| .file "log1pf.s" |
| |
| |
| // Copyright (c) 2000 - 2003, Intel Corporation |
| // All rights reserved. |
| // |
| // Contributed 2000 by the Intel Numerics Group, Intel Corporation |
| // |
| // Redistribution and use in source and binary forms, with or without |
| // modification, are permitted provided that the following conditions are |
| // met: |
| // |
| // * Redistributions of source code must retain the above copyright |
| // notice, this list of conditions and the following disclaimer. |
| // |
| // * Redistributions in binary form must reproduce the above copyright |
| // notice, this list of conditions and the following disclaimer in the |
| // documentation and/or other materials provided with the distribution. |
| // |
| // * The name of Intel Corporation may not be used to endorse or promote |
| // products derived from this software without specific prior written |
| // permission. |
| |
| // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS |
| // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, |
| // EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, |
| // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR |
| // PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY |
| // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING |
| // NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS |
| // SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| // |
| // Intel Corporation is the author of this code, and requests that all |
| // problem reports or change requests be submitted to it directly at |
| // http://www.intel.com/software/products/opensource/libraries/num.htm. |
| // |
| // History |
| //============================================================== |
| // 02/02/00 Initial version |
| // 04/04/00 Unwind support added |
| // 08/15/00 Bundle added after call to __libm_error_support to properly |
| // set [the previously overwritten] GR_Parameter_RESULT. |
| // 06/29/01 Improved speed of all paths |
| // 05/20/02 Cleaned up namespace and sf0 syntax |
| // 10/02/02 Improved performance by basing on log algorithm |
| // 02/10/03 Reordered header: .section, .global, .proc, .align |
| // 04/18/03 Eliminate possible WAW dependency warning |
| // 12/16/03 Fixed parameter passing to/from error handling routine |
| // |
| // API |
| //============================================================== |
| // float log1pf(float) |
| // |
| // log1p(x) = log(x+1) |
| // |
| // Overview of operation |
| //============================================================== |
| // Background |
| // ---------- |
| // |
| // This algorithm is based on fact that |
| // log1p(x) = log(1+x) and |
| // log(a b) = log(a) + log(b). |
| // In our case we have 1+x = 2^N f, where 1 <= f < 2. |
| // So |
