sysdeps/ia64/fpu/e_acosl.S

   1 .file "acosl.s"
   2
   3
   4 // Copyright (c) 2001 - 2003, Intel Corporation
   5 // All rights reserved.
   6 //
   7 // Contributed 2001 by the Intel Numerics Group, Intel Corporation
   8 //
   9 // Redistribution and use in source and binary forms, with or without
  10 // modification, are permitted provided that the following conditions are
  11 // met:
  12 //
  13 // * Redistributions of source code must retain the above copyright
  14 // notice, this list of conditions and the following disclaimer.
  15 //
  16 // * Redistributions in binary form must reproduce the above copyright
  17 // notice, this list of conditions and the following disclaimer in the
  18 // documentation and/or other materials provided with the distribution.
  19 //
  20 // * The name of Intel Corporation may not be used to endorse or promote
  21 // products derived from this software without specific prior written
  22 // permission.
  23
  24 // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  25 // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  26 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
  27 // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
  28 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
  29 // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
  30 // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
  31 // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
  32 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
  33 // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
  34 // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  35 //
  36 // Intel Corporation is the author of this code, and requests that all
  37 // problem reports or change requests be submitted to it directly at
  38 // http://www.intel.com/software/products/opensource/libraries/num.htm.
  39 //
  40 // History
  41 //==============================================================
  42 // 08/28/01 New version
  43 // 05/20/02 Cleaned up namespace and sf0 syntax
  44 // 02/06/03 Reordered header: .section, .global, .proc, .align
  45 //
  46 // API
  47 //==============================================================
  48 // long double acosl(long double)
  49 //
  50 // Overview of operation
  51 //==============================================================
  52 // Background
  53 //
  54 // Implementation
  55 //
  56 // For |s| in [2^{-4}, sqrt(2)/2]:
  57 // Let t= 2^k*1.b1 b2..b6 1, where s= 2^k*1.b1 b2.. b52
  58 // acos(s)= pi/2-asin(t)-asin(r), where r= s*sqrt(1-t^2)-t*sqrt(1-s^2), i.e.
  59 // r= (s-t)*sqrt(1-t^2)-t*sqrt(1-t^2)*(sqrt((1-s^2)/(1-t^2))-1)
  60 // asin(r)-r evaluated as 9-degree polynomial (c3*r^3+c5*r^5+c7*r^7+c9*r^9)
  61 // The 64-bit significands of sqrt(1-t^2), 1/(1-t^2) are read from the table,
  62 // along with the high and low parts of asin(t) (stored as two double precision
  63 // values)
  64 //
  65 // |s| in (sqrt(2)/2, sqrt(255/256)):
  66 // Let t= 2^k*1.b1 b2..b6 1, where (1-s^2)*frsqrta(1-s^2)= 2^k*1.b1 b2..b6..
  67 // acos(|s|)= asin(t)-asin(r)
  68 // acos(-|s|)=pi-asin(t)+asin(r),   r= s*t-sqrt(1-s^2)*sqrt(1-t^2)
  69 // To minimize accumulated errors, r is computed as
  70 // r= (t*s)_s-t^2*y*z+z*y*(t^2-1+s^2)_s+z*y*(1-s^2)_s*x+z'*y*(1-s^2)*PS29+
  71 // +(t*s-(t*s)_s)+z*y*((t^2-1-(t^2-1+s^2)_s)+s^2)+z*y*(1-s^2-(1-s^2)_s)+
  72 // +ez*z'*y*(1-s^2)*(1-x),
  73 // where y= frsqrta(1-s^2), z= (sqrt(1-t^2))_s (rounded to 24 significant bits)
  74 // z'= sqrt(1-t^2), x= ((1-s^2)*y^2-1)/2
  75 //
  76 // |s|<2^{-4}: evaluate asin(s) as 17-degree polynomial, return pi/2-asin(s)
  77 // (or simply return pi/2-s, if|s|<2^{-64})
  78 //
  79 // |s| in [sqrt(255/256), 1): acos(|s|)= asin(sqrt(1-s^2))
  80 // acos(-|s|)= pi-asin(sqrt(1-s^2))
  81 // use 17-degree polynomial for asin(sqrt(1-s^2)),
  82 // 9-degree polynomial to evaluate sqrt(1-s^2)
  83 // High order term is (pi)_high-(y*(1-s^2))_high, for s<0,
  84 // or y*(1-s^2)_s, for s>0
  85 //
  86
  87
  88
  89 // Registers used
  90 //==============================================================
  91 // f6-f15, f32-f36
  92 // r2-r3, r23-r23
  93 // p6, p7, p8, p12
  94 //
  95
  96
  97        GR_SAVE_B0= r33
  98        GR_SAVE_PFS= r34
  99        GR_SAVE_GP= r35 // This reg. can safely be used
 100        GR_SAVE_SP= r36
 101
 102        GR_Parameter_X= r37
 103        GR_Parameter_Y= r38
 104        GR_Parameter_RESULT= r39
 105        GR_Parameter_TAG= r40
 106
 107        FR_X= f10
 108        FR_Y= f1
 109        FR_RESULT= f8
 110
 111
 112
 113 RODATA
 114
 115 .align 16
 116
 117 LOCAL_OBJECT_START(T_table)
 118
 119 // stores 64-bit significand of 1/(1-t^2), 64-bit significand of sqrt(1-t^2),
 120 // asin(t)_high (double precision), asin(t)_low (double precision)
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 302 data8 0x8420cc9659487cd7, 0xfbf81841c8082dc4
 303 data8 0x3fc6be97a21daf00, 0x3cc2ac8330e59aa5
 304 data8 0x84390ec132759ecb, 0xfbe0fa06e24cc390
 305 data8 0x3fc6ffa0b6ef05e0, 0x3ccc1a030fee56c4
 306 data8 0x84519e3a29df811a, 0xfbc9989a85ce0954
 307 data8 0x3fc740afcccca000, 0x3cc19692a5301ca6
 308 data8 0x846a7b527842d61b, 0xfbb1f3e9f8e45dc4
 309 data8 0x3fc781c4f633e2c0, 0x3cc0e98f3868a508
 310 data8 0x8483a65c8434b5f0, 0xfb9a0be244f4af45
 311 data8 0x3fc7c2e045b12140, 0x3cb2a8d309754420
 312 data8 0x849d1fabe4e97dd7, 0xfb81e070362116d1
 313 data8 0x3fc80401cddfd120, 0x3ca7a44544aa4ce6
 314 data8 0x84b6e795650817ea, 0xfb6971805af8411e
 315 data8 0x3fc84529a16ac020, 0x3c9e3b709c7d6f94
 316 data8 0x84d0fe6f0589da92, 0xfb50beff0423a2f5
 317 data8 0x3fc88657d30c49e0, 0x3cc60d65a7f0a278
 318 data8 0x84eb649000a73014, 0xfb37c8d84414755c
 319 data8 0x3fc8c78c758e8e80, 0x3cc94b2ee984c2b7
 320 data8 0x85061a50ccd13781, 0xfb1e8ef7eeaf764b
 321 data8 0x3fc908c79bcba900, 0x3cc8540ae794a2fe
 322 data8 0x8521200b1fb8916e, 0xfb05114998f76a83
 323 data8 0x3fc94a0958ade6c0, 0x3ca127f49839fa9c
 324 data8 0x853c7619f1618bf6, 0xfaeb4fb898b65d19
 325 data8 0x3fc98b51bf2ffee0, 0x3c8c9ba7a803909a
 326 data8 0x85581cd97f45e274, 0xfad14a3004259931
 327 data8 0x3fc9cca0e25d4ac0, 0x3cba458e91d3bf54
 328 data8 0x857414a74f8446b4, 0xfab7009ab1945a54
 329 data8 0x3fca0df6d551fe80, 0x3cc78ea1d329d2b2
 330 data8 0x85905de2341dea46, 0xfa9c72e3370d2fbc
 331 data8 0x3fca4f53ab3b6200, 0x3ccf60dca86d57ef
 332 data8 0x85acf8ea4e423ff8, 0xfa81a0f3e9fa0ee9
 333 data8 0x3fca90b777580aa0, 0x3ca4c4e2ec8a867e
 334 data8 0x85c9e62111a92e7d, 0xfa668ab6dec711b1
 335 data8 0x3fcad2224cf814e0, 0x3c303de5980d071c
 336 data8 0x85e725e947fbee97, 0xfa4b3015e883dbfe
 337 data8 0x3fcb13943f7d5f80, 0x3cc29d4eefa5cb1e
 338 data8 0x8604b8a7144cd054, 0xfa2f90fa9883a543
 339 data8 0x3fcb550d625bc6a0, 0x3c9e01a746152daf
 340 data8 0x86229ebff69e2415, 0xfa13ad4e3dfbe1c1
 341 data8 0x3fcb968dc9195ea0, 0x3ccc091bd73ae518
 342 data8 0x8640d89acf78858c, 0xf9f784f9e5a1877b
 343 data8 0x3fcbd815874eb160, 0x3cb5f4b89875e187
 344 data8 0x865f669fe390c7f5, 0xf9db17e65944eacf
 345 data8 0x3fcc19a4b0a6f9c0, 0x3cc5c0bc2b0bbf14
 346 data8 0x867e4938df7dc45f, 0xf9be65fc1f6c2e6e
 347 data8 0x3fcc5b3b58e061e0, 0x3cc1ca70df8f57e7
 348 data8 0x869d80d0db7e4c0c, 0xf9a16f237aec427a
 349 data8 0x3fcc9cd993cc4040, 0x3cbae93acc85eccf
 350 data8 0x86bd0dd45f4f8265, 0xf98433446a806e70
 351 data8 0x3fccde7f754f5660, 0x3cb22f70e64568d0
 352 data8 0x86dcf0b16613e37a, 0xf966b246a8606170
 353 data8 0x3fcd202d11620fa0, 0x3c962030e5d4c849
 354 data8 0x86fd29d7624b3d5d, 0xf948ec11a9d4c45b
 355 data8 0x3fcd61e27c10c0a0, 0x3cc7083c91d59217
 356 data8 0x871db9b741dbe44a, 0xf92ae08c9eca4941
