 0x3b63198aUL
subsd(xmm4, xmm3);
movq(xmm7, Address(rax, 8));
unpcklpd(xmm0, xmm0);
movdqu(xmm3, xmm4);
subsd(xmm4, xmm2);
mulpd(xmm5, xmm0);
subpd(xmm0, xmm2);
mulsd(xmm7, xmm4);
subsd(xmm3, xmm4);
mulpd(xmm5, xmm0);
mulpd(xmm0, xmm0);
subsd(xmm3, xmm2);
movdqu(xmm2, Address(rax, 0));
subsd(xmm1, xmm3);
movq(xmm3, Address(rax, 24));
addsd(xmm2, xmm3);
subsd(xmm7, xmm2);
subsd(xmm1, xmm6);
movdqu(xmm6, ExternalAddress(SC_2)); //0x11111111UL, 0x3f811111UL, 0x55555555UL, 0x3fa55555UL
mulsd(xmm2, xmm4);
mulpd(xmm6, xmm0);
mulsd(xmm3, xmm4);
mulpd(xmm2, xmm0);
mulpd(xmm0, xmm0);
addpd(xmm5, ExternalAddress(SC_3)); //0x1a01a01aUL, 0xbf2a01a0UL, 0x16c16c17UL, 0xbf56c16cUL
mulsd(xmm4, Address(rax, 0));
addpd(xmm6, ExternalAddress(SC_1)); //0x55555555UL, 0xbfc55555UL, 0x00000000UL, 0xbfe00000UL
mulpd(xmm5, xmm0);
movdqu(xmm0, xmm3);
addsd(xmm3, Address(rax, 8));
mulpd(xmm1, xmm7);
movdqu(xmm7, xmm4);
addsd(xmm4, xmm3);
addpd(xmm6, xmm5);
movq(xmm5, Address(rax, 8));
subsd(xmm5, xmm3);
subsd(xmm3, xmm4);
addsd(xmm1, Address(rax, 16));
mulpd(xmm6, xmm2);
addsd(xmm5, xmm0);
addsd(xmm3, xmm7);
addsd(xmm1, xmm5);
addsd(xmm1, xmm3);
addsd(xmm1, xmm6);
unpckhpd(xmm6, xmm6);
movdqu(xmm0, xmm4);
addsd(xmm1, xmm6);
addsd(xmm0, xmm1);
jmp(B1_4);
bind(L_2TAG_PACKET_7_0_1);
addl(edx, 64);
movq(r9, r10);
movq(r10, r8);
movl(r8, 0);
cmpq(r9, 0);
jcc(Assembler::notEqual, L_2TAG_PACKET_8_0_1);
addl(edx, 64);
movq(r9, r10);
movq(r10, r8);
cmpq(r9, 0);
jcc(Assembler::notEqual, L_2TAG_PACKET_8_0_1);
xorpd(xmm0, xmm0);
xorpd(xmm6, xmm6);
jmp(L_2TAG_PACKET_11_0_1);
bind(L_2TAG_PACKET_9_0_1);
jcc(Assembler::equal, L_2TAG_PACKET_10_0_1);
negl(ecx);
shrq(r10);
movq(rax, r9);
shrq(r9);
subl(edx, ecx);
negl(ecx);
addl(ecx, 64);
shlq(rax);
orq(r10, rax);
jmp(L_2TAG_PACKET_10_0_1);
bind(L_2TAG_PACKET_3_0_1);
negl(ecx);
shlq(r9, 32);
orq(r9, r11);
shlq(r9);
movq(rdi, r9);
testl(r9, INT_MIN);
jcc(Assembler::notEqual, L_2TAG_PACKET_12_0_1);
shrl(r9);
movl(rbx, 0);
shrq(rdi, 3);
jmp(L_2TAG_PACKET_6_0_1);
bind(L_2TAG_PACKET_4_0_1);
shrl(r9);
movl(rbx, 536870912);
shrl(rbx);
shlq(r9, 32);
orq(r9, r11);
shlq(rbx, 32);
addl(rdi, 536870912);
movl(rcx, 0);
movl(r11, 0);
subq(rcx, r8);
sbbq(r11, r10);
sbbq(rbx, r9);
movq(r8, rcx);
movq(r10, r11);
movq(r9, rbx);
movl(rbx, 32768);
jmp(L_2TAG_PACKET_5_0_1);
bind(L_2TAG_PACKET_12_0_1);
shrl(r9);
mov64(rbx, 0x100000000);
shrq(rbx);
movl(rcx, 0);
movl(r11, 0);
