| .file "erfc.s" |
| |
| |
| // Copyright (c) 2001 - 2005, Intel Corporation |
| // All rights reserved. |
| // |
| // Contributed 2001 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 |
| //============================================================== |
| // 11/12/01 Initial version |
| // 05/20/02 Cleaned up namespace and sf0 syntax |
| // 02/06/03 Reordered header: .section, .global, .proc, .align |
| // 03/31/05 Reformatted delimiters between data tables |
| // |
| // API |
| //============================================================== |
| // double erfc(double) |
| // |
| // Overview of operation |
| //============================================================== |
| // 1. 0 <= x <= 28.0 |
| // |
| // erfc(x) = P14(z) * exp( -x^2 ), z = x - x(i). |
| // |
| // Comment: |
| // |
| // Let x(i) = -1.0 + 2^(i/4),i=0,...19. So we have 20 unequal |
| // argument intervals [x(i),x(i+1)] with length ratio q = 2^(1/4). |
| // Values x(i) we have in the table erfc_xb_table. |
| // |
| // Let x(i)<= x < x(i+1). |
| // We can find i as exponent of number (x + 1)^4. |
| // |
| // Let P14(z) - polynomial approximation of degree 14 for function |
| // erfc(z+x(i)) * exp( (z+x(i))^2) and 0 <= z <= x(i+1)-x(i). |
| // Polynomial coeffitients we have in the table erfc_p_table. |
| // |
| // So we can find result for erfc(x) as above. |
| // Algorithm description for exp function see below. |
| // |
| // 2. -6 <= x < 0 |
| // |
| // erfc(x) = 2.0 - erfc(-x) |
| // |
| // 3. x > 28.0 |
| // erfc(x) ~=~ 0.0 |
| // |
| // 4. x < -6.0 |
| // erfc(x) ~=~ 2.0 |
| |
| // Special values |
| //============================================================== |
| // erfc(+0) = 1.0 |
| // erfc(-0) = 1.0 |
| |
| // erfc(+qnan) = +qnan |
| // erfc(-qnan) = -qnan |
| // erfc(+snan) = +qnan |
| // erfc(-snan) = -qnan |
| |
| // erfc(-inf) = 2.0 |
| // erfc(+inf) = +0 |
| |
| //============================================================== |
| // Take double exp(double) from libm_64. |
| // |
| // Overview of operation |
| //============================================================== |
| // Take the input x. w is "how many log2/128 in x?" |
| // w = x * 128/log2 |
| // n = int(w) |
| // x = n log2/128 + r + delta |
| |
| // n = 128M + index_1 + 2^4 index_2 |
| // x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta |
| |
| // exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta) |
| // Construct 2^M |
| // Get 2^(index_1/128) from table_1; |
| // Get 2^(index_2/8) from table_2; |
| // Calculate exp(r) by series |
| // r = x - n (log2/128)_high |
| // delta = - n (log2/128)_low |
| // Calculate exp(delta) as 1 + delta |
| //============================================================== |
| // Comment for exp for erfc: |
| // |
| // We use quad precision for calculate input argument -x^2 and add |
| // result low bits to value delta in exp. |
| |
| // Registers used |
| //============================================================== |
| // Floating Point registers used: |
| // f8, input |
| // f9 -> f15, f32 -> f93 |
| |
| // General registers used: |
| // r32 -> r68 |
| |
| // Predicate registers used: |
| // p6 -> p15 |
| |
| // Assembly macros |
| //============================================================== |
| |
| exp_GR_rshf = r33 |
| EXP_AD_TB1 = r34 |
| EXP_AD_TB2 = r35 |
| EXP_AD_P = r36 |
| exp_GR_N = r37 |
| exp_GR_index_1 = r38 |
| exp_GR_index_2_16 = r39 |
| exp_GR_biased_M = r40 |
| EXP_AD_T1 = r41 |
| EXP_AD_T2 = r42 |
| exp_GR_sig_inv_ln2 = r43 |
| exp_GR_17ones = r44 |
| exp_TB1_size = r45 |
| exp_TB2_size = r46 |
| exp_GR_rshf_2to56 = r47 |
| exp_GR_exp_2tom56 = r48 |
| |
| // GR for erfc(x) |
| //============================================================== |
| GR_POS_ARG_ASYMP = r49 |
| GR_NEG_ARG_ASYMP = r50 |
| GR_ARG_ASYMP = r51 |
| GR_ERFC_XB_TB = r52 |
| GR_ERFC_P_TB = r53 |
| GR_IndxPlusBias = r54 |
| GR_BIAS = r55 |
| GR_P_A12 = r56 |
| GR_P_A13 = r57 |
| GR_AbsArg = r58 |
| GR_ShftXBi = r59 |
| GR_ShftPi = r60 |
| GR_mBIAS = r61 |
| GR_ShftPi_bias = r62 |
| GR_ShftXBi_bias = r63 |
| GR_ShftA12 = r64 |
| GR_ShftA13 = r65 |
| GR_EpsNorm = r66 |
| GR_0x1 = r67 |
| GR_ShftPi_8 = r68 |
| |
| // GR for __libm_support call |
| |
| //============================================================== |
| |
| GR_SAVE_B0 = r61 |
| GR_SAVE_PFS = r62 |
| GR_SAVE_GP = r63 |
| GR_SAVE_SP = r64 |
| |
| GR_Parameter_X = r65 |
| GR_Parameter_Y = r66 |
| GR_Parameter_RESULT = r67 |
| GR_Parameter_TAG = r68 |
| |
| |
| // FR for exp(-x^2) |
| //============================================================== |
| FR_X = f10 |
| FR_Y = f1 |
| FR_RESULT = f8 |
| |
| EXP_2TOM56 = f6 |
| EXP_INV_LN2_2TO63 = f7 |
| EXP_W_2TO56_RSH = f9 |
| EXP_RSHF_2TO56 = f10 |
| |
| exp_P4 = f11 |
| exp_P3 = f12 |
| exp_P2 = f13 |
| exp_P1 = f14 |
| exp_ln2_by_128_hi = f15 |
| |
| exp_ln2_by_128_lo = f32 |
| EXP_RSHF = f33 |
| EXP_Nfloat = f34 |
| exp_r = f35 |
| exp_f = f36 |
| exp_rsq = f37 |
| exp_rcube = f38 |
| EXP_2M = f39 |
| exp_S1 = f40 |
| exp_T1 = f41 |
| exp_rP4pP3 = f42 |
| exp_P_lo = f43 |
| exp_P_hi = f44 |
| exp_P = f45 |
| exp_S = f46 |
| EXP_NORM_f8 = f47 |
| exp_S2 = f48 |
| exp_T2 = f49 |
| |
| // FR for erfc(x) |
| //============================================================== |
| FR_AbsArg = f50 |
| FR_Tmp = f51 |
| FR_Xb = f52 |
| FR_A0 = f53 |
| FR_A1 = f54 |
| FR_A2 = f55 |
| FR_A3 = f56 |
| FR_A4 = f57 |
| FR_A5 = f58 |
| FR_A6 = f59 |
| FR_A7 = f60 |
| FR_A8 = f61 |
| FR_A9 = f62 |
| FR_A10 = f63 |
| FR_A11 = f64 |
| FR_A12 = f65 |
| FR_A13 = f66 |
| FR_A14 = f67 |
