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/* Copyright (c) 2018, Cavium. All rights reserved. (By BELLSOFT)
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* Copyright (c) 2016, Intel Corporation.
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* Intel Math Library (LIBM) Source Code
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*
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* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
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*
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* This code is free software; you can redistribute it and/or modify it
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* under the terms of the GNU General Public License version 2 only, as
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* published by the Free Software Foundation.
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*
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* This code is distributed in the hope that it will be useful, but WITHOUT
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* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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* version 2 for more details (a copy is included in the LICENSE file that
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* accompanied this code).
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*
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* You should have received a copy of the GNU General Public License version
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* 2 along with this work; if not, write to the Free Software Foundation,
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* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
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*
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* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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* or visit www.oracle.com if you need additional information or have any
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* questions.
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*
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*/
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#include "precompiled.hpp"
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#include "asm/assembler.hpp"
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#include "asm/assembler.inline.hpp"
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#include "macroAssembler_aarch64.hpp"
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// Algorithm idea is taken from x86 hotspot intrinsic and adapted for AARCH64.
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//
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// For mathematical background please refer to the following literature:
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//
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// Tang, Ping-Tak Peter.
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// Table-driven implementation of the logarithm function
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// in IEEE floating-point arithmetic.
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// ACM Transactions on Mathematical Software (TOMS) 16, no. 4, 1990: 378-400.
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/******************************************************************************/
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// ALGORITHM DESCRIPTION - LOG()
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// ---------------------
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//