subq(rcx, r8);
sbbq(r11, r10);
sbbq(rbx, r9);
movq(r8, rcx);
movq(r10, r11);
movq(r9, rbx);
movl(rbx, 32768);
shrq(rdi, 3);
addl(rdi, 536870912);
jmp(L_2TAG_PACKET_6_0_1);
bind(L_2TAG_PACKET_2_0_1);
movsd(xmm0, Address(rsp, 8));
mulsd(xmm0, ExternalAddress(NEG_ZERO)); //0x00000000UL, 0x80000000UL
movq(Address(rsp, 0), xmm0);
bind(L_2TAG_PACKET_13_0_1);
bind(B1_4);
addq(rsp, 16);
pop(rbx);
}
#else
// The 32 bit code is at most SSE2 compliant
ALIGNED_(16) juint _static_const_table_cos[] =
{
0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
0x00000000UL, 0x00000000UL, 0x3ff00000UL, 0x176d6d31UL, 0xbf73b92eUL,
0xbc29b42cUL, 0x3fb917a6UL, 0xe0000000UL, 0xbc3e2718UL, 0x00000000UL,
0x3ff00000UL, 0x011469fbUL, 0xbf93ad06UL, 0x3c69a60bUL, 0x3fc8f8b8UL,
0xc0000000UL, 0xbc626d19UL, 0x00000000UL, 0x3ff00000UL, 0x939d225aUL,
0xbfa60beaUL, 0x2ed59f06UL, 0x3fd29406UL, 0xa0000000UL, 0xbc75d28dUL,
0x00000000UL, 0x3ff00000UL, 0x866b95cfUL, 0xbfb37ca1UL, 0xa6aea963UL,
0x3fd87de2UL, 0xe0000000UL, 0xbc672cedUL, 0x00000000UL, 0x3ff00000UL,
0x73fa1279UL, 0xbfbe3a68UL, 0x3806f63bUL, 0x3fde2b5dUL, 0x20000000UL,
0x3c5e0d89UL, 0x00000000UL, 0x3ff00000UL, 0x5bc57974UL, 0xbfc59267UL,
0x39ae68c8UL, 0x3fe1c73bUL, 0x20000000UL, 0x3c8b25ddUL, 0x00000000UL,
0x3ff00000UL, 0x53aba2fdUL, 0xbfcd0dfeUL, 0x25091dd6UL, 0x3fe44cf3UL,
0x20000000UL, 0x3c68076aUL, 0x00000000UL, 0x3ff00000UL, 0x99fcef32UL,
0x3fca8279UL, 0x667f3bcdUL, 0x3fe6a09eUL, 0x20000000UL, 0xbc8bdd34UL,
0x00000000UL, 0x3fe00000UL, 0x94247758UL, 0x3fc133ccUL, 0x6b151741UL,
0x3fe8bc80UL, 0x20000000UL, 0xbc82c5e1UL, 0x00000000UL, 0x3fe00000UL,
0x9ae68c87UL, 0x3fac73b3UL, 0x290ea1a3UL, 0x3fea9b66UL, 0xe0000000UL,
0x3c39f630UL, 0x00000000UL, 0x3fe00000UL, 0x7f909c4eUL, 0xbf9d4a2cUL,
0xf180bdb1UL, 0x3fec38b2UL, 0x80000000UL, 0xbc76e0b1UL, 0x00000000UL,
0x3fe00000UL, 0x65455a75UL, 0xbfbe0875UL, 0xcf328d46UL, 0x3fed906bUL,
0x20000000UL, 0x3c7457e6UL, 0x00000000UL, 0x3fe00000UL, 0x76acf82dUL,
0x3fa4a031UL, 0x56c62ddaUL, 0x3fee9f41UL, 0xe0000000UL, 0x3c8760b1UL,
0x00000000UL, 0x3fd00000UL, 0x0e5967d5UL, 0xbfac1d1fUL, 0xcff75cb0UL,
0x3fef6297UL, 0x20000000UL, 0x3c756217UL, 0x00000000UL, 0x3fd00000UL,
0x0f592f50UL, 0xbf9ba165UL, 0xa3d12526UL, 0x3fefd88dUL, 0x40000000UL,
0xbc887df6UL, 0x00000000UL, 0x3fc00000UL, 0x00000000UL, 0x00000000UL,
0x00000000UL, 0x3ff00000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
