1.file "log2.s" 2 3 4// Copyright (c) 2000 - 2003, Intel Corporation 5// All rights reserved. 6// 7// 8// Redistribution and use in source and binary forms, with or without 9// modification, are permitted provided that the following conditions are 10// met: 11// 12// * Redistributions of source code must retain the above copyright 13// notice, this list of conditions and the following disclaimer. 14// 15// * Redistributions in binary form must reproduce the above copyright 16// notice, this list of conditions and the following disclaimer in the 17// documentation and/or other materials provided with the distribution. 18// 19// * The name of Intel Corporation may not be used to endorse or promote 20// products derived from this software without specific prior written 21// permission. 22 23// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 24// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 25// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR 26// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS 27// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, 28// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 29// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 30// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY 31// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING 32// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 33// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 34// 35// Intel Corporation is the author of this code, and requests that all 36// problem reports or change requests be submitted to it directly at 37// http://www.intel.com/software/products/opensource/libraries/num.htm. 38// 39// History 40//================================================================= 41// 09/11/00 Initial version 42// 03/19/01 Added one polynomial coefficient, to improve accuracy 43// 05/20/02 Cleaned up namespace and sf0 syntax 44// 02/10/03 Reordered header: .section, .global, .proc, .align 45// 04/18/03 Reformatted T[255] 46// 47// API 48//================================================================= 49// double log2(double) 50// 51// Overview of operation 52//================================================================= 53// Background 54// 55// Implementation 56// 57// Let x = 2^l * m, where m=1.b1 b2 ... b8 b9 ... b52 58// y=frcpa(m), r=m*y-1, f=b1 b2 .. b8 (table index) 59// j=0 if f<128; j=1 if f>=128 60// T is a table that stores log2(1/y) (in entries 1..255) rounded to 61// double extended precision; f is used as an index; T[255]=0 62// 63// If f=0 and b9=0, r is set to 2^{-8}* 0.b9 b10 ... b52 = m-1 (fractional part of m), 64// and 0 is used instead of T[0] 65// (polynomial evaluation only, for m=1+r, 0<=r<2^{-9}) 66// If f=255, r is set to (m-2)/2 (T[255]=0, and only polynomial evaluation is used 67// for m=2(1-r'), 0<=r'<2^{-9}) 68// 69// log2(x) is approximated as 70// (l-j) + T[f] + (c1*r+c2*r^2+...