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|
.file "cbrtl.s"
// Copyright (c) 2000 - 2004, Intel Corporation
// All rights reserved.
//
// Contributed 2000 by the Intel Numerics Group, Intel Corporation
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at
// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// History
//==============================================================
// 04/28/00 Initial version
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/06/03 Reordered header:.section,.global,.proc,.align
// 11/23/04 Reformatted routine and improved speed
//
// API
//==============================================================
// long double cbrtl(long double)
//
// Overview of operation
//==============================================================
// Background
//
// Implementation
//
// The result is computed as
// cbrt(x)= cbrt(1 - (1 - x*y)) * (1/cbrt(y))
// where y = frcpa(x) = (-1)^sgn_y * 2^(3*k+j) * m_y,
// m_y in [1,2), j in {0,1,2}
//
// cbrt(1 - (1 - x*y)) is approximated by a degree-6 polynomial
// in r= 1 - x*y :
// P = 1 - c_1 r - c_2 * r^2 - c_3 * r^3 - c_4 * r^4 - c_5 * r^5 - c_6 * r^6
//
//
// The values (1/cbrt(y)) are stored as two tables of constants T_hi
// (double-extended precision) and D (single precision) as follows:
// T_hi (1 + D)= 1/cbrt(y) to about 80 bits of accuracy
//
// The tables are only stored for three exponent values (i.e.
// only for 2^j * m_y, where j in {0,1,2} and m_y covers the 256
// possible mantissas for an frcpa result); the index is formed
// by the 8 leading mantissa bits of x, which is the same index used
// by the hardware to get frcpa(x).
//
// The table values are multiplied by 2^k where e is the exponent of
// the input number. This multiplication is carried out in parallel with
// the polynomial evaluation:
// T= 2^(k) * T_hi
//
//=======================================================================
//===============
// Special values
//==============================================================
// Registers used
//==============================================================
// p6, p7, p12
FR_R = f6
FR_C1 = f7
FR_C2 = f9
FR_C3 = f10
FR_C4 = f11
FR_C5 = f12
FR_C6 = f13
FR_XNORM = f14
FR_D = f15
FR_SPECIAL = f32
FR_RCP = f33
FR_R2 = f34
FR_P1 = f35
FR_P2 = f36
FR_P3 = f37
FR_P4 = f38
FR_P5 = f39
FR_R3 = f40
FR_T = f41
FR_TF = f42
FR_P = f43
FR_SGNEXP = f44
GR_ADDR = r2
GR_C_START = r2
GR_ARGSIG = r3
GR_NORMSIG = r15
GR_D_ADDR = r16
GR_D_START = r16
GR_INDEX2 = r17
GR_IX2 = r17
GR_NORMEXP = r18
GR_EXP5 = r19
GR_EXP3 = r20
GR_EXP6 = r20
GR_EXP17 = r21
GR_TMP1 = r21
GR_SGNMASK = r22
GR_T_INDEX = r23
GR_IX_T = r23
GR_IX_D = r24
GR_D_INDEX = r24
GR_TMP2 = r25
GR_TMP3 = r25
GR_TMP4 = r25
GR_EXP_RES = r26
GR_BIAS23 = r27
GR_EXPBIAS = r27
