| .file "asinh.s" |
| |
| |
| // Copyright (c) 2000 - 2005, 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 |
| // ============================================================== |
| // 04/02/01 Initial version |
| // 04/19/01 Improved speed of the paths #1,2,3,4,5 |
| // 10/18/01 Improved accuracy |
| // 05/20/02 Cleaned up namespace and sf0 syntax |
| // 02/06/03 Reordered header: .section, .global, .proc, .align |
| // 05/21/03 Improved performance, fixed to handle unorms |
| // 03/31/05 Reformatted delimiters between data tables |
| // |
| // API |
| // ============================================================== |
| // double asinh(double) |
| // |
| // Overview of operation |
| // ============================================================== |
| // |
| // There are 7 paths: |
| // 1. x = 0.0 |
| // Return asinh(x) = 0.0 |
| // |
| // 2. 0.0 <|x| < 2^(-3) |
| // Return asinh(x) = POL13(x), |
| // where POL13(x) = (x^2*C13 + ...)*x^2 + C5)*x^2 + C3)*x^3 + x |
| // |
| // 3. 2^(-3) <= |x| < 2^63 |
| // Return asinh(x) = sign(x)*(log(|x| + sqrt(x^2 + 1.0))) |
| // To compute x + sqrt(x^2 + 1.0) modified Newton Raphson method is used |
| // (3 iterations) |
| // Algorithm description for log function see below. |
| // |
| // 4. 2^63 <= |x| < +INF |
| // Return asinh(x) = sign(x)*log(2*|x|) |
| // Algorithm description for log function see below. |
| // |
| // 5. x = INF |
| // Return asinh(x) = INF |
| // |
| // 6. x = [S,Q]NaN |
| // Return asinh(x) = QNaN |
| // |
| // 7. x = denormal |
| // Return asinh(x) = x correctly rounded |
| // |
| //============================================================== |
| // Algorithm Description for log(x) function |
| // Below we are using the fact that inequality x - 1.0 > 2^(-6) is always |
| // true for this asinh implementation |
| // |
| // 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 |
| //============================================================== |
| // C = frcpa(x) |
| // r = C * x - 1 |
| // |
| // Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 + P4*r^5 + P5*r^6 |
| // |
| // 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-extended |
| // |
| // |
| // Registers used |
| //============================================================== |
| // Floating Point registers used: |
| // f8, input |
| // f9 -> f15, f32 -> f68 |
| |
| // General registers used: |
| // r14 -> r27 |
| |
| // Predicate registers used: |
| // p6 -> p14 |
| |
| // p6 to filter out case when x = [Q,S]NaN or INF or zero |
| // p7 to filter out case when x < 0.0 |
| // p8 to select path #2 |
| // p9 used in the frcpa from path #3 |
| // p11 to filter out case when x >= 0 |
| // p12 to filter out case when x = unorm |
| // p13 to select path #4 |
| // Assembly macros |
| //============================================================== |
| log_GR_exp_17_ones = r14 |
| log_GR_signexp_f8 = r15 |
| log_table_address2 = r16 |
| log_GR_exp_16_ones = r17 |
| log_GR_exp_f8 = r18 |
| log_GR_true_exp_f8 = r19 |
| log_GR_significand_f8 = r20 |
| log_GR_index = r21 |
| log_GR_comp2 = r22 |
| asinh_GR_f8 = r23 |
| asinh_GR_comp = r24 |
| asinh_GR_f8 = r25 |
| log_table_address3 = r26 |
| NR_table_address = r27 |
| |
| //============================================================== |
| log_y = f9 |
| NR1 = f10 |
| NR2 = f11 |
| log_y_rs = f12 |
| log_y_rs_iter = f13 |
| log_y_rs_iter1 = f14 |
| fNormX = f15 |
| asinh_w_sq = f32 |
| log_C13 = f33 |
| log_C11 = f34 |
| log_P3 = f35 |
| log_P2 = f36 |
| log_P1 = f37 |
| log_P5 = f38 |
| log_P4 = f39 |
| log_C3 = f40 |
| log_C5 = f41 |
| log_C7 = f42 |
| log2 = f43 |
| asinh_f8 = f44 |
| log_C = f45 |
| log_arg = f46 |
| log_C9 = f47 |
| asinh_w_four = f48 |
| log_int_Nfloat = f49 |
| log_r = f50 |
| log_rsq = f51 |
| log_rp_p4 = f52 |
| log_rp_p32 = f53 |
| log_rcube = f54 |
| log_rp_p10 = f55 |
| log_rp_p2 = f56 |
| log_Nfloat = f57 |
| log_T = f58 |
| log_r2P_r = f59 |
| log_T_plus_Nlog2 = f60 |
| asinh_w_3 = f61 |
| asinh_w_5 = f62 |
| asinh_w_cube = f63 |
| asinh_w_7 = f64 |
| log_arg_early = f65 |
| asinh_w_9 = f66 |
| asinh_w_13 = f67 |
| asinh_w_seven = f68 |
| |
| // Data tables |
| //============================================================== |
| |
| RODATA |
| .align 16 |
| |
