1.file "acoshl.s" 2 3 4// Copyright (c) 2000 - 2005, 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//********************************************************************* 40// 41// History: 42// 10/01/01 Initial version 43// 10/10/01 Performance inproved 44// 12/11/01 Changed huges_logp to not be global 45// 01/02/02 Corrected .restore syntax 46// 05/20/02 Cleaned up namespace and sf0 syntax 47// 08/14/02 Changed mli templates to mlx 48// 02/06/03 Reorganized data tables 49// 03/31/05 Reformatted delimiters between data tables 50// 51//********************************************************************* 52// 53// API 54//============================================================== 55// long double acoshl(long double); 56// 57// Overview of operation 58//============================================================== 59// 60// There are 6 paths: 61// 1. x = 1 62// Return acoshl(x) = 0; 63// 64// 2. x < 1 65// Return acoshl(x) = Nan (Domain error, error handler call with tag 135); 66// 67// 3. x = [S,Q]Nan or +INF 68// Return acoshl(x) = x + x; 69// 70// 4. 'Near 1': 1 < x < 1+1/8 71// Return acoshl(x) = sqrtl(2*y)*(1-P(y)/Q(y)), 72// where y = 1, P(y)/Q(y) - rational approximation 73// 74// 5. 'Huges': x > 0.5*2^64 75// Return acoshl(x) = (logl(2*x-1)); 76// 77// 6. 'Main path': 1+1/8 < x < 0.5*2^64 78// b_hi + b_lo = x + sqrt(x^2 - 1); 79// acoshl(x) = logl_special(b_hi, b_lo); 80// 81// Algorithm description 82//============================================================== 83// 84// I. Near 1 path algorithm 85// ************************************************************** 86// The formula is acoshl(x) = sqrtl(2*y)*(1-P(y)/Q(y)), 87// where y = 1, P(y)/Q(y) - rational approximation 88// 89// 1) y = x - 1, y2 = 2 * y 90// 91// 2) Compute in parallel sqrtl(2*y) and P(y)/Q(y) 92// a) sqrtl computation method described below (main path algorithm, item 2)) 93// As result we obtain (gg+gl) - multiprecision result 94// as pair of double extended values 95// b) P(y) and Q(y) calculated without any extra precision manipulations 96// c) P/Q division: 97// y = frcpa(Q) initial approximation of 1/Q 98// z = P*y initial approximation of P/Q 99// 100// e = 1 - b*y 101// e2 = e + e^2 102// e1 = e^2 103// y1 = y + y*e2 = y + y*(e+e^2) 104// 105// e3 = e + e1^2 106// y2 = y + y1*e3 = y + y*(e+e^2+..+e^6) 107// 108// r = P - Q*z 109// e = 1 - Q*y2 110// xx = z + r*y2 high part of a/b 111// 112// y3 = y2 + y2*e4 113// r1 = P - Q*xx 114// xl = r1*y3 low part of a/b 115// 116// 3) res = sqrt(2*y) - sqrt(2*y)*(P(y)/Q(y)) = 117// = (gg+gl) - (gg + gl)*(xx+xl); 118// 119// a) hh = gg*xx; hl = gg*xl; lh = gl*xx; ll = gl*xl; 120// b) res = ((((gl + ll) + lh) + hl) + hh) + gg; 121// (exactly in this order) 122// 123// II. Main path algorithm 124// ( thanks to Peter Markstein for the idea of sqrt(x^2+1) computation! ) 125// ********************************************************************** 126// 127// There are 3 parts of x+sqrt(x^2-1) computation: 128// 129// 1) m2 = (m2_hi+m2_lo) = x^2-1 obtaining 130// ------------------------------------ 131// m2_hi = x2_hi - 1, where x2_hi = x * x; 132// m2_lo = x2_lo + p1_lo, where 133// x2_lo = FMS(x*x-x2_hi), 134// p1_lo = (1 + m2_hi) - x2_hi; 135// 136// 2) g = (g_hi+g_lo) = sqrt(m2) = sqrt(m2_hi+m2_lo) 137// ---------------------------------------------- 138// r = invsqrt(m2_hi) (8-bit reciprocal square root approximation); 139// g = m2_hi * r (first 8 bit-approximation of sqrt); 140// 141// h = 0.5 * r; 142// e = 0.5 - g * h; 143// g = g * e + g (second 16 bit-approximation of sqrt); 144// 145// h = h * e + h; 146// e = 0.5 - g * h; 147// g = g * e + g (third 32 bit-approximation of sqrt); 148// 149// h = h * e + h; 150// e = 0.5 - g * h; 151// g_hi = g * e + g (fourth 64 bit-approximation of sqrt); 152// 153// Remainder computation: 154// h = h * e + h; 155// d = (m2_hi - g_hi * g_hi) + m2_lo; 156// g_lo = d * h; 157// 158// 3) b = (b_hi + b_lo) = x + g, where g = (g_hi + g_lo) = sqrt(x^2-1) 159// ------------------------------------------------------------------- 160// b_hi = (g_hi + x) + gl; 161// b_lo = (x - b_hi) + g_hi + gl; 162// 163// Now we pass b presented as sum b_hi + b_lo to special version 164// of logl function which accept a pair of arguments as 165// mutiprecision value. 166// 167// Special log algorithm overview 168// ================================ 169// Here we use a table lookup method. The basic idea is that in 170// order to compute logl(Arg) for an argument Arg in [1,2), 171// we construct a value G such that G*Arg is close to 1 and that 172// logl(1/G) is obtainable easily from a table of values calculated 173// beforehand. Thus 174// 175// logl(Arg) = logl(1/G) + logl((G*Arg - 1)) 176// 177// Because |G*Arg - 1| is small, the second term on the right hand 178// side can be approximated by a short polynomial. We elaborate 179// this method in four steps. 