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.file "logf.s"
// Copyright (c) 2000, 2001, Intel Corporation// All rights reserved.// // Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.// // WARRANTY DISCLAIMER// // 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://developer.intel.com/opensource.//// History//==============================================================// 3/01/00 Initial version// 8/15/00 Bundle added after call to __libm_error_support to properly// set [the previously overwritten] GR_Parameter_RESULT.// 1/10/01 Improved speed, fixed flags for neg denormals////// API//==============================================================// float logf(float)// float log10f(float)//// Overview of operation//==============================================================// Background//// Consider x = 2^N 1.f1 f2 f3 f4...f63// Log(x) = log(frcpa(x) x/frcpa(x))// = log(1/frcpa(x)) + log(frcpa(x) x)// = -log(frcpa(x)) + log(frcpa(x) x)//// frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)//// -log(frcpa(x)) = -log(C) // = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))//// -log(frcpa(x)) = -log(C) // = +Nlog2 - log(frcpa(1.f1 f2 ... f63))//// -log(frcpa(x)) = -log(C) // = +Nlog2 + log(frcpa(1.f1 f2 ... f63))//// Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
// Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)// Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)// Log(x) = +Nlog2 + T + log(frcpa(x) x)//// Log(x) = +Nlog2 + T + log(C x)//// Cx = 1 + r//// Log(x) = +Nlog2 + T + log(1+r)// Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....)//// 1.f1 f2 ... f8 has 256 entries.// They are 1 + k/2^8, k = 0 ... 255// These 256 values are the table entries.//// Implementation//===============// CASE 1: |x-1| >= 2^-8// C = frcpa(x)// r = C * x - 1//// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4//// x = f * 2*n where f is 1.f_1f_2f_3....f_63// Nfloat = float(n) where n is the true unbiased exponent// pre-index = f_1f_2....f_8// index = pre_index * 16// get the dxt table entry at index + offset = T//// result = (T + Nfloat * log(2)) + rseries//// The T table is calculated as follows// Form x_k = 1 + k/2^8 where k goes from 0... 255// y_k = frcpa(x_k)// log(1/y_k) in quad and round to double
// CASE 2: |x-1| < 2^-6// w = x - 1//// Form wseries = w + Q1*w^2 + Q2*w^3 + Q3*w^4//// result = wseries
// Special values //==============================================================
// log(+0) = -inf// log(-0) = -inf
// log(+qnan) = +qnan // log(-qnan) = -qnan // log(+snan) = +qnan // log(-snan) = -qnan
// log(-n) = QNAN Indefinite// log(-inf) = QNAN Indefinite
// log(+inf) = +inf
// Registers used//==============================================================// Floating Point registers used: // f8, input// f9 -> f15, f32 -> f47
// General registers used: // r32 -> r51
// Predicate registers used:// p6 -> p15