 357 data8 0x3fcda39fc97be7c0, 0x3cc9258579e57211
 358 data8 0x873ea0c3722d6af2, 0xf90c8f9e71633363
 359 data8 0x3fcde5650dd86d60, 0x3ca4755a9ea582a9
 360 data8 0x875fdf6fe45529e8, 0xf8edf92dc5875319
 361 data8 0x3fce27325d6fe520, 0x3cbc1e2b6c1954f9
 362 data8 0x878176321154e2bc, 0xf8cf1d20f87270b8
 363 data8 0x3fce6907cca0d060, 0x3cb6ca4804750830
 364 data8 0x87a36580fe6bccf5, 0xf8affb5e20412199
 365 data8 0x3fceaae56fdee040, 0x3cad6b310d6fd46c
 366 data8 0x87c5add5417a5cb9, 0xf89093cb0b7c0233
 367 data8 0x3fceeccb5bb33900, 0x3cc16e99cedadb20
 368 data8 0x87e84fa9057914ca, 0xf870e64d40a15036
 369 data8 0x3fcf2eb9a4bcb600, 0x3cc75ee47c8b09e9
 370 data8 0x880b4b780f02b709, 0xf850f2c9fdacdf78
 371 data8 0x3fcf70b05fb02e20, 0x3cad6350d379f41a
 372 data8 0x882ea1bfc0f228ac, 0xf830b926379e6465
 373 data8 0x3fcfb2afa158b8a0, 0x3cce0ccd9f829985
 374 data8 0x885252ff21146108, 0xf810394699fe0e8e
 375 data8 0x3fcff4b77e97f3e0, 0x3c9b30faa7a4c703
 376 data8 0x88765fb6dceebbb3, 0xf7ef730f865f6df0
 377 data8 0x3fd01b6406332540, 0x3cdc5772c9e0b9bd
 378 data8 0x88ad1f69be2cc730, 0xf7bdc59bc9cfbd97
 379 data8 0x3fd04cf8ad203480, 0x3caeef44fe21a74a
 380 data8 0x88f763f70ae2245e, 0xf77a91c868a9c54e
 381 data8 0x3fd08f23ce0162a0, 0x3cd6290ab3fe5889
 382 data8 0x89431fc7bc0c2910, 0xf73642973c91298e
 383 data8 0x3fd0d1610f0c1ec0, 0x3cc67401a01f08cf
 384 data8 0x8990573407c7738e, 0xf6f0d71d1d7a2dd6
 385 data8 0x3fd113b0c65d88c0, 0x3cc7aa4020fe546f
 386 data8 0x89df0eb108594653, 0xf6aa4e6a05cfdef2
 387 data8 0x3fd156134ada6fe0, 0x3cc87369da09600c
 388 data8 0x8a2f4ad16e0ed78a, 0xf662a78900c35249
 389 data8 0x3fd19888f43427a0, 0x3cc62b220f38e49c
 390 data8 0x8a811046373e0819, 0xf619e180181d97cc
 391 data8 0x3fd1db121aed7720, 0x3ca3ede7490b52f4
 392 data8 0x8ad463df6ea0fa2c, 0xf5cffb504190f9a2
 393 data8 0x3fd21daf185fa360, 0x3caafad98c1d6c1b
 394 data8 0x8b294a8cf0488daf, 0xf584f3f54b8604e6
 395 data8 0x3fd2606046bf95a0, 0x3cdb2d704eeb08fa
 396 data8 0x8b7fc95f35647757, 0xf538ca65c960b582
 397 data8 0x3fd2a32601231ec0, 0x3cc661619fa2f126
 398 data8 0x8bd7e588272276f8, 0xf4eb7d92ff39fccb
 399 data8 0x3fd2e600a3865760, 0x3c8a2a36a99aca4a
 400 data8 0x8c31a45bf8e9255e, 0xf49d0c68cd09b689
 401 data8 0x3fd328f08ad12000, 0x3cb9efaf1d7ab552
 402 data8 0x8c8d0b520a35eb18, 0xf44d75cd993cfad2
 403 data8 0x3fd36bf614dcc040, 0x3ccacbb590bef70d
 404 data8 0x8cea2005d068f23d, 0xf3fcb8a23ab4942b
 405 data8 0x3fd3af11a079a6c0, 0x3cd9775872cf037d
 406 data8 0x8d48e837c8cd5027, 0xf3aad3c1e2273908
 407 data8 0x3fd3f2438d754b40, 0x3ca03304f667109a
 408 data8 0x8da969ce732f3ac7, 0xf357c60202e2fd7e
 409 data8 0x3fd4358c3ca032e0, 0x3caecf2504ff1a9d
 410 data8 0x8e0baad75555e361, 0xf3038e323ae9463a
 411 data8 0x3fd478ec0fd419c0, 0x3cc64bdc3d703971
 412 data8 0x8e6fb18807ba877e, 0xf2ae2b1c3a6057f7
 413 data8 0x3fd4bc6369fa40e0, 0x3cbb7122ec245cf2
 414 data8 0x8ed5843f4bda74d5, 0xf2579b83aa556f0c
 415 data8 0x3fd4fff2af11e2c0, 0x3c9cfa2dc792d394
 416 data8 0x8f3d29862c861fef, 0xf1ffde2612ca1909
 417 data8 0x3fd5439a4436d000, 0x3cc38d46d310526b
 418 data8 0x8fa6a81128940b2d, 0xf1a6f1bac0075669
 419 data8 0x3fd5875a8fa83520, 0x3cd8bf59b8153f8a
 420 data8 0x901206c1686317a6, 0xf14cd4f2a730d480
 421 data8 0x3fd5cb33f8cf8ac0, 0x3c9502b5c4d0e431
 422 data8 0x907f4ca5fe9cf739, 0xf0f186784a125726
 423 data8 0x3fd60f26e847b120, 0x3cc8a1a5e0acaa33
 424 data8 0x90ee80fd34aeda5e, 0xf09504ef9a212f18
 425 data8 0x3fd65333c7e43aa0, 0x3cae5b029cb1f26e
 426 data8 0x915fab35e37421c6, 0xf0374ef5daab5c45
 427 data8 0x3fd6975b02b8e360, 0x3cd5aa1c280c45e6
 428 data8 0x91d2d2f0d894d73c, 0xefd86321822dbb51
 429 data8 0x3fd6db9d05213b20, 0x3cbecf2c093ccd8b
 430 data8 0x9248000249200009, 0xef7840021aca5a72
 431 data8 0x3fd71ffa3cc87fc0, 0x3cb8d273f08d00d9
 432 data8 0x92bf3a7351f081d2, 0xef16e42021d7cbd5
 433 data8 0x3fd7647318b1ad20, 0x3cbce099d79cdc46
 434 data8 0x93388a8386725713, 0xeeb44dfce6820283
 435 data8 0x3fd7a908093fc1e0, 0x3ccb033ec17a30d9
 436 data8 0x93b3f8aa8e653812, 0xee507c126774fa45
 437 data8 0x3fd7edb9803e3c20, 0x3cc10aedb48671eb
 438 data8 0x94318d99d341ade4, 0xedeb6cd32f891afb
 439 data8 0x3fd83287f0e9cf80, 0x3c994c0c1505cd2a
 440 data8 0x94b1523e3dedc630, 0xed851eaa3168f43c
 441 data8 0x3fd87773cff956e0, 0x3cda3b7bce6a6b16
 442 data8 0x95334fc20577563f, 0xed1d8ffaa2279669
 443 data8 0x3fd8bc7d93a70440, 0x3cd4922edc792ce2
 444 data8 0x95b78f8e8f92f274, 0xecb4bf1fd2be72da
 445 data8 0x3fd901a5b3b9cf40, 0x3cd3fea1b00f9d0d
 446 data8 0x963e1b4e63a87c3f, 0xec4aaa6d08694cc1
 447 data8 0x3fd946eca98f2700, 0x3cdba4032d968ff1
 448 data8 0x96c6fcef314074fc, 0xebdf502d53d65fea
 449 data8 0x3fd98c52f024e800, 0x3cbe7be1ab8c95c9
 450 data8 0x97523ea3eab028b2, 0xeb72aea36720793e
 451 data8 0x3fd9d1d904239860, 0x3cd72d08a6a22b70
 452 data8 0x97dfeae6f4ee4a9a, 0xeb04c4096a884e94
 453 data8 0x3fda177f63e8ef00, 0x3cd818c3c1ebfac7
 454 data8 0x98700c7c6d85d119, 0xea958e90cfe1efd7
 455 data8 0x3fda5d468f92a540, 0x3cdf45fbfaa080fe
 456 data8 0x9902ae7487a9caa1, 0xea250c6224aab21a
 457 data8 0x3fdaa32f090998e0, 0x3cd715a9353cede4
 458 data8 0x9997dc2e017a9550, 0xe9b33b9ce2bb7638
 459 data8 0x3fdae939540d3f00, 0x3cc545c014943439
 460 data8 0x9a2fa158b29b649b, 0xe9401a573f8aa706
 461 data8 0x3fdb2f65f63f6c60, 0x3cd4a63c2f2ca8e2
 462 data8 0x9aca09f835466186, 0xe8cba69df9f0bf35
 463 data8 0x3fdb75b5773075e0, 0x3cda310ce1b217ec
 464 data8 0x9b672266ab1e0136, 0xe855de74266193d4
 465 data8 0x3fdbbc28606babc0, 0x3cdc84b75cca6c44
 466 data8 0x9c06f7579f0b7bd5, 0xe7debfd2f98c060b
 467 data8 0x3fdc02bf3d843420, 0x3cd225d967ffb922
 468 data8 0x9ca995db058cabdc, 0xe76648a991511c6e
 469 data8 0x3fdc497a9c224780, 0x3cde08101c5b825b
 470 data8 0x9d4f0b605ce71e88, 0xe6ec76dcbc02d9a7
 471 data8 0x3fdc905b0c10d420, 0x3cb1abbaa3edf120
 472 data8 0x9df765b9eecad5e6, 0xe6714846bdda7318
 473 data8 0x3fdcd7611f4b8a00, 0x3cbf6217ae80aadf
 474 data8 0x9ea2b320350540fe, 0xe5f4bab71494cd6b
 475 data8 0x3fdd1e8d6a0d56c0, 0x3cb726e048cc235c
 476 data8 0x9f51023562fc5676, 0xe576cbf239235ecb
 477 data8 0x3fdd65e082df5260, 0x3cd9e66872bd5250
 478 data8 0xa002620915c2a2f6, 0xe4f779b15f5ec5a7
 479 data8 0x3fddad5b02a82420, 0x3c89743b0b57534b
 480 data8 0xa0b6e21c2caf9992, 0xe476c1a233a7873e
 481 data8 0x3fddf4fd84bbe160, 0x3cbf7adea9ee3338
 482 data8 0xa16e9264cc83a6b2, 0xe3f4a16696608191
 483 data8 0x3fde3cc8a6ec6ee0, 0x3cce46f5a51f49c6
 484 data8 0xa22983528f3d8d49, 0xe3711694552da8a8
 485 data8 0x3fde84bd099a6600, 0x3cdc78f6490a2d31
 486 data8 0xa2e7c5d2e2e69460, 0xe2ec1eb4e1e0a5fb
 487 data8 0x3fdeccdb4fc685c0, 0x3cdd3aedb56a4825
 488 data8 0xa3a96b5599bd2532, 0xe265b74506fbe1c9
 489 data8 0x3fdf15241f23b3e0, 0x3cd440f3c6d65f65
 490 data8 0xa46e85d1ae49d7de, 0xe1ddddb499b3606f
 491 data8 0x3fdf5d98202994a0, 0x3cd6c44bd3fb745a
 492 data8 0xa53727ca3e11b99e, 0xe1548f662951b00d
 493 data8 0x3fdfa637fe27bf60, 0x3ca8ad1cd33054dd
 494 data8 0xa6036453bdc20186, 0xe0c9c9aeabe5e481
 495 data8 0x3fdfef0467599580, 0x3cc0f1ac0685d78a
 496 data8 0xa6d34f1969dda338, 0xe03d89d5281e4f81
 497 data8 0x3fe01bff067d6220, 0x3cc0731e8a9ef057
 498 data8 0xa7a6fc62f7246ff3, 0xdfafcd125c323f54
 499 data8 0x3fe04092d1ae3b40, 0x3ccabda24b59906d
 500 data8 0xa87e811a861df9b9, 0xdf20909061bb9760
 501 data8 0x3fe0653df0fd9fc0, 0x3ce94c8dcc722278
 502 data8 0xa959f2d2dd687200, 0xde8fd16a4e5f88bd
 503 data8 0x3fe08a00c1cae320, 0x3ce6b888bb60a274
 504 data8 0xaa3967cdeea58bda, 0xddfd8cabd1240d22
 505 data8 0x3fe0aedba3221c00, 0x3ced5941cd486e46
 506 data8 0xab904fd587263c84, 0xdd1f4472e1cf64ed
 507 data8 0x3fe0e651e85229c0, 0x3cdb6701042299b1
 508 data8 0xad686d44dd5a74bb, 0xdbf173e1f6b46e92
 509 data8 0x3fe1309cbf4cdb20, 0x3cbf1be7bb3f0ec5
