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Diffstat (limited to 'sysdeps/ia64/fpu/e_logf.S')
| -rw-r--r-- | sysdeps/ia64/fpu/e_logf.S | 946 |
1 files changed, 946 insertions, 0 deletions
diff --git a/sysdeps/ia64/fpu/e_logf.S b/sysdeps/ia64/fpu/e_logf.S new file mode 100644 index 0000000000..1799e4c1c2 --- /dev/null +++ b/sysdeps/ia64/fpu/e_logf.S @@ -0,0 +1,946 @@ +.file "logf.s" + +// Copyright (c) 2000, 2001, Intel Corporation +// All rights reserved. +// +// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story, +// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation. +// +// 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 +//============================================================== +// 3/01/00 Initial version +// 8/15/00 Bundle added after call to __libm_error_support to properly +// set [the previously overwritten] GR_Parameter_RESULT. +// 1/10/01 Improved speed, fixed flags for neg denormals +// +// +// API +//============================================================== +// float logf(float) +// float log10f(float) +// +// Overview of operation +//============================================================== +// Background +// +// Consider x = 2^N 1.f1 f2 f3 f4...f63 +// Log(x) = log(frcpa(x) x/frcpa(x)) +// = log(1/frcpa(x)) + log(frcpa(x) x) +// = -log(frcpa(x)) + log(frcpa(x) x) +// +// frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63) +// +// -log(frcpa(x)) = -log(C) +// = -log(2^-N) - log(frcpa(1.f1 f2 ... f63)) +// +// -log(frcpa(x)) = -log(C) +// = +Nlog2 - log(frcpa(1.f1 f2 ... f63)) +// +// -log(frcpa(x)) = -log(C) +// = +Nlog2 + log(frcpa(1.f1 f2 ... f63)) +// +// Log(x) = log(1/frcpa(x)) + log(frcpa(x) x) + +// Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x) +// Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x) +// Log(x) = +Nlog2 + T + log(frcpa(x) x) +// +// Log(x) = +Nlog2 + T + log(C x) +// +// Cx = 1 + r +// +// Log(x) = +Nlog2 + T + log(1+r) +// Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....) +// +// 1.f1 f2 ... f8 has 256 entries. +// They are 1 + k/2^8, k = 0 ... 255 +// These 256 values are the table entries. +// +// Implementation +//=============== +// CASE 1: |x-1| >= 2^-8 +// C = frcpa(x) +// r = C * x - 1 +// +// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 +// +// x = f * 2*n where f is 1.f_1f_2f_3....f_63 +// Nfloat = float(n) where n is the true unbiased exponent +// pre-index = f_1f_2....f_8 +// index = pre_index * 16 +// get the dxt table entry at index + offset = T +// +// result = (T + Nfloat * log(2)) + rseries +// +// The T table is calculated as follows +// Form x_k = 1 + k/2^8 where k goes from 0... 255 +// y_k = frcpa(x_k) +// log(1/y_k) in quad and round to double + +// CASE 2: |x-1| < 2^-6 +// w = x - 1 +// +// Form wseries = w + Q1*w^2 + Q2*w^3 + Q3*w^4 +// +// result = wseries + +// Special values +//============================================================== + + +// log(+0) = -inf +// log(-0) = -inf + +// log(+qnan) = +qnan +// log(-qnan) = -qnan +// log(+snan) = +qnan +// log(-snan) = -qnan + +// log(-n) = QNAN Indefinite +// log(-inf) = QNAN Indefinite + +// log(+inf) = +inf + +// Registers used +//============================================================== +// Floating Point registers used: +// f8, input +// f9 -> f15, f32 -> f47 + +// General registers used: +// r32 -> r51 + +// Predicate registers used: +// p6 -> p15 + +// p8 log base e +// p6 log base e special +// p9 used in the frcpa +// p13 log base e large W +// p14 log base e small w + +// p7 log base 10 +// p10 log base 10 large W +// p11 log base 10 small w +// p12 log base 10 special + +#include "libm_support.h" + +// Assembly macros +//============================================================== + +log_int_Nfloat = f9 +log_Nfloat = f10 + +log_P3 = f11 +log_P2 = f12 +log_P1 = f13 +log_inv_ln10 = f14 +log_log2 = f15 + +log_w = f32 +log_T = f33 +log_rp_p32 = f34 +log_rp_p2 = f35 +log_rp_p10 = f36 +log_rsq = f37 +log_T_plus_Nlog2 = f38 +log_r = f39 +log_C = f40 +log_rp_q32 = f41 +log_rp_q2 = f42 +log_rp_q10 = f43 +log_wsq = f44 +log_Q = f45 +log_inv_ln10 = f46 +log_NORM_f8 = f47 + +// =================================== + +log_GR_exp_17_ones = r33 +log_GR_exp_16_ones = r34 +log_GR_exp_f8 = r35 +log_GR_signexp_f8 = r36 +log_GR_true_exp_f8 = r37 +log_GR_significand_f8 = r38 +log_GR_index = r39 +log_AD_1 = r40 +log_GR_signexp_w = r41 +log_GR_fff7 = r42 +log_AD_2 = r43 +log_GR_exp_w = r44 + +GR_SAVE_B0 = r45 +GR_SAVE_GP = r46 +GR_SAVE_PFS = r47 + +GR_Parameter_X = r48 +GR_Parameter_Y = r49 +GR_Parameter_RESULT = r50 +log_GR_tag = r51 + + +// Data tables +//============================================================== + +#ifdef _LIBC +.rodata +#else +.data +#endif + +.align 16 + +log_table_1: +ASM_TYPE_DIRECTIVE(log_table_1,@object) +data8 0xbfd0001008f39d59 // p3 +data8 0x3fd5556073e0c45a // p2 +ASM_SIZE_DIRECTIVE(log_table_1) + +log_table_2: +ASM_TYPE_DIRECTIVE(log_table_2,@object) +data8 0xbfdffffffffaea15 // p1 +data8 0x3fdbcb7b1526e50e // 1/ln10 +data8 0x3fe62e42fefa39ef // Log(2) +data8 0x0 // pad + +data8 0x3F60040155D5889E //log(1/frcpa(1+ 0/256) +data8 0x3F78121214586B54 //log(1/frcpa(1+ 1/256) +data8 0x3F841929F96832F0 //log(1/frcpa(1+ 2/256) +data8 0x3F8C317384C75F06 //log(1/frcpa(1+ 3/256) +data8 0x3F91A6B91AC73386 //log(1/frcpa(1+ 4/256) +data8 0x3F95BA9A5D9AC039 //log(1/frcpa(1+ 5/256) +data8 0x3F99D2A8074325F4 //log(1/frcpa(1+ 6/256) +data8 0x3F9D6B2725979802 //log(1/frcpa(1+ 7/256) +data8 0x3FA0C58FA19DFAAA //log(1/frcpa(1+ 8/256) +data8 0x3FA2954C78CBCE1B //log(1/frcpa(1+ 9/256) +data8 0x3FA4A94D2DA96C56 //log(1/frcpa(1+ 10/256) +data8 0x3FA67C94F2D4BB58 //log(1/frcpa(1+ 11/256) +data8 0x3FA85188B630F068 //log(1/frcpa(1+ 12/256) +data8 0x3FAA6B8ABE73AF4C //log(1/frcpa(1+ 13/256) +data8 0x3FAC441E06F72A9E //log(1/frcpa(1+ 14/256) +data8 0x3FAE1E6713606D07 //log(1/frcpa(1+ 15/256) +data8 0x3FAFFA6911AB9301 //log(1/frcpa(1+ 16/256) +data8 0x3FB0EC139C5DA601 //log(1/frcpa(1+ 17/256) +data8 0x3FB1DBD2643D190B //log(1/frcpa(1+ 18/256) +data8 0x3FB2CC7284FE5F1C //log(1/frcpa(1+ 19/256) +data8 0x3FB3BDF5A7D1EE64 //log(1/frcpa(1+ 20/256) +data8 0x3FB4B05D7AA012E0 //log(1/frcpa(1+ 21/256) +data8 0x3FB580DB7CEB5702 //log(1/frcpa(1+ 22/256) +data8 0x3FB674F089365A7A //log(1/frcpa(1+ 23/256) +data8 0x3FB769EF2C6B568D //log(1/frcpa(1+ 24/256) +data8 0x3FB85FD927506A48 //log(1/frcpa(1+ 25/256) +data8 0x3FB9335E5D594989 //log(1/frcpa(1+ 26/256) +data8 0x3FBA2B0220C8E5F5 //log(1/frcpa(1+ 27/256) +data8 0x3FBB0004AC1A86AC //log(1/frcpa(1+ 28/256) +data8 