| LOCAL_OBJECT_START(log_table_1) |
| data8 0xBFC5555DA7212371 // P5 |
| data8 0x3FC999A19EEF5826 // P4 |
| data8 0xBFCFFFFFFFFEF009 // P3 |
| data8 0x3FD555555554ECB2 // P2 |
| data8 0xBFE0000000000000 // P1 = -0.5 |
| data8 0x0000000000000000 // pad |
| data8 0xb17217f7d1cf79ac, 0x00003ffe // log2 |
| LOCAL_OBJECT_END(log_table_1) |
| |
| LOCAL_OBJECT_START(log_table_2) |
| data8 0x3FE0000000000000 // 0.5 |
| data8 0x4008000000000000 // 3.0 |
| // |
| data8 0x8824BE4D74BC4F00, 0x00003FF9 // C13 |
| data8 0xB725A2CD9556CC57, 0x0000BFF9 // C11 |
| data8 0xF8E339127FBFF49D, 0x00003FF9 // C9 |
| data8 0xB6DB6D7DCE17CB78, 0x0000BFFA // C7 |
| data8 0x999999998802CCEF, 0x00003FFB // C5 |
| data8 0xAAAAAAAAAAA8DC40, 0x0000BFFC // C3 |
| LOCAL_OBJECT_END(log_table_2) |
| |
| |
| LOCAL_OBJECT_START(log_table_3) |
| data8 0x80200aaeac44ef38 , 0x00003ff6 // log(1/frcpa(1+ 0/2^-8)) |
| // |
| data8 0xc09090a2c35aa070 , 0x00003ff7 // log(1/frcpa(1+ 1/2^-8)) |
| data8 0xa0c94fcb41977c75 , 0x00003ff8 // log(1/frcpa(1+ 2/2^-8)) |
| data8 0xe18b9c263af83301 , 0x00003ff8 // log(1/frcpa(1+ 3/2^-8)) |
| data8 0x8d35c8d6399c30ea , 0x00003ff9 // log(1/frcpa(1+ 4/2^-8)) |
| data8 0xadd4d2ecd601cbb8 , 0x00003ff9 // log(1/frcpa(1+ 5/2^-8)) |
| // |
| data8 0xce95403a192f9f01 , 0x00003ff9 // log(1/frcpa(1+ 6/2^-8)) |
| data8 0xeb59392cbcc01096 , 0x00003ff9 // log(1/frcpa(1+ 7/2^-8)) |
| data8 0x862c7d0cefd54c5d , 0x00003ffa // log(1/frcpa(1+ 8/2^-8)) |
| data8 0x94aa63c65e70d499 , 0x00003ffa // log(1/frcpa(1+ 9/2^-8)) |
| data8 0xa54a696d4b62b382 , 0x00003ffa // log(1/frcpa(1+ 10/2^-8)) |
| // |
| data8 0xb3e4a796a5dac208 , 0x00003ffa // log(1/frcpa(1+ 11/2^-8)) |
| data8 0xc28c45b1878340a9 , 0x00003ffa // log(1/frcpa(1+ 12/2^-8)) |
| data8 0xd35c55f39d7a6235 , 0x00003ffa // log(1/frcpa(1+ 13/2^-8)) |
| data8 0xe220f037b954f1f5 , 0x00003ffa // log(1/frcpa(1+ 14/2^-8)) |
| data8 0xf0f3389b036834f3 , 0x00003ffa // log(1/frcpa(1+ 15/2^-8)) |
| // |
| data8 0xffd3488d5c980465 , 0x00003ffa // log(1/frcpa(1+ 16/2^-8)) |
| data8 0x87609ce2ed300490 , 0x00003ffb // log(1/frcpa(1+ 17/2^-8)) |
| data8 0x8ede9321e8c85927 , 0x00003ffb // log(1/frcpa(1+ 18/2^-8)) |
| data8 0x96639427f2f8e2f4 , 0x00003ffb // log(1/frcpa(1+ 19/2^-8)) |
| data8 0x9defad3e8f73217b , 0x00003ffb // log(1/frcpa(1+ 20/2^-8)) |
| // |
| data8 0xa582ebd50097029c , 0x00003ffb // log(1/frcpa(1+ 21/2^-8)) |
| data8 0xac06dbe75ab80fee , 0x00003ffb // log(1/frcpa(1+ 22/2^-8)) |
| data8 0xb3a78449b2d3ccca , 0x00003ffb // log(1/frcpa(1+ 23/2^-8)) |
| data8 0xbb4f79635ab46bb2 , 0x00003ffb // log(1/frcpa(1+ 24/2^-8)) |
| data8 0xc2fec93a83523f3f , 0x00003ffb // log(1/frcpa(1+ 25/2^-8)) |
| // |
| data8 0xc99af2eaca4c4571 , 0x00003ffb // log(1/frcpa(1+ 26/2^-8)) |
| data8 0xd1581106472fa653 , 0x00003ffb // log(1/frcpa(1+ 27/2^-8)) |
| data8 0xd8002560d4355f2e , 0x00003ffb // log(1/frcpa(1+ 28/2^-8)) |
| data8 0xdfcb43b4fe508632 , 0x00003ffb // log(1/frcpa(1+ 29/2^-8)) |
| data8 0xe67f6dff709d4119 , 0x00003ffb // log(1/frcpa(1+ 30/2^-8)) |
| // |
| data8 0xed393b1c22351280 , 0x00003ffb // log(1/frcpa(1+ 31/2^-8)) |
| data8 0xf5192bff087bcc35 , 0x00003ffb // log(1/frcpa(1+ 32/2^-8)) |
| data8 0xfbdf4ff6dfef2fa3 , 0x00003ffb // log(1/frcpa(1+ 33/2^-8)) |
| data8 0x81559a97f92f9cc7 , 0x00003ffc // log(1/frcpa(1+ 34/2^-8)) |
| data8 0x84be72bce90266e8 , 0x00003ffc // log(1/frcpa(1+ 35/2^-8)) |
| // |
| data8 0x88bc74113f23def2 , 0x00003ffc // log(1/frcpa(1+ 36/2^-8)) |
| data8 0x8c2ba3edf6799d11 , 0x00003ffc // log(1/frcpa(1+ 37/2^-8)) |
| data8 0x8f9dc92f92ea08b1 , 0x00003ffc // log(1/frcpa(1+ 38/2^-8)) |
| data8 0x9312e8f36efab5a7 , 0x00003ffc // log(1/frcpa(1+ 39/2^-8)) |
| data8 0x968b08643409ceb6 , 0x00003ffc // log(1/frcpa(1+ 40/2^-8)) |
| // |
| data8 0x9a062cba08a1708c , 0x00003ffc // log(1/frcpa(1+ 41/2^-8)) |
| data8 0x9d845b3abf95485c , 0x00003ffc // log(1/frcpa(1+ 42/2^-8)) |
| data8 0xa06fd841bc001bb4 , 0x00003ffc // log(1/frcpa(1+ 43/2^-8)) |
| data8 0xa3f3a74652fbe0db , 0x00003ffc // log(1/frcpa(1+ 44/2^-8)) |
| data8 0xa77a8fb2336f20f5 , 0x00003ffc // log(1/frcpa(1+ 45/2^-8)) |
| // |
| data8 0xab0497015d28b0a0 , 0x00003ffc // log(1/frcpa(1+ 46/2^-8)) |
| data8 0xae91c2be6ba6a615 , 0x00003ffc // log(1/frcpa(1+ 47/2^-8)) |
| data8 0xb189d1b99aebb20b , 0x00003ffc // log(1/frcpa(1+ 48/2^-8)) |