+c7*r^7), if f>0 71// 72 73 74// Special values 75//================================================================= 76// log2(0)=-inf, raises Divide by Zero 77// log2(+inf)=inf 78// log2(x)=NaN, raises Invalid if x<0 79// 80 81 82// Registers used 83//============================================================== 84// f6-f15, f32-f33 85// r2-r3, r23-r30 86// p6,p7,p8,p12 87// 88 89 90GR_SAVE_B0 = r33 91GR_SAVE_PFS = r34 92GR_SAVE_GP = r35 // This reg. can safely be used 93GR_SAVE_SP = r36 94 95GR_Parameter_X = r37 96GR_Parameter_Y = r38 97GR_Parameter_RESULT = r39 98GR_Parameter_TAG = r40 99 100FR_X = f10 101FR_Y = f1 102FR_RESULT = f8 103 104 105 106 107// Data tables 108//============================================================== 109 110RODATA 111 112.align 16 113 114LOCAL_OBJECT_START(poly_coeffs) 115 116data8 0xbfd0000000000000, 0x3fc999999999999a //C_4, C_5 117data8 0xbfc5555555555555, 0x3fc2492492492492 //C_6, C_7 118data8 0xb8aa3b295c17f0bc, 0x00003fff // C_1 119data8 0xaaaaaaaaaaaaaaab, 0x00003ffd // C_3=1/3 120LOCAL_OBJECT_END(poly_coeffs) 121 122 123LOCAL_OBJECT_START(T_table) 124 125data8 0xb8d8752172fed131, 0x00003ff6 126data8 0x8ae7f475764180a3, 0x00003ff8 127data8 0xe7f73862e72ee35d, 0x00003ff8 128data8 0xa2b25310c941a2f2, 0x00003ff9 129data8 0xcbb91d671abb2e85, 0x00003ff9 130data8 0xfac91e34daa50483, 0x00003ff9 131data8 0x9504a5042eb495c5, 0x00003ffa 132data8 0xa9c4a0bbb580ee02, 0x00003ffa 133data8 0xc19264dc8a5e3bf9, 0x00003ffa 134data8 0xd67aa6703ebf4a77, 0x00003ffa 135data8 0xee76cac6d6e08ce7, 0x00003ffa 136data8 0x81c3f7de5434ed04, 0x00003ffb 137data8 0x8c563033a3ce01e4, 0x00003ffb 138data8 0x9876e9f09a98661c, 0x00003ffb 139data8 0xa31e0ac9b2326ce2, 0x00003ffb 140data8 0xadcf09e1fd10e4a5, 0x00003ffb 141data8 0xb889f992cf03cdb6, 0x00003ffb 142data8 0xc34eec68d901a714, 0x00003ffb 143data8 0xce1df524e9909ed9, 0x00003ffb 144data8 0xd8f726bcb0b80ad0, 0x00003ffb 145data8 0xe3da945b878e27d1, 0x00003ffb 146data8 0xeec851633b76a320, 0x00003ffb 147data8 0xf82ea4bb6101421a, 0x00003ffb 148data8 0x8197ddd7736b2864, 0x00003ffc 149data8 0x871dad4f994253f0, 0x00003ffc 150data8 0x8ca8cae3e892d549, 0x00003ffc 151data8 0x916d6e1559a4b697, 0x00003ffc 152data8 0x97028118efabeb7d, 0x00003ffc 153data8 0x9bcfbce1592ad5d5, 0x00003ffc 154data8 0xa16ee95d0da54a91, 0x00003ffc 155data8 0xa644dcf3403fa5d0, 0x00003ffc 