| // log(1+x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f) |
| // |
| // To calculate log(f) we do following |
| // log(f) = log(f * frcpa(f) / frcpa(f)) = |
| // = log(f * frcpa(f)) + log(1/frcpa(f)) |
| // |
| // According to definition of IA-64's frcpa instruction it's a |
| // floating point that approximates 1/f using a lookup on the |
| // top of 8 bits of the input number's + 1 significand with relative |
| // error < 2^(-8.886). So we have following |
| // |
| // |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256 |
| // |
| // and |
| // |
| // log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) = |
| // = log(1 + r) + T |
| // |
| // The first value can be computed by polynomial P(r) approximating |
| // log(1 + r) on |r| < 1/256 and the second is precomputed tabular |
| // value defined by top 8 bit of f. |
| // |
| // Finally we have that log(1+x) ~ (N*log(2) + T) + P(r) |
| // |
| // Note that if input argument is close to 0.0 (in our case it means |
| // that |x| < 1/256) we can use just polynomial approximation |
| // because 1+x = 2^0 * f = f = 1 + r and |
| // log(1+x) = log(1 + r) ~ P(r) |
| // |
| // |
| // Implementation |
| // -------------- |
| // |
| // 1. |x| >= 2^(-8), and x > -1 |
| // InvX = frcpa(x+1) |
| // r = InvX*(x+1) - 1 |
| // P(r) = r*((1 - A2*4) + r^2*(A3 - A4*r)) = r*P2(r), |
| // A4,A3,A2 are created with setf instruction. |
| // We use Taylor series and so A4 = 1/4, A3 = 1/3, |
| // A2 = 1/2 rounded to double. |
| // |
| // N = float(n) where n is true unbiased exponent of x |
| // |
| // T is tabular value of log(1/frcpa(x)) calculated in quad precision |
| // and rounded to double. To load T we get bits from 55 to 62 of register |
| // format significand as index and calculate address |
| // ad_T = table_base_addr + 8 * index |
| // |
| // L1 (log(2)) is calculated in quad precision and rounded to double; |
| // it's created with setf |
| // |
| // And final result = P2(r)*r + (T + N*L1) |
| // |
| // |
| // 2. 2^(-40) <= |x| < 2^(-8) |
| // r = x |
| // P(r) = r*((1 - A2*4) + r^2*(A3 - A4*r)) = r*P2(r), |
| // A4,A3,A2 are the same as in case |x| >= 1/256 |
| // |
| // And final result = P2(r)*r |
| // |
| // 3. 0 < |x| < 2^(-40) |
| // Although log1p(x) is basically x, we would like to preserve the inexactness |
| // nature as well as consistent behavior under different rounding modes. |
| // We can do this by computing the result as |
| // |
| // log1p(x) = x - x*x |
| // |
| // |
| // Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are |
| // filtered and processed on special branches. |
| // |
| |
| // |
| // Special values |
| //============================================================== |
| // |
| // log1p(-1) = -inf // Call error support |