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// x=2^k * mx, mx in [1,2)
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//
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// Get B~1/mx based on the output of frecpe instruction (B0)
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// B = int((B0*2^7+0.5))/2^7
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//
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// Reduced argument: r=B*mx-1.0 (computed accurately in high and low parts)
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//
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// Result: k*log(2) - log(B) + p(r) if |x-1| >= small value (2^-6) and
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// p(r) is a degree 7 polynomial
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// -log(B) read from data table (high, low parts)
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// Result is formed from high and low parts
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//
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// Special cases:
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// 1. log(NaN) = quiet NaN
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// 2. log(+INF) = that INF
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// 3. log(0) = -INF
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// 4. log(1) = +0
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// 5. log(x) = NaN if x < -0, including -INF
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//
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/******************************************************************************/
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// Table with p(r) polynomial coefficients
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// and table representation of logarithm values (hi and low parts)
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__attribute__ ((aligned(64))) juint _L_tbl[] =
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{
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// coefficients of p(r) polynomial:
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// _coeff[]
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0x00000000UL, 0xbfd00000UL, // C1_0 = -0.25
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0x92492492UL, 0x3fc24924UL, // C1_1 = 0.14285714285714285
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0x55555555UL, 0x3fd55555UL, // C2_0 = 0.3333333333333333
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0x3d6fb175UL, 0xbfc5555eUL, // C2_1 = -0.16666772842235003
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0x00000000UL, 0xbfe00000UL, // C3_0 = -0.5
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0x9999999aUL, 0x3fc99999UL, // C3_1 = 0.2
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// _log2[]
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0xfefa3800UL, 0x3fa62e42UL, // C4_0 = 0.043321698784993146
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0x93c76730UL, 0x3ceef357UL, // C4_1 = 3.436201886692732e-15
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// _L_tbl[] with logarithm values (hi and low parts)
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0xfefa3800UL, 0x3fe62e42UL, 0x93c76730UL, 0x3d2ef357UL, 0xaa241800UL,
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0x3fe5ee82UL, 0x0cda46beUL, 0x3d220238UL, 0x5c364800UL, 0x3fe5af40UL,
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0xac10c9fbUL, 0x3d2dfa63UL, 0x26bb8c00UL, 0x3fe5707aUL, 0xff3303ddUL,
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0x3d09980bUL, 0x26867800UL, 0x3fe5322eUL, 0x5d257531UL, 0x3d05ccc4UL,