156data8 0xab1ee14ffd659064, 0x00003ffc 157data8 0xb0cd12faebcc6757, 0x00003ffc 158data8 0xb5affdf9b3b221e0, 0x00003ffc 159data8 0xba970fb307c6ade1, 0x00003ffc 160data8 0xbf824f3a9f3e7561, 0x00003ffc 161data8 0xc544c055fde99333, 0x00003ffc 162data8 0xca39266532bdf26c, 0x00003ffc 163data8 0xcf31d124b8fa2f56, 0x00003ffc 164data8 0xd42ec7f59017b6ab, 0x00003ffc 165data8 0xd930124bea9a2c67, 0x00003ffc 166data8 0xde35b7af70e4dab3, 0x00003ffc 167data8 0xe33fbfbb8533ef03, 0x00003ffc 168data8 0xe77625911a7dcef3, 0x00003ffc 169data8 0xec884bd689cc12e3, 0x00003ffc 170data8 0xf19eeabf9e99a40a, 0x00003ffc 171data8 0xf6ba0a35e3d88051, 0x00003ffc 172data8 0xfbd9b237f7b4192b, 0x00003ffc 173data8 0x80111d4a1ee0c79e, 0x00003ffd 174data8 0x82a523a5f875bbfc, 0x00003ffd 175data8 0x84ccecdc92cd0815, 0x00003ffd 176data8 0x87653369d92c057a, 0x00003ffd 177data8 0x89ffd1742da3aa21, 0x00003ffd 178data8 0x8c2d2227d053d9b6, 0x00003ffd 179data8 0x8e5c189793f7f798, 0x00003ffd 180data8 0x90fd0a20e72f3c96, 0x00003ffd 181data8 0x932fa937301e59ae, 0x00003ffd 182data8 0x95d5061a5f0f5f7f, 0x00003ffd 183data8 0x980b5a2ef10e7023, 0x00003ffd 184data8 0x9a4361c5514d3c27, 0x00003ffd 185data8 0x9c7d1f7d541313fd, 0x00003ffd 186data8 0x9f2b16040b500d04, 0x00003ffd 187data8 0xa168a0fa9db22c98, 0x00003ffd 188data8 0xa3a7eaa1f9116293, 0x00003ffd 189data8 0xa5e8f5b4072a3d44, 0x00003ffd 190data8 0xa82bc4f11a5e88aa, 0x00003ffd 191data8 0xaa705b2001db8317, 0x00003ffd 192data8 0xacb6bb0e1e0f8005, 0x00003ffd 193data8 0xaefee78f75707221, 0x00003ffd 194data8 0xb148e37ec994dd99, 0x00003ffd 195data8 0xb394b1bdaca0bc17, 0x00003ffd 196data8 0xb5e255349707e496, 0x00003ffd 197data8 0xb831d0d2fda791cc, 0x00003ffd 198data8 0xba83278f6838ab20, 0x00003ffd 199data8 0xbcd65c67881c7d47, 0x00003ffd 200data8 0xbeb3e0f21d72dc92, 0x00003ffd 201data8 0xc10a7a03457d35dc, 0x00003ffd 202data8 0xc362f9b6f51eddd3, 0x00003ffd 203data8 0xc5bd6326ebfce656, 0x00003ffd 204data8 0xc7a0b3d0637c8f97, 0x00003ffd 205data8 0xc9fe96af0df8e4b5, 0x00003ffd 206data8 0xcc5e6c214b4a2cd7, 0x00003ffd 207data8 0xce46199f374d29cf, 0x00003ffd 208data8 0xd0a978a14c0d9ebe, 0x00003ffd 209data8 0xd293fecafec7f9b5, 0x00003ffd 210data8 0xd4faf1f6f5cf32e6, 0x00003ffd 211data8 0xd6e8595abaad34d1, 0x00003ffd 212data8 0xd952eb7a8ffc1593, 0x00003ffd 213data8 0xdb433ccd805f171e, 0x00003ffd 214data8 0xddb178dc43e6bd84, 0x00003ffd 215data8 0xdfa4bcfb333342a4, 0x00003ffd 216data8 0xe19953741ccea015, 0x00003ffd 217data8 0xe40cee16a2ff21c5, 0x00003ffd 218data8 0xe6048470cdbde8ea, 0x00003ffd 219data8 0xe7fd7308d6895b14, 0x00003ffd 220data8 0xe9f7bbb6a1ff9f87, 0x00003ffd 221data8 0xec7280138809433d, 