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.file "log.s"
// Copyright (c) 2000, 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//==============================================================// 2/02/00 Initial version// 4/04/00 Unwind support added// 6/16/00 Updated table to be rounded correctly// 8/15/00 Bundle added after call to __libm_error_support to properly// set [the previously overwritten] GR_Parameter_RESULT.// 8/17/00 Improved speed of main path by 5 cycles// Shortened path for x=1.0////// API//==============================================================// double log(double)// double log10(double)//// 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//===============// input = x// C = frcpa(x)// r = C * x - 1//// Form the series P1 + P2 * x + P_3 * x^2 + P_4 * X^3 + P_5 * x^4// P_series = r(r(r(r * P5 +P4) + P3) + P2) + P1
// 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
// Yhi = (T + Nfloat * log(2)) + r
// answer = P_series * r*r + Yhi
// 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-extended
// 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 Idefinite
// log(+inf) = +inf
// Registers used//==============================================================// Floating Point registers used: // f8, input// f9 -> f15, f32 -> f68
// General registers used: // r32 -> r54
// Predicate registers used:// p6 -> p14
// 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_P5 = f11 log_P4 = f12 log_P3 = f13 log_P2 = f14 log_P1 = f15
log_log2 = f32 log_T = f33
log_rp_p4 = f34 log_rp_p3 = f35 log_rp_p2 = f36 log_pseries = f37
log_rsq = f40
log_T_plus_Nlog2 = f41 log_Yhi = f42
log_r = f43log_C = f44
log_w = f45log_Q8 = f46log_Q7 = f47log_Q3 = f48log_Q4 = f49 log_Q6 = f50 log_Q2 = f51log_Q5 = f52log_Q1 = f53
log_rp_q7 = f54 log_rp_q6 = f55log_Qlo = f56
log_rp_q3 = f57log_rp_q2 = f58log_Qhi = f59
log_wsq = f60log_w4 = f61log_Q = f62
log_inv_ln10 = f63log_log10_hi = f64log_log10_lo = f65
log_neg_one = f66log_NORM_f8 = f67log_r2P_r = f68
// ===================================
log_GR_exp_17_ones = r33log_GR_exp_16_ones = r34log_GR_exp_f8 = r35log_GR_signexp_f8 = r36log_GR_true_exp_f8 = r37
log_GR_significand_f8 = r38
log_GR_sig_no_explicit = r39log_GR_sig_f1f8 = r39log_GR_sig_f1f8_times_16 = r39
log_GR_AD_p_table = r40
log_GR_signexp_w = r41log_GR_fff9 = r42
//////////////////////////////////////////////////////////////log_GR_AD_q_table = r43log_GR_AD_inv_ln_10 = r44// r45 unusedlog_GR_exp_w = r46// r47 is unused
GR_SAVE_B0 = r48GR_SAVE_GP = r49GR_SAVE_PFS = r50
GR_Parameter_X = r51GR_Parameter_Y = r52GR_Parameter_RESULT = r53log_GR_tag = r54
// Data tables//==============================================================
.data
.align 16
log_q_table:data8 0x3FBC756AC654273B // Q8data8 0xBFC001A42489AB4D // Q7data8 0xBFD00000000019AC // Q3data8 0x3FC99999999A169B // Q4data8 0x3FC2492479AA0DF8 // Q6data8 0x3FD5555555555555 // Q2data8 0xBFC5555544986F52 // Q5data8 0xBFE0000000000000 // Q1
log_p_table:data8 0xBFC5555DA7212371 // P5data8 0x3FC999A19EEF5826 // P4data8 0xBFCFFFFFFFFEF009 // P3data8 0x3FD555555554ECB2 // P2data8 0xBFE0000000000000 // P1data8 0x0000000000000000 // pad so that dxt values on on 16 byte boundaries