GR_EXP_MOD_3 = r28
GR_SIGN = r29
GR_EXPSIGNRES = r29
GR_REMTMP = r30
GR_NORMEXPSGN = r31
// Data tables
//==============================================================
RODATA
.align 16
LOCAL_OBJECT_START(poly_coeffs)
data8 0xaaaaaaaaaaaaaab1, 0x00003ffd // C_1
data8 0xe38e38e38e38e3e0, 0x00003ffb // C_2
data8 0x3faf9add3c0be9a6, 0x3fa511e8d2b1f749 // C_3, C_4
data8 0x3f9ee71b2c6ebe99, 0x3f9809180fd0340c // C_5, C_6
LOCAL_OBJECT_END(poly_coeffs)
LOCAL_OBJECT_START(T_table)
data8 0x80155c748c374836, 0x8040404b0879f7f9
data8 0x806b5dce4b405c10, 0x8096b586974669b1
data8 0x80bcd273d952a028, 0x80e898c52813f2f3
data8 0x81149add67c2d208, 0x813b4e2c856b6e9a
data8 0x8167c1dde03de7aa, 0x818ed973b811135e
data8 0x81bbc0c33e13ec98, 0x81e33e69fbe7504a
data8 0x820aec524e3c23e9, 0x823880f78e70b805
data8 0x826097a62a8e5200, 0x8288dfe00e9b5eaf
data8 0x82b15a10c5371624, 0x82da06a527b18937
data8 0x8302e60b635ab394, 0x832bf8b2feec2f0e
data8 0x83553f0ce00e276b, 0x837eb98b50f8322a
data8 0x83a270f44c84f699, 0x83cc4d7cfcfac5ca
data8 0x83f65f78a8872b4c, 0x8420a75f2f7b53c8
data8 0x844510461ff14209, 0x846fbd91b930bed2
data8 0x84947e18234f3294, 0x84bf92755825045a
data8 0x84e4ac0ee112ba51, 0x8509ef44b86f20be
data8 0x85359d5d91768427, 0x855b3bd5b7384357
data8 0x858104f0c415f79a, 0x85a6f90390d29864
data8 0x85d3772fcd56a1dd, 0x85f9c982fcc002f3
data8 0x862047e0e7ea554b, 0x8646f2a26f7f5852
data8 0x866dca21754096b5, 0x8694ceb8dfd17a37
data8 0x86bc00c49e9307e8, 0x86dccd74fce79610
data8 0x870453c845acf90f, 0x872c089a1e90342c
data8 0x8753ec4a92d16c5e, 0x877bff3aca19f6b4
data8 0x879d88b6fe1c324c, 0x87c5f346dbf98c3a
data8 0x87e7c653efacef2c, 0x881089d4e73ffefc
data8 0x88397e6a366f2a8a, 0x885bc559e5e1c081
data8 0x887e2ee392bb7a93, 0x88a7a8587e404257
data8 0x88ca5eda67594784, 0x88f4356166bd590e
data8 0x89173a0acf5ce026, 0x893a62a098b6a57b
data8 0x895daf637236ae2c, 0x89883b9d1c2fa9c5
data8 0x89abd8dd374a5d7b, 0x89cf9b1dcd197fa0
data8 0x89f382a258ea79de, 0x8a178faf06648f29
data8 0x8a3bc288b3e1d18a, 0x8a601b74f4d1f835
data8 0x8a849aba14274764, 0x8aa9409f16cdbc9b
data8 0x8ace0d6bbe2cb316, 0x8af301688ab33558
data8 0x8b181cdebe6f3206, 0x8b3d60185fafcb7c
data8 0x8b62cb603bb2fad0, 0x8b80d7d6bc4104de
data8 0x8ba68bf73ac74f39, 0x8bcc68fb9f9f7335
data8 0x8bf26f31c534fca2, 0x8c10f86e13a1a1f9
data8 0x8c3749916cc6abb5, 0x8c5dc4c4f7706032
data8 0x8c7cac3a8c42e3e0, 0x8ca373f1b7bf2716
data8 0x8cc29907fb951294, 0x8ce9ae4e9492aac8
data8 0x8d0911dddbfdad0e, 0x8d3075c4f20f04ee
data8 0x8d5018a9d4de77d5, 0x8d77cc47dd143515
data8 0x8d97af6352739cb7, 0x8db7af523167800f
data8 0x8ddfd80bc68c32ff, 0x8e00197e1e7c88fe
data8 0x8e207859f77e20e7, 0x8e40f4ce60c9f8e2
data8 0x8e69ba46cf2fde4d, 0x8e8a7a00bd7ae63e
data8 0x8eab57ef1cf2f529, 0x8ecc5442cffb1dad
data8 0x8eed6f2d2a4acbfe, 0x8f0ea8dff24441ff