// p8 log base e// p6 log base e special// p9 used in the frcpa// p13 log base e large W// p14 log base e small w
// p7 log base 10// p10 log base 10 large W// p11 log base 10 small w// p12 log base 10 special
// Assembly macros//==============================================================
log_int_Nfloat = f9 log_Nfloat = f10
log_P3 = f11 log_P2 = f12 log_P1 = f13 log_inv_ln10 = f14log_log2 = f15
log_w = f32log_T = f33 log_rp_p32 = f34 log_rp_p2 = f35 log_rp_p10 = f36log_rsq = f37 log_T_plus_Nlog2 = f38 log_r = f39log_C = f40log_rp_q32 = f41log_rp_q2 = f42log_rp_q10 = f43log_wsq = f44log_Q = f45log_inv_ln10 = f46log_NORM_f8 = f47
// ===================================
log_GR_exp_17_ones = r33log_GR_exp_16_ones = r34log_GR_exp_f8 = r35log_GR_signexp_f8 = r36log_GR_true_exp_f8 = r37log_GR_significand_f8 = r38log_GR_index = r39log_AD_1 = r40log_GR_signexp_w = r41log_GR_fff7 = r42log_AD_2 = r43log_GR_exp_w = r44
GR_SAVE_B0 = r45GR_SAVE_GP = r46GR_SAVE_PFS = r47
GR_Parameter_X = r48GR_Parameter_Y = r49GR_Parameter_RESULT = r50log_GR_tag = r51
// Data tables//==============================================================
.data
.align 16
log_table_1:data8 0xbfd0001008f39d59 // p3data8 0x3fd5556073e0c45a // p2
log_table_2:data8 0xbfdffffffffaea15 // p1data8 0x3fdbcb7b1526e50e // 1/ln10data8 0x3fe62e42fefa39ef // Log(2)data8 0x0 // pad
data8 0x3F60040155D5889E //log(1/frcpa(1+ 0/256)data8 0x3F78121214586B54 //log(1/frcpa(1+ 1/256)data8 0x3F841929F96832F0 //log(1/frcpa(1+ 2/256)data8 0x3F8C317384C75F06 //log(1/frcpa(1+ 3/256)data8 0x3F91A6B91AC73386 //log(1/frcpa(1+ 4/256)data8 0x3F95BA9A5D9AC039 //log(1/frcpa(1+ 5/256)data8 0x3F99D2A8074325F4 //log(1/frcpa(1+ 6/256)data8 0x3F9D6B2725979802 //log(1/frcpa(1+ 7/256)data8 0x3FA0C58FA19DFAAA //log(1/frcpa(1+ 8/256)data8 0x3FA2954C78CBCE1B //log(1/frcpa(1+ 9/256)data8 0x3FA4A94D2DA96C56 //log(1/frcpa(1+ 10/256)data8 0x3FA67C94F2D4BB58 //log(1/frcpa(1+ 11/256)data8 0x3FA85188B630F068 //log(1/frcpa(1+ 12/256)data8 0x3FAA6B8ABE73AF4C //log(1/frcpa(1+ 13/256)data8 0x3FAC441E06F72A9E //log(1/frcpa(1+ 14/256)data8 0x3FAE1E6713606D07 //log(1/frcpa(1+ 15/256)data8 0x3FAFFA6911AB9301 //log(1/frcpa(1+ 16/256)data8 0x3FB0EC139C5DA601 //log(1/frcpa(1+ 17/256)data8 0x3FB1DBD2643D190B //log(1/frcpa(1+ 18/256)data8 0x3FB2CC7284FE5F1C //log(1/frcpa(1+ 19/256)data8 0x3FB3BDF5A7D1EE64 //log(1/frcpa(1+ 20/256)data8 0x3FB4B05D7AA012E0 //log(1/frcpa(1+ 21/256)data8 0x3FB580DB7CEB5702 //log(1/frcpa(1+ 22/256)data8 0x3FB674F089365A7A //log(1/frcpa(1+ 23/256)data8 0x3FB769EF2C6B568D //log(1/frcpa(1+ 24/256)data8 0x3FB85FD927506A48 //log(1/frcpa(1+ 25/256)data8 0x3FB9335E5D594989 //log(1/frcpa(1+ 26/256)data8 0x3FBA2B0220C8E5F5 //log(1/frcpa(1+ 27/256)data8 0x3FBB0004AC1A86AC //log(1/frcpa(1+ 28/256)data8 0x3FBBF968769FCA11 //log(1/frcpa(1+ 29/256)data8 0x3FBCCFEDBFEE13A8 //log(1/frcpa(1+ 30/256)data8 0x3FBDA727638446A2 //log(1/frcpa(1+ 31/256)data8 0x3FBEA3257FE10F7A //log(1/frcpa(1+ 32/256)data8 0x3FBF7BE9FEDBFDE6 //log(1/frcpa(1+ 33/256)data8 