data8 0xde5bd8a937287195, 0x00003ffd // double-extended 1/ln(10)data8 0xb17217f7d1cf79ac, 0x00003ffe // log2// b17217f7d1cf79ab c9e3b39803f2f6a
data8 0x80200aaeac44ef38 , 0x00003ff6 // log(1/frcpa(1+ 0/2^-8))
data8 0xc09090a2c35aa070 , 0x00003ff7 // log(1/frcpa(1+ 1/2^-8))data8 0xa0c94fcb41977c75 , 0x00003ff8 // log(1/frcpa(1+ 2/2^-8))data8 0xe18b9c263af83301 , 0x00003ff8 // log(1/frcpa(1+ 3/2^-8))data8 0x8d35c8d6399c30ea , 0x00003ff9 // log(1/frcpa(1+ 4/2^-8))data8 0xadd4d2ecd601cbb8 , 0x00003ff9 // log(1/frcpa(1+ 5/2^-8))
data8 0xce95403a192f9f01 , 0x00003ff9 // log(1/frcpa(1+ 6/2^-8))data8 0xeb59392cbcc01096 , 0x00003ff9 // log(1/frcpa(1+ 7/2^-8))data8 0x862c7d0cefd54c5d , 0x00003ffa // log(1/frcpa(1+ 8/2^-8))data8 0x94aa63c65e70d499 , 0x00003ffa // log(1/frcpa(1+ 9/2^-8))data8 0xa54a696d4b62b382 , 0x00003ffa // log(1/frcpa(1+ 10/2^-8))
data8 0xb3e4a796a5dac208 , 0x00003ffa // log(1/frcpa(1+ 11/2^-8))data8 0xc28c45b1878340a9 , 0x00003ffa // log(1/frcpa(1+ 12/2^-8))data8 0xd35c55f39d7a6235 , 0x00003ffa // log(1/frcpa(1+ 13/2^-8))data8 0xe220f037b954f1f5 , 0x00003ffa // log(1/frcpa(1+ 14/2^-8))data8 0xf0f3389b036834f3 , 0x00003ffa // log(1/frcpa(1+ 15/2^-8))
data8 0xffd3488d5c980465 , 0x00003ffa // log(1/frcpa(1+ 16/2^-8))data8 0x87609ce2ed300490 , 0x00003ffb // log(1/frcpa(1+ 17/2^-8))data8 0x8ede9321e8c85927 , 0x00003ffb // log(1/frcpa(1+ 18/2^-8))data8 0x96639427f2f8e2f4 , 0x00003ffb // log(1/frcpa(1+ 19/2^-8))data8 0x9defad3e8f73217b , 0x00003ffb // log(1/frcpa(1+ 20/2^-8))
data8 0xa582ebd50097029c , 0x00003ffb // log(1/frcpa(1+ 21/2^-8))data8 0xac06dbe75ab80fee , 0x00003ffb // log(1/frcpa(1+ 22/2^-8))data8 0xb3a78449b2d3ccca , 0x00003ffb // log(1/frcpa(1+ 23/2^-8))data8 0xbb4f79635ab46bb2 , 0x00003ffb // log(1/frcpa(1+ 24/2^-8))data8 0xc2fec93a83523f3f , 0x00003ffb // log(1/frcpa(1+ 25/2^-8))
data8 0xc99af2eaca4c4571 , 0x00003ffb // log(1/frcpa(1+ 26/2^-8))data8 0xd1581106472fa653 , 0x00003ffb // log(1/frcpa(1+ 27/2^-8))data8 0xd8002560d4355f2e , 0x00003ffb // log(1/frcpa(1+ 28/2^-8))data8 0xdfcb43b4fe508632 , 0x00003ffb // log(1/frcpa(1+ 29/2^-8))data8 0xe67f6dff709d4119 , 0x00003ffb // log(1/frcpa(1+ 30/2^-8))
data8 0xed393b1c22351280 , 0x00003ffb // log(1/frcpa(1+ 31/2^-8))data8 0xf5192bff087bcc35 , 0x00003ffb // log(1/frcpa(1+ 32/2^-8))data8 0xfbdf4ff6dfef2fa3 , 0x00003ffb // log(1/frcpa(1+ 33/2^-8))data8 0x81559a97f92f9cc7 , 0x00003ffc // log(1/frcpa(1+ 34/2^-8))data8 0x84be72bce90266e8 , 0x00003ffc // log(1/frcpa(1+ 35/2^-8))
data8 0x88bc74113f23def2 , 0x00003ffc // log(1/frcpa(1+ 36/2^-8))data8 0x8c2ba3edf6799d11 , 0x00003ffc // log(1/frcpa(1+ 37/2^-8))data8 0x8f9dc92f92ea08b1 , 0x00003ffc // log(1/frcpa(1+ 38/2^-8))data8 0x9312e8f36efab5a7 , 0x00003ffc // log(1/frcpa(1+ 39/2^-8))data8 0x968b08643409ceb6 , 0x00003ffc // log(1/frcpa(1+ 40/2^-8))
data8 0x9a062cba08a1708c , 0x00003ffc // log(1/frcpa(1+ 41/2^-8))data8 0x9d845b3abf95485c , 0x00003ffc // log(1/frcpa(1+ 42/2^-8))data8 0xa06fd841bc001bb4 , 0x00003ffc // log(1/frcpa(1+ 43/2^-8))data8 0xa3f3a74652fbe0db , 0x00003ffc // log(1/frcpa(1+ 44/2^-8))data8 0xa77a8fb2336f20f5 , 0x00003ffc // log(1/frcpa(1+ 45/2^-8))
data8 0xab0497015d28b0a0 , 0x00003ffc // log(1/frcpa(1+ 46/2^-8))data8 0xae91c2be6ba6a615 , 0x00003ffc // log(1/frcpa(1+ 47/2^-8))data8 0xb189d1b99aebb20b , 0x00003ffc // log(1/frcpa(1+ 48/2^-8))data8 0xb51cced5de9c1b2c , 0x00003ffc // log(1/frcpa(1+ 49/2^-8))data8 0xb819bee9e720d42f , 0x00003ffc // log(1/frcpa(1+ 50/2^-8))