| data8 0xb51cced5de9c1b2c , 0x00003ffc // log(1/frcpa(1+ 49/2^-8)) |
| data8 0xb819bee9e720d42f , 0x00003ffc // log(1/frcpa(1+ 50/2^-8)) |
| // |
| data8 0xbbb2a0947b093a5d , 0x00003ffc // log(1/frcpa(1+ 51/2^-8)) |
| data8 0xbf4ec1505811684a , 0x00003ffc // log(1/frcpa(1+ 52/2^-8)) |
| data8 0xc2535bacfa8975ff , 0x00003ffc // log(1/frcpa(1+ 53/2^-8)) |
| data8 0xc55a3eafad187eb8 , 0x00003ffc // log(1/frcpa(1+ 54/2^-8)) |
| data8 0xc8ff2484b2c0da74 , 0x00003ffc // log(1/frcpa(1+ 55/2^-8)) |
| // |
| data8 0xcc0b1a008d53ab76 , 0x00003ffc // log(1/frcpa(1+ 56/2^-8)) |
| data8 0xcfb6203844b3209b , 0x00003ffc // log(1/frcpa(1+ 57/2^-8)) |
| data8 0xd2c73949a47a19f5 , 0x00003ffc // log(1/frcpa(1+ 58/2^-8)) |
| data8 0xd5daae18b49d6695 , 0x00003ffc // log(1/frcpa(1+ 59/2^-8)) |
| data8 0xd8f08248cf7e8019 , 0x00003ffc // log(1/frcpa(1+ 60/2^-8)) |
| // |
| data8 0xdca7749f1b3e540e , 0x00003ffc // log(1/frcpa(1+ 61/2^-8)) |
| data8 0xdfc28e033aaaf7c7 , 0x00003ffc // log(1/frcpa(1+ 62/2^-8)) |
| data8 0xe2e012a5f91d2f55 , 0x00003ffc // log(1/frcpa(1+ 63/2^-8)) |
| data8 0xe600064ed9e292a8 , 0x00003ffc // log(1/frcpa(1+ 64/2^-8)) |
| data8 0xe9226cce42b39f60 , 0x00003ffc // log(1/frcpa(1+ 65/2^-8)) |
| // |
| data8 0xec4749fd97a28360 , 0x00003ffc // log(1/frcpa(1+ 66/2^-8)) |
| data8 0xef6ea1bf57780495 , 0x00003ffc // log(1/frcpa(1+ 67/2^-8)) |
| data8 0xf29877ff38809091 , 0x00003ffc // log(1/frcpa(1+ 68/2^-8)) |
| data8 0xf5c4d0b245cb89be , 0x00003ffc // log(1/frcpa(1+ 69/2^-8)) |
| data8 0xf8f3afd6fcdef3aa , 0x00003ffc // log(1/frcpa(1+ 70/2^-8)) |
| // |
| data8 0xfc2519756be1abc7 , 0x00003ffc // log(1/frcpa(1+ 71/2^-8)) |
| data8 0xff59119f503e6832 , 0x00003ffc // log(1/frcpa(1+ 72/2^-8)) |
| data8 0x8147ce381ae0e146 , 0x00003ffd // log(1/frcpa(1+ 73/2^-8)) |
| data8 0x82e45f06cb1ad0f2 , 0x00003ffd // log(1/frcpa(1+ 74/2^-8)) |
| data8 0x842f5c7c573cbaa2 , 0x00003ffd // log(1/frcpa(1+ 75/2^-8)) |
| // |
| data8 0x85ce471968c8893a , 0x00003ffd // log(1/frcpa(1+ 76/2^-8)) |
| data8 0x876e8305bc04066d , 0x00003ffd // log(1/frcpa(1+ 77/2^-8)) |
| data8 0x891012678031fbb3 , 0x00003ffd // log(1/frcpa(1+ 78/2^-8)) |
| data8 0x8a5f1493d766a05f , 0x00003ffd // log(1/frcpa(1+ 79/2^-8)) |
| data8 0x8c030c778c56fa00 , 0x00003ffd // log(1/frcpa(1+ 80/2^-8)) |
| // |
| data8 0x8da85df17e31d9ae , 0x00003ffd // log(1/frcpa(1+ 81/2^-8)) |
| data8 0x8efa663e7921687e , 0x00003ffd // log(1/frcpa(1+ 82/2^-8)) |
| data8 0x90a22b6875c6a1f8 , 0x00003ffd // log(1/frcpa(1+ 83/2^-8)) |
| data8 0x91f62cc8f5d24837 , 0x00003ffd // log(1/frcpa(1+ 84/2^-8)) |
| data8 0x93a06cfc3857d980 , 0x00003ffd // log(1/frcpa(1+ 85/2^-8)) |
| // |
| data8 0x94f66d5e6fd01ced , 0x00003ffd // log(1/frcpa(1+ 86/2^-8)) |
| data8 0x96a330156e6772f2 , 0x00003ffd // log(1/frcpa(1+ 87/2^-8)) |
| data8 0x97fb3582754ea25b , 0x00003ffd // log(1/frcpa(1+ 88/2^-8)) |
| data8 0x99aa8259aad1bbf2 , 0x00003ffd // log(1/frcpa(1+ 89/2^-8)) |
| data8 0x9b0492f6227ae4a8 , 0x00003ffd // log(1/frcpa(1+ 90/2^-8)) |
| // |
| data8 0x9c5f8e199bf3a7a5 , 0x00003ffd // log(1/frcpa(1+ 91/2^-8)) |
| data8 0x9e1293b9998c1daa , 0x00003ffd // log(1/frcpa(1+ 92/2^-8)) |
| data8 0x9f6fa31e0b41f308 , 0x00003ffd // log(1/frcpa(1+ 93/2^-8)) |
| data8 0xa0cda11eaf46390e , 0x00003ffd // log(1/frcpa(1+ 94/2^-8)) |
| data8 0xa22c8f029cfa45aa , 0x00003ffd // log(1/frcpa(1+ 95/2^-8)) |
| // |
| data8 0xa3e48badb7856b34 , 0x00003ffd // log(1/frcpa(1+ 96/2^-8)) |
| data8 0xa5459a0aa95849f9 , 0x00003ffd // log(1/frcpa(1+ 97/2^-8)) |
| data8 0xa6a79c84480cfebd , 0x00003ffd // log(1/frcpa(1+ 98/2^-8)) |
| data8 0xa80a946d0fcb3eb2 , 0x00003ffd // log(1/frcpa(1+ 99/2^-8)) |
| data8 0xa96e831a3ea7b314 , 0x00003ffd // log(1/frcpa(1+100/2^-8)) |
| // |
| data8 0xaad369e3dc544e3b , 0x00003ffd // log(1/frcpa(1+101/2^-8)) |
| data8 0xac92e9588952c815 , 0x00003ffd // log(1/frcpa(1+102/2^-8)) |
| data8 0xadfa035aa1ed8fdc , 0x00003ffd // log(1/frcpa(1+103/2^-8)) |
| data8 0xaf6219eae1ad6e34 , 0x00003ffd // log(1/frcpa(1+104/2^-8)) |
| data8 0xb0cb2e6d8160f753 , 0x00003ffd // log(1/frcpa(1+105/2^-8)) |
| // |
| data8 0xb2354249ad950f72 , 0x00003ffd // log(1/frcpa(1+106/2^-8)) |
| data8 0xb3a056e98ef4a3b4 , 0x00003ffd // log(1/frcpa(1+107/2^-8)) |
