/* * Copyright (c) 2016, 2024, Intel Corporation. All rights reserved. * Copyright (C) 2021 THL A29 Limited, a Tencent company. All rights reserved. * 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 "macroAssembler_x86.hpp" #include "stubGenerator_x86_64.hpp" /******************************************************************************/ // ALGORITHM DESCRIPTION - EXP() // --------------------- // // Description: // Let K = 64 (table size). // x x/log(2) n // e = 2 = 2 * T[j] * (1 + P(y)) // where // x = m*log(2)/K + y, y in [-log(2)/K..log(2)/K] // m = n*K + j, m,n,j - signed integer, j in [-K/2..K/2] // j/K // values of 2 are tabulated as T[j] = T_hi[j] ( 1 + T_lo[j]). // // P(y) is a minimax polynomial approximation of exp(x)-1 // on small interval [-log(2)/K..log(2)/K] (were calculated by Maple V). // // To avoid problems with arithmetic overflow and underflow, // n n1 n2 // value of 2 is safely computed as 2 * 2 where n1 in [-BIAS/2..BIAS/2] // where BIAS is a value of exponent bias. // // Special cases: // exp(NaN) = NaN // exp(+INF) = +INF // exp(-INF) = 0 // exp(x) = 1 for subnormals // for finite argument, only exp(0)=1 is exact // For IEEE double // if x > 709.782712893383973096 then exp(x) overflow // if x < -745.133219101941108420 then exp(x) underflow // /******************************************************************************/ ATTRIBUTE_ALIGNED(16) static const juint _cv[] = { 0x652b82feUL, 0x40571547UL, 0x652b82feUL, 0x40571547UL, 0xfefa0000UL, 0x3f862e42UL, 0xfefa0000UL, 0x3f862e42UL, 0xbc9e3b3aUL, 0x3d1cf79aUL, 0xbc9e3b3aUL, 0x3d1cf79aUL, 0xfffffffeUL, 0x3fdfffffUL, 0xfffffffeUL, 0x3fdfffffUL, 0xe3289860UL, 0x3f56c15cUL, 0x555b9e25UL, 0x3fa55555UL, 0xc090cf0fUL, 0x3f811115UL, 0x55548ba1UL, 0x3fc55555UL }; ATTRIBUTE_ALIGNED(16) static const juint _mmask[] = { 0xffffffc0UL, 0x00000000UL, 0xffffffc0UL, 0x00000000UL }; ATTRIBUTE_ALIGNED(16) static const juint _bias[] = { 0x0000ffc0UL, 0x00000000UL, 0x0000ffc0UL, 0x00000000UL }; ATTRIBUTE_ALIGNED(16) static const juint _Tbl_addr[] = { 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0e03754dUL, 0x3cad7bbfUL, 0x3e778060UL, 0x00002c9aUL, 0x3567f613UL, 0x3c8cd252UL, 0xd3158574UL, 0x000059b0UL, 0x61e6c861UL, 0x3c60f74eUL, 0x18759bc8UL, 0x00008745UL, 0x5d837b6cUL, 0x3c979aa6UL, 0x6cf9890fUL, 0x0000b558UL, 0x702f9cd1UL, 0x3c3ebe3dUL, 0x32d3d1a2UL, 0x0000e3ecUL, 0x1e63bcd8UL, 0x3ca3516eUL, 0xd0125b50UL, 0x00011301UL, 0x26f0387bUL, 0x3ca4c554UL, 0xaea92ddfUL, 0x0001429aUL, 0x62523fb6UL, 0x3ca95153UL, 