sysdeps/ia64/fpu/e_asinl.S

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