sysdeps/ia64/fpu/e_acosl.S

   1 .file "acosl.s"
   2
   3
   4 // Copyright (c) 2001 - 2003, Intel Corporation
   5 // All rights reserved.
   6 //
   7 //
   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 acosl(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 // acos(s)= pi/2-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 // acos(|s|)= asin(t)-asin(r)
  67 // acos(-|s|)=pi-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 asin(s) as 17-degree polynomial, return pi/2-asin(s)
  76 // (or simply return pi/2-s, if|s|<2^{-64})
  77 //
  78 // |s| in [sqrt(255/256), 1): acos(|s|)= asin(sqrt(1-s^2))
  79 // acos(-|s|)= pi-asin(sqrt(1-s^2))
  80 // use 17-degree polynomial for asin(sqrt(1-s^2)),
  81 // 9-degree polynomial to evaluate sqrt(1-s^2)
  82 // High order term is (pi)_high-(y*(1-s^2))_high, for s<0,
  83 // or y*(1-s^2)_s, for s>0
  84 //
  85
  86
  87
  88 // Registers used
  89 //==============================================================
  90 // f6-f15, f32-f36
  91 // r2-r3, r23-r23
  92 // p6, p7, p8, p12
  93 //
  94
  95
  96        GR_SAVE_B0= r33
  97        GR_SAVE_PFS= r34
  98        GR_SAVE_GP= r35 // This reg. can safely be used
  99        GR_SAVE_SP= r36
 100
 101        GR_Parameter_X= r37
 102        GR_Parameter_Y= r38
 103        GR_Parameter_RESULT= r39
 104        GR_Parameter_TAG= r40
 105
 106        FR_X= f10
 107        FR_Y= f1
 108        FR_RESULT= f8
 109
 110
 111
 112 RODATA
 113
 114 .align 16
 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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 302 data8 0x3fc6be97a21daf00, 0x3cc2ac8330e59aa5
 303 data8 0x84390ec132759ecb, 0xfbe0fa06e24cc390
 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        // pi (low, high)
 654 data8 0x3CA1A62633145C07, 0x400921FB54442D18
 655 LOCAL_OBJECT_END(poly_coeffs)
 656
 657
 658 R_DBL_S = r21
 659 R_EXP0 = r22
 660 R_EXP = r15
 661 R_SGNMASK = r23
 662 R_TMP = r24
 663 R_TMP2 = r25
 664 R_INDEX = r26
 665 R_TMP3 = r27
 666 R_TMP03 = r27
 667 R_TMP4 = r28
 668 R_TMP5 = r23
 669 R_TMP6 = r22
 670 R_TMP7 = r21
 671 R_T = r29
 672 R_BIAS = r20
 673
 674 F_T = f6
 675 F_1S2 = f7
 676 F_1S2_S = f9
 677 F_INV_1T2 = f10
 678 F_SQRT_1T2 = f11
 679 F_S2T2 = f12
 680 F_X = f13
 681 F_D = f14
 682 F_2M64 = f15
 683
 684 F_CS2 = f32
 685 F_CS3 = f33
 686 F_CS4 = f34
 687 F_CS5 = f35
 688 F_CS6 = f36
 689 F_CS7 = f37
 690 F_CS8 = f38
 691 F_CS9 = f39
 692 F_S23 = f40
 693 F_S45 = f41
 694 F_S67 = f42
 695 F_S89 = f43
 696 F_S25 = f44
 697 F_S69 = f45
 698 F_S29 = f46
 699 F_X2 = f47
 700 F_X4 = f48
 701 F_TSQRT = f49
 702 F_DTX = f50
 703 F_R = f51
 704 F_R2 = f52
 705 F_R3 = f53
 706 F_R4 = f54
 707
 708 F_C3 = f55
 709 F_C5 = f56
 710 F_C7 = f57
 711 F_C9 = f58
 712 F_P79 = f59
 713 F_P35 = f60
 714 F_P39 = f61
 715
 716 F_ATHI = f62
 717 F_ATLO = f63
 718
 719 F_T1 = f64
 720 F_Y = f65
 721 F_Y2 = f66
 722 F_ANDMASK = f67
 723 F_ORMASK = f68
 724 F_S = f69
 725 F_05 = f70
 726 F_SQRT_1S2 = f71
 727 F_DS = f72
 728 F_Z = f73
 729 F_1T2 = f74
 730 F_DZ = f75
 731 F_ZE = f76
 732 F_YZ = f77
 733 F_Y1S2 = f78
 734 F_Y1S2X = f79
 735 F_1X = f80
 736 F_ST = f81
 737 F_1T2_ST = f82
 738 F_TSS = f83
 739 F_Y1S2X2 = f84
 740 F_DZ_TERM = f85
 741 F_DTS = f86
 742 F_DS2X = f87
 743 F_T2 = f88
 744 F_ZY1S2S = f89
 745 F_Y1S2_1X = f90
 746 F_TS = f91
 747 F_PI2_LO = f92
 748 F_PI2_HI = f93
 749 F_S19 = f94
 750 F_INV1T2_2 = f95
 751 F_CORR = f96
 752 F_DZ0 = f97
 753
 754 F_C11 = f98
 755 F_C13 = f99
 756 F_C15 = f100
 757 F_C17 = f101
 758 F_P1113 = f102
 759 F_P1517 = f103
 760 F_P1117 = f104
 761 F_P317 = f105
 762 F_R8 = f106
 763 F_HI = f107
 764 F_1S2_HI = f108
 765 F_DS2 = f109
 766 F_Y2_2 = f110
 767 //F_S2 = f111
 768 //F_S_DS2 = f112
 769 F_S_1S2S = f113
 770 F_XL = f114
 771 F_2M128 = f115
 772 F_1AS = f116
 773 F_AS = f117
 774
 775
 776
 777 .section .text
 778 GLOBAL_LIBM_ENTRY(acosl)
 779
 780 {.mfi
 781        // get exponent, mantissa (rounded to double precision) of s
 782        getf.d R_DBL_S = f8
 783        // 1-s^2
 784        fnma.s1 F_1S2 = f8, f8, f1
 785        // r2 = pointer to T_table
 786        addl r2 = @ltoff(T_table), gp
 787 }
 788
 789 {.mfi
 790        // sign mask
 791        mov R_SGNMASK = 0x20000
 792        nop.f 0
 793        // bias-63-1
 794        mov R_TMP03 = 0xffff-64;;
 795 }
 796
 797
 798 {.mfi
 799        // get exponent of s
 800        getf.exp R_EXP = f8
 801        nop.f 0
 802        // R_TMP4 = 2^45
 803        shl R_TMP4 = R_SGNMASK, 45-17
 804 }
 805
 806 {.mlx
 807        // load bias-4
 808        mov R_TMP = 0xffff-4
 809        // load RU(sqrt(2)/2) to integer register (in double format, shifted left by 1)
 810        movl R_TMP2 = 0x7fcd413cccfe779a;;
 811 }
 812
 813
 814 {.mfi
 815        // load 2^{-64} in FP register
 816        setf.exp F_2M64 = R_TMP03
 817        nop.f 0
 818        // index = (0x7-exponent)|b1 b2.. b6
 819        extr.u R_INDEX = R_DBL_S, 46, 9
 820 }
 821
 822 {.mfi
 823        // get t = sign|exponent|b1 b2.. b6 1 x.. x
 824        or R_T = R_DBL_S, R_TMP4
 825        nop.f 0
 826        // R_TMP4 = 2^45-1
 827        sub R_TMP4 = R_TMP4, r0, 1;;
 828 }
 829
 830
 831 {.mfi
 832        // get t = sign|exponent|b1 b2.. b6 1 0.. 0
 833        andcm R_T = R_T, R_TMP4
 834        nop.f 0