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0x835a5000UL, 0x3fe4f45aUL, 0x6d93b8fbUL, 0xbd2e6c51UL, 0x6f970c00UL,
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0x3fe4b6fdUL, 0xed4c541cUL, 0x3cef7115UL, 0x27e8a400UL, 0x3fe47a15UL,
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0xf94d60aaUL, 0xbd22cb6aUL, 0xf2f92400UL, 0x3fe43d9fUL, 0x481051f7UL,
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0xbcfd984fUL, 0x2125cc00UL, 0x3fe4019cUL, 0x30f0c74cUL, 0xbd26ce79UL,
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0x0c36c000UL, 0x3fe3c608UL, 0x7cfe13c2UL, 0xbd02b736UL, 0x17197800UL,
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0x3fe38ae2UL, 0xbb5569a4UL, 0xbd218b7aUL, 0xad9d8c00UL, 0x3fe35028UL,
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0x9527e6acUL, 0x3d10b83fUL, 0x44340800UL, 0x3fe315daUL, 0xc5a0ed9cUL,
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0xbd274e93UL, 0x57b0e000UL, 0x3fe2dbf5UL, 0x07b9dc11UL, 0xbd17a6e5UL,
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0x6d0ec000UL, 0x3fe2a278UL, 0xe797882dUL, 0x3d206d2bUL, 0x1134dc00UL,
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0x3fe26962UL, 0x05226250UL, 0xbd0b61f1UL, 0xd8bebc00UL, 0x3fe230b0UL,
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0x6e48667bUL, 0x3d12fc06UL, 0x5fc61800UL, 0x3fe1f863UL, 0xc9fe81d3UL,
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0xbd2a7242UL, 0x49ae6000UL, 0x3fe1c078UL, 0xed70e667UL, 0x3cccacdeUL,
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0x40f23c00UL, 0x3fe188eeUL, 0xf8ab4650UL, 0x3d14cc4eUL, 0xf6f29800UL,
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0x3fe151c3UL, 0xa293ae49UL, 0xbd2edd97UL, 0x23c75c00UL, 0x3fe11af8UL,
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0xbb9ddcb2UL, 0xbd258647UL, 0x8611cc00UL, 0x3fe0e489UL, 0x07801742UL,
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0x3d1c2998UL, 0xe2d05400UL, 0x3fe0ae76UL, 0x887e7e27UL, 0x3d1f486bUL,
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0x0533c400UL, 0x3fe078bfUL, 0x41edf5fdUL, 0x3d268122UL, 0xbe760400UL,
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0x3fe04360UL, 0xe79539e0UL, 0xbd04c45fUL, 0xe5b20800UL, 0x3fe00e5aUL,
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0xb1727b1cUL, 0xbd053ba3UL, 0xaf7a4800UL, 0x3fdfb358UL, 0x3c164935UL,
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0x3d0085faUL, 0xee031800UL, 0x3fdf4aa7UL, 0x6f014a8bUL, 0x3d12cde5UL,
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0x56b41000UL, 0x3fdee2a1UL, 0x5a470251UL, 0x3d2f27f4UL, 0xc3ddb000UL,
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0x3fde7b42UL, 0x5372bd08UL, 0xbd246550UL, 0x1a272800UL, 0x3fde148aUL,
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0x07322938UL, 0xbd1326b2UL, 0x484c9800UL, 0x3fddae75UL, 0x60dc616aUL,
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0xbd1ea42dUL, 0x46def800UL, 0x3fdd4902UL, 0xe9a767a8UL, 0x3d235bafUL,
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0x18064800UL, 0x3fdce42fUL, 0x3ec7a6b0UL, 0xbd0797c3UL, 0xc7455800UL,
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0x3fdc7ff9UL, 0xc15249aeUL, 0xbd29b6ddUL, 0x693fa000UL, 0x3fdc1c60UL,
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0x7fe8e180UL, 0x3d2cec80UL, 0x1b80e000UL, 0x3fdbb961UL, 0xf40a666dUL,
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0x3d27d85bUL, 0x04462800UL, 0x3fdb56faUL, 0x2d841995UL, 0x3d109525UL,
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0x5248d000UL, 0x3fdaf529UL, 0x52774458UL, 0xbd217cc5UL, 0x3c8ad800UL,
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0x3fda93edUL, 0xbea77a5dUL, 0x3d1e36f2UL, 0x0224f800UL, 0x3fda3344UL,
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0x7f9d79f5UL, 0x3d23c645UL, 0xea15f000UL, 0x3fd9d32bUL, 0x10d0c0b0UL,