0x00003ffd 222data8 0xee6fda4365cd051f, 0x00003ffd 223data8 0xf06e94a122ff1f12, 0x00003ffd 224data8 0xf26eb1151441fce5, 0x00003ffd 225data8 0xf470318b88a77e2f, 0x00003ffd 226data8 0xf67317f4d4c8aa58, 0x00003ffd 227data8 0xf8f8b250a9c4cde6, 0x00003ffd 228data8 0xfafec54831f1a484, 0x00003ffd 229data8 0xfd06449bf3eaea1e, 0x00003ffd 230data8 0xff0f324ddb19ab67, 0x00003ffd 231data8 0x808cc8320a9acf15, 0x00003ffe 232data8 0x8192b0748f2cef06, 0x00003ffe 233data8 0x829952f5e6a24ee5, 0x00003ffe 234data8 0x83a0b0bfafe1424e, 0x00003ffe 235data8 0x8466b29f9c41caea, 0x00003ffe 236data8 0x856f5aae0881d857, 0x00003ffe 237data8 0x8678c0eae8ee8190, 0x00003ffe 238data8 0x8782e6685676b9d7, 0x00003ffe 239data8 0x888dcc3abc4554ec, 0x00003ffe 240data8 0x89997378de7b98b8, 0x00003ffe 241data8 0x8aa5dd3be1044279, 0x00003ffe 242data8 0x8b6facdfd0360ab8, 0x00003ffe 243data8 0x8c7d6db7169e0cdb, 0x00003ffe 244data8 0x8d8bf424d6e130b2, 0x00003ffe 245data8 0x8e575b506f409fa6, 0x00003ffe 246data8 0x8f673e418776492c, 0x00003ffe 247data8 0x9077e9ed700ef9ba, 0x00003ffe 248data8 0x9144ef1baec80b20, 0x00003ffe 249data8 0x9256fcdb537f035f, 0x00003ffe 250data8 0x9369d68d75e7e1d6, 0x00003ffe 251data8 0x943880613b8f9f1e, 0x00003ffe 252data8 0x954cc1d9e0d94206, 0x00003ffe 253data8 0xd3c70a37bdf7a294, 0x0000bffd 254data8 0xd19bb053fb0284ec, 0x0000bffd 255data8 0xcffa1a3b7dafb8bf, 0x0000bffd 256data8 0xcdcbe1e2776479ee, 0x0000bffd 257data8 0xcc282218b8bfdda2, 0x0000bffd 258data8 0xc9f703a9afcb38ac, 0x0000bffd 259data8 0xc851146ab89593c6, 0x0000bffd 260data8 0xc61d08265927a860, 0x0000bffd 261data8 0xc474e39705912d26, 0x0000bffd 262data8 0xc23de19ec30c6e3e, 0x0000bffd 263data8 0xc09381cc45db45b4, 0x0000bffd 264data8 0xbee82b4e025ff90c, 0x0000bffd 265data8 0xbcace101149788ec, 0x0000bffd 266data8 0xbaff46962ea47964, 0x0000bffd 267data8 0xb950b1be5e0c14a2, 0x0000bffd 268data8 0xb7110e6ce866f2bc, 0x0000bffd 269data8 0xb5602ccc2a81db52, 0x0000bffd 270data8 0xb3ae4ce740fc8ef1, 0x0000bffd 271data8 0xb1fb6d92c8240ccc, 0x0000bffd 272data8 0xafb609c09b244abc, 0x0000bffd 273data8 0xae00d1cfdeb43cfd, 0x0000bffd 274data8 0xac4a967a8c8c9bd0, 0x0000bffd 275data8 0xaa93568c249e6c52, 0x0000bffd 276data8 0xa8db10cdff375343, 0x0000bffd 277data8 0xa68e6fc5a42376e3, 0x0000bffd 278data8 0xa4d3c25e68dc57f2, 0x0000bffd 279data8 0xa3180b0c192a3816, 0x0000bffd 280data8 0xa15b488e7aa329a0, 0x0000bffd 281data8 0x9f9d79a30f0e1d5f, 0x0000bffd 282data8 0x9dde9d050ee7d4ac, 0x0000bffd 283data8 0x9c1eb16d63d7356c, 0x0000bffd 284data8 0x9a5db592a310c36a, 0x0000bffd 285data8 0x989ba82907a9016f, 0x0000bffd 286data8 0x96d887e26cd57b79, 0x0000bffd 287data8 0x9514536e481c3a4f, 