| // |
| // log1p(+qnan) = +qnan |
| // log1p(-qnan) = -qnan |
| // log1p(+snan) = +qnan |
| // log1p(-snan) = -qnan |
| // |
| // log1p(x),x<-1= QNAN Indefinite // Call error support |
| // log1p(-inf) = QNAN Indefinite |
| // log1p(+inf) = +inf |
| // log1p(+/-0) = +/-0 |
| // |
| // |
| // Registers used |
| //============================================================== |
| // Floating Point registers used: |
| // f8, input |
| // f7 -> f15, f32 -> f36 |
| // |
| // General registers used: |
| // r8 -> r11 |
| // r14 -> r22 |
| // |
| // Predicate registers used: |
| // p6 -> p12 |
| |
| // Assembly macros |
| //============================================================== |
| GR_TAG = r8 |
| GR_ad_T = r9 |
| GR_Exp = r10 |
| GR_N = r11 |
| |
| GR_signexp_x = r14 |
| GR_exp_mask = r15 |
| GR_exp_bias = r16 |
| GR_05 = r17 |
| GR_A3 = r18 |
| GR_Sig = r19 |
| GR_Ind = r19 |
| GR_exp_x = r20 |
| GR_Ln2 = r21 |
| GR_025 = r22 |
| |
| |
| GR_SAVE_B0 = r33 |
| GR_SAVE_PFS = r34 |
| GR_SAVE_GP = r35 |
| GR_SAVE_SP = r36 |
| |
| GR_Parameter_X = r37 |
| GR_Parameter_Y = r38 |
| GR_Parameter_RESULT = r39 |
| GR_Parameter_TAG = r40 |
| |
| |
| |
| FR_NormX = f7 |
| FR_RcpX = f9 |
| FR_r = f10 |
| FR_r2 = f11 |
| FR_r4 = f12 |
| FR_N = f13 |
| FR_Ln2 = f14 |
| FR_Xp1 = f15 |
| |
| FR_A4 = f33 |
| FR_A3 = f34 |
| FR_A2 = f35 |
| |
| FR_T = f36 |
| FR_NxLn2pT = f36 |
| |
| |
| |
| FR_Y = f1 |
| FR_X = f10 |
| FR_RESULT = f8 |
| |
| |
| // Data |
| //============================================================== |
| RODATA |
| .align 16 |
| |
| LOCAL_OBJECT_START(log_data) |
| // ln(1/frcpa(1+i/256)), i=0...255 |
| data8 0x3F60040155D5889E // 0 |
| data8 0x3F78121214586B54 // 1 |
| data8 0x3F841929F96832F0 // 2 |
| data8 0x3F8C317384C75F06 // 3 |
| data8 0x3F91A6B91AC73386 // 4 |
| data8 0x3F95BA9A5D9AC039 // 5 |
| data8 0x3F99D2A8074325F4 // 6 |
| data8 0x3F9D6B2725979802 // 7 |
| data8 0x3FA0C58FA19DFAAA // 8 |
| data8 0x3FA2954C78CBCE1B // 9 |
| data8 0x3FA4A94D2DA96C56 // 10 |
| data8 0x3FA67C94F2D4BB58 // 11 |
| data8 0x3FA85188B630F068 // 12 |
| data8 0x3FAA6B8ABE73AF4C // 13 |
| data8 0x3FAC441E06F72A9E // 14 |
| data8 0x3FAE1E6713606D07 // 15 |
| data8 0x3FAFFA6911AB9301 // 16 |
| data8 0x3FB0EC139C5DA601 // 17 |
| data8 0x3FB1DBD2643D190B // 18 |
| data8 0x3FB2CC7284FE5F1C // 19 |
| data8 0x3FB3BDF5A7D1EE64 // 20 |
| data8 0x3FB4B05D7AA012E0 // 21 |
| data8 0x3FB580DB7CEB5702 // 22 |
| data8 0x3FB674F089365A7A // 23 |
| data8 0x3FB769EF2C6B568D // 24 |
| data8 0x3FB85FD927506A48 // 25 |
| data8 0x3FB9335E5D594989 // 26 |
| data8 0x3FBA2B0220C8E5F5 // 27 |
| data8 0x3FBB0004AC1A86AC // 28 |
| data8 0x3FBBF968769FCA11 // 29 |
| data8 0x3FBCCFEDBFEE13A8 // 30 |
| data8 0x3FBDA727638446A2 // 31 |
| data8 0x3FBEA3257FE10F7A // 32 |
