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