 510 data8 0xaf524e15640ebee4, 0xdabd54896f1029f6
 511 data8 0x3fe17b4ee1641300, 0x3ce81dd055b792f1
 512 data8 0xb14eca24ef7db3fa, 0xd982cb9ae2f47e41
 513 data8 0x3fe1c66b9ffd6660, 0x3cd98ea31eb5ddc7
 514 data8 0xb35ec807669920ce, 0xd841bd1b8291d0b6
 515 data8 0x3fe211f66db3a5a0, 0x3ca480c35a27b4a2
 516 data8 0xb5833e4755e04dd1, 0xd6fa0bd3150b6930
 517 data8 0x3fe25df2e05b6c40, 0x3ca4bc324287a351
 518 data8 0xb7bd34c8000b7bd3, 0xd5ab9939a7d23aa1
 519 data8 0x3fe2aa64b32f7780, 0x3cba67314933077c
 520 data8 0xba0dc64d126cc135, 0xd4564563ce924481
 521 data8 0x3fe2f74fc9289ac0, 0x3cec1a1dc0efc5ec
 522 data8 0xbc76222cbbfa74a6, 0xd2f9eeed501125a8
 523 data8 0x3fe344b82f859ac0, 0x3ceeef218de413ac
 524 data8 0xbef78e31985291a9, 0xd19672e2182f78be
 525 data8 0x3fe392a22087b7e0, 0x3cd2619ba201204c
 526 data8 0xc19368b2b0629572, 0xd02baca5427e436a
 527 data8 0x3fe3e11206694520, 0x3cb5d0b3143fe689
 528 data8 0xc44b2ae8c6733e51, 0xceb975d60b6eae5d
 529 data8 0x3fe4300c7e945020, 0x3cbd367143da6582
 530 data8 0xc7206b894212dfef, 0xcd3fa6326ff0ac9a
 531 data8 0x3fe47f965d201d60, 0x3ce797c7a4ec1d63
 532 data8 0xca14e1b0622de526, 0xcbbe13773c3c5338
 533 data8 0x3fe4cfb4b09d1a20, 0x3cedfadb5347143c
 534 data8 0xcd2a6825eae65f82, 0xca34913d425a5ae9
 535 data8 0x3fe5206cc637e000, 0x3ce2798b38e54193
 536 data8 0xd06301095e1351ee, 0xc8a2f0d3679c08c0
 537 data8 0x3fe571c42e3d0be0, 0x3ccd7cb9c6c2ca68
 538 data8 0xd3c0d9f50057adda, 0xc70901152d59d16b
 539 data8 0x3fe5c3c0c108f940, 0x3ceb6c13563180ab
 540 data8 0xd74650a98cc14789, 0xc5668e3d4cbf8828
 541 data8 0x3fe61668a46ffa80, 0x3caa9092e9e3c0e5
 542 data8 0xdaf5f8579dcc8f8f, 0xc3bb61b3eed42d02
 543 data8 0x3fe669c251ad69e0, 0x3cccf896ef3b4fee
 544 data8 0xded29f9f9a6171b4, 0xc20741d7f8e8e8af
 545 data8 0x3fe6bdd49bea05c0, 0x3cdc6b29937c575d
 546 data8 0xe2df5765854ccdb0, 0xc049f1c2d1b8014b
 547 data8 0x3fe712a6b76c6e80, 0x3ce1ddc6f2922321
 548 data8 0xe71f7a9b94fcb4c3, 0xbe833105ec291e91
 549 data8 0x3fe76840418978a0, 0x3ccda46e85432c3d
 550 data8 0xeb96b72d3374b91e, 0xbcb2bb61493b28b3
 551 data8 0x3fe7bea9496d5a40, 0x3ce37b42ec6e17d3
 552 data8 0xf049183c3f53c39b, 0xbad848720223d3a8
 553 data8 0x3fe815ea59dab0a0, 0x3cb03ad41bfc415b
 554 data8 0xf53b11ec7f415f15, 0xb8f38b57c53c9c48
 555 data8 0x3fe86e0c84010760, 0x3cc03bfcfb17fe1f
 556 data8 0xfa718f05adbf2c33, 0xb70432500286b185
 557 data8 0x3fe8c7196b9225c0, 0x3ced99fcc6866ba9
 558 data8 0xfff200c3f5489608, 0xb509e6454dca33cc
 559 data8 0x3fe9211b54441080, 0x3cb789cb53515688
 560 // The following table entries are not used
 561 //data8 0x82e138a0fac48700, 0xb3044a513a8e6132
 562 //data8 0x3fe97c1d30f5b7c0, 0x3ce1eb765612d1d0
 563 //data8 0x85f4cc7fc670d021, 0xb0f2fb2ea6cbbc88
 564 //data8 0x3fe9d82ab4b5fde0, 0x3ced3fe6f27e8039
 565 //data8 0x89377c1387d5b908, 0xaed58e9a09014d5c
 566 //data8 0x3fea355065f87fa0, 0x3cbef481d25f5b58
 567 //data8 0x8cad7a2c98dec333, 0xacab929ce114d451
 568 //data8 0x3fea939bb451e2a0, 0x3c8e92b4fbf4560f
 569 //data8 0x905b7dfc99583025, 0xaa748cc0dbbbc0ec
 570 //data8 0x3feaf31b11270220, 0x3cdced8c61bd7bd5
 571 //data8 0x9446d8191f80dd42, 0xa82ff92687235baf
 572 //data8 0x3feb53de0bcffc20, 0x3cbe1722fb47509e
 573 //data8 0x98758ba086e4000a, 0xa5dd497a9c184f58
 574 //data8 0x3febb5f571cb0560, 0x3ce0c7774329a613
 575 //data8 0x9cee6c7bf18e4e24, 0xa37be3c3cd1de51b
 576 //data8 0x3fec197373bc7be0, 0x3ce08ebdb55c3177
 577 //data8 0xa1b944000a1b9440, 0xa10b2101b4f27e03
 578 //data8 0x3fec7e6bd023da60, 0x3ce5fc5fd4995959
 579 //data8 0xa6defd8ba04d3e38, 0x9e8a4b93cad088ec
 580 //data8 0x3fece4f404e29b20, 0x3cea3413401132b5
 581 //data8 0xac69dd408a10c62d, 0x9bf89d5d17ddae8c
 582 //data8 0x3fed4d2388f63600, 0x3cd5a7fb0d1d4276
 583 //data8 0xb265c39cbd80f97a, 0x99553d969fec7beb
 584 //data8 0x3fedb714101e0a00, 0x3cdbda21f01193f2
 585 //data8 0xb8e081a16ae4ae73, 0x969f3e3ed2a0516c
 586 //data8 0x3fee22e1da97bb00, 0x3ce7231177f85f71
 587 //data8 0xbfea427678945732, 0x93d5990f9ee787af
 588 //data8 0x3fee90ac13b18220, 0x3ce3c8a5453363a5
 589 //data8 0xc79611399b8c90c5, 0x90f72bde80febc31
 590 //data8 0x3fef009542b712e0, 0x3ce218fd79e8cb56
 591 //data8 0xcffa8425040624d7, 0x8e02b4418574ebed
 592 //data8 0x3fef72c3d2c57520, 0x3cd32a717f82203f
 593 //data8 0xd93299cddcf9cf23, 0x8af6ca48e9c44024
 594 //data8 0x3fefe762b77744c0, 0x3ce53478a6bbcf94
 595 //data8 0xe35eda760af69ad9, 0x87d1da0d7f45678b
 596 //data8 0x3ff02f511b223c00, 0x3ced6e11782c28fc
 597 //data8 0xeea6d733421da0a6, 0x84921bbe64ae029a
 598 //data8 0x3ff06c5c6f8ce9c0, 0x3ce71fc71c1ffc02
 599 //data8 0xfb3b2c73fc6195cc, 0x813589ba3a5651b6
 600 //data8 0x3ff0aaf2613700a0, 0x3cf2a72d2fd94ef3
 601 //data8 0x84ac1fcec4203245, 0xfb73a828893df19e
 602 //data8 0x3ff0eb367c3fd600, 0x3cf8054c158610de
 603 //data8 0x8ca50621110c60e6, 0xf438a14c158d867c
 604 //data8 0x3ff12d51caa6b580, 0x3ce6bce9748739b6
 605 //data8 0x95b8c2062d6f8161, 0xecb3ccdd37b369da
 606 //data8 0x3ff1717418520340, 0x3ca5c2732533177c
 607 //data8 0xa0262917caab4ad1, 0xe4dde4ddc81fd119
 608 //data8 0x3ff1b7d59dd40ba0, 0x3cc4c7c98e870ff5
 609 //data8 0xac402c688b72f3f4, 0xdcae469be46d4c8d
 610 //data8 0x3ff200b93cc5a540, 0x3c8dd6dc1bfe865a
 611 //data8 0xba76968b9eabd9ab, 0xd41a8f3df1115f7f
 612 //data8 0x3ff24c6f8f6affa0, 0x3cf1acb6d2a7eff7
 613 //data8 0xcb63c87c23a71dc5, 0xcb161074c17f54ec
 614 //data8 0x3ff29b5b338b7c80, 0x3ce9b5845f6ec746
 615 //data8 0xdfe323b8653af367, 0xc19107d99ab27e42
 616 //data8 0x3ff2edf6fac7f5a0, 0x3cf77f961925fa02
 617 //data8 0xf93746caaba3e1f1, 0xb777744a9df03bff
 618 //data8 0x3ff344df237486c0, 0x3cf6ddf5f6ddda43
 619 //data8 0x8ca77052f6c340f0, 0xacaf476f13806648
 620 //data8 0x3ff3a0dfa4bb4ae0, 0x3cfee01bbd761bff
 621 //data8 0xa1a48604a81d5c62, 0xa11575d30c0aae50
 622 //data8 0x3ff4030b73c55360, 0x3cf1cf0e0324d37c
 623 //data8 0xbe45074b05579024, 0x9478e362a07dd287
 624 //data8 0x3ff46ce4c738c4e0, 0x3ce3179555367d12
 625 //data8 0xe7a08b5693d214ec, 0x8690e3575b8a7c3b
 626 //data8 0x3ff4e0a887c40a80, 0x3cfbd5d46bfefe69
 627 //data8 0x94503d69396d91c7, 0xedd2ce885ff04028
 628 //data8 0x3ff561ebd9c18cc0, 0x3cf331bd176b233b
 629 //data8 0xced1d96c5bb209e6, 0xc965278083808702
 630 //data8 0x3ff5f71d7ff42c80, 0x3ce3301cc0b5a48c
 631 //data8 0xabac2cee0fc24e20, 0x9c4eb1136094cbbd
 632 //data8 0x3ff6ae4c63222720, 0x3cf5ff46874ee51e
 633 //data8 0x8040201008040201, 0xb4d7ac4d9acb1bf4
 634 //data8 0x3ff7b7d33b928c40, 0x3cfacdee584023bb
 635 LOCAL_OBJECT_END(T_table)
 636
 637
 638
 639 .align 16
 640
 641 LOCAL_OBJECT_START(poly_coeffs)
 642        // C_3
 643 data8 0xaaaaaaaaaaaaaaab, 0x0000000000003ffc
 644        // C_5
 645 data8 0x999999999999999a, 0x0000000000003ffb
 646        // C_7, C_9
 647 data8 0x3fa6db6db6db6db7, 0x3f9f1c71c71c71c8
 648        // pi/2 (low, high)
 649 data8 0x3C91A62633145C07, 0x3FF921FB54442D18
 650        // C_11, C_13
 651 data8 0x3f96e8ba2e8ba2e9, 0x3f91c4ec4ec4ec4e
 652        // C_15, C_17
 653 data8 0x3f8c99999999999a, 0x3f87a87878787223
 654        // pi (low, high)
 655 data8 0x3CA1A62633145C07, 0x400921FB54442D18
 656 LOCAL_OBJECT_END(poly_coeffs)
 657
 658
 659 R_DBL_S = r21
 660 R_EXP0 = r22
 661 R_EXP = r15
 662 R_SGNMASK = r23
 663 R_TMP = r24
 664 R_TMP2 = r25
 665 R_INDEX = r26
 666 R_TMP3 = r27
 667 R_TMP03 = r27
 668 R_TMP4 = r28
 669 R_TMP5 = r23
 670 R_TMP6 = r22
 671 R_TMP7 = r21
 672 R_T = r29
 673 R_BIAS = r20
 674
 675 F_T = f6
 676 F_1S2 = f7
 677 F_1S2_S = f9
 678 F_INV_1T2 = f10
 679 F_SQRT_1T2 = f11
 680 F_S2T2 = f12
 681 F_X = f13
 682 F_D = f14
 683 F_2M64 = f15
 684
 685 F_CS2 = f32
 686 F_CS3 = f33
 687 F_CS4 = f34
 688 F_CS5 = f35
 689 F_CS6 = f36
 690 F_CS7 = f37
 691 F_CS8 = f38