data8 0xbbb2a0947b093a5d , 0x00003ffc // log(1/frcpa(1+ 51/2^-8))data8 0xbf4ec1505811684a , 0x00003ffc // log(1/frcpa(1+ 52/2^-8))data8 0xc2535bacfa8975ff , 0x00003ffc // log(1/frcpa(1+ 53/2^-8))data8 0xc55a3eafad187eb8 , 0x00003ffc // log(1/frcpa(1+ 54/2^-8))data8 0xc8ff2484b2c0da74 , 0x00003ffc // log(1/frcpa(1+ 55/2^-8))
data8 0xcc0b1a008d53ab76 , 0x00003ffc // log(1/frcpa(1+ 56/2^-8))data8 0xcfb6203844b3209b , 0x00003ffc // log(1/frcpa(1+ 57/2^-8))data8 0xd2c73949a47a19f5 , 0x00003ffc // log(1/frcpa(1+ 58/2^-8))data8 0xd5daae18b49d6695 , 0x00003ffc // log(1/frcpa(1+ 59/2^-8))data8 0xd8f08248cf7e8019 , 0x00003ffc // log(1/frcpa(1+ 60/2^-8))
data8 0xdca7749f1b3e540e , 0x00003ffc // log(1/frcpa(1+ 61/2^-8))data8 0xdfc28e033aaaf7c7 , 0x00003ffc // log(1/frcpa(1+ 62/2^-8))data8 0xe2e012a5f91d2f55 , 0x00003ffc // log(1/frcpa(1+ 63/2^-8))data8 0xe600064ed9e292a8 , 0x00003ffc // log(1/frcpa(1+ 64/2^-8))data8 0xe9226cce42b39f60 , 0x00003ffc // log(1/frcpa(1+ 65/2^-8))
data8 0xec4749fd97a28360 , 0x00003ffc // log(1/frcpa(1+ 66/2^-8))data8 0xef6ea1bf57780495 , 0x00003ffc // log(1/frcpa(1+ 67/2^-8))data8 0xf29877ff38809091 , 0x00003ffc // log(1/frcpa(1+ 68/2^-8))data8 0xf5c4d0b245cb89be , 0x00003ffc // log(1/frcpa(1+ 69/2^-8))data8 0xf8f3afd6fcdef3aa , 0x00003ffc // log(1/frcpa(1+ 70/2^-8))
data8 0xfc2519756be1abc7 , 0x00003ffc // log(1/frcpa(1+ 71/2^-8))data8 0xff59119f503e6832 , 0x00003ffc // log(1/frcpa(1+ 72/2^-8))data8 0x8147ce381ae0e146 , 0x00003ffd // log(1/frcpa(1+ 73/2^-8))data8 0x82e45f06cb1ad0f2 , 0x00003ffd // log(1/frcpa(1+ 74/2^-8))data8 0x842f5c7c573cbaa2 , 0x00003ffd // log(1/frcpa(1+ 75/2^-8))
data8 0x85ce471968c8893a , 0x00003ffd // log(1/frcpa(1+ 76/2^-8))data8 0x876e8305bc04066d , 0x00003ffd // log(1/frcpa(1+ 77/2^-8))data8 0x891012678031fbb3 , 0x00003ffd // log(1/frcpa(1+ 78/2^-8))data8 0x8a5f1493d766a05f , 0x00003ffd // log(1/frcpa(1+ 79/2^-8))data8 0x8c030c778c56fa00 , 0x00003ffd // log(1/frcpa(1+ 80/2^-8))
data8 0x8da85df17e31d9ae , 0x00003ffd // log(1/frcpa(1+ 81/2^-8))data8 0x8efa663e7921687e , 0x00003ffd // log(1/frcpa(1+ 82/2^-8))data8 0x90a22b6875c6a1f8 , 0x00003ffd // log(1/frcpa(1+ 83/2^-8))data8 0x91f62cc8f5d24837 , 0x00003ffd // log(1/frcpa(1+ 84/2^-8))data8 0x93a06cfc3857d980 , 0x00003ffd // log(1/frcpa(1+ 85/2^-8))
data8 0x94f66d5e6fd01ced , 0x00003ffd // log(1/frcpa(1+ 86/2^-8))data8 0x96a330156e6772f2 , 0x00003ffd // log(1/frcpa(1+ 87/2^-8))data8 0x97fb3582754ea25b , 0x00003ffd // log(1/frcpa(1+ 88/2^-8))data8 0x99aa8259aad1bbf2 , 0x00003ffd // log(1/frcpa(1+ 89/2^-8))data8 0x9b0492f6227ae4a8 , 0x00003ffd // log(1/frcpa(1+ 90/2^-8))
data8 0x9c5f8e199bf3a7a5 , 0x00003ffd // log(1/frcpa(1+ 91/2^-8))data8 0x9e1293b9998c1daa , 0x00003ffd // log(1/frcpa(1+ 92/2^-8))data8 0x9f6fa31e0b41f308 , 0x00003ffd // log(1/frcpa(1+ 93/2^-8))data8 0xa0cda11eaf46390e , 0x00003ffd // log(1/frcpa(1+ 94/2^-8))data8 0xa22c8f029cfa45aa , 0x00003ffd // log(1/frcpa(1+ 95/2^-8))
data8 0xa3e48badb7856b34 , 0x00003ffd // log(1/frcpa(1+ 96/2^-8))data8 0xa5459a0aa95849f9 , 0x00003ffd // log(1/frcpa(1+ 97/2^-8))data8 0xa6a79c84480cfebd , 0x00003ffd // log(1/frcpa(1+ 98/2^-8))data8 0xa80a946d0fcb3eb2 , 0x00003ffd // log(1/frcpa(1+ 99/2^-8))data8 0xa96e831a3ea7b314 , 0x00003ffd // log(1/frcpa(1+100/2^-8))