| |
| FR_P14_0_1 = f68 |
| FR_P14_0_2 = f69 |
| FR_P14_1_1 = f70 |
| FR_P14_1_2 = f71 |
| FR_P14_2_1 = f72 |
| FR_P14_2_2 = f73 |
| FR_P14_3_1 = f74 |
| FR_P14_3_2 = f75 |
| FR_P14_6_1 = f76 |
| |
| FR_P14_7_1 = f77 |
| FR_P14_7_2 = f78 |
| FR_P14_8_1 = f79 |
| FR_P14_8_2 = f80 |
| FR_P14_12_1 = f81 |
| FR_P14_13_1 = f82 |
| FR_P14_13_2 = f83 |
| FR_Pol = f84 |
| FR_Exp = f85 |
| FR_2 = f86 |
| f8_sq_lo = f87 |
| FR_LocArg = f88 |
| FR_Tmpf = f89 |
| FR_Tmp1 = f90 |
| FR_EpsNorm = f91 |
| FR_UnfBound = f92 |
| FR_NormX = f93 |
| |
| |
| // Data tables |
| //============================================================== |
| RODATA |
| .align 16 |
| |
| // ************* DO NOT CHANGE ORDER OF THESE TABLES ******************** |
| |
| LOCAL_OBJECT_START(exp_table_1) |
| |
| data8 0x403a8b12fc6e4892 , 0 // underflow boundary |
| data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi |
| data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo |
| // |
| // Table 1 is 2^(index_1/128) where |
| // index_1 goes from 0 to 15 |
| // |
| data8 0x8000000000000000 , 0x00003FFF |
| data8 0x80B1ED4FD999AB6C , 0x00003FFF |
| data8 0x8164D1F3BC030773 , 0x00003FFF |
| data8 0x8218AF4373FC25EC , 0x00003FFF |
| data8 0x82CD8698AC2BA1D7 , 0x00003FFF |
| data8 0x8383594EEFB6EE37 , 0x00003FFF |
| data8 0x843A28C3ACDE4046 , 0x00003FFF |
| data8 0x84F1F656379C1A29 , 0x00003FFF |
| data8 0x85AAC367CC487B15 , 0x00003FFF |
| data8 0x8664915B923FBA04 , 0x00003FFF |
| data8 0x871F61969E8D1010 , 0x00003FFF |
| data8 0x87DB357FF698D792 , 0x00003FFF |
| data8 0x88980E8092DA8527 , 0x00003FFF |
| data8 0x8955EE03618E5FDD , 0x00003FFF |
| data8 0x8A14D575496EFD9A , 0x00003FFF |
| data8 0x8AD4C6452C728924 , 0x00003FFF |
| LOCAL_OBJECT_END(exp_table_1) |
| |
| // Table 2 is 2^(index_1/8) where |
| // index_2 goes from 0 to 7 |
| LOCAL_OBJECT_START(exp_table_2) |
| data8 0x8000000000000000 , 0x00003FFF |
| data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF |
| data8 0x9837F0518DB8A96F , 0x00003FFF |
| data8 0xA5FED6A9B15138EA , 0x00003FFF |
| data8 0xB504F333F9DE6484 , 0x00003FFF |
| data8 0xC5672A115506DADD , 0x00003FFF |
| data8 0xD744FCCAD69D6AF4 , 0x00003FFF |
| data8 0xEAC0C6E7DD24392F , 0x00003FFF |
| LOCAL_OBJECT_END(exp_table_2) |
| |
| LOCAL_OBJECT_START(exp_p_table) |
| data8 0x3f8111116da21757 //P_4 |
| data8 0x3fa55555d787761c //P_3 |
| data8 0x3fc5555555555414 //P_2 |
| data8 0x3fdffffffffffd6a //P_1 |
| LOCAL_OBJECT_END(exp_p_table) |
| |
| LOCAL_OBJECT_START(erfc_xb_table) |
| data8 0x0000000000000000, 0x00000000 //XB[0] = +0.00000000000000000000e-01L |
| data8 0xC1BF828C6DC54B7A, 0x00003FFC //XB[1] = +1.89207115002721066717e-01L |
| data8 0xD413CCCFE7799211, 0x00003FFD //XB[2] = +4.14213562373095048802e-01L |
| data8 0xAE89F995AD3AD5E8, 0x00003FFE //XB[3] = +6.81792830507429086062e-01L |
| data8 0x8000000000000000, 0x00003FFF //XB[4] = +1.00000000000000000000e+00L |
| data8 0xB06FE0A31B7152DF, 0x00003FFF //XB[5] = +1.37841423000544213343e+00L |
| data8 0xEA09E667F3BCC909, 0x00003FFF //XB[6] = +1.82842712474619009760e+00L |
| data8 0x9744FCCAD69D6AF4, 0x00004000 //XB[7] = +2.36358566101485817212e+00L |
| data8 0xC000000000000000, 0x00004000 //XB[8] = +3.00000000000000000000e+00L |
| data8 0xF06FE0A31B7152DF, 0x00004000 //XB[9] = +3.75682846001088426687e+00L |
| data8 0x9504F333F9DE6484, 0x00004001 //XB[10] = +4.65685424949238019521e+00L |
| data8 0xB744FCCAD69D6AF4, 0x00004001 //XB[11] = +5.72717132202971634425e+00L |
| data8 0xE000000000000000, 0x00004001 //XB[12] = +7.00000000000000000000e+00L |
| data8 0x8837F0518DB8A96F, 0x00004002 //XB[13] = +8.51365692002176853374e+00L |
| data8 0xA504F333F9DE6484, 0x00004002 //XB[14] = +1.03137084989847603904e+01L |
| data8 0xC744FCCAD69D6AF4, 0x00004002 //XB[15] = +1.24543426440594326885e+01L |
| data8 0xF000000000000000, 0x00004002 //XB[16] = +1.50000000000000000000e+01L |
| data8 0x9037F0518DB8A96F, 0x00004003 //XB[17] = +1.80273138400435370675e+01L |
| data8 0xAD04F333F9DE6484, 0x00004003 //XB[18] = +2.16274169979695207808e+01L |
| data8 0xCF44FCCAD69D6AF4, 0x00004003 //XB[19] = +2.59086852881188653770e+01L |
| LOCAL_OBJECT_END(erfc_xb_table) |
| |
| LOCAL_OBJECT_START(erfc_p_table) |
| |
| // Pol0 |
| data8 0x8000000000000000, 0x00003FFF //A0 = +1.00000000000000000000e+00L |
| data8 0x906EBA8214DB688D, 0x0000BFFF //A1 = -1.12837916709551257389e+00L |
| data8 0xFFFFFFFFFFFFFFEB, 0x00003FFE //A2 = +9.99999999999999998841e-01L |
| data8 0xC093A3581BCF2925, 0x0000BFFE //A3 = -7.52252778063674869885e-01L |
| data8 0xFFFFFFFFFFF7CDBD, 0x00003FFD //A4 = +4.99999999999985440383e-01L |
| data8 0x9A0FB5E014AE3EFB, 0x0000BFFD //A5 = -3.00901111224757482205e-01L |
| data8 0xAAAAAAAA4672B0BD, 0x00003FFC //A6 = +1.66666666643879582201e-01L |
| data8 0xB011F45C9F590FC0, 0x0000BFFB //A7 = -8.59717455640916223912e-02L |
| data8 0xAAAAA89474161033, 0x00003FFA //A8 = +4.16666588928413935202e-02L |
| data8 0x9C818E2CE37D4214, 0x0000BFF9 //A9 = -1.91047455656271634308e-02L |
| data8 0x8885969315AB76A1, 0x00003FF8 //A10 = +8.33263115449753085659e-03L |
| data8 0xE36112A686F5165B, 0x0000BFF6 //A11 = -3.46953111013788405745e-03L |
| data8 0xB3DD6B2DB3307D2E, 0x00003FF5 //A12 = +1.37226041156280127011e-03L |
| data8 0x8018A34267FED226, 0x0000BFF4 //A13 = -4.88648380816410282971e-04L |
| data8 0xFBBA6A7AEBD3ABD9, 0x00003FF1 //A14 = +1.20033353451879025825e-04L |
| // Pol1 |
| data8 0xD15A1EF03BB91E71, 0x00003FFE //A0 = +8.17781385088640600540e-01L |
| data8 0xD1A4ADDAC3337118, 0x0000BFFE //A1 = -8.18919053944410683867e-01L |