 835        // eliminate sign from R_DBL_S (shift left by 1)
 836        shl R_TMP3 = R_DBL_S, 1
 837 }
 838
 839 {.mfi
 840        // R_BIAS = 3*2^6
 841        mov R_BIAS = 0xc0
 842        nop.f 0
 843        // eliminate sign from R_EXP
 844        andcm R_EXP0 = R_EXP, R_SGNMASK;;
 845 }
 846
 847
 848
 849 {.mfi
 850        // load start address for T_table
 851        ld8 r2 = [r2]
 852        nop.f 0
 853        // p8 = 1 if |s|> = sqrt(2)/2
 854        cmp.geu p8, p0 = R_TMP3, R_TMP2
 855 }
 856
 857 {.mlx
 858        // p7 = 1 if |s|<2^{-4} (exponent of s<bias-4)
 859        cmp.lt p7, p0 = R_EXP0, R_TMP
 860        // sqrt coefficient cs8 = -33*13/128
 861        movl R_TMP2 = 0xc0568000;;
 862 }
 863
 864
 865
 866 {.mbb
 867        // load t in FP register
 868        setf.d F_T = R_T
 869        // if |s|<2^{-4}, take alternate path
 870  (p7) br.cond.spnt SMALL_S
 871        // if |s|> = sqrt(2)/2, take alternate path
 872  (p8) br.cond.sptk LARGE_S
 873 }
 874
 875 {.mlx
 876        // index = (4-exponent)|b1 b2.. b6
 877        sub R_INDEX = R_INDEX, R_BIAS
 878        // sqrt coefficient cs9 = 55*13/128
 879        movl R_TMP = 0x40b2c000;;
 880 }
 881
 882
 883 {.mfi
 884        // sqrt coefficient cs8 = -33*13/128
 885        setf.s F_CS8 = R_TMP2
 886        nop.f 0
 887        // shift R_INDEX by 5
 888        shl R_INDEX = R_INDEX, 5
 889 }
 890
 891 {.mfi
 892        // sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
 893        mov R_TMP4 = 0xffff - 1
 894        nop.f 0
 895        // sqrt coefficient cs6 = -21/16
 896        mov R_TMP6 = 0xbfa8;;
 897 }
 898
 899
 900 {.mlx
 901        // table index
 902        add r2 = r2, R_INDEX
 903        // sqrt coefficient cs7 = 33/16
 904        movl R_TMP2 = 0x40040000;;
 905 }
 906
 907
 908 {.mmi
 909        // load cs9 = 55*13/128
 910        setf.s F_CS9 = R_TMP
 911        // sqrt coefficient cs5 = 7/8
 912        mov R_TMP3 = 0x3f60
 913        // sqrt coefficient cs6 = 21/16
 914        shl R_TMP6 = R_TMP6, 16;;
 915 }
 916
 917
 918 {.mmi
 919        // load significand of 1/(1-t^2)
 920        ldf8 F_INV_1T2 = [r2], 8
 921        // sqrt coefficient cs7 = 33/16
 922        setf.s F_CS7 = R_TMP2
 923        // sqrt coefficient cs4 = -5/8
 924        mov R_TMP5 = 0xbf20;;
 925 }
 926
 927
 928 {.mmi
 929        // load significand of sqrt(1-t^2)
 930        ldf8 F_SQRT_1T2 = [r2], 8
 931        // sqrt coefficient cs6 = 21/16
 932        setf.s F_CS6 = R_TMP6
 933        // sqrt coefficient cs5 = 7/8
 934        shl R_TMP3 = R_TMP3, 16;;
 935 }
 936
 937
 938 {.mmi
 939        // sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
 940        setf.exp F_CS3 = R_TMP4
 941        // r3 = pointer to polynomial coefficients
 942        addl r3 = @ltoff(poly_coeffs), gp
 943        // sqrt coefficient cs4 = -5/8
 944        shl R_TMP5 = R_TMP5, 16;;
 945 }
 946
 947
 948 {.mfi
 949        // sqrt coefficient cs5 = 7/8
 950        setf.s F_CS5 = R_TMP3
 951        // d = s-t
 952        fms.s1 F_D = f8, f1, F_T
 953        // set p6 = 1 if s<0, p11 = 1 if s> = 0
 954        cmp.ge p6, p11 = R_EXP, R_DBL_S
 955 }
 956
 957 {.mfi
 958        // r3 = load start address to polynomial coefficients
 959        ld8 r3 = [r3]
 960        // s+t
 961        fma.s1 F_S2T2 = f8, f1, F_T
 962        nop.i 0;;
 963 }
 964
 965
 966 {.mfi
 967        // sqrt coefficient cs4 = -5/8
 968        setf.s F_CS4 = R_TMP5
 969        // s^2-t^2
 970        fma.s1 F_S2T2 = F_S2T2, F_D, f0
 971        nop.i 0;;
 972 }
 973
 974
 975 {.mfi
 976        // load C3
 977        ldfe F_C3 = [r3], 16
 978        // 0.5/(1-t^2) = 2^{-64}*(2^63/(1-t^2))
 979        fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
 980        nop.i 0;;
 981 }
 982
 983 {.mfi
 984        // load C_5
 985        ldfe F_C5 = [r3], 16
 986        // set correct exponent for sqrt(1-t^2)
 987        fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
 988        nop.i 0;;
 989 }
 990
 991
 992 {.mfi
 993        // load C_7, C_9
 994        ldfpd F_C7, F_C9 = [r3], 16
 995        // x = -(s^2-t^2)/(1-t^2)/2
 996        fnma.s1 F_X = F_INV_1T2, F_S2T2, f0
 997        nop.i 0;;
 998 }
 999
1000
1001 {.mmf
1002        // load asin(t)_high, asin(t)_low
1003        ldfpd F_ATHI, F_ATLO = [r2]
1004            // load pi/2
1005            ldfpd F_PI2_LO, F_PI2_HI = [r3]
1006        // t*sqrt(1-t^2)
1007        fma.s1 F_TSQRT = F_T, F_SQRT_1T2, f0;;
1008 }
1009
1010
1011 {.mfi
1012        nop.m 0
1013        // cs9*x+cs8
1014        fma.s1 F_S89 = F_CS9, F_X, F_CS8
1015        nop.i 0
1016 }
1017
1018 {.mfi
1019        nop.m 0
1020        // cs7*x+cs6
1021        fma.s1 F_S67 = F_CS7, F_X, F_CS6
1022        nop.i 0;;
1023 }
1024
1025 {.mfi
1026        nop.m 0
1027        // cs5*x+cs4
1028        fma.s1 F_S45 = F_CS5, F_X, F_CS4
1029        nop.i 0
1030 }
1031
1032 {.mfi
1033        nop.m 0
1034        // x*x
1035        fma.s1 F_X2 = F_X, F_X, f0
1036        nop.i 0;;
1037 }
1038
1039
1040 {.mfi
1041        nop.m 0
1042        // (s-t)-t*x
1043        fnma.s1 F_DTX = F_T, F_X, F_D
1044        nop.i 0
1045 }
1046
1047 {.mfi
1048        nop.m 0
1049        // cs3*x+cs2 (cs2 = -0.5 = -cs3)
1050        fms.s1 F_S23 = F_CS3, F_X, F_CS3
1051        nop.i 0;;
1052 }
1053
1054 {.mfi
1055   nop.m 0
1056   // if sign is negative, negate table values: asin(t)_low