0x3FC02AB352FF25F4 //log(1/frcpa(1+ 34/256)data8 0x3FC097CE579D204D //log(1/frcpa(1+ 35/256)data8 0x3FC1178E8227E47C //log(1/frcpa(1+ 36/256)data8 0x3FC185747DBECF34 //log(1/frcpa(1+ 37/256)data8 0x3FC1F3B925F25D41 //log(1/frcpa(1+ 38/256)data8 0x3FC2625D1E6DDF57 //log(1/frcpa(1+ 39/256)data8 0x3FC2D1610C86813A //log(1/frcpa(1+ 40/256)data8 0x3FC340C59741142E //log(1/frcpa(1+ 41/256)data8 0x3FC3B08B6757F2A9 //log(1/frcpa(1+ 42/256)data8 0x3FC40DFB08378003 //log(1/frcpa(1+ 43/256)data8 0x3FC47E74E8CA5F7C //log(1/frcpa(1+ 44/256)data8 0x3FC4EF51F6466DE4 //log(1/frcpa(1+ 45/256)data8 0x3FC56092E02BA516 //log(1/frcpa(1+ 46/256)data8 0x3FC5D23857CD74D5 //log(1/frcpa(1+ 47/256)data8 0x3FC6313A37335D76 //log(1/frcpa(1+ 48/256)data8 0x3FC6A399DABBD383 //log(1/frcpa(1+ 49/256)data8 0x3FC70337DD3CE41B //log(1/frcpa(1+ 50/256)data8 0x3FC77654128F6127 //log(1/frcpa(1+ 51/256)data8 0x3FC7E9D82A0B022D //log(1/frcpa(1+ 52/256)data8 0x3FC84A6B759F512F //log(1/frcpa(1+ 53/256)data8 0x3FC8AB47D5F5A310 //log(1/frcpa(1+ 54/256)data8 0x3FC91FE49096581B //log(1/frcpa(1+ 55/256)data8 0x3FC981634011AA75 //log(1/frcpa(1+ 56/256)data8 0x3FC9F6C407089664 //log(1/frcpa(1+ 57/256)data8 0x3FCA58E729348F43 //log(1/frcpa(1+ 58/256)data8 0x3FCABB55C31693AD //log(1/frcpa(1+ 59/256)data8 0x3FCB1E104919EFD0 //log(1/frcpa(1+ 60/256)data8 0x3FCB94EE93E367CB //log(1/frcpa(1+ 61/256)data8 0x3FCBF851C067555F //log(1/frcpa(1+ 62/256)data8 0x3FCC5C0254BF23A6 //log(1/frcpa(1+ 63/256)data8 0x3FCCC000C9DB3C52 //log(1/frcpa(1+ 64/256)data8 0x3FCD244D99C85674 //log(1/frcpa(1+ 65/256)data8 0x3FCD88E93FB2F450 //log(1/frcpa(1+ 66/256)data8 0x3FCDEDD437EAEF01 //log(1/frcpa(1+ 67/256)data8 0x3FCE530EFFE71012 //log(1/frcpa(1+ 68/256)data8 0x3FCEB89A1648B971 //log(1/frcpa(1+ 69/256)data8 0x3FCF1E75FADF9BDE //log(1/frcpa(1+ 70/256)data8 0x3FCF84A32EAD7C35 //log(1/frcpa(1+ 71/256)data8 0x3FCFEB2233EA07CD //log(1/frcpa(1+ 72/256)data8 0x3FD028F9C7035C1C //log(1/frcpa(1+ 73/256)data8 0x3FD05C8BE0D9635A //log(1/frcpa(1+ 74/256)data8 0x3FD085EB8F8AE797 //log(1/frcpa(1+ 75/256)data8 0x3FD0B9C8E32D1911 //log(1/frcpa(1+ 76/256)data8 0x3FD0EDD060B78081 //log(1/frcpa(1+ 77/256)data8 0x3FD122024CF0063F //log(1/frcpa(1+ 78/256)data8 0x3FD14BE2927AECD4 //log(1/frcpa(1+ 79/256)data8 0x3FD180618EF18ADF //log(1/frcpa(1+ 80/256)data8 0x3FD1B50BBE2FC63B //log(1/frcpa(1+ 81/256)data8 0x3FD1DF4CC7CF242D //log(1/frcpa(1+ 82/256)data8 0x3FD214456D0EB8D4 //log(1/frcpa(1+ 83/256)data8 0x3FD23EC5991EBA49 //log(1/frcpa(1+ 84/256)data8 0x3FD2740D9F870AFB //log(1/frcpa(1+ 85/256)data8 0x3FD29ECDABCDFA04 //log(1/frcpa(1+ 86/256)data8 0x3FD2D46602ADCCEE //log(1/frcpa(1+ 87/256)data8 0x3FD2FF66B04EA9D4 //log(1/frcpa(1+ 88/256)data8 0x3FD335504B355A37 //log(1/frcpa(1+ 89/256)data8 0x3FD360925EC44F5D //log(1/frcpa(1+ 90/256)data8 0x3FD38BF1C3337E75 //log(1/frcpa(1+ 91/256)data8 0x3FD3C25277333184 //log(1/frcpa(1+ 92/256)data8 0x3FD3EDF463C1683E //log(1/frcpa(1+ 93/256)data8 0x3FD419B423D5E8C7 //log(1/frcpa(1+ 94/256)data8 0x3FD44591E0539F49 //log(1/frcpa(1+ 95/256)data8 0x3FD47C9175B6F0AD //log(1/frcpa(1+ 96/256)data8 0x3FD4A8B341552B09 //log(1/frcpa(1+ 97/256)data8 0x3FD4D4F3908901A0 //log(1/frcpa(1+ 98/256)data8 0x3FD501528DA1F968 //log(1/frcpa(1+ 99/256)data8 0x3FD52DD06347D4F6 //log(1/frcpa(1+ 100/256)data8 0x3FD55A6D3C7B8A8A //log(1/frcpa(1+ 101/256)data8 0x3FD5925D2B112A59 //log(1/frcpa(1+ 102/256)data8 0x3FD5BF406B543DB2 //log(1/frcpa(1+ 103/256)data8 0x3FD5EC433D5C35AE //log(1/frcpa(1+ 104/256)data8 0x3FD61965CDB02C1F //log(1/frcpa(1+ 105/256)data8 0x3FD646A84935B2A2 //log(1/frcpa(1+ 106/256)data8 0x3FD6740ADD31DE94 //log(1/frcpa(1+ 107/256)data8 0x3FD6A18DB74A58C5 //log(1/frcpa(1+ 108/256)data8 0x3FD6CF31058670EC //log(1/frcpa(1+ 109/256)data8 0x3FD6F180E852F0BA //log(1/frcpa(1+ 110/256)data8 0x3FD71F5D71B894F0 //log(1/frcpa(1+ 111/256)data8 0x3FD74D5AEFD66D5C //log(1/frcpa(1+ 112/256)data8 0x3FD77B79922BD37E //log(1/frcpa(1+ 113/256)data8 0x3FD7A9B9889F19E2 //log(1/frcpa(1+ 114/256)data8 0x3FD7D81B037EB6A6 //log(1/frcpa(1+ 115/256)data8 0x3FD8069E33827231 //log(1/frcpa(1+ 116/256)data8 0x3FD82996D3EF8BCB //log(1/frcpa(1+ 117/256)data8 0x3FD85855776DCBFB //log(1/frcpa(1+ 118/256)data8 0x3FD8873658327CCF //log(1/frcpa(1+ 119/256)data8 0x3FD8AA75973AB8CF //log(1/frcpa(1+ 120/256)data8 0x3FD8D992DC8824E5 //log(1/frcpa(1+ 121/256)data8 0x3FD908D2EA7D9512 //log(1/frcpa(1+ 122/256)data8 0x3FD92C59E79C0E56 //log(1/frcpa(1+ 123/256)data8 0x3FD95BD750EE3ED3 //log(1/frcpa(1+ 124/256)data8 0x3FD98B7811A3EE5B //log(1/frcpa(1+ 125/256)data8 0x3FD9AF47F33D406C //log(1/frcpa(1+ 126/256)data8 0x3FD9DF270C1914A8 //log(1/frcpa(1+ 127/256)data8 0x3FDA0325ED14FDA4 //log(1/frcpa(1+ 128/256)data8 0x3FDA33440224FA79 //log(1/frcpa(1+ 129/256)data8 0x3FDA57725E80C383 //log(1/frcpa(1+ 130/256)data8 0x3FDA87D0165DD199 //log(1/frcpa(1+ 131/256)data8 0x3FDAAC2E6C03F896 //log(1/frcpa(1+ 132/256)data8 0x3FDADCCC6FDF6A81 //log(1/frcpa(1+ 133/256)data8 0x3FDB015B3EB1E790 //log(1/frcpa(1+ 134/256)data8 0x3FDB323A3A635948 //log(1/frcpa(1+ 135/256)data8 0x3FDB56FA04462909 //log(1/frcpa(1+ 136/256)data8 0x3FDB881AA659BC93 //log(1/frcpa(1+ 137/256)data8 0x3FDBAD0BEF3DB165 //log(1/frcpa(1+ 138/256)data8 0x3FDBD21297781C2F //log(1/frcpa(1+ 139/256)data8 0x3FDC039236F08819 //log(1/frcpa(1+ 140/256)data8 0x3FDC28CB1E4D32FD //log(1/frcpa(1+ 141/256)data8 0x3FDC4E19B84723C2 //log(1/frcpa(1+ 142/256)data8 0x3FDC7FF9C74554C9 //log(1/frcpa(1+ 143/256)data8 0x3FDCA57B64E9DB05 //log(1/frcpa(1+ 144/256)data8 0x3FDCCB130A5CEBB0 //log(1/frcpa(1+ 145/256)data8 0x3FDCF0C0D18F326F //log(1/frcpa(1+ 146/256)data8 0x3FDD232075B5A201 //log(1/frcpa(1+ 147/256)data8 0x3FDD490246DEFA6B //log(1/frcpa(1+ 148/256)data8 0x3FDD6EFA918D25CD //log(1/frcpa(1+ 149/256)data8 0x3FDD9509707AE52F //log(1/frcpa(1+ 150/256)data8 0x3FDDBB2EFE92C554 //log(1/frcpa(1+ 151/256)data8 0x3FDDEE2F3445E4AF //log(1/frcpa(1+ 152/256)data8 0x3FDE148A1A2726CE //log(1/frcpa(1+ 153/256)data8 0x3FDE3AFC0A49FF40 //log(1/frcpa(1+ 154/256)data8 0x3FDE6185206D516E //log(1/frcpa(1+ 155/256)data8 0x3FDE882578823D52 //log(1/frcpa(1+ 156/256)data8 0x3FDEAEDD2EAC990C //log(1/frcpa(1+ 157/256)data8 0x3FDED5AC5F436BE3 //log(1/frcpa(1+ 158/256)data8 0x3FDEFC9326D16AB9 //log(1/frcpa(1+ 159/256)data8 0x3FDF2391A2157600 //log(1/frcpa(1+ 160/256)data8 0x3FDF4AA7EE03192D //log(1/frcpa(1+ 161/256)data8 0x3FDF71D627C30BB0 //log(1/frcpa(1+ 162/256)data8 0x3FDF991C6CB3B379 //log(1/frcpa(1+ 163/256)data8 0x3FDFC07ADA69A910 //log(1/frcpa(1+ 164/256)data8 0x3FDFE7F18EB03D3E //log(1/frcpa(1+ 165/256)data8 0x3FE007C053C5002E //log(1/frcpa(1+ 166/256)data8 0x3FE01B942198A5A1 //log(1/frcpa(1+ 167/256)data8 0x3FE02F74400C64EB //log(1/frcpa(1+ 168/256)data8 0x3FE04360BE7603AD //log(1/frcpa(1+ 169/256)data8 0x3FE05759AC47FE34 //log(1/frcpa(1+ 170/256)data8 0x3FE06B5F1911CF52 //log(1/frcpa(1+ 171/256)data8 0x3FE078BF0533C568 //log(1/frcpa(1+ 172/256)data8 0x3FE08CD9687E7B0E //log(1/frcpa(1+ 173/256)data8 0x3FE0A10074CF9019 //log(1/frcpa(1+ 174/256)data8 0x3FE0B5343A234477 //log(1/frcpa(1+ 175/256)data8 0x3FE0C974C89431CE //log(1/frcpa(1+ 176/256)data8 0x3FE0DDC2305B9886 //log(1/frcpa(1+ 177/256)data8 0x3FE0EB524BAFC918 //log(1/frcpa(1+ 178/256)data8 0x3FE0FFB54213A476 //log(1/frcpa(1+ 179/256)data8 0x3FE114253DA97D9F //log(1/frcpa(1+ 180/256)data8 0x3FE128A24F1D9AFF //log(1/frcpa(1+ 181/256)data8 0x3FE1365252BF0865 //log(1/frcpa(1+ 182/256)data8 0x3FE14AE558B4A92D //log(1/frcpa(1+ 183/256)data8 0x3FE15F85A19C765B //log(1/frcpa(1+ 184/256)data8 0x3FE16D4D38C119FA //log(1/frcpa(1+ 185/256)data8 0x3FE18203C20DD133 //log(1/frcpa(1+ 186/256)data8 0x3FE196C7BC4B1F3B //log(1/frcpa(1+ 187/256)data8 0x3FE1A4A738B7A33C //log(1/frcpa(1+ 188/256)data8 0x3FE1B981C0C9653D //log(1/frcpa(1+ 189/256)data8 0x3FE1CE69E8BB106B //log(1/frcpa(1+ 190/256)data8 0x3FE1DC619DE06944 //log(1/frcpa(1+ 191/256)data8 0x3FE1F160A2AD0DA4 //log(1/frcpa(1+ 192/256)data8 0x3FE2066D7740737E //log(1/frcpa(1+ 193/256)data8 0x3FE2147DBA47A394 //log(1/frcpa(1+ 194/256)data8 0x3FE229A1BC5EBAC3 //log(1/frcpa(1+ 195/256)data8 0x3FE237C1841A502E //log(1/frcpa(1+ 196/256)data8 0x3FE24CFCE6F80D9A //log(1/frcpa(1+ 197/256)data8 0x3FE25B2C55CD5762 //log(1/frcpa(1+ 198/256)data8 0x3FE2707F4D5F7C41 //log(1/frcpa(1+ 199/256)data8 0x3FE285E0842CA384 //log(1/frcpa(1+ 200/256)data8 0x3FE294294708B773 //log(1/frcpa(1+ 201/256)data8 0x3FE2A9A2670AFF0C //log(1/frcpa(1+ 202/256)data8 0x3FE2B7FB2C8D1CC1 //log(1/frcpa(1+ 203/256)data8 0x3FE2C65A6395F5F5 //log(1/frcpa(1+ 204/256)data8 0x3FE2DBF557B0DF43 //log(1/frcpa(1+ 205/256)data8 0x3FE2EA64C3F97655 //log(1/frcpa(1+ 206/256)data8 0x3FE3001823684D73 //log(1/frcpa(1+ 207/256)data8 0x3FE30E97E9A8B5CD //log(1/frcpa(1+ 208/256)data8 0x3FE32463EBDD34EA //log(1/frcpa(1+ 209/256)data8 0x3FE332F4314AD796 //log(1/frcpa(1+ 210/256)data8 0x3FE348D90E7464D0 //log(1/frcpa(1+ 211/256)data8 0x3FE35779F8C43D6E //log(1/frcpa(1+ 