0x00000000UL, 0x0f592f50UL, 0x3f9ba165UL, 0xa3d12526UL, 0x3fefd88dUL,
0x40000000UL, 0xbc887df6UL, 0x00000000UL, 0xbfc00000UL, 0x0e5967d5UL,
0x3fac1d1fUL, 0xcff75cb0UL, 0x3fef6297UL, 0x20000000UL, 0x3c756217UL,
0x00000000UL, 0xbfd00000UL, 0x76acf82dUL, 0xbfa4a031UL, 0x56c62ddaUL,
0x3fee9f41UL, 0xe0000000UL, 0x3c8760b1UL, 0x00000000UL, 0xbfd00000UL,
0x65455a75UL, 0x3fbe0875UL, 0xcf328d46UL, 0x3fed906bUL, 0x20000000UL,
0x3c7457e6UL, 0x00000000UL, 0xbfe00000UL, 0x7f909c4eUL, 0x3f9d4a2cUL,
0xf180bdb1UL, 0x3fec38b2UL, 0x80000000UL, 0xbc76e0b1UL, 0x00000000UL,
0xbfe00000UL, 0x9ae68c87UL, 0xbfac73b3UL, 0x290ea1a3UL, 0x3fea9b66UL,
0xe0000000UL, 0x3c39f630UL, 0x00000000UL, 0xbfe00000UL, 0x94247758UL,
0xbfc133ccUL, 0x6b151741UL, 0x3fe8bc80UL, 0x20000000UL, 0xbc82c5e1UL,
0x00000000UL, 0xbfe00000UL, 0x99fcef32UL, 0xbfca8279UL, 0x667f3bcdUL,
0x3fe6a09eUL, 0x20000000UL, 0xbc8bdd34UL, 0x00000000UL, 0xbfe00000UL,
0x53aba2fdUL, 0x3fcd0dfeUL, 0x25091dd6UL, 0x3fe44cf3UL, 0x20000000UL,
0x3c68076aUL, 0x00000000UL, 0xbff00000UL, 0x5bc57974UL, 0x3fc59267UL,
0x39ae68c8UL, 0x3fe1c73bUL, 0x20000000UL, 0x3c8b25ddUL, 0x00000000UL,
0xbff00000UL, 0x73fa1279UL, 0x3fbe3a68UL, 0x3806f63bUL, 0x3fde2b5dUL,
0x20000000UL, 0x3c5e0d89UL, 0x00000000UL, 0xbff00000UL, 0x866b95cfUL,
0x3fb37ca1UL, 0xa6aea963UL, 0x3fd87de2UL, 0xe0000000UL, 0xbc672cedUL,
0x00000000UL, 0xbff00000UL, 0x939d225aUL, 0x3fa60beaUL, 0x2ed59f06UL,
0x3fd29406UL, 0xa0000000UL, 0xbc75d28dUL, 0x00000000UL, 0xbff00000UL,
0x011469fbUL, 0x3f93ad06UL, 0x3c69a60bUL, 0x3fc8f8b8UL, 0xc0000000UL,
0xbc626d19UL, 0x00000000UL, 0xbff00000UL, 0x176d6d31UL, 0x3f73b92eUL,
0xbc29b42cUL, 0x3fb917a6UL, 0xe0000000UL, 0xbc3e2718UL, 0x00000000UL,
0xbff00000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
0x00000000UL, 0x00000000UL, 0x00000000UL, 0xbff00000UL, 0x176d6d31UL,
0x3f73b92eUL, 0xbc29b42cUL, 0xbfb917a6UL, 0xe0000000UL, 0x3c3e2718UL,
0x00000000UL, 0xbff00000UL, 0x011469fbUL, 0x3f93ad06UL, 0x3c69a60bUL,
0xbfc8f8b8UL, 0xc0000000UL, 0x3c626d19UL, 0x00000000UL, 0xbff00000UL,
0x939d225aUL, 0x3fa60beaUL, 0x2ed59f06UL, 0xbfd29406UL, 0xa0000000UL,
0x3c75d28dUL, 0x00000000UL, 0xbff00000UL, 0x866b95cfUL, 0x3fb37ca1UL,
0xa6aea963UL, 0xbfd87de2UL, 0xe0000000UL, 0x3c672cedUL, 0x00000000UL,
0xbff00000UL, 0x73fa1279UL, 0x3fbe3a68UL, 0x3806f63bUL, 0xbfde2b5dUL,
0x20000000UL, 0xbc5e0d89UL, 0x00000000UL, 0xbff00000UL, 0x5bc57974UL,
0x3fc59267UL, 0x39ae68c8UL, 0xbfe1c73bUL, 0x20000000UL, 0xbc8b25ddUL,