data8 0xaad369e3dc544e3b , 0x00003ffd // log(1/frcpa(1+101/2^-8))data8 0xac92e9588952c815 , 0x00003ffd // log(1/frcpa(1+102/2^-8))data8 0xadfa035aa1ed8fdc , 0x00003ffd // log(1/frcpa(1+103/2^-8))data8 0xaf6219eae1ad6e34 , 0x00003ffd // log(1/frcpa(1+104/2^-8))data8 0xb0cb2e6d8160f753 , 0x00003ffd // log(1/frcpa(1+105/2^-8))
data8 0xb2354249ad950f72 , 0x00003ffd // log(1/frcpa(1+106/2^-8))data8 0xb3a056e98ef4a3b4 , 0x00003ffd // log(1/frcpa(1+107/2^-8))data8 0xb50c6dba52c6292a , 0x00003ffd // log(1/frcpa(1+108/2^-8))data8 0xb679882c33876165 , 0x00003ffd // log(1/frcpa(1+109/2^-8))data8 0xb78c07429785cedc , 0x00003ffd // log(1/frcpa(1+110/2^-8))
data8 0xb8faeb8dc4a77d24 , 0x00003ffd // log(1/frcpa(1+111/2^-8))data8 0xba6ad77eb36ae0d6 , 0x00003ffd // log(1/frcpa(1+112/2^-8))data8 0xbbdbcc915e9bee50 , 0x00003ffd // log(1/frcpa(1+113/2^-8))data8 0xbd4dcc44f8cf12ef , 0x00003ffd // log(1/frcpa(1+114/2^-8))data8 0xbec0d81bf5b531fa , 0x00003ffd // log(1/frcpa(1+115/2^-8))
data8 0xc034f19c139186f4 , 0x00003ffd // log(1/frcpa(1+116/2^-8))data8 0xc14cb69f7c5e55ab , 0x00003ffd // log(1/frcpa(1+117/2^-8))data8 0xc2c2abbb6e5fd56f , 0x00003ffd // log(1/frcpa(1+118/2^-8))data8 0xc439b2c193e6771e , 0x00003ffd // log(1/frcpa(1+119/2^-8))data8 0xc553acb9d5c67733 , 0x00003ffd // log(1/frcpa(1+120/2^-8))
data8 0xc6cc96e441272441 , 0x00003ffd // log(1/frcpa(1+121/2^-8))data8 0xc8469753eca88c30 , 0x00003ffd // log(1/frcpa(1+122/2^-8))data8 0xc962cf3ce072b05c , 0x00003ffd // log(1/frcpa(1+123/2^-8))data8 0xcadeba8771f694aa , 0x00003ffd // log(1/frcpa(1+124/2^-8))data8 0xcc5bc08d1f72da94 , 0x00003ffd // log(1/frcpa(1+125/2^-8))
data8 0xcd7a3f99ea035c29 , 0x00003ffd // log(1/frcpa(1+126/2^-8))data8 0xcef93860c8a53c35 , 0x00003ffd // log(1/frcpa(1+127/2^-8))data8 0xd0192f68a7ed23df , 0x00003ffd // log(1/frcpa(1+128/2^-8))data8 0xd19a201127d3c645 , 0x00003ffd // log(1/frcpa(1+129/2^-8))data8 0xd2bb92f4061c172c , 0x00003ffd // log(1/frcpa(1+130/2^-8))
data8 0xd43e80b2ee8cc8fc , 0x00003ffd // log(1/frcpa(1+131/2^-8))data8 0xd56173601fc4ade4 , 0x00003ffd // log(1/frcpa(1+132/2^-8))data8 0xd6e6637efb54086f , 0x00003ffd // log(1/frcpa(1+133/2^-8))data8 0xd80ad9f58f3c8193 , 0x00003ffd // log(1/frcpa(1+134/2^-8))data8 0xd991d1d31aca41f8 , 0x00003ffd // log(1/frcpa(1+135/2^-8))
data8 0xdab7d02231484a93 , 0x00003ffd // log(1/frcpa(1+136/2^-8))data8 0xdc40d532cde49a54 , 0x00003ffd // log(1/frcpa(1+137/2^-8))data8 0xdd685f79ed8b265e , 0x00003ffd // log(1/frcpa(1+138/2^-8))data8 0xde9094bbc0e17b1d , 0x00003ffd // log(1/frcpa(1+139/2^-8))data8 0xe01c91b78440c425 , 0x00003ffd // log(1/frcpa(1+140/2^-8))
data8 0xe14658f26997e729 , 0x00003ffd // log(1/frcpa(1+141/2^-8))data8 0xe270cdc2391e0d23 , 0x00003ffd // log(1/frcpa(1+142/2^-8))data8 0xe3ffce3a2aa64922 , 0x00003ffd // log(1/frcpa(1+143/2^-8))data8 0xe52bdb274ed82887 , 0x00003ffd // log(1/frcpa(1+144/2^-8))data8 0xe6589852e75d7df6 , 0x00003ffd // log(1/frcpa(1+145/2^-8))
data8 0xe786068c79937a7d , 0x00003ffd // log(1/frcpa(1+146/2^-8))data8 0xe91903adad100911 , 0x00003ffd // log(1/frcpa(1+147/2^-8))data8 0xea481236f7d35bb0 , 0x00003ffd // log(1/frcpa(1+148/2^-8))data8 0xeb77d48c692e6b14 , 0x00003ffd // log(1/frcpa(1+149/2^-8))data8 0xeca84b83d7297b87 , 0x00003ffd // log(1/frcpa(1+150/2^-8))
