/* * Copyright (c) 2025, Intel Corporation. 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 // --------------------- // // x=2^{3*k+j} * 1.b1 b2 ... b5 b6 ... b52 // Let r=(x*2^{-3k-j} - 1.b1 b2 ... b5 1)* rcp[b1 b2 ..b5], // where rcp[b1 b2 .. b5]=1/(1.b1 b2 b3 b4 b5 1) in double precision // cbrt(2^j * 1. b1 b2 .. b5 1) is approximated as T[j][b1..b5]+D[j][b1..b5] // (T stores the high 53 bits, D stores the low order bits) // Result=2^k*T+(2^k*T*r)*P+2^k*D // where P=p1+p2*r+..+p8*r^7 // // Special cases: // cbrt(NaN) = quiet NaN // cbrt(+/-INF) = +/-INF // cbrt(+/-0) = +/-0 // /******************************************************************************/ ATTRIBUTE_ALIGNED(4) static const juint _SIG_MASK[] = { 0, 1032192 }; ATTRIBUTE_ALIGNED(4) static const juint _EXP_MASK[] = { 0, 3220176896 }; ATTRIBUTE_ALIGNED(4) static const juint _EXP_MSK2[] = { 0, 3220193280 }; ATTRIBUTE_ALIGNED(4) static const juint _EXP_MSK3[] = { 4294967295, 1048575 }; ATTRIBUTE_ALIGNED(4) static const juint _SCALE63[] = { 0, 1138753536 }; ATTRIBUTE_ALIGNED(4) static const juint _ZERON[] = { 0, 2147483648 }; ATTRIBUTE_ALIGNED(4) static const juint _INF[] = { 0, 2146435072 }; ATTRIBUTE_ALIGNED(4) static const juint _NEG_INF[] = { 0, 4293918720 }; ATTRIBUTE_ALIGNED(16) static const juint _coeff_table[] = { 1553778919, 3213899486, 3534952507, 3215266280, 1646371399, 3214412045, 477218588, 3216798151, 3582521621, 1066628362, 1007461464, 1068473053, 889629714, 1067378449, 1431655765, 1070945621 }; ATTRIBUTE_ALIGNED(4) static const juint _rcp_table[] = { 528611360, 3220144632, 2884679527, 3220082993, 1991868891, 3220024928, 2298714891, 3219970134, 58835168, 3219918343, 3035110223, 3219869313, 1617585086, 3219822831, 2500867033, 3219778702, 4241943008, 3219736752, 258732970, 3219696825, 404232216, 3219658776, 2172167368, 3219622476, 1544257904, 3219587808, 377579543, 3219554664, 1616385542, 3219522945, 813783277, 3219492562, 3940743189, 3219463431, 2689777499, 3219435478, 1700977147, 3219408632, 3169102082, 3219382828, 327235604, 3219358008, 1244336319, 3219334115, 1300311200, 3219311099, 3095471925, 3219288912, 2166487928, 3219267511, 2913108253, 3219246854, 293672978, 3219226904, 288737297, 3219207624, 1810275472, 3219188981, 174592167, 3219170945, 3539053052, 3219153485, 2164392968, 3219136576 }; ATTRIBUTE_ALIGNED(4) static const juint _cbrt_table[] = { 572345495, 1072698681, 1998204467, 1072709382, 3861501553, 1072719872, 2268192434, 1072730162, 2981979308, 1072740260, 270859143, 1072750176, 2958651392, 1072759916, 313113243, 1072769490, 919449400, 1072778903, 2809328903, 1072788162, 2222981587, 1072797274, 2352530781, 1072806244, 594152517, 1072815078, 1555767199, 1072823780, 4282421314, 1072832355, 2355578597, 1072840809, 1162590619, 1072849145, 797864051, 1072857367, 431273680, 1072865479, 2669831148, 1072873484, 733477752, 1072881387, 4280220604, 1072889189, 801961634, 1072896896, 2915370760, 1072904508, 1159613482, 1072912030, 2689944798, 1072919463, 1248687822, 