data8 0x8f385c95d696b817, 0x8f59dc43edd930f3
data8 0x8f7b7b5f5ffad1c4, 0x8f9d3a1bea165f38
data8 0x8fbf18adc34b66da, 0x8fe117499e356095
data8 0x90033624aa685f8d, 0x9025757495f36b86
data8 0x903f3a5dcc091203, 0x9061b2fceb2bdbab
data8 0x90844ca7211032a7, 0x90a7079403e6a15d
data8 0x90c9e3fbafd63799, 0x90ece216c8a16ee4
data8 0x9110021e7b516f0a, 0x912a708a39be9075
data8 0x914dcc7b31146370, 0x91714af8cfe984d5
data8 0x918c00a6f3795e97, 0x91afbc299ed0295d
data8 0x91d39add3e958db0, 0x91ee9920a8974d92
data8 0x9212b5fcac537c19, 0x9236f6b256923fcf
data8 0x92523ee6f90dcfc3, 0x9276bef031e6eb79
data8 0x929236ec237a24ad, 0x92b6f70b7efe9dc3
data8 0x92d29f61eec7dc2b, 0x92f7a05d5b8ba92f
data8 0x931379a403be5c16, 0x9338bc44de2e3f34
data8 0x9354c71412c69486, 0x937a4c273907e262
data8 0x93968919f6e7975d, 0x93bc516fdd4680c9
data8 0x93d8c123d9be59b2, 0x93f546c955e60076
data8 0x941b70a65879079f, 0x943829f337410591
data8 0x9454f995765bc4d2, 0x947b86b57f5842ed
data8 0x94988aeb23470f86, 0x94b5a5dc9695f42a
data8 0x94d2d7a9170d8b42, 0x94f9e87dd78bf019
data8 0x95175019a503d89e, 0x9534cefa625fcb3a
data8 0x955265405c491a25, 0x9570130c1f9bb857
data8 0x9597ca4119525184, 0x95b5af6fb5aa4d3c
data8 0x95d3ac9273aafd7a, 0x95f1c1cafdfd3684
data8 0x960fef3b430b8d5f, 0x962e350575b409c5
data8 0x964c934c0dfc1708, 0x966b0a31c9c6bc7d
data8 0x968999d9ad8d264e, 0x96a8426705198795
data8 0x96c703fd64445ee5, 0x96e5dec0a7b4268d
data8 0x9704d2d4f59f79f3, 0x9723e05ebe91b9b0
data8 0x97430782be323831, 0x97624865fc0df8bf
data8 0x9781a32dcc640b2a, 0x97a117ffd0f48e46
data8 0x97c0a701f9d263c9, 0x97e0505a8637a036
data8 0x97f57a9fb0b08c6e, 0x9815503365914a9d
data8 0x98354085054fd204, 0x98554bbbf8a77902
data8 0x987571fffb7f94f6, 0x9895b3791dd03c23
data8 0x98ab43a5fc65d0c8, 0x98cbb2d196bd713d
data8 0x98ec3d9ec7b6f21a, 0x990ce436db5e8344
data8 0x9922b8218160967a, 0x99438d686f75779d
data8 0x99647eea131fa20b, 0x997a85045a47c6d0
data8 0x999ba5f14f8add02, 0x99bce38b5465ecae
data8 0x99d31ca0887f30f9, 0x99f48a669c74c09e
data8 0x9a16154eb445c873, 0x9a2c822ec198d667
data8 0x9a4e3e080cd91b78, 0x9a70177afe52322e
data8 0x9a86b8fa94eebe10, 0x9aa8c42866ae2958
data8 0x9abf86f9e12fc45e, 0x9ae1c462fc05f49d
data8 0x9af8a8dc936b84d0, 0x9b1b19033be35730
data8 0x9b3da7daf04c2892, 0x9b54c2e4c8a9012b
data8 0x9b77854e6c661200, 0x9b8ec2e678d56d2f
data8 0x9ba60e6a5ca133b6, 0x9bc919ea66a151a4
data8 0x9be0887c09ef82bb, 0x9c03c8d5fffc3503
data8 0x9c1b5ad21a81cbb9, 0x9c3ed09216e9ca02
data8 0x9c568656c0423def, 0x9c7a320af242ce60
data8 0x9c920bf7a8c01dc2, 0x9ca9f475d98b159c
data8 0x9ccdeca60e80b5f8, 0x9ce5f9d4653d4902
data8 0x9cfe15cb38bfdd8e, 0x9d225b983f6c1f96
data8 0x9d3a9cca32261ed7, 0x9d52ecfccebe1768
data8 0x9d77818d95b82f86, 0x9d8ff7893fa4706c
data8 0x9da87cbef36f2a5e, 0x9dcd6140b4a35aeb
data8 0x9de60cd06dc6e2d4, 0x9dfec7d4cc43b76f