212/256)data8 0x3FE36621961A6A99 //log(1/frcpa(1+ 213/256)data8 0x3FE37C299F3C366A //log(1/frcpa(1+ 214/256)data8 0x3FE38AE2171976E7 //log(1/frcpa(1+ 215/256)data8 0x3FE399A157A603E7 //log(1/frcpa(1+ 216/256)data8 0x3FE3AFCCFE77B9D1 //log(1/frcpa(1+ 217/256)data8 0x3FE3BE9D503533B5 //log(1/frcpa(1+ 218/256)data8 0x3FE3CD7480B4A8A3 //log(1/frcpa(1+ 219/256)data8 0x3FE3E3C43918F76C //log(1/frcpa(1+ 220/256)data8 0x3FE3F2ACB27ED6C7 //log(1/frcpa(1+ 221/256)data8 0x3FE4019C2125CA93 //log(1/frcpa(1+ 222/256)data8 0x3FE4181061389722 //log(1/frcpa(1+ 223/256)data8 0x3FE42711518DF545 //log(1/frcpa(1+ 224/256)data8 0x3FE436194E12B6BF //log(1/frcpa(1+ 225/256)data8 0x3FE445285D68EA69 //log(1/frcpa(1+ 226/256)data8 0x3FE45BCC464C893A //log(1/frcpa(1+ 227/256)data8 0x3FE46AED21F117FC //log(1/frcpa(1+ 228/256)data8 0x3FE47A1527E8A2D3 //log(1/frcpa(1+ 229/256)data8 0x3FE489445EFFFCCC //log(1/frcpa(1+ 230/256)data8 0x3FE4A018BCB69835 //log(1/frcpa(1+ 231/256)data8 0x3FE4AF5A0C9D65D7 //log(1/frcpa(1+ 232/256)data8 0x3FE4BEA2A5BDBE87 //log(1/frcpa(1+ 233/256)data8 0x3FE4CDF28F10AC46 //log(1/frcpa(1+ 234/256)data8 0x3FE4DD49CF994058 //log(1/frcpa(1+ 235/256)data8 0x3FE4ECA86E64A684 //log(1/frcpa(1+ 236/256)data8 0x3FE503C43CD8EB68 //log(1/frcpa(1+ 237/256)data8 0x3FE513356667FC57 //log(1/frcpa(1+ 238/256)data8 0x3FE522AE0738A3D8 //log(1/frcpa(1+ 239/256)data8 0x3FE5322E26867857 //log(1/frcpa(1+ 240/256)data8 0x3FE541B5CB979809 //log(1/frcpa(1+ 241/256)data8 0x3FE55144FDBCBD62 //log(1/frcpa(1+ 242/256)data8 0x3FE560DBC45153C7 //log(1/frcpa(1+ 243/256)data8 0x3FE5707A26BB8C66 //log(1/frcpa(1+ 244/256)data8 0x3FE587F60ED5B900 //log(1/frcpa(1+ 245/256)data8 0x3FE597A7977C8F31 //log(1/frcpa(1+ 246/256)data8 0x3FE5A760D634BB8B //log(1/frcpa(1+ 247/256)data8 0x3FE5B721D295F10F //log(1/frcpa(1+ 248/256)data8 0x3FE5C6EA94431EF9 //log(1/frcpa(1+ 249/256)data8 0x3FE5D6BB22EA86F6 //log(1/frcpa(1+ 250/256)data8 0x3FE5E6938645D390 //log(1/frcpa(1+ 251/256)data8 0x3FE5F673C61A2ED2 //log(1/frcpa(1+ 252/256)data8 0x3FE6065BEA385926 //log(1/frcpa(1+ 253/256)data8 0x3FE6164BFA7CC06B //log(1/frcpa(1+ 254/256)data8 0x3FE62643FECF9743 //log(1/frcpa(1+ 255/256)
.align 32.global logf#
.global log10f#
// log10 has p7 true, p8 false// log has p8 true, p7 false
.section .text.proc log10f#
.align 32
log10f: { .mfi alloc r32=ar.pfs,1,15,4,0 frcpa.s1 log_C,p9 = f1,f8 cmp.eq.unc p7,p8 = r0, r0 }{ .mfb addl log_AD_1 = @ltoff(log_table_1), gp fnorm.s1 log_NORM_f8 = f8 br.sptk LOG_LOG10_X };;
.endp log10f
.section .text.proc logf#
.align 32logf:
{ .mfi alloc r32=ar.pfs,1,15,4,0 frcpa.s1 log_C,p9 = f1,f8 cmp.eq.unc p8,p7 = r0, r0 }{ .mfi addl log_AD_1 = @ltoff(log_table_1), gp fnorm.s1 log_NORM_f8 = f8 nop.i 999};;
LOG_LOG10_X:
{ .mfi getf.exp log_GR_signexp_f8 = f8 // If x unorm then must recompute fclass.m.unc p15,p0 = f8, 0x0b // Test for x=unorm mov log_GR_fff7 = 0xfff7}{ .mfi ld8 log_AD_1 = [log_AD_1] fms.s1 log_w = f8,f1,f1 mov log_GR_exp_17_ones = 0x1ffff};;