| data8 0x3FBF7BE9FEDBFDE6 // 33 |
| data8 0x3FC02AB352FF25F4 // 34 |
| data8 0x3FC097CE579D204D // 35 |
| data8 0x3FC1178E8227E47C // 36 |
| data8 0x3FC185747DBECF34 // 37 |
| data8 0x3FC1F3B925F25D41 // 38 |
| data8 0x3FC2625D1E6DDF57 // 39 |
| data8 0x3FC2D1610C86813A // 40 |
| data8 0x3FC340C59741142E // 41 |
| data8 0x3FC3B08B6757F2A9 // 42 |
| data8 0x3FC40DFB08378003 // 43 |
| data8 0x3FC47E74E8CA5F7C // 44 |
| data8 0x3FC4EF51F6466DE4 // 45 |
| data8 0x3FC56092E02BA516 // 46 |
| data8 0x3FC5D23857CD74D5 // 47 |
| data8 0x3FC6313A37335D76 // 48 |
| data8 0x3FC6A399DABBD383 // 49 |
| data8 0x3FC70337DD3CE41B // 50 |
| data8 0x3FC77654128F6127 // 51 |
| data8 0x3FC7E9D82A0B022D // 52 |
| data8 0x3FC84A6B759F512F // 53 |
| data8 0x3FC8AB47D5F5A310 // 54 |
| data8 0x3FC91FE49096581B // 55 |
| data8 0x3FC981634011AA75 // 56 |
| data8 0x3FC9F6C407089664 // 57 |
| data8 0x3FCA58E729348F43 // 58 |
| data8 0x3FCABB55C31693AD // 59 |
| data8 0x3FCB1E104919EFD0 // 60 |
| data8 0x3FCB94EE93E367CB // 61 |
| data8 0x3FCBF851C067555F // 62 |
| data8 0x3FCC5C0254BF23A6 // 63 |
| data8 0x3FCCC000C9DB3C52 // 64 |
| data8 0x3FCD244D99C85674 // 65 |
| data8 0x3FCD88E93FB2F450 // 66 |
| data8 0x3FCDEDD437EAEF01 // 67 |
| data8 0x3FCE530EFFE71012 // 68 |
| data8 0x3FCEB89A1648B971 // 69 |
| data8 0x3FCF1E75FADF9BDE // 70 |
| data8 0x3FCF84A32EAD7C35 // 71 |
| data8 0x3FCFEB2233EA07CD // 72 |
| data8 0x3FD028F9C7035C1C // 73 |
| data8 0x3FD05C8BE0D9635A // 74 |
| data8 0x3FD085EB8F8AE797 // 75 |
| data8 0x3FD0B9C8E32D1911 // 76 |
| data8 0x3FD0EDD060B78081 // 77 |
| data8 0x3FD122024CF0063F // 78 |
| data8 0x3FD14BE2927AECD4 // 79 |
| data8 0x3FD180618EF18ADF // 80 |
| data8 0x3FD1B50BBE2FC63B // 81 |
| data8 0x3FD1DF4CC7CF242D // 82 |
| data8 0x3FD214456D0EB8D4 // 83 |
| data8 0x3FD23EC5991EBA49 // 84 |
| data8 0x3FD2740D9F870AFB // 85 |
| data8 0x3FD29ECDABCDFA04 // 86 |
| data8 0x3FD2D46602ADCCEE // 87 |
| data8 0x3FD2FF66B04EA9D4 // 88 |
| data8 0x3FD335504B355A37 // 89 |
| data8 0x3FD360925EC44F5D // 90 |
| data8 0x3FD38BF1C3337E75 // 91 |
| data8 0x3FD3C25277333184 // 92 |
| data8 0x3FD3EDF463C1683E // 93 |
| data8 0x3FD419B423D5E8C7 // 94 |
| data8 0x3FD44591E0539F49 // 95 |
| data8 0x3FD47C9175B6F0AD // 96 |
| data8 0x3FD4A8B341552B09 // 97 |
| data8 0x3FD4D4F3908901A0 // 98 |
| data8 0x3FD501528DA1F968 // 99 |
| data8 0x3FD52DD06347D4F6 // 100 |
| data8 0x3FD55A6D3C7B8A8A // 101 |
| data8 0x3FD5925D2B112A59 // 102 |
| data8 0x3FD5BF406B543DB2 // 103 |
| data8 0x3FD5EC433D5C35AE // 104 |
| data8 0x3FD61965CDB02C1F // 105 |
| data8 0x3FD646A84935B2A2 // 106 |
| data8 0x3FD6740ADD31DE94 // 107 |
| data8 0x3FD6A18DB74A58C5 // 108 |
| data8 0x3FD6CF31058670EC // 109 |
| data8 0x3FD6F180E852F0BA // 110 |