0x3FBBF968769FCA11 //log(1/frcpa(1+ 29/256) +data8 0x3FBCCFEDBFEE13A8 //log(1/frcpa(1+ 30/256) +data8 0x3FBDA727638446A2 //log(1/frcpa(1+ 31/256) +data8 0x3FBEA3257FE10F7A //log(1/frcpa(1+ 32/256) +data8 0x3FBF7BE9FEDBFDE6 //log(1/frcpa(1+ 33/256) +data8 0x3FC02AB352FF25F4 //log(1/frcpa(1+ 34/256) +data8 0x3FC097CE579D204D //log(1/frcpa(1+ 35/256) +data8 0x3FC1178E8227E47C //log(1/frcpa(1+ 36/256) +data8 0x3FC185747DBECF34 //log(1/frcpa(1+ 37/256) +data8 0x3FC1F3B925F25D41 //log(1/frcpa(1+ 38/256) +data8 0x3FC2625D1E6DDF57 //log(1/frcpa(1+ 39/256) +data8 0x3FC2D1610C86813A //log(1/frcpa(1+ 40/256) +data8 0x3FC340C59741142E //log(1/frcpa(1+ 41/256) +data8 0x3FC3B08B6757F2A9 //log(1/frcpa(1+ 42/256) +data8 0x3FC40DFB08378003 //log(1/frcpa(1+ 43/256) +data8 0x3FC47E74E8CA5F7C //log(1/frcpa(1+ 44/256) +data8 0x3FC4EF51F6466DE4 //log(1/frcpa(1+ 45/256) +data8 0x3FC56092E02BA516 //log(1/frcpa(1+ 46/256) +data8 0x3FC5D23857CD74D5 //log(1/frcpa(1+ 47/256) +data8 0x3FC6313A37335D76 //log(1/frcpa(1+ 48/256) +data8 0x3FC6A399DABBD383 //log(1/frcpa(1+ 49/256) +data8 0x3FC70337DD3CE41B //log(1/frcpa(1+ 50/256) +data8 0x3FC77654128F6127 //log(1/frcpa(1+ 51/256) +data8 0x3FC7E9D82A0B022D //log(1/frcpa(1+ 52/256) +data8 0x3FC84A6B759F512F //log(1/frcpa(1+ 53/256) +data8 0x3FC8AB47D5F5A310 //log(1/frcpa(1+ 54/256) +data8 0x3FC91FE49096581B //log(1/frcpa(1+ 55/256) +data8 0x3FC981634011AA75 //log(1/frcpa(1+ 56/256) +data8 0x3FC9F6C407089664 //log(1/frcpa(1+ 57/256) +data8 0x3FCA58E729348F43 //log(1/frcpa(1+ 58/256) +data8 0x3FCABB55C31693AD //log(1/frcpa(1+ 59/256) +data8 0x3FCB1E104919EFD0 //log(1/frcpa(1+ 60/256) +data8 0x3FCB94EE93E367CB //log(1/frcpa(1+ 61/256) +data8 0x3FCBF851C067555F //log(1/frcpa(1+ 62/256) +data8 0x3FCC5C0254BF23A6 //log(1/frcpa(1+ 63/256) +data8 0x3FCCC000C9DB3C52 //log(1/frcpa(1+ 64/256) +data8 0x3FCD244D99C85674 //log(1/frcpa(1+ 65/256) +data8 0x3FCD88E93FB2F450 //log(1/frcpa(1+ 66/256) +data8 0x3FCDEDD437EAEF01 //log(1/frcpa(1+ 67/256) +data8 0x3FCE530EFFE71012 //log(1/frcpa(1+ 68/256) +data8 0x3FCEB89A1648B971 //log(1/frcpa(1+ 69/256) +data8 0x3FCF1E75FADF9BDE //log(1/frcpa(1+ 70/256) +data8 0x3FCF84A32EAD7C35 //log(1/frcpa(1+ 71/256) +data8 0x3FCFEB2233EA07CD //log(1/frcpa(1+ 72/256) +data8 0x3FD028F9C7035C1C //log(1/frcpa(1+ 73/256) +data8 0x3FD05C8BE0D9635A //log(1/frcpa(1+ 74/256) +data8 0x3FD085EB8F8AE797 //log(1/frcpa(1+ 75/256) +data8 0x3FD0B9C8E32D1911 //log(1/frcpa(1+ 76/256) +data8 0x3FD0EDD060B78081 //log(1/frcpa(1+ 77/256) +data8 0x3FD122024CF0063F //log(1/frcpa(1+ 78/256) +data8 0x3FD14BE2927AECD4 //log(1/frcpa(1+ 79/256) +data8 0x3FD180618EF18ADF //log(1/frcpa(1+ 80/256) +data8 0x3FD1B50BBE2FC63B //log(1/frcpa(1+ 81/256) +data8 0x3FD1DF4CC7CF242D //log(1/frcpa(1+ 82/256) +data8 0x3FD214456D0EB8D4 //log(1/frcpa(1+ 83/256) +data8 0x3FD23EC5991EBA49 //log(1/frcpa(1+ 84/256) +data8 0x3FD2740D9F870AFB //log(1/frcpa(1+ 85/256) +data8 0x3FD29ECDABCDFA04 //log(1/frcpa(1+ 86/256) +data8 0x3FD2D46602ADCCEE //log(1/frcpa(1+ 87/256) +data8 0x3FD2FF66B04EA9D4 //log(1/frcpa(1+ 88/256) +data8 0x3FD335504B355A37 //log(1/frcpa(1+ 89/256) +data8 0x3FD360925EC44F5D //log(1/frcpa(1+ 90/256) +data8 0x3FD38BF1C3337E75 //log(1/frcpa(1+ 91/256) +data8 0x3FD3C25277333184 //log(1/frcpa(1+ 92/256) +data8 0x3FD3EDF463C1683E //log(1/frcpa(1+ 93/256) +data8 0x3FD419B423D5E8C7 //log(1/frcpa(1+ 94/256) +data8 0x3FD44591E0539F49 //log(1/frcpa(1+ 95/256) +data8 0x3FD47C9175B6F0AD //log(1/frcpa(1+ 96/256) +data8 0x3FD4A8B341552B09 //log(1/frcpa(1+ 97/256) +data8 0x3FD4D4F3908901A0 //log(1/frcpa(1+ 98/256) +data8 0x3FD501528DA1F968 //log(1/frcpa(1+ 99/256) +data8 0x3FD52DD06347D4F6 //log(1/frcpa(1+ 100/256) +data8 0x3FD55A6D3C7B8A8A //log(1/frcpa(1+ 101/256) +data8 0x3FD5925D2B112A59 //log(1/frcpa(1+ 102/256) +data8 0x3FD5BF406B543DB2 //log(1/frcpa(1+ 103/256) +data8 0x3FD5EC433D5C35AE //log(1/frcpa(1+ 104/256) +data8 0x3FD61965CDB02C1F //log(1/frcpa(1+ 105/256) +data8 0x3FD646A84935B2A2 //log(1/frcpa(1+ 106/256) +data8 0x3FD6740ADD31DE94 //log(1/frcpa(1+ 107/256) +data8 0x3FD6A18DB74A58C5 //log(1/frcpa(1+ 108/256) +data8 0x3FD6CF31058670EC //log(1/frcpa(1+ 109/256) +data8 0x3FD6F180E852F0BA //log(1/frcpa(1+ 110/256) +data8 0x3FD71F5D71B894F0 //log(1/frcpa(1+ 111/256) +data8 0x3FD74D5AEFD66D5C //log(1/frcpa(1+ 112/256) +data8 0x3FD77B79922BD37E //log(1/frcpa(1+ 113/256) +data8 0x3FD7A9B9889F19E2 //log(1/frcpa(1+ 114/256) +data8 0x3FD7D81B037EB6A6 //log(1/frcpa(1+ 115/256) +data8 0x3FD8069E33827231 //log(1/frcpa(1+ 116/256) +data8 0x3FD82996D3EF8BCB //log(1/frcpa(1+ 117/256) +data8 0x3FD85855776DCBFB //log(1/frcpa(1+ 118/256) +data8 0x3FD8873658327CCF //log(1/frcpa(1+ 119/256) +data8 0x3FD8AA75973AB8CF //log(1/frcpa(1+ 120/256) +data8 0x3FD8D992DC8824E5 //log(1/frcpa(1+ 121/256) +data8 0x3FD908D2EA7D9512 //log(1/frcpa(1+ 122/256) +data8 0x3FD92C59E79C0E56 //log(1/frcpa(1+ 123/256) +data8 0x3FD95BD750EE3ED3 //log(1/frcpa(1+ 124/256) +data8 0x3FD98B7811A3EE5B //log(1/frcpa(1+ 125/256) +data8 0x3FD9AF47F33D406C //log(1/frcpa(1+ 126/256) +data8 0x3FD9DF270C1914A8 //log(1/frcpa(1+ 127/256) +data8 0x3FDA0325ED14FDA4 //log(1/frcpa(1+ 128/256) +data8 0x3FDA33440224FA79 //log(1/frcpa(1+ 129/256) +data8 0x3FDA57725E80C383 //log(1/frcpa(1+ 130/256) +data8 0x3FDA87D0165DD199 //log(1/frcpa(1+ 131/256) +data8 0x3FDAAC2E6C03F896 //log(1/frcpa(1+ 132/256) +data8 0x3FDADCCC6FDF6A81 //log(1/frcpa(1+ 133/256) +data8 0x3FDB015B3EB1E790 //log(1/frcpa(1+ 134/256) +data8 0x3FDB323A3A635948 //log(1/frcpa(1+ 135/256) +data8 0x3FDB56FA04462909 //log(1/frcpa(1+ 136/256) +data8 0x3FDB881AA659BC93 //log(1/frcpa(1+ 137/256) +data8 0x3FDBAD0BEF3DB165 //log(1/frcpa(1+ 138/256) +data8 0x3FDBD21297781C2F //log(1/frcpa(1+ 139/256) +data8 0x3FDC039236F08819 //log(1/frcpa(1+ 140/256) +data8 0x3FDC28CB1E4D32FD //log(1/frcpa(1+ 141/256) +data8 0x3FDC4E19B84723C2 //log(1/frcpa(1+ 142/256) +data8 0x3FDC7FF9C74554C9 //log(1/frcpa(1+ 143/256) +data8 0x3FDCA57B64E9DB05 //log(1/frcpa(1+ 144/256) +data8 0x3FDCCB130A5CEBB0 //log(1/frcpa(1+ 145/256) +data8 0x3FDCF0C0D18F326F //log(1/frcpa(1+ 146/256) +data8 0x3FDD232075B5A201 //log(1/frcpa(1+ 147/256) +data8 0x3FDD490246DEFA6B //log(1/frcpa(1+ 148/256) +data8 0x3FDD6EFA918D25CD //log(1/frcpa(1+ 149/256) +data8 0x3FDD9509707AE52F //log(1/frcpa(1+ 150/256) +data8 0x3FDDBB2EFE92C554 //log(1/frcpa(1+ 151/256) +data8 0x3FDDEE2F3445E4AF //log(1/frcpa(1+ 152/256) +data8 0x3FDE148A1A2726CE //log(1/frcpa(1+ 153/256) +data8 0x3FDE3AFC0A49FF40 //log(1/frcpa(1+ 154/256) +data8 0x3FDE6185206D516E //log(1/frcpa(1+ 155/256) +data8 0x3FDE882578823D52 //log(1/frcpa(1+ 