 692 F_CS9 = f39
 693 F_S23 = f40
 694 F_S45 = f41
 695 F_S67 = f42
 696 F_S89 = f43
 697 F_S25 = f44
 698 F_S69 = f45
 699 F_S29 = f46
 700 F_X2 = f47
 701 F_X4 = f48
 702 F_TSQRT = f49
 703 F_DTX = f50
 704 F_R = f51
 705 F_R2 = f52
 706 F_R3 = f53
 707 F_R4 = f54
 708
 709 F_C3 = f55
 710 F_C5 = f56
 711 F_C7 = f57
 712 F_C9 = f58
 713 F_P79 = f59
 714 F_P35 = f60
 715 F_P39 = f61
 716
 717 F_ATHI = f62
 718 F_ATLO = f63
 719
 720 F_T1 = f64
 721 F_Y = f65
 722 F_Y2 = f66
 723 F_ANDMASK = f67
 724 F_ORMASK = f68
 725 F_S = f69
 726 F_05 = f70
 727 F_SQRT_1S2 = f71
 728 F_DS = f72
 729 F_Z = f73
 730 F_1T2 = f74
 731 F_DZ = f75
 732 F_ZE = f76
 733 F_YZ = f77
 734 F_Y1S2 = f78
 735 F_Y1S2X = f79
 736 F_1X = f80
 737 F_ST = f81
 738 F_1T2_ST = f82
 739 F_TSS = f83
 740 F_Y1S2X2 = f84
 741 F_DZ_TERM = f85
 742 F_DTS = f86
 743 F_DS2X = f87
 744 F_T2 = f88
 745 F_ZY1S2S = f89
 746 F_Y1S2_1X = f90
 747 F_TS = f91
 748 F_PI2_LO = f92
 749 F_PI2_HI = f93
 750 F_S19 = f94
 751 F_INV1T2_2 = f95
 752 F_CORR = f96
 753 F_DZ0 = f97
 754
 755 F_C11 = f98
 756 F_C13 = f99
 757 F_C15 = f100
 758 F_C17 = f101
 759 F_P1113 = f102
 760 F_P1517 = f103
 761 F_P1117 = f104
 762 F_P317 = f105
 763 F_R8 = f106
 764 F_HI = f107
 765 F_1S2_HI = f108
 766 F_DS2 = f109
 767 F_Y2_2 = f110
 768 //F_S2 = f111
 769 //F_S_DS2 = f112
 770 F_S_1S2S = f113
 771 F_XL = f114
 772 F_2M128 = f115
 773 F_1AS = f116
 774 F_AS = f117
 775
 776
 777
 778 .section .text
 779 GLOBAL_LIBM_ENTRY(acosl)
 780
 781 {.mfi
 782        // get exponent, mantissa (rounded to double precision) of s
 783        getf.d R_DBL_S = f8
 784        // 1-s^2
 785        fnma.s1 F_1S2 = f8, f8, f1
 786        // r2 = pointer to T_table
 787        addl r2 = @ltoff(T_table), gp
 788 }
 789
 790 {.mfi
 791        // sign mask
 792        mov R_SGNMASK = 0x20000
 793        nop.f 0
 794        // bias-63-1
 795        mov R_TMP03 = 0xffff-64;;
 796 }
 797
 798
 799 {.mfi
 800        // get exponent of s
 801        getf.exp R_EXP = f8
 802        nop.f 0
 803        // R_TMP4 = 2^45
 804        shl R_TMP4 = R_SGNMASK, 45-17
 805 }
 806
 807 {.mlx
 808        // load bias-4
 809        mov R_TMP = 0xffff-4
 810        // load RU(sqrt(2)/2) to integer register (in double format, shifted left by 1)
 811        movl R_TMP2 = 0x7fcd413cccfe779a;;
 812 }
 813
 814
 815 {.mfi
 816        // load 2^{-64} in FP register
 817        setf.exp F_2M64 = R_TMP03
 818        nop.f 0
 819        // index = (0x7-exponent)|b1 b2.. b6
 820        extr.u R_INDEX = R_DBL_S, 46, 9
 821 }
 822
 823 {.mfi
 824        // get t = sign|exponent|b1 b2.. b6 1 x.. x
 825        or R_T = R_DBL_S, R_TMP4
 826        nop.f 0
 827        // R_TMP4 = 2^45-1
 828        sub R_TMP4 = R_TMP4, r0, 1;;
 829 }
 830
 831
 832 {.mfi
 833        // get t = sign|exponent|b1 b2.. b6 1 0.. 0
 834        andcm R_T = R_T, R_TMP4
 835        nop.f 0
 836        // eliminate sign from R_DBL_S (shift left by 1)
 837        shl R_TMP3 = R_DBL_S, 1
 838 }
 839
 840 {.mfi
 841        // R_BIAS = 3*2^6
 842        mov R_BIAS = 0xc0
 843        nop.f 0
 844        // eliminate sign from R_EXP
 845        andcm R_EXP0 = R_EXP, R_SGNMASK;;
 846 }
 847
 848
 849
 850 {.mfi
 851        // load start address for T_table
 852        ld8 r2 = [r2]
 853        nop.f 0
 854        // p8 = 1 if |s|> = sqrt(2)/2
 855        cmp.geu p8, p0 = R_TMP3, R_TMP2
 856 }
 857
 858 {.mlx
 859        // p7 = 1 if |s|<2^{-4} (exponent of s<bias-4)
 860        cmp.lt p7, p0 = R_EXP0, R_TMP
 861        // sqrt coefficient cs8 = -33*13/128
 862        movl R_TMP2 = 0xc0568000;;
 863 }
 864
 865
 866
 867 {.mbb
 868        // load t in FP register
 869        setf.d F_T = R_T
 870        // if |s|<2^{-4}, take alternate path
 871  (p7) br.cond.spnt SMALL_S
 872        // if |s|> = sqrt(2)/2, take alternate path
 873  (p8) br.cond.sptk LARGE_S
 874 }
 875
 876 {.mlx
 877        // index = (4-exponent)|b1 b2.. b6
 878        sub R_INDEX = R_INDEX, R_BIAS
 879        // sqrt coefficient cs9 = 55*13/128
 880        movl R_TMP = 0x40b2c000;;
 881 }
 882
 883
 884 {.mfi
 885        // sqrt coefficient cs8 = -33*13/128
 886        setf.s F_CS8 = R_TMP2
 887        nop.f 0
 888        // shift R_INDEX by 5
 889        shl R_INDEX = R_INDEX, 5
 890 }
 891
 892 {.mfi
 893        // sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
 894        mov R_TMP4 = 0xffff - 1
 895        nop.f 0
 896        // sqrt coefficient cs6 = -21/16
 897        mov R_TMP6 = 0xbfa8;;
 898 }
 899
 900
 901 {.mlx
 902        // table index
 903        add r2 = r2, R_INDEX
 904        // sqrt coefficient cs7 = 33/16
 905        movl R_TMP2 = 0x40040000;;
 906 }
 907
 908
 909 {.mmi
 910        // load cs9 = 55*13/128
 911        setf.s F_CS9 = R_TMP
 912        // sqrt coefficient cs5 = 7/8
 913        mov R_TMP3 = 0x3f60
 914        // sqrt coefficient cs6 = 21/16
 915        shl R_TMP6 = R_TMP6, 16;;
 916 }
 917
 918
 919 {.mmi
 920        // load significand of 1/(1-t^2)
 921        ldf8 F_INV_1T2 = [r2], 8
 922        // sqrt coefficient cs7 = 33/16
 923        setf.s F_CS7 = R_TMP2
 924        // sqrt coefficient cs4 = -5/8
 925        mov R_TMP5 = 0xbf20;;
 926 }
 927
 928
 929 {.mmi
 930        // load significand of sqrt(1-t^2)
 931        ldf8 F_SQRT_1T2 = [r2], 8
 932        // sqrt coefficient cs6 = 21/16
 933        setf.s F_CS6 = R_TMP6
 934        // sqrt coefficient cs5 = 7/8
 935        shl R_TMP3 = R_TMP3, 16;;
 936 }
 937
 938
 939 {.mmi
 940        // sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
 941        setf.exp F_CS3 = R_TMP4
 942        // r3 = pointer to polynomial coefficients
 943        addl r3 = @ltoff(poly_coeffs), gp
 944        // sqrt coefficient cs4 = -5/8
 945        shl R_TMP5 = R_TMP5, 16;;
 946 }
 947
 948
 949 {.mfi
 950        // sqrt coefficient cs5 = 7/8
 951        setf.s F_CS5 = R_TMP3
 952        // d = s-t
 953        fms.s1 F_D = f8, f1, F_T
 954        // set p6 = 1 if s<0, p11 = 1 if s> = 0
 955        cmp.ge p6, p11 = R_EXP, R_DBL_S
 956 }
 957
 958 {.mfi
 959        // r3 = load start address to polynomial coefficients
 960        ld8 r3 = [r3]
 961        // s+t
 962        fma.s1 F_S2T2 = f8, f1, F_T
 963        nop.i 0;;
 964 }
 965
 966
 967 {.mfi
 968        // sqrt coefficient cs4 = -5/8
 969        setf.s F_CS4 = R_TMP5
 970        // s^2-t^2
 971        fma.s1 F_S2T2 = F_S2T2, F_D, f0
 972        nop.i 0;;
 973 }
 974
 975
 976 {.mfi
 977        // load C3
 978        ldfe F_C3 = [r3], 16
 979        // 0.5/(1-t^2) = 2^{-64}*(2^63/(1-t^2))
 980        fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
 981        nop.i 0;;
 982 }
 983
 984 {.mfi
 985        // load C_5
 986        ldfe F_C5 = [r3], 16
 987        // set correct exponent for sqrt(1-t^2)
 988        fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
 989        nop.i 0;;
 990 }
 991
 992
 993 {.mfi
 994        // load C_7, C_9
 995        ldfpd F_C7, F_C9 = [r3], 16
 996        // x = -(s^2-t^2)/(1-t^2)/2
 997        fnma.s1 F_X = F_INV_1T2, F_S2T2, f0
 998        nop.i 0;;
 999 }
1000
1001
1002 {.mmf
1003        // load asin(t)_high, asin(t)_low
1004        ldfpd F_ATHI, F_ATLO = [r2]
1005            // load pi/2
1006            ldfpd F_PI2_LO, F_PI2_HI = [r3]
1007        // t*sqrt(1-t^2)
1008        fma.s1 F_TSQRT = F_T, F_SQRT_1T2, f0;;
1009 }
1010
1011
1012 {.mfi
1013        nop.m 0
1014        // cs9*x+cs8
1015        fma.s1 F_S89 = F_CS9, F_X, F_CS8
1016        nop.i 0
1017 }
1018
1019 {.mfi
1020        nop.m 0
1021        // cs7*x+cs6
1022        fma.s1 F_S67 = F_CS7, F_X, F_CS6
1023        nop.i 0;;
1024 }
1025