0x0000bffd 288data8 0x934f0979a3715fc9, 0x0000bffd 289data8 0x9188a8af1742a9d5, 0x0000bffd 290data8 0x8fc12fb6c470995f, 0x0000bffd 291data8 0x8df89d364e34f8f1, 0x0000bffd 292data8 0x8c2eefd0d3f67dd6, 0x0000bffd 293data8 0x8a642626eb093d54, 0x0000bffd 294data8 0x88983ed6985bae58, 0x0000bffd 295data8 0x86cb387b4a0feec6, 0x0000bffd 296data8 0x84fd11add101024b, 0x0000bffd 297data8 0x83c856dd81804b78, 0x0000bffd 298data8 0x81f84c2c62afd6f1, 0x0000bffd 299data8 0x80271d3e4be5ea5a, 0x0000bffd 300data8 0xfca991447e7b485d, 0x0000bffc 301data8 0xf90299c904793a3c, 0x0000bffc 302data8 0xf559511d2dc1ed69, 0x0000bffc 303data8 0xf2e72afee9bd2aee, 0x0000bffc 304data8 0xef39ff1d8a40770e, 0x0000bffc 305data8 0xeb8a7a2311c935dc, 0x0000bffc 306data8 0xe7d8990dc620012f, 0x0000bffc 307data8 0xe560b1e3b86e44b6, 0x0000bffc 308data8 0xe1aadb38caee80c4, 0x0000bffc 309data8 0xddf2a051f81b76a4, 0x0000bffc 310data8 0xdb7678bafcaf4b5f, 0x0000bffc 311data8 0xd7ba3a8f0df19bfc, 0x0000bffc 312data8 0xd3fb8fdbdd5cebdb, 0x0000bffc 313data8 0xd17b191905c35652, 0x0000bffc 314data8 0xcdb85d29cefd7121, 0x0000bffc 315data8 0xc9f32c3c88221ef6, 0x0000bffc 316data8 0xc76e5741a95b5dae, 0x0000bffc 317data8 0xc3a506d80d38c718, 0x0000bffc 318data8 0xbfd938ccef8b68c1, 0x0000bffc 319data8 0xbd4ff63e82eef78c, 0x0000bffc 320data8 0xb97ffa2b563865bd, 0x0000bffc 321data8 0xb6f3eb3011eddcea, 0x0000bffc 322data8 0xb31fb7d64898b3e6, 0x0000bffc 323data8 0xb090d63a409e7880, 0x0000bffc 324data8 0xacb8623c7ffa4f39, 0x0000bffc 325data8 0xa8dd5c83d2e45246, 0x0000bffc 326data8 0xa649e998a8d91f2e, 0x0000bffc 327data8 0xa26a93fed6faa94f, 0x0000bffc 328data8 0x9fd43df079d0db1f, 0x0000bffc 329data8 0x9d3cbe69aecac4c2, 0x0000bffc 330data8 0x99574f13c570d0fb, 0x0000bffc 331data8 0x96bce349bf7ee6c7, 0x0000bffc 332data8 0x92d30c9b86cee18e, 0x0000bffc 333data8 0x9035adef17c5bd5c, 0x0000bffc 334data8 0x8c4765e8e8b5f251, 0x0000bffc 335data8 0x89a70da448316ffa, 0x0000bffc 336data8 0x85b44a24474af78a, 0x0000bffc 337data8 0x8310f17aab5adf70, 0x0000bffc 338data8 0x806c6388d0965f29, 0x0000bffc 339data8 0xf8e69092bf0c5ead, 0x0000bffb 340data8 0xf397608bfd2d90e6, 0x0000bffb 341data8 0xee45be24d0eedbc4, 0x0000bffb 342data8 0xe646af233db881e9, 0x0000bffb 343data8 0xe0eee4e1ce3d06fb, 0x0000bffb 344data8 0xdb94a049e6e87a4f, 0x0000bffb 345data8 0xd3888ef9a4249f5a, 0x0000bffb 346data8 0xce280e6fbac39194, 0x0000bffb 347data8 0xc8c50b72319ad574, 0x0000bffb 348data8 0xc0abcd39f41e329b, 0x0000bffb 349data8 0xbb4279cfa7f9667b, 0x0000bffb 350data8 0xb5d69bac77ec398a, 0x0000bffb 351data8 0xb068306bf20d6233, 0x0000bffb 352data8 0xa83dc1b019ddb6a8, 0x0000bffb 353data8 