data8 0xedd977f4962aa158 , 0x00003ffd // log(1/frcpa(1+151/2^-8))data8 0xef7179a22f257754 , 0x00003ffd // log(1/frcpa(1+152/2^-8))data8 0xf0a450d139366ca7 , 0x00003ffd // log(1/frcpa(1+153/2^-8))data8 0xf1d7e0524ff9ffdb , 0x00003ffd // log(1/frcpa(1+154/2^-8))data8 0xf30c29036a8b6cae , 0x00003ffd // log(1/frcpa(1+155/2^-8))
data8 0xf4412bc411ea8d92 , 0x00003ffd // log(1/frcpa(1+156/2^-8))data8 0xf576e97564c8619d , 0x00003ffd // log(1/frcpa(1+157/2^-8))data8 0xf6ad62fa1b5f172f , 0x00003ffd // log(1/frcpa(1+158/2^-8))data8 0xf7e499368b55c542 , 0x00003ffd // log(1/frcpa(1+159/2^-8))data8 0xf91c8d10abaffe22 , 0x00003ffd // log(1/frcpa(1+160/2^-8))
data8 0xfa553f7018c966f3 , 0x00003ffd // log(1/frcpa(1+161/2^-8))data8 0xfb8eb13e185d802c , 0x00003ffd // log(1/frcpa(1+162/2^-8))data8 0xfcc8e3659d9bcbed , 0x00003ffd // log(1/frcpa(1+163/2^-8))data8 0xfe03d6d34d487fd2 , 0x00003ffd // log(1/frcpa(1+164/2^-8))data8 0xff3f8c7581e9f0ae , 0x00003ffd // log(1/frcpa(1+165/2^-8))
data8 0x803e029e280173ae , 0x00003ffe // log(1/frcpa(1+166/2^-8))data8 0x80dca10cc52d0757 , 0x00003ffe // log(1/frcpa(1+167/2^-8))data8 0x817ba200632755a1 , 0x00003ffe // log(1/frcpa(1+168/2^-8))data8 0x821b05f3b01d6774 , 0x00003ffe // log(1/frcpa(1+169/2^-8))data8 0x82bacd623ff19d06 , 0x00003ffe // log(1/frcpa(1+170/2^-8))
data8 0x835af8c88e7a8f47 , 0x00003ffe // log(1/frcpa(1+171/2^-8))data8 0x83c5f8299e2b4091 , 0x00003ffe // log(1/frcpa(1+172/2^-8))data8 0x8466cb43f3d87300 , 0x00003ffe // log(1/frcpa(1+173/2^-8))data8 0x850803a67c80ca4b , 0x00003ffe // log(1/frcpa(1+174/2^-8))data8 0x85a9a1d11a23b461 , 0x00003ffe // log(1/frcpa(1+175/2^-8))
data8 0x864ba644a18e6e05 , 0x00003ffe // log(1/frcpa(1+176/2^-8))data8 0x86ee1182dcc432f7 , 0x00003ffe // log(1/frcpa(1+177/2^-8))data8 0x875a925d7e48c316 , 0x00003ffe // log(1/frcpa(1+178/2^-8))data8 0x87fdaa109d23aef7 , 0x00003ffe // log(1/frcpa(1+179/2^-8))data8 0x88a129ed4becfaf2 , 0x00003ffe // log(1/frcpa(1+180/2^-8))
data8 0x89451278ecd7f9cf , 0x00003ffe // log(1/frcpa(1+181/2^-8))data8 0x89b29295f8432617 , 0x00003ffe // log(1/frcpa(1+182/2^-8))data8 0x8a572ac5a5496882 , 0x00003ffe // log(1/frcpa(1+183/2^-8))data8 0x8afc2d0ce3b2dadf , 0x00003ffe // log(1/frcpa(1+184/2^-8))data8 0x8b6a69c608cfd3af , 0x00003ffe // log(1/frcpa(1+185/2^-8))
data8 0x8c101e106e899a83 , 0x00003ffe // log(1/frcpa(1+186/2^-8))data8 0x8cb63de258f9d626 , 0x00003ffe // log(1/frcpa(1+187/2^-8))data8 0x8d2539c5bd19e2b1 , 0x00003ffe // log(1/frcpa(1+188/2^-8))data8 0x8dcc0e064b29e6f1 , 0x00003ffe // log(1/frcpa(1+189/2^-8))data8 0x8e734f45d88357ae , 0x00003ffe // log(1/frcpa(1+190/2^-8))
data8 0x8ee30cef034a20db , 0x00003ffe // log(1/frcpa(1+191/2^-8))data8 0x8f8b0515686d1d06 , 0x00003ffe // log(1/frcpa(1+192/2^-8))data8 0x90336bba039bf32f , 0x00003ffe // log(1/frcpa(1+193/2^-8))data8 0x90a3edd23d1c9d58 , 0x00003ffe // log(1/frcpa(1+194/2^-8))data8 0x914d0de2f5d61b32 , 0x00003ffe // log(1/frcpa(1+195/2^-8))
data8 0x91be0c20d28173b5 , 0x00003ffe // log(1/frcpa(1+196/2^-8))data8 0x9267e737c06cd34a , 0x00003ffe // log(1/frcpa(1+197/2^-8))data8 0x92d962ae6abb1237 , 0x00003ffe // log(1/frcpa(1+198/2^-8))data8 0x9383fa6afbe2074c , 0x00003ffe // log(1/frcpa(1+199/2^-8))data8 0x942f0421651c1c4e , 0x00003ffe // log(1/frcpa(1+200/2^-8))