| data8 0xA9AF9FFA2AD18CB0, 0x00003FFE //A2 = +6.62836073471060947628e-01L |
| data8 0xECB77514F0F151B3, 0x0000BFFD //A3 = -4.62337168508812580002e-01L |
| data8 0x934AB35EA5CD5EEB, 0x00003FFD //A4 = +2.87679295829458273854e-01L |
| data8 0xA71410A68C1EF21C, 0x0000BFFC //A5 = -1.63162479558223113104e-01L |
| data8 0xAF506A335238094A, 0x00003FFB //A6 = +8.56025978958108330224e-02L |
| data8 0xABFDF67F968765A7, 0x0000BFFA //A7 = -4.19902447551140139048e-02L |
| data8 0x9F0B0165A6CDCA99, 0x00003FF9 //A8 = +1.94144274984979538382e-02L |
| data8 0x8B8197BFC346CDEA, 0x0000BFF8 //A9 = -8.51478404279186775501e-03L |
| data8 0xE950D763FE51AB1E, 0x00003FF6 //A10 = +3.56011637267641495904e-03L |
| data8 0xBA821A59FC05FBAD, 0x0000BFF5 //A11 = -1.42294475244146555952e-03L |
| data8 0x8D535042E11A0D89, 0x00003FF4 //A12 = +5.39113782651680545599e-04L |
| data8 0xBE589447DB26564E, 0x0000BFF2 //A13 = -1.81528103431449706486e-04L |
| data8 0xABC8C7EF636F5B0A, 0x00003FF0 //A14 = +4.09565689009869217620e-05L |
| // Pol2 |
| data8 0xA9973ABB272898B2, 0x00003FFE //A0 = +6.62463827792779356910e-01L |
| data8 0x945F1A7993F7AADD, 0x0000BFFE //A1 = -5.79576162988785154930e-01L |
| data8 0xD84439C6609A8A62, 0x00003FFD //A2 = +4.22395520654665085222e-01L |
| data8 0x8A1BBAA7E9CB8C52, 0x0000BFFD //A3 = -2.69742806431984313298e-01L |
| data8 0x9F0F67364B466975, 0x00003FFC //A4 = +1.55332195938916594663e-01L |
| data8 0xA843F180287DAF7F, 0x0000BFFB //A5 = -8.21608416782158837025e-02L |
| data8 0xA59D71B7C690E545, 0x00003FFA //A6 = +4.04333536247671644540e-02L |
| data8 0x991A733518C74874, 0x0000BFF9 //A7 = -1.86893701691354422481e-02L |
| data8 0x85E7F91148F9F6D2, 0x00003FF8 //A8 = +8.17298243522623724858e-03L |
| data8 0xDEE0607CC9D6777E, 0x0000BFF6 //A9 = -3.40082507754089306495e-03L |
| data8 0xB145D2CC470B306B, 0x00003FF5 //A10 = +1.35248373238824318949e-03L |
| data8 0x86FAEBB4438A20FA, 0x0000BFF4 //A11 = -5.14908443679775343409e-04L |
| data8 0xC2503856CE48A657, 0x00003FF2 //A12 = +1.85311660448280465934e-04L |
| data8 0xF52642F22A26965B, 0x0000BFF0 //A13 = -5.84481856856861454591e-05L |
| data8 0xC98588E1A95FFDBD, 0x00003FEE //A14 = +1.20116245684500489648e-05L |
| // Pol3 |
| data8 0x887CBA2C47B1E2B5, 0x00003FFE //A0 = +5.33153186617432643784e-01L |
| data8 0xCD81909CF194328E, 0x0000BFFD //A1 = -4.01379126699602646289e-01L |
| data8 0x84DCA15C52122372, 0x00003FFD //A2 = +2.59495775718310530164e-01L |
| data8 0x993AA9C76AD28157, 0x0000BFFC //A3 = -1.49637844845261107836e-01L |
| data8 0xA140CD8A96FADBA5, 0x00003FFB //A4 = +7.87368829650154013961e-02L |
| data8 0x9D36B25E76E56EEA, 0x0000BFFA //A5 = -3.83822410143975630292e-02L |
| data8 0x8F8BCC2C0536ECD3, 0x00003FF9 //A6 = +1.75227153523910189727e-02L |
| data8 0xF77EDC644BA17AF9, 0x0000BFF7 //A7 = -7.55296479527793552675e-03L |
| data8 0xCAB8AC76793C1151, 0x00003FF6 //A8 = +3.09328279988546711083e-03L |
| data8 0x9E8FCBC793D555AF, 0x0000BFF5 //A9 = -1.20972979110659888616e-03L |
| data8 0xEDC1328664A0CE79, 0x00003FF3 //A10 = +4.53481058502015766058e-04L |
| data8 0xAAE3CAAB9D117591, 0x0000BFF2 //A11 = -1.62973223928790256249e-04L |
| data8 0xE7704D06A3080C19, 0x00003FF0 //A12 = +5.51792801195012080688e-05L |
| data8 0x875A5B53E510F305, 0x0000BFEF //A13 = -1.61353297293572230995e-05L |
| data8 0xC8F10CDDB9CC9A42, 0x00003FEC //A14 = +2.99426321046583353559e-06L |
| // Pol4 |
| data8 0xDAEC3C07CAB590C1, 0x00003FFD //A0 = +4.27583576155807004411e-01L |
| data8 0x8BE271F8BE0280AC, 0x0000BFFD //A1 = -2.73212014783898564863e-01L |
| data8 0x9E13941E19661429, 0x00003FFC //A2 = +1.54371561371908397882e-01L |
| data8 0xA241BFC48377449D, 0x0000BFFB //A3 = -7.92269689413235358504e-02L |
| data8 0x99E56877AD00D1AE, 0x00003FFA //A4 = +3.75722962151600767952e-02L |
| data8 0x887E78DA3BA57C80, 0x0000BFF9 //A5 = -1.66618690872055148862e-02L |
| data8 0xE465CAA9F4D54FD8, 0x00003FF7 //A6 = +6.97014232347351913821e-03L |
| data8 0xB57930370208D4A7, 0x0000BFF6 //A7 = -2.76906420823065422653e-03L |
| data8 0x89A90B5DF0C0C55E, 0x00003FF5 //A8 = +1.05026496655247749532e-03L |
| data8 0xC83DB867F08D93C6, 0x0000BFF3 //A9 = -3.81929578900287685559e-04L |
| data8 0x8C0C9113FC8061FA, 0x00003FF2 //A10 = +1.33561218944256209215e-04L |
| data8 0xBC17A73E9CA51313, 0x0000BFF0 //A11 = -4.48447217225392170834e-05L |
| data8 0xED10FE8FC0E44CAD, 0x00003FEE //A12 = +1.41302576244352578317e-05L |
| data8 0xFE49912328516F81, 0x0000BFEC //A13 = -3.78917710289305330220e-06L |
| data8 0xA8F6077E25DAFD33, 0x00003FEA //A14 = +6.29428967202166402369e-07L |
| // Pol5 |
| data8 0xAF72220985BED710, 0x00003FFD //A0 = +3.42667640364081975844e-01L |
| data8 0xBC1CB559042410AB, 0x0000BFFC //A1 = -1.83703263815036934677e-01L |
| data8 0xB730BF62E0B63A3C, 0x00003FFB //A2 = +8.94484474229911741150e-02L |
| data8 0xA4F307B1D1A1534E, 0x0000BFFA //A3 = -4.02708340235238993824e-02L |
| data8 0x8B0327F5117861DB, 0x00003FF9 //A4 = +1.69692783752415790321e-02L |
| data8 0xDD4059307B2B081C, 0x0000BFF7 //A5 = -6.75205569219747369303e-03L |
| data8 0xA761D738974FECF6, 0x00003FF6 //A6 = +2.55404953403837072821e-03L |
| data8 0xF208F6D704F4B487, 0x0000BFF4 //A7 = -9.23290315545127419886e-04L |
| data8 0xA7F3658D34EC10B9, 0x00003FF3 //A8 = +3.20340668304962386053e-04L |
| data8 0xE079C35CEFD4E6D6, 0x0000BFF1 //A9 = -1.07038324953715640850e-04L |
| data8 0x90C5CDD19BB3DD2F, 0x00003FF0 //A10 = +3.45164947021915687751e-05L |
| data8 0xB3911863705825F6, 0x0000BFEE //A11 = -1.07030140392753204852e-05L |
| data8 0xD023CF5C3F915685, 0x00003FEC //A12 = +3.10152594473606007552e-06L |
| data8 0xCA7016FADFF584F5, 0x0000BFEA //A13 = -7.54139761055503416594e-07L |