0x3c7d517aUL, 0x000172b8UL, 0x3f1353bfUL, 0x3c8b898cUL, 0xeb6fcb75UL, 0x0001a35bUL, 0x3e3a2f5fUL, 0x3c9aecf7UL, 0x3168b9aaUL, 0x0001d487UL, 0x44a6c38dUL, 0x3c8a6f41UL, 0x88628cd6UL, 0x0002063bUL, 0xe3a8a894UL, 0x3c968efdUL, 0x6e756238UL, 0x0002387aUL, 0x981fe7f2UL, 0x3c80472bUL, 0x65e27cddUL, 0x00026b45UL, 0x6d09ab31UL, 0x3c82f7e1UL, 0xf51fdee1UL, 0x00029e9dUL, 0x720c0ab3UL, 0x3c8b3782UL, 0xa6e4030bUL, 0x0002d285UL, 0x4db0abb6UL, 0x3c834d75UL, 0x0a31b715UL, 0x000306feUL, 0x5dd3f84aUL, 0x3c8fdd39UL, 0xb26416ffUL, 0x00033c08UL, 0xcc187d29UL, 0x3ca12f8cUL, 0x373aa9caUL, 0x000371a7UL, 0x738b5e8bUL, 0x3ca7d229UL, 0x34e59ff6UL, 0x0003a7dbUL, 0xa72a4c6dUL, 0x3c859f48UL, 0x4c123422UL, 0x0003dea6UL, 0x259d9205UL, 0x3ca8b846UL, 0x21f72e29UL, 0x0004160aUL, 0x60c2ac12UL, 0x3c4363edUL, 0x6061892dUL, 0x00044e08UL, 0xdaa10379UL, 0x3c6ecce1UL, 0xb5c13cd0UL, 0x000486a2UL, 0xbb7aafb0UL, 0x3c7690ceUL, 0xd5362a27UL, 0x0004bfdaUL, 0x9b282a09UL, 0x3ca083ccUL, 0x769d2ca6UL, 0x0004f9b2UL, 0xc1aae707UL, 0x3ca509b0UL, 0x569d4f81UL, 0x0005342bUL, 0x18fdd78eUL, 0x3c933505UL, 0x36b527daUL, 0x00056f47UL, 0xe21c5409UL, 0x3c9063e1UL, 0xdd485429UL, 0x0005ab07UL, 0x2b64c035UL, 0x3c9432e6UL, 0x15ad2148UL, 0x0005e76fUL, 0x99f08c0aUL, 0x3ca01284UL, 0xb03a5584UL, 0x0006247eUL, 0x0073dc06UL, 0x3c99f087UL, 0x82552224UL, 0x00066238UL, 0x0da05571UL, 0x3c998d4dUL, 0x667f3bccUL, 0x0006a09eUL, 0x86ce4786UL, 0x3ca52bb9UL, 0x3c651a2eUL, 0x0006dfb2UL, 0x206f0dabUL, 0x3ca32092UL, 0xe8ec5f73UL, 0x00071f75UL, 0x8e17a7a6UL, 0x3ca06122UL, 0x564267c8UL, 0x00075febUL, 0x461e9f86UL, 0x3ca244acUL, 0x73eb0186UL, 0x0007a114UL, 0xabd66c55UL, 0x3c65ebe1UL, 0x36cf4e62UL, 0x0007e2f3UL, 0xbbff67d0UL, 0x3c96fe9fUL, 0x994cce12UL, 0x00082589UL, 0x14c801dfUL, 0x3c951f14UL, 0x9b4492ecUL, 0x000868d9UL, 0xc1f0eab4UL, 0x3c8db72fUL, 0x422aa0dbUL, 0x0008ace5UL, 0x59f35f44UL, 0x3c7bf683UL, 0x99157736UL, 0x0008f1aeUL, 0x9c06283cUL, 0x3ca360baUL, 0xb0cdc5e4UL, 0x00093737UL, 0x20f962aaUL, 0x3c95e8d1UL, 0x9fde4e4fUL, 0x00097d82UL, 0x2b91ce27UL, 0x3c71affcUL, 0x82a3f090UL, 0x0009c491UL, 0x589a2ebdUL, 0x3c9b6d34UL, 0x7b5de564UL, 0x000a0c66UL, 0x9ab89880UL, 0x3c95277cUL, 0xb23e255cUL, 0x000a5503UL, 0x6e735ab3UL, 0x3c846984UL, 0x5579fdbfUL, 0x000a9e6bUL, 0x92cb3387UL, 0x3c8c1a77UL, 0x995ad3adUL, 0x000ae89fUL, 0xdc2d1d96UL, 0x3ca22466UL, 0xb84f15faUL, 0x000b33a2UL, 0xb19505aeUL, 0x3ca1112eUL, 0xf2fb5e46UL, 0x000b7f76UL, 0x0a5fddcdUL, 0x3c74ffd7UL, 0x904bc1d2UL, 0x000bcc1eUL, 0x30af0cb3UL, 0x3c736eaeUL, 0xdd85529cUL, 0x000c199bUL, 0xd10959acUL, 0x3c84e08fUL, 