data8 0x94a14a3845bb985e , 0x00003ffe // log(1/frcpa(1+201/2^-8))data8 0x954d133857f861e7 , 0x00003ffe // log(1/frcpa(1+202/2^-8))data8 0x95bfd96468e604c4 , 0x00003ffe // log(1/frcpa(1+203/2^-8))data8 0x9632d31cafafa858 , 0x00003ffe // log(1/frcpa(1+204/2^-8))data8 0x96dfaabd86fa1647 , 0x00003ffe // log(1/frcpa(1+205/2^-8))
data8 0x9753261fcbb2a594 , 0x00003ffe // log(1/frcpa(1+206/2^-8))data8 0x9800c11b426b996d , 0x00003ffe // log(1/frcpa(1+207/2^-8))data8 0x9874bf4d45ae663c , 0x00003ffe // log(1/frcpa(1+208/2^-8))data8 0x99231f5ee9a74f79 , 0x00003ffe // log(1/frcpa(1+209/2^-8))data8 0x9997a18a56bcad28 , 0x00003ffe // log(1/frcpa(1+210/2^-8))
data8 0x9a46c873a3267e79 , 0x00003ffe // log(1/frcpa(1+211/2^-8))data8 0x9abbcfc621eb6cb6 , 0x00003ffe // log(1/frcpa(1+212/2^-8))data8 0x9b310cb0d354c990 , 0x00003ffe // log(1/frcpa(1+213/2^-8))data8 0x9be14cf9e1b3515c , 0x00003ffe // log(1/frcpa(1+214/2^-8))data8 0x9c5710b8cbb73a43 , 0x00003ffe // log(1/frcpa(1+215/2^-8))
data8 0x9ccd0abd301f399c , 0x00003ffe // log(1/frcpa(1+216/2^-8))data8 0x9d7e67f3bdce8888 , 0x00003ffe // log(1/frcpa(1+217/2^-8))data8 0x9df4ea81a99daa01 , 0x00003ffe // log(1/frcpa(1+218/2^-8))data8 0x9e6ba405a54514ba , 0x00003ffe // log(1/frcpa(1+219/2^-8))data8 0x9f1e21c8c7bb62b3 , 0x00003ffe // log(1/frcpa(1+220/2^-8))
data8 0x9f956593f6b6355c , 0x00003ffe // log(1/frcpa(1+221/2^-8))data8 0xa00ce1092e5498c3 , 0x00003ffe // log(1/frcpa(1+222/2^-8))data8 0xa0c08309c4b912c1 , 0x00003ffe // log(1/frcpa(1+223/2^-8))data8 0xa1388a8c6faa2afa , 0x00003ffe // log(1/frcpa(1+224/2^-8))data8 0xa1b0ca7095b5f985 , 0x00003ffe // log(1/frcpa(1+225/2^-8))
data8 0xa22942eb47534a00 , 0x00003ffe // log(1/frcpa(1+226/2^-8))data8 0xa2de62326449d0a3 , 0x00003ffe // log(1/frcpa(1+227/2^-8))data8 0xa357690f88bfe345 , 0x00003ffe // log(1/frcpa(1+228/2^-8))data8 0xa3d0a93f45169a4b , 0x00003ffe // log(1/frcpa(1+229/2^-8))data8 0xa44a22f7ffe65f30 , 0x00003ffe // log(1/frcpa(1+230/2^-8))
data8 0xa500c5e5b4c1aa36 , 0x00003ffe // log(1/frcpa(1+231/2^-8))data8 0xa57ad064eb2ebbc2 , 0x00003ffe // log(1/frcpa(1+232/2^-8))data8 0xa5f5152dedf4384e , 0x00003ffe // log(1/frcpa(1+233/2^-8))data8 0xa66f9478856233ec , 0x00003ffe // log(1/frcpa(1+234/2^-8))data8 0xa6ea4e7cca02c32e , 0x00003ffe // log(1/frcpa(1+235/2^-8))
data8 0xa765437325341ccf , 0x00003ffe // log(1/frcpa(1+236/2^-8))data8 0xa81e21e6c75b4020 , 0x00003ffe // log(1/frcpa(1+237/2^-8))data8 0xa899ab333fe2b9ca , 0x00003ffe // log(1/frcpa(1+238/2^-8))data8 0xa9157039c51ebe71 , 0x00003ffe // log(1/frcpa(1+239/2^-8))data8 0xa991713433c2b999 , 0x00003ffe // log(1/frcpa(1+240/2^-8))
data8 0xaa0dae5cbcc048b3 , 0x00003ffe // log(1/frcpa(1+241/2^-8))data8 0xaa8a27ede5eb13ad , 0x00003ffe // log(1/frcpa(1+242/2^-8))data8 0xab06de228a9e3499 , 0x00003ffe // log(1/frcpa(1+243/2^-8))data8 0xab83d135dc633301 , 0x00003ffe // log(1/frcpa(1+244/2^-8))data8 0xac3fb076adc7fe7a , 0x00003ffe // log(1/frcpa(1+245/2^-8))
data8 0xacbd3cbbe47988f1 , 0x00003ffe // log(1/frcpa(1+246/2^-8))data8 0xad3b06b1a5dc57c3 , 0x00003ffe // log(1/frcpa(1+247/2^-8))data8 0xadb90e94af887717 , 0x00003ffe // log(1/frcpa(1+248/2^-8))data8 0xae3754a218f7c816 , 0x00003ffe // log(1/frcpa(1+249/2^-8))data8 0xaeb5d9175437afa2 , 0x00003ffe // log(1/frcpa(1+250/2^-8))