1057   (p6) fnma.s1 F_ATLO = F_ATLO, f1, f0
1058   nop.i 0
1059 }
1060
1061 {.mfi
1062   nop.m 0
1063   // if sign is negative, negate table values: asin(t)_high
1064   (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0
1065   nop.i 0;;
1066 }
1067
1068
1069 {.mfi
1070        nop.m 0
1071        // cs9*x^3+cs8*x^2+cs7*x+cs6
1072        fma.s1 F_S69 = F_S89, F_X2, F_S67
1073        nop.i 0
1074 }
1075
1076 {.mfi
1077        nop.m 0
1078        // x^4
1079        fma.s1 F_X4 = F_X2, F_X2, f0
1080        nop.i 0;;
1081 }
1082
1083
1084 {.mfi
1085        nop.m 0
1086        // t*sqrt(1-t^2)*x^2
1087        fma.s1 F_TSQRT = F_TSQRT, F_X2, f0
1088        nop.i 0
1089 }
1090
1091 {.mfi
1092        nop.m 0
1093        // cs5*x^3+cs4*x^2+cs3*x+cs2
1094        fma.s1 F_S25 = F_S45, F_X2, F_S23
1095        nop.i 0;;
1096 }
1097
1098
1099 {.mfi
1100        nop.m 0
1101        // ((s-t)-t*x)*sqrt(1-t^2)
1102        fma.s1 F_DTX = F_DTX, F_SQRT_1T2, f0
1103        nop.i 0;;
1104 }
1105
1106 {.mfi
1107        nop.m 0
1108        // (pi/2)_high - asin(t)_high
1109        fnma.s1 F_ATHI = F_ATHI, f1, F_PI2_HI
1110        nop.i 0
1111 }
1112
1113 {.mfi
1114        nop.m 0
1115        // asin(t)_low - (pi/2)_low
1116        fnma.s1 F_ATLO = F_PI2_LO, f1, F_ATLO
1117            nop.i 0;;
1118 }
1119
1120
1121 {.mfi
1122        nop.m 0
1123        // PS29 = cs9*x^7+..+cs5*x^3+cs4*x^2+cs3*x+cs2
1124        fma.s1 F_S29 = F_S69, F_X4, F_S25
1125        nop.i 0;;
1126 }
1127
1128
1129
1130 {.mfi
1131        nop.m 0
1132        // R = ((s-t)-t*x)*sqrt(1-t^2)-t*sqrt(1-t^2)*x^2*PS29
1133        fnma.s1 F_R = F_S29, F_TSQRT, F_DTX
1134        nop.i 0;;
1135 }
1136
1137
1138 {.mfi
1139        nop.m 0
1140        // R^2
1141        fma.s1 F_R2 = F_R, F_R, f0
1142        nop.i 0;;
1143 }
1144
1145
1146 {.mfi
1147        nop.m 0
1148        // c7+c9*R^2
1149        fma.s1 F_P79 = F_C9, F_R2, F_C7
1150        nop.i 0
1151 }
1152
1153 {.mfi
1154        nop.m 0
1155        // c3+c5*R^2
1156        fma.s1 F_P35 = F_C5, F_R2, F_C3
1157        nop.i 0;;
1158 }
1159
1160 {.mfi
1161        nop.m 0
1162        // R^3
1163        fma.s1 F_R4 = F_R2, F_R2, f0
1164        nop.i 0;;
1165 }
1166
1167 {.mfi
1168        nop.m 0
1169        // R^3
1170        fma.s1 F_R3 = F_R2, F_R, f0
1171        nop.i 0;;
1172 }
1173
1174
1175
1176 {.mfi
1177        nop.m 0
1178        // c3+c5*R^2+c7*R^4+c9*R^6
1179        fma.s1 F_P39 = F_P79, F_R4, F_P35
1180        nop.i 0;;
1181 }
1182
1183
1184 {.mfi
1185        nop.m 0
1186        // asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1187        fma.s1 F_P39 = F_P39, F_R3, F_ATLO
1188        nop.i 0;;
1189 }
1190
1191
1192 {.mfi
1193        nop.m 0
1194        // R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1195        fma.s1 F_P39 = F_P39, f1, F_R
1196        nop.i 0;;
1197 }
1198
1199
1200 {.mfb
1201        nop.m 0
1202        // result = (pi/2)-asin(t)_high+R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1203        fnma.s0 f8 = F_P39, f1, F_ATHI
1204        // return
1205        br.ret.sptk b0;;
1206 }
1207
1208
1209
1210
1211 LARGE_S:
1212
1213 {.mfi
1214        // bias-1
1215        mov R_TMP3 = 0xffff - 1
1216        // y ~ 1/sqrt(1-s^2)
1217        frsqrta.s1 F_Y, p7 = F_1S2
1218        // c9 = 55*13*17/128
1219        mov R_TMP4 = 0x10af7b
1220 }
1221
1222 {.mlx
1223        // c8 = -33*13*15/128
1224        mov R_TMP5 = 0x184923
1225        movl R_TMP2 = 0xff00000000000000;;
1226 }
1227
1228 {.mfi
1229        // set p6 = 1 if s<0, p11 = 1 if s>0
1230        cmp.ge p6, p11 = R_EXP, R_DBL_S
1231        // 1-s^2
1232        fnma.s1 F_1S2 = f8, f8, f1
1233        // set p9 = 1
1234        cmp.eq p9, p0 = r0, r0;;
1235 }
1236
1237
1238 {.mfi
1239        // load 0.5
1240        setf.exp F_05 = R_TMP3
1241        // (1-s^2) rounded to single precision
1242        fnma.s.s1 F_1S2_S = f8, f8, f1
1243        // c9 = 55*13*17/128
1244        shl R_TMP4 = R_TMP4, 10
1245 }
1246
1247 {.mlx
1248        // AND mask for getting t ~ sqrt(1-s^2)
1249        setf.sig F_ANDMASK = R_TMP2
1250        // OR mask
1251        movl R_TMP2 = 0x0100000000000000;;
1252 }
1253
1254 .pred.rel "mutex", p6, p11
1255 {.mfi
1256        nop.m 0
1257            // 1-|s|
1258  (p6)  fma.s1 F_1AS = f8, f1, f1
1259        nop.i 0
1260 }
1261
1262 {.mfi
1263        nop.m 0
1264        // 1-|s|
1265  (p11) fnma.s1 F_1AS = f8, f1, f1
1266        nop.i 0;;
1267 }
1268
1269
1270 {.mfi
1271        // c9 = 55*13*17/128
1272        setf.s F_CS9 = R_TMP4
1273            // |s|
1274  (p6)  fnma.s1 F_AS = f8, f1, f0
1275        // c8 = -33*13*15/128
1276        shl R_TMP5 = R_TMP5, 11
1277 }
1278
1279 {.mfi
1280        // c7 = 33*13/16
1281        mov R_TMP4 = 0x41d68
1282            // |s|
1283  (p11) fma.s1 F_AS = f8, f1, f0
1284        nop.i 0;;
1285 }
1286
1287
1288 {.mfi
1289        setf.sig F_ORMASK = R_TMP2
1290        // y^2
1291        fma.s1 F_Y2 = F_Y, F_Y, f0
1292        // c7 = 33*13/16
1293        shl R_TMP4 = R_TMP4, 12
1294 }
1295
1296 {.mfi
1297        // c6 = -33*7/16
1298        mov R_TMP6 = 0xc1670
1299        // y' ~ sqrt(1-s^2)
1300        fma.s1 F_T1 = F_Y, F_1S2, f0
1301        // c5 = 63/8
1302        mov R_TMP7 = 0x40fc;;
1303 }
1304
1305
1306 {.mlx
1307        // load c8 = -33*13*15/128
1308        setf.s F_CS8 = R_TMP5