180// 181// Step 0: Initialization 182// 183// We need to calculate logl( X+1 ). Obtain N, S_hi such that 184// 185// X = 2^N * ( S_hi + S_lo ) exactly 186// 187// where S_hi in [1,2) and S_lo is a correction to S_hi in the sense 188// that |S_lo| <= ulp(S_hi). 189// 190// For the special version of logl: S_lo = b_lo 191// !-----------------------------------------------! 192// 193// Step 1: Argument Reduction 194// 195// Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate 196// 197// G := G_1 * G_2 * G_3 198// r := (G * S_hi - 1) + G * S_lo 199// 200// These G_j's have the property that the product is exactly 201// representable and that |r| < 2^(-12) as a result. 202// 203// Step 2: Approximation 204// 205// logl(1 + r) is approximated by a short polynomial poly(r). 206// 207// Step 3: Reconstruction 208// 209// Finally, logl( X ) = logl( X+1 ) is given by 210// 211// logl( X ) = logl( 2^N * (S_hi + S_lo) ) 212// ~=~ N*logl(2) + logl(1/G) + logl(1 + r) 213// ~=~ N*logl(2) + logl(1/G) + poly(r). 214// 215// For detailed description see logl or log1pl function, regular path. 216// 217// Registers used 218//============================================================== 219// Floating Point registers used: 220// f8, input 221// f32 -> f95 (64 registers) 222 223// General registers used: 224// r32 -> r67 (36 registers) 225 226// Predicate registers used: 227// p7 -> p11 228// p7 for 'NaNs, Inf' path 229// p8 for 'near 1' path 230// p9 for 'huges' path 231// p10 for x = 1 232// p11 for x < 1 233// 234//********************************************************************* 235// IEEE Special Conditions: 236// 237// acoshl(+inf) = +inf 238// acoshl(-inf) = QNaN 239// acoshl(1) = 0 240// acoshl(x<1) = QNaN 241// acoshl(SNaN) = QNaN 242// acoshl(QNaN) = QNaN 243// 244 245// Data tables 246//============================================================== 247 248RODATA 249.align 64 250 251// Near 1 path rational approximation coefficients 252LOCAL_OBJECT_START(Poly_P) 253data8 0xB0978143F695D40F, 0x3FF1 // .84205539791447100108478906277453574946e-4 254data8 0xB9800D841A8CAD29, 0x3FF6 // .28305085180397409672905983082168721069e-2 255data8 0xC889F455758C1725, 0x3FF9 // .24479844297887530847660233111267222945e-1 256data8 0x9BE1DFF006F45F12, 0x3FFB // .76114415657565879842941751209926938306e-1 257data8 0x9E34AF4D372861E0, 0x3FFB // .77248925727776366270605984806795850504e-1 258data8 0xF3DC502AEE14C4AE, 0x3FA6 // .3077953476682583606615438814166025592e-26 259LOCAL_OBJECT_END(Poly_P) 260 261// 262LOCAL_OBJECT_START(Poly_Q) 263data8 0xF76E3FD3C7680357, 0x3FF1 // .11798413344703621030038719253730708525e-3 264data8 0xD107D2E7273263AE, 0x3FF7 // .63791065024872525660782716786703188820e-2 265data8 0xB609BE5CDE206AEF, 0x3FFB // .88885771950814004376363335821980079985e-1 266data8 0xF7DEACAC28067C8A, 0x3FFD // .48412074662702495416825113623936037072302 267data8 0x8F9BE5890CEC7E38, 0x3FFF // 1.1219450873557867470217771071068369729526 268data8 0xED4F06F3D2BC92D1, 0x3FFE // .92698710873331639524734537734804056798748 269LOCAL_OBJECT_END(Poly_Q) 270 271// Q coeffs 272LOCAL_OBJECT_START(Constants_Q) 273data4 0x00000000,0xB1721800,0x00003FFE,0x00000000 274data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000 275data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000 276data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000 277data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000 278data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000 279LOCAL_OBJECT_END(Constants_Q) 280 281// Z1 - 16 bit fixed 282LOCAL_OBJECT_START(Constants_Z_1) 283data4 0x00008000 284data4 0x00007879 285data4 0x000071C8 286data4 0x00006BCB 287data4 0x00006667 288data4 0x00006187 289data4 0x00005D18 290data4 0x0000590C 291data4 0x00005556 292data4 0x000051EC 293data4 0x00004EC5 294data4 0x00004BDB 295data4 0x00004925 296data4 0x0000469F 297data4 0x00004445 298data4 0x00004211 299LOCAL_OBJECT_END(Constants_Z_1) 300 301// G1 and H1 - IEEE single and h1 - IEEE double 302LOCAL_OBJECT_START(Constants_G_H_h1) 303data4 0x3F800000,0x00000000 304data8 0x0000000000000000 305data4 0x3F70F0F0,0x3D785196 306data8 0x3DA163A6617D741C 307data4 0x3F638E38,0x3DF13843 308data8 0x3E2C55E6CBD3D5BB 309data4 0x3F579430,0x3E2FF9A0 310data8 0xBE3EB0BFD86EA5E7 311data4 0x3F4CCCC8,0x3E647FD6 312data8 0x3E2E6A8C86B12760 313data4 0x3F430C30,0x3E8B3AE7 314data8 0x3E47574C5C0739BA 315data4 0x3F3A2E88,0x3EA30C68 316data8 0x3E20E30F13E8AF2F 317data4 0x3F321640,0x3EB9CEC8 318data8 0xBE42885BF2C630BD 319data4 0x3F2AAAA8,0x3ECF9927 320data8 0x3E497F3497E577C6 321data4 0x3F23D708,0x3EE47FC5 322data8 0x3E3E6A6EA6B0A5AB 323data4 0x3F1D89D8,0x3EF8947D 324data8 0xBDF43E3CD328D9BE 325data4 0x3F17B420,0x3F05F3A1 326data8 0x3E4094C30ADB090A 327data4 0x3F124920,0x3F0F4303 328data8 0xBE28FBB2FC1FE510 329data4 0x3F0D3DC8,0x3F183EBF 330data8 0x3E3A789510FDE3FA 331data4 0x3F088888,0x3F20EC80 332data8 0x3E508CE57CC8C98F 333data4 0x3F042108,0x3F29516A 334data8 0xBE534874A223106C 335LOCAL_OBJECT_END(Constants_G_H_h1) 336 337// Z2 - 16 bit fixed 338LOCAL_OBJECT_START(Constants_Z_2) 