1072926811, 2967951030, 1072934075, 630170432, 1072941259, 3760898254, 1072948363, 0, 1072955392, 2370273294, 1072962345, 1261754802, 1072972640, 546334065, 1072986123, 1054893830, 1072999340, 1571187597, 1073012304, 1107975175, 1073025027, 3606909377, 1073037519, 1113616747, 1073049792, 4154744632, 1073061853, 3358931423, 1073073713, 4060702372, 1073085379, 747576176, 1073096860, 3023138255, 1073108161, 1419988548, 1073119291, 1914185305, 1073130255, 294389948, 1073141060, 3761802570, 1073151710, 978281566, 1073162213, 823148820, 1073172572, 2420954441, 1073182792, 3815449908, 1073192878, 2046058587, 1073202835, 1807524753, 1073212666, 2628681401, 1073222375, 3225667357, 1073231966, 1555307421, 1073241443, 3454043099, 1073250808, 1208137896, 1073260066, 3659916772, 1073269218, 1886261264, 1073278269, 3593647839, 1073287220, 3086012205, 1073296075, 2769796922, 1073304836, 888716057, 1073317807, 2201465623, 1073334794, 164369365, 1073351447, 3462666733, 1073367780, 2773905457, 1073383810, 1342879088, 1073399550, 2543933975, 1073415012, 1684477781, 1073430209, 3532178543, 1073445151, 1147747300, 1073459850, 1928031793, 1073474314, 2079717015, 1073488553, 4016765315, 1073502575, 3670431139, 1073516389, 3549227225, 1073530002, 11637607, 1073543422, 588220169, 1073556654, 2635407503, 1073569705, 2042029317, 1073582582, 1925128962, 1073595290, 4136375664, 1073607834, 759964600, 1073620221, 4257606771, 1073632453, 297278907, 1073644538, 3655053093, 1073656477, 2442253172, 1073668277, 1111876799, 1073679941, 3330973139, 1073691472, 3438879452, 1073702875, 3671565478, 1073714153, 1317849547, 1073725310, 1642364115, 1073736348 }; ATTRIBUTE_ALIGNED(4) static const juint _D_table[] = { 4050900474, 1014427190, 1157977860, 1016444461, 1374568199, 1017271387, 2809163288, 1016882676, 3742377377, 1013168191, 3101606597, 1017541672, 65224358, 1017217597, 2691591250, 1017266643, 4020758549, 1017689313, 1316310992, 1018030788, 1031537856, 1014090882, 3261395239, 1016413641, 886424999, 1016313335, 3114776834, 1014195875, 1681120620, 1017825416, 1329600273, 1016625740, 465474623, 1017097119, 4251633980, 1017169077, 1986990133, 1017710645, 752958613, 1017159641, 2216216792, 1018020163, 4282860129, 1015924861, 1557627859, 1016039538, 3889219754, 1018086237, 3684996408, 1017353275, 723532103, 1017717141, 2951149676, 1012528470, 831890937, 1017830553, 1031212645, 1017387331, 2741737450, 1017604974, 2863311531, 1003776682, 4276736099, 1013153088, 4111778382, 1015673686, 1728065769, 1016413986, 2708718031, 1018078833, 1069335005, 1015291224, 700037144, 1016482032, 2904566452, 1017226861, 4074156649, 1017622651, 25019565, 1015245366, 3601952608, 1015771755, 3267129373, 1017904664, 503203103, 1014921629, 2122011730, 1018027866, 3927295461, 1014189456, 2790625147, 1016024251, 1330460186, 1016940346, 4033568463, 1015538390, 3695818227, 1017509621, 257573361, 1017208868, 3227697852, 1017337964, 234118548, 1017169577, 4009025803, 1017278524, 1948343394, 1017749310, 678398162, 1018144239, 