156/256) +data8 0x3FDEAEDD2EAC990C //log(1/frcpa(1+ 157/256) +data8 0x3FDED5AC5F436BE3 //log(1/frcpa(1+ 158/256) +data8 0x3FDEFC9326D16AB9 //log(1/frcpa(1+ 159/256) +data8 0x3FDF2391A2157600 //log(1/frcpa(1+ 160/256) +data8 0x3FDF4AA7EE03192D //log(1/frcpa(1+ 161/256) +data8 0x3FDF71D627C30BB0 //log(1/frcpa(1+ 162/256) +data8 0x3FDF991C6CB3B379 //log(1/frcpa(1+ 163/256) +data8 0x3FDFC07ADA69A910 //log(1/frcpa(1+ 164/256) +data8 0x3FDFE7F18EB03D3E //log(1/frcpa(1+ 165/256) +data8 0x3FE007C053C5002E //log(1/frcpa(1+ 166/256) +data8 0x3FE01B942198A5A1 //log(1/frcpa(1+ 167/256) +data8 0x3FE02F74400C64EB //log(1/frcpa(1+ 168/256) +data8 0x3FE04360BE7603AD //log(1/frcpa(1+ 169/256) +data8 0x3FE05759AC47FE34 //log(1/frcpa(1+ 170/256) +data8 0x3FE06B5F1911CF52 //log(1/frcpa(1+ 171/256) +data8 0x3FE078BF0533C568 //log(1/frcpa(1+ 172/256) +data8 0x3FE08CD9687E7B0E //log(1/frcpa(1+ 173/256) +data8 0x3FE0A10074CF9019 //log(1/frcpa(1+ 174/256) +data8 0x3FE0B5343A234477 //log(1/frcpa(1+ 175/256) +data8 0x3FE0C974C89431CE //log(1/frcpa(1+ 176/256) +data8 0x3FE0DDC2305B9886 //log(1/frcpa(1+ 177/256) +data8 0x3FE0EB524BAFC918 //log(1/frcpa(1+ 178/256) +data8 0x3FE0FFB54213A476 //log(1/frcpa(1+ 179/256) +data8 0x3FE114253DA97D9F //log(1/frcpa(1+ 180/256) +data8 0x3FE128A24F1D9AFF //log(1/frcpa(1+ 181/256) +data8 0x3FE1365252BF0865 //log(1/frcpa(1+ 182/256) +data8 0x3FE14AE558B4A92D //log(1/frcpa(1+ 183/256) +data8 0x3FE15F85A19C765B //log(1/frcpa(1+ 184/256) +data8 0x3FE16D4D38C119FA //log(1/frcpa(1+ 185/256) +data8 0x3FE18203C20DD133 //log(1/frcpa(1+ 186/256) +data8 0x3FE196C7BC4B1F3B //log(1/frcpa(1+ 187/256) +data8 0x3FE1A4A738B7A33C //log(1/frcpa(1+ 188/256) +data8 0x3FE1B981C0C9653D //log(1/frcpa(1+ 189/256) +data8 0x3FE1CE69E8BB106B //log(1/frcpa(1+ 190/256) +data8 0x3FE1DC619DE06944 //log(1/frcpa(1+ 191/256) +data8 0x3FE1F160A2AD0DA4 //log(1/frcpa(1+ 192/256) +data8 0x3FE2066D7740737E //log(1/frcpa(1+ 193/256) +data8 0x3FE2147DBA47A394 //log(1/frcpa(1+ 194/256) +data8 0x3FE229A1BC5EBAC3 //log(1/frcpa(1+ 195/256) +data8 0x3FE237C1841A502E //log(1/frcpa(1+ 196/256) +data8 0x3FE24CFCE6F80D9A //log(1/frcpa(1+ 197/256) +data8 0x3FE25B2C55CD5762 //log(1/frcpa(1+ 198/256) +data8 0x3FE2707F4D5F7C41 //log(1/frcpa(1+ 199/256) +data8 0x3FE285E0842CA384 //log(1/frcpa(1+ 200/256) +data8 0x3FE294294708B773 //log(1/frcpa(1+ 201/256) +data8 0x3FE2A9A2670AFF0C //log(1/frcpa(1+ 202/256) +data8 0x3FE2B7FB2C8D1CC1 //log(1/frcpa(1+ 203/256) +data8 0x3FE2C65A6395F5F5 //log(1/frcpa(1+ 204/256) +data8 0x3FE2DBF557B0DF43 //log(1/frcpa(1+ 205/256) +data8 0x3FE2EA64C3F97655 //log(1/frcpa(1+ 206/256) +data8 0x3FE3001823684D73 //log(1/frcpa(1+ 207/256) +data8 0x3FE30E97E9A8B5CD //log(1/frcpa(1+ 208/256) +data8 0x3FE32463EBDD34EA //log(1/frcpa(1+ 209/256) +data8 0x3FE332F4314AD796 //log(1/frcpa(1+ 210/256) +data8 0x3FE348D90E7464D0 //log(1/frcpa(1+ 211/256) +data8 0x3FE35779F8C43D6E //log(1/frcpa(1+ 212/256) +data8 0x3FE36621961A6A99 //log(1/frcpa(1+ 213/256) +data8 0x3FE37C299F3C366A //log(1/frcpa(1+ 214/256) +data8 0x3FE38AE2171976E7 //log(1/frcpa(1+ 215/256) +data8 0x3FE399A157A603E7 //log(1/frcpa(1+ 216/256) +data8 0x3FE3AFCCFE77B9D1 //log(1/frcpa(1+ 217/256) +data8 0x3FE3BE9D503533B5 //log(1/frcpa(1+ 218/256) +data8 0x3FE3CD7480B4A8A3 //log(1/frcpa(1+ 