339data4 0x00008000 340data4 0x00007F81 341data4 0x00007F02 342data4 0x00007E85 343data4 0x00007E08 344data4 0x00007D8D 345data4 0x00007D12 346data4 0x00007C98 347data4 0x00007C20 348data4 0x00007BA8 349data4 0x00007B31 350data4 0x00007ABB 351data4 0x00007A45 352data4 0x000079D1 353data4 0x0000795D 354data4 0x000078EB 355LOCAL_OBJECT_END(Constants_Z_2) 356 357// G2 and H2 - IEEE single and h2 - IEEE double 358LOCAL_OBJECT_START(Constants_G_H_h2) 359data4 0x3F800000,0x00000000 360data8 0x0000000000000000 361data4 0x3F7F00F8,0x3B7F875D 362data8 0x3DB5A11622C42273 363data4 0x3F7E03F8,0x3BFF015B 364data8 0x3DE620CF21F86ED3 365data4 0x3F7D08E0,0x3C3EE393 366data8 0xBDAFA07E484F34ED 367data4 0x3F7C0FC0,0x3C7E0586 368data8 0xBDFE07F03860BCF6 369data4 0x3F7B1880,0x3C9E75D2 370data8 0x3DEA370FA78093D6 371data4 0x3F7A2328,0x3CBDC97A 372data8 0x3DFF579172A753D0 373data4 0x3F792FB0,0x3CDCFE47 374data8 0x3DFEBE6CA7EF896B 375data4 0x3F783E08,0x3CFC15D0 376data8 0x3E0CF156409ECB43 377data4 0x3F774E38,0x3D0D874D 378data8 0xBE0B6F97FFEF71DF 379data4 0x3F766038,0x3D1CF49B 380data8 0xBE0804835D59EEE8 381data4 0x3F757400,0x3D2C531D 382data8 0x3E1F91E9A9192A74 383data4 0x3F748988,0x3D3BA322 384data8 0xBE139A06BF72A8CD 385data4 0x3F73A0D0,0x3D4AE46F 386data8 0x3E1D9202F8FBA6CF 387data4 0x3F72B9D0,0x3D5A1756 388data8 0xBE1DCCC4BA796223 389data4 0x3F71D488,0x3D693B9D 390data8 0xBE049391B6B7C239 391LOCAL_OBJECT_END(Constants_G_H_h2) 392 393// G3 and H3 - IEEE single and h3 - IEEE double 394LOCAL_OBJECT_START(Constants_G_H_h3) 395data4 0x3F7FFC00,0x38800100 396data8 0x3D355595562224CD 397data4 0x3F7FF400,0x39400480 398data8 0x3D8200A206136FF6 399data4 0x3F7FEC00,0x39A00640 400data8 0x3DA4D68DE8DE9AF0 401data4 0x3F7FE400,0x39E00C41 402data8 0xBD8B4291B10238DC 403data4 0x3F7FDC00,0x3A100A21 404data8 0xBD89CCB83B1952CA 405data4 0x3F7FD400,0x3A300F22 406data8 0xBDB107071DC46826 407data4 0x3F7FCC08,0x3A4FF51C 408data8 0x3DB6FCB9F43307DB 409data4 0x3F7FC408,0x3A6FFC1D 410data8 0xBD9B7C4762DC7872 411data4 0x3F7FBC10,0x3A87F20B 412data8 0xBDC3725E3F89154A 413data4 0x3F7FB410,0x3A97F68B 414data8 0xBD93519D62B9D392 415data4 0x3F7FAC18,0x3AA7EB86 416data8 0x3DC184410F21BD9D 417data4 0x3F7FA420,0x3AB7E101 418data8 0xBDA64B952245E0A6 419data4 0x3F7F9C20,0x3AC7E701 420data8 0x3DB4B0ECAABB34B8 421data4 0x3F7F9428,0x3AD7DD7B 422data8 0x3D9923376DC40A7E 423data4 0x3F7F8C30,0x3AE7D474 424data8 0x3DC6E17B4F2083D3 425data4 0x3F7F8438,0x3AF7CBED 426data8 0x3DAE314B811D4394 427data4 0x3F7F7C40,0x3B03E1F3 428data8 0xBDD46F21B08F2DB1 429data4 0x3F7F7448,0x3B0BDE2F 430data8 0xBDDC30A46D34522B 431data4 0x3F7F6C50,0x3B13DAAA 432data8 0x3DCB0070B1F473DB 433data4 0x3F7F6458,0x3B1BD766 434data8 0xBDD65DDC6AD282FD 435data4 0x3F7F5C68,0x3B23CC5C 436data8 0xBDCDAB83F153761A 437data4 0x3F7F5470,0x3B2BC997 438data8 0xBDDADA40341D0F8F 439data4 0x3F7F4C78,0x3B33C711 440data8 0x3DCD1BD7EBC394E8 441data4 0x3F7F4488,0x3B3BBCC6 442data8 0xBDC3532B52E3E695 443data4 0x3F7F3C90,0x3B43BAC0 444data8 0xBDA3961EE846B3DE 445data4 0x3F7F34A0,0x3B4BB0F4 446data8 0xBDDADF06785778D4 447data4 0x3F7F2CA8,0x3B53AF6D 448data8 0x3DCC3ED1E55CE212 449data4 0x3F7F24B8,0x3B5BA620 450data8 0xBDBA31039E382C15 451data4 0x3F7F1CC8,0x3B639D12 452data8 0x3D635A0B5C5AF197 453data4 0x3F7F14D8,0x3B6B9444 454data8 0xBDDCCB1971D34EFC 455data4 0x3F7F0CE0,0x3B7393BC 456data8 0x3DC7450252CD7ADA 457data4 0x3F7F04F0,0x3B7B8B6D 458data8 0xBDB68F177D7F2A42 459LOCAL_OBJECT_END(Constants_G_H_h3) 460 461// Assembly macros 462//============================================================== 463 464// Floating Point Registers 465 466FR_Arg = f8 467FR_Res = f8 468 469 470FR_PP0 = f32 471FR_PP1 = f33 472FR_PP2 = f34 473FR_PP3 = f35 474FR_PP4 = f36 475FR_PP5 = f37 476FR_QQ0 = f38 477FR_QQ1 = f39 478FR_QQ2 = f40 479FR_QQ3 = f41 480FR_QQ4 = f42 481FR_QQ5 = f43 482 483FR_Q1 = f44 484FR_Q2 = f45 485FR_Q3 = f46 486FR_Q4 = f47 487 488FR_Half = f48 489FR_Two = f49 490 491FR_log2_hi = f50 492FR_log2_lo = f51 493 494 495FR_X2 = f52 496FR_M2 = f53 497FR_M2L = f54 498FR_Rcp = f55 499FR_GG = f56 500FR_HH = f57 501FR_EE = f58 502FR_DD = f59 503FR_GL = f60 504FR_Tmp = f61 505 506 507FR_XM1 = f62 508FR_2XM1 = f63 509FR_XM12 = f64 510 511 512 513 // Special logl registers 514FR_XLog_Hi = f65 515FR_XLog_Lo = f66 516 517FR_Y_hi = f67 518FR_Y_lo = f68 519 520FR_S_hi = f69 521FR_S_lo = f70 522 523FR_poly_lo = f71 524FR_poly_hi = f72 525 526FR_G = f73 527FR_H = f74 528FR_h = f75 529 530FR_G2 = f76 531FR_H2 = f77 532FR_h2 = f78 533 534FR_r = f79 535FR_rsq = f80 536FR_rcub = f81 537 538FR_float_N = f82 539 540FR_G3 = f83 541FR_H3 = f84 542FR_h3 = f85 543 544FR_2_to_minus_N = f86 545 546 547 // Near 1 registers 548FR_PP = f65 549FR_QQ = f66 550 551 552FR_PV6 = f69 553FR_PV4 = f70 554FR_PV3 = f71 555FR_PV2 = f72 556 557FR_QV6 = f73 558FR_QV4 = f74 559FR_QV3 = f75 560FR_QV2 = f76 561 562FR_Y0 = f77 563FR_Q0 = f78 564FR_E0 = f79 565FR_E2 = f80 566FR_E1 = f81 567FR_Y1 = f82 568FR_E3 = f83 569FR_Y2 = f84 570FR_R0 = f85 571FR_E4 = f86 