0xa2c8eb1886c2d024, 0x0000bffb 354data8 0x9d517ee93f8e16c0, 0x0000bffb 355data8 0x97d77aae659b92fb, 0x0000bffb 356data8 0x8f9b91da5736d415, 0x0000bffb 357data8 0x8a1b06b09b7fd1d1, 0x0000bffb 358data8 0x8497daca0a2e077a, 0x0000bffb 359data8 0xfe241745a453f10c, 0x0000bffa 360data8 0xf3132d6708d723c5, 0x0000bffa 361data8 0xe7fcf2e21a0e7d77, 0x0000bffa 362data8 0xd75198b04afb8da9, 0x0000bffa 363data8 0xcc2dfe1a4a8ca305, 0x0000bffa 364data8 0xc10500d63aa65882, 0x0000bffa 365data8 0xb5d69bac77ec398a, 0x0000bffa 366data8 0xaaa2c95dc66abcde, 0x0000bffa 367data8 0x9f6984a342d13101, 0x0000bffa 368data8 0x942ac82e5387ac51, 0x0000bffa 369data8 0x88e68ea899a0976c, 0x0000bffa 370data8 0xefebc4409ccf872e, 0x0000bff9 371data8 0xd947b0c6642ef69e, 0x0000bff9 372data8 0xc2987d51e043d407, 0x0000bff9 373data8 0xabde1eeee6bfd257, 0x0000bff9 374data8 0x95188a9917cf2e01, 0x0000bff9 375data8 0xfc8f6a777c1b7f1e, 0x0000bff8 376data8 0xced727635c59725c, 0x0000bff8 377data8 0xa108358a4c904615, 0x0000bff8 378data8 0xe644fcbeb3ac9c90, 0x0000bff7 379data8 0x8a4bd667bf08e7de, 0x0000bff7 380data8 0x0000000000000000 // T[255] Low 381data8 0x0000000000000000 // T[255] High 382LOCAL_OBJECT_END(T_table) 383 384 385 386.section .text 387WEAK_LIBM_ENTRY(log2) 388 389{ .mfi 390 alloc r32=ar.pfs,1,4,4,0 391 // y=frcpa(x) 392 frcpa.s1 f6,p0=f1,f8 393 // will form significand of 1.5 (to test whether the index is 128 or above) 394 mov r24=0xc 395} 396{.mfi 397 nop.m 0 398 // normalize x 399 fma.s1 f7=f8,f1,f0 400 // r2 = pointer to C_1...C_6 followed by T_table 401 addl r2 = @ltoff(poly_coeffs), gp;; 402} 403{.mfi 404 // get significand 405 getf.sig r25=f8 406 // f8 denormal ? 407 fclass.m p8,p10=f8,0x9 408 // will form significand of 1.5 (to test whether the index is 128 or above) 409 shl r24=r24,60 410} 411{.mfi 412 mov r26=0x804 413 nop.f 0 414 // r23=bias-1 415 mov r23=0xfffe;; 416} 417 418{.mmf 419 getf.exp r29=f8 420 // load start address for C_1...C_6 followed by T_table 421 ld8 r2=[r2] 422 // will continue only for positive normal/denormal numbers 423 fclass.nm.unc p12,p7 = f8, 0x19 ;; 424} 425 426.pred.rel "mutex",p8,p10 427{.mfi 428 // denormal input, repeat get significand (after normalization) 429 (p8) getf.sig r25=f7 430 // x=1 ? 431 fcmp.eq.s0 p6,p0=f8,f1 432 // get T_index 433 (p10) shr.u r28=r25,63-8 434} 435{.mfi 436 // f32=0.5 437 setf.exp f32=r23 438 nop.f 0 439 // r27=bias 440 mov r27=0xffff;; 441} 442 443{.mmi 444 // denormal input, repeat get exponent (after normalization) 445 (p8) getf.exp r29=f7 446 mov r23=0xff 447 // r26=0x80400...0 (threshold for using polynomial approximation) 448 shl r26=r26,64-12;; 449} 