| data8 0xb50c6dba52c6292a , 0x00003ffd // log(1/frcpa(1+108/2^-8)) |
| data8 0xb679882c33876165 , 0x00003ffd // log(1/frcpa(1+109/2^-8)) |
| data8 0xb78c07429785cedc , 0x00003ffd // log(1/frcpa(1+110/2^-8)) |
| // |
| data8 0xb8faeb8dc4a77d24 , 0x00003ffd // log(1/frcpa(1+111/2^-8)) |
| data8 0xba6ad77eb36ae0d6 , 0x00003ffd // log(1/frcpa(1+112/2^-8)) |
| data8 0xbbdbcc915e9bee50 , 0x00003ffd // log(1/frcpa(1+113/2^-8)) |
| data8 0xbd4dcc44f8cf12ef , 0x00003ffd // log(1/frcpa(1+114/2^-8)) |
| data8 0xbec0d81bf5b531fa , 0x00003ffd // log(1/frcpa(1+115/2^-8)) |
| // |
| data8 0xc034f19c139186f4 , 0x00003ffd // log(1/frcpa(1+116/2^-8)) |
| data8 0xc14cb69f7c5e55ab , 0x00003ffd // log(1/frcpa(1+117/2^-8)) |
| data8 0xc2c2abbb6e5fd56f , 0x00003ffd // log(1/frcpa(1+118/2^-8)) |
| data8 0xc439b2c193e6771e , 0x00003ffd // log(1/frcpa(1+119/2^-8)) |
| data8 0xc553acb9d5c67733 , 0x00003ffd // log(1/frcpa(1+120/2^-8)) |
| // |
| data8 0xc6cc96e441272441 , 0x00003ffd // log(1/frcpa(1+121/2^-8)) |
| data8 0xc8469753eca88c30 , 0x00003ffd // log(1/frcpa(1+122/2^-8)) |
| data8 0xc962cf3ce072b05c , 0x00003ffd // log(1/frcpa(1+123/2^-8)) |
| data8 0xcadeba8771f694aa , 0x00003ffd // log(1/frcpa(1+124/2^-8)) |
| data8 0xcc5bc08d1f72da94 , 0x00003ffd // log(1/frcpa(1+125/2^-8)) |
| // |
| data8 0xcd7a3f99ea035c29 , 0x00003ffd // log(1/frcpa(1+126/2^-8)) |
| data8 0xcef93860c8a53c35 , 0x00003ffd // log(1/frcpa(1+127/2^-8)) |
| data8 0xd0192f68a7ed23df , 0x00003ffd // log(1/frcpa(1+128/2^-8)) |
| data8 0xd19a201127d3c645 , 0x00003ffd // log(1/frcpa(1+129/2^-8)) |
| data8 0xd2bb92f4061c172c , 0x00003ffd // log(1/frcpa(1+130/2^-8)) |
| // |
| data8 0xd43e80b2ee8cc8fc , 0x00003ffd // log(1/frcpa(1+131/2^-8)) |
| data8 0xd56173601fc4ade4 , 0x00003ffd // log(1/frcpa(1+132/2^-8)) |
| data8 0xd6e6637efb54086f , 0x00003ffd // log(1/frcpa(1+133/2^-8)) |
| data8 0xd80ad9f58f3c8193 , 0x00003ffd // log(1/frcpa(1+134/2^-8)) |
| data8 0xd991d1d31aca41f8 , 0x00003ffd // log(1/frcpa(1+135/2^-8)) |
| // |
| data8 0xdab7d02231484a93 , 0x00003ffd // log(1/frcpa(1+136/2^-8)) |
| data8 0xdc40d532cde49a54 , 0x00003ffd // log(1/frcpa(1+137/2^-8)) |
| data8 0xdd685f79ed8b265e , 0x00003ffd // log(1/frcpa(1+138/2^-8)) |
| data8 0xde9094bbc0e17b1d , 0x00003ffd // log(1/frcpa(1+139/2^-8)) |
| data8 0xe01c91b78440c425 , 0x00003ffd // log(1/frcpa(1+140/2^-8)) |
| // |
| data8 0xe14658f26997e729 , 0x00003ffd // log(1/frcpa(1+141/2^-8)) |
| data8 0xe270cdc2391e0d23 , 0x00003ffd // log(1/frcpa(1+142/2^-8)) |
| data8 0xe3ffce3a2aa64922 , 0x00003ffd // log(1/frcpa(1+143/2^-8)) |
| data8 0xe52bdb274ed82887 , 0x00003ffd // log(1/frcpa(1+144/2^-8)) |
| data8 0xe6589852e75d7df6 , 0x00003ffd // log(1/frcpa(1+145/2^-8)) |
| // |
| data8 0xe786068c79937a7d , 0x00003ffd // log(1/frcpa(1+146/2^-8)) |
| data8 0xe91903adad100911 , 0x00003ffd // log(1/frcpa(1+147/2^-8)) |
| data8 0xea481236f7d35bb0 , 0x00003ffd // log(1/frcpa(1+148/2^-8)) |
| data8 0xeb77d48c692e6b14 , 0x00003ffd // log(1/frcpa(1+149/2^-8)) |
| data8 0xeca84b83d7297b87 , 0x00003ffd // log(1/frcpa(1+150/2^-8)) |
| // |
| data8 0xedd977f4962aa158 , 0x00003ffd // log(1/frcpa(1+151/2^-8)) |
| data8 0xef7179a22f257754 , 0x00003ffd // log(1/frcpa(1+152/2^-8)) |
| data8 0xf0a450d139366ca7 , 0x00003ffd // log(1/frcpa(1+153/2^-8)) |
| data8 0xf1d7e0524ff9ffdb , 0x00003ffd // log(1/frcpa(1+154/2^-8)) |
| data8 0xf30c29036a8b6cae , 0x00003ffd // log(1/frcpa(1+155/2^-8)) |
| // |
| data8 0xf4412bc411ea8d92 , 0x00003ffd // log(1/frcpa(1+156/2^-8)) |
| data8 0xf576e97564c8619d , 0x00003ffd // log(1/frcpa(1+157/2^-8)) |
| data8 0xf6ad62fa1b5f172f , 0x00003ffd // log(1/frcpa(1+158/2^-8)) |
| data8 0xf7e499368b55c542 , 0x00003ffd // log(1/frcpa(1+159/2^-8)) |
| data8 0xf91c8d10abaffe22 , 0x00003ffd // log(1/frcpa(1+160/2^-8)) |
| // |
| data8 0xfa553f7018c966f3 , 0x00003ffd // log(1/frcpa(1+161/2^-8)) |
| data8 0xfb8eb13e185d802c , 0x00003ffd // log(1/frcpa(1+162/2^-8)) |
| data8 0xfcc8e3659d9bcbed , 0x00003ffd // log(1/frcpa(1+163/2^-8)) |
| data8 0xfe03d6d34d487fd2 , 0x00003ffd // log(1/frcpa(1+164/2^-8)) |
| data8 0xff3f8c7581e9f0ae , 0x00003ffd // log(1/frcpa(1+165/2^-8)) |
| // |
| data8 0x803e029e280173ae , 0x00003ffe // log(1/frcpa(1+166/2^-8)) |
| data8 0x80dca10cc52d0757 , 0x00003ffe // log(1/frcpa(1+167/2^-8)) |