1309        // c4 = -35/8
1310        movl R_TMP5 = 0xc08c0000;;
1311 }
1312
1313 {.mfi
1314        // r3 = pointer to polynomial coefficients
1315        addl r3 = @ltoff(poly_coeffs), gp
1316        // 1-s-(1-s^2)_s
1317        fnma.s1 F_DS = F_1S2_S, f1, F_1AS
1318        // p9 = 0 if p7 = 1 (p9 = 1 for special cases only)
1319  (p7) cmp.ne p9, p0 = r0, r0
1320 }
1321
1322 {.mlx
1323        // load c7 = 33*13/16
1324        setf.s F_CS7 = R_TMP4
1325        // c3 = 5/2
1326        movl R_TMP4 = 0x40200000;;
1327 }
1328
1329
1330 {.mlx
1331        // load c4 = -35/8
1332        setf.s F_CS4 = R_TMP5
1333        // c2 = -3/2
1334        movl R_TMP5 = 0xbfc00000;;
1335 }
1336
1337
1338 {.mfi
1339        // load c3 = 5/2
1340        setf.s F_CS3 = R_TMP4
1341        // x = (1-s^2)_s*y^2-1
1342        fms.s1 F_X = F_1S2_S, F_Y2, f1
1343        // c6 = -33*7/16
1344        shl R_TMP6 = R_TMP6, 12
1345 }
1346
1347 {.mfi
1348        nop.m 0
1349        // y^2/2
1350        fma.s1 F_Y2_2 = F_Y2, F_05, f0
1351        nop.i 0;;
1352 }
1353
1354
1355 {.mfi
1356        // load c6 = -33*7/16
1357        setf.s F_CS6 = R_TMP6
1358        // eliminate lower bits from y'
1359        fand F_T = F_T1, F_ANDMASK
1360        // c5 = 63/8
1361        shl R_TMP7 = R_TMP7, 16
1362 }
1363
1364
1365 {.mfb
1366        // r3 = load start address to polynomial coefficients
1367        ld8 r3 = [r3]
1368        // 1-(1-s^2)_s-s^2
1369        fma.s1 F_DS = F_AS, F_1AS, F_DS
1370        // p9 = 1 if s is a special input (NaN, or |s|> = 1)
1371  (p9) br.cond.spnt acosl_SPECIAL_CASES;;
1372 }
1373
1374 {.mmf
1375        // get exponent, significand of y' (in single prec.)
1376        getf.s R_TMP = F_T1
1377        // load c3 = -3/2
1378        setf.s F_CS2 = R_TMP5
1379        // y*(1-s^2)
1380        fma.s1 F_Y1S2 = F_Y, F_1S2, f0;;
1381 }
1382
1383
1384
1385 {.mfi
1386        nop.m 0
1387        // if s<0, set s = -s
1388  (p6) fnma.s1 f8 = f8, f1, f0
1389        nop.i 0;;
1390 }
1391
1392
1393 {.mfi
1394        // load c5 = 63/8
1395        setf.s F_CS5 = R_TMP7
1396        // x = (1-s^2)_s*y^2-1+(1-(1-s^2)_s-s^2)*y^2
1397        fma.s1 F_X = F_DS, F_Y2, F_X
1398        // for t = 2^k*1.b1 b2.., get 7-k|b1.. b6
1399        extr.u R_INDEX = R_TMP, 17, 9;;
1400 }
1401
1402
1403 {.mmi
1404        // index = (4-exponent)|b1 b2.. b6
1405        sub R_INDEX = R_INDEX, R_BIAS
1406        nop.m 0
1407        // get exponent of y
1408        shr.u R_TMP2 = R_TMP, 23;;
1409 }
1410
1411 {.mmi
1412        // load C3
1413        ldfe F_C3 = [r3], 16
1414        // set p8 = 1 if y'<2^{-4}
1415        cmp.gt p8, p0 = 0x7b, R_TMP2
1416        // shift R_INDEX by 5
1417        shl R_INDEX = R_INDEX, 5;;
1418 }
1419
1420
1421 {.mfb
1422        // get table index for sqrt(1-t^2)
1423        add r2 = r2, R_INDEX
1424        // get t = 2^k*1.b1 b2.. b7 1
1425        for F_T = F_T, F_ORMASK
1426  (p8) br.cond.spnt VERY_LARGE_INPUT;;
1427 }
1428
1429
1430
1431 {.mmf
1432        // load C5
1433        ldfe F_C5 = [r3], 16
1434        // load 1/(1-t^2)
1435        ldfp8 F_INV_1T2, F_SQRT_1T2 = [r2], 16
1436        // x = ((1-s^2)*y^2-1)/2
1437        fma.s1 F_X = F_X, F_05, f0;;
1438 }
1439
1440
1441
1442 {.mmf
1443        nop.m 0
1444        // C7, C9
1445        ldfpd F_C7, F_C9 = [r3], 16
1446        // set correct exponent for t
1447        fmerge.se F_T = F_T1, F_T;;
1448 }
1449
1450
1451
1452 {.mfi
1453        // get address for loading pi
1454            add r3 = 48, r3
1455        // c9*x+c8
1456        fma.s1 F_S89 = F_X, F_CS9, F_CS8
1457        nop.i 0
1458 }
1459
1460 {.mfi
1461        nop.m 0
1462        // x^2
1463        fma.s1 F_X2 = F_X, F_X, f0
1464        nop.i 0;;
1465 }
1466
1467
1468 {.mfi
1469        // pi (low, high)
1470        ldfpd F_PI2_LO, F_PI2_HI = [r3]
1471        // y*(1-s^2)*x
1472        fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
1473        nop.i 0
1474 }
1475
1476 {.mfi
1477        nop.m 0
1478        // c7*x+c6
1479        fma.s1 F_S67 = F_X, F_CS7, F_CS6
1480        nop.i 0;;
1481 }
1482
1483
1484 {.mfi
1485        nop.m 0
1486        // 1-x
1487        fnma.s1 F_1X = F_X, f1, f1
1488        nop.i 0
1489 }
1490
1491 {.mfi
1492        nop.m 0
1493        // c3*x+c2
1494        fma.s1 F_S23 = F_X, F_CS3, F_CS2
1495        nop.i 0;;
1496 }
1497
1498
1499 {.mfi
1500        nop.m 0
1501        // 1-t^2
1502        fnma.s1 F_1T2 = F_T, F_T, f1
1503        nop.i 0
1504 }
1505
1506 {.mfi
1507        // load asin(t)_high, asin(t)_low
1508        ldfpd F_ATHI, F_ATLO = [r2]
1509        // c5*x+c4
1510        fma.s1 F_S45 = F_X, F_CS5, F_CS4
1511        nop.i 0;;
1512 }
1513
1514
1515
1516 {.mfi
1517        nop.m 0
1518        // t*s
1519        fma.s1 F_TS = F_T, f8, f0
1520        nop.i 0
1521 }
1522
1523 {.mfi
1524        nop.m 0
1525        // 0.5/(1-t^2)
1526        fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
1527        nop.i 0;;
1528 }
1529
1530 {.mfi
1531        nop.m 0
1532        // z~sqrt(1-t^2), rounded to 24 significant bits
1533        fma.s.s1 F_Z = F_SQRT_1T2, F_2M64, f0
1534        nop.i 0
1535 }
1536
1537 {.mfi
1538        nop.m 0
1539        // sqrt(1-t^2)
1540        fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
1541        nop.i 0;;
1542 }
1543
1544
1545 {.mfi
1546        nop.m 0
1547        // y*(1-s^2)*x^2