1026 {.mfi
1027        nop.m 0
1028        // cs5*x+cs4
1029        fma.s1 F_S45 = F_CS5, F_X, F_CS4
1030        nop.i 0
1031 }
1032
1033 {.mfi
1034        nop.m 0
1035        // x*x
1036        fma.s1 F_X2 = F_X, F_X, f0
1037        nop.i 0;;
1038 }
1039
1040
1041 {.mfi
1042        nop.m 0
1043        // (s-t)-t*x
1044        fnma.s1 F_DTX = F_T, F_X, F_D
1045        nop.i 0
1046 }
1047
1048 {.mfi
1049        nop.m 0
1050        // cs3*x+cs2 (cs2 = -0.5 = -cs3)
1051        fms.s1 F_S23 = F_CS3, F_X, F_CS3
1052        nop.i 0;;
1053 }
1054
1055 {.mfi
1056   nop.m 0
1057   // if sign is negative, negate table values: asin(t)_low
1058   (p6) fnma.s1 F_ATLO = F_ATLO, f1, f0
1059   nop.i 0
1060 }
1061
1062 {.mfi
1063   nop.m 0
1064   // if sign is negative, negate table values: asin(t)_high
1065   (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0
1066   nop.i 0;;
1067 }
1068
1069
1070 {.mfi
1071        nop.m 0
1072        // cs9*x^3+cs8*x^2+cs7*x+cs6
1073        fma.s1 F_S69 = F_S89, F_X2, F_S67
1074        nop.i 0
1075 }
1076
1077 {.mfi
1078        nop.m 0
1079        // x^4
1080        fma.s1 F_X4 = F_X2, F_X2, f0
1081        nop.i 0;;
1082 }
1083
1084
1085 {.mfi
1086        nop.m 0
1087        // t*sqrt(1-t^2)*x^2
1088        fma.s1 F_TSQRT = F_TSQRT, F_X2, f0
1089        nop.i 0
1090 }
1091
1092 {.mfi
1093        nop.m 0
1094        // cs5*x^3+cs4*x^2+cs3*x+cs2
1095        fma.s1 F_S25 = F_S45, F_X2, F_S23
1096        nop.i 0;;
1097 }
1098
1099
1100 {.mfi
1101        nop.m 0
1102        // ((s-t)-t*x)*sqrt(1-t^2)
1103        fma.s1 F_DTX = F_DTX, F_SQRT_1T2, f0
1104        nop.i 0;;
1105 }
1106
1107 {.mfi
1108        nop.m 0
1109        // (pi/2)_high - asin(t)_high
1110        fnma.s1 F_ATHI = F_ATHI, f1, F_PI2_HI
1111        nop.i 0
1112 }
1113
1114 {.mfi
1115        nop.m 0
1116        // asin(t)_low - (pi/2)_low
1117        fnma.s1 F_ATLO = F_PI2_LO, f1, F_ATLO
1118            nop.i 0;;
1119 }
1120
1121
1122 {.mfi
1123        nop.m 0
1124        // PS29 = cs9*x^7+..+cs5*x^3+cs4*x^2+cs3*x+cs2
1125        fma.s1 F_S29 = F_S69, F_X4, F_S25
1126        nop.i 0;;
1127 }
1128
1129
1130
1131 {.mfi
1132        nop.m 0
1133        // R = ((s-t)-t*x)*sqrt(1-t^2)-t*sqrt(1-t^2)*x^2*PS29
1134        fnma.s1 F_R = F_S29, F_TSQRT, F_DTX
1135        nop.i 0;;
1136 }
1137
1138
1139 {.mfi
1140        nop.m 0
1141        // R^2
1142        fma.s1 F_R2 = F_R, F_R, f0
1143        nop.i 0;;
1144 }
1145
1146
1147 {.mfi
1148        nop.m 0
1149        // c7+c9*R^2
1150        fma.s1 F_P79 = F_C9, F_R2, F_C7
1151        nop.i 0
1152 }
1153
1154 {.mfi
1155        nop.m 0
1156        // c3+c5*R^2
1157        fma.s1 F_P35 = F_C5, F_R2, F_C3
1158        nop.i 0;;
1159 }
1160
1161 {.mfi
1162        nop.m 0
1163        // R^3
1164        fma.s1 F_R4 = F_R2, F_R2, f0
1165        nop.i 0;;
1166 }
1167
1168 {.mfi
1169        nop.m 0
1170        // R^3
1171        fma.s1 F_R3 = F_R2, F_R, f0
1172        nop.i 0;;
1173 }
1174
1175
1176
1177 {.mfi
1178        nop.m 0
1179        // c3+c5*R^2+c7*R^4+c9*R^6
1180        fma.s1 F_P39 = F_P79, F_R4, F_P35
1181        nop.i 0;;
1182 }
1183
1184
1185 {.mfi
1186        nop.m 0
1187        // asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1188        fma.s1 F_P39 = F_P39, F_R3, F_ATLO
1189        nop.i 0;;
1190 }
1191
1192
1193 {.mfi
1194        nop.m 0
1195        // R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1196        fma.s1 F_P39 = F_P39, f1, F_R
1197        nop.i 0;;
1198 }
1199
1200
1201 {.mfb
1202        nop.m 0
1203        // result = (pi/2)-asin(t)_high+R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1204        fnma.s0 f8 = F_P39, f1, F_ATHI
1205        // return
1206        br.ret.sptk b0;;
1207 }
1208
1209
1210
1211
1212 LARGE_S:
1213
1214 {.mfi
1215        // bias-1
1216        mov R_TMP3 = 0xffff - 1
1217        // y ~ 1/sqrt(1-s^2)
1218        frsqrta.s1 F_Y, p7 = F_1S2
1219        // c9 = 55*13*17/128
1220        mov R_TMP4 = 0x10af7b
1221 }
1222
1223 {.mlx
1224        // c8 = -33*13*15/128
1225        mov R_TMP5 = 0x184923
1226        movl R_TMP2 = 0xff00000000000000;;
1227 }
1228
1229 {.mfi
1230        // set p6 = 1 if s<0, p11 = 1 if s>0
1231        cmp.ge p6, p11 = R_EXP, R_DBL_S
1232        // 1-s^2
1233        fnma.s1 F_1S2 = f8, f8, f1
1234        // set p9 = 1
1235        cmp.eq p9, p0 = r0, r0;;
1236 }
1237
1238
1239 {.mfi
1240        // load 0.5
1241        setf.exp F_05 = R_TMP3
1242        // (1-s^2) rounded to single precision
1243        fnma.s.s1 F_1S2_S = f8, f8, f1
1244        // c9 = 55*13*17/128
1245        shl R_TMP4 = R_TMP4, 10
1246 }
1247
1248 {.mlx
1249        // AND mask for getting t ~ sqrt(1-s^2)
1250        setf.sig F_ANDMASK = R_TMP2
1251        // OR mask
1252        movl R_TMP2 = 0x0100000000000000;;
1253 }
1254
1255 .pred.rel "mutex", p6, p11
1256 {.mfi
1257        nop.m 0
1258            // 1-|s|
1259  (p6)  fma.s1 F_1AS = f8, f1, f1
1260        nop.i 0
1261 }
1262
1263 {.mfi
1264        nop.m 0
1265        // 1-|s|
1266  (p11) fnma.s1 F_1AS = f8, f1, f1
1267        nop.i 0;;
1268 }
1269
1270
1271 {.mfi
1272        // c9 = 55*13*17/128
1273        setf.s F_CS9 = R_TMP4
1274            // |s|
1275  (p6)  fnma.s1 F_AS = f8, f1, f0
1276        // c8 = -33*13*15/128
1277        shl R_TMP5 = R_TMP5, 11
1278 }
1279
1280 {.mfi
1281        // c7 = 33*13/16
1282        mov R_TMP4 = 0x41d68
1283            // |s|
1284  (p11) fma.s1 F_AS = f8, f1, f0
1285        nop.i 0;;
1286 }
1287
1288
1289 {.mfi
1290        setf.sig F_ORMASK = R_TMP2
1291        // y^2
1292        fma.s1 F_Y2 = F_Y, F_Y, f0
1293        // c7 = 33*13/16
1294        shl R_TMP4 = R_TMP4, 12
1295 }
1296
1297 {.mfi
1298        // c6 = -33*7/16
1299        mov R_TMP6 = 0xc1670
1300        // y' ~ sqrt(1-s^2)
1301        fma.s1 F_T1 = F_Y, F_1S2, f0
1302        // c5 = 63/8
1303        mov R_TMP7 = 0x40fc;;
1304 }
1305
1306
1307 {.mlx
1308        // load c8 = -33*13*15/128
1309        setf.s F_CS8 = R_TMP5
1310        // c4 = -35/8
1311        movl R_TMP5 = 0xc08c0000;;
1312 }
1313
1314 {.mfi
1315        // r3 = pointer to polynomial coefficients
1316        addl r3 = @ltoff(poly_coeffs), gp
1317        // 1-s-(1-s^2)_s
1318        fnma.s1 F_DS = F_1S2_S, f1, F_1AS
1319        // p9 = 0 if p7 = 1 (p9 = 1 for special cases only)
1320  (p7) cmp.ne p9, p0 = r0, r0
1321 }
1322
1323 {.mlx
1324        // load c7 = 33*13/16
1325        setf.s F_CS7 = R_TMP4
1326        // c3 = 5/2
1327        movl R_TMP4 = 0x40200000;;
1328 }
1329
1330
1331 {.mlx
1332        // load c4 = -35/8
1333        setf.s F_CS4 = R_TMP5
1334        // c2 = -3/2
1335        movl R_TMP5 = 0xbfc00000;;
1336 }
1337
1338
1339 {.mfi
1340        // load c3 = 5/2
1341        setf.s F_CS3 = R_TMP4
1342        // x = (1-s^2)_s*y^2-1
1343        fms.s1 F_X = F_1S2_S, F_Y2, f1
1344        // c6 = -33*7/16
1345        shl R_TMP6 = R_TMP6, 12
1346 }
1347
1348 {.mfi
1349        nop.m 0
1350        // y^2/2
1351        fma.s1 F_Y2_2 = F_Y2, F_05, f0
1352        nop.i 0;;
1353 }
1354
1355
1356 {.mfi
1357        // load c6 = -33*7/16
1358        setf.s F_CS6 = R_TMP6
1359        // eliminate lower bits from y'
1360        fand F_T = F_T1, F_ANDMASK
1361        // c5 = 63/8
1362        shl R_TMP7 = R_TMP7, 16
1363 }
1364
1365
1366 {.mfb
1367        // r3 = load start address to polynomial coefficients
1368        ld8 r3 = [r3]
1369        // 1-(1-s^2)_s-s^2
1370        fma.s1 F_DS = F_AS, F_1AS, F_DS
1371        // p9 = 1 if s is a special input (NaN, or |s|> = 1)
1372  (p9) br.cond.spnt acosl_SPECIAL_CASES;;
1373 }
1374
1375 {.mmf
1376        // get exponent, significand of y' (in single prec.)