| data8 0xEEBB5CC0901D2BB0, 0x00003FE7 //A14 = +1.11168196441717301549e-07L |
| // Pol6 |
| data8 0x8CD1160326A754AF, 0x00003FFD //A0 = +2.75032699474947383325e-01L |
| data8 0xFB22A4C657119388, 0x0000BFFB //A1 = -1.22624671271190511269e-01L |
| data8 0xD02B2CA872A774E9, 0x00003FFA //A2 = +5.08224243596176920409e-02L |
| data8 0xA23302E146E9E406, 0x0000BFF9 //A3 = -1.97997146844646077750e-02L |
| data8 0xEF8918FEDE237C98, 0x00003FF7 //A4 = +7.31004448401605074486e-03L |
| data8 0xA8A8B598FA20D881, 0x0000BFF6 //A5 = -2.57353242430059589053e-03L |
| data8 0xE3964D9788BFF50F, 0x00003FF4 //A6 = +8.68175969920725727944e-04L |
| data8 0x93B83C10B7210AC7, 0x0000BFF3 //A7 = -2.81752903983413936245e-04L |
| data8 0xB913B752B0D56A42, 0x00003FF1 //A8 = +8.82515983758695613094e-05L |
| data8 0xE0623EFA0B1E8DE9, 0x0000BFEF //A9 = -2.67486302195396417310e-05L |
| data8 0x83C4D1A4019E1D2E, 0x00003FEE //A10 = +7.85403393879249335151e-06L |
| data8 0x950CBA5D80D8125E, 0x0000BFEC //A11 = -2.22101388436550539151e-06L |
| data8 0x9CE72C0409A3E800, 0x00003FEA //A12 = +5.84509280984781223375e-07L |
| data8 0x88CCD7A000D1C213, 0x0000BFE8 //A13 = -1.27405082040077425019e-07L |
| data8 0x8DF4EC84F093B1C0, 0x00003FE5 //A14 = +1.65259388738830506389e-08L |
| // Pol7 |
| data8 0xE2BF82A153B1B82E, 0x00003FFC //A0 = +2.21433678719152843912e-01L |
| data8 0xA72A9AE0BD7F29D5, 0x0000BFFB //A1 = -8.16242313227913578068e-02L |
| data8 0xE98939292289EDBE, 0x00003FF9 //A2 = +2.85078159732432477516e-02L |
| data8 0x9B93E5E0EEFF9516, 0x0000BFF8 //A3 = -9.49571084105114051468e-03L |
| data8 0xC6B39897AABC47BC, 0x00003FF6 //A4 = +3.03194499398790451607e-03L |
| data8 0xF442AC7D84DDF1E0, 0x0000BFF4 //A5 = -9.31779649708690069328e-04L |
| data8 0x90FBD9F8B41DF23E, 0x00003FF3 //A6 = +2.76534642660360753287e-04L |
| data8 0xA6AC59077C78B437, 0x0000BFF1 //A7 = -7.94759910003852154521e-05L |
| data8 0xB9FC0BADD531E5E9, 0x00003FEF //A8 = +2.21710864553358009804e-05L |
| data8 0xC9CFC8CD93648856, 0x0000BFED //A9 = -6.01445608619100503330e-06L |
| data8 0xD4FA51B86A9B2494, 0x00003FEB //A10 = +1.58680833469323702924e-06L |
| data8 0xD8D0ED030032926D, 0x0000BFE9 //A11 = -4.03851487695924456733e-07L |
| data8 0xCCA1CA2AC3EB8973, 0x00003FE7 //A12 = +9.52891963880517988726e-08L |
| data8 0x9E26A080F9DA39DE, 0x0000BFE5 //A13 = -1.84111863600343741644e-08L |
| data8 0x8F3DC58F64A92C62, 0x00003FE2 //A14 = +2.08443519336792003049e-09L |
| // Pol8 |
| data8 0xB74C13E914E9666F, 0x00003FFC //A0 = +1.79001151181389950418e-01L |
| data8 0xDEB57268A58B763B, 0x0000BFFA //A1 = -5.43722600071728705200e-02L |
| data8 0x821FF0D4C605A4CD, 0x00003FF9 //A2 = +1.58843711598712515609e-02L |
| data8 0x92C830DD423DB924, 0x0000BFF7 //A3 = -4.47943101836927657394e-03L |
| data8 0xA04E61767A095BB6, 0x00003FF5 //A4 = +1.22303905230942532198e-03L |
| data8 0xA9EF64E0F6654358, 0x0000BFF3 //A5 = -3.24125543666296226957e-04L |
| data8 0xAF39C8969BD163E8, 0x00003FF1 //A6 = +8.35541329311315562274e-05L |
| data8 0xB01273B34197330C, 0x0000BFEF //A7 = -2.09894273215824495783e-05L |
| data8 0xACAE4C820B99EBAC, 0x00003FED //A8 = +5.14629050848703676006e-06L |
| data8 0xA57BF2AEA52B92DF, 0x0000BFEB //A9 = -1.23295315941138567172e-06L |
| data8 0x9AD6FE7A852DA239, 0x00003FE9 //A10 = +2.88411640627675721042e-07L |
| data8 0x8BFE95FCD7B92763, 0x0000BFE7 //A11 = -6.51900079707465044843e-08L |
| data8 0xE9F15C8E7F58CF90, 0x00003FE4 //A12 = +1.36172642554216769522e-08L |
| data8 0x9E90F22B11FAF8B5, 0x0000BFE2 //A13 = -2.30744183054978535129e-09L |
| data8 0xF8CF74F1A138FBBA, 0x00003FDE //A14 = +2.26291720693360003233e-10L |
| // Pol9 |
| data8 0x94D45274A831ED57, 0x00003FFC //A0 = +1.45341194505862183128e-01L |
| data8 0x94D4518B699A4A68, 0x0000BFFA //A1 = -3.63352952323113355459e-02L |
| data8 0x90C3B59FF403A916, 0x00003FF8 //A2 = +8.83572327421709216515e-03L |
| data8 0x893B796D0E9B4867, 0x0000BFF6 //A3 = -2.09399904729894563201e-03L |
| data8 0xFDFFA94903DCB8EA, 0x00003FF3 //A4 = +4.84464029001979577664e-04L |
| data8 0xE5CE7C2E4B05CF16, 0x0000BFF1 //A5 = -1.09580317663729186599e-04L |
| data8 0xCB88CC8F1146FDAE, 0x00003FEF //A6 = +2.42631878042764234194e-05L |
| data8 0xB0AA52C6F44E47C8, 0x0000BFED //A7 = -5.26503698764159271674e-06L |
| data8 0x966DD813170F8EBD, 0x00003FEB //A8 = +1.12078397189300511086e-06L |
| data8 0xFB75782788A6E378, 0x0000BFE8 //A9 = -2.34189317246047219283e-07L |
| data8 0xCDF787C4E5FDCF2A, 0x00003FE6 //A10 = +4.79554094892420966704e-08L |
| data8 0xA34CD3DFAC12AA45, 0x0000BFE4 //A11 = -9.50531730989412282035e-09L |
| data8 0xEEBB49645DE0E34C, 0x00003FE1 //A12 = +1.73700091999434388879e-09L |
| data8 0x8C86D8677DEACFBA, 0x0000BFDF //A13 = -2.55616650187281815453e-10L |
| data8 0xBDB223D0FE2A7D6B, 0x00003FDB //A14 = +2.15659223402509415592e-11L |
| // Pol10 |
| data8 0xF2C1812715E4050A, 0x00003FFB //A0 = +1.18533143048567888157e-01L |
| data8 0xC7DA2C565ADAEE57, 0x0000BFF9 //A1 = -2.43960252726894623056e-02L |
| data8 0xA15CEFFD632F697D, 0x00003FF7 //A2 = +4.92440908672041077933e-03L |
| data8 0xFFCFF4D3FB118F69, 0x0000BFF4 //A3 = -9.75846593969603576904e-04L |
| data8 0xC73F437D2F226C56, 0x00003FF2 //A4 = +1.90016864347860462550e-04L |
| data8 0x989D7E1F60845811, 0x0000BFF0 //A5 = -3.63863004988760879054e-05L |
| data8 0xE615A5A669361BE1, 0x00003FED //A6 = +6.85705419984646959791e-06L |
| data8 0xAACD08E0BE6270F8, 0x0000BFEB //A7 = -1.27256599602163049440e-06L |
| data8 0xF9DEE9C1C02A3062, 0x00003FE8 //A8 = +2.32710274258898439253e-07L |
| data8 0xB420E960508A3003, 0x0000BFE6 //A9 = -4.19394488070741280136e-08L |