1548        fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
1549        nop.i 0
1550 }
1551
1552 {.mfi
1553        nop.m 0
1554        // x^4
1555        fma.s1 F_X4 = F_X2, F_X2, f0
1556        nop.i 0;;
1557 }
1558
1559
1560 {.mfi
1561        nop.m 0
1562        // s*t rounded to 24 significant bits
1563        fma.s.s1 F_TSS = F_T, f8, f0
1564        nop.i 0
1565 }
1566
1567 {.mfi
1568        nop.m 0
1569        // c9*x^3+..+c6
1570        fma.s1 F_S69 = F_X2, F_S89, F_S67
1571        nop.i 0;;
1572 }
1573
1574
1575 {.mfi
1576        nop.m 0
1577        // ST = (t^2-1+s^2) rounded to 24 significant bits
1578        fms.s.s1 F_ST = f8, f8, F_1T2
1579        nop.i 0
1580 }
1581
1582 {.mfi
1583        nop.m 0
1584        // c5*x^3+..+c2
1585        fma.s1 F_S25 = F_X2, F_S45, F_S23
1586        nop.i 0;;
1587 }
1588
1589
1590 {.mfi
1591        nop.m 0
1592        // 0.25/(1-t^2)
1593        fma.s1 F_INV1T2_2 = F_05, F_INV_1T2, f0
1594        nop.i 0
1595 }
1596
1597 {.mfi
1598        nop.m 0
1599        // t*s-sqrt(1-t^2)*(1-s^2)*y
1600        fnma.s1 F_TS = F_Y1S2, F_SQRT_1T2, F_TS
1601        nop.i 0;;
1602 }
1603
1604
1605 {.mfi
1606        nop.m 0
1607        // z*0.5/(1-t^2)
1608        fma.s1 F_ZE = F_INV_1T2, F_SQRT_1T2, f0
1609        nop.i 0
1610 }
1611
1612 {.mfi
1613        nop.m 0
1614        // z^2+t^2-1
1615        fms.s1 F_DZ0 = F_Z, F_Z, F_1T2
1616        nop.i 0;;
1617 }
1618
1619
1620 {.mfi
1621        nop.m 0
1622        // (1-s^2-(1-s^2)_s)*x
1623        fma.s1 F_DS2X = F_X, F_DS, f0
1624        nop.i 0;;
1625 }
1626
1627
1628 {.mfi
1629        nop.m 0
1630        // t*s-(t*s)_s
1631        fms.s1 F_DTS = F_T, f8, F_TSS
1632        nop.i 0
1633 }
1634
1635 {.mfi
1636        nop.m 0
1637        // c9*x^7+..+c2
1638        fma.s1 F_S29 = F_X4, F_S69, F_S25
1639        nop.i 0;;
1640 }
1641
1642
1643 {.mfi
1644        nop.m 0
1645        // y*z
1646        fma.s1 F_YZ = F_Z, F_Y, f0
1647        nop.i 0
1648 }
1649
1650 {.mfi
1651        nop.m 0
1652        // t^2
1653        fma.s1 F_T2 = F_T, F_T, f0
1654        nop.i 0;;
1655 }
1656
1657
1658 {.mfi
1659        nop.m 0
1660        // 1-t^2+ST
1661        fma.s1 F_1T2_ST = F_ST, f1, F_1T2
1662        nop.i 0;;
1663 }
1664
1665
1666 {.mfi
1667        nop.m 0
1668        // y*(1-s^2)(1-x)
1669        fma.s1 F_Y1S2_1X = F_Y1S2, F_1X, f0
1670        nop.i 0
1671 }
1672
1673 {.mfi
1674        nop.m 0
1675        // dz ~ sqrt(1-t^2)-z
1676        fma.s1 F_DZ = F_DZ0, F_ZE, f0
1677        nop.i 0;;
1678 }
1679
1680
1681 {.mfi
1682        nop.m 0
1683        // -1+correction for sqrt(1-t^2)-z
1684        fnma.s1 F_CORR = F_INV1T2_2, F_DZ0, f0
1685        nop.i 0;;
1686 }
1687
1688
1689 {.mfi
1690        nop.m 0
1691        // (PS29*x^2+x)*y*(1-s^2)
1692        fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
1693        nop.i 0;;
1694 }
1695
1696 {.mfi
1697        nop.m 0
1698        // z*y*(1-s^2)_s
1699        fma.s1 F_ZY1S2S = F_YZ, F_1S2_S, f0
1700        nop.i 0
1701 }
1702
1703 {.mfi
1704        nop.m 0
1705        // s^2-(1-t^2+ST)
1706        fms.s1 F_1T2_ST = f8, f8, F_1T2_ST
1707        nop.i 0;;
1708 }
1709
1710
1711 {.mfi
1712        nop.m 0
1713        // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x
1714        fma.s1 F_DTS = F_YZ, F_DS2X, F_DTS
1715        nop.i 0
1716 }
1717
1718 {.mfi
1719        nop.m 0
1720        // dz*y*(1-s^2)*(1-x)
1721        fma.s1 F_DZ_TERM = F_DZ, F_Y1S2_1X, f0
1722        nop.i 0;;
1723 }
1724
1725
1726 {.mfi
1727        nop.m 0
1728        // R = t*s-sqrt(1-t^2)*(1-s^2)*y+sqrt(1-t^2)*(1-s^2)*y*PS19
1729        // (used for polynomial evaluation)
1730        fma.s1 F_R = F_S19, F_SQRT_1T2, F_TS
1731        nop.i 0;;
1732 }
1733
1734
1735 {.mfi
1736        nop.m 0
1737        // (PS29*x^2)*y*(1-s^2)
1738        fma.s1 F_S29 = F_Y1S2X2, F_S29, f0
1739        nop.i 0
1740 }
1741
1742 {.mfi
1743        nop.m 0
1744        // apply correction to dz*y*(1-s^2)*(1-x)
1745        fma.s1 F_DZ_TERM = F_DZ_TERM, F_CORR, F_DZ_TERM
1746        nop.i 0;;
1747 }
1748
1749
1750 {.mfi
1751        nop.m 0
1752        // R^2
1753        fma.s1 F_R2 = F_R, F_R, f0
1754        nop.i 0;;
1755 }
1756
1757
1758 {.mfi
1759        nop.m 0
1760        // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x+dz*y*(1-s^2)*(1-x)
1761        fma.s1 F_DZ_TERM = F_DZ_TERM, f1, F_DTS
1762        nop.i 0;;
1763 }
1764
1765
1766 {.mfi
1767        nop.m 0
1768        // c7+c9*R^2
1769        fma.s1 F_P79 = F_C9, F_R2, F_C7
1770        nop.i 0
1771 }
1772
1773 {.mfi
1774        nop.m 0
1775        // c3+c5*R^2
1776        fma.s1 F_P35 = F_C5, F_R2, F_C3
1777        nop.i 0;;
1778 }
1779
1780 {.mfi
1781        nop.m 0
1782        // asin(t)_low-(pi)_low (if s<0)
1783  (p6)  fms.s1 F_ATLO = F_ATLO, f1, F_PI2_LO
1784        nop.i 0
1785 }
1786
1787 {.mfi
1788        nop.m 0
1789        // R^4
1790        fma.s1 F_R4 = F_R2, F_R2, f0
1791        nop.i 0;;
1792 }
1793
1794 {.mfi
1795        nop.m 0
1796        // R^3
1797        fma.s1 F_R3 = F_R2, F_R, f0
1798        nop.i 0;;
1799 }
1800
1801
1802 {.mfi
1803        nop.m 0
1804        // (t*s)_s-t^2*y*z
1805        fnma.s1 F_TSS = F_T2, F_YZ, F_TSS
1806        nop.i 0
1807 }
1808
1809 {.mfi
1810        nop.m 0
1811        // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)
