.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. // // 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://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 #include "libm_support.h" // Assembly macros //============================================================== log_int_Nfloat = f9 log_Nfloat = f10 log_P3 = f11 log_P2 = f12 log_P1 = f13 log_inv_ln10 = f14 log_log2 = f15 log_w = f32 log_T = f33 log_rp_p32 = f34 log_rp_p2 = f35 log_rp_p10 = f36 log_rsq = f37 log_T_plus_Nlog2 = f38 log_r = f39 log_C = f40 log_rp_q32 = f41 log_rp_q2 = f42 log_rp_q10 = f43 log_wsq = f44 log_Q = f45 log_inv_ln10 = f46 log_NORM_f8 = f47 // =================================== log_GR_exp_17_ones = r33 log_GR_exp_16_ones = r34 log_GR_exp_f8 = r35 log_GR_signexp_f8 = r36 log_GR_true_exp_f8 = r37 log_GR_significand_f8 = r38 log_GR_index = r39 log_AD_1 = r40 log_GR_signexp_w = r41 log_GR_fff7 = r42 log_AD_2 = r43 log_GR_exp_w = r44 GR_SAVE_B0 = r45 GR_SAVE_GP = r46 GR_SAVE_PFS = r47 GR_Parameter_X = r48 GR_Parameter_Y = r49 GR_Parameter_RESULT = r50 log_GR_tag = r51 // Data tables //============================================================== #ifdef _LIBC .rodata #else .data #endif .align 16 log_table_1: ASM_TYPE_DIRECTIVE(log_table_1,@object) data8 0xbfd0001008f39d59 // p3 data8 0x3fd5556073e0c45a // p2 ASM_SIZE_DIRECTIVE(log_table_1) log_table_2: ASM_TYPE_DIRECTIVE(log_table_2,@object) data8 0xbfdffffffffaea15 // p1 data8 0x3fdbcb7b1526e50e // 1/ln10 data8 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) ASM_SIZE_DIRECTIVE(log_table_2) .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: #ifdef _LIBC .global __ieee754_log10f .type __ieee754_log10f,@function __ieee754_log10f: #endif { .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 L(LOG_LOG10_X) } ;; .endp log10f ASM_SIZE_DIRECTIVE(log10f) ASM_SIZE_DIRECTIVE(__ieee754_log10f) .section .text .proc logf# .align 32 logf: #ifdef _LIBC .global __ieee754_logf .type __ieee754_logf,@function __ieee754_logf: #endif { .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 } ;; L(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 L(LOG_DENORM) } ;; L(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 L(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 L(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 ;; } L(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 L(LOG_COMMON) } ;; L(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 logf ASM_SIZE_DIRECTIVE(logf) ASM_SIZE_DIRECTIVE(__ieee754_logf) // 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 sp 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 ASM_SIZE_DIRECTIVE(__libm_error_region) .type __libm_error_support#,@function .global __libm_error_support#