| data8 0x3FD71F5D71B894F0 // 111 |
| data8 0x3FD74D5AEFD66D5C // 112 |
| data8 0x3FD77B79922BD37E // 113 |
| data8 0x3FD7A9B9889F19E2 // 114 |
| data8 0x3FD7D81B037EB6A6 // 115 |
| data8 0x3FD8069E33827231 // 116 |
| data8 0x3FD82996D3EF8BCB // 117 |
| data8 0x3FD85855776DCBFB // 118 |
| data8 0x3FD8873658327CCF // 119 |
| data8 0x3FD8AA75973AB8CF // 120 |
| data8 0x3FD8D992DC8824E5 // 121 |
| data8 0x3FD908D2EA7D9512 // 122 |
| data8 0x3FD92C59E79C0E56 // 123 |
| data8 0x3FD95BD750EE3ED3 // 124 |
| data8 0x3FD98B7811A3EE5B // 125 |
| data8 0x3FD9AF47F33D406C // 126 |
| data8 0x3FD9DF270C1914A8 // 127 |
| data8 0x3FDA0325ED14FDA4 // 128 |
| data8 0x3FDA33440224FA79 // 129 |
| data8 0x3FDA57725E80C383 // 130 |
| data8 0x3FDA87D0165DD199 // 131 |
| data8 0x3FDAAC2E6C03F896 // 132 |
| data8 0x3FDADCCC6FDF6A81 // 133 |
| data8 0x3FDB015B3EB1E790 // 134 |
| data8 0x3FDB323A3A635948 // 135 |
| data8 0x3FDB56FA04462909 // 136 |
| data8 0x3FDB881AA659BC93 // 137 |
| data8 0x3FDBAD0BEF3DB165 // 138 |
| data8 0x3FDBD21297781C2F // 139 |
| data8 0x3FDC039236F08819 // 140 |
| data8 0x3FDC28CB1E4D32FD // 141 |
| data8 0x3FDC4E19B84723C2 // 142 |
| data8 0x3FDC7FF9C74554C9 // 143 |
| data8 0x3FDCA57B64E9DB05 // 144 |
| data8 0x3FDCCB130A5CEBB0 // 145 |
| data8 0x3FDCF0C0D18F326F // 146 |
| data8 0x3FDD232075B5A201 // 147 |
| data8 0x3FDD490246DEFA6B // 148 |
| data8 0x3FDD6EFA918D25CD // 149 |
| data8 0x3FDD9509707AE52F // 150 |
| data8 0x3FDDBB2EFE92C554 // 151 |
| data8 0x3FDDEE2F3445E4AF // 152 |
| data8 0x3FDE148A1A2726CE // 153 |
| data8 0x3FDE3AFC0A49FF40 // 154 |
| data8 0x3FDE6185206D516E // 155 |
| data8 0x3FDE882578823D52 // 156 |
| data8 0x3FDEAEDD2EAC990C // 157 |
| data8 0x3FDED5AC5F436BE3 // 158 |
| data8 0x3FDEFC9326D16AB9 // 159 |
| data8 0x3FDF2391A2157600 // 160 |
| data8 0x3FDF4AA7EE03192D // 161 |
| data8 0x3FDF71D627C30BB0 // 162 |
| data8 0x3FDF991C6CB3B379 // 163 |
| data8 0x3FDFC07ADA69A910 // 164 |
| data8 0x3FDFE7F18EB03D3E // 165 |
| data8 0x3FE007C053C5002E // 166 |
| data8 0x3FE01B942198A5A1 // 167 |
| data8 0x3FE02F74400C64EB // 168 |
| data8 0x3FE04360BE7603AD // 169 |
| data8 0x3FE05759AC47FE34 // 170 |
| data8 0x3FE06B5F1911CF52 // 171 |
| data8 0x3FE078BF0533C568 // 172 |
| data8 0x3FE08CD9687E7B0E // 173 |
| data8 0x3FE0A10074CF9019 // 174 |
| data8 0x3FE0B5343A234477 // 175 |
| data8 0x3FE0C974C89431CE // 176 |
| data8 0x3FE0DDC2305B9886 // 177 |
| data8 0x3FE0EB524BAFC918 // 178 |
| data8 0x3FE0FFB54213A476 // 179 |
| data8 0x3FE114253DA97D9F // 180 |
| data8 0x3FE128A24F1D9AFF // 181 |
| data8 0x3FE1365252BF0865 // 182 |
| data8 0x3FE14AE558B4A92D // 183 |
| data8 0x3FE15F85A19C765B // 184 |
| data8 0x3FE16D4D38C119FA // 185 |
| data8 0x3FE18203C20DD133 // 186 |
| data8 0x3FE196C7BC4B1F3B // 187 |