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0xbd26279eUL, 0x43135800UL, 0x3fd973a3UL, 0xa502d9f0UL, 0xbd152313UL,
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0x635bf800UL, 0x3fd914a8UL, 0x2ee6307dUL, 0xbd1766b5UL, 0xa88b3000UL,
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0x3fd8b639UL, 0xe5e70470UL, 0xbd205ae1UL, 0x776dc800UL, 0x3fd85855UL,
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0x3333778aUL, 0x3d2fd56fUL, 0x3bd81800UL, 0x3fd7fafaUL, 0xc812566aUL,
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0xbd272090UL, 0x687cf800UL, 0x3fd79e26UL, 0x2efd1778UL, 0x3d29ec7dUL,
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0x76c67800UL, 0x3fd741d8UL, 0x49dc60b3UL, 0x3d2d8b09UL, 0xe6af1800UL,
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0x3fd6e60eUL, 0x7c222d87UL, 0x3d172165UL, 0x3e9c6800UL, 0x3fd68ac8UL,
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0x2756eba0UL, 0x3d20a0d3UL, 0x0b3ab000UL, 0x3fd63003UL, 0xe731ae00UL,
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0xbd2db623UL, 0xdf596000UL, 0x3fd5d5bdUL, 0x08a465dcUL, 0xbd0a0b2aUL,
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0x53c8d000UL, 0x3fd57bf7UL, 0xee5d40efUL, 0x3d1fadedUL, 0x0738a000UL,
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0x3fd522aeUL, 0x8164c759UL, 0x3d2ebe70UL, 0x9e173000UL, 0x3fd4c9e0UL,
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0x1b0ad8a4UL, 0xbd2e2089UL, 0xc271c800UL, 0x3fd4718dUL, 0x0967d675UL,
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0xbd2f27ceUL, 0x23d5e800UL, 0x3fd419b4UL, 0xec90e09dUL, 0x3d08e436UL,
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0x77333000UL, 0x3fd3c252UL, 0xb606bd5cUL, 0x3d183b54UL, 0x76be1000UL,
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0x3fd36b67UL, 0xb0f177c8UL, 0x3d116ecdUL, 0xe1d36000UL, 0x3fd314f1UL,
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0xd3213cb8UL, 0xbd28e27aUL, 0x7cdc9000UL, 0x3fd2bef0UL, 0x4a5004f4UL,
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0x3d2a9cfaUL, 0x1134d800UL, 0x3fd26962UL, 0xdf5bb3b6UL, 0x3d2c93c1UL,
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0x6d0eb800UL, 0x3fd21445UL, 0xba46baeaUL, 0x3d0a87deUL, 0x635a6800UL,
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0x3fd1bf99UL, 0x5147bdb7UL, 0x3d2ca6edUL, 0xcbacf800UL, 0x3fd16b5cUL,
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0xf7a51681UL, 0x3d2b9acdUL, 0x8227e800UL, 0x3fd1178eUL, 0x63a5f01cUL,
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0xbd2c210eUL, 0x67616000UL, 0x3fd0c42dUL, 0x163ceae9UL, 0x3d27188bUL,
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0x604d5800UL, 0x3fd07138UL, 0x16ed4e91UL, 0x3cf89cdbUL, 0x5626c800UL,
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0x3fd01eaeUL, 0x1485e94aUL, 0xbd16f08cUL, 0x6cb3b000UL, 0x3fcf991cUL,
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0xca0cdf30UL, 0x3d1bcbecUL, 0xe4dd0000UL, 0x3fcef5adUL, 0x65bb8e11UL,
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0xbcca2115UL, 0xffe71000UL, 0x3fce530eUL, 0x6041f430UL, 0x3cc21227UL,
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0xb0d49000UL, 0x3fcdb13dUL, 0xf715b035UL, 0xbd2aff2aUL, 0xf2656000UL,
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0x3fcd1037UL, 0x75b6f6e4UL, 0xbd084a7eUL, 0xc6f01000UL, 0x3fcc6ffbUL,
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0xc5962bd2UL, 0xbcf1ec72UL, 0x383be000UL, 0x3fcbd087UL, 0x595412b6UL,
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0xbd2d4bc4UL, 0x575bd000UL, 0x3fcb31d8UL, 0x4eace1aaUL, 0xbd0c358dUL,
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0x3c8ae000UL, 0x3fca93edUL, 0x50562169UL, 0xbd287243UL, 0x07089000UL,