1377        getf.s R_TMP = F_T1
1378        // load c3 = -3/2
1379        setf.s F_CS2 = R_TMP5
1380        // y*(1-s^2)
1381        fma.s1 F_Y1S2 = F_Y, F_1S2, f0;;
1382 }
1383
1384
1385
1386 {.mfi
1387        nop.m 0
1388        // if s<0, set s = -s
1389  (p6) fnma.s1 f8 = f8, f1, f0
1390        nop.i 0;;
1391 }
1392
1393
1394 {.mfi
1395        // load c5 = 63/8
1396        setf.s F_CS5 = R_TMP7
1397        // x = (1-s^2)_s*y^2-1+(1-(1-s^2)_s-s^2)*y^2
1398        fma.s1 F_X = F_DS, F_Y2, F_X
1399        // for t = 2^k*1.b1 b2.., get 7-k|b1.. b6
1400        extr.u R_INDEX = R_TMP, 17, 9;;
1401 }
1402
1403
1404 {.mmi
1405        // index = (4-exponent)|b1 b2.. b6
1406        sub R_INDEX = R_INDEX, R_BIAS
1407        nop.m 0
1408        // get exponent of y
1409        shr.u R_TMP2 = R_TMP, 23;;
1410 }
1411
1412 {.mmi
1413        // load C3
1414        ldfe F_C3 = [r3], 16
1415        // set p8 = 1 if y'<2^{-4}
1416        cmp.gt p8, p0 = 0x7b, R_TMP2
1417        // shift R_INDEX by 5
1418        shl R_INDEX = R_INDEX, 5;;
1419 }
1420
1421
1422 {.mfb
1423        // get table index for sqrt(1-t^2)
1424        add r2 = r2, R_INDEX
1425        // get t = 2^k*1.b1 b2.. b7 1
1426        for F_T = F_T, F_ORMASK
1427  (p8) br.cond.spnt VERY_LARGE_INPUT;;
1428 }
1429
1430
1431
1432 {.mmf
1433        // load C5
1434        ldfe F_C5 = [r3], 16
1435        // load 1/(1-t^2)
1436        ldfp8 F_INV_1T2, F_SQRT_1T2 = [r2], 16
1437        // x = ((1-s^2)*y^2-1)/2
1438        fma.s1 F_X = F_X, F_05, f0;;
1439 }
1440
1441
1442
1443 {.mmf
1444        nop.m 0
1445        // C7, C9
1446        ldfpd F_C7, F_C9 = [r3], 16
1447        // set correct exponent for t
1448        fmerge.se F_T = F_T1, F_T;;
1449 }
1450
1451
1452
1453 {.mfi
1454        // get address for loading pi
1455            add r3 = 48, r3
1456        // c9*x+c8
1457        fma.s1 F_S89 = F_X, F_CS9, F_CS8
1458        nop.i 0
1459 }
1460
1461 {.mfi
1462        nop.m 0
1463        // x^2
1464        fma.s1 F_X2 = F_X, F_X, f0
1465        nop.i 0;;
1466 }
1467
1468
1469 {.mfi
1470        // pi (low, high)
1471        ldfpd F_PI2_LO, F_PI2_HI = [r3]
1472        // y*(1-s^2)*x
1473        fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
1474        nop.i 0
1475 }
1476
1477 {.mfi
1478        nop.m 0
1479        // c7*x+c6
1480        fma.s1 F_S67 = F_X, F_CS7, F_CS6
1481        nop.i 0;;
1482 }
1483
1484
1485 {.mfi
1486        nop.m 0
1487        // 1-x
1488        fnma.s1 F_1X = F_X, f1, f1
1489        nop.i 0
1490 }
1491
1492 {.mfi
1493        nop.m 0
1494        // c3*x+c2
1495        fma.s1 F_S23 = F_X, F_CS3, F_CS2
1496        nop.i 0;;
1497 }
1498
1499
1500 {.mfi
1501        nop.m 0
1502        // 1-t^2
1503        fnma.s1 F_1T2 = F_T, F_T, f1
1504        nop.i 0
1505 }
1506
1507 {.mfi
1508        // load asin(t)_high, asin(t)_low
1509        ldfpd F_ATHI, F_ATLO = [r2]
1510        // c5*x+c4
1511        fma.s1 F_S45 = F_X, F_CS5, F_CS4
1512        nop.i 0;;
1513 }
1514
1515
1516
1517 {.mfi
1518        nop.m 0
1519        // t*s
1520        fma.s1 F_TS = F_T, f8, f0
1521        nop.i 0
1522 }
1523
1524 {.mfi
1525        nop.m 0
1526        // 0.5/(1-t^2)
1527        fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
1528        nop.i 0;;
1529 }
1530
1531 {.mfi
1532        nop.m 0
1533        // z~sqrt(1-t^2), rounded to 24 significant bits
1534        fma.s.s1 F_Z = F_SQRT_1T2, F_2M64, f0
1535        nop.i 0
1536 }
1537
1538 {.mfi
1539        nop.m 0
1540        // sqrt(1-t^2)
1541        fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
1542        nop.i 0;;
1543 }
1544
1545
1546 {.mfi
1547        nop.m 0
1548        // y*(1-s^2)*x^2
1549        fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
1550        nop.i 0
1551 }
1552
1553 {.mfi
1554        nop.m 0
1555        // x^4
1556        fma.s1 F_X4 = F_X2, F_X2, f0
1557        nop.i 0;;
1558 }
1559
1560
1561 {.mfi
1562        nop.m 0
1563        // s*t rounded to 24 significant bits
1564        fma.s.s1 F_TSS = F_T, f8, f0
1565        nop.i 0
1566 }
1567
1568 {.mfi
1569        nop.m 0
1570        // c9*x^3+..+c6
1571        fma.s1 F_S69 = F_X2, F_S89, F_S67
1572        nop.i 0;;
1573 }
1574
1575
1576 {.mfi
1577        nop.m 0
1578        // ST = (t^2-1+s^2) rounded to 24 significant bits
1579        fms.s.s1 F_ST = f8, f8, F_1T2
1580        nop.i 0
1581 }
1582
1583 {.mfi
1584        nop.m 0
1585        // c5*x^3+..+c2
1586        fma.s1 F_S25 = F_X2, F_S45, F_S23
1587        nop.i 0;;
1588 }
1589
1590
1591 {.mfi
1592        nop.m 0
1593        // 0.25/(1-t^2)
1594        fma.s1 F_INV1T2_2 = F_05, F_INV_1T2, f0
1595        nop.i 0
1596 }
1597
1598 {.mfi
1599        nop.m 0
1600        // t*s-sqrt(1-t^2)*(1-s^2)*y
1601        fnma.s1 F_TS = F_Y1S2, F_SQRT_1T2, F_TS
1602        nop.i 0;;
1603 }
1604
1605
1606 {.mfi
1607        nop.m 0
1608        // z*0.5/(1-t^2)
1609        fma.s1 F_ZE = F_INV_1T2, F_SQRT_1T2, f0
1610        nop.i 0
1611 }
1612
1613 {.mfi
1614        nop.m 0
1615        // z^2+t^2-1
1616        fms.s1 F_DZ0 = F_Z, F_Z, F_1T2
1617        nop.i 0;;
1618 }
1619
1620
1621 {.mfi
1622        nop.m 0
1623        // (1-s^2-(1-s^2)_s)*x
1624        fma.s1 F_DS2X = F_X, F_DS, f0
1625        nop.i 0;;
1626 }
1627
1628
1629 {.mfi
1630        nop.m 0
1631        // t*s-(t*s)_s
1632        fms.s1 F_DTS = F_T, f8, F_TSS
1633        nop.i 0
1634 }
1635
1636 {.mfi
1637        nop.m 0
1638        // c9*x^7+..+c2
1639        fma.s1 F_S29 = F_X4, F_S69, F_S25
1640        nop.i 0;;
1641 }
1642
1643
1644 {.mfi
1645        nop.m 0
1646        // y*z
1647        fma.s1 F_YZ = F_Z, F_Y, f0
1648        nop.i 0
1649 }
1650
1651 {.mfi
1652        nop.m 0
1653        // t^2
1654        fma.s1 F_T2 = F_T, F_T, f0
1655        nop.i 0;;
1656 }
1657
1658
1659 {.mfi
1660        nop.m 0
1661        // 1-t^2+ST
1662        fma.s1 F_1T2_ST = F_ST, f1, F_1T2
1663        nop.i 0;;
1664 }
1665
1666
1667 {.mfi
1668        nop.m 0
1669        // y*(1-s^2)(1-x)
1670        fma.s1 F_Y1S2_1X = F_Y1S2, F_1X, f0
1671        nop.i 0
1672 }
1673
1674 {.mfi
1675        nop.m 0
1676        // dz ~ sqrt(1-t^2)-z
1677        fma.s1 F_DZ = F_DZ0, F_ZE, f0
1678        nop.i 0;;
1679 }
1680
1681
1682 {.mfi
1683        nop.m 0
1684        // -1+correction for sqrt(1-t^2)-z
1685        fnma.s1 F_CORR = F_INV1T2_2, F_DZ0, f0
1686        nop.i 0;;
1687 }
1688
1689
1690 {.mfi
1691        nop.m 0
1692        // (PS29*x^2+x)*y*(1-s^2)
1693        fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
1694        nop.i 0;;
1695 }
1696
1697 {.mfi
1698        nop.m 0
1699        // z*y*(1-s^2)_s
1700        fma.s1 F_ZY1S2S = F_YZ, F_1S2_S, f0
1701        nop.i 0
1702 }
1703
1704 {.mfi
1705        nop.m 0
1706        // s^2-(1-t^2+ST)
1707        fms.s1 F_1T2_ST = f8, f8, F_1T2_ST
1708        nop.i 0;;
1709 }
1710
1711
1712 {.mfi
1713        nop.m 0
1714        // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x
1715        fma.s1 F_DTS = F_YZ, F_DS2X, F_DTS
1716        nop.i 0
1717 }
1718
1719 {.mfi
1720        nop.m 0
1721        // dz*y*(1-s^2)*(1-x)
1722        fma.s1 F_DZ_TERM = F_DZ, F_Y1S2_1X, f0
1723        nop.i 0;;
1724 }
1725
1726
1727 {.mfi
1728        nop.m 0
1729        // R = t*s-sqrt(1-t^2)*(1-s^2)*y+sqrt(1-t^2)*(1-s^2)*y*PS19
1730        // (used for polynomial evaluation)
1731        fma.s1 F_R = F_S19, F_SQRT_1T2, F_TS
1732        nop.i 0;;
1733 }
1734
1735
1736 {.mfi
1737        nop.m 0
1738        // (PS29*x^2)*y*(1-s^2)
1739        fma.s1 F_S29 = F_Y1S2X2, F_S29, f0
1740        nop.i 0
1741 }
1742
1743 {.mfi
1744        nop.m 0
1745        // apply correction to dz*y*(1-s^2)*(1-x)
1746        fma.s1 F_DZ_TERM = F_DZ_TERM, F_CORR, F_DZ_TERM
1747        nop.i 0;;
1748 }
1749
1750
1751 {.mfi
1752        nop.m 0
1753        // R^2
1754        fma.s1 F_R2 = F_R, F_R, f0
1755        nop.i 0;;
1756 }
1757
1758
1759 {.mfi
1760        nop.m 0
1761        // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x+dz*y*(1-s^2)*(1-x)
1762        fma.s1 F_DZ_TERM = F_DZ_TERM, f1, F_DTS
1763        nop.i 0;;
1764 }
1765
1766
1767 {.mfi
1768        nop.m 0
1769        // c7+c9*R^2
1770        fma.s1 F_P79 = F_C9, F_R2, F_C7
1771        nop.i 0
1772 }
1773
1774 {.mfi
1775        nop.m 0
1776        // c3+c5*R^2
1777        fma.s1 F_P35 = F_C5, F_R2, F_C3
1778        nop.i 0;;
1779 }
1780
1781 {.mfi
1782        nop.m 0
1783        // asin(t)_low-(pi)_low (if s<0)
1784  (p6)  fms.s1 F_ATLO = F_ATLO, f1, F_PI2_LO