| data8 0xFF5E3ECA229CB0C7, 0x00003FE3 //A10 = +7.43219121339261970485e-09L |
| data8 0xAF86504D78D35E89, 0x0000BFE1 //A11 = -1.27711000692808421573e-09L |
| data8 0xDE1CE78ADB6DDF04, 0x00003FDE //A12 = +2.02010513073041015283e-10L |
| data8 0xE124FFAA267301A5, 0x0000BFDB //A13 = -2.55959692063871343080e-11L |
| data8 0x81F1BEBEFBE168D2, 0x00003FD8 //A14 = +1.84661980716000872722e-12L |
| // Pol11 |
| data8 0xC6CE5D7D18203EAA, 0x00003FFB //A0 = +9.70732978630764996752e-02L |
| data8 0x86E8A30A76923C88, 0x0000BFF9 //A1 = -1.64683517829920230086e-02L |
| data8 0xB4A1CBB7576B4183, 0x00003FF6 //A2 = +2.75622581042760461528e-03L |
| data8 0xEEB782FBC8BB352B, 0x0000BFF3 //A3 = -4.55316242981110299585e-04L |
| data8 0x9BC489CC00C7E63A, 0x00003FF1 //A4 = +7.42758405750422020216e-05L |
| data8 0xC8D418A9F2A78515, 0x0000BFEE //A5 = -1.19703114831817055481e-05L |
| data8 0xFFE671DCEE8665A8, 0x00003FEB //A6 = +1.90660487794668853072e-06L |
| data8 0xA1313247D3E35365, 0x0000BFE9 //A7 = -3.00243820009225833104e-07L |
| data8 0xC8D5A87C970712B1, 0x00003FE6 //A8 = +4.67604496871825103188e-08L |
| data8 0xF77258CEF4675E25, 0x0000BFE3 //A9 = -7.20164586117313631144e-09L |
| data8 0x96549D79C0F33C27, 0x00003FE1 //A10 = +1.09379854902340983112e-09L |
| data8 0xB16A6CC5A3AE6E01, 0x0000BFDE //A11 = -1.61358659378896671620e-10L |
| data8 0xC0970F2551C52F96, 0x00003FDB //A12 = +2.18949565869759698947e-11L |
| data8 0xA6E029ABB3BB500C, 0x0000BFD8 //A13 = -2.37144541649446501026e-12L |
| data8 0xA3E43F3857D1B6A5, 0x00003FD4 //A14 = +1.45564973108152568130e-13L |
| // Pol12 |
| data8 0xA36E35FC807B3E64, 0x00003FFB //A0 = +7.98000543291529334886e-02L |
| data8 0xB725A29237C8F94F, 0x0000BFF8 //A1 = -1.11784064873715046550e-02L |
| data8 0xCB51EF23EAD5F327, 0x00003FF5 //A2 = +1.55120891755237931425e-03L |
| data8 0xDFA838770AE711A2, 0x0000BFF2 //A3 = -2.13296043002775850891e-04L |
| data8 0xF3D7B777730B202D, 0x00003FEF //A4 = +2.90683082614108095819e-05L |
| data8 0x83C5FF0D475796DD, 0x0000BFED //A5 = -3.92715403535014263671e-06L |
| data8 0x8D37B41345244FD5, 0x00003FEA //A6 = +5.26076523514903487927e-07L |
| data8 0x9616B7E9C40C1DCC, 0x0000BFE7 //A7 = -6.98905176445499510102e-08L |
| data8 0x9E38FDF61B26699A, 0x00003FE4 //A8 = +9.20976891314475742405e-09L |
| data8 0xA565DFE27AEA03A1, 0x0000BFE1 //A9 = -1.20342845518628622757e-09L |
| data8 0xAAEB9EFB497EC812, 0x00003FDE //A10 = +1.55451193328690040046e-10L |
| data8 0xABD305A38349EAEB, 0x0000BFDB //A11 = -1.95341618552982314342e-11L |
| data8 0x9EDB00104DB66DD9, 0x00003FD8 //A12 = +2.25747200093121867690e-12L |
| data8 0xE9F80AF513F2B8AB, 0x0000BFD4 //A13 = -2.07806143133802417637e-13L |
| data8 0xC2B840C3859AB166, 0x00003FD0 //A14 = +1.08091168358477817812e-14L |
| // Pol13 |
| data8 0x86CD0BF01914407A, 0x00003FFB //A0 = +6.58207829138836028568e-02L |
| data8 0xF9F4A17FA70807C3, 0x0000BFF7 //A1 = -7.62803922344113067603e-03L |
| data8 0xE63BF84EDE20EDAA, 0x00003FF4 //A2 = +8.78273993036530088653e-04L |
| data8 0xD2B746011B39D879, 0x0000BFF1 //A3 = -1.00477176633442906101e-04L |
| data8 0xBFA4F1F66023C975, 0x00003FEE //A4 = +1.14228914411837438985e-05L |
| data8 0xAD3A05E1F1F0EA8F, 0x0000BFEB //A5 = -1.29063913420827451449e-06L |
| data8 0x9BA1F2E56DBE1B49, 0x00003FE8 //A6 = +1.44944165416032280452e-07L |
| data8 0x8AFE93AF627BAFA6, 0x0000BFE5 //A7 = -1.61810825806733824014e-08L |
| data8 0xF6CEAB6E78304875, 0x00003FE1 //A8 = +1.79575947795401009493e-09L |
| data8 0xD9BFD64FD9166ECF, 0x0000BFDE //A9 = -1.98041892772535870322e-10L |
| data8 0xBE482C8AEA403737, 0x00003FDB //A10 = +2.16325508593741350803e-11L |
| data8 0xA1FB98FA19E62A4F, 0x0000BFD8 //A11 = -2.30191407969654156362e-12L |
| data8 0xFDB2E0599016AD1E, 0x00003FD4 //A12 = +2.25329742249079975388e-13L |
| data8 0x9E179A99CDD4BF4B, 0x0000BFD1 //A13 = -1.75517603530017718494e-14L |
| data8 0xDE4DE992A707C7BC, 0x00003FCC //A14 = +7.71273133169032472595e-16L |
| // Pol14 |
| data8 0xDF0639E60CF6E96C, 0x00003FFA //A0 = +5.44492971101228988138e-02L |
| data8 0xAB6737B6065BD1C2, 0x0000BFF7 //A1 = -5.23081035867078490333e-03L |
| data8 0x8322CC0765FD9C27, 0x00003FF4 //A2 = +5.00243857322493802503e-04L |
| data8 0xC7C37C447AABC9BE, 0x0000BFF0 //A3 = -4.76273572257807668623e-05L |
| data8 0x977C068C67DD09B3, 0x00003FED //A4 = +4.51458915834329225528e-06L |
| data8 0xE4C00648054CBD72, 0x0000BFE9 //A5 = -4.26080256412742187632e-07L |
| data8 0xABF9032C426C0F54, 0x00003FE6 //A6 = +4.00405155179176153559e-08L |
| data8 0x80BD82177111B70D, 0x0000BFE3 //A7 = -3.74683488305340664541e-09L |
| data8 0xBFEFB2BBFC4AAE16, 0x00003FDF //A8 = +3.49130134089615132836e-10L |
| data8 0x8E68BCEC2A2F6025, 0x0000BFDC //A9 = -3.23800879252444001040e-11L |
| data8 0xD19FEF92B2157585, 0x00003FD8 //A10 = +2.97894685764287382560e-12L |
| data8 0x967A0ECC142382D9, 0x0000BFD5 //A11 = -2.67300472044743953909e-13L |
| data8 0xC6D8869855133985, 0x00003FD1 //A12 = +2.20763189681614758000e-14L |
| data8 0xD10AC0B228ABCECC, 0x0000BFCD //A13 = -1.45052027893524847250e-15L |
| data8 0xF7C6DEB4522487A3, 0x00003FC8 //A14 = +5.37280367113168366711e-17L |
| // Pol15 |
| data8 0xB8F57DECFAC3B255, 0x00003FFA //A0 = +4.51559943173131409760e-02L |
| data8 0xEC1B8A6C822C036F, 0x0000BFF6 //A1 = -3.60271577347565115947e-03L |
| data8 0x963A6DD66951B72E, 0x00003FF3 //A2 = +2.86537625289770759336e-04L |
| data8 0xBE93F9E80DF4AE0A, 0x0000BFEF //A3 = -2.27186718010906557773e-05L |
| data8 0xF10589FC10D908E0, 0x00003FEB //A4 = +1.79575113004740124999e-06L |
| data8 0x97F1A2435C7877EF, 0x0000BFE8 //A5 = -1.41508767557208714648e-07L |