| data8 0x3FE1A4A738B7A33C // 188 |
| data8 0x3FE1B981C0C9653D // 189 |
| data8 0x3FE1CE69E8BB106B // 190 |
| data8 0x3FE1DC619DE06944 // 191 |
| data8 0x3FE1F160A2AD0DA4 // 192 |
| data8 0x3FE2066D7740737E // 193 |
| data8 0x3FE2147DBA47A394 // 194 |
| data8 0x3FE229A1BC5EBAC3 // 195 |
| data8 0x3FE237C1841A502E // 196 |
| data8 0x3FE24CFCE6F80D9A // 197 |
| data8 0x3FE25B2C55CD5762 // 198 |
| data8 0x3FE2707F4D5F7C41 // 199 |
| data8 0x3FE285E0842CA384 // 200 |
| data8 0x3FE294294708B773 // 201 |
| data8 0x3FE2A9A2670AFF0C // 202 |
| data8 0x3FE2B7FB2C8D1CC1 // 203 |
| data8 0x3FE2C65A6395F5F5 // 204 |
| data8 0x3FE2DBF557B0DF43 // 205 |
| data8 0x3FE2EA64C3F97655 // 206 |
| data8 0x3FE3001823684D73 // 207 |
| data8 0x3FE30E97E9A8B5CD // 208 |
| data8 0x3FE32463EBDD34EA // 209 |
| data8 0x3FE332F4314AD796 // 210 |
| data8 0x3FE348D90E7464D0 // 211 |
| data8 0x3FE35779F8C43D6E // 212 |
| data8 0x3FE36621961A6A99 // 213 |
| data8 0x3FE37C299F3C366A // 214 |
| data8 0x3FE38AE2171976E7 // 215 |
| data8 0x3FE399A157A603E7 // 216 |
| data8 0x3FE3AFCCFE77B9D1 // 217 |
| data8 0x3FE3BE9D503533B5 // 218 |
| data8 0x3FE3CD7480B4A8A3 // 219 |
| data8 0x3FE3E3C43918F76C // 220 |
| data8 0x3FE3F2ACB27ED6C7 // 221 |
| data8 0x3FE4019C2125CA93 // 222 |
| data8 0x3FE4181061389722 // 223 |
| data8 0x3FE42711518DF545 // 224 |
| data8 0x3FE436194E12B6BF // 225 |
| data8 0x3FE445285D68EA69 // 226 |
| data8 0x3FE45BCC464C893A // 227 |
| data8 0x3FE46AED21F117FC // 228 |
| data8 0x3FE47A1527E8A2D3 // 229 |
| data8 0x3FE489445EFFFCCC // 230 |
| data8 0x3FE4A018BCB69835 // 231 |
| data8 0x3FE4AF5A0C9D65D7 // 232 |
| data8 0x3FE4BEA2A5BDBE87 // 233 |
| data8 0x3FE4CDF28F10AC46 // 234 |
| data8 0x3FE4DD49CF994058 // 235 |
| data8 0x3FE4ECA86E64A684 // 236 |
| data8 0x3FE503C43CD8EB68 // 237 |
| data8 0x3FE513356667FC57 // 238 |
| data8 0x3FE522AE0738A3D8 // 239 |
| data8 0x3FE5322E26867857 // 240 |
| data8 0x3FE541B5CB979809 // 241 |
| data8 0x3FE55144FDBCBD62 // 242 |
| data8 0x3FE560DBC45153C7 // 243 |
| data8 0x3FE5707A26BB8C66 // 244 |
| data8 0x3FE587F60ED5B900 // 245 |
| data8 0x3FE597A7977C8F31 // 246 |
| data8 0x3FE5A760D634BB8B // 247 |
| data8 0x3FE5B721D295F10F // 248 |
| data8 0x3FE5C6EA94431EF9 // 249 |
| data8 0x3FE5D6BB22EA86F6 // 250 |
| data8 0x3FE5E6938645D390 // 251 |
| data8 0x3FE5F673C61A2ED2 // 252 |
| data8 0x3FE6065BEA385926 // 253 |
| data8 0x3FE6164BFA7CC06B // 254 |
| data8 0x3FE62643FECF9743 // 255 |
| LOCAL_OBJECT_END(log_data) |
| |
| |
| // Code |
| //============================================================== |
| |
| .section .text |
| GLOBAL_IEEE754_ENTRY(log1pf) |
| { .mfi |
| getf.exp GR_signexp_x = f8 // if x is unorm then must recompute |
| fadd.s1 FR_Xp1 = f8, f1 // Form 1+x |
| mov GR_05 = 0xfffe |
| } |
| { .mlx |