572FR_Y3 = f87 573FR_R1 = f88 574FR_X_Hi = f89 575FR_X_lo = f90 576 577FR_HH = f91 578FR_LL = f92 579FR_HL = f93 580FR_LH = f94 581 582 583 584 // Error handler registers 585FR_Arg_X = f95 586FR_Arg_Y = f0 587 588 589// General Purpose Registers 590 591 // General prolog registers 592GR_PFS = r32 593GR_OneP125 = r33 594GR_TwoP63 = r34 595GR_Arg = r35 596GR_Half = r36 597 598 // Near 1 path registers 599GR_Poly_P = r37 600GR_Poly_Q = r38 601 602 // Special logl registers 603GR_Index1 = r39 604GR_Index2 = r40 605GR_signif = r41 606GR_X_0 = r42 607GR_X_1 = r43 608GR_X_2 = r44 609GR_minus_N = r45 610GR_Z_1 = r46 611GR_Z_2 = r47 612GR_N = r48 613GR_Bias = r49 614GR_M = r50 615GR_Index3 = r51 616GR_exp_2tom80 = r52 617GR_exp_mask = r53 618GR_exp_2tom7 = r54 619GR_ad_ln10 = r55 620GR_ad_tbl_1 = r56 621GR_ad_tbl_2 = r57 622GR_ad_tbl_3 = r58 623GR_ad_q = r59 624GR_ad_z_1 = r60 625GR_ad_z_2 = r61 626GR_ad_z_3 = r62 627 628// 629// Added for unwind support 630// 631GR_SAVE_PFS = r32 632GR_SAVE_B0 = r33 633GR_SAVE_GP = r34 634 635GR_Parameter_X = r64 636GR_Parameter_Y = r65 637GR_Parameter_RESULT = r66 638GR_Parameter_TAG = r67 639 640 641 642.section .text 643GLOBAL_LIBM_ENTRY(acoshl) 644 645{ .mfi 646 alloc GR_PFS = ar.pfs,0,32,4,0 // Local frame allocation 647 fcmp.lt.s1 p11, p0 = FR_Arg, f1 // if arg is less than 1 648 mov GR_Half = 0xfffe // 0.5's exp 649} 650{ .mfi 651 addl GR_Poly_Q = @ltoff(Poly_Q), gp // Address of Q-coeff table 652 fma.s1 FR_X2 = FR_Arg, FR_Arg, f0 // Obtain x^2 653 addl GR_Poly_P = @ltoff(Poly_P), gp // Address of P-coeff table 654};; 655 656{ .mfi 657 getf.d GR_Arg = FR_Arg // get argument as double (int64) 658 fma.s0 FR_Two = f1, f1, f1 // construct 2.0 659 addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp // logl tables 660} 661{ .mlx 662 nop.m 0 663 movl GR_TwoP63 = 0x43E8000000000000 // 0.5*2^63 (huge arguments) 664};; 665 666{ .mfi 667 ld8 GR_Poly_P = [GR_Poly_P] // get actual P-coeff table address 668 fcmp.eq.s1 p10, p0 = FR_Arg, f1 // if arg == 1 (return 0) 669 nop.i 0 670} 671{ .mlx 672 ld8 GR_Poly_Q = [GR_Poly_Q] // get actual Q-coeff table address 673 movl GR_OneP125 = 0x3FF2000000000000 // 1.125 (near 1 path bound) 674};; 675 676{ .mfi 677 ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1 678 fclass.m p7,p0 = FR_Arg, 0xe3 // if arg NaN inf 679 cmp.le p9, p0 = GR_TwoP63, GR_Arg // if arg > 0.5*2^63 ('huges') 680} 681{ .mfb 682 cmp.ge p8, p0 = GR_OneP125, GR_Arg // if arg<1.125 -near 1 path 683 fms.s1 FR_XM1 = FR_Arg, f1, f1 // X0 = X-1 (for near 1 path) 684(p11) br.cond.spnt acoshl_lt_pone // error branch (less than 1) 685};; 686 687{ .mmi 688 setf.exp FR_Half = GR_Half // construct 0.5 689(p9) setf.s FR_XLog_Lo = r0 // Low of logl arg=0 (Huges path) 690 mov GR_exp_mask = 0x1FFFF // Create exponent mask 691};; 692 693{ .mmf 694(p8) ldfe FR_PP5 = [GR_Poly_P],16 // Load P5 695(p8) ldfe FR_QQ5 = [GR_Poly_Q],16 // Load Q5 696 fms.s1 FR_M2 = FR_X2, f1, f1 // m2 = x^2 - 1 697};; 698 699{ .mfi 700(p8) ldfe FR_QQ4 = [GR_Poly_Q],16 // Load Q4 701 fms.s1 FR_M2L = FR_Arg, FR_Arg, FR_X2 // low part of 702 // m2 = fma(X*X - m2) 703 add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1 704} 705{ .mfb 706(p8) ldfe FR_PP4 = [GR_Poly_P],16 // Load P4 707(p7) fma.s0 FR_Res = FR_Arg,f1,FR_Arg // r = a + a (Nan, Inf) 708(p7) br.ret.spnt b0 // return (Nan, Inf) 709};; 710 711{ .mfi 712(p8) ldfe FR_PP3 = [GR_Poly_P],16 // Load P3 713 nop.f 0 714 add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_P 715} 716{ .mfb 717(p8) ldfe FR_QQ3 = [GR_Poly_Q],16 // Load Q3 718(p9) fms.s1 FR_XLog_Hi = FR_Two, FR_Arg, f1 // Hi of log arg = 2*X-1 719(p9) br.cond.spnt huges_logl // special version of log 720} 721;; 722 723{ .mfi 724(p8) ldfe FR_PP2 = [GR_Poly_P],16 // Load P2 725(p8) fma.s1 FR_2XM1 = FR_Two, FR_XM1, f0 // 2X0 = 2 * X0 726 add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2 727} 728{ .mfb 729(p8) ldfe FR_QQ2 = [GR_Poly_Q],16 // Load Q2 730(p10) fma.s0 FR_Res = f0,f1,f0 // r = 0 (arg = 1) 731(p10) br.ret.spnt b0 // return (arg = 1) 732};; 733 734{ .mmi 735(p8) ldfe FR_PP1 = [GR_Poly_P],16 // Load P1 736(p8) ldfe FR_QQ1 = [GR_Poly_Q],16 // Load Q1 737 add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2 738} 739;; 740 741{ .mfi 742(p8) ldfe FR_PP0 = [GR_Poly_P] // Load P0 743 fma.s1 FR_Tmp = f1, f1, FR_M2 // Tmp = 1 + m2 744 add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3 745} 746{ .mfb 747(p8) ldfe FR_QQ0 = [GR_Poly_Q] 748 nop.f 0 749(p8) br.cond.spnt near_1 // near 1 path 750};; 751{ .mfi 752 ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi 753 nop.f 0 754 mov GR_Bias = 0x0FFFF // Create exponent bias 755};; 756{ .mfi 757 nop.m 0 758 frsqrta.s1 FR_Rcp, p0 = FR_M2 // Rcp = 1/m2 reciprocal appr. 759 nop.i 0 760};; 761 762{ .mfi 763 ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo 764 fms.s1 FR_Tmp = FR_X2, f1, FR_Tmp // Tmp = x^2 - Tmp 765 nop.i 0 766};; 767 768{ .mfi 769 ldfe FR_Q4 = [GR_ad_q],16 // Load Q4 770 fma.s1 FR_GG = FR_Rcp, FR_M2, f0 // g = Rcp * m2 771 // 8 bit Newton Raphson iteration 772 nop.i 0 773} 774{ .mfi 775 nop.m 0 776 fma.s1 FR_HH = FR_Half, FR_Rcp, f0 // h = 0.5 * Rcp 777 nop.i 0 778};; 779{ .mfi 780 ldfe FR_Q3 = [GR_ad_q],16 // Load Q3 781 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h 782 nop.i 0 783} 784{ .mfi 785 nop.m 0 786 fma.s1 FR_M2L = FR_Tmp, f1, FR_M2L // low part of m2 = Tmp+m2l 787 nop.i 0 788};; 789 790{ .mfi 791 ldfe FR_Q2 = [GR_ad_q],16 // Load Q2 792 fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g 793 // 16 bit Newton Raphson iteration 794 nop.i 0 795} 796{ .mfi 797 nop.m 0 798 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h 799 nop.i 0 800};; 801 802{ .mfi 803 ldfe FR_Q1 = [GR_ad_q] // Load Q1 804 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h 805 nop.i 0 806};; 807{ .mfi 808 nop.m 0 809 fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g 810 // 32 bit Newton Raphson iteration 811 nop.i 0 812} 813{ .mfi 814 nop.m 0 815 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h 816 nop.i 0 817};; 818 819{ .mfi 820 nop.m 0 821 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h 822 nop.i 0 823};; 824 825{ .mfi 826 nop.m 0 827 fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g 828 // 64 bit Newton Raphson iteration 829 nop.i 0 830} 831{ .mfi 832 nop.m 0 833 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h 834 nop.i 0 835};; 836 837{ .mfi 838 nop.m 0 839 fnma.s1 FR_DD = FR_GG, FR_GG, FR_M2 // Remainder d = g * g - p2 840 nop.i 0 841} 842{ .mfi 843 nop.m 0 844 fma.s1 FR_XLog_Hi = FR_Arg, f1, FR_GG // bh = z + gh 845 nop.i 0 846};; 847 848{ .mfi 849 nop.m 0 850 fma.s1 FR_DD = FR_DD, f1, FR_M2L // add p2l: d = d + p2l 851 nop.i 0 852};; 853 854{ .mfi 855 getf.sig GR_signif = FR_XLog_Hi // Get significand of x+1 856 nop.f 0 857 mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7 858};; 859 860{ .mfi 861 nop.m 0 862 fma.s1 FR_GL = FR_DD, FR_HH, f0 // gl = d * h 863 extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif 864} 865{ .mfi 866 nop.m 0 867 fma.s1 FR_XLog_Hi = FR_DD, FR_HH, FR_XLog_Hi // bh = bh + gl 868 nop.i 0 869};; 870 871 872 873{ .mmi 874 shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1 875 shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1 876 extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of signif. 877};; 878 879{ .mmi 880 ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 881 nop.m 0 882 nop.i 0 883};; 884 885{ .mmi 886 ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 887 nop.m 0 888 nop.i 0 889};; 890 891{ .mfi 892 nop.m 0 893 fms.s1 FR_XLog_Lo = FR_Arg, f1, FR_XLog_Hi // bl = x - bh 894 pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1 895};; 896 897// WE CANNOT USE GR_X_1 IN NEXT 3 CYCLES BECAUSE OF POSSIBLE 10 CLOCKS STALL! 898// "DEAD" ZONE! 899 900{ .mfi 901 nop.m 0 902 nop.f 0 903 nop.i 0 904};; 905 906{ .mfi 907 nop.m 0 908 fmerge.se FR_S_hi = f1,FR_XLog_Hi // Form |x+1| 909 nop.i 0 910};; 911 912 913{ .mmi 914 getf.exp GR_N = FR_XLog_Hi // Get N = exponent of x+1 915 ldfd FR_h = [GR_ad_tbl_1] // Load h_1 916 nop.i 0 917};; 918 919{ .mfi 920 nop.m 0 921 nop.f 0 922 extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 923};; 924 925{ .mfi 926 shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2 927 fma.s1 FR_XLog_Lo = FR_XLog_Lo, f1, FR_GG // bl = bl + gg 928 mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80 929} 930{ .mfi 931 shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2 932 nop.f 0 933 sub GR_N = GR_N, GR_Bias // sub bias from exp 934};; 935 936{ .mmi 937 ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 938 ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 939 sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N) 940};; 941 942{ .mmi 943 ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 944 nop.m 0 945 nop.i 0 946};; 947 948{ .mmi 949 setf.sig FR_float_N = GR_N // Put integer N into rightmost sign 950 setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N) 951 pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2 952};; 953 954// WE CANNOT USE GR_X_2 IN NEXT 3 CYCLES ("DEAD" ZONE!) 955// BECAUSE OF POSSIBLE 10 CLOCKS STALL! 956// (Just nops added - nothing to do here) 957 958{ .mfi 959 nop.m 0 960 fma.s1 FR_XLog_Lo = FR_XLog_Lo, f1, FR_GL // bl = bl + gl 961 nop.i 0 962};; 963{ .mfi 964 nop.m 0 965 nop.f 0 966 nop.i 0 967};; 968{ .mfi 969 nop.m 0 970 nop.f 0 971 nop.i 0 972};; 973 974{ .mfi 975 nop.m 0 976 nop.f 0 977 extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 978};; 979 980{ .mfi 981 shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3 982 nop.f 0 983 nop.i 0 984};; 985 986{ .mfi 987 ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3 988 nop.f 0 989 nop.i 0 990};; 991 992{ .mfi 993 ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 994 fcvt.xf FR_float_N = FR_float_N 995 nop.i 0 996};; 997 998{ .mfi 999 nop.m 0 1000 fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 1001 nop.i 0 1002} 1003{ .mfi 1004 nop.m 0 1005 fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 1006 nop.i 0 1007};; 1008 1009{ .mfi 1010 nop.m 0 1011 fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 1012 nop.i 0 1013} 1014{ .mfi 1015 nop.m 0 1016 fma.s1 FR_S_lo = FR_XLog_Lo, FR_2_to_minus_N, f0 //S_lo=S_lo*2^(-N) 1017 nop.i 0 1018};; 1019 1020{ .mfi 1021 nop.m 0 1022 fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3 1023 nop.i 0 1024} 1025{ .mfi 1026 nop.m 0 1027 fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3 1028 nop.i 0 1029};; 1030 1031{ .mfi 1032 nop.m 0 1033 fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 1034 nop.i 0 1035};; 1036 1037{ .mfi 1038 nop.m 0 1039 fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1 1040 nop.i 0 1041} 1042{ .mfi 1043 nop.m 0 1044 fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi=N*log2_hi+H 1045 nop.i 0 1046};; 1047 1048{ .mfi 1049 nop.m 0 1050 fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h=N*log2_lo+h 1051 nop.i 0 1052} 1053{ .mfi 1054 nop.m 0 1055 fma.s1 FR_r = FR_G, FR_S_lo, FR_r // r=G*S_lo+(G*S_hi-1) 1056 nop.i 0 1057};; 1058 1059{ .mfi 1060 nop.m 0 1061 fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3 1062 nop.i 0 1063} 1064{ .mfi 1065 nop.m 0 1066 fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r 1067 nop.i 0 1068};; 1069 1070{ .mfi 1071 nop.m 0 1072 fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo=poly_lo*r+Q2 1073 nop.i 0 1074} 1075{ .mfi 1076 nop.m 0 1077 fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 1078 nop.i 0 1079};; 1080 1081{ .mfi 1082 nop.m 0 1083 fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r 1084 nop.i 0 1085};; 1086 1087{ .mfi 1088 nop.m 0 1089 fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h 1090 nop.i 0 1091};; 1092 1093{ .mfi 1094 nop.m 0 1095 fadd.s0 FR_Y_lo = FR_poly_hi, FR_poly_lo 1096 // Y_lo=poly_hi+poly_lo 1097 nop.i 0 1098};; 1099 1100{ .mfb 1101 nop.m 0 1102 fadd.s0 FR_Res = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi 1103 br.ret.sptk b0 // Common exit for 2^-7 < x < inf 1104};; 1105 1106 1107huges_logl: 1108{ .mmi 1109 getf.sig GR_signif = FR_XLog_Hi // Get significand of x+1 1110 mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7 1111 nop.i 0 1112};; 1113 1114{ .mfi 1115 add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1 1116 nop.f 0 1117 add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_P 1118} 1119{ .mfi 1120 add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2 1121 nop.f 0 1122 add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2 1123};; 1124 1125{ .mfi 1126 add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3 1127 nop.f 0 1128 extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif 1129};; 1130 1131{ .mfi 1132 shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1 1133 nop.f 0 1134 extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of signif. 1135};; 1136 1137{ .mfi 1138 ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1 1139 nop.f 0 1140 mov GR_exp_mask = 0x1FFFF // Create exponent mask 1141} 1142{ .mfi 1143 shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1 1144 nop.f 0 1145 mov GR_Bias = 0x0FFFF // Create exponent bias 1146};; 1147 1148{ .mfi 1149 ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1 1150 fmerge.se FR_S_hi = f1,FR_XLog_Hi // Form |x| 1151 nop.i 0 1152};; 1153 1154{ .mmi 1155 getf.exp GR_N = FR_XLog_Hi // Get N = exponent of x+1 1156 ldfd FR_h = [GR_ad_tbl_1] // Load h_1 1157 nop.i 0 1158};; 1159 1160{ .mfi 1161 ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi 1162 nop.f 0 1163 pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1 1164};; 1165 1166{ .mmi 1167 ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo 1168 sub GR_N = GR_N, GR_Bias 1169 mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80 1170};; 1171 1172{ .mfi 1173 ldfe FR_Q4 = [GR_ad_q],16 // Load Q4 1174 nop.f 0 1175 sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N) 1176};; 1177 1178{ .mmf 1179 ldfe FR_Q3 = [GR_ad_q],16 // Load Q3 1180 setf.sig FR_float_N = GR_N // Put integer N into rightmost sign 1181 nop.f 0 1182};; 1183 1184{ .mmi 1185 ldfe FR_Q2 = [GR_ad_q],16 // Load Q2 1186 nop.m 0 1187 extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1 1188};; 1189 1190{ .mmi 1191 ldfe FR_Q1 = [GR_ad_q] // Load Q1 1192 shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2 1193 nop.i 0 1194};; 1195 1196{ .mmi 1197 ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2 1198 shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2 1199 nop.i 0 1200};; 1201 1202{ .mmi 1203 ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2 1204 nop.m 0 1205 nop.i 0 1206};; 1207 1208{ .mmf 1209 ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2 1210 setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N) 1211 nop.f 0 1212};; 1213 1214{ .mfi 1215 nop.m 0 1216 nop.f 0 1217 pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1*Z_2 1218};; 1219 1220// WE CANNOT USE GR_X_2 IN NEXT 3 CYCLES ("DEAD" ZONE!) 1221// BECAUSE OF POSSIBLE 10 CLOCKS STALL! 