0x00000000UL, 0xbff00000UL, 0x53aba2fdUL, 0x3fcd0dfeUL, 0x25091dd6UL,
0xbfe44cf3UL, 0x20000000UL, 0xbc68076aUL, 0x00000000UL, 0xbff00000UL,
0x99fcef32UL, 0xbfca8279UL, 0x667f3bcdUL, 0xbfe6a09eUL, 0x20000000UL,
0x3c8bdd34UL, 0x00000000UL, 0xbfe00000UL, 0x94247758UL, 0xbfc133ccUL,
0x6b151741UL, 0xbfe8bc80UL, 0x20000000UL, 0x3c82c5e1UL, 0x00000000UL,
0xbfe00000UL, 0x9ae68c87UL, 0xbfac73b3UL, 0x290ea1a3UL, 0xbfea9b66UL,
0xe0000000UL, 0xbc39f630UL, 0x00000000UL, 0xbfe00000UL, 0x7f909c4eUL,
0x3f9d4a2cUL, 0xf180bdb1UL, 0xbfec38b2UL, 0x80000000UL, 0x3c76e0b1UL,
0x00000000UL, 0xbfe00000UL, 0x65455a75UL, 0x3fbe0875UL, 0xcf328d46UL,
0xbfed906bUL, 0x20000000UL, 0xbc7457e6UL, 0x00000000UL, 0xbfe00000UL,
0x76acf82dUL, 0xbfa4a031UL, 0x56c62ddaUL, 0xbfee9f41UL, 0xe0000000UL,
0xbc8760b1UL, 0x00000000UL, 0xbfd00000UL, 0x0e5967d5UL, 0x3fac1d1fUL,
0xcff75cb0UL, 0xbfef6297UL, 0x20000000UL, 0xbc756217UL, 0x00000000UL,
0xbfd00000UL, 0x0f592f50UL, 0x3f9ba165UL, 0xa3d12526UL, 0xbfefd88dUL,
0x40000000UL, 0x3c887df6UL, 0x00000000UL, 0xbfc00000UL, 0x00000000UL,
0x00000000UL, 0x00000000UL, 0xbff00000UL, 0x00000000UL, 0x00000000UL,
0x00000000UL, 0x00000000UL, 0x0f592f50UL, 0xbf9ba165UL, 0xa3d12526UL,
0xbfefd88dUL, 0x40000000UL, 0x3c887df6UL, 0x00000000UL, 0x3fc00000UL,
0x0e5967d5UL, 0xbfac1d1fUL, 0xcff75cb0UL, 0xbfef6297UL, 0x20000000UL,
0xbc756217UL, 0x00000000UL, 0x3fd00000UL, 0x76acf82dUL, 0x3fa4a031UL,
0x56c62ddaUL, 0xbfee9f41UL, 0xe0000000UL, 0xbc8760b1UL, 0x00000000UL,
0x3fd00000UL, 0x65455a75UL, 0xbfbe0875UL, 0xcf328d46UL, 0xbfed906bUL,
0x20000000UL, 0xbc7457e6UL, 0x00000000UL, 0x3fe00000UL, 0x7f909c4eUL,
0xbf9d4a2cUL, 0xf180bdb1UL, 0xbfec38b2UL, 0x80000000UL, 0x3c76e0b1UL,
0x00000000UL, 0x3fe00000UL, 0x9ae68c87UL, 0x3fac73b3UL, 0x290ea1a3UL,
0xbfea9b66UL, 0xe0000000UL, 0xbc39f630UL, 0x00000000UL, 0x3fe00000UL,
0x94247758UL, 0x3fc133ccUL, 0x6b151741UL, 0xbfe8bc80UL, 0x20000000UL,
0x3c82c5e1UL, 0x00000000UL, 0x3fe00000UL, 0x99fcef32UL, 0x3fca8279UL,
0x667f3bcdUL, 0xbfe6a09eUL, 0x20000000UL, 0x3c8bdd34UL, 0x00000000UL,
0x3fe00000UL, 0x53aba2fdUL, 0xbfcd0dfeUL, 0x25091dd6UL, 0xbfe44cf3UL,
0x20000000UL, 0xbc68076aUL, 0x00000000UL, 0x3ff00000UL, 0x5bc57974UL,
0xbfc59267UL, 0x39ae68c8UL, 0xbfe1c73bUL, 0x20000000UL, 0xbc8b25ddUL,
0x00000000UL, 0x3ff00000UL, 0x73fa1279UL, 0xbfbe3a68UL, 0x3806f63bUL,
0xbfde2b5dUL, 0x20000000UL, 0xbc5e0d89UL, 0x00000000UL, 0x3ff00000UL,
