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Diffstat (limited to 'sysdeps/ia64/fpu/s_log1pf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/s_log1pf.S | 788 |
1 files changed, 788 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/s_log1pf.S b/sysdeps/ia64/fpu/s_log1pf.S new file mode 100644 index 0000000..b04b18e --- /dev/null +++ b/sysdeps/ia64/fpu/s_log1pf.S @@ -0,0 +1,788 @@ +.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# |