450 451{.mfb 452 add r3=48,r2 453 // r=1-x*y 454 fms.s1 f6=f6,f8,f1 455 (p12) br.cond.spnt SPECIAL_LOG2 456} 457{.mfi 458 // load C_4, C_5 459 ldfpd f10,f11=[r2],16 460 nop.f 0 461 cmp.geu p12,p0=r25,r24;; 462} 463 464{.mmi 465 // load C_6, C_7 466 ldfpd f12,f13=[r2],16 467 // r27=bias-1 (if index >=128, will add exponent+1) 468 (p12) mov r27=0xfffe 469 (p8) shr.u r28=r25,63-8;; 470} 471 472 473{.mfi 474 // load C_1 475 ldfe f14=[r2],32 476 fmerge.se f7=f1,f7 477 // if first 9 bits after leading 1 are all zero, then p8=1 478 cmp.ltu p8,p12=r25,r26 479} 480{.mfi 481 // load C_3 482 ldfe f15=[r3] 483 nop.f 0 484 // get T_index 485 and r28=r28,r23;; 486} 487{.mfi 488 // r29=exponent-bias 489 sub r29=r29,r27 490 // x=1, return 0 491 (p6) fma.d.s0 f8=f0,f0,f0 492 // get T address 493 shladd r2=r28,4,r2 494} 495{.mfb 496 // first 8 bits after leading 1 are all ones ? 497 cmp.eq p10,p0=r23,r28 498 // if first 8 bits after leading bit are 0, use polynomial approx. only 499 (p8) fms.s1 f6=f7,f1,f1 500 // x=1, return 501 (p6) br.ret.spnt b0;; 502} 503{.mfi 504 // r26=1 505 mov r26=1 506 // if first 8 bits after leading 1 are all ones, use polynomial approx. only 507 (p10) fms.s1 f6=f7,f32,f1 508 nop.i 0;; 509} 510 511.pred.rel "mutex",p8,p12 512{.mmf 513 // load T (unless first 9 bits after leading 1 are 0) 514 (p12) ldfe f33=[r2] 515 // f8=expon - bias 516 setf.sig f8=r29 517 // set T=0 (if first 9 bits after leading 1 are 0) 518 (p8) fma.s1 f33=f0,f0,f0;; 519} 520 521{.mfi 522 nop.m 0 523 // P12=1-0.5*r 524 fnma.s1 f32=f32,f6,f1 525 // r26=2^{63} 526 shl r26=r26,63 527} 528{.mfi 529 nop.m 0 530 // r2=r*r 531 fma.s1 f7=f6,f6,f0 532 nop.i 0;; 533} 534{.mfi 535 // significand(x)=1 ? 536 cmp.eq p0,p6=r26,r25 537 // P67=C_6+C_7*r 538 fma.s1 f13=f13,f6,f12 539 nop.i 0 540} 541{.mfi 542 nop.m 0 543 // P45=C_4+C_5*r 544 fma.s1 f10=f11,f6,f10 545 nop.i 0;; 546} 547 548{.mfi 549 nop.m 0 550 // C_1*r 551 (p6) fma.s1 f14=f14,f6,f0 552 nop.i 0;; 553} 554{.mfi 555 nop.m 0 556 // normalize additive term (l=exponent of x) 557 fcvt.xf f8=f8 558 nop.i 0 559} 560{.mfi 561 nop.m 0 562 // P13=1-0.5*r+C_3*r^2 563 (p6) fma.s1 f15=f15,f7,f32 564 nop.i 0;; 565} 566 567{.mfi 568 nop.m 0 569 // P47=P45+r2*P67 570 (p6) fma.s1 f13=f13,f7,f10 571 // if significand(x)=1, return exponent (l) 572 nop.i 0 573} 574{.mfi 575 nop.m 0 576 // r3=r^3 577 (p6) fma.s1 f7=f7,f6,f0 578 nop.i 0;; 579} 580 581{.mfi 582 nop.m 0 583 // add T+l 584 (p6) fma.s1 f8=f8,f1,f33 585 nop.i 0 586} 587{.mfi 588 nop.m 0 589 // P17=P13+r3*P47 590 (p6) fma.s1 f13=f13,f7,f15 591 nop.i 0;; 592} 593 594{.mfb 595 nop.m 0 596 // result=T+l+(C_1*r)*P16 597 (p6) fma.d.s0 f8=f13,f14,f8 598 // return 599 br.ret.sptk b0;; 600} 601 602 603SPECIAL_LOG2: 604{.mfi 605 nop.m 0 606 // x=+Infinity ? 