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0x3fc9f6c4UL, 0x6865817aUL, 0x3d29904dUL, 0xdcf70000UL, 0x3fc95a5aUL,
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148 |
0x58a0ff6fUL, 0x3d07f228UL, 0xeb390000UL, 0x3fc8beafUL, 0xaae92cd1UL,
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149 |
0xbd073d54UL, 0x6551a000UL, 0x3fc823c1UL, 0x9a631e83UL, 0x3d1e0ddbUL,
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0x85445000UL, 0x3fc7898dUL, 0x70914305UL, 0xbd1c6610UL, 0x8b757000UL,
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0x3fc6f012UL, 0xe59c21e1UL, 0xbd25118dUL, 0xbe8c1000UL, 0x3fc6574eUL,
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152 |
0x2c3c2e78UL, 0x3d19cf8bUL, 0x6b544000UL, 0x3fc5bf40UL, 0xeb68981cUL,
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153 |
0xbd127023UL, 0xe4a1b000UL, 0x3fc527e5UL, 0xe5697dc7UL, 0x3d2633e8UL,
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154 |
0x8333b000UL, 0x3fc4913dUL, 0x54fdb678UL, 0x3d258379UL, 0xa5993000UL,
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0x3fc3fb45UL, 0x7e6a354dUL, 0xbd2cd1d8UL, 0xb0159000UL, 0x3fc365fcUL,
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156 |
0x234b7289UL, 0x3cc62fa8UL, 0x0c868000UL, 0x3fc2d161UL, 0xcb81b4a1UL,
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157 |
0x3d039d6cUL, 0x2a49c000UL, 0x3fc23d71UL, 0x8fd3df5cUL, 0x3d100d23UL,
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158 |
0x7e23f000UL, 0x3fc1aa2bUL, 0x44389934UL, 0x3d2ca78eUL, 0x8227e000UL,
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159 |
0x3fc1178eUL, 0xce2d07f2UL, 0x3d21ef78UL, 0xb59e4000UL, 0x3fc08598UL,
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160 |
0x7009902cUL, 0xbd27e5ddUL, 0x39dbe000UL, 0x3fbfe891UL, 0x4fa10afdUL,
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161 |
0xbd2534d6UL, 0x830a2000UL, 0x3fbec739UL, 0xafe645e0UL, 0xbd2dc068UL,
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162 |
0x63844000UL, 0x3fbda727UL, 0x1fa71733UL, 0x3d1a8940UL, 0x01bc4000UL,
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163 |
0x3fbc8858UL, 0xc65aacd3UL, 0x3d2646d1UL, 0x8dad6000UL, 0x3fbb6ac8UL,
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164 |
0x2bf768e5UL, 0xbd139080UL, 0x40b1c000UL, 0x3fba4e76UL, 0xb94407c8UL,
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165 |
0xbd0e42b6UL, 0x5d594000UL, 0x3fb9335eUL, 0x3abd47daUL, 0x3d23115cUL,
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166 |
0x2f40e000UL, 0x3fb8197eUL, 0xf96ffdf7UL, 0x3d0f80dcUL, 0x0aeac000UL,
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167 |
0x3fb700d3UL, 0xa99ded32UL, 0x3cec1e8dUL, 0x4d97a000UL, 0x3fb5e95aUL,
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168 |
0x3c5d1d1eUL, 0xbd2c6906UL, 0x5d208000UL, 0x3fb4d311UL, 0x82f4e1efUL,
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169 |
0xbcf53a25UL, 0xa7d1e000UL, 0x3fb3bdf5UL, 0xa5db4ed7UL, 0x3d2cc85eUL,
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170 |
0xa4472000UL, 0x3fb2aa04UL, 0xae9c697dUL, 0xbd20b6e8UL, 0xd1466000UL,
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171 |
0x3fb1973bUL, 0x560d9e9bUL, 0xbd25325dUL, 0xb59e4000UL, 0x3fb08598UL,
|
|
172 |
0x7009902cUL, 0xbd17e5ddUL, 0xc006c000UL, 0x3faeea31UL, 0x4fc93b7bUL,
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173 |
0xbd0e113eUL, 0xcdddc000UL, 0x3faccb73UL, 0x47d82807UL, 0xbd1a68f2UL,
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174 |
0xd0fb0000UL, 0x3faaaef2UL, 0x353bb42eUL, 0x3d20fc1aUL, 0x149fc000UL,
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175 |
0x3fa894aaUL, 0xd05a267dUL, 0xbd197995UL, 0xf2d4c000UL, 0x3fa67c94UL,
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176 |