data8 0x9e17925ec9fccc4a, 0x9e3cdf6db57dc075
data8 0x9e55d110b63637a8, 0x9e6ed27594550d2e
data8 0x9e87e3adc385d393, 0x9ead9b54b37a1055
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LOCAL_OBJECT_END(T_table)
LOCAL_OBJECT_START(D_table)
data4 0x1e50f488, 0x1ebdc559, 0x1e649ec1, 0x9eed9b2c
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data4 0x1f60d56f, 0x1ea84424, 0x9e88f4fb, 0x1f205c09
data4 0x1ec9ae4e, 0x1d2d5738, 0x9f2c9f6d, 0x1e0765c2
data4 0x1e8bbdd7, 0x9f16d9f1, 0x9ea62627, 0x1f13904c
data4 0x1e566ab8, 0x9dca3d1a, 0x9e91f2a1, 0x9f14641c
data4 0x9f278946, 0x1f490c1e, 0x1f575eb6, 0x1f50b3fd
data4 0x9da32efb, 0x1ea95e59, 0x9e41e058, 0x9eada15f
data4 0x9e4fe66c, 0x1f3abc98, 0x1f1b8d1e, 0x9ece97e4
data4 0x1d188aed, 0x9e89b6ee, 0x1f287478, 0x9e8a161a
data4 0x1e4749f7, 0x9e68084a, 0x1e867f33, 0x9f462b63
data4 0x1db30792, 0x1f59a767, 0x9d1da4ae, 0x9f472a33
data4 0x1d1e91cd, 0x9f414824, 0x9f473d4f, 0x1f4b5783
data4 0x9f5b04b8, 0x9f5c205b, 0x1f309617, 0x9f0d6852
data4 0x9d96a609, 0x9f0965c2, 0x9e23f467, 0x9f089884
data4 0x9ec71458, 0x9ed6e955, 0x1e5e8691, 0x1f5b2bbc
data4 0x9f128268, 0x1ed40f5b, 0x1dc430ce, 0x1f345986
data4 0x1d778f72, 0x1e9b11d6, 0x9f5a40be, 0x9e07f61a
data4 0x9ed641a7, 0x9f334787, 0x1e952fd0, 0x1edeb5e2
data4 0x9e9f3eb1, 0x9e379fd9, 0x1f13102a, 0x9e5e80e1
data4 0x1c757944, 0x1dae2260, 0x1f183ab7, 0x1e55d576
data4 0x9e6bb99f, 0x9f52d7cb, 0x9e73a0f5, 0x1d4e1d14
data4 0x9dd05b53, 0x1f2261e4, 0x9d4ee73d, 0x1ede515e
data4 0x1f22a573, 0x9ecac348, 0x1e6a2ac0, 0x1e2787d2
data4 0x9eb64b87, 0x1f0c69c6, 0x9f470a01, 0x9d7c1686
data4 0x1e468ebe, 0x9f21ee2f, 0x9ee52116, 0x9e20f715
data4 0x1ed18533, 0x9f005b38, 0x9f20cb95, 0x1da72967
data4 0x1f1ba5d7, 0x1e2f8b16, 0x9c794f96, 0x9ca74ea3
data4 0x1f410555, 0x9eff2b96, 0x1ce8f0b1, 0x1f0cee77
data4 0x1f191edd, 0x9ed5fcbc, 0x1f30f242, 0x9e0ad369
data4 0x1ed8f3c8, 0x1f52bb0e, 0x9e9ce408, 0x1f18907f
data4 0x9ecdad40, 0x9e8af91d, 0x1d46698a, 0x9f4b93d6
data4 0x9f3f5d33, 0x1e2e52f7, 0x9f13aeec, 0x9f3b1969
data4 0x1f0996f4, 0x9f2a03df, 0x1e264767, 0x1f3ab1fb
data4 0x9f3193c9, 0x9f21ce22, 0x9eab624c, 0x9ecd8fb1
data4 0x1eaf9a85, 0x1f0c6a2c, 0x1eecbe61, 0x1f3fead9
data4 0x1f1d3a29, 0x1e9099ce, 0x1eadd875, 0x1e4dbfb8
data4 0x9dc640d2, 0x1f413680, 0x9f3f57b3, 0x1dfa1553
data4 0x1ec71c6b, 0x1e00cc00, 0x9f271e55, 0x1e5a88bb
data4 0x1f46cc2b, 0x1ee80ff9, 0x9e29c6f3, 0x1f15e229
data4 0x9ea83d66, 0x1f37408e, 0x9dacb66e, 0x1e6f6259
data4 0x9f106973, 0x1dd4e5ac, 0x1cbfdcc8, 0x9f231c9f
data4 0x9e8677e4, 0x9e9e695a, 0x1efd782b, 0x9dd26959
data4 0x9e80af69, 0x1f386fb3, 0x1f022e8c, 0x9e839967
data4 0x1ce6796f, 0x1e4c22c2, 0x1e57ef24, 0x1e919804
data4 0x9d7ea090, 0x1e40140a, 0x1f261b46, 0x1db75be2
data4 0x1f145019, 0x9e3102b9, 0x9e22507b, 0x1eae813c