1785        nop.i 0
1786 }
1787
1788 {.mfi
1789        nop.m 0
1790        // R^4
1791        fma.s1 F_R4 = F_R2, F_R2, f0
1792        nop.i 0;;
1793 }
1794
1795 {.mfi
1796        nop.m 0
1797        // R^3
1798        fma.s1 F_R3 = F_R2, F_R, f0
1799        nop.i 0;;
1800 }
1801
1802
1803 {.mfi
1804        nop.m 0
1805        // (t*s)_s-t^2*y*z
1806        fnma.s1 F_TSS = F_T2, F_YZ, F_TSS
1807        nop.i 0
1808 }
1809
1810 {.mfi
1811        nop.m 0
1812        // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)
1813        fma.s1 F_DZ_TERM = F_YZ, F_1T2_ST, F_DZ_TERM
1814        nop.i 0;;
1815 }
1816
1817
1818 {.mfi
1819        nop.m 0
1820        // (pi)_hi-asin(t)_hi (if s<0)
1821  (p6)  fms.s1 F_ATHI = F_PI2_HI, f1, F_ATHI
1822        nop.i 0
1823 }
1824
1825 {.mfi
1826        nop.m 0
1827        // c3+c5*R^2+c7*R^4+c9*R^6
1828        fma.s1 F_P39 = F_P79, F_R4, F_P35
1829        nop.i 0;;
1830 }
1831
1832
1833 {.mfi
1834        nop.m 0
1835        // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)+
1836        // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29
1837        fma.s1 F_DZ_TERM = F_SQRT_1T2, F_S29, F_DZ_TERM
1838        nop.i 0;;
1839 }
1840
1841
1842 {.mfi
1843        nop.m 0
1844        // (t*s)_s-t^2*y*z+z*y*ST
1845        fma.s1 F_TSS = F_YZ, F_ST, F_TSS
1846        nop.i 0
1847 }
1848
1849 {.mfi
1850        nop.m 0
1851        // -asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1852        fms.s1 F_P39 = F_P39, F_R3, F_ATLO
1853        nop.i 0;;
1854 }
1855
1856
1857 {.mfi
1858        nop.m 0
1859        // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
1860        // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 +
1861        // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1862        fma.s1 F_DZ_TERM = F_P39, f1, F_DZ_TERM
1863        nop.i 0;;
1864 }
1865
1866
1867 {.mfi
1868        nop.m 0
1869        // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
1870        // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x +
1871        // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1872        fma.s1 F_DZ_TERM = F_ZY1S2S, F_X, F_DZ_TERM
1873        nop.i 0;;
1874 }
1875
1876
1877 {.mfi
1878        nop.m 0
1879        // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
1880        // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x +
1881        // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) +
1882        // + (t*s)_s-t^2*y*z+z*y*ST
1883        fma.s1 F_DZ_TERM = F_TSS, f1, F_DZ_TERM
1884        nop.i 0;;
1885 }
1886
1887
1888 .pred.rel "mutex", p6, p11
1889 {.mfi
1890        nop.m 0
1891        // result: add high part of table value
1892        // s>0 in this case
1893  (p11) fnma.s0 f8 = F_DZ_TERM, f1, F_ATHI
1894        nop.i 0
1895 }
1896
1897 {.mfb
1898        nop.m 0
1899        // result: add high part of pi-table value
1900        // if s<0
1901  (p6)  fma.s0 f8 = F_DZ_TERM, f1, F_ATHI
1902        br.ret.sptk b0;;
1903 }
1904
1905
1906
1907
1908
1909
1910 SMALL_S:
1911
1912        // use 15-term polynomial approximation
1913
1914 {.mmi
1915        // r3 = pointer to polynomial coefficients
1916        addl r3 = @ltoff(poly_coeffs), gp;;
1917        // load start address for coefficients
1918        ld8 r3 = [r3]
1919        mov R_TMP = 0x3fbf;;
1920 }
1921
1922
1923 {.mmi
1924        add r2 = 64, r3
1925        ldfe F_C3 = [r3], 16
1926        // p7 = 1 if |s|<2^{-64} (exponent of s<bias-64)
1927        cmp.lt p7, p0 = R_EXP0, R_TMP;;
1928 }
1929
1930 {.mmf
1931        ldfe F_C5 = [r3], 16
1932        ldfpd F_C11, F_C13 = [r2], 16
1933            nop.f 0;;
1934 }
1935
1936 {.mmf
1937        ldfpd F_C7, F_C9 = [r3], 16
1938        ldfpd F_C15, F_C17 = [r2]
1939        nop.f 0;;
1940 }
1941
1942
1943
1944 {.mfb
1945        // load pi/2
1946        ldfpd F_PI2_LO, F_PI2_HI = [r3]
1947        // s^2
1948        fma.s1 F_R2 = f8, f8, f0
1949            // |s|<2^{-64}
1950   (p7) br.cond.spnt  RETURN_PI2;;
1951 }
1952
1953
1954 {.mfi
1955        nop.m 0
1956        // s^3
1957        fma.s1 F_R3 = f8, F_R2, f0
1958        nop.i 0
1959 }
1960
1961 {.mfi
1962        nop.m 0
1963        // s^4
1964        fma.s1 F_R4 = F_R2, F_R2, f0
1965        nop.i 0;;
1966 }
1967
1968
1969 {.mfi
1970        nop.m 0
1971        // c3+c5*s^2
1972        fma.s1 F_P35 = F_C5, F_R2, F_C3
1973        nop.i 0
1974 }
1975
1976 {.mfi
1977        nop.m 0
1978        // c11+c13*s^2
1979        fma.s1 F_P1113 = F_C13, F_R2, F_C11
1980        nop.i 0;;
1981 }
1982
1983
1984 {.mfi
1985        nop.m 0
1986        // c7+c9*s^2
1987        fma.s1 F_P79 = F_C9, F_R2, F_C7
1988        nop.i 0
1989 }
1990
1991 {.mfi
1992        nop.m 0
1993        // c15+c17*s^2
1994        fma.s1 F_P1517 = F_C17, F_R2, F_C15
1995        nop.i 0;;
1996 }
1997
1998 {.mfi
1999        nop.m 0
2000            // (pi/2)_high-s_high
2001            fnma.s1 F_T = f8, f1, F_PI2_HI
2002            nop.i 0
2003 }
2004 {.mfi
2005        nop.m 0
2006        // s^8
2007        fma.s1 F_R8 = F_R4, F_R4, f0
2008        nop.i 0;;
2009 }
2010
2011
2012 {.mfi
2013        nop.m 0
2014        // c3+c5*s^2+c7*s^4+c9*s^6
2015        fma.s1 F_P39 = F_P79, F_R4, F_P35
2016        nop.i 0
2017 }
2018
2019 {.mfi
2020        nop.m 0
2021        // c11+c13*s^2+c15*s^4+c17*s^6
2022        fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
2023        nop.i 0;;
2024 }
2025
2026 {.mfi
2027        nop.m 0
2028            // -s_high
2029            fms.s1 F_S = F_T, f1, F_PI2_HI
2030            nop.i 0;;
2031 }
2032
2033 {.mfi
2034        nop.m 0
2035        // c3+..+c17*s^14
2036        fma.s1 F_P317 = F_R8, F_P1117, F_P39
2037        nop.i 0;;
2038 }
2039
2040 {.mfi
2041        nop.m 0
2042            // s_low
2043            fma.s1 F_DS = f8, f1, F_S
2044            nop.i 0;;
2045 }
2046
2047 {.mfi
2048        nop.m 0
2049        // (pi/2)_low-s^3*(c3+..+c17*s^14)
2050        fnma.s0 F_P317 = F_P317, F_R3, F_PI2_LO
2051            nop.i 0;;
2052 }
2053
2054 {.mfi
2055        nop.m 0
2056            // (pi/2)_low-s_low-s^3*(c3+..+c17*s^14)
2057            fms.s1 F_P317 = F_P317, f1, F_DS
2058            nop.i 0;;
2059 }
2060
2061 {.mfb
2062        nop.m 0
2063            // result: pi/2-s-c3*s^3-..-c17*s^17
2064            fma.s0 f8 = F_T, f1, F_P317
2065        br.ret.sptk b0;;
2066 }
2067
2068
2069
2070
2071
2072 RETURN_PI2:
2073
2074 {.mfi
2075        nop.m 0
2076        // (pi/2)_low-s
2077            fms.s0 F_PI2_LO = F_PI2_LO, f1, f8
2078            nop.i 0;;
2079 }
2080
2081 {.mfb
2082        nop.m 0
2083            // (pi/2)-s
2084            fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO
2085            br.ret.sptk b0;;
2086 }
2087
2088
2089
2090
2091
2092 VERY_LARGE_INPUT:
2093
2094
2095 {.mmf
2096        // pointer to pi_low, pi_high
2097            add r2 = 80, r3
2098        // load C5
2099        ldfe F_C5 = [r3], 16
2100        // x = ((1-(s^2)_s)*y^2-1)/2-(s^2-(s^2)_s)*y^2/2
2101        fma.s1 F_X = F_X, F_05, f0;;
2102 }
2103
2104 .pred.rel "mutex", p6, p11
2105 {.mmf
2106        // load pi (low, high), if s<0
2107  (p6)  ldfpd F_PI2_LO, F_PI2_HI = [r2]
2108        // C7, C9
2109        ldfpd F_C7, F_C9 = [r3], 16
2110            // if s>0, set F_PI2_LO=0
2111  (p11) fma.s1 F_PI2_HI = f0, f0, f0;;
2112 }
2113
2114 {.mfi
2115        nop.m 0
2116  (p11) fma.s1 F_PI2_LO = f0, f0, f0
2117        nop.i 0;;
2118 }
2119
2120 {.mfi
2121        // adjust address for C_11
2122            add r3 = 16, r3
2123        // c9*x+c8
2124        fma.s1 F_S89 = F_X, F_CS9, F_CS8
2125        nop.i 0
2126 }
2127
2128 {.mfi
2129        nop.m 0
2130        // x^2
2131        fma.s1 F_X2 = F_X, F_X, f0
2132        nop.i 0;;
2133 }
2134
2135
2136 {.mfi
2137        nop.m 0
2138        // y*(1-s^2)*x
2139        fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
2140        nop.i 0
2141 }
2142
2143 {.mfi
2144        // C11, C13
2145        ldfpd F_C11, F_C13 = [r3], 16
2146        // c7*x+c6
2147        fma.s1 F_S67 = F_X, F_CS7, F_CS6
2148        nop.i 0;;
2149 }
2150
2151
2152 {.mfi
2153        // C15, C17
2154        ldfpd F_C15, F_C17 = [r3], 16
2155        // c3*x+c2
2156        fma.s1 F_S23 = F_X, F_CS3, F_CS2
2157        nop.i 0;;
2158 }
2159
2160
2161 {.mfi
2162        nop.m 0
2163        // c5*x+c4
2164        fma.s1 F_S45 = F_X, F_CS5, F_CS4
2165        nop.i 0;;
2166 }
2167
2168
2169
2170
2171 {.mfi
2172        nop.m 0
2173        // y*(1-s^2)*x^2