0xec19afa2UL, 0xbd029efbUL, 0xd42e0000UL, 0x3fa466aeUL, 0x75bdfd28UL,
|
|
177 |
0xbd2c1673UL, 0x2f8d0000UL, 0x3fa252f3UL, 0xe021b67bUL, 0x3d283e9aUL,
|
|
178 |
0x89e74000UL, 0x3fa0415dUL, 0x5cf1d753UL, 0x3d0111c0UL, 0xec148000UL,
|
|
179 |
0x3f9c63d2UL, 0x3f9eb2f3UL, 0x3d2578c6UL, 0x28c90000UL, 0x3f984925UL,
|
|
180 |
0x325a0c34UL, 0xbd2aa0baUL, 0x25980000UL, 0x3f9432a9UL, 0x928637feUL,
|
|
181 |
0x3d098139UL, 0x58938000UL, 0x3f902056UL, 0x06e2f7d2UL, 0xbd23dc5bUL,
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182 |
0xa3890000UL, 0x3f882448UL, 0xda74f640UL, 0xbd275577UL, 0x75890000UL,
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183 |
0x3f801015UL, 0x999d2be8UL, 0xbd10c76bUL, 0x59580000UL, 0x3f700805UL,
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184 |
0xcb31c67bUL, 0x3d2166afUL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
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185 |
0x80000000UL
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186 |
};
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187 |
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188 |
// BEGIN dlog PSEUDO CODE:
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189 |
// double dlog(double X) {
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// // p(r) polynomial coefficients initialized from _L_tbl table
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191 |
// double C1_0 = _L_tbl[0];
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192 |
// double C1_1 = _L_tbl[1];
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193 |
// double C2_0 = _L_tbl[2];
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194 |
// double C2_1 = _L_tbl[3];
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195 |
// double C3_0 = _L_tbl[4];
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196 |
// double C3_1 = _L_tbl[5];
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197 |
// double C4_0 = _L_tbl[6];
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198 |
// double C4_1 = _L_tbl[7];
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199 |
// // NOTE: operations with coefficients above are mostly vectorized in assembly
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200 |
// // Check corner cases first
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201 |
// if (X == 1.0d || AS_LONG_BITS(X) + 0x0010000000000000 <= 0x0010000000000000) {
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// // NOTE: AS_LONG_BITS(X) + 0x0010000000000000 <= 0x0010000000000000 means
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203 |
// // that X < 0 or X >= 0x7FF0000000000000 (0x7FF* is NaN or INF)
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204 |
// if (X < 0 || X is NaN) return NaN;
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205 |
// if (X == 1.0d) return 0.0d;
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206 |
// if (X == 0.0d) return -INFINITY;
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207 |
// if (X is INFINITY) return INFINITY;
|
|
208 |
// }
|
|
209 |
// // double representation is 2^exponent * mantissa
|
|
210 |
// // split X into two multipliers: 2^exponent and 1.0 * mantissa
|
|
211 |
// // pseudo function: zeroExponent(X) return value of X with exponent == 0
|
|
212 |
// float vtmp5 = 1/(float)(zeroExponent(X)); // reciprocal estimate
|
|
213 |
// // pseudo function: HI16(X) returns high 16 bits of double value
|
|
214 |
// int hiWord = HI16(X);
|
|
215 |
// double vtmp1 = (double) 0x77F0 << 48 | mantissa(X);
|
|
216 |
// hiWord -= 16;
|
|
217 |
// if (AS_LONG_BITS(hiWord) > 0x8000) {
|
|
218 |
// // SMALL_VALUE branch
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|
219 |