| data8 0x817ba200632755a1 , 0x00003ffe // log(1/frcpa(1+168/2^-8)) |
| data8 0x821b05f3b01d6774 , 0x00003ffe // log(1/frcpa(1+169/2^-8)) |
| data8 0x82bacd623ff19d06 , 0x00003ffe // log(1/frcpa(1+170/2^-8)) |
| // |
| data8 0x835af8c88e7a8f47 , 0x00003ffe // log(1/frcpa(1+171/2^-8)) |
| data8 0x83c5f8299e2b4091 , 0x00003ffe // log(1/frcpa(1+172/2^-8)) |
| data8 0x8466cb43f3d87300 , 0x00003ffe // log(1/frcpa(1+173/2^-8)) |
| data8 0x850803a67c80ca4b , 0x00003ffe // log(1/frcpa(1+174/2^-8)) |
| data8 0x85a9a1d11a23b461 , 0x00003ffe // log(1/frcpa(1+175/2^-8)) |
| // |
| data8 0x864ba644a18e6e05 , 0x00003ffe // log(1/frcpa(1+176/2^-8)) |
| data8 0x86ee1182dcc432f7 , 0x00003ffe // log(1/frcpa(1+177/2^-8)) |
| data8 0x875a925d7e48c316 , 0x00003ffe // log(1/frcpa(1+178/2^-8)) |
| data8 0x87fdaa109d23aef7 , 0x00003ffe // log(1/frcpa(1+179/2^-8)) |
| data8 0x88a129ed4becfaf2 , 0x00003ffe // log(1/frcpa(1+180/2^-8)) |
| // |
| data8 0x89451278ecd7f9cf , 0x00003ffe // log(1/frcpa(1+181/2^-8)) |
| data8 0x89b29295f8432617 , 0x00003ffe // log(1/frcpa(1+182/2^-8)) |
| data8 0x8a572ac5a5496882 , 0x00003ffe // log(1/frcpa(1+183/2^-8)) |
| data8 0x8afc2d0ce3b2dadf , 0x00003ffe // log(1/frcpa(1+184/2^-8)) |
| data8 0x8b6a69c608cfd3af , 0x00003ffe // log(1/frcpa(1+185/2^-8)) |
| // |
| data8 0x8c101e106e899a83 , 0x00003ffe // log(1/frcpa(1+186/2^-8)) |
| data8 0x8cb63de258f9d626 , 0x00003ffe // log(1/frcpa(1+187/2^-8)) |
| data8 0x8d2539c5bd19e2b1 , 0x00003ffe // log(1/frcpa(1+188/2^-8)) |
| data8 0x8dcc0e064b29e6f1 , 0x00003ffe // log(1/frcpa(1+189/2^-8)) |
| data8 0x8e734f45d88357ae , 0x00003ffe // log(1/frcpa(1+190/2^-8)) |
| // |
| data8 0x8ee30cef034a20db , 0x00003ffe // log(1/frcpa(1+191/2^-8)) |
| data8 0x8f8b0515686d1d06 , 0x00003ffe // log(1/frcpa(1+192/2^-8)) |
| data8 0x90336bba039bf32f , 0x00003ffe // log(1/frcpa(1+193/2^-8)) |
| data8 0x90a3edd23d1c9d58 , 0x00003ffe // log(1/frcpa(1+194/2^-8)) |
| data8 0x914d0de2f5d61b32 , 0x00003ffe // log(1/frcpa(1+195/2^-8)) |
| // |
| data8 0x91be0c20d28173b5 , 0x00003ffe // log(1/frcpa(1+196/2^-8)) |
| data8 0x9267e737c06cd34a , 0x00003ffe // log(1/frcpa(1+197/2^-8)) |
| data8 0x92d962ae6abb1237 , 0x00003ffe // log(1/frcpa(1+198/2^-8)) |
| data8 0x9383fa6afbe2074c , 0x00003ffe // log(1/frcpa(1+199/2^-8)) |
| data8 0x942f0421651c1c4e , 0x00003ffe // log(1/frcpa(1+200/2^-8)) |
| // |
| data8 0x94a14a3845bb985e , 0x00003ffe // log(1/frcpa(1+201/2^-8)) |
| data8 0x954d133857f861e7 , 0x00003ffe // log(1/frcpa(1+202/2^-8)) |
| data8 0x95bfd96468e604c4 , 0x00003ffe // log(1/frcpa(1+203/2^-8)) |
| data8 0x9632d31cafafa858 , 0x00003ffe // log(1/frcpa(1+204/2^-8)) |
| data8 0x96dfaabd86fa1647 , 0x00003ffe // log(1/frcpa(1+205/2^-8)) |
| // |
| data8 0x9753261fcbb2a594 , 0x00003ffe // log(1/frcpa(1+206/2^-8)) |
| data8 0x9800c11b426b996d , 0x00003ffe // log(1/frcpa(1+207/2^-8)) |
| data8 0x9874bf4d45ae663c , 0x00003ffe // log(1/frcpa(1+208/2^-8)) |
| data8 0x99231f5ee9a74f79 , 0x00003ffe // log(1/frcpa(1+209/2^-8)) |
| data8 0x9997a18a56bcad28 , 0x00003ffe // log(1/frcpa(1+210/2^-8)) |
| // |
| data8 0x9a46c873a3267e79 , 0x00003ffe // log(1/frcpa(1+211/2^-8)) |
| data8 0x9abbcfc621eb6cb6 , 0x00003ffe // log(1/frcpa(1+212/2^-8)) |
| data8 0x9b310cb0d354c990 , 0x00003ffe // log(1/frcpa(1+213/2^-8)) |
| data8 0x9be14cf9e1b3515c , 0x00003ffe // log(1/frcpa(1+214/2^-8)) |
| data8 0x9c5710b8cbb73a43 , 0x00003ffe // log(1/frcpa(1+215/2^-8)) |
| // |
| data8 0x9ccd0abd301f399c , 0x00003ffe // log(1/frcpa(1+216/2^-8)) |
| data8 0x9d7e67f3bdce8888 , 0x00003ffe // log(1/frcpa(1+217/2^-8)) |
| data8 0x9df4ea81a99daa01 , 0x00003ffe // log(1/frcpa(1+218/2^-8)) |
| data8 0x9e6ba405a54514ba , 0x00003ffe // log(1/frcpa(1+219/2^-8)) |
| data8 0x9f1e21c8c7bb62b3 , 0x00003ffe // log(1/frcpa(1+220/2^-8)) |
| // |
| data8 0x9f956593f6b6355c , 0x00003ffe // log(1/frcpa(1+221/2^-8)) |
| data8 0xa00ce1092e5498c3 , 0x00003ffe // log(1/frcpa(1+222/2^-8)) |
| data8 0xa0c08309c4b912c1 , 0x00003ffe // log(1/frcpa(1+223/2^-8)) |
| data8 0xa1388a8c6faa2afa , 0x00003ffe // log(1/frcpa(1+224/2^-8)) |
| data8 0xa1b0ca7095b5f985 , 0x00003ffe // log(1/frcpa(1+225/2^-8)) |
| // |
| data8 0xa22942eb47534a00 , 0x00003ffe // log(1/frcpa(1+226/2^-8)) |
| data8 0xa2de62326449d0a3 , 0x00003ffe // log(1/frcpa(1+227/2^-8)) |