| addl GR_ad_T = @ltoff(log_data),gp |
| movl GR_A3 = 0x3fd5555555555555 // double precision memory |
| // representation of A3 |
| } |
| ;; |
| |
| { .mfi |
| ld8 GR_ad_T = [GR_ad_T] |
| fclass.m p8,p0 = f8,0xb // Is x unorm? |
| mov GR_exp_mask = 0x1ffff |
| } |
| { .mfi |
| mov GR_025 = 0xfffd // Exponent of 0.25 |
| fnorm.s1 FR_NormX = f8 // Normalize x |
| mov GR_exp_bias = 0xffff |
| } |
| ;; |
| |
| { .mfi |
| setf.exp FR_A2 = GR_05 // create A2 = 0.5 |
| fclass.m p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf? |
| nop.i 0 |
| } |
| { .mib |
| setf.d FR_A3 = GR_A3 // create A3 |
| nop.i 0 |
| (p8) br.cond.spnt log1p_unorm // Branch if x=unorm |
| } |
| ;; |
| |
| log1p_common: |
| { .mfi |
| setf.exp FR_A4 = GR_025 // create A4 = 0.25 |
| frcpa.s1 FR_RcpX,p0 = f1,FR_Xp1 |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| (p9) fma.s.s0 f8 = f8,f1,f0 // set V-flag |
| (p9) br.ret.spnt b0 // exit for NaN, NaT and +Inf |
| } |
| ;; |
| |
| { .mfi |
| getf.exp GR_Exp = FR_Xp1 // signexp of x+1 |
| fclass.m p10,p0 = FR_Xp1,0x3A // is 1+x < 0? |
| and GR_exp_x = GR_exp_mask, GR_signexp_x // biased exponent of x |
| } |
| { .mlx |
| nop.m 0 |
| movl GR_Ln2 = 0x3FE62E42FEFA39EF // double precision memory |
| // representation of log(2) |
| } |
| ;; |
| |
| { .mfi |
| getf.sig GR_Sig = FR_Xp1 // get significand to calculate index |
| // for T if |x| >= 2^-8 |
| fcmp.eq.s1 p12,p0 = f8,f0 // is x equal to 0? |
| sub GR_exp_x = GR_exp_x, GR_exp_bias // true exponent of x |
| } |
| ;; |
| |
| { .mfi |
| sub GR_N = GR_Exp,GR_exp_bias // true exponent of x+1 |
| fcmp.eq.s1 p11,p0 = FR_Xp1,f0 // is x = -1? |
| cmp.gt p6,p7 = -8, GR_exp_x // Is |x| < 2^-8 |
| } |
| { .mfb |
| nop.m 0 |
| nop.f 0 |
| (p10) br.cond.spnt log1p_lt_minus_1 // jump if x < -1 |
| } |
| ;; |
| |
| // p6 is true if |x| < 1/256 |
| // p7 is true if |x| >= 1/256 |
| .pred.rel "mutex",p6,p7 |
| { .mfi |
| nop.m 0 |
| (p6) fms.s1 FR_r = f8,f1,f0 // range reduction for |x|<1/256 |
| (p6) cmp.gt.unc p10,p0 = -40, GR_exp_x // Is |x| < 2^-40 |
| } |
| { .mfb |
| (p7) setf.sig FR_N = GR_N // copy unbiased exponent of x to the |
| // significand field of FR_N |
| (p7) fms.s1 FR_r = FR_RcpX,FR_Xp1,f1 // range reduction for |x|>=1/256 |
| (p12) br.ret.spnt b0 // exit for x=0, return x |
| } |
| ;; |
| |
| { .mib |
| setf.d FR_Ln2 = GR_Ln2 // create log(2) |
| (p7) extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index |
| (p11) br.cond.spnt log1p_eq_minus_1 // jump if x = -1 |
| } |
| ;; |
| |
| { .mmf |
| (p7) shladd GR_ad_T = GR_Ind,3,GR_ad_T // address of T |
| nop.m 0 |
| (p10) fnma.s.s0 f8 = f8,f8,f8 // If |x| very small, result=x-x*x |
| } |
| ;; |
| |
| { .mmb |
| (p7) ldfd FR_T = [GR_ad_T] |
| nop.m 0 |