1812        fma.s1 F_DZ_TERM = F_YZ, F_1T2_ST, F_DZ_TERM
1813        nop.i 0;;
1814 }
1815
1816
1817 {.mfi
1818        nop.m 0
1819        // (pi)_hi-asin(t)_hi (if s<0)
1820  (p6)  fms.s1 F_ATHI = F_PI2_HI, f1, F_ATHI
1821        nop.i 0
1822 }
1823
1824 {.mfi
1825        nop.m 0
1826        // c3+c5*R^2+c7*R^4+c9*R^6
1827        fma.s1 F_P39 = F_P79, F_R4, F_P35
1828        nop.i 0;;
1829 }
1830
1831
1832 {.mfi
1833        nop.m 0
1834        // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)+
1835        // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29
1836        fma.s1 F_DZ_TERM = F_SQRT_1T2, F_S29, F_DZ_TERM
1837        nop.i 0;;
1838 }
1839
1840
1841 {.mfi
1842        nop.m 0
1843        // (t*s)_s-t^2*y*z+z*y*ST
1844        fma.s1 F_TSS = F_YZ, F_ST, F_TSS
1845        nop.i 0
1846 }
1847
1848 {.mfi
1849        nop.m 0
1850        // -asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1851        fms.s1 F_P39 = F_P39, F_R3, F_ATLO
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 +
1860        // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
1861        fma.s1 F_DZ_TERM = F_P39, f1, 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        fma.s1 F_DZ_TERM = F_ZY1S2S, F_X, F_DZ_TERM
1872        nop.i 0;;
1873 }
1874
1875
1876 {.mfi
1877        nop.m 0
1878        // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
1879        // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x +
1880        // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) +
1881        // + (t*s)_s-t^2*y*z+z*y*ST
1882        fma.s1 F_DZ_TERM = F_TSS, f1, F_DZ_TERM
1883        nop.i 0;;
1884 }
1885
1886
1887 .pred.rel "mutex", p6, p11
1888 {.mfi
1889        nop.m 0
1890        // result: add high part of table value
1891        // s>0 in this case
1892  (p11) fnma.s0 f8 = F_DZ_TERM, f1, F_ATHI
1893        nop.i 0
1894 }
1895
1896 {.mfb
1897        nop.m 0
1898        // result: add high part of pi-table value
1899        // if s<0
1900  (p6)  fma.s0 f8 = F_DZ_TERM, f1, F_ATHI
1901        br.ret.sptk b0;;
1902 }
1903
1904
1905
1906
1907
1908
1909 SMALL_S:
1910
1911        // use 15-term polynomial approximation
1912
1913 {.mmi
1914        // r3 = pointer to polynomial coefficients
1915        addl r3 = @ltoff(poly_coeffs), gp;;
1916        // load start address for coefficients
1917        ld8 r3 = [r3]
1918        mov R_TMP = 0x3fbf;;
1919 }
1920
1921
1922 {.mmi
1923        add r2 = 64, r3
1924        ldfe F_C3 = [r3], 16
1925        // p7 = 1 if |s|<2^{-64} (exponent of s<bias-64)
1926        cmp.lt p7, p0 = R_EXP0, R_TMP;;
1927 }
1928
1929 {.mmf
1930        ldfe F_C5 = [r3], 16
1931        ldfpd F_C11, F_C13 = [r2], 16
1932            nop.f 0;;
1933 }
1934
1935 {.mmf
1936        ldfpd F_C7, F_C9 = [r3], 16
1937        ldfpd F_C15, F_C17 = [r2]
1938        nop.f 0;;
1939 }
1940
1941
1942
1943 {.mfb
1944        // load pi/2
1945        ldfpd F_PI2_LO, F_PI2_HI = [r3]
1946        // s^2
1947        fma.s1 F_R2 = f8, f8, f0
1948            // |s|<2^{-64}
1949   (p7) br.cond.spnt  RETURN_PI2;;
1950 }
1951
1952
1953 {.mfi
1954        nop.m 0
1955        // s^3
1956        fma.s1 F_R3 = f8, F_R2, f0
1957        nop.i 0
1958 }
1959
1960 {.mfi
1961        nop.m 0
1962        // s^4
1963        fma.s1 F_R4 = F_R2, F_R2, f0
1964        nop.i 0;;
1965 }
1966
1967
1968 {.mfi
1969        nop.m 0
1970        // c3+c5*s^2
1971        fma.s1 F_P35 = F_C5, F_R2, F_C3
1972        nop.i 0
1973 }
1974
1975 {.mfi
1976        nop.m 0
1977        // c11+c13*s^2
1978        fma.s1 F_P1113 = F_C13, F_R2, F_C11
1979        nop.i 0;;
1980 }
1981
1982
1983 {.mfi
1984        nop.m 0
1985        // c7+c9*s^2
1986        fma.s1 F_P79 = F_C9, F_R2, F_C7
1987        nop.i 0
1988 }
1989
1990 {.mfi
1991        nop.m 0
1992        // c15+c17*s^2
1993        fma.s1 F_P1517 = F_C17, F_R2, F_C15
1994        nop.i 0;;
1995 }
1996
1997 {.mfi
1998        nop.m 0
1999            // (pi/2)_high-s_high
2000            fnma.s1 F_T = f8, f1, F_PI2_HI
2001            nop.i 0
2002 }
2003 {.mfi
2004        nop.m 0
2005        // s^8
2006        fma.s1 F_R8 = F_R4, F_R4, f0
2007        nop.i 0;;
2008 }
2009
2010
2011 {.mfi
2012        nop.m 0
2013        // c3+c5*s^2+c7*s^4+c9*s^6
2014        fma.s1 F_P39 = F_P79, F_R4, F_P35
2015        nop.i 0
2016 }
2017
2018 {.mfi
2019        nop.m 0
2020        // c11+c13*s^2+c15*s^4+c17*s^6
2021        fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
2022        nop.i 0;;
2023 }
2024
2025 {.mfi
2026        nop.m 0
2027            // -s_high
2028            fms.s1 F_S = F_T, f1, F_PI2_HI
2029            nop.i 0;;
2030 }
2031
2032 {.mfi
2033        nop.m 0
2034        // c3+..+c17*s^14
2035        fma.s1 F_P317 = F_R8, F_P1117, F_P39
2036        nop.i 0;;
2037 }
2038
2039 {.mfi
2040        nop.m 0
2041            // s_low
2042            fma.s1 F_DS = f8, f1, F_S
2043            nop.i 0;;
2044 }
2045
2046 {.mfi
2047        nop.m 0
2048        // (pi/2)_low-s^3*(c3+..+c17*s^14)
2049        fnma.s0 F_P317 = F_P317, F_R3, F_PI2_LO
2050            nop.i 0;;
2051 }
2052
2053 {.mfi
2054        nop.m 0
2055            // (pi/2)_low-s_low-s^3*(c3+..+c17*s^14)
2056            fms.s1 F_P317 = F_P317, f1, F_DS
2057            nop.i 0;;
2058 }
2059
2060 {.mfb
2061        nop.m 0
2062            // result: pi/2-s-c3*s^3-..-c17*s^17
2063            fma.s0 f8 = F_T, f1, F_P317