data8 0xaf349c322e9c7cee , 0x00003ffe // log(1/frcpa(1+251/2^-8))data8 0xafb39e30d1768d1c , 0x00003ffe // log(1/frcpa(1+252/2^-8))data8 0xb032df51c2c93116 , 0x00003ffe // log(1/frcpa(1+253/2^-8))data8 0xb0b25fd3e6035ad9 , 0x00003ffe // log(1/frcpa(1+254/2^-8))data8 0xb1321ff67cba178c , 0x00003ffe // log(1/frcpa(1+255/2^-8))
.align 32.global log#
.global log10#
// log10 has p7 true, p8 false// log has p8 true, p7 false
.section .text.proc log10#
.align 32
log10: { .mfi alloc r32=ar.pfs,1,18,4,0 (p0) frcpa.s1 log_C,p9 = f1,f8 (p0) cmp.eq.unc p7,p8 = r0, r0 }{ .mfb(p0) addl r40 = @ltoff(log_p_table), gp(p0) fnorm log_NORM_f8 = f8 (p0) br.sptk LOG_LN_X };;
.endp log10
.section .text.proc log#
.align 32log:
{ .mfi alloc r32=ar.pfs,1,18,4,0 (p0) frcpa.s1 log_C,p9 = f1,f8 (p0) cmp.eq.unc p8,p7 = r0, r0 }{ .mfi(p0) addl r40 = @ltoff(log_p_table), gp(p0) fnorm log_NORM_f8 = f8 nop.i 999};;
LOG_LN_X:
{ .mmf(p0) addl r43 = @ltoff(log_q_table), gp ld8 r40 = [r40](p0) fms.s1 log_w = f8,f1,f1 };;
{ .mmi ld8 r43 = [r43](p0) mov log_GR_exp_16_ones = 0xffff(p0) mov log_GR_exp_17_ones = 0x1ffff};;
{.mfi(p0) ldfpd log_P5,log_P4 = [r40],16 nop.f 999(p0) mov log_GR_fff9 = 0xfff9 ;;
}
{ .mmi(p0) ldfpd log_Q8,log_Q7 = [r43],16 nop.m 999 nop.i 999 ;;
}
{ .mmi(p0) ldfpd log_Q3,log_Q4 = [r43],16 (p0) ldfd log_P3 = [r40],8 nop.i 999 ;;
}
{ .mmf(p0) ldfd log_Q6 = [r43],8 (p0) ldfd log_P2 = [r40],8 (p0) fms.s1 log_r = log_C,f8,f1 ;;
}
{ .mmf(p0) ldfd log_Q2 = [r43],8(p0) ldfd log_P1 = [r40],16 (p0) fma.s1 log_wsq = log_w, log_w, f0;;
}
{ .mmi(p0) getf.sig log_GR_significand_f8 = log_NORM_f8 (p0) ldfe log_inv_ln10 = [r40],16 nop.i 999 ;;
}
{ .mmf(p0) getf.exp log_GR_signexp_f8 = log_NORM_f8 (p0) ldfd log_Q5 = [r43],8 (p0) fcmp.eq.s1 p10,p0 = log_NORM_f8, f1;;
}
{ .mmf(p0) getf.exp log_GR_signexp_w = log_w(p0) ldfe log_log2 = [r40],16 (p0) fclass.m.unc p6,p0 = f8, 0xa7 ;;
}
{ .mfi(p0) ldfd log_Q1 = [r43],16 (p0) fclass.m.unc p12,p0 = f8, 0x1a (p0) shl r39 = log_GR_significand_f8,1 }{ .mfi nop.m 999(p0) fma.s1 log_rsq = log_r, log_r, f0 (p0) and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones ;;
}
{ .mfi(p0) sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones (p0) fma.s1 log_rp_p4 = log_P5, log_r, log_P4 // u1 (p0) shr.u r39 = r39,56 }{ .mfi nop.m 999(p0) fma.s1 log_w4 = log_wsq, log_wsq, f0(p0) and log_GR_exp_w = log_GR_exp_17_ones, log_GR_signexp_w ;;
}
{ .mfi nop.m 999(p0) fma.s1 log_rp_q7 = log_Q8, log_w, log_Q7 // v1 shl r39 = r39,4 ;;
}
// p13 <== Large W ln// p14 <== small w ln{ .mfi(p0) setf.sig log_int_Nfloat = log_GR_true_exp_f8(p10) fmerge.s f8 = f0, f0(p0) add r40 = r39,r40 }{ .mfb(p8) cmp.ge.unc p13,p14 = log_GR_exp_w, log_GR_fff9(p0) fma.s1 log_rp_q3 = log_Q4, log_w, log_Q3 // v2(p10) br.ret.spnt b0 // Exit for x=1.0;;
}
{ .mbb nop.m 999(p6) br.cond.spnt LOG_NAN_ZERO_INF_PN (p12) br.cond.spnt LOG_NAN_ZERO_INF_PN;;
}
{ .mbb(p0) ldfe log_T = [r40] nop.b 999 nop.b 999;;
}
{ .mfi nop.m 999(p0) fma.s1 log_rp_p3 = log_rp_p4, log_r, log_P3 // u2(p7) cmp.ge.unc p10,p11 = log_GR_exp_w, log_GR_fff9 ;;
}