1222// (Just nops added - nothing to do here) 1223 1224{ .mfi 1225 nop.m 0 1226 nop.f 0 1227 nop.i 0 1228};; 1229 1230{ .mfi 1231 nop.m 0 1232 nop.f 0 1233 nop.i 0 1234};; 1235 1236{ .mfi 1237 nop.m 0 1238 nop.f 0 1239 nop.i 0 1240};; 1241 1242{ .mfi 1243 nop.m 0 1244 nop.f 0 1245 extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2 1246};; 1247 1248{ .mfi 1249 shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3 1250 fcvt.xf FR_float_N = FR_float_N 1251 nop.i 0 1252};; 1253 1254{ .mfi 1255 ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3 1256 nop.f 0 1257 nop.i 0 1258};; 1259 1260{ .mfi 1261 ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3 1262 fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2 1263 nop.i 0 1264} 1265{ .mfi 1266 nop.m 0 1267 fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2 1268 nop.i 0 1269};; 1270 1271{ .mmf 1272 nop.m 0 1273 nop.m 0 1274 fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2 1275};; 1276 1277{ .mfi 1278 nop.m 0 1279 fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2)*G_3 1280 nop.i 0 1281} 1282{ .mfi 1283 nop.m 0 1284 fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2)+H_3 1285 nop.i 0 1286};; 1287 1288{ .mfi 1289 nop.m 0 1290 fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3 1291 nop.i 0 1292};; 1293 1294{ .mfi 1295 nop.m 0 1296 fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1 1297 nop.i 0 1298} 1299{ .mfi 1300 nop.m 0 1301 fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi=N*log2_hi+H 1302 nop.i 0 1303};; 1304 1305{ .mfi 1306 nop.m 0 1307 fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h = N*log2_lo+h 1308 nop.i 0 1309};; 1310 1311{ .mfi 1312 nop.m 0 1313 fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3 1314 nop.i 0 1315} 1316{ .mfi 1317 nop.m 0 1318 fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r 1319 nop.i 0 1320};; 1321 1322{ .mfi 1323 nop.m 0 1324 fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo=poly_lo*r+Q2 1325 nop.i 0 1326} 1327{ .mfi 1328 nop.m 0 1329 fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3 1330 nop.i 0 1331};; 1332 1333{ .mfi 1334 nop.m 0 1335 fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r 1336 nop.i 0 1337};; 1338 1339{ .mfi 1340 nop.m 0 1341 fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h 1342 nop.i 0 1343};; 1344{ .mfi 1345 nop.m 0 1346 fadd.s0 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo=poly_hi+poly_lo 1347 nop.i 0 1348};; 1349{ .mfb 1350 nop.m 0 1351 fadd.s0 FR_Res = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi 1352 br.ret.sptk b0 // Common exit 1353};; 1354 1355 1356// NEAR ONE INTERVAL 1357near_1: 1358{ .mfi 1359 nop.m 0 1360 frsqrta.s1 FR_Rcp, p0 = FR_2XM1 // Rcp = 1/x reciprocal appr. &SQRT& 1361 nop.i 0 1362};; 1363 1364{ .mfi 1365 nop.m 0 1366 fma.s1 FR_PV6 = FR_PP5, FR_XM1, FR_PP4 // pv6 = P5*xm1+P4 $POLY$ 1367 nop.i 0 1368} 1369{ .mfi 1370 nop.m 0 1371 fma.s1 FR_QV6 = FR_QQ5, FR_XM1, FR_QQ4 // qv6 = Q5*xm1+Q4 $POLY$ 1372 nop.i 0 1373};; 1374 1375{ .mfi 1376 nop.m 0 1377 fma.s1 FR_PV4 = FR_PP3, FR_XM1, FR_PP2 // pv4 = P3*xm1+P2 $POLY$ 1378 nop.i 0 1379} 1380{ .mfi 1381 nop.m 0 1382 fma.s1 FR_QV4 = FR_QQ3, FR_XM1, FR_QQ2 // qv4 = Q3*xm1+Q2 $POLY$ 1383 nop.i 0 1384};; 1385 1386{ .mfi 1387 nop.m 0 1388 fma.s1 FR_XM12 = FR_XM1, FR_XM1, f0 // xm1^2 = xm1 * xm1 $POLY$ 1389 nop.i 0 1390};; 1391 1392{ .mfi 1393 nop.m 0 1394 fma.s1 FR_PV2 = FR_PP1, FR_XM1, FR_PP0 // pv2 = P1*xm1+P0 $POLY$ 1395 nop.i 0 1396} 1397{ .mfi 1398 nop.m 0 1399 fma.s1 FR_QV2 = FR_QQ1, FR_XM1, FR_QQ0 // qv2 = Q1*xm1+Q0 $POLY$ 1400 nop.i 0 1401};; 1402 1403{ .mfi 1404 nop.m 0 1405 fma.s1 FR_GG = FR_Rcp, FR_2XM1, f0 // g = Rcp * x &SQRT& 1406 nop.i 0 1407} 1408{ .mfi 1409 nop.m 0 1410 fma.s1 FR_HH = FR_Half, FR_Rcp, f0 // h = 0.5 * Rcp &SQRT& 1411 nop.i 0 1412};; 1413 1414 1415{ .mfi 1416 nop.m 0 1417 fma.s1 FR_PV3 = FR_XM12, FR_PV6, FR_PV4//pv3=pv6*xm1^2+pv4 $POLY$ 1418 nop.i 0 1419} 1420{ .mfi 1421 nop.m 0 1422 fma.s1 FR_QV3 = FR_XM12, FR_QV6, FR_QV4//qv3=qv6*xm1^2+qv4 $POLY$ 1423 nop.i 0 1424};; 1425 1426 1427{ .mfi 1428 nop.m 0 1429 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h &SQRT& 1430 nop.i 0 1431};; 1432 1433{ .mfi 1434 nop.m 0 1435 fma.s1 FR_PP = FR_XM12, FR_PV3, FR_PV2 //pp=pv3*xm1^2+pv2 $POLY$ 1436 nop.i 0 1437} 1438{ .mfi 1439 nop.m 0 1440 fma.s1 FR_QQ = FR_XM12, FR_QV3, FR_QV2 //qq=qv3*xm1^2+qv2 $POLY$ 1441 nop.i 0 1442};; 1443 1444{ .mfi 1445 nop.m 0 1446 fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g &SQRT& 1447 nop.i 0 1448} 1449{ .mfi 1450 nop.m 0 1451 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h &SQRT& 1452 nop.i 0 1453};; 1454 1455{ .mfi 1456 nop.m 0 1457 frcpa.s1 FR_Y0,p0 = f1,FR_QQ // y = frcpa(b) #DIV# 1458 nop.i 0 1459} 1460{ .mfi 1461 nop.m 0 1462 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g*h &SQRT& 1463 nop.i 0 1464};; 1465 1466{ .mfi 1467 nop.m 0 1468 fma.s1 FR_Q0 = FR_PP,FR_Y0,f0 // q = a*y #DIV# 1469 nop.i 0 1470} 1471{ .mfi 1472 nop.m 0 1473 fnma.s1 FR_E0 = FR_Y0,FR_QQ,f1 // e = 1 - b*y #DIV# 1474 nop.i 0 1475};; 1476 1477{ .mfi 1478 nop.m 0 1479 fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g &SQRT& 1480 nop.i 0 1481} 1482{ .mfi 1483 nop.m 0 1484 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h &SQRT& 1485 nop.i 0 1486};; 1487 1488{ .mfi 1489 nop.m 0 1490 fma.s1 FR_E2 = FR_E0,FR_E0,FR_E0 // e2 = e+e^2 #DIV# 1491 nop.i 0 1492} 1493{ .mfi 1494 nop.m 0 1495 fma.s1 FR_E1 = FR_E0,FR_E0,f0 // e1 = e^2 #DIV# 1496 nop.i 0 1497};; 1498 1499{ .mfi 1500 nop.m 0 1501 fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h &SQRT& 1502 nop.i 0 1503} 1504{ .mfi 1505 nop.m 0 1506 fnma.s1 FR_DD = FR_GG, FR_GG, FR_2XM1 // d = x - g * g &SQRT& 1507 nop.i 0 1508};; 1509 1510{ .mfi 1511 nop.m 0 1512 fma.s1 FR_Y1 = FR_Y0,FR_E2,FR_Y0 // y1 = y+y*e2 #DIV# 1513 nop.i 0 1514} 1515{ .mfi 1516 nop.m 0 1517 fma.s1 FR_E3 = FR_E1,FR_E1,FR_E0 // e3 = e+e1^2 #DIV# 1518 nop.i 0 1519};; 1520 1521{ .mfi 1522 nop.m 0 1523 fma.s1 FR_GG = FR_DD, FR_HH, FR_GG // g = d * h + g &SQRT& 1524 nop.i 0 1525} 1526{ .mfi 1527 nop.m 0 1528 fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h &SQRT& 1529 nop.i 0 1530};; 1531 1532{ .mfi 1533 nop.m 0 1534 fma.s1 FR_Y2 = FR_Y1,FR_E3,FR_Y0 // y2 = y+y1*e3 #DIV# 1535 nop.i 0 1536} 1537{ .mfi 1538 nop.m 0 1539 fnma.s1 FR_R0 = FR_QQ,FR_Q0,FR_PP // r = a-b*q #DIV# 1540 nop.i 0 1541};; 1542 1543{ .mfi 1544 nop.m 0 1545 fnma.s1 FR_DD = FR_GG, FR_GG, FR_2XM1 // d = x - g * g &SQRT& 1546 nop.i 0 1547};; 1548 1549{ .mfi 1550 nop.m 0 1551 fnma.s1 FR_E4 = FR_QQ,FR_Y2,f1 // e4 = 1-b*y2 #DIV# 1552 nop.i 0 1553} 1554{ .mfi 1555 nop.m 0 1556 fma.s1 FR_X_Hi = FR_R0,FR_Y2,FR_Q0 // x = q+r*y2 #DIV# 1557 nop.i 0 1558};; 1559 1560{ .mfi 1561 nop.m 0 1562 fma.s1 FR_GL = FR_DD, FR_HH, f0 // gl = d * h &SQRT& 1563 nop.i 0 1564};; 1565 1566{ .mfi 1567 nop.m 0 1568 fma.s1 FR_Y3 = FR_Y2,FR_E4,FR_Y2 // y3 = y2+y2*e4 #DIV# 1569 nop.i 0 1570} 1571{ .mfi 1572 nop.m 0 1573 fnma.s1 FR_R1 = FR_QQ,FR_X_Hi,FR_PP // r1 = a-b*x #DIV# 1574 nop.i 0 1575};; 1576 1577{ .mfi 1578 nop.m 0 1579 fma.s1 FR_HH = FR_GG, FR_X_Hi, f0 // hh = gg * x_hi 1580 nop.i 0 1581} 1582{ .mfi 1583 nop.m 0 1584 fma.s1 FR_LH = FR_GL, FR_X_Hi, f0 // lh = gl * x_hi 1585 nop.i 0 1586};; 1587 1588{ .mfi 1589 nop.m 0 1590 fma.s1 FR_X_lo = FR_R1,FR_Y3,f0 // x_lo = r1*y3 #DIV# 1591 nop.i 0 1592};; 1593 1594{ .mfi 1595 nop.m 0 1596 fma.s1 FR_LL = FR_GL, FR_X_lo, f0 // ll = gl*x_lo 1597 nop.i 0 1598} 1599{ .mfi 1600 nop.m 0 1601 fma.s1 FR_HL = FR_GG, FR_X_lo, f0 // hl = gg * x_lo 1602 nop.i 0 1603};; 1604 1605{ .mfi 1606 nop.m 0 1607 fms.s1 FR_Res = FR_GL, f1, FR_LL // res = gl + ll 1608 nop.i 0 1609};; 1610 1611{ .mfi 1612 nop.m 0 1613 fms.s1 FR_Res = FR_Res, f1, FR_LH // res = res + lh 1614 nop.i 0 1615};; 1616 1617{ .mfi 1618 nop.m 0 1619 fms.s1 FR_Res = FR_Res, f1, FR_HL // res = res + hl 1620 nop.i 0 1621};; 1622 1623{ .mfi 1624 nop.m 0 1625 fms.s1 FR_Res = FR_Res, f1, FR_HH // res = res + hh 1626 nop.i 0 1627};; 1628 1629{ .mfb 1630 nop.m 0 1631 fma.s0 FR_Res = FR_Res, f1, FR_GG // result = res + gg 1632 br.ret.sptk b0 // Exit for near 1 path 1633};; 1634// NEAR ONE INTERVAL END 1635 1636 1637 1638 1639acoshl_lt_pone: 1640{ .mfi 1641 nop.m 0 1642 fmerge.s FR_Arg_X = FR_Arg, FR_Arg 1643 nop.i 0 1644};; 1645{ .mfb 1646 mov GR_Parameter_TAG = 135 1647 frcpa.s0 FR_Res,p0 = f0,f0 // get QNaN,and raise invalid 1648 br.cond.sptk __libm_error_region // exit if x < 1.0 1649};; 1650 1651GLOBAL_LIBM_END(acoshl) 1652libm_alias_ldouble_other (acosh, acosh) 1653 1654 1655 1656LOCAL_LIBM_ENTRY(__libm_error_region) 1657.prologue 1658{ .mfi 1659 add GR_Parameter_Y = -32,sp // Parameter 2 value 1660 nop.f 0 1661.save ar.pfs,GR_SAVE_PFS 1662 mov GR_SAVE_PFS = ar.pfs // Save ar.pfs 1663} 1664{ .mfi 1665.fframe 64 1666 add sp = -64,sp // Create new stack 1667 nop.f 0 1668 mov GR_SAVE_GP = gp // Save gp 1669};; 1670 1671{ .mmi 1672 stfe [GR_Parameter_Y] = FR_Arg_Y,16 // Parameter 2 to stack 1673 add GR_Parameter_X = 16,sp // Parameter 1 address 1674.save b0,GR_SAVE_B0 1675 mov GR_SAVE_B0 = b0 // Save b0 1676};; 1677 1678.body 1679{ .mib 1680 stfe [GR_Parameter_X] = FR_Arg_X // Parameter 1 to stack 1681 add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address 1682 nop.b 0 1683} 1684{ .mib 1685 stfe [GR_Parameter_Y] = FR_Res // Parameter 3 to stack 1686 add GR_Parameter_Y = -16,GR_Parameter_Y 1687 br.call.sptk b0 = __libm_error_support# // Error handling function 1688};; 1689 1690{ .mmi 1691 nop.m 0 1692 nop.m 0 1693 add GR_Parameter_RESULT = 48,sp 1694};; 1695 1696{ .mmi 1697 ldfe f8 = [GR_Parameter_RESULT] // Get return res 1698.restore sp 1699 add sp = 64,sp // Restore stack pointer 1700 mov b0 = GR_SAVE_B0 // Restore return address 1701};; 1702 1703{ .mib 1704 mov gp = GR_SAVE_GP // Restore gp 1705 mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs 1706 br.ret.sptk b0 // Return 1707};; 1708 1709LOCAL_LIBM_END(__libm_error_region#) 1710 1711.type __libm_error_support#,@function 1712.global __libm_error_support# 1713