2064        br.ret.sptk b0;;
2065 }
2066
2067
2068
2069
2070
2071 RETURN_PI2:
2072
2073 {.mfi
2074        nop.m 0
2075        // (pi/2)_low-s
2076            fms.s0 F_PI2_LO = F_PI2_LO, f1, f8
2077            nop.i 0;;
2078 }
2079
2080 {.mfb
2081        nop.m 0
2082            // (pi/2)-s
2083            fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO
2084            br.ret.sptk b0;;
2085 }
2086
2087
2088
2089
2090
2091 VERY_LARGE_INPUT:
2092
2093
2094 {.mmf
2095        // pointer to pi_low, pi_high
2096            add r2 = 80, r3
2097        // load C5
2098        ldfe F_C5 = [r3], 16
2099        // x = ((1-(s^2)_s)*y^2-1)/2-(s^2-(s^2)_s)*y^2/2
2100        fma.s1 F_X = F_X, F_05, f0;;
2101 }
2102
2103 .pred.rel "mutex", p6, p11
2104 {.mmf
2105        // load pi (low, high), if s<0
2106  (p6)  ldfpd F_PI2_LO, F_PI2_HI = [r2]
2107        // C7, C9
2108        ldfpd F_C7, F_C9 = [r3], 16
2109            // if s>0, set F_PI2_LO=0
2110  (p11) fma.s1 F_PI2_HI = f0, f0, f0;;
2111 }
2112
2113 {.mfi
2114        nop.m 0
2115  (p11) fma.s1 F_PI2_LO = f0, f0, f0
2116        nop.i 0;;
2117 }
2118
2119 {.mfi
2120        // adjust address for C_11
2121            add r3 = 16, r3
2122        // c9*x+c8
2123        fma.s1 F_S89 = F_X, F_CS9, F_CS8
2124        nop.i 0
2125 }
2126
2127 {.mfi
2128        nop.m 0
2129        // x^2
2130        fma.s1 F_X2 = F_X, F_X, f0
2131        nop.i 0;;
2132 }
2133
2134
2135 {.mfi
2136        nop.m 0
2137        // y*(1-s^2)*x
2138        fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
2139        nop.i 0
2140 }
2141
2142 {.mfi
2143        // C11, C13
2144        ldfpd F_C11, F_C13 = [r3], 16
2145        // c7*x+c6
2146        fma.s1 F_S67 = F_X, F_CS7, F_CS6
2147        nop.i 0;;
2148 }
2149
2150
2151 {.mfi
2152        // C15, C17
2153        ldfpd F_C15, F_C17 = [r3], 16
2154        // c3*x+c2
2155        fma.s1 F_S23 = F_X, F_CS3, F_CS2
2156        nop.i 0;;
2157 }
2158
2159
2160 {.mfi
2161        nop.m 0
2162        // c5*x+c4
2163        fma.s1 F_S45 = F_X, F_CS5, F_CS4
2164        nop.i 0;;
2165 }
2166
2167
2168
2169
2170 {.mfi
2171        nop.m 0
2172        // y*(1-s^2)*x^2
2173        fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
2174        nop.i 0
2175 }
2176
2177 {.mfi
2178        nop.m 0
2179        // x^4
2180        fma.s1 F_X4 = F_X2, F_X2, f0
2181        nop.i 0;;
2182 }
2183
2184
2185 {.mfi
2186        nop.m 0
2187        // c9*x^3+..+c6
2188        fma.s1 F_S69 = F_X2, F_S89, F_S67
2189        nop.i 0;;
2190 }
2191
2192
2193 {.mfi
2194        nop.m 0
2195        // c5*x^3+..+c2
2196        fma.s1 F_S25 = F_X2, F_S45, F_S23
2197        nop.i 0;;
2198 }
2199
2200
2201
2202 {.mfi
2203        nop.m 0
2204        // (pi)_high-y*(1-s^2)_s
2205        fnma.s1 F_HI = F_Y, F_1S2_S, F_PI2_HI
2206        nop.i 0;;
2207 }
2208
2209
2210 {.mfi
2211        nop.m 0
2212        // c9*x^7+..+c2
2213        fma.s1 F_S29 = F_X4, F_S69, F_S25
2214        nop.i 0;;
2215 }
2216
2217
2218 {.mfi
2219        nop.m 0
2220        // -(y*(1-s^2)_s)_high
2221        fms.s1 F_1S2_HI = F_HI, f1, F_PI2_HI
2222        nop.i 0;;
2223 }
2224
2225
2226 {.mfi
2227        nop.m 0
2228        // (PS29*x^2+x)*y*(1-s^2)
2229        fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
2230        nop.i 0;;
2231 }
2232
2233
2234 {.mfi
2235        nop.m 0
2236        // y*(1-s^2)_s-(y*(1-s^2))_high
2237        fma.s1 F_DS2 = F_Y, F_1S2_S, F_1S2_HI
2238        nop.i 0;;
2239 }
2240
2241
2242
2243 {.mfi
2244        nop.m 0
2245        // R ~ sqrt(1-s^2)
2246        // (used for polynomial evaluation)
2247        fnma.s1 F_R = F_S19, f1, F_Y1S2
2248        nop.i 0;;
2249 }
2250
2251
2252 {.mfi
2253        nop.m 0
2254        // y*(1-s^2)-(y*(1-s^2))_high
2255        fma.s1 F_DS2 = F_Y, F_DS, F_DS2
2256        nop.i 0
2257 }
2258
2259 {.mfi
2260        nop.m 0
2261        // (pi)_low+(PS29*x^2)*y*(1-s^2)
2262        fma.s1 F_S29 = F_Y1S2X2, F_S29, F_PI2_LO
2263        nop.i 0;;
2264 }
2265
2266
2267 {.mfi
2268        nop.m 0
2269        // R^2
2270        fma.s1 F_R2 = F_R, F_R, f0
2271        nop.i 0;;
2272 }
2273
2274
2275 {.mfi
2276        nop.m 0
2277            // if s<0
2278        // (pi)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)
2279        fms.s1 F_S29 = F_S29, f1, F_DS2
2280        nop.i 0;;
2281 }
2282
2283
2284 {.mfi
2285        nop.m 0
2286        // c7+c9*R^2
2287        fma.s1 F_P79 = F_C9, F_R2, F_C7
2288        nop.i 0
2289 }
2290
2291 {.mfi
2292        nop.m 0
2293        // c3+c5*R^2
2294        fma.s1 F_P35 = F_C5, F_R2, F_C3
2295        nop.i 0;;
2296 }
2297
2298
2299
2300 {.mfi
2301        nop.m 0
2302        // R^4
2303        fma.s1 F_R4 = F_R2, F_R2, f0
2304        nop.i 0
2305 }
2306
2307 {.mfi
2308        nop.m 0
2309        // R^3
2310        fma.s1 F_R3 = F_R2, F_R, f0
2311        nop.i 0;;
2312 }
2313
2314
2315 {.mfi
2316        nop.m 0
2317        // c11+c13*R^2
2318        fma.s1 F_P1113 = F_C13, F_R2, F_C11
2319        nop.i 0
2320 }
2321
2322 {.mfi
2323        nop.m 0
2324        // c15+c17*R^2
2325        fma.s1 F_P1517 = F_C17, F_R2, F_C15
2326        nop.i 0;;
2327 }
2328
2329
2330 {.mfi
2331        nop.m 0
2332        // (pi)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)+y*(1-s^2)*x
2333        fma.s1 F_S29 = F_Y1S2, F_X, F_S29
2334        nop.i 0;;