data4 0x1f117e97, 0x1f282296, 0x1f3814b3, 0x1e17977b
data4 0x1f39d6ff, 0x9f1c81b9, 0x9eb5bcad, 0x1f0f596e
data4 0x1e757fd5, 0x9f090daa, 0x9f2532fc, 0x9eebafbb
data4 0x1f086556, 0x9eeedde8, 0x9f32e174, 0x1e33c030
data4 0x1f1f145a, 0x1e6e556c, 0x1e419ffb, 0x9eb6019a
data4 0x9e872a2e, 0x1e113136, 0x1e93096f, 0x1f39be40
data4 0x1f1665ad, 0x9db81d7d, 0x9cd29091, 0x1e3f4af7
data4 0x9f23176c, 0x9eccf9b3, 0x1f34fc6c, 0x9ed36894
data4 0x1ef08e06, 0x9f3b46bb, 0x9f2c850b, 0x1f1565a4
data4 0x1e887bc3, 0x1e92629c, 0x9f11ac9e, 0x9e5579f3
data4 0x1e4d5790, 0x9ee1c3d1, 0x9e916aec, 0x9eb8d9b8
data4 0x1db46105, 0x1e168663, 0x1f26a942, 0x9f0f0383
data4 0x9f079032, 0x9ecae1d8, 0x1ed3b34c, 0x9edc5ee6
data4 0x9e8a75a7, 0x1f3c3de2, 0x9ee5041e, 0x1f08c727
data4 0x1d02d7ae, 0x9f36adda, 0x9ef9a857, 0x9ef5cb3a
data4 0x9eee73da, 0x9da5d629, 0x1e0e99be, 0x1e5159b9
data4 0x1f2eac89, 0x9e8eedc5, 0x1dd0ec90, 0x1f229aff
data4 0x1ed9c3e6, 0x1e95c55a, 0x9f0c24e4, 0x1e8afed6
data4 0x1e599a96, 0x1e881b21, 0x1eab84b9, 0x9ba2bb0e
data4 0x9e33ab10, 0x1f1710b5, 0x1ebfa271, 0x9e90bbc5
data4 0x9f32515b, 0x9b32aae8, 0x1eda455c, 0x1da8186e
data4 0x9e8917ff, 0x1ec4d08e, 0x1c90069d, 0x9f2f1d29
data4 0x9ecee86d, 0x9f234d1f, 0x1f370724, 0x1da87496
data4 0x1e7959f0, 0x9e8ada34, 0x1f1c7f6f, 0x1edd576b
data4 0x9de91e8b, 0x1ec4ef89, 0x1f32078a, 0x1e9925e2
data4 0x9d8eeccb, 0x9ea3d011, 0x1f231fdf, 0x9f1dbdfa
data4 0x1e7507a3, 0x1ec42614, 0x9e8693cb, 0x9ec68398
data4 0x1d5b05fb, 0x1de32119, 0x9f003429, 0x9ec16d92
data4 0x9f095315, 0x9f119d2c, 0x9ed0c984, 0x9f090662
data4 0x9e59aa1f, 0x9ed4e64a, 0x9f2798a7, 0x9f23624d
data4 0x1e0467d9, 0x1f22e7e7, 0x1e915256, 0x9cb4df70
data4 0x9e6f687c, 0x9e3c35e5, 0x9e5757ab, 0x9f031fa1
data4 0x1f25bff7, 0x1f0e58c2, 0x1ef3ce04, 0x1f002ecb
data4 0x9ebdc836, 0x9ed657dd, 0x9f149441, 0x9e8544b2
data4 0x1cd8ff1e, 0x1e9bb463, 0x1eaa1c5c, 0x1f200c1a
data4 0x1edbfbaf, 0x1f18724d, 0x9ed63c22, 0x9f08e045
data4 0x1f13ad07, 0x9e949311, 0x9f0c50d4, 0x1e824516
data4 0x1d5e52ba, 0x1d583fbd, 0x1e3b60a9, 0x9effe6d3
data4 0x1f0d0508, 0x1f00be77, 0x9e404bfa, 0x9e1ca381
data4 0x9f084dd8, 0x9e6db85d, 0x1db698e4, 0x9ebd1871
data4 0x9ecc2679, 0x1ee68442, 0x1edb1050, 0x9dbc96a4
data4 0x9f27c1f4, 0x1c99b756, 0x1eb4400a, 0x9f24390a
data4 0x1d927875, 0x9f074faa, 0x1e9dc2c3, 0x1f13c0d2
data4 0x1e3c9685, 0x9e6b6f75, 0x9db9cb31, 0x1ea5f3aa
data4 0x9d992c61, 0x1f1015e4, 0x1f194f70, 0x9e19d2b3
data4 0x9d89116c, 0x1f23cd35, 0x1e33d3a2, 0x1ee331b8
data4 0x1d5ba7ec, 0x9f273788, 0x9e6907f4, 0x9ed5f912
data4 0x9edd458d, 0x1e2ca7b2, 0x1ef81fe4, 0x1dc7ade6
data4 0x1e876e51, 0x9f04ec89, 0x1f1da63a, 0x1ec02bd0
data4 0x9e71326f, 0x1e7847b4, 0x1f0de618, 0x9e036cb6
data4 0x1eec61e2, 0x1ef1758b, 0x9ee880a3, 0x1ed269d7
data4 0x1e27edd3, 0x9e8a81a1, 0x1eacb84d, 0x9e1aad37
data4 0x1f1aa8f7, 0x1e9bbd90, 0x1ea1b61f, 0x9ed41c2f