| (p10) br.ret.spnt b0 // Exit if |x| < 2^-40 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fnma.s1 FR_A2 = FR_A2,FR_r,f1 // 1.0 - A2*r |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fnma.s1 FR_A3 = FR_A4,FR_r,FR_A3 // A3 - A4*r |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| (p7) fcvt.xf FR_N = FR_N |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| // (A3*r+A2)*r^2+r |
| fma.s1 FR_A2 = FR_A3,FR_r2,FR_A2 // (A4*r+A3)*r^2+(A2*r+1) |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| // N*Ln2hi+T |
| (p7) fma.s1 FR_NxLn2pT = FR_N,FR_Ln2,FR_T |
| nop.i 0 |
| } |
| ;; |
| |
| .pred.rel "mutex",p6,p7 |
| { .mfi |
| nop.m 0 |
| (p6) fma.s.s0 f8 = FR_A2,FR_r,f0 // result if 2^(-40) <= |x| < 1/256 |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| (p7) fma.s.s0 f8 = FR_A2,FR_r,FR_NxLn2pT // result if |x| >= 1/256 |
| br.ret.sptk b0 // Exit if |x| >= 2^(-40) |
| } |
| ;; |
| |
| .align 32 |
| log1p_unorm: |
| // Here if x=unorm |
| { .mfb |
| getf.exp GR_signexp_x = FR_NormX // recompute biased exponent |
| nop.f 0 |
| br.cond.sptk log1p_common |
| } |
| ;; |
| |
| .align 32 |
| log1p_eq_minus_1: |
| // Here if x=-1 |
| { .mfi |
| nop.m 0 |
| fmerge.s FR_X = f8,f8 // keep input argument for subsequent |
| // call of __libm_error_support# |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| mov GR_TAG = 142 // set libm error in case of log1p(-1). |
| frcpa.s0 f8,p0 = f8,f0 // log1p(-1) should be equal to -INF. |
| // We can get it using frcpa because it |
| // sets result to the IEEE-754 mandated |
| // quotient of f8/f0. |
| nop.i 0 |
| } |
| { .mib |
| nop.m 0 |
| nop.i 0 |
| br.cond.sptk log_libm_err |
| } |
| ;; |
| |
| .align 32 |
| log1p_lt_minus_1: |
| // Here if x < -1 |
| { .mfi |
| nop.m 0 |
| fmerge.s FR_X = f8,f8 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| mov GR_TAG = 143 // set libm error in case of x < -1. |
| frcpa.s0 f8,p0 = f0,f0 // log1p(x) x < -1 should be equal to NaN. |
| // We can get it using frcpa because it |
| // sets result to the IEEE-754 mandated |
| // quotient of f0/f0 i.e. NaN. |
| nop.i 0 |
| } |
| ;; |
| |
| .align 32 |
| log_libm_err: |
| { .mmi |
| alloc r32 = ar.pfs,1,4,4,0 |
| mov GR_Parameter_TAG = GR_TAG |
| nop.i 0 |
| } |
| ;; |
| |
| GLOBAL_IEEE754_END(log1pf) |
| |
| |
| 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 |
| stfs [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 |
| stfs [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 |
| stfs [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 |
| add GR_Parameter_RESULT = 48,sp |
| nop.m 0 |
| nop.i 0 |
| };; |
| { .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 |
| };; |
| LOCAL_LIBM_END(__libm_error_region) |
| |
| .type __libm_error_support#,@function |
| .global __libm_error_support# |
| |