2335 }
2336
2337
2338 {.mfi
2339        nop.m 0
2340        // c11+c13*R^2+c15*R^4+c17*R^6
2341        fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
2342        nop.i 0
2343 }
2344
2345 {.mfi
2346        nop.m 0
2347        // c3+c5*R^2+c7*R^4+c9*R^6
2348        fma.s1 F_P39 = F_P79, F_R4, F_P35
2349        nop.i 0;;
2350 }
2351
2352
2353
2354 {.mfi
2355        nop.m 0
2356        // R^8
2357        fma.s1 F_R8 = F_R4, F_R4, f0
2358        nop.i 0;;
2359 }
2360
2361
2362 {.mfi
2363        nop.m 0
2364        // c3+c5*R^2+c7*R^4+c9*R^6+..+c17*R^14
2365        fma.s1 F_P317 = F_P1117, F_R8, F_P39
2366        nop.i 0;;
2367 }
2368
2369
2370 {.mfi
2371        nop.m 0
2372        // (pi)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
2373        // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
2374        fnma.s1 F_S29 = F_P317, F_R3, F_S29
2375        nop.i 0;;
2376 }
2377
2378 .pred.rel "mutex", p6, p11
2379 {.mfi
2380        nop.m 0
2381        // Result (if s<0):
2382        // (pi)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
2383        // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
2384        // +(pi)_high-(y*(1-s^2))_high
2385  (p6)  fma.s0 f8 = F_S29, f1, F_HI
2386        nop.i 0
2387 }
2388
2389 {.mfb
2390        nop.m 0
2391            // Result (if s>0):
2392        // (PS29*x^2)*y*(1-s^2)-
2393        // -y*(1-s^2)*x + P3, 17
2394        // +(y*(1-s^2))
2395  (p11) fms.s0 f8 = F_Y, F_1S2_S, F_S29
2396        br.ret.sptk b0;;
2397 }
2398
2399
2400
2401
2402
2403
2404 acosl_SPECIAL_CASES:
2405
2406 {.mfi
2407        alloc r32 = ar.pfs, 1, 4, 4, 0
2408        // check if the input is a NaN, or unsupported format
2409        // (i.e. not infinity or normal/denormal)
2410        fclass.nm p7, p8 = f8, 0x3f
2411        // pointer to pi/2
2412        add r3 = 96, r3;;
2413 }
2414
2415
2416 {.mfi
2417        // load pi/2
2418        ldfpd F_PI2_HI, F_PI2_LO = [r3]
2419        // get |s|
2420        fmerge.s F_S = f0, f8
2421        nop.i 0
2422 }
2423
2424 {.mfb
2425        nop.m 0
2426        // if NaN, quietize it, and return
2427  (p7) fma.s0 f8 = f8, f1, f0
2428  (p7) br.ret.spnt b0;;
2429 }
2430
2431
2432 {.mfi
2433        nop.m 0
2434        // |s| = 1 ?
2435        fcmp.eq.s0 p9, p10 = F_S, f1
2436        nop.i 0
2437 }
2438
2439 {.mfi
2440        nop.m 0
2441        // load FR_X
2442        fma.s1 FR_X = f8, f1, f0
2443        // load error tag
2444        mov GR_Parameter_TAG = 57;;
2445 }
2446
2447
2448 {.mfi
2449        nop.m 0
2450        // if s = 1, result is 0
2451  (p9)  fma.s0 f8 = f0, f0, f0
2452        // set p6=0 for |s|>1
2453  (p10) cmp.ne p6, p0 = r0, r0;;
2454 }
2455
2456
2457 {.mfb
2458        nop.m 0
2459        //  if s = -1, result is pi
2460  (p6) fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO
2461        // return if |s| = 1
2462  (p9) br.ret.sptk b0;;
2463 }
2464
2465
2466 {.mfi
2467        nop.m 0
2468        // get Infinity
2469        frcpa.s1 FR_RESULT, p0 = f1, f0
2470        nop.i 0;;
2471 }
2472
2473
2474 {.mfb
2475        nop.m 0
2476        // return QNaN indefinite (0*Infinity)
2477        fma.s0 FR_RESULT = f0, FR_RESULT, f0
2478        nop.b 0;;
2479 }
2480
2481
2482 GLOBAL_LIBM_END(acosl)
2483 libm_alias_ldouble_other (acos, acos)
2484
2485
2486 LOCAL_LIBM_ENTRY(__libm_error_region)
2487 .prologue
2488 // (1)
2489 { .mfi
2490         add   GR_Parameter_Y=-32,sp             // Parameter 2 value
2491         nop.f 0
2492 .save   ar.pfs,GR_SAVE_PFS
2493         mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
2494 }
2495 { .mfi
2496 .fframe 64
2497         add sp=-64,sp                          // Create new stack
2498         nop.f 0
2499         mov GR_SAVE_GP=gp                      // Save gp
2500 };;
2501
2502
2503 // (2)
2504 { .mmi
2505         stfe [GR_Parameter_Y] = f1,16         // Store Parameter 2 on stack
2506         add GR_Parameter_X = 16,sp            // Parameter 1 address
2507 .save   b0, GR_SAVE_B0
2508         mov GR_SAVE_B0=b0                     // Save b0
2509 };;
2510
2511 .body
2512 // (3)
2513 { .mib
2514         stfe [GR_Parameter_X] = FR_X              // Store Parameter 1 on stack
2515         add   GR_Parameter_RESULT = 0,GR_Parameter_Y
2516         nop.b 0                                 // Parameter 3 address
2517 }
2518 { .mib
2519         stfe [GR_Parameter_Y] = FR_RESULT             // Store Parameter 3 on stack
2520         add   GR_Parameter_Y = -16,GR_Parameter_Y
2521         br.call.sptk b0=__libm_error_support#   // Call error handling function
2522 };;
2523 { .mmi
2524         nop.m 0
2525         nop.m 0
2526         add   GR_Parameter_RESULT = 48,sp
2527 };;
2528
2529 // (4)
2530 { .mmi
2531         ldfe  f8 = [GR_Parameter_RESULT]       // Get return result off stack
2532 .restore sp
2533         add   sp = 64,sp                       // Restore stack pointer
2534         mov   b0 = GR_SAVE_B0                  // Restore return address
2535 };;
2536
2537 { .mib
2538         mov   gp = GR_SAVE_GP                  // Restore gp
2539         mov   ar.pfs = GR_SAVE_PFS             // Restore ar.pfs
2540         br.ret.sptk     b0                     // Return
2541 };;
2542
2543 LOCAL_LIBM_END(__libm_error_region)
2544
2545 .type   __libm_error_support#,@function
2546 .global __libm_error_support#