219/256) +data8 0x3FE3E3C43918F76C //log(1/frcpa(1+ 220/256) +data8 0x3FE3F2ACB27ED6C7 //log(1/frcpa(1+ 221/256) +data8 0x3FE4019C2125CA93 //log(1/frcpa(1+ 222/256) +data8 0x3FE4181061389722 //log(1/frcpa(1+ 223/256) +data8 0x3FE42711518DF545 //log(1/frcpa(1+ 224/256) +data8 0x3FE436194E12B6BF //log(1/frcpa(1+ 225/256) +data8 0x3FE445285D68EA69 //log(1/frcpa(1+ 226/256) +data8 0x3FE45BCC464C893A //log(1/frcpa(1+ 227/256) +data8 0x3FE46AED21F117FC //log(1/frcpa(1+ 228/256) +data8 0x3FE47A1527E8A2D3 //log(1/frcpa(1+ 229/256) +data8 0x3FE489445EFFFCCC //log(1/frcpa(1+ 230/256) +data8 0x3FE4A018BCB69835 //log(1/frcpa(1+ 231/256) +data8 0x3FE4AF5A0C9D65D7 //log(1/frcpa(1+ 232/256) +data8 0x3FE4BEA2A5BDBE87 //log(1/frcpa(1+ 233/256) +data8 0x3FE4CDF28F10AC46 //log(1/frcpa(1+ 234/256) +data8 0x3FE4DD49CF994058 //log(1/frcpa(1+ 235/256) +data8 0x3FE4ECA86E64A684 //log(1/frcpa(1+ 236/256) +data8 0x3FE503C43CD8EB68 //log(1/frcpa(1+ 237/256) +data8 0x3FE513356667FC57 //log(1/frcpa(1+ 238/256) +data8 0x3FE522AE0738A3D8 //log(1/frcpa(1+ 239/256) +data8 0x3FE5322E26867857 //log(1/frcpa(1+ 240/256) +data8 0x3FE541B5CB979809 //log(1/frcpa(1+ 241/256) +data8 0x3FE55144FDBCBD62 //log(1/frcpa(1+ 242/256) +data8 0x3FE560DBC45153C7 //log(1/frcpa(1+ 243/256) +data8 0x3FE5707A26BB8C66 //log(1/frcpa(1+ 244/256) +data8 0x3FE587F60ED5B900 //log(1/frcpa(1+ 245/256) +data8 0x3FE597A7977C8F31 //log(1/frcpa(1+ 246/256) +data8 0x3FE5A760D634BB8B //log(1/frcpa(1+ 247/256) +data8 0x3FE5B721D295F10F //log(1/frcpa(1+ 248/256) +data8 0x3FE5C6EA94431EF9 //log(1/frcpa(1+ 249/256) +data8 0x3FE5D6BB22EA86F6 //log(1/frcpa(1+ 250/256) +data8 0x3FE5E6938645D390 //log(1/frcpa(1+ 251/256) +data8 0x3FE5F673C61A2ED2 //log(1/frcpa(1+ 252/256) +data8 0x3FE6065BEA385926 //log(1/frcpa(1+ 253/256) +data8 0x3FE6164BFA7CC06B //log(1/frcpa(1+ 254/256) +data8 0x3FE62643FECF9743 //log(1/frcpa(1+ 255/256) +ASM_SIZE_DIRECTIVE(log_table_2) + + +.align 32 +.global logf# +.global log10f# + +// log10 has p7 true, p8 false +// log has p8 true, p7 false + +.section .text +.proc log10f# +.align 32 + +log10f: +#ifdef _LIBC +.global __ieee754_log10f +.type __ieee754_log10f,@function +__ieee754_log10f: +#endif +{ .mfi + alloc r32=ar.pfs,1,15,4,0 + frcpa.s1 log_C,p9 = f1,f8 + cmp.eq.unc p7,p8 = r0, r0 +} +{ .mfb + addl log_AD_1 = @ltoff(log_table_1), gp + fnorm.s1 log_NORM_f8 = f8 + br.sptk L(LOG_LOG10_X) +} +;; + +.endp log10f +ASM_SIZE_DIRECTIVE(log10f) +ASM_SIZE_DIRECTIVE(__ieee754_log10f) + + + +.section .text +.proc logf# +.align 32 +logf: +#ifdef _LIBC +.global __ieee754_logf +.type __ieee754_logf,@function +__ieee754_logf: +#endif + +{ .mfi + alloc r32=ar.pfs,1,15,4,0 + frcpa.s1 log_C,p9 = f1,f8 + cmp.eq.unc p8,p7 = r0, r0 +} +{ .mfi + addl log_AD_1 = @ltoff(log_table_1), gp + fnorm.s1 log_NORM_f8 = f8 + nop.i 999 +} +;; + +L(LOG_LOG10_X): + +{ .mfi + getf.exp log_GR_signexp_f8 = f8 // If x unorm then must recompute + fclass.m.unc p15,p0 = f8, 0x0b // Test for x=unorm + mov log_GR_fff7 = 0xfff7 +} +{ .mfi + ld8 log_AD_1 = [log_AD_1] + fms.s1 log_w = f8,f1,f1 + mov log_GR_exp_17_ones = 0x1ffff +} +;; + +{ .mmi + getf.sig log_GR_significand_f8 = f8 // If x unorm then must recompute + mov log_GR_exp_16_ones = 0xffff + nop.i 999 +} +;; + +{ .mmb + adds log_AD_2 = 0x10, log_AD_1 + and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones +(p15) br.cond.spnt L(LOG_DENORM) +} +;; + +L(LOG_COMMON): +{.mfi + ldfpd log_P3,log_P2 = [log_AD_1],16 + fclass.m.unc p6,p0 = f8, 0xc3 // Test for x=nan + shl log_GR_index = log_GR_significand_f8,1 +} +{.mfi + sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones + nop.f 999 + nop.i 999 +} +;; + +{ .mfi + ldfpd log_P1,log_inv_ln10 = [log_AD_2],16 + fclass.m.unc p11,p0 = f8, 0x21 // Test for x=+inf + shr.u log_GR_index = log_GR_index,56 +} +{ .mfi + setf.sig log_int_Nfloat = log_GR_true_exp_f8 + nop.f 999 + nop.i 999 +} +;; + + +{ .mfi + ldfd log_log2 = [log_AD_2],16 + fma.s1 log_wsq = log_w, log_w, f0 + nop.i 999 +} +{ .mfb + nop.m 999 +(p6) fma.s.s0 f8 = f8,f1,f0 // quietize nan result if x=nan +(p6) br.ret.spnt b0 // Exit for x=nan +} +;; + + +{ .mfi + shladd log_AD_2 = log_GR_index,3,log_AD_2 + fcmp.eq.s1 p10,p0 = log_NORM_f8, f1 // Test for x=+1.0 + nop.i 999 +} +{ .mfb + nop.m 999 + fms.s1 log_r = log_C,f8,f1 +(p11) br.ret.spnt b0 // Exit for x=+inf +} +;; + + +{ .mmf + nop.m 999 + nop.m 999 + fclass.m.unc p6,p0 = f8, 0x07 // Test for x=0 +} +;; + + +{ .mfb + ldfd log_T = [log_AD_2] +(p10) fmerge.s f8 = f0, f0 +(p10) br.ret.spnt b0 // Exit for x=1.0 +;; +} + +{ .mfi + getf.exp log_GR_signexp_w = log_w + fclass.m.unc p12,p0 = f8, 0x3a // Test for x neg norm, unorm, inf + nop.i 999 +} +;; + +{ .mmb + nop.m 999 + nop.m 999 +(p6) br.cond.spnt L(LOG_ZERO_NEG) // Branch if x=0 +;; +} + + +{ .mfi + and log_GR_exp_w = log_GR_exp_17_ones, log_GR_signexp_w + nop.f 999 + nop.i 999 +} +{ .mfb + nop.m 999 + fma.s1 log_rsq = log_r, log_r, f0 +(p12) br.cond.spnt L(LOG_ZERO_NEG) // Branch if x<0 +;; +} + +{ .mfi + nop.m 999 + fma.s1 log_rp_p32 = log_P3, log_r, log_P2 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 log_rp_q32 = log_P3, log_w, log_P2 + nop.i 999 +;; +} + +{ .mfi + nop.m 999 + fcvt.xf log_Nfloat = log_int_Nfloat + nop.i 999 ;; +} + +{ .mfi + nop.m 999 + fma.s1 log_rp_p10 = log_P1, log_r, f1 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 log_rp_q10 = log_P1, log_w, f1 + nop.i 999 +;; +} + +// p13 <== large w log +// p14 <== small w log +{ .mfi +(p8) cmp.ge.unc p13,p14 = log_GR_exp_w, log_GR_fff7 + fcmp.eq.s0 p6,p0 = f8,f0 // Sets flag on +denormal input + nop.i 999 +;; +} + +// p10 <== large w log10 +// p11 <== small w log10 +{ .mfi +(p7) cmp.ge.unc p10,p11 = log_GR_exp_w, log_GR_fff7 + nop.f 999 + nop.i 999 ;; +} + +{ .mfi + nop.m 999 + fma.s1 log_T_plus_Nlog2 = log_Nfloat,log_log2, log_T + nop.i 999 ;; +} + + +{ .mfi + nop.m 999 + fma.s1 log_rp_p2 = log_rp_p32, log_rsq, log_rp_p10 + nop.i 999 +} +{ .mfi + nop.m 999 + fma.s1 log_rp_q2 = log_rp_q32, log_wsq, log_rp_q10 + nop.i 999 +;; +} + + +// small w, log <== p14 +{ .mfi + nop.m 999 +(p14) fma.s f8 = log_rp_q2, log_w, f0 + nop.i 999 +} +{ .mfi + nop.m 999 +(p11) fma.s1 log_Q = log_rp_q2, log_w, f0 + nop.i 999 ;; +} + + +// large w, log <== p13 +.pred.rel "mutex",p13,p10 +{ .mfi + nop.m 999 +(p13) fma.s f8 = log_rp_p2, log_r, log_T_plus_Nlog2 + nop.i 999 +} +{ .mfi + nop.m 999 +(p10) fma.s1 log_Q = log_rp_p2, log_r, log_T_plus_Nlog2 + nop.i 999 ;; +} + + +// log10 +{ .mfb + nop.m 999 +(p7) fma.s f8 = log_inv_ln10,log_Q,f0 + br.ret.sptk b0 +;; +} + + +L(LOG_DENORM): +{ .mmi + getf.exp log_GR_signexp_f8 = log_NORM_f8 + nop.m 999 + nop.i 999 +} +;; +{ .mmb + getf.sig log_GR_significand_f8 = log_NORM_f8 + and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones + br.cond.sptk L(LOG_COMMON) +} +;; + +L(LOG_ZERO_NEG): + +// qnan snan inf norm unorm 0 -+ +// 0 0 0 0 0 1 11 0x7 +// 0 0 1 1 1 0 10 0x3a + +// Save x (f8) in f10 +{ .mfi + nop.m 999 + fmerge.s f10 = f8,f8 + nop.i 999 ;; +} + +// p8 p9 means ln(+-0) = -inf +// p7 p10 means log(+-0) = -inf + +// p13 means ln(-) +// p14 means log(-) + + +{ .mfi + nop.m 999 + fmerge.ns f6 = f1,f1 // Form -1.0 + nop.i 999 ;; +} + +// p9 means ln(+-0) = -inf +// p10 means log(+-0) = -inf +// Log(+-0) = -inf + +{ .mfi + nop.m 999 +(p8) fclass.m.unc p9,p0 = f10, 0x07 + nop.i 999 +} +{ .mfi + nop.m 999 +(p7) fclass.m.unc p10,p0 = f10, 0x07 + nop.i 999 ;; +} + + +// p13 ln(-) +// p14 log(-) + +// Log(-inf, -normal, -unnormal) = QNAN indefinite +{ .mfi + nop.m 999 +(p8) fclass.m.unc p13,p0 = f10, 0x3a + nop.i 999 +} +{ .mfi + nop.m 999 +(p7) fclass.m.unc p14,p0 = f10, 0x3a + nop.i 999 ;; +} + + +.pred.rel "mutex",p9,p10 +{ .mfi +(p9) mov log_GR_tag = 4 +(p9) frcpa f8,p11 = f6,f0 + nop.i 999 +} +{ .mfi +(p10) mov log_GR_tag = 10 +(p10) frcpa f8,p12 = f6,f0 + nop.i 999 ;; +} + +.pred.rel "mutex",p13,p14 +{ .mfi +(p13) mov log_GR_tag = 5 +(p13) frcpa f8,p11 = f0,f0 + nop.i 999 +} +{ .mfb +(p14) mov log_GR_tag = 11 +(p14) frcpa f8,p12 = f0,f0 + br.cond.sptk __libm_error_region ;; +} +.endp logf +ASM_SIZE_DIRECTIVE(logf) +ASM_SIZE_DIRECTIVE(__ieee754_logf) + + +// Stack operations when calling error support. +// (1) (2) (3) (call) (4) +// sp -> + psp -> + psp -> + sp -> + +// | | | | +// | | <- GR_Y R3 ->| <- GR_RESULT | -> f8 +// | | | | +// | <-GR_Y Y2->| Y2 ->| <- GR_Y | +// | | | | +// | | <- GR_X X1 ->| | +// | | | | +// sp-64 -> + sp -> + sp -> + + +// save ar.pfs save b0 restore gp +// save gp restore ar.pfs + + + +.proc __libm_error_region +__libm_error_region: +.prologue + +// (1) +{ .mfi + add GR_Parameter_Y=-32,sp // Parameter 2 value + nop.f 0 +.save ar.pfs,GR_SAVE_PFS + mov GR_SAVE_PFS=ar.pfs // Save ar.pfs +} +{ .mfi +.fframe 64 + add sp=-64,sp // Create new stack + nop.f 0 + mov GR_SAVE_GP=gp // Save gp +};; + + +// (2) +{ .mmi + stfs [GR_Parameter_Y] = f1,16 // STORE Parameter 2 on stack + add GR_Parameter_X = 16,sp // Parameter 1 address +.save b0, GR_SAVE_B0 + mov GR_SAVE_B0=b0 // Save b0 +};; + +.body +// (3) +{ .mib + stfs [GR_Parameter_X] = f10 // STORE Parameter 1 on stack + add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address + nop.b 0 +} +{ .mib + stfs [GR_Parameter_Y] = f8 // STORE Parameter 3 on stack + add GR_Parameter_Y = -16,GR_Parameter_Y + br.call.sptk b0=__libm_error_support# // Call error handling function +};; + +{ .mmi + nop.m 0 + nop.m 0 + add GR_Parameter_RESULT = 48,sp +};; + +// (4) +{ .mmi + ldfs f8 = [GR_Parameter_RESULT] // Get return result off stack +.restore sp + add sp = 64,sp // Restore stack pointer + mov b0 = GR_SAVE_B0 // Restore return address +};; +{ .mib + mov gp = GR_SAVE_GP // Restore gp + mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs + br.ret.sptk b0 // Return +};; + +.endp __libm_error_region +ASM_SIZE_DIRECTIVE(__libm_error_region) + + +.type __libm_error_support#,@function +.global __libm_error_support# |