607 fclass.m p7,p0=f8,0x21 608 nop.i 0;; 609} 610{.mfi 611 nop.m 0 612 // x=+/-Zero ? 613 fclass.m p8,p0=f8,0x7 614 nop.i 0;; 615} 616{.mfi 617 nop.m 0 618 // x=-Infinity, -normal, -denormal ? 619 fclass.m p6,p0=f8,0x3a 620 nop.i 0;; 621} 622{.mfb 623 nop.m 0 624 // log2(+Infinity)=+Infinity 625 nop.f 0 626 (p7) br.ret.spnt b0;; 627} 628{.mfi 629 (p8) mov GR_Parameter_TAG = 170 630 // log2(+/-0)=-infinity, raises Divide by Zero 631 // set f8=-0 632 (p8) fmerge.ns f8=f0,f8 633 nop.i 0;; 634} 635{.mfb 636 nop.m 0 637 (p8) frcpa.s0 f8,p0=f1,f8 638 (p8) br.cond.sptk __libm_error_region;; 639} 640{.mfb 641 (p6) mov GR_Parameter_TAG = 171 642 // x<0: return NaN, raise Invalid 643 (p6) frcpa.s0 f8,p0=f0,f0 644 (p6) br.cond.sptk __libm_error_region;; 645} 646 647 648{.mfb 649 nop.m 0 650 // Remaining cases: NaNs 651 fma.d.s0 f8=f8,f1,f0 652 br.ret.sptk b0;; 653} 654 655WEAK_LIBM_END(log2) 656libm_alias_double_other (__log2, log2) 657#ifdef SHARED 658.symver log2,log2@@GLIBC_2.29 659.weak __log2_compat 660.set __log2_compat,__log2 661.symver __log2_compat,log2@GLIBC_2.2 662#endif 663 664 665LOCAL_LIBM_ENTRY(__libm_error_region) 666.prologue 667{ .mfi 668 add GR_Parameter_Y=-32,sp // Parameter 2 value 669 nop.f 0 670.save ar.pfs,GR_SAVE_PFS 671 mov GR_SAVE_PFS=ar.pfs // Save ar.pfs 672} 673{ .mfi 674.fframe 64 675 add sp=-64,sp // Create new stack 676 nop.f 0 677 mov GR_SAVE_GP=gp // Save gp 678};; 679{ .mmi 680 stfd [GR_Parameter_Y] = FR_Y,16 // STORE Parameter 2 on stack 681 add GR_Parameter_X = 16,sp // Parameter 1 address 682.save b0, GR_SAVE_B0 683 mov GR_SAVE_B0=b0 // Save b0 684};; 685.body 686{ .mib 687 stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack 688 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address 689 nop.b 0 690} 691{ .mib 692 stfd [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack 693 add GR_Parameter_Y = -16,GR_Parameter_Y 694 br.call.sptk b0=__libm_error_support# // Call error handling function 695};; 696{ .mmi 697 nop.m 0 698 nop.m 0 699 add GR_Parameter_RESULT = 48,sp 700};; 701{ .mmi 702 ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack 703.restore sp 704 add sp = 64,sp // Restore stack pointer 705 mov b0 = GR_SAVE_B0 // Restore return address 706};; 707{ .mib 708 mov gp = GR_SAVE_GP // Restore gp 709 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs 710 br.ret.sptk b0 // Return 711};; 712 713LOCAL_LIBM_END(__libm_error_region) 714.type __libm_error_support#,@function 715.global __libm_error_support# 716