{ .mfi nop.m 999(p0) fma.s1 log_rp_q6 = log_rp_q7, log_w, log_Q6 // v3 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 log_rp_q2 = log_rp_q3, log_w, log_Q2 // v4 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 log_rp_p2 = log_rp_p3, log_r, log_P2 // u3 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 log_Qlo = log_rp_q6, log_w, log_Q5 nop.i 999 }{ .mfi nop.m 999(p0) fcvt.xf log_Nfloat = log_int_Nfloat nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 log_Qhi = log_rp_q2, log_w, log_Q1 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 log_pseries = log_rp_p2, log_r, log_P1 nop.i 999 ;;
}
{ .mfi nop.m 999(p0) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log_log2, log_T nop.i 999}{ .mfi nop.m 999(p0) fma.s1 log_Q = log_Qlo, log_w4, log_Qhi nop.i 999 ;;
}
// small w, ln <== p13// small w, log10 <== p10.pred.rel "mutex",p13,p10{ .mfi nop.m 999(p13) fma.s1 log_r2P_r = log_rsq, log_pseries, log_r nop.i 999 }{ .mfi nop.m 999(p10) fma.s1 log_r2P_r = log_rsq, log_pseries, log_r nop.i 999 ;;
}
// small w, ln <== p14// small w, log10 <== p11.pred.rel "mutex",p14,p11{ .mfi nop.m 999(p14) fma.d f8 = log_wsq, log_Q, log_w nop.i 999 }{ .mfi nop.m 999(p11) fma.s1 f8 = log_wsq, log_Q, log_w nop.i 999 ;;
}
{ .mfi nop.m 999(p10) fma.s1 log_log10_hi = log_T_plus_Nlog2, log_inv_ln10,f0 nop.i 999 ;;
}
// large W, ln <== p13// large Ww, log <== p10.pred.rel "mutex",p13,p10{ .mfi nop.m 999(p13) fadd.d f8 = log_T_plus_Nlog2, log_r2P_r nop.i 999 }{ .mfi nop.m 999(p10) fma.s1 log_log10_lo = log_inv_ln10, log_r2P_r,f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p11) fma.d f8 = log_inv_ln10,f8,f0 (p0) nop.i 999 ;;
}
{ .mfb nop.m 999(p10) fma.d f8 = log_log10_hi, f1, log_log10_lo (p0) br.ret.sptk b0 ;;
}
LOG_NAN_ZERO_INF_PN:
// qnan snan inf norm unorm 0 -+// 1 1 0 0 0 0 11 0xc3// 0 0 0 0 0 1 11 0x7// 0 0 1 1 1 0 10 0x3a// 0 0 1 0 0 0 01 0x21
// Save x (f8) in f10
{ .mfi nop.m 999(p0) fmerge.s f10 = f8,f8 nop.i 999}
// p11 NAN// p12 means log(+inf)
// Later p11, p12 used for frcpa// p8 p9 means ln(+-0) = -inf// p7 p10 means log(+-0) = -inf
// p13 means ln(-)// p14 means log(-)
// Log(+nan, -nan)// At this point we know it is quiet// So return
{ .mfi nop.m 999(p0) fclass.m.unc p11,p0 = f8, 0xc3 nop.i 999 }{ .mfi nop.m 999(p0) fmerge.ns f6 = f1,f1 nop.i 999 ;;
}
{ .mfb nop.m 999(p0) fclass.m.unc p12,p0 = f8, 0x21 nop.b 999 ;;
}
{ .mbb nop.m 999(p11) br.ret.sptk b0 (p12) br.ret.sptk b0 ;;
}
// We stay in ERROR RETURN.// Input is not a NAN
// 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{ .mmi(p9) mov log_GR_tag = 2 (p10) mov log_GR_tag = 8 nop.i 999 ;;
}
.pred.rel "mutex",p13,p14{ .mmi(p13) mov log_GR_tag = 3 (p14) mov log_GR_tag = 9 nop.i 999 ;;
}
.pred.rel "mutex",p9,p10{ .mfi nop.m 999(p9) frcpa f8,p11 = f6,f0 nop.i 999}{ .mfi nop.m 999(p10) frcpa f8,p12 = f6,f0 nop.i 999 ;;
}
{ .mfi nop.m 999(p13) frcpa f8,p11 = f0,f0 nop.i 999}{ .mfb nop.m 999(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 stfd [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 stfd [GR_Parameter_X] = f10 // STORE Parameter 1 on stack add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address nop.b 0 }{ .mib stfd [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 ldfd 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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