data4 0x1dbb5dd6, 0x1f0ec733, 0x9df06b1b, 0x1e06fef1
data4 0x9edede3a, 0x1edeb5e2, 0x1f0e63ee, 0x9db316bb
data4 0x9efc1ad3, 0x1f01fbb5, 0x9cc0d078, 0x1ea28b36
data4 0x9e9dd205, 0x9e791534, 0x1da1c8d5, 0x9e8195cc
data4 0x1f0681a4, 0x1eeaf1e2, 0x9ef83b37, 0x9f22a92b
data4 0x1eabc4ce, 0x1f10eefb, 0x1e06d9aa, 0x1e7cacd5
data4 0x1f1ea087, 0x1eb21983, 0x9f100c78, 0x1e840abe
data4 0x9efab66c, 0x1f183fa8, 0x9e84ee68, 0x9eea083d
data4 0x9ee23a74, 0x1f1351d7, 0x9ec5d42a, 0x9f071f57
data4 0x9ef578d9, 0x9f1aa7e7, 0x1eb02044, 0x1f151a2e
data4 0x9c0dc8b2, 0x9ef4087a, 0x1ec12b93, 0x1c1a946b
data4 0x1e89946f, 0x9dafe8c3, 0x1d295288, 0x9e8497ab
data4 0x1ec000c6, 0x1e102f29, 0x1e542256, 0x1e67d44d
data4 0x1ef688d8, 0x1f0e0f29, 0x1e67861f, 0x1e869748
data4 0x1ee6aa6e, 0x9e4d228b, 0x9e50be5b, 0x1e9fe225
data4 0x9ea34102, 0x9e628a3b, 0x9ed9fd83, 0x1ecd7109
data4 0x1f1864ff, 0x1ea19b76, 0x1db0d1c9, 0x9dff519b
data4 0x1e8fea71, 0x9ee82e9a, 0x9f08919b, 0x9ef5c8ae
data4 0x9ee446a4, 0x1ea59444, 0x1eb74230, 0x1ea13fbf
data4 0x9ea6a3ea, 0x1e5f2797, 0x9e0adb07, 0x9d3adadd
data4 0x1ebf2ee2, 0x1da19bfa, 0x1e8dea6d, 0x1ec4fea9
data4 0x1e669f22, 0x1dc5f919, 0x9ed25caa, 0x1ee475b1
data4 0x1ed0603e, 0x9eacb35c, 0x1dc00b27, 0x1e2f9991
data4 0x1e7b0406, 0x1eaa3387, 0x9d865bde, 0x1eb78a48
data4 0x1c40ae2e, 0x1ee9838b, 0x9f0f0d7f, 0x1e3e5d26
data4 0x1e99e7a6, 0x9e681ccf, 0x9e93ed65, 0x9eeb6a66
data4 0x1e29e9af, 0x9e96f923, 0x9e74f11d, 0x9f1474da
data4 0x1eec2ea7, 0x1ebf7aa3, 0x9c25dcca, 0x9f0553c2
data4 0x9e599efd, 0x1d2ab490, 0x1e95d7cd, 0x9ee4b20e
data4 0x9d988ce5, 0x9ef9787e, 0x9dbbba5b, 0x9f12c304
data4 0x1e3b9d70, 0x1e7bcae8, 0x9d98bb6e, 0x9e8e6b01
data4 0x9f07d03b, 0x9d67c822, 0x9f0ef69e, 0x1c7c0fe3
data4 0x9e9bfbb9, 0x9e83b84b, 0x1efbf15e, 0x9ecfa6a6
data4 0x9c91158e, 0x9ecf6770, 0x1ee1e3a8, 0x9dc95ec0
data4 0x1ef603f7, 0x1d5e52ba, 0x1c477d1b, 0x9e955cd8
data4 0x1ed665b0, 0x9e8376c4, 0x9c0ee88e, 0x1e8c989e
data4 0x1ea2df29, 0x9d961e5c, 0x1e101813, 0x1e7fffff
data4 0x9e5abff4, 0x1dbddd71, 0x1eb69100, 0x1e71f114
data4 0x1e9ca798, 0x1ef62c8d, 0x9db4e55a, 0x1dbe69ce
data4 0x9ef1c01f, 0x1f044a2a, 0x9eb9e0d7, 0x9ee59745
data4 0x9e874803, 0x1ea0b418, 0x9e13572a, 0x1ddbb3a2
data4 0x9ec0e391, 0x1e89fba1, 0x1ee8b261, 0x9e5d25f0
data4 0x9ef222cb, 0x9ef135ec, 0x1ea04b9a, 0x9f04291f
data4 0x9e969254, 0x9ee32f08, 0x9ed909d3, 0x9e362640
data4 0x9ec20735, 0x1e50131b, 0x9ed4e049, 0x1ee8e817
data4 0x1e1e09c0, 0x9ea643c5, 0x9e5a1ab6, 0x9e389059
data4 0x1e560947, 0x1d02b877, 0x1e4475ab, 0x9ea9aaf6
data4 0x1e95bc5e, 0x1eaf6afd, 0x1d43067d, 0x9d043821
data4 0x9e97baa9, 0x1de5c4f9, 0x9e9a0069, 0x9e1b9944
data4 0x1eb13686, 0x9eb907eb, 0x1e059589, 0x1cbd0f93
data4 0x9eb7e6ae, 0x1e9fa175, 0x1ee5bdf4, 0x1e8052f7
data4 0x9c80d1e3, 0x1bfbe28e, 0x9e672b3b, 0x9ecacf19