| data8 0xa357690f88bfe345 , 0x00003ffe // log(1/frcpa(1+228/2^-8)) |
| data8 0xa3d0a93f45169a4b , 0x00003ffe // log(1/frcpa(1+229/2^-8)) |
| data8 0xa44a22f7ffe65f30 , 0x00003ffe // log(1/frcpa(1+230/2^-8)) |
| // |
| data8 0xa500c5e5b4c1aa36 , 0x00003ffe // log(1/frcpa(1+231/2^-8)) |
| data8 0xa57ad064eb2ebbc2 , 0x00003ffe // log(1/frcpa(1+232/2^-8)) |
| data8 0xa5f5152dedf4384e , 0x00003ffe // log(1/frcpa(1+233/2^-8)) |
| data8 0xa66f9478856233ec , 0x00003ffe // log(1/frcpa(1+234/2^-8)) |
| data8 0xa6ea4e7cca02c32e , 0x00003ffe // log(1/frcpa(1+235/2^-8)) |
| // |
| data8 0xa765437325341ccf , 0x00003ffe // log(1/frcpa(1+236/2^-8)) |
| data8 0xa81e21e6c75b4020 , 0x00003ffe // log(1/frcpa(1+237/2^-8)) |
| data8 0xa899ab333fe2b9ca , 0x00003ffe // log(1/frcpa(1+238/2^-8)) |
| data8 0xa9157039c51ebe71 , 0x00003ffe // log(1/frcpa(1+239/2^-8)) |
| data8 0xa991713433c2b999 , 0x00003ffe // log(1/frcpa(1+240/2^-8)) |
| // |
| data8 0xaa0dae5cbcc048b3 , 0x00003ffe // log(1/frcpa(1+241/2^-8)) |
| data8 0xaa8a27ede5eb13ad , 0x00003ffe // log(1/frcpa(1+242/2^-8)) |
| data8 0xab06de228a9e3499 , 0x00003ffe // log(1/frcpa(1+243/2^-8)) |
| data8 0xab83d135dc633301 , 0x00003ffe // log(1/frcpa(1+244/2^-8)) |
| data8 0xac3fb076adc7fe7a , 0x00003ffe // log(1/frcpa(1+245/2^-8)) |
| // |
| data8 0xacbd3cbbe47988f1 , 0x00003ffe // log(1/frcpa(1+246/2^-8)) |
| data8 0xad3b06b1a5dc57c3 , 0x00003ffe // log(1/frcpa(1+247/2^-8)) |
| data8 0xadb90e94af887717 , 0x00003ffe // log(1/frcpa(1+248/2^-8)) |
| data8 0xae3754a218f7c816 , 0x00003ffe // log(1/frcpa(1+249/2^-8)) |
| data8 0xaeb5d9175437afa2 , 0x00003ffe // log(1/frcpa(1+250/2^-8)) |
| // |
| data8 0xaf349c322e9c7cee , 0x00003ffe // log(1/frcpa(1+251/2^-8)) |
| data8 0xafb39e30d1768d1c , 0x00003ffe // log(1/frcpa(1+252/2^-8)) |
| data8 0xb032df51c2c93116 , 0x00003ffe // log(1/frcpa(1+253/2^-8)) |
| data8 0xb0b25fd3e6035ad9 , 0x00003ffe // log(1/frcpa(1+254/2^-8)) |
| data8 0xb1321ff67cba178c , 0x00003ffe // log(1/frcpa(1+255/2^-8)) |
| LOCAL_OBJECT_END(log_table_3) |
| |
| |
| .section .text |
| GLOBAL_LIBM_ENTRY(asinh) |
| |
| { .mfi |
| getf.exp asinh_GR_f8 = f8 // Must recompute later if x unorm |
| fclass.m p12,p0 = f8, 0x0b // Test x unorm |
| mov log_GR_exp_17_ones = 0x1ffff |
| } |
| { .mfi |
| addl NR_table_address = @ltoff(log_table_1), gp |
| fma.s1 log_y = f8, f8, f1 // y = x^2 + 1 |
| mov asinh_GR_comp = 0xfffc |
| } |
| ;; |
| |
| { .mfi |
| mov log_GR_exp_16_ones = 0xffff //BIAS |
| fclass.m p6,p0 = f8, 0xe7 // Test for x = NaN and inf and zero |
| mov log_GR_comp2 = 0x1003e |
| } |
| { .mfi |
| ld8 NR_table_address = [NR_table_address] |
| fma.s1 asinh_w_sq = f8,f8,f0 // x^2 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fcmp.lt.s1 p7,p11 = f8,f0 // if x<0 |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| fnorm.s1 fNormX = f8 // Normalize x |
| (p12) br.cond.spnt ASINH_UNORM // Branch if x=unorm |
| } |
| ;; |
| |
| ASINH_COMMON: |
| // Return here if x=unorm and not denorm |
| { .mfi |
| //to get second table address |
| adds log_table_address2 = 0x40, NR_table_address |
| fma.s1 log_arg = f8,f1,f8 |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| (p6) fma.d.s0 f8 = f8,f1,f8 // quietize nan result if x=nan |
| (p6) br.ret.spnt b0 // Exit for x=nan and inf and zero |
| } |
| ;; |
| |
| { .mfi |
| ldfpd NR1,NR2 = [log_table_address2],16 |
| frsqrta.s1 log_y_rs,p0 = log_y // z=1/sqrt(y) |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| ldfe log_C13 = [log_table_address2],16 |
| nop.f 0 |
| and asinh_GR_f8 = asinh_GR_f8,log_GR_exp_17_ones |
| } |
| ;; |
| |
| { .mib |
| ldfe log_C11 = [log_table_address2],16 |
| cmp.le p13,p0 = log_GR_comp2,asinh_GR_f8 |
| (p13) br.cond.spnt LOG_COMMON1 // Branch if path 4, |x| >= 2^63 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 log_y_rs_iter = log_y_rs,log_y,f0 // y*z |
| nop.i 0 |
| } |
| ;; |
| |
| .pred.rel "mutex",p7,p11 |
| { .mfi |
| nop.m 0 |
| (p11) mov asinh_f8 = fNormX |
| nop.i 0 |
| } |
| { .mfb |
| cmp.gt p8,p0 = asinh_GR_comp,asinh_GR_f8 |
| (p7) fnma.s1 asinh_f8 = fNormX,f1,f0 |
| (p8) br.cond.spnt ASINH_NEAR_ZERO // Branch if path 2, 0 < |x| < 2^-3 |
| } |
| ;; |
| |
| // Here if main path, 2^-3 <= |x| < 2^63 |