{ .mmi getf.sig log_GR_significand_f8 = f8 // If x unorm then must recompute mov log_GR_exp_16_ones = 0xffff nop.i 999};;
{ .mmb adds log_AD_2 = 0x10, log_AD_1 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones (p15) br.cond.spnt LOG_DENORM };;
LOG_COMMON:{.mfi ldfpd log_P3,log_P2 = [log_AD_1],16 fclass.m.unc p6,p0 = f8, 0xc3 // Test for x=nan shl log_GR_index = log_GR_significand_f8,1 }{.mfi sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones nop.f 999 nop.i 999};;
{ .mfi ldfpd log_P1,log_inv_ln10 = [log_AD_2],16 fclass.m.unc p11,p0 = f8, 0x21 // Test for x=+inf shr.u log_GR_index = log_GR_index,56}{ .mfi setf.sig log_int_Nfloat = log_GR_true_exp_f8 nop.f 999 nop.i 999};;
{ .mfi ldfd log_log2 = [log_AD_2],16 fma.s1 log_wsq = log_w, log_w, f0 nop.i 999}{ .mfb nop.m 999(p6) fma.s.s0 f8 = f8,f1,f0 // quietize nan result if x=nan(p6) br.ret.spnt b0 // Exit for x=nan};;
{ .mfi shladd log_AD_2 = log_GR_index,3,log_AD_2 fcmp.eq.s1 p10,p0 = log_NORM_f8, f1 // Test for x=+1.0 nop.i 999}{ .mfb nop.m 999 fms.s1 log_r = log_C,f8,f1(p11) br.ret.spnt b0 // Exit for x=+inf};;
{ .mmf nop.m 999 nop.m 999 fclass.m.unc p6,p0 = f8, 0x07 // Test for x=0};;
{ .mfb ldfd log_T = [log_AD_2](p10) fmerge.s f8 = f0, f0(p10) br.ret.spnt b0 // Exit for x=1.0;;
}
{ .mfi getf.exp log_GR_signexp_w = log_w fclass.m.unc p12,p0 = f8, 0x3a // Test for x neg norm, unorm, inf nop.i 999};;
{ .mmb nop.m 999 nop.m 999(p6) br.cond.spnt LOG_ZERO_NEG // Branch if x=0;;
}
{ .mfi and log_GR_exp_w = log_GR_exp_17_ones, log_GR_signexp_w nop.f 999 nop.i 999}{ .mfb nop.m 999 fma.s1 log_rsq = log_r, log_r, f0 (p12) br.cond.spnt LOG_ZERO_NEG // Branch if x<0;;
}
{ .mfi nop.m 999 fma.s1 log_rp_p32 = log_P3, log_r, log_P2 nop.i 999}{ .mfi nop.m 999 fma.s1 log_rp_q32 = log_P3, log_w, log_P2 nop.i 999;;
}
{ .mfi nop.m 999 fcvt.xf log_Nfloat = log_int_Nfloat nop.i 999 ;;
}
{ .mfi nop.m 999 fma.s1 log_rp_p10 = log_P1, log_r, f1 nop.i 999}{ .mfi nop.m 999 fma.s1 log_rp_q10 = log_P1, log_w, f1 nop.i 999;;
}
// p13 <== large w log// p14 <== small w log{ .mfi(p8) cmp.ge.unc p13,p14 = log_GR_exp_w, log_GR_fff7 fcmp.eq.s0 p6,p0 = f8,f0 // Sets flag on +denormal input nop.i 999;;
}
// p10 <== large w log10// p11 <== small w log10{ .mfi(p7) cmp.ge.unc p10,p11 = log_GR_exp_w, log_GR_fff7 nop.f 999 nop.i 999 ;;
}
{ .mfi nop.m 999 fma.s1 log_T_plus_Nlog2 = log_Nfloat,log_log2, log_T nop.i 999 ;;
}
{ .mfi nop.m 999 fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10 nop.i 999}{ .mfi nop.m 999 fma.s1 log_rp_q2 = log_rp_q32, log_wsq, log_rp_q10 nop.i 999;;
}
// small w, log <== p14{ .mfi nop.m 999(p14) fma.s f8 = log_rp_q2, log_w, f0 nop.i 999}{ .mfi nop.m 999(p11) fma.s1 log_Q = log_rp_q2, log_w, f0 nop.i 999 ;;
}
// large w, log <== p13.pred.rel "mutex",p13,p10{ .mfi nop.m 999(p13) fma.s f8 = log_rp_p2, log_r, log_T_plus_Nlog2 nop.i 999 }{ .mfi nop.m 999(p10) fma.s1 log_Q = log_rp_p2, log_r, log_T_plus_Nlog2 nop.i 999 ;;
}