data4 0x9e3c04be, 0x1dfe8c5c, 0x1e1ba9cb, 0x1eb40b1e
data4 0x1ec7e7f6, 0x9d0d45b3, 0x1ef0113b, 0x9a155fa3
data4 0x1e28ec3b, 0x1e7ca8df, 0x9d2f91b4, 0x1eccd9ed
data4 0x9ed943bc, 0x9ccaab19, 0x9e8a5c58, 0x1ec3bca8
data4 0x1ed78dc7, 0x9ed391a8, 0x9e938f6e, 0x9ec4a030
data4 0x9e80346e, 0x1e7a4686, 0x9e284315, 0x9e39584c
data4 0x1ebdc9b4, 0x9e9cfce5, 0x9ef55c65, 0x1e2941e7
data4 0x9efbe59f, 0x1d87c41b, 0x1e40befc, 0x1e3d05b5
data4 0x1de9ea67, 0x1ec9a21c, 0x1decb69a, 0x1df6e75a
data4 0x9e8030ab, 0x9db20540, 0x9ef1e977, 0x1e3cdc43
data4 0x1e0492b0, 0x9e91d872, 0x1e775346, 0x9e939978
data4 0x1eb2714e, 0x1e49a203, 0x9e10195a, 0x1ef1ffc3
data4 0x9ea8b709, 0x9e832e27, 0x1ed5ac3b, 0x1edb20a6
data4 0x1e4dbd4e, 0x1efbb932, 0x1d8170ec, 0x1e6c4849
data4 0x1f008e17, 0x1e8000c4, 0x1d855ecf, 0x9e37cb85
data4 0x1ecffdf5, 0x1eba6519, 0x9edbe600, 0x1ea3e5e7
data4 0x1ed4fb39, 0x1f00be77, 0x1e6f4484, 0x9e9e7107
data4 0x9e30b29d, 0x9ee6e174, 0x1e3a2656, 0x9dd72f3f
data4 0x9ee12138, 0x1ed16fed, 0x9ece8a02, 0x9ca5b249
data4 0x9eafd508, 0x9ef0e9fc, 0x1d1307ac, 0x1eecee20
data4 0x1cf60c6f, 0x9d556216, 0x9eaed175, 0x9ec919f4
data4 0x1ec2c988, 0x1cd82772, 0x9dc99456, 0x1eab0467
data4 0x1e89b36f, 0x1c757944, 0x1eef9abd, 0x9e98664d
LOCAL_OBJECT_END(D_table)
.section .text
GLOBAL_LIBM_ENTRY(cbrtl)
{ .mfi
getf.sig GR_ARGSIG = f8
// will continue on main path only for normal/denormal numbers
// all other values will be filtered out and will exit early
fclass.nm.unc p12, p7 = f8, 0x1b
// GR_ADDR = pointer to C_1...C_6 followed by T_table
addl GR_ADDR = @ltoff(poly_coeffs), gp
}
{ .mfi
// GR_BIAS23 = 2/3*bias -63 = 0xaaaa-0x3f = 0xaa6b
mov GR_BIAS23 = 0xaa6b
// normalize a
fma.s1 FR_XNORM = f8, f1, f0
// GR_D_ADDR = pointer to D table
addl GR_D_ADDR = @ltoff(D_table), gp
}
;;
{ .mmf
// load start address for C_1...C_6 followed by T_table
ld8 GR_C_START = [ GR_ADDR ]
// load start address of D table
ld8 GR_D_START = [ GR_D_ADDR ]
// y = frcpa(a)
frcpa.s1 FR_RCP, p6 = f1, f8
}
;;
{ .mmi
// get normalized significand
getf.sig GR_NORMSIG = FR_XNORM
// get exponent
getf.exp GR_NORMEXPSGN = FR_XNORM
(p7) cmp.eq p12, p0 = GR_ARGSIG, r0
}
;;
{ .mii
// load C_1
ldfe FR_C1 = [ GR_C_START ], 16
mov GR_SGNMASK = 0x20000
nop.i 0
}
;;
{ .mfb
// load C_2
ldfe FR_C2 = [ GR_C_START ], 16
(p12) fma.s0 f8 = f8, f1, f0
// NaN/Infinities exit early
(p12) br.ret.spnt b0
}
;;
{ .mfi
// load C_3, C_4
ldfpd FR_C3, FR_C4 = [ GR_C_START ], 16
// y = frcpa(a), set flags and result when argument is 0
// only used when p6=0
frcpa.s0 f8, p0 = f1, f8
nop.i 0
}
;;
{ .mii
// get GR_SIGN = sign
and GR_SIGN = GR_NORMEXPSGN, GR_SGNMASK
// eliminate leading 1 from GR_NORMSIG = 2nd table index
shl GR_INDEX2 = GR_NORMSIG, 1
// eliminate sign from exponent
andcm GR_NORMEXP = GR_NORMEXPSGN, GR_SGNMASK
}