// vtmp0 = vtmp1 = vtmp0 * AS_DOUBLE_BITS(0x47F0000000000000);
|
|
220 |
// hiWord = HI16(vtmp1);
|
|
221 |
// vtmp0 = AS_DOUBLE_BITS(AS_LONG_BITS(vtmp0) |= 0x3FF0000000000000);
|
|
222 |
// vtmp5 = (double) (1/(float)vtmp0);
|
|
223 |
// vtmp1 <<= 12;
|
|
224 |
// vtmp1 >>= 12;
|
|
225 |
// }
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|
226 |
// // MAIN branch
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|
227 |
// double vtmp3 = AS_LONG_BITS(vtmp1) & 0xffffe00000000000; // hi part
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|
228 |
// int intB0 = AS_INT_BITS(vtmp5) + 0x8000;
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|
229 |
// double vtmp0 = AS_DOUBLE_BITS(0xffffe00000000000 & (intB0<<29));
|
|
230 |
// int index = (intB0 >> 16) && 0xFF;
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|
231 |
// double hiTableValue = _L_tbl[8+index]; // vtmp2[0]
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|
232 |
// double lowTableValue = _L_tbl[16+index]; // vtmp2[1]
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|
233 |
// vtmp5 = AS_DOUBLE_BITS(hiWord & 0x7FF0 - 0x3FE0); // 0x3FE = 1023 << 4
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|
234 |
// vtmp1 -= vtmp3; // low part
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|
235 |
// vtmp3 = vtmp3*vtmp0 - 1.0;
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|
236 |
// hiTableValue += C4_0 * vtmp5;
|
|
237 |
// lowTableValue += C4_1 * vtmp5;
|
|
238 |
// double r = vtmp1 * vtmp0 + vtmp3; // r = B*mx-1.0, computed in hi and low parts
|
|
239 |
// vtmp0 = hiTableValue + r;
|
|
240 |
// hiTableValue -= vtmp0;
|
|
241 |
// double r2 = r*r;
|
|
242 |
// double r3 = r2*r;
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|
243 |
// double p7 = C3_0*r2 + C2_0*r3 + C1_0*r2*r2 + C3_1*r3*r2 + C2_1*r3*r3
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|
244 |
// + C1_1*r3*r2*r2; // degree 7 polynomial
|
|
245 |
// return p7 + (vtmp0 + ((r + hiTableValue) + lowTableValue));
|
|
246 |
// }
|
|
247 |
//
|
|
248 |
// END dlog PSEUDO CODE
|
|
249 |
|
|
250 |
|
|
251 |
// Generate log(X). X passed in register v0. Return log(X) into v0.
|
|
252 |
// Generator parameters: 10 temporary FPU registers and temporary general
|
|
253 |
// purpose registers
|
|
254 |
void MacroAssembler::fast_log(FloatRegister vtmp0, FloatRegister vtmp1,
|
|
255 |
FloatRegister vtmp2, FloatRegister vtmp3,
|
|
256 |
FloatRegister vtmp4, FloatRegister vtmp5,
|
|
257 |
FloatRegister C1, FloatRegister C2,
|
|
258 |
FloatRegister C3, FloatRegister C4,
|
|
259 |
Register tmp1, Register tmp2, Register tmp3,
|
|
260 |
Register tmp4, Register tmp5) {
|
|
261 |
Label DONE, CHECK_CORNER_CASES, SMALL_VALUE, MAIN,
|
|
262 |
CHECKED_CORNER_CASES, RETURN_MINF_OR_NAN;
|
|
263 |
const long INF_OR_NAN_PREFIX = 0x7FF0;
|
|
264 |
const long MINF_OR_MNAN_PREFIX = 0xFFF0;
|
|
265 |
const long ONE_PREFIX = 0x3FF0;
|
|
266 |
movz(tmp2, ONE_PREFIX, 48);
|
|
267 |
movz(tmp4, 0x0010, 48);
|
|
268 |
fmovd(rscratch1, v0); // rscratch1 = AS_LONG_BITS(X)
|
|
269 |
lea(rscratch2, ExternalAddress((address)_L_tbl));
|
|
270 |
movz(tmp5, 0x7F);
|
|
271 |
add(tmp1, rscratch1, tmp4);
|
|
272 |
cmp(tmp2, rscratch1);
|
|
273 |
lsr(tmp3, rscratch1, 29);
|
|
274 |
ccmp(tmp1, tmp4, 0b1101 /* LE */, NE);
|
|
275 |
bfm(tmp3, tmp5, 41, 8);
|
|
276 |
fmovs(vtmp5, tmp3);
|
|
277 |
// Load coefficients from table. All coefficients are organized to be
|
|
278 |
// in specific order, because load below will load it in vectors to be used
|
|
279 |
// later in vector instructions. Load will be performed in parallel while
|
|
280 |
// branches are taken. C1 will contain vector of {C1_0, C1_1}, C2 =
|
|
281 |
// {C2_0, C2_1}, C3 = {C3_0, C3_1}, C4 = {C4_0, C4_1}
|
|