// log10{ .mfb nop.m 999(p7) fma.s f8 = log_inv_ln10,log_Q,f0 br.ret.sptk b0 ;;
}
LOG_DENORM:{ .mmi getf.exp log_GR_signexp_f8 = log_NORM_f8 nop.m 999 nop.i 999};;
{ .mmb getf.sig log_GR_significand_f8 = log_NORM_f8 and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones br.cond.sptk LOG_COMMON};;
LOG_ZERO_NEG:
// qnan snan inf norm unorm 0 -+// 0 0 0 0 0 1 11 0x7// 0 0 1 1 1 0 10 0x3a
// Save x (f8) in f10{ .mfi nop.m 999 fmerge.s f10 = f8,f8 nop.i 999 ;;
}
// p8 p9 means ln(+-0) = -inf// p7 p10 means log(+-0) = -inf
// p13 means ln(-)// p14 means log(-)
{ .mfi nop.m 999 fmerge.ns f6 = f1,f1 // Form -1.0 nop.i 999 ;;
}
// p9 means ln(+-0) = -inf// p10 means log(+-0) = -inf// Log(+-0) = -inf
{ .mfi nop.m 999(p8) fclass.m.unc p9,p0 = f10, 0x07 nop.i 999}{ .mfi nop.m 999(p7) fclass.m.unc p10,p0 = f10, 0x07 nop.i 999 ;;
}
// p13 ln(-)// p14 log(-)
// Log(-inf, -normal, -unnormal) = QNAN indefinite{ .mfi nop.m 999(p8) fclass.m.unc p13,p0 = f10, 0x3a nop.i 999 }{ .mfi nop.m 999(p7) fclass.m.unc p14,p0 = f10, 0x3a nop.i 999 ;;
}
.pred.rel "mutex",p9,p10{ .mfi(p9) mov log_GR_tag = 4 (p9) frcpa f8,p11 = f6,f0 nop.i 999}{ .mfi(p10) mov log_GR_tag = 10 (p10) frcpa f8,p12 = f6,f0 nop.i 999 ;;
}
.pred.rel "mutex",p13,p14{ .mfi(p13) mov log_GR_tag = 5 (p13) frcpa f8,p11 = f0,f0 nop.i 999}{ .mfb(p14) mov log_GR_tag = 11 (p14) frcpa f8,p12 = f0,f0 br.cond.sptk __libm_error_region ;;
}.endp log
// Stack operations when calling error support.// (1) (2) (3) (call) (4)// sp -> + psp -> + psp -> + sp -> +// | | | |// | | <- GR_Y R3 ->| <- GR_RESULT | -> f8// | | | |// | <-GR_Y Y2->| Y2 ->| <- GR_Y |// | | | |// | | <- GR_X X1 ->| |// | | | |// sp-64 -> + sp -> + sp -> + +// save ar.pfs save b0 restore gp// save gp restore ar.pfs
.proc __libm_error_region__libm_error_region:.prologue
// (1){ .mfi add GR_Parameter_Y=-32,sp // Parameter 2 value nop.f 0.save ar.pfs,GR_SAVE_PFS mov GR_SAVE_PFS=ar.pfs // Save ar.pfs}{ .mfi.fframe 64 add sp=-64,sp // Create new stack nop.f 0 mov GR_SAVE_GP=gp // Save gp};;
// (2){ .mmi stfs [GR_Parameter_Y] = f1,16 // STORE Parameter 2 on stack add GR_Parameter_X = 16,sp // Parameter 1 address.save b0, GR_SAVE_B0 mov GR_SAVE_B0=b0 // Save b0};;
.body// (3){ .mib stfs [GR_Parameter_X] = f10 // STORE Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address nop.b 0 }{ .mib stfs [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack add GR_Parameter_Y = -16,GR_Parameter_Y br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi nop.m 0 nop.m 0 add GR_Parameter_RESULT = 48,sp};;
// (4){ .mmi ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack.restore add sp = 64,sp // Restore stack pointer mov b0 = GR_SAVE_B0 // Restore return address};;
{ .mib mov gp = GR_SAVE_GP // Restore gp mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs br.ret.sptk b0 // Return};;
.endp __libm_error_region
.type __libm_error_support#,@function
.global __libm_error_support#
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