0x866b95cfUL, 0xbfb37ca1UL, 0xa6aea963UL, 0xbfd87de2UL, 0xe0000000UL,
0x3c672cedUL, 0x00000000UL, 0x3ff00000UL, 0x939d225aUL, 0xbfa60beaUL,
0x2ed59f06UL, 0xbfd29406UL, 0xa0000000UL, 0x3c75d28dUL, 0x00000000UL,
0x3ff00000UL, 0x011469fbUL, 0xbf93ad06UL, 0x3c69a60bUL, 0xbfc8f8b8UL,
0xc0000000UL, 0x3c626d19UL, 0x00000000UL, 0x3ff00000UL, 0x176d6d31UL,
0xbf73b92eUL, 0xbc29b42cUL, 0xbfb917a6UL, 0xe0000000UL, 0x3c3e2718UL,
0x00000000UL, 0x3ff00000UL, 0x55555555UL, 0xbfc55555UL, 0x00000000UL,
0xbfe00000UL, 0x11111111UL, 0x3f811111UL, 0x55555555UL, 0x3fa55555UL,
0x1a01a01aUL, 0xbf2a01a0UL, 0x16c16c17UL, 0xbf56c16cUL, 0xa556c734UL,
0x3ec71de3UL, 0x1a01a01aUL, 0x3efa01a0UL, 0x1a600000UL, 0x3d90b461UL,
0x1a600000UL, 0x3d90b461UL, 0x54400000UL, 0x3fb921fbUL, 0x00000000UL,
0x00000000UL, 0x2e037073UL, 0x3b63198aUL, 0x00000000UL, 0x00000000UL,
0x6dc9c883UL, 0x40245f30UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
0x43380000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x3ff00000UL,
0x00000000UL, 0x00000000UL, 0x00000000UL, 0x80000000UL, 0x00000000UL,
0x00000000UL, 0x00000000UL, 0x80000000UL, 0x00000000UL, 0x00000000UL,
0x00000000UL, 0x3fe00000UL, 0x00000000UL, 0x3fe00000UL
};
//registers,
// input: (rbp + 8)
// scratch: xmm1, xmm2, xmm3, xmm4, xmm5, xmm6, xmm7
// rax, rdx, rcx, rbx (tmp)
// Code generated by Intel C compiler for LIBM library
void MacroAssembler::fast_cos(XMMRegister xmm0, XMMRegister xmm1, XMMRegister xmm2, XMMRegister xmm3, XMMRegister xmm4, XMMRegister xmm5, XMMRegister xmm6, XMMRegister xmm7, Register eax, Register ecx, Register edx, Register tmp) {
Label L_2TAG_PACKET_0_0_2, L_2TAG_PACKET_1_0_2, L_2TAG_PACKET_2_0_2, L_2TAG_PACKET_3_0_2;
Label L_2TAG_PACKET_4_0_2, L_2TAG_PACKET_5_0_2, L_2TAG_PACKET_6_0_2, L_2TAG_PACKET_7_0_2;
Label L_2TAG_PACKET_8_0_2, L_2TAG_PACKET_9_0_2, L_2TAG_PACKET_10_0_2, L_2TAG_PACKET_11_0_2;
Label L_2TAG_PACKET_12_0_2, L_2TAG_PACKET_13_0_2, B1_3, B1_5, start;
assert_different_registers(tmp, eax, ecx, edx);
address static_const_table_cos = (address)_static_const_table_cos;
bind(start);
subl(rsp, 120);
movl(Address(rsp, 56), tmp);
lea(tmp, ExternalAddress(static_const_table_cos));
movsd(xmm0, Address(rsp, 128));
pextrw(eax, xmm0, 3);
andl(eax, 32767);
subl(eax, 12336);
cmpl(eax, 4293);
jcc(Assembler::above, L_2TAG_PACKET_0_0_2);
movsd(xmm1, Address(tmp, 2160));
mulsd(xmm1, xmm0);
movdqu(xmm5, Address(tmp, 2240));