| ///////////////////////////////// The first iteration ///////////////////////// |
| { .mfi |
| ldfpd log_P5,log_P4 = [NR_table_address],16 |
| fnma.s1 log_y_rs_iter = log_y_rs_iter,log_y_rs,NR2 // 3-(y*z)*z |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 log_y_rs_iter1 = log_y_rs,NR1,f0 // 0.5*z |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| ldfpd log_P3,log_P2 = [NR_table_address],16 |
| // (0.5*z)*(3-(y*z)*z) |
| fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs_iter,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| /////////////////////////// The second iteration ///////////////////////////// |
| { .mfi |
| ldfd log_P1 = [NR_table_address],16 |
| fma.s1 log_y_rs = log_y_rs_iter,log_y,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| ldfe log2 = [NR_table_address],16 |
| // (0.5*z)*(3-(y*z)*z) |
| fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs,f0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| // (0.5*z)*(3-(y*z)*z) |
| fma.s1 log_arg_early = log_y_rs_iter1,log_y_rs,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| ////////////////////////////////// The third iteration //////////////////////// |
| { .mfi |
| nop.m 0 |
| fma.s1 log_y_rs = log_y_rs_iter,log_y,f0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 log_arg_early = log_arg_early,log_y,asinh_f8 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 log_y_rs_iter1 = log_y_rs_iter1,log_y,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| frcpa.s1 log_C,p0 = f1,log_arg_early |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| getf.exp log_GR_signexp_f8 = log_arg_early |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| getf.sig log_GR_significand_f8 = log_arg_early |
| // (0.5*z)*(3-(y*z)*z)*y + |x| |
| fma.s1 log_arg = log_y_rs_iter1,log_y_rs,asinh_f8 |
| //to get third table address |
| adds log_table_address3 = 0x70, NR_table_address |
| } |
| ;; |
| |
| ///////////////////////////////// The end NR iterations ///////////////////// |
| { .mfi |
| nop.m 0 |
| nop.f 0 |
| //significant bit destruction |
| and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones |
| } |
| ;; |
| |
| { .mfi |
| //BIAS subtraction |
| sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones |
| (p7) fnma.s1 log2 = log2,f1,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| setf.sig log_int_Nfloat = log_GR_true_exp_f8 |
| fms.s1 log_r = log_C,log_arg,f1 // C = frcpa(x); r = C * x - 1 |
| extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits |
| } |
| ;; |
| |
| { .mmi |
| //pre-index*16 + index |
| shladd log_table_address3 = log_GR_index,4,log_table_address3 |
| ;; |
| ldfe log_T = [log_table_address3] |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 log_rsq = log_r, log_r, f0 //r^2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 log_rp_p4 = log_P5, log_r, log_P4 //P5*r + P4 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| //convert N to the floating-point format |
| fcvt.xf log_Nfloat = log_int_Nfloat |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 log_rcube = log_rsq, log_r, f0 //r^3 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 log_rp_p10 = log_rsq, log_P1, log_r //P1*r^2 + r |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| //(P5*r + P4)*r^2 + P3*r + P2 |
| fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32 |
| nop.i 0 |
| } |
| ;; |
| |
| .pred.rel "mutex",p7,p11 |
| { .mfi |
| nop.m 0 |
| (p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| (p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| //((P5*r + P4)*r^2 + P3*r + P2)*w^3 + P1*r^2 + r |
| fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| // N*log2 + T + ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r |
| (p11) fadd.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| // -N*log2 - T - ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r |
| (p7) fsub.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r |
| br.ret.sptk b0 // Exit main path, path 3: 2^-3 <= |x| < 2^63 |
| } |
| ;; |
| |
| // Here if path 4, |x| >= 2^63 |
| LOG_COMMON1: |
| { .mfi |
| ldfpd log_P5,log_P4 = [NR_table_address],16 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| ldfpd log_P3,log_P2 = [NR_table_address],16 |
| frcpa.s1 log_C,p0 = f1,log_arg |
| nop.i 0 |
| } |
| ;; |
| |
| { .mmi |