| data8 0xBEFF2FB5F00E9327, 0x00003FE4 //A6 = +1.11174782364058338591e-08L |
| data8 0xEF5E09DC714DF198, 0x0000BFE0 //A7 = -8.70813302639377671664e-10L |
| data8 0x958A6EB9408970A4, 0x00003FDD //A8 = +6.80032608255179732632e-11L |
| data8 0xBA31F40954675710, 0x0000BFD9 //A9 = -5.29198388081297293593e-12L |
| data8 0xE63B9CEEDC4CF0E6, 0x00003FD5 //A10 = +4.08975721481205179918e-13L |
| data8 0x8AF8F1E3FED32CEC, 0x0000BFD2 //A11 = -3.08580807479307213059e-14L |
| data8 0x9A88033A08842BEA, 0x00003FCE //A12 = +2.14455258045503137285e-15L |
| data8 0x88BCF775B7B3A939, 0x0000BFCA //A13 = -1.18601440246395438386e-16L |
| data8 0x88687B63A5B7135E, 0x00003FC5 //A14 = +3.69734984736162880476e-18L |
| // Pol16 |
| data8 0x99B8A501204BF3E7, 0x00003FFA //A0 = +3.75296063885057657456e-02L |
| data8 0xA33FA20D2867C79C, 0x0000BFF6 //A1 = -2.49097544033960143953e-03L |
| data8 0xACFD14CA6AA55829, 0x00003FF2 //A2 = +1.64974783411741182991e-04L |
| data8 0xB6E9B4ED9B378B09, 0x0000BFEE //A3 = -1.09024594422859744844e-05L |
| data8 0xC0FD95D38ADCF301, 0x00003FEA //A4 = +7.18945888498730738040e-07L |
| data8 0xCB302F7AAFFFA074, 0x0000BFE6 //A5 = -4.73084450875945514829e-08L |
| data8 0xD578674188198402, 0x00003FE2 //A6 = +3.10640208133938026422e-09L |
| data8 0xDFCC6ED4219E7FC4, 0x0000BFDE //A7 = -2.03543610142159316364e-10L |
| data8 0xEA1F448AA373E4A9, 0x00003FDA //A8 = +1.33083028465054001215e-11L |
| data8 0xF44780B8EACD37B5, 0x0000BFD6 //A9 = -8.67854438613319891312e-13L |
| data8 0xFD55794492F53AEE, 0x00003FD2 //A10 = +5.62514216652784597182e-14L |
| data8 0x805C040421E7A098, 0x0000BFCF //A11 = -3.56269003968981157635e-15L |
| data8 0xEFCCD20DE93A138E, 0x00003FCA //A12 = +2.07993414310230172191e-16L |
| data8 0xB259764466732080, 0x0000BFC6 //A13 = -9.66834364652262630640e-18L |
| data8 0x9597C1DB6AF830E4, 0x00003FC1 //A14 = +2.53420063550355940811e-19L |
| // Pol17 |
| data8 0xFFFCBD66BAA4368C, 0x00003FF9 //A0 = +3.12484454387527380657e-02L |
| data8 0xE28174723762D197, 0x0000BFF5 //A1 = -1.72810121976742793952e-03L |
| data8 0xC81D832836019EC4, 0x00003FF1 //A2 = +9.54224026432644399736e-05L |
| data8 0xB0885530C7D7AB5B, 0x0000BFED //A3 = -5.26107996417947739207e-06L |
| data8 0x9B7EA64F62F6FD06, 0x00003FE9 //A4 = +2.89631495607631932854e-07L |
| data8 0x88C24ACAA9042166, 0x0000BFE5 //A5 = -1.59208376111789845204e-08L |
| data8 0xF033E5CD9B7F2822, 0x00003FE0 //A6 = +8.73852423930118273815e-10L |
| data8 0xD2A1B161FB4DFBFE, 0x0000BFDC //A7 = -4.78920839886600387264e-11L |
| data8 0xB86B27FCBB5A1E9D, 0x00003FD8 //A8 = +2.62074563162805723295e-12L |
| data8 0xA124E1303F08E508, 0x0000BFD4 //A9 = -1.43124677534734729453e-13L |
| data8 0x8C0B270950D7C697, 0x00003FD0 //A10 = +7.77397948226387851915e-15L |
| data8 0xEE034E350C65D2D9, 0x0000BFCB //A11 = -4.12886586201102092942e-16L |
| data8 0xBA94473E52495304, 0x00003FC7 //A12 = +2.02289587087169937807e-17L |
| data8 0xE913D34CBB853CEE, 0x0000BFC2 //A13 = -7.89697093687557412061e-19L |
| data8 0xA44576A85E8CAB59, 0x00003FBD //A14 = +1.73929048516879172258e-20L |
| // Pol18 |
| data8 0xD579A3FE4622DED2, 0x00003FF9 //A0 = +2.60589793198885278242e-02L |
| data8 0x9D97EB84E7CD89C8, 0x0000BFF5 //A1 = -1.20234251012583627659e-03L |
| data8 0xE86EFDC2CCA5C47B, 0x00003FF0 //A2 = +5.54164790116744315389e-05L |
| data8 0xAB39FA5621E39B15, 0x0000BFEC //A3 = -2.55147332073979814633e-06L |
| data8 0xFC0244F58F8D8097, 0x00003FE7 //A4 = +1.17350772365097747003e-07L |
| data8 0xB941D44B71B14FE2, 0x0000BFE3 //A5 = -5.39169255673480031672e-09L |
| data8 0x880B4A40B6F2C901, 0x00003FDF //A6 = +2.47462779512141204748e-10L |
| data8 0xC7998AE5652CDCFC, 0x0000BFDA //A7 = -1.13459336509953900777e-11L |
| data8 0x92438AA45915CD95, 0x00003FD6 //A8 = +5.19633524685027215673e-13L |
| data8 0xD6067243AD3AEAE6, 0x0000BFD1 //A9 = -2.37615683835509918256e-14L |
| data8 0x9BD0722A07669E4D, 0x00003FCD //A10 = +1.08117849400479298186e-15L |
| data8 0xDDF6F1B79F50E3C4, 0x0000BFC8 //A11 = -4.81309059042573202592e-17L |
| data8 0x91F283C0351A9ACA, 0x00003FC4 //A12 = +1.97795505638619048412e-18L |
| data8 0x990BC4FAFA9C7542, 0x0000BFBF //A13 = -6.48174913943425248713e-20L |
| data8 0xB536865B89676892, 0x00003FB9 //A14 = +1.19916696090758913485e-21L |
| // Pol19 |
| data8 0xB241CEB1B7C953F1, 0x00003FF9 //A0 = +2.17598950382519671244e-02L |
| data8 0xDBD6FBA9B11B85E1, 0x0000BFF4 //A1 = -8.38622198373701898430e-04L |
| data8 0x877605B1AD082441, 0x00003FF0 //A2 = +3.22964249573360786077e-05L |
| data8 0xA6D04DC067A5D310, 0x0000BFEB //A3 = -1.24285881515578912302e-06L |
| data8 0xCD458A72BC161315, 0x00003FE6 //A4 = +4.77935289502172654216e-08L |
| data8 0xFC6902CFB5DE90A2, 0x0000BFE1 //A5 = -1.83652591038905929358e-09L |
| data8 0x9B12B0707DFE615C, 0x00003FDD //A6 = +7.05190381049444126079e-11L |
| data8 0xBE67972F2C8EE5AE, 0x0000BFD8 //A7 = -2.70581282732878853626e-12L |
| data8 0xE99D8CAF9A3FFE02, 0x00003FD3 //A8 = +1.03746090805854376435e-13L |
| data8 0x8F35F5BBEF9E4299, 0x0000BFCF //A9 = -3.97489765699919189983e-15L |
| data8 0xAF6E62C3C91B7178, 0x00003FCA //A10 = +1.52162305785839987182e-16L |
| data8 0xD6636229C1646963, 0x0000BFC5 //A11 = -5.81100425482928485309e-18L |
| data8 0x810331BF289E068F, 0x00003FC1 //A12 = +2.18555638648715837944e-19L |
| data8 0x8E3D07CA59546B83, 0x0000BFBC //A13 = -7.53003820427900359431e-21L |
| data8 0xD5970B291ED73560, 0x00003FB6 //A14 = +1.76677518655145552907e-22L |
| LOCAL_OBJECT_END(erfc_p_table) |
| |
| |
| .section .text |
| GLOBAL_LIBM_ENTRY(erfc) |
| |
| { .mfi |
| alloc r32 = ar.pfs, 0, 33, 4, 0 |
| fma.s1 FR_Tmp = f1, f1, f8 // |x|+1, if x >= 0 |