movsd(xmm4, Address(tmp, 2224));
pand(xmm4, xmm0);
por(xmm5, xmm4);
movsd(xmm3, Address(tmp, 2128));
movdqu(xmm2, Address(tmp, 2112));
addpd(xmm1, xmm5);
cvttsd2sil(edx, xmm1);
cvtsi2sdl(xmm1, edx);
mulsd(xmm3, xmm1);
unpcklpd(xmm1, xmm1);
addl(edx, 1865232);
movdqu(xmm4, xmm0);
andl(edx, 63);
movdqu(xmm5, Address(tmp, 2096));
lea(eax, Address(tmp, 0));
shll(edx, 5);
addl(eax, edx);
mulpd(xmm2, xmm1);
subsd(xmm0, xmm3);
mulsd(xmm1, Address(tmp, 2144));
subsd(xmm4, xmm3);
movsd(xmm7, Address(eax, 8));
unpcklpd(xmm0, xmm0);
movapd(xmm3, xmm4);
subsd(xmm4, xmm2);
mulpd(xmm5, xmm0);
subpd(xmm0, xmm2);
movdqu(xmm6, Address(tmp, 2064));
mulsd(xmm7, xmm4);
subsd(xmm3, xmm4);
mulpd(xmm5, xmm0);
mulpd(xmm0, xmm0);
subsd(xmm3, xmm2);
movdqu(xmm2, Address(eax, 0));
subsd(xmm1, xmm3);
movsd(xmm3, Address(eax, 24));
addsd(xmm2, xmm3);
subsd(xmm7, xmm2);
mulsd(xmm2, xmm4);
mulpd(xmm6, xmm0);
mulsd(xmm3, xmm4);
mulpd(xmm2, xmm0);
mulpd(xmm0, xmm0);
addpd(xmm5, Address(tmp, 2080));
mulsd(xmm4, Address(eax, 0));
addpd(xmm6, Address(tmp, 2048));
mulpd(xmm5, xmm0);
movapd(xmm0, xmm3);
addsd(xmm3, Address(eax, 8));
mulpd(xmm1, xmm7);
movapd(xmm7, xmm4);
addsd(xmm4, xmm3);
addpd(xmm6, xmm5);
movsd(xmm5, Address(eax, 8));
subsd(xmm5, xmm3);
subsd(xmm3, xmm4);
addsd(xmm1, Address(eax, 16));
mulpd(xmm6, xmm2);
addsd(xmm5, xmm0);
addsd(xmm3, xmm7);
addsd(xmm1, xmm5);
addsd(xmm1, xmm3);
addsd(xmm1, xmm6);
unpckhpd(xmm6, xmm6);
addsd(xmm1, xmm6);
addsd(xmm4, xmm1);
movsd(Address(rsp, 0), xmm4);
fld_d(Address(rsp, 0));
jmp(L_2TAG_PACKET_1_0_2);
bind(L_2TAG_PACKET_0_0_2);
jcc(Assembler::greater, L_2TAG_PACKET_2_0_2);
pextrw(eax, xmm0, 3);
andl(eax, 32767);
pinsrw(xmm0, eax, 3);
movsd(xmm1, Address(tmp, 2192));
subsd(xmm1, xmm0);
movsd(Address(rsp, 0), xmm1);
fld_d(Address(rsp, 0));
jmp(L_2TAG_PACKET_1_0_2);
bind(L_2TAG_PACKET_2_0_2);
movl(eax, Address(rsp, 132));
andl(eax, 2146435072);
cmpl(eax, 2146435072);
jcc(Assembler::equal, L_2TAG_PACKET_3_0_2);
subl(rsp, 32);
movsd(Address(rsp, 0), xmm0);
lea(eax, Address(rsp, 40));
movl(Address(rsp, 8), eax);
movl(eax, 1);
movl(Address(rsp, 12), eax);
call(RuntimeAddress(CAST_FROM_FN_PTR(address, StubRoutines::dlibm_sin_cos_huge())));
addl(rsp, 32);
fld_d(Address(rsp, 8));
jmp(L_2TAG_PACKET_1_0_2);
bind(L_2TAG_PACKET_3_0_2);
fld_d(Address(rsp, 128));
fmul_d(Address(tmp, 2208));
bind(L_2TAG_PACKET_1_0_2);
movl(tmp, Address(rsp, 56));
}
#endif