282 |
ld1(C1, C2, C3, C4, T2D, post(rscratch2, 64));
|
|
283 |
br(LE, CHECK_CORNER_CASES);
|
|
284 |
bind(CHECKED_CORNER_CASES);
|
|
285 |
// all corner cases are handled
|
|
286 |
frecpe(vtmp5, vtmp5, S); // vtmp5 ~= 1/vtmp5
|
|
287 |
lsr(tmp2, rscratch1, 48);
|
|
288 |
movz(tmp4, 0x77f0, 48);
|
|
289 |
fmovd(vtmp4, 1.0d);
|
|
290 |
movz(tmp1, INF_OR_NAN_PREFIX, 48);
|
|
291 |
bfm(tmp4, rscratch1, 0, 51); // tmp4 = 0x77F0 << 48 | mantissa(X)
|
|
292 |
// vtmp1 = AS_DOUBLE_BITS(0x77F0 << 48 | mantissa(X)) == mx
|
|
293 |
fmovd(vtmp1, tmp4);
|
|
294 |
subw(tmp2, tmp2, 16);
|
|
295 |
cmp(tmp2, 0x8000);
|
|
296 |
br(GE, SMALL_VALUE);
|
|
297 |
bind(MAIN);
|
|
298 |
fmovs(tmp3, vtmp5); // int intB0 = AS_INT_BITS(B);
|
|
299 |
mov(tmp5, 0x3FE0);
|
|
300 |
mov(rscratch1, 0xffffe00000000000);
|
|
301 |
andr(tmp2, tmp2, tmp1, LSR, 48); // hiWord & 0x7FF0
|
|
302 |
sub(tmp2, tmp2, tmp5); // tmp2 = hiWord & 0x7FF0 - 0x3FE0
|
|
303 |
scvtfwd(vtmp5, tmp2); // vtmp5 = (double)tmp2;
|
|
304 |
addw(tmp3, tmp3, 0x8000); // tmp3 = B
|
|
305 |
andr(tmp4, tmp4, rscratch1); // tmp4 == hi_part(mx)
|
|
306 |
andr(rscratch1, rscratch1, tmp3, LSL, 29); // rscratch1 = hi_part(B)
|
|
307 |
ubfm(tmp3, tmp3, 16, 23); // int index = (intB0 >> 16) && 0xFF
|
|
308 |
ldrq(vtmp2, Address(rscratch2, tmp3, Address::lsl(4))); // vtmp2 = _L_tbl[index]
|
|
309 |
// AS_LONG_BITS(vtmp1) & 0xffffe00000000000 // hi_part(mx)
|
|
310 |
fmovd(vtmp3, tmp4);
|
|
311 |
fmovd(vtmp0, rscratch1); // vtmp0 = hi_part(B)
|
|
312 |
fsubd(vtmp1, vtmp1, vtmp3); // vtmp1 -= vtmp3; // low_part(mx)
|
|
313 |
fnmsub(vtmp3, vtmp3, vtmp0, vtmp4); // vtmp3 = vtmp3*vtmp0 - vtmp4
|
|
314 |
fmlavs(vtmp2, T2D, C4, vtmp5, 0); // vtmp2 += {C4} * vtmp5
|
|
315 |
// vtmp1 = r = vtmp1 * vtmp0 + vtmp3 == low_part(mx) * hi_part(B) + (hi_part(mx)*hi_part(B) - 1.0)
|
|
316 |
fmaddd(vtmp1, vtmp1, vtmp0, vtmp3);
|
|
317 |
ins(vtmp5, D, vtmp2, 0, 1); // vtmp5 = vtmp2[1];
|
|
318 |
faddd(vtmp0, vtmp2, vtmp1); // vtmp0 = vtmp2 + vtmp1
|
|
319 |
fmlavs(C3, T2D, C2, vtmp1, 0); // {C3} += {C2}*vtmp1
|
|
320 |
fsubd(vtmp2, vtmp2, vtmp0); // vtmp2 -= vtmp0
|
|
321 |
fmuld(vtmp3, vtmp1, vtmp1); // vtmp3 = vtmp1*vtmp1
|
|
322 |
faddd(C4, vtmp1, vtmp2); // C4[0] = vtmp1 + vtmp2
|
|
323 |
fmlavs(C3, T2D, C1, vtmp3, 0); // {C3} += {C1}*vtmp3
|
|
324 |
faddd(C4, C4, vtmp5); // C4 += vtmp5
|
|
325 |
fmuld(vtmp4, vtmp3, vtmp1); // vtmp4 = vtmp3*vtmp1
|
|
326 |
faddd(vtmp0, vtmp0, C4); // vtmp0 += C4
|
|
327 |
fmlavs(C3, T2D, vtmp4, C3, 1); // {C3} += {vtmp4}*C3[1]
|
|
328 |
fmaddd(vtmp0, C3, vtmp3, vtmp0); // vtmp0 = C3 * vtmp3 + vtmp0
|
|
329 |
ret(lr);
|
|
330 |
|
|
331 |
block_comment("if (AS_LONG_BITS(hiWord) > 0x8000)"); {
|
|
332 |
bind(SMALL_VALUE);
|
|
333 |
movz(tmp2, 0x47F0, 48);
|
|
334 |
fmovd(vtmp1, tmp2);
|
|
335 |
fmuld(vtmp0, vtmp1, v0);
|
|
336 |
fmovd(vtmp1, vtmp0);
|
|
337 |
umov(tmp2, vtmp1, S, 3);
|
|
338 |
orr(vtmp0, T16B, vtmp0, vtmp4);
|
|
339 |
ushr(vtmp5, T2D, vtmp0, 27);
|
|
340 |
ushr(vtmp5, T4S, vtmp5, 2);
|
|
341 |
frecpe(vtmp5, vtmp5, S);
|
|
342 |
shl(vtmp1, T2D, vtmp1, 12);
|
|
343 |
ushr(vtmp1, T2D, vtmp1, 12);
|
|
344 |
b(MAIN);
|
|
345 |
}
|
|
346 |
|
|
347 |
block_comment("Corner cases"); {
|
|
348 |
bind(RETURN_MINF_OR_NAN);
|
|
349 |
movz(tmp1, MINF_OR_MNAN_PREFIX, 48);
|
|
350 |
orr(rscratch1, rscratch1, tmp1);
|
|
351 |
fmovd(v0, rscratch1);
|
|
352 |
ret(lr);
|
|
353 |
bind(CHECK_CORNER_CASES);
|
|
354 |
movz(tmp1, INF_OR_NAN_PREFIX, 48);
|
|
355 |
cmp(rscratch1, zr);
|
|
356 |
br(LE, RETURN_MINF_OR_NAN);
|
|
357 |
cmp(rscratch1, tmp1);
|
|
358 |
br(GE, DONE);
|
|
359 |
cmp(rscratch1, tmp2);
|
|
360 |
br(NE, CHECKED_CORNER_CASES);
|
|
361 |
fmovd(v0, 0.0d);
|
|
362 |
}
|
|
363 |
bind(DONE);
|
|
364 |
ret(lr);
|
|
365 |
}
|