| getf.exp log_GR_signexp_f8 = log_arg |
| ldfd log_P1 = [NR_table_address],16 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mmi |
| getf.sig log_GR_significand_f8 = log_arg |
| ldfe log2 = [NR_table_address],16 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| adds log_table_address3 = 0x70, NR_table_address |
| nop.f 0 |
| //significant bit destruction |
| and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones |
| } |
| ;; |
| |
| { .mmf |
| nop.m 0 |
| //BIAS subtraction |
| sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones |
| fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1 |
| } |
| ;; |
| |
| { .mfi |
| setf.sig log_int_Nfloat = log_GR_true_exp_f8 |
| nop.f 0 |
| extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits |
| } |
| ;; |
| |
| { .mmi |
| //pre-index*16 + index |
| shladd log_table_address3 = log_GR_index,4,log_table_address3 |
| ;; |
| ldfe log_T = [log_table_address3] |
| nop.i 0 |
| |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 log_rsq = log_r, log_r, f0 //r^2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 log_rp_p4 = log_P5, log_r, log_P4 //P5*r + P4 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| (p7) fnma.s1 log2 = log2,f1,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 log_rcube = log_rsq, log_r, f0 //r^3 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 log_rp_p10 = log_rsq, log_P1, log_r //P1*r^2 + r |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| //convert N to the floating-point format |
| fcvt.xf log_Nfloat = log_int_Nfloat |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| //(P5*r + P4)*r^2 + P3*r + P2 |
| fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| (p7) fnma.s1 log_T = log_T,f1,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| //((P5*r + P4)*r^2 + P3*r + P2)*w^3 + P1*r^2 + r |
| fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10 |
| nop.i 0 |
| } |
| ;; |
| |
| .pred.rel "mutex",p7,p11 |
| { .mfi |
| nop.m 0 |
| // N*log2 + T + ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r |
| (p11) fadd.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| // -N*log2 - T - ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r |
| (p7) fsub.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r |
| br.ret.sptk b0 // Exit path 4, |x| >= 2^63 |
| } |
| ;; |
| |
| // Here is path 2, 0 < |x| < 2^-3 |
| ASINH_NEAR_ZERO: |
| { .mfi |
| ldfe log_C9 = [log_table_address2],16 |
| fma.s1 asinh_w_cube = asinh_w_sq,fNormX,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| ldfe log_C7 = [log_table_address2],16 |
| fma.s1 asinh_w_four = asinh_w_sq,asinh_w_sq,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| ldfe log_C5 = [log_table_address2],16 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| ldfe log_C3 = [log_table_address2],16 |
| nop.f 0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 asinh_w_13 = log_C13,asinh_w_sq,log_C11 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 asinh_w_9 = log_C9,asinh_w_sq,log_C7 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 asinh_w_3 = log_C5,asinh_w_sq,log_C3 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 asinh_w_seven = asinh_w_four,asinh_w_cube,f0 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 asinh_w_7 = asinh_w_13,asinh_w_four,asinh_w_9 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 asinh_w_5 = asinh_w_3,asinh_w_cube,fNormX |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 0 |
| fma.d.s0 f8 = asinh_w_7,asinh_w_seven,asinh_w_5 |
| br.ret.sptk b0 // Exit path 2 (0.0 <|x| < 2^(-3)) |
| } |
| ;; |
| |
| ASINH_UNORM: |
| // Here if x=unorm |
| { .mfi |
| getf.exp asinh_GR_f8 = fNormX // Recompute if x unorm |
| fclass.m p0,p13 = fNormX, 0x0b // Test x denorm |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 0 |
| fcmp.eq.s0 p14,p0 = f8, f0 // Dummy to set denormal flag |
| (p13) br.cond.sptk ASINH_COMMON // Continue if x unorm and not denorm |
| } |
| ;; |
| |
| .pred.rel "mutex",p7,p11 |
| { .mfi |
| nop.m 0 |
| (p7) fma.d.s0 f8 = f8,f8,f8 // Result x+x^2 if x=-denorm |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| (p11) fnma.d.s0 f8 = f8,f8,f8 // Result x-x^2 if x=+denorm |
| br.ret.spnt b0 // Exit if denorm |
| } |
| ;; |
| |
| GLOBAL_LIBM_END(asinh) |
| |