| nop.i 0 |
| } |
| { .mfi |
| addl EXP_AD_TB1 = @ltoff(exp_table_1), gp |
| fms.s1 FR_Tmp1 = f1, f1, f8 // |x|+1, if x < 0 |
| mov exp_GR_rshf_2to56 = 0x4768 // begin 1.1 2^(63+56) |
| };; |
| |
| { .mfi |
| ld8 EXP_AD_TB1 = [EXP_AD_TB1] |
| fcmp.ge.s1 p6,p7 = f8, f0 // p6: x >= 0 ,p7: x<0 |
| mov exp_GR_rshf_2to56 = 0x4768 // begin 1.1 2^(63+56) |
| } |
| { .mlx |
| mov exp_TB1_size = 0x100 |
| movl exp_GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc //signif. of 1/ln2 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fclass.m p8,p0 = f8,0x07 // p8: x = 0 |
| shl exp_GR_rshf_2to56 = exp_GR_rshf_2to56, 48 //end 1.1 2^(63+56) |
| } |
| { .mfi |
| mov exp_GR_exp_2tom56 = 0xffff-56 |
| fnma.s1 EXP_NORM_f8 = f8, f8, f0 // high bits for -x^2 |
| nop.i 0 |
| };; |
| |
| |
| .pred.rel "mutex",p6,p7 |
| { .mfi |
| setf.sig EXP_INV_LN2_2TO63 = exp_GR_sig_inv_ln2 // form 1/ln2 * 2^63 |
| (p6) fma.s1 FR_AbsArg = f1, f0, f8 // |x|, if x >= 0 |
| mov GR_POS_ARG_ASYMP = 0x403C |
| } |
| { .mfi |
| mov GR_NEG_ARG_ASYMP = 0x4018 |
| (p7) fms.s1 FR_AbsArg = f1, f0, f8 // |x|, if x < 0 |
| mov exp_GR_rshf = 0x43e8 // begin 1.1 2^63 for right shift |
| };; |
| |
| { .mfi |
| setf.exp EXP_2TOM56 = exp_GR_exp_2tom56 // 2^-56 for scaling Nfloat |
| fclass.m p10,p0 = f8, 0x21 // p10: x = +inf |
| mov exp_GR_17ones = 0x1FFFF |
| } |
| { .mlx |
| setf.d EXP_RSHF_2TO56 = exp_GR_rshf_2to56 // const 1.10*2^(63+56) |
| movl GR_ERFC_XB_TB = 0x1A0 |
| };; |
| |
| |
| .pred.rel "mutex",p6,p7 |
| { .mfi |
| ldfd FR_UnfBound = [EXP_AD_TB1], 16 |
| (p6) fma.s1 FR_Tmp = FR_Tmp, FR_Tmp, f0 // (|x|+1)^2,x >=0 |
| shl exp_GR_rshf = exp_GR_rshf, 48 //end 1.1 2^63 for right shift |
| } |
| { .mfi |
| nop.m 0 |
| (p7) fma.s1 FR_Tmp = FR_Tmp1, FR_Tmp1, f0 // (|x|+1)^2, x<0 |
| mov GR_0x1 = 0x1 |
| };; |
| |
| { .mfi |
| mov GR_BIAS = 0x0FFFF |
| fclass.m p9,p0 = f8, 0x22 // p9: x = -inf |
| shl GR_EpsNorm = GR_0x1,53 |
| } |
| { .mfb |
| mov exp_TB2_size = 0x80 |
| (p8) fma.d.s0 f8 = f1, f1, f0 //p8: y = 1.0, x = 0 |
| (p8) br.ret.spnt b0 //p8: quick exit for x = 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fclass.m p11,p0 = f8, 0xc3 // p11: x = nan |
| nop.i 0 |
| } |
| { .mfi |
| setf.d EXP_RSHF = exp_GR_rshf //Form right shift const 1.100 * 2^63 |
| fma.s1 FR_NormX = f8,f1,f0 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| setf.d FR_EpsNorm = GR_EpsNorm |
| nop.f 0 |
| (p6) shl GR_ARG_ASYMP = GR_POS_ARG_ASYMP, 48//p6:ARG_ASYMP= 28.0,x>=0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_2 = f1, f1, f1 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| ldfe exp_ln2_by_128_hi = [EXP_AD_TB1],16 |
| fma.s1 f8_sq_lo = f8, f8, EXP_NORM_f8 // low bits for -x^2 |
| (p7) shl GR_ARG_ASYMP = GR_NEG_ARG_ASYMP, 48//p6:ARG_ASYMP= 6.0,x < 0 |
| };; |
| |
| { .mfi |
| sub GR_mBIAS = r0, GR_BIAS |
| fma.s1 FR_Tmp = FR_Tmp, FR_Tmp, f0 // (|x|+1)^4 |
| nop.i 0 |
| } |
| { .mfi |
| ldfe exp_ln2_by_128_lo = [EXP_AD_TB1], 16 |
| nop.f 0 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| getf.d GR_AbsArg = FR_AbsArg |
| nop.f 0 |
| add GR_ERFC_XB_TB = GR_ERFC_XB_TB, EXP_AD_TB1//pointer to XB_TBL |
| } |
| { .mfb |
| shladd GR_ShftPi_bias = GR_BIAS, 4, GR_mBIAS // BIAS * 2^4 - BIAS |
| (p9) fma.d.s0 f8 = f1, f1, f1 // p9: y = 2 for x = -inf |
| (p9) br.ret.spnt b0 // p9: quick exit for x = -inf |
| };; |
| |
| { .mfi |
| add GR_ERFC_P_TB = 0x140, GR_ERFC_XB_TB // pointer to P_TBL |
| fma.s1 EXP_W_2TO56_RSH = EXP_NORM_f8,EXP_INV_LN2_2TO63,EXP_RSHF_2TO56 |
| shladd GR_ShftPi_bias = GR_ShftPi_bias, 4, r0 // BIAS * 240 |
| } |
| { .mfb |
| nop.m 0 |
| (p10) fma.d.s0 f8 = f0, f1, f0 // p10: y = 0 for x = +inf |
| (p10) br.ret.spnt b0 // p10: quick exit for x = +inf |
| };; |
| |
| |
| .pred.rel "mutex",p6,p7 |
| { .mfi |
| (p6) cmp.gt.unc p15,p0 = GR_AbsArg,GR_ARG_ASYMP //p15: x > 28.0,p6: x >= 0 |
| nop.f 0 |
| (p7) cmp.gt.unc p14,p0 = GR_AbsArg, GR_ARG_ASYMP //p14: x < - 6.0,p7: x < 0 |
| } |
| { .mfb |
| add EXP_AD_TB2 = exp_TB1_size, EXP_AD_TB1 |
| (p11) fma.d.s0 f8 = f8, f1, f0 //p11: y = x for x = nan |
| (p11) br.ret.spnt b0 //p11: quick exit for x = nan |
| };; |
| |
| { .mfi |
| add EXP_AD_P = exp_TB2_size, EXP_AD_TB2 |
| fms.s1 f8_sq_lo = f1, f1, f8_sq_lo // 1 - low bits for -x^2 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| ldfpd exp_P4, exp_P3 = [EXP_AD_P], 16 |
| fmerge.s FR_X = f8,f8 |
| shladd GR_ShftXBi_bias = GR_mBIAS, 4, r0 |
| } |
| { .mfb |
| nop.m 0 |
| (p14) fnma.d.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,FR_2 //p14:y ~=~ 2,x< -6.0 |
| (p14) br.ret.spnt b0 //p14: quick exit for x < -6.0 |
| };; |
| |
| //p15: y ~=~ 0.0(result with underflow error), x > ARG_ASYMP = 28, |
| { .mfi |
| ldfpd exp_P2, exp_P1 = [EXP_AD_P] |
| fma.d.s0 FR_Tmpf = f1, f1, FR_EpsNorm // flag i |
| nop.i 0 |
| } |
| { .mfb |
| (p15) mov GR_Parameter_TAG = 208 |
| (p15) fma.d.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,f0 |
| (p15) br.cond.spnt __libm_error_region |
| };; |
| |
| //p8: x < 27.0, result without ungerflow error |
| { .mfi |
| getf.exp GR_IndxPlusBias = FR_Tmp // exp + bias for (|x|+1)^4 |
| fcmp.lt.s1 p8,p0 = FR_NormX,FR_UnfBound |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fms.s1 EXP_Nfloat = EXP_W_2TO56_RSH, EXP_2TOM56, EXP_RSHF |
| nop.i 0 |
| };; |
| |
| { .mmi |
| shladd GR_ShftXBi = GR_IndxPlusBias, 4, GR_ShftXBi_bias |
| shladd GR_ShftPi = GR_IndxPlusBias, 4, GR_ShftPi_bias |
| shl GR_ShftPi_8 = GR_IndxPlusBias, 8 |
| };; |
| |
| { .mmi |
| getf.sig exp_GR_N = EXP_W_2TO56_RSH |
| add GR_ERFC_XB_TB = GR_ERFC_XB_TB, GR_ShftXBi// pointer to XB[i] |