3083864863, 1016669086, 2415453452, 1017890370, 175467344, 1017330033, 3197359580, 1010339928, 2071276951, 1015941358, 268372543, 1016737773, 938132959, 1017389108, 1816750559, 1017337448, 4119203749, 1017152174, 2578653878, 1013108497, 2470331096, 1014678606, 123855735, 1016553320, 1265650889, 1014782687, 3414398172, 1017182638, 1040773369, 1016158401, 3483628886, 1016886550, 4140499405, 1016191425, 3893477850, 1016964495, 3935319771, 1009634717, 2978982660, 1015027112, 2452709923, 1017990229, 3190365712, 1015835149, 4237588139, 1015832925, 2610678389, 1017962711, 2127316774, 1017405770, 824267502, 1017959463, 2165924042, 1017912225, 2774007076, 1013257418, 4123916326, 1017582284, 1976417958, 1016959909, 4092806412, 1017711279, 119251817, 1015363631, 3475418768, 1017675415, 1972580503, 1015470684, 815541017, 1017517969, 2429917451, 1017397776, 4062888482, 1016749897, 68284153, 1017925678, 2207779246, 1016320298, 1183466520, 1017408657, 143326427, 1017060403 }; #define __ _masm-> address StubGenerator::generate_libmCbrt() { StubGenStubId stub_id = StubGenStubId::dcbrt_id; StubCodeMark mark(this, stub_id); address start = __ pc(); 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; Label B1_1, B1_2, B1_4; address SIG_MASK = (address)_SIG_MASK; address EXP_MASK = (address)_EXP_MASK; address EXP_MSK2 = (address)_EXP_MSK2; address EXP_MSK3 = (address)_EXP_MSK3; address SCALE63 = (address)_SCALE63; address ZERON = (address)_ZERON; address INF = (address)_INF; address NEG_INF = (address)_NEG_INF; address coeff_table = (address)_coeff_table; address rcp_table = (address)_rcp_table; address cbrt_table = (address)_cbrt_table; address D_table = (address)_D_table; __ enter(); // required for proper stackwalking of RuntimeStub frame __ bind(B1_1); __ subq(rsp, 24); __ movsd(Address(rsp), xmm0); __ bind(B1_2); __ movq(xmm7, xmm0); __ movl(rdx, 524032); __ movsd(xmm5, ExternalAddress(EXP_MSK3), r11 /*rscratch*/); __ movsd(xmm3, ExternalAddress(EXP_MSK2), r11 /*rscratch*/); __ psrlq(xmm7, 44); __ pextrw(rcx, xmm7, 0); __ movdl(rax, xmm7); __ movsd(xmm1, ExternalAddress(EXP_MASK), r11 /*rscratch*/); __ movsd(xmm2, ExternalAddress(SIG_MASK), r11 /*rscratch*/); __ andl(rcx, 248); __ lea(r8, ExternalAddress(rcp_table)); __ movsd(xmm4, Address(rcx, r8, Address::times_1)); __ movq(r9, rax); __ andl(rdx, rax); __ cmpl(rdx, 0); __ jcc(Assembler::equal, L_2TAG_PACKET_0_0_1); // Branch only if |x| is denormalized __ cmpl(rdx, 524032); __ jcc(Assembler::equal, L_2TAG_PACKET_1_0_1); // Branch only if |x| is INF or NaN __ shrl(rdx, 8); __ shrq(r9, 8); __ andpd(xmm2, xmm0); __ andpd(xmm0, xmm5); __ orpd(xmm3, xmm2); __ orpd(xmm1, xmm0); __ movapd(xmm5, ExternalAddress(coeff_table), r11 /*rscratch*/); __ movl(rax, 5462); __ movapd(xmm6, ExternalAddress(coeff_table + 16), r11 /*rscratch*/); __ mull(rdx); __ movq(rdx, r9); __ andq(r9, 2047); __ shrl(rax, 14); __ andl(rdx, 2048); __ subq(r9, rax); __ subq(r9, rax); __ subq(r9, rax); __ shlq(r9, 8); __ addl(rax, 682); __ orl(rax, rdx); __ movdl(xmm7, rax); __ addq(rcx, r9); __ psllq(xmm7, 52); __ bind(L_2TAG_PACKET_2_0_1); __ movapd(xmm2, ExternalAddress(coeff_table + 32), r11 /*rscratch*/); __ movapd(xmm0, ExternalAddress(coeff_table + 48), r11 /*rscratch*/); __ subsd(xmm1, xmm3); __ movq(xmm3, xmm7); __ lea(r8, ExternalAddress(cbrt_table)); __ mulsd(xmm7, Address(rcx, r8, Address::times_1)); __ mulsd(xmm1, xmm4); __ lea(r8, ExternalAddress(D_table)); __ mulsd(xmm3, Address(rcx, r8, Address::times_1)); __ movapd(xmm4, xmm1); __ unpcklpd(xmm1, xmm1); __ mulpd(xmm5, xmm1); __ mulpd(xmm6, xmm1); __ mulpd(xmm1, xmm1); __ addpd(xmm2, xmm5); __ addpd(xmm0, xmm6); __ mulpd(xmm2, xmm1); __ mulpd(xmm1, xmm1); __ mulsd(xmm4, xmm7); __ addpd(xmm0, xmm2); __ mulsd(xmm1, xmm0); __ unpckhpd(xmm0, xmm0); __ addsd(xmm0, xmm1); __ mulsd(xmm0, xmm4); __ addsd(xmm0, xmm3); __ addsd(xmm0, xmm7); __ jmp(B1_4); __ bind(L_2TAG_PACKET_0_0_1); __ mulsd(xmm0, ExternalAddress(SCALE63), r11 /*rscratch*/); __ movq(xmm7, xmm0); __ movl(rdx, 524032); __ psrlq(xmm7, 44); __ pextrw(rcx, xmm7, 0); __ movdl(rax, xmm7); __ andl(rcx, 248); __ lea(r8, ExternalAddress(rcp_table)); __ movsd(xmm4, Address(rcx, r8, Address::times_1)); __ movq(r9, rax); __ andl(rdx, rax); __ shrl(rdx, 8); __ shrq(r9, 8); __ cmpl(rdx, 0); __ jcc(Assembler::equal, L_2TAG_PACKET_3_0_1); // Branch only if |x| is zero __ andpd(xmm2, xmm0); __ andpd(xmm0, xmm5); __ orpd(xmm3, xmm2); __ orpd(xmm1, xmm0); __ movapd(xmm5, ExternalAddress(coeff_table), r11 /*rscratch*/); __ movl(rax, 5462); __ movapd(xmm6, ExternalAddress(coeff_table + 16), r11 /*rscratch*/); __ mull(rdx); __ movq(rdx, r9); __ andq(r9, 2047); __ shrl(rax, 14); __ andl(rdx, 2048); __ subq(r9, rax); __ subq(r9, rax); __ subq(r9, rax); __ shlq(r9, 8); __ addl(rax, 661); __ orl(rax, rdx); __ movdl(xmm7, rax); __ addq(rcx, r9); __ psllq(xmm7, 52); __ jmp(L_2TAG_PACKET_2_0_1); __ bind(L_2TAG_PACKET_3_0_1); __ cmpq(r9, 0); __ jcc(Assembler::notEqual, L_2TAG_PACKET_4_0_1); // Branch only if x is negative zero __ xorpd(xmm0, xmm0); __ jmp(B1_4); __ bind(L_2TAG_PACKET_4_0_1); __ movsd(xmm0, ExternalAddress(ZERON), r11 /*rscratch*/); __ jmp(B1_4); __ bind(L_2TAG_PACKET_1_0_1); __ movl(rax, Address(rsp, 4)); __ movl(rdx, Address(rsp)); __ movl(rcx, rax); __ andl(rcx, 2147483647); __ cmpl(rcx, 2146435072); __ jcc(Assembler::above, L_2TAG_PACKET_5_0_1); // Branch only if |x| is NaN __ cmpl(rdx, 0); __ jcc(Assembler::notEqual, L_2TAG_PACKET_5_0_1); // Branch only if |x| is NaN __ cmpl(rax, 2146435072); __ jcc(Assembler::notEqual, L_2TAG_PACKET_6_0_1); // Branch only if x is negative INF __ movsd(xmm0, ExternalAddress(INF), r11 /*rscratch*/); __ jmp(B1_4); __ bind(L_2TAG_PACKET_6_0_1); __ movsd(xmm0, ExternalAddress(NEG_INF), r11 /*rscratch*/); __ jmp(B1_4); __ bind(L_2TAG_PACKET_5_0_1); __ movsd(xmm0, Address(rsp)); __ addsd(xmm0, xmm0); __ movq(Address(rsp, 8), xmm0); __ bind(B1_4); __ addq(rsp, 24); __ leave(); // required for proper stackwalking of RuntimeStub frame __ ret(0); return start; } #undef __