0x2e57d14bUL, 0x000c67f1UL, 0x6c921968UL, 0x3c676b2cUL, 0xdcef9069UL, 0x000cb720UL, 0x36df99b3UL, 0x3c937009UL, 0x4a07897bUL, 0x000d072dUL, 0xa63d07a7UL, 0x3c74a385UL, 0xdcfba487UL, 0x000d5818UL, 0xd5c192acUL, 0x3c8e5a50UL, 0x03db3285UL, 0x000da9e6UL, 0x1c4a9792UL, 0x3c98bb73UL, 0x337b9b5eUL, 0x000dfc97UL, 0x603a88d3UL, 0x3c74b604UL, 0xe78b3ff6UL, 0x000e502eUL, 0x92094926UL, 0x3c916f27UL, 0xa2a490d9UL, 0x000ea4afUL, 0x41aa2008UL, 0x3c8ec3bcUL, 0xee615a27UL, 0x000efa1bUL, 0x31d185eeUL, 0x3c8a64a9UL, 0x5b6e4540UL, 0x000f5076UL, 0x4d91cd9dUL, 0x3c77893bUL, 0x819e90d8UL, 0x000fa7c1UL }; ATTRIBUTE_ALIGNED(16) static const juint _ALLONES[] = { 0xffffffffUL, 0xffffffffUL, 0xffffffffUL, 0xffffffffUL }; ATTRIBUTE_ALIGNED(16) static const juint _ebias[] = { 0x00000000UL, 0x3ff00000UL, 0x00000000UL, 0x3ff00000UL }; ATTRIBUTE_ALIGNED(4) static const juint _XMAX[] = { 0xffffffffUL, 0x7fefffffUL }; ATTRIBUTE_ALIGNED(4) static const juint _XMIN[] = { 0x00000000UL, 0x00100000UL }; ATTRIBUTE_ALIGNED(4) static const juint _INF[] = { 0x00000000UL, 0x7ff00000UL }; #define __ _masm-> address StubGenerator::generate_libmExp() { StubGenStubId stub_id = StubGenStubId::dexp_id; StubCodeMark mark(this, stub_id); address start = __ pc(); 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, B1_3, B1_5; address cv = (address)_cv; address mmask = (address)_mmask; address bias = (address)_bias; address Tbl_addr = (address)_Tbl_addr; address ALLONES = (address)_ALLONES; address ebias = (address)_ebias; address XMAX = (address)_XMAX; address XMIN = (address)_XMIN; address INF = (address)_INF; __ enter(); // required for proper stackwalking of RuntimeStub frame __ subq(rsp, 24); __ movsd(Address(rsp, 8), xmm0); __ unpcklpd(xmm0, xmm0); __ movdqu(xmm1, ExternalAddress(cv), r11 /*rscratch*/); // 0x652b82feUL, 0x40571547UL, 0x652b82feUL, 0x40571547UL __ movdqu(xmm2, ExternalAddress(cv + 16), r11 /*rscratch*/); // 0xfefa0000UL, 0x3f862e42UL, 0xfefa0000UL, 0x3f862e42UL __ movdqu(xmm3, ExternalAddress(cv + 32), r11 /*rscratch*/); // 0xbc9e3b3aUL, 0x3d1cf79aUL, 0xbc9e3b3aUL, 0x3d1cf79aUL __ movdqu(xmm6, ExternalAddress(SHIFTER), r11 /*rscratch*/); // 0x00000000UL, 0x43380000UL, 0x00000000UL, 0x43380000UL __ pextrw(rax, xmm0, 3); __ andl(rax, 32767); __ movl(rdx, 16527); __ subl(rdx, rax); __ subl(rax, 15504); __ orl(rdx, rax); __ cmpl(rdx, INT_MIN); __ jcc(Assembler::aboveEqual, L_2TAG_PACKET_0_0_2); __ mulpd(xmm1, xmm0); __ addpd(xmm1, xmm6); __ movapd(xmm7, xmm1); __ subpd(xmm1, xmm6); __ mulpd(xmm2, xmm1); __ movdqu(xmm4, ExternalAddress(cv + 64), r11 /*rscratch*/); // 0xe3289860UL, 0x3f56c15cUL, 0x555b9e25UL, 0x3fa55555UL __ mulpd(xmm3, xmm1); __ movdqu(xmm5, ExternalAddress(cv + 80), r11 /*rscratch*/); // 0xc090cf0fUL, 0x3f811115UL, 0x55548ba1UL, 0x3fc55555UL __ subpd(xmm0, xmm2); __ movdl(rax, xmm7); __ movl(rcx, rax); __ andl(rcx, 63); __ shll(rcx, 4); __ sarl(rax, 6); __ movl(rdx, rax); __ movdqu(xmm6, ExternalAddress(mmask), r11 /*rscratch*/); // 0xffffffc0UL, 0x00000000UL, 0xffffffc0UL, 0x00000000UL __ pand(xmm7, xmm6); __ movdqu(xmm6, ExternalAddress(bias), r11 /*rscratch*/); // 0x0000ffc0UL, 0x00000000UL, 0x0000ffc0UL, 0x00000000UL __ paddq(xmm7, xmm6); __ psllq(xmm7, 46); __ subpd(xmm0, xmm3); __ lea(r11, ExternalAddress(Tbl_addr)); __ movdqu(xmm2, Address(rcx, r11)); __ mulpd(xmm4, xmm0); __ movapd(xmm6, xmm0); __ movapd(xmm1, xmm0); __ mulpd(xmm6, xmm6); __ mulpd(xmm0, xmm6); __ addpd(xmm5, xmm4); __ mulsd(xmm0, xmm6); __ mulpd(xmm6, ExternalAddress(cv + 48), r11 /*rscratch*/); // 0xfffffffeUL, 0x3fdfffffUL, 0xfffffffeUL, 0x3fdfffffUL __ addsd(xmm1, xmm2); __ unpckhpd(xmm2, xmm2); __ mulpd(xmm0, xmm5); __ addsd(xmm1, xmm0); __ por(xmm2, xmm7); __ unpckhpd(xmm0, xmm0); __ addsd(xmm0, xmm1); __ addsd(xmm0, xmm6); __ addl(rdx, 894); __ cmpl(rdx, 1916); __ jcc(Assembler::above, L_2TAG_PACKET_1_0_2); __ mulsd(xmm0, xmm2); __ addsd(xmm0, xmm2); __ jmp(B1_5); __ bind(L_2TAG_PACKET_1_0_2); __ xorpd(xmm3, xmm3); __ movdqu(xmm4, ExternalAddress(ALLONES), r11 /*rscratch*/); // 0xffffffffUL, 0xffffffffUL, 0xffffffffUL, 0xffffffffUL __ movl(rdx, -1022); __ subl(rdx, rax); __ movdl(xmm5, rdx); __ psllq(xmm4, xmm5); __ movl(rcx, rax); __ sarl(rax, 1); __ pinsrw(xmm3, rax, 3); __ movdqu(xmm6, ExternalAddress(ebias), r11 /*rscratch*/); // 0x00000000UL, 0x3ff00000UL, 0x00000000UL, 0x3ff00000UL __ psllq(xmm3, 4); __ psubd(xmm2, xmm3); __ mulsd(xmm0, xmm2); __ cmpl(rdx, 52); __ jcc(Assembler::greater, L_2TAG_PACKET_2_0_2); __ pand(xmm4, xmm2); __ paddd(xmm3, xmm6); __ subsd(xmm2, xmm4); __ addsd(xmm0, xmm2); __ cmpl(rcx, 1023); __ jcc(Assembler::greaterEqual, L_2TAG_PACKET_3_0_2); __ pextrw(rcx, xmm0, 3); __ andl(rcx, 32768); __ orl(rdx, rcx); __ cmpl(rdx, 0); __ jcc(Assembler::equal, L_2TAG_PACKET_4_0_2); __ movapd(xmm6, xmm0); __ addsd(xmm0, xmm4); __ mulsd(xmm0, xmm3); __ pextrw(rcx, xmm0, 3); __ andl(rcx, 32752); __ cmpl(rcx, 0); __ jcc(Assembler::equal, L_2TAG_PACKET_5_0_2); __ jmp(B1_5); __ bind(L_2TAG_PACKET_5_0_2); __ mulsd(xmm6, xmm3); __ mulsd(xmm4, xmm3); __ movdqu(xmm0, xmm6); __ pxor(xmm6, xmm4); __ psrad(xmm6, 31); __ pshufd(xmm6, xmm6, 85); __ psllq(xmm0, 1); __ psrlq(xmm0, 1); __ pxor(xmm0, xmm6); __ psrlq(xmm6, 63); __ paddq(xmm0, xmm6); __ paddq(xmm0, xmm4); __ movl(Address(rsp, 0), 15); __ jmp(L_2TAG_PACKET_6_0_2); __ bind(L_2TAG_PACKET_4_0_2); __ addsd(xmm0, xmm4); __ mulsd(xmm0, xmm3); __ jmp(B1_5); __ bind(L_2TAG_PACKET_3_0_2); __ addsd(xmm0, xmm4); __ mulsd(xmm0, xmm3); __ pextrw(rcx, xmm0, 3); __ andl(rcx, 32752); __ cmpl(rcx, 32752); __ jcc(Assembler::aboveEqual, L_2TAG_PACKET_7_0_2); __ jmp(B1_5); __ bind(L_2TAG_PACKET_2_0_2); __ paddd(xmm3, xmm6); __ addpd(xmm0, xmm2); __ mulsd(xmm0, xmm3); __ movl(Address(rsp, 0), 15); __ jmp(L_2TAG_PACKET_6_0_2); __ bind(L_2TAG_PACKET_8_0_2); __ cmpl(rax, 2146435072); __ jcc(Assembler::aboveEqual, L_2TAG_PACKET_9_0_2); __ movl(rax, Address(rsp, 12)); __ cmpl(rax, INT_MIN); __ jcc(Assembler::aboveEqual, L_2TAG_PACKET_10_0_2); __ movsd(xmm0, ExternalAddress(XMAX), r11 /*rscratch*/); // 0xffffffffUL, 0x7fefffffUL __ mulsd(xmm0, xmm0); __ bind(L_2TAG_PACKET_7_0_2); __ movl(Address(rsp, 0), 14); __ jmp(L_2TAG_PACKET_6_0_2); __ bind(L_2TAG_PACKET_10_0_2); __ movsd(xmm0, ExternalAddress(XMIN), r11 /*rscratch*/); // 0x00000000UL, 0x00100000UL __ mulsd(xmm0, xmm0); __ movl(Address(rsp, 0), 15); __ jmp(L_2TAG_PACKET_6_0_2); __ bind(L_2TAG_PACKET_9_0_2); __ movl(rdx, Address(rsp, 8)); __ cmpl(rax, 2146435072); __ jcc(Assembler::above, L_2TAG_PACKET_11_0_2); __ cmpl(rdx, 0); __ jcc(Assembler::notEqual, L_2TAG_PACKET_11_0_2); __ movl(rax, Address(rsp, 12)); __ cmpl(rax, 2146435072); __ jcc(Assembler::notEqual, L_2TAG_PACKET_12_0_2); __ movsd(xmm0, ExternalAddress(INF), r11 /*rscratch*/); // 0x00000000UL, 0x7ff00000UL __ jmp(B1_5); __ bind(L_2TAG_PACKET_12_0_2); __ movsd(xmm0, ExternalAddress(ZERO), r11 /*rscratch*/); // 0x00000000UL, 0x00000000UL __ jmp(B1_5); __ bind(L_2TAG_PACKET_11_0_2); __ movsd(xmm0, Address(rsp, 8)); __ addsd(xmm0, xmm0); __ jmp(B1_5); __ bind(L_2TAG_PACKET_0_0_2); __ movl(rax, Address(rsp, 12)); __ andl(rax, 2147483647); __ cmpl(rax, 1083179008); __ jcc(Assembler::aboveEqual, L_2TAG_PACKET_8_0_2); __ movsd(Address(rsp, 8), xmm0); __ addsd(xmm0, ExternalAddress(ONE), r11 /*rscratch*/); // 0x00000000UL, 0x3ff00000UL __ jmp(B1_5); __ bind(L_2TAG_PACKET_6_0_2); __ movq(Address(rsp, 16), xmm0); __ bind(B1_3); __ movq(xmm0, Address(rsp, 16)); __ bind(B1_5); __ addq(rsp, 24); __ leave(); // required for proper stackwalking of RuntimeStub frame __ ret(0); return start; } #undef __