;;
{ .mfi
// load C_5, C_6
(p6) ldfpd FR_C5, FR_C6 = [ GR_C_START ], 16
// r = 1-a*y
(p6) fnma.s1 FR_R = FR_RCP, FR_XNORM, f1
// Start computation of floor(exponent/3) by
// computing (2^20+2)/3*exponent = exponent*0x55556
// 1: exponent* = 5;
// (2^{16}-1)/3 = 0x5555:
// will form 0x5555*exponent by using shladd's
shladd GR_EXP5 = GR_NORMEXP, 2, GR_NORMEXP
}
;;
{ .mib
// Next several integer steps compute floor(exponent/3)
// GR_TMP1 = (5*expon)*16
shladd GR_TMP1 = GR_EXP5, 4, r0
// GR_EXP3 = 3*exponent
shladd GR_EXP3 = GR_NORMEXP, 1, GR_NORMEXP
nop.b 0
}
;;
{ .mmi
// GR_EXP6 = 6*exponent
shladd GR_EXP6 = GR_EXP3, 1, r0
// GR_EXP17 = 17*expon
add GR_EXP17 = GR_EXP5, GR_TMP1
// GR_IX2 = 2nd table index (8 bits)
shr.u GR_IX2 = GR_INDEX2, 56
}
;;
{ .mmi
// adjust T_table pointer by 2nd index
shladd GR_T_INDEX = GR_IX2, 3, GR_C_START
// adjust D_table pointer by 2nd index
shladd GR_D_INDEX = GR_IX2, 2, GR_D_START
// GR_TMP2 = (17*expon)*16^2
shl GR_TMP2 = GR_EXP17, 8
}
;;
{ .mmi
// GR_TMP3 = expon*(2^16-1)/3
add GR_TMP3 = GR_EXP17, GR_TMP2
;;
// GR_TMP4 = expon*(2^20+2)/3 = expon*0x55556
shladd GR_TMP4 = GR_TMP3, 4, GR_EXP6
nop.i 0
}
;;
{ .mii
nop.m 0
// GR_EXP_RES = floor(expon/3)
shr.u GR_EXP_RES = GR_TMP4, 20
nop.i 0
}
;;
{ .mmi
nop.m 0
// r16 = 3*exponent
shladd r16 = GR_EXP_RES, 1, GR_EXP_RES
// bias exponent
add GR_EXPBIAS = GR_BIAS23, GR_EXP_RES
}
;;
{ .mmi
// get remainder of exponent/3
sub GR_EXP_MOD_3 = GR_NORMEXP, r16
;;
// add sign to exponent
or GR_EXPSIGNRES = GR_EXPBIAS, GR_SIGN
// remainder << = 8
shl GR_REMTMP = GR_EXP_MOD_3, 8
}
;;
{ .mfi
// adjust D_table pointer by 1st index
shladd GR_IX_D = GR_REMTMP, 2, GR_D_INDEX
// P_1 = C_1+C_2*r
(p6) fma.s1 FR_P1 = FR_C2, FR_R, FR_C1
// adjust T_table pointer by 1st index
shladd GR_IX_T = GR_REMTMP, 3, GR_T_INDEX
}
{ .mfi
// FR_SGNEXP = sign*2^{exponent/3}
(p6) setf.exp FR_SGNEXP = GR_EXPSIGNRES
// r^2 = r*r
(p6) fma.s1 FR_R2 = FR_R, FR_R, f0
nop.i 0
}
;;
{ .mfi
// load D
(p6) ldfs FR_D = [ GR_IX_D ]
// P_2 = C_3+C_4*r
(p6) fma.s1 FR_P2 = FR_C4, FR_R, FR_C3
nop.i 0
}
{ .mfi
// load T
(p6) ldf8 FR_T = [ GR_IX_T ]
// P_3 = C_5+C_6*r
(p6) fma.s1 FR_P3 = FR_C6, FR_R, FR_C5
nop.i 0
}
;;
{ .mfi
nop.m 0
// P_4 = D-r*P_1
(p6) fnma.s1 FR_P4 = FR_R, FR_P1, FR_D
nop.i 0
}
{ .mfi
nop.m 0
// r^3 = r*r^2
(p6) fma.s1 FR_R3 = FR_R, FR_R2, f0
nop.i 0
}
;;
{ .mfi
nop.m 0
// P_5 = P_2+r2*P_3
(p6) fma.s1 FR_P5 = FR_R2, FR_P3, FR_P2
nop.i 0
}
;;
{ .mfi
nop.m 0
// T = T*(sign*2^{exponent/3})
(p6) fma.s1 FR_TF = FR_T, FR_SGNEXP, f0
nop.i 0
}
{ .mfi
nop.m 0
// P = P_4-r3*P_5
(p6) fnma.s1 FR_P = FR_R3, FR_P5, FR_P4
nop.i 0
}
;;
{ .mfb
nop.m 0
// result = T+T*p
(p6) fma.s0 f8 = FR_TF, FR_P, FR_TF
br.ret.sptk b0
}
;;
GLOBAL_LIBM_END(cbrtl)
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