2174        fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
2175        nop.i 0
2176 }
2177
2178 {.mfi
2179        nop.m 0
2180        // x^4
2181        fma.s1 F_X4 = F_X2, F_X2, f0
2182        nop.i 0;;
2183 }
2184
2185
2186 {.mfi
2187        nop.m 0
2188        // c9*x^3+..+c6
2189        fma.s1 F_S69 = F_X2, F_S89, F_S67
2190        nop.i 0;;
2191 }
2192
2193
2194 {.mfi
2195        nop.m 0
2196        // c5*x^3+..+c2
2197        fma.s1 F_S25 = F_X2, F_S45, F_S23
2198        nop.i 0;;
2199 }
2200
2201
2202
2203 {.mfi
2204        nop.m 0
2205        // (pi)_high-y*(1-s^2)_s
2206        fnma.s1 F_HI = F_Y, F_1S2_S, F_PI2_HI
2207        nop.i 0;;
2208 }
2209
2210
2211 {.mfi
2212        nop.m 0
2213        // c9*x^7+..+c2
2214        fma.s1 F_S29 = F_X4, F_S69, F_S25
2215        nop.i 0;;
2216 }
2217
2218
2219 {.mfi
2220        nop.m 0
2221        // -(y*(1-s^2)_s)_high
2222        fms.s1 F_1S2_HI = F_HI, f1, F_PI2_HI
2223        nop.i 0;;
2224 }
2225
2226
2227 {.mfi
2228        nop.m 0
2229        // (PS29*x^2+x)*y*(1-s^2)
2230        fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
2231        nop.i 0;;
2232 }
2233
2234
2235 {.mfi
2236        nop.m 0
2237        // y*(1-s^2)_s-(y*(1-s^2))_high
2238        fma.s1 F_DS2 = F_Y, F_1S2_S, F_1S2_HI
2239        nop.i 0;;
2240 }
2241
2242
2243
2244 {.mfi
2245        nop.m 0
2246        // R ~ sqrt(1-s^2)
2247        // (used for polynomial evaluation)
2248        fnma.s1 F_R = F_S19, f1, F_Y1S2
2249        nop.i 0;;
2250 }
2251
2252
2253 {.mfi
2254        nop.m 0
2255        // y*(1-s^2)-(y*(1-s^2))_high
2256        fma.s1 F_DS2 = F_Y, F_DS, F_DS2
2257        nop.i 0
2258 }
2259
2260 {.mfi
2261        nop.m 0
2262        // (pi)_low+(PS29*x^2)*y*(1-s^2)
2263        fma.s1 F_S29 = F_Y1S2X2, F_S29, F_PI2_LO
2264        nop.i 0;;
2265 }
2266
2267
2268 {.mfi
2269        nop.m 0
2270        // R^2
2271        fma.s1 F_R2 = F_R, F_R, f0
2272        nop.i 0;;
2273 }
2274
2275
2276 {.mfi
2277        nop.m 0
2278            // if s<0
2279        // (pi)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)
2280        fms.s1 F_S29 = F_S29, f1, F_DS2
2281        nop.i 0;;
2282 }
2283
2284
2285 {.mfi
2286        nop.m 0
2287        // c7+c9*R^2
2288        fma.s1 F_P79 = F_C9, F_R2, F_C7
2289        nop.i 0
2290 }
2291
2292 {.mfi
2293        nop.m 0
2294        // c3+c5*R^2
2295        fma.s1 F_P35 = F_C5, F_R2, F_C3
2296        nop.i 0;;
2297 }
2298
2299
2300
2301 {.mfi
2302        nop.m 0
2303        // R^4
2304        fma.s1 F_R4 = F_R2, F_R2, f0
2305        nop.i 0
2306 }
2307
2308 {.mfi
2309        nop.m 0
2310        // R^3
2311        fma.s1 F_R3 = F_R2, F_R, f0
2312        nop.i 0;;
2313 }
2314
2315
2316 {.mfi
2317        nop.m 0
2318        // c11+c13*R^2
2319        fma.s1 F_P1113 = F_C13, F_R2, F_C11
2320        nop.i 0
2321 }
2322
2323 {.mfi
2324        nop.m 0
2325        // c15+c17*R^2
2326        fma.s1 F_P1517 = F_C17, F_R2, F_C15
2327        nop.i 0;;
2328 }
2329
2330
2331 {.mfi
2332        nop.m 0
2333        // (pi)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)+y*(1-s^2)*x
2334        fma.s1 F_S29 = F_Y1S2, F_X, F_S29
2335        nop.i 0;;
2336 }
2337
2338
2339 {.mfi
2340        nop.m 0
2341        // c11+c13*R^2+c15*R^4+c17*R^6
2342        fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
2343        nop.i 0
2344 }
2345
2346 {.mfi
2347        nop.m 0
2348        // c3+c5*R^2+c7*R^4+c9*R^6
2349        fma.s1 F_P39 = F_P79, F_R4, F_P35
2350        nop.i 0;;
2351 }
2352
2353
2354
2355 {.mfi
2356        nop.m 0
2357        // R^8
2358        fma.s1 F_R8 = F_R4, F_R4, f0
2359        nop.i 0;;
2360 }
2361
2362
2363 {.mfi
2364        nop.m 0
2365        // c3+c5*R^2+c7*R^4+c9*R^6+..+c17*R^14
2366        fma.s1 F_P317 = F_P1117, F_R8, F_P39
2367        nop.i 0;;
2368 }
2369
2370
2371 {.mfi
2372        nop.m 0
2373        // (pi)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
2374        // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
2375        fnma.s1 F_S29 = F_P317, F_R3, F_S29
2376        nop.i 0;;
2377 }
2378
2379 .pred.rel "mutex", p6, p11
2380 {.mfi
2381        nop.m 0
2382        // Result (if s<0):
2383        // (pi)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
2384        // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
2385        // +(pi)_high-(y*(1-s^2))_high
2386  (p6)  fma.s0 f8 = F_S29, f1, F_HI
2387        nop.i 0
2388 }
2389
2390 {.mfb
2391        nop.m 0
2392            // Result (if s>0):
2393        // (PS29*x^2)*y*(1-s^2)-
2394        // -y*(1-s^2)*x + P3, 17
2395        // +(y*(1-s^2))
2396  (p11) fms.s0 f8 = F_Y, F_1S2_S, F_S29
2397        br.ret.sptk b0;;
2398 }
2399
2400
2401
2402
2403
2404
2405 acosl_SPECIAL_CASES:
2406
2407 {.mfi
2408        alloc r32 = ar.pfs, 1, 4, 4, 0
2409        // check if the input is a NaN, or unsupported format
2410        // (i.e. not infinity or normal/denormal)
2411        fclass.nm p7, p8 = f8, 0x3f
2412        // pointer to pi/2
2413        add r3 = 96, r3;;
2414 }
2415
2416
2417 {.mfi
2418        // load pi/2
2419        ldfpd F_PI2_HI, F_PI2_LO = [r3]
2420        // get |s|
2421        fmerge.s F_S = f0, f8
2422        nop.i 0
2423 }
2424
2425 {.mfb
2426        nop.m 0
2427        // if NaN, quietize it, and return
2428  (p7) fma.s0 f8 = f8, f1, f0
2429  (p7) br.ret.spnt b0;;
2430 }
2431
2432
2433 {.mfi
2434        nop.m 0
2435        // |s| = 1 ?
2436        fcmp.eq.s0 p9, p10 = F_S, f1
2437        nop.i 0
2438 }
2439
2440 {.mfi
2441        nop.m 0
2442        // load FR_X
2443        fma.s1 FR_X = f8, f1, f0
2444        // load error tag
2445        mov GR_Parameter_TAG = 57;;
2446 }
2447
2448
2449 {.mfi
2450        nop.m 0
2451        // if s = 1, result is 0
2452  (p9)  fma.s0 f8 = f0, f0, f0
2453        // set p6=0 for |s|>1
2454  (p10) cmp.ne p6, p0 = r0, r0;;
2455 }
2456
2457
2458 {.mfb
2459        nop.m 0
2460        //  if s = -1, result is pi
2461  (p6) fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO
2462        // return if |s| = 1
2463  (p9) br.ret.sptk b0;;
2464 }
2465
2466
2467 {.mfi
2468        nop.m 0
2469        // get Infinity
2470        frcpa.s1 FR_RESULT, p0 = f1, f0
2471        nop.i 0;;
2472 }
2473
2474
2475 {.mfb
2476        nop.m 0
2477        // return QNaN indefinite (0*Infinity)
2478        fma.s0 FR_RESULT = f0, FR_RESULT, f0
2479        nop.b 0;;
2480 }
2481
2482
2483 GLOBAL_LIBM_END(acosl)
2484
2485
2486 LOCAL_LIBM_ENTRY(__libm_error_region)
2487 .prologue
2488 // (1)
2489 { .mfi
2490         add   GR_Parameter_Y=-32,sp             // Parameter 2 value
2491         nop.f 0
2492 .save   ar.pfs,GR_SAVE_PFS
2493         mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
2494 }
2495 { .mfi
2496 .fframe 64
2497         add sp=-64,sp                          // Create new stack
2498         nop.f 0
2499         mov GR_SAVE_GP=gp                      // Save gp
2500 };;
2501
2502
2503 // (2)
2504 { .mmi
2505         stfe [GR_Parameter_Y] = f1,16         // Store Parameter 2 on stack
2506         add GR_Parameter_X = 16,sp            // Parameter 1 address
2507 .save   b0, GR_SAVE_B0
2508         mov GR_SAVE_B0=b0                     // Save b0
2509 };;
2510
2511 .body
2512 // (3)
2513 { .mib
2514         stfe [GR_Parameter_X] = FR_X              // Store Parameter 1 on stack
2515         add   GR_Parameter_RESULT = 0,GR_Parameter_Y
2516         nop.b 0                                 // Parameter 3 address
2517 }
2518 { .mib
2519         stfe [GR_Parameter_Y] = FR_RESULT             // Store Parameter 3 on stack
2520         add   GR_Parameter_Y = -16,GR_Parameter_Y
2521         br.call.sptk b0=__libm_error_support#   // Call error handling function
2522 };;
2523 { .mmi
2524         nop.m 0
2525         nop.m 0
2526         add   GR_Parameter_RESULT = 48,sp
2527 };;
2528
2529 // (4)
2530 { .mmi
2531         ldfe  f8 = [GR_Parameter_RESULT]       // Get return result off stack
2532 .restore sp
2533         add   sp = 64,sp                       // Restore stack pointer
2534         mov   b0 = GR_SAVE_B0                  // Restore return address
2535 };;
2536
2537 { .mib
2538         mov   gp = GR_SAVE_GP                  // Restore gp
2539         mov   ar.pfs = GR_SAVE_PFS             // Restore ar.pfs
2540         br.ret.sptk     b0                     // Return
2541 };;
2542
2543 LOCAL_LIBM_END(__libm_error_region)
2544
2545 .type   __libm_error_support#,@function
2546 .global __libm_error_support#