| sub GR_ShftPi = GR_ShftPi_8, GR_ShftPi // (256-16)*i |
| };; |
| |
| { .mmi |
| ldfe FR_Xb = [GR_ERFC_XB_TB] |
| add GR_ShftA12 = 0xC0, GR_ShftPi // pointer shift for A12 |
| add GR_ShftA13 = 0xD0, GR_ShftPi // pointer shift for A13 |
| };; |
| |
| { .mfi |
| add GR_P_A13 = GR_ERFC_P_TB, GR_ShftA13 // pointer to A13 |
| nop.f 0 |
| and exp_GR_index_1 = 0x0f, exp_GR_N |
| } |
| { .mfi |
| add GR_P_A12 = GR_ERFC_P_TB, GR_ShftA12 // pointer to A12 |
| fnma.s1 exp_r = EXP_Nfloat, exp_ln2_by_128_hi, EXP_NORM_f8 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| ldfe FR_A12 = [GR_P_A12], -64 |
| nop.f 0 |
| and exp_GR_index_2_16 = 0x70, exp_GR_N |
| } |
| { .mfi |
| ldfe FR_A13 = [GR_P_A13], -64 |
| nop.f 0 |
| shladd EXP_AD_T1 = exp_GR_index_1, 4, EXP_AD_TB1 |
| };; |
| |
| { .mmi |
| ldfe FR_A8 = [GR_P_A12], 32 |
| ldfe FR_A9 = [GR_P_A13], 32 |
| add EXP_AD_T2 = EXP_AD_TB2, exp_GR_index_2_16 |
| };; |
| |
| { .mmi |
| ldfe FR_A10 = [GR_P_A12], -96 |
| ldfe FR_A11 = [GR_P_A13], -96 |
| nop.i 0 |
| };; |
| |
| { .mmi |
| ldfe FR_A4 = [GR_P_A12], 32 |
| ldfe FR_A5 = [GR_P_A13], 32 |
| shr r2 = exp_GR_N, 0x7 |
| };; |
| |
| { .mfi |
| ldfe FR_A6 = [GR_P_A12], -64 |
| fma.s1 exp_rP4pP3 = exp_r, exp_P4, exp_P3 |
| nop.i 0 |
| } |
| { .mfi |
| ldfe FR_A7 = [GR_P_A13], -64 |
| fma.s1 exp_rsq = exp_r, exp_r, f0 |
| nop.i 0 |
| };; |
| |
| { .mmi |
| ldfe FR_A2 = [GR_P_A12], -32 |
| ldfe FR_A3 = [GR_P_A13], -32 |
| addl exp_GR_biased_M = 0xffff, r2 |
| };; |
| |
| { .mmi |
| ldfe FR_A0 = [GR_P_A12], 224 |
| ldfe FR_A1 = [GR_P_A13] |
| nop.i 0 |
| };; |
| |
| { .mfi |
| ldfe FR_A14 = [GR_P_A12] |
| fms.s1 FR_LocArg = FR_AbsArg, f1, FR_Xb // xloc = x - x[i] |
| nop.i 0 |
| };; |
| |
| { .mmi |
| setf.exp EXP_2M = exp_GR_biased_M |
| ldfe exp_T1 = [EXP_AD_T1] |
| nop.i 0 |
| };; |
| |
| { .mfi |
| ldfe exp_T2 = [EXP_AD_T2] |
| fma.s1 exp_P_hi = exp_rsq, exp_P1, exp_r |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 exp_rcube = exp_r, exp_rsq, f0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 exp_P_lo = exp_r, exp_rP4pP3, exp_P2 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fnma.s1 exp_f = EXP_Nfloat, exp_ln2_by_128_lo, f8_sq_lo |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_0_1 = FR_LocArg, FR_LocArg, f0 // xloc ^2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_0_2 = FR_A13, FR_LocArg, FR_A12 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_1_1 = FR_A9, FR_LocArg, FR_A8 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_1_2 = FR_A11, FR_LocArg, FR_A10 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_2_1 = FR_A5, FR_LocArg, FR_A4 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_2_2 = FR_A7, FR_LocArg, FR_A6 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_3_1 = FR_A1, FR_LocArg, FR_A0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_3_2 = FR_A3, FR_LocArg, FR_A2 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_6_1 = FR_P14_0_1, FR_A14, FR_P14_0_2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_7_2 = FR_P14_0_1, FR_P14_0_1, f0 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_7_1 = FR_P14_0_1, FR_P14_1_2, FR_P14_1_1 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 exp_S2 = exp_f, exp_T2, f0 |
| nop.i 0 |
| };; |
| { .mfi |
| nop.m 0 |
| fma.s1 exp_S1 = EXP_2M, exp_T1, f0 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_8_1 = FR_P14_0_1, FR_P14_3_2, FR_P14_3_1 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_8_2 = FR_P14_0_1, FR_P14_2_2, FR_P14_2_1 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_12_1 = FR_P14_7_2, FR_P14_6_1, FR_P14_7_1 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 exp_S = exp_S1, exp_S2, f0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 exp_P = exp_rcube, exp_P_lo, exp_P_hi |
| nop.i 0 |
| };; |
| |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_13_1 = FR_P14_7_2, FR_P14_8_2, FR_P14_8_1 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_P14_13_2 = FR_P14_7_2, FR_P14_7_2, f0 // xloc^8 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_Exp = exp_S, exp_P, exp_S // exp(-x^2) |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_Pol = FR_P14_13_2, FR_P14_12_1, FR_P14_13_1 |
| nop.i 0 |
| };; |
| |
| { .mfi |
| nop.m 0 |
| fma.d.s0 FR_Tmpf = f8, f1, f0 // flag d |
| nop.i 0 |
| };; |
| |
| //p6: result for 0 < x < = 28.0, |
| //p7: result for -6.0 <= x < 0, |
| //p8: exit for - 6.0 <= x < UnfBound ~=~ 26.54.. |
| |
| .pred.rel "mutex",p6,p7 |
| { .mfi |
| nop.m 0 |
| (p6) fma.d.s0 f8 = FR_Exp, FR_Pol, f0 |
| nop.i 0 |
| } |
| { .mfb |
| mov GR_Parameter_TAG = 208 |
| (p7) fnma.d.s0 f8 = FR_Exp, FR_Pol, FR_2 |
| (p8) br.ret.sptk b0 |
| };; |
| |
| GLOBAL_LIBM_END(erfc) |
| |
| // call via (p15) br.cond.spnt __libm_error_region |
| // for x > ARG_ASYMP = 28.0 |
| // or |
| // |
| // after .endp erfc for UnfBound < = x < = ARG_ASYMP = 28.0 |
| |
| LOCAL_LIBM_ENTRY(__libm_error_region) |
| .prologue |
| { .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 |
| };; |
| { .mmi |
| stfd [GR_Parameter_Y] = FR_Y,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 |
| { .mib |
| stfd [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack |
| add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address |
| nop.b 0 |
| } |
| { .mib |
| stfd [GR_Parameter_Y] = FR_RESULT // 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 |
| };; |
| { .mmi |
| ldfd 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 |
| };; |
| |
| LOCAL_LIBM_END(__libm_error_region) |
| .type __libm_error_support#,@function |
| .global __libm_error_support# |
| |
| |
| |
