| .file "atanhf.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 |
| //============================================================== |
| // 05/22/01 Initial version |
| // 05/20/02 Cleaned up namespace and sf0 syntax |
| // 08/06/02 Improved Itanium 2 performance |
| // 02/06/03 Reordered header: .section, .global, .proc, .align |
| // 05/26/03 Improved performance, fixed to handle unorms |
| // |
| // API |
| //============================================================== |
| // float atanhf(float) |
| // |
| // Overview of operation |
| //============================================================== |
| // Background |
| // |
| // |
| // There are 7 paths: |
| // 1. x = +/-0.0 |
| // Return atanhf(x) = +/-0.0 |
| // |
| // 2. 0.0 < |x| <= MAX_DENORMAL_ABS |
| // Return atanhf(x) = x + sign(x)*x^2 |
| // |
| // 3. MAX_DENORMAL_ABS < |x| < 2^(-20) |
| // Return atanhf(x) = Pol3(x), where Pol3(x) = x + x^3 |
| // |
| // 4. 2^(-20) <= |x| < 1 |
| // Return atanhf(x) = 0.5 * (log(1 + x) - log(1 - x)) |
| // Algorithm description for log function see below. |
| // |
| // 5. |x| = 1 |
| // Return atanhf(x) = sign(x) * +INF |
| // |
| // 6. 1 < |x| <= +INF |
| // Return atanhf(x) = QNaN |
| // |
| // 7. x = [S,Q]NaN |
| // Return atanhf(x) = QNaN |
| // |
| //============================================================== |
| // Algorithm Description for log(x) function |
| // |
| // Consider x = 2^N * 1.f1 f2 f3 f4...f63 |
| // log(x) = log(x * frcpa(x) / frcpa(x)) |
| // = log(x * frcpa(x)) + log(1/frcpa(x)) |
| // = log(x * frcpa(x)) - log(frcpa(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) |
| // = N*log2 - log(frcpa(1.f1 f2 ... f63)) |
| // |
| // |
| // log(x) = log(1/frcpa(x)) + log(frcpa(x) x) |
| // |
| // log(x) = N*log2 + log(1./frcpa(1.f1 f2 ... f63)) + log(x * frcpa(x)) |
| // log(x) = N*log2 + T + log(frcpa(x) x) |
| // |
| // Log(x) = N*log2 + T + log(C * x) |
| // |
| // C * x = 1 + r |
| // |
| // log(x) = N*log2 + T + log(1 + r) |
| // log(x) = N*log2 + T + Series(r) |
| // |
| // 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 |
| // |
| // 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 |
| // f32 -> f59 |
| |
| // General registers used: |
| // r14 -> r29, r32 -> r39 |
| |
| // Predicate registers used: |
| // p6 -> p9 |
| |
| // p6 to filter out case when |x| >= 1 |
| // p7 to filter out case when x = [Q,S]NaN or +/-0 |
| // p8 to filter out case when |x| < 2^(-20) |
| // p9 to filter out case when x = denormal |
| |
| |
| // Assembly macros |
| //============================================================== |
| DataPtr = r14 |
| RcpTablePtrM = r15 |
| RcpTablePtrP = r16 |
| rExpbMask = r17 |
| rBias = r18 |
| rNearZeroBound = r19 |
| rArgSExpb = r20 |
| rArgExpb = r21 |
| rExpbm = r22 |
| rExpbp = r23 |
| rSigm = r24 |
| rSigp = r25 |
| rNm = r26 |
| rNp = r27 |
| rIndm = r28 |
| rIndp = r29 |
| |
| GR_SAVE_B0 = r33 |
| GR_SAVE_GP = r34 |
| GR_SAVE_PFS = r35 |
| |
| GR_Parameter_X = r36 |
| GR_Parameter_Y = r37 |
| GR_Parameter_RESULT = r38 |
| atanh_GR_tag = r39 |
| |
| //============================================================== |
| fOneMx = f33 |
| fOnePx = f34 |
| fRm2 = f35 |
| fRm3 = f36 |
| fRp2 = f37 |
| fRp3 = f38 |
| fRcpM = f39 |
| fRcpP = f40 |
| fRp = f41 |
| fRm = f42 |
| fN4CvtM = f43 |
| fN4CvtP = f44 |
| fNm = f45 |
| fNp = f46 |
| fLogTm = f47 |
| fLogTp = f48 |
| fLog2 = f49 |
| fArgAbs = f50 |
| fNormX = f50 |
| fP32m = f51 |
| fP32p = f52 |
| fP10m = f53 |
| fP10p = f54 |
| fX2 = f55 |
| fP3 = f56 |
| fP2 = f57 |
| fP1 = f58 |
| fHalf = f59 |
| |
| |
| |
| // Data tables |
| //============================================================== |
| |
| RODATA |
| |
| .align 16 |
| |
| LOCAL_OBJECT_START(atanhf_data) |
| data8 0xbfc0001008f39d59 // P3*0.5 |
| data8 0x3fc5556073e0c45a // P2*0.5 |
| data8 0xbfcffffffffaea15 // P1*0.5 |
| data8 0x3fe0000000000000 // 0.5 |
| data8 0x3fd62e42fefa39ef // 0.5*ln(2) |
| data8 0x0000000000000000 // pad |
| LOCAL_OBJECT_END(atanhf_data) |
| |
| LOCAL_OBJECT_START(atanhf_data2) |
| data8 0x3f50040155d5889e //log(1/frcpa(1+0/256))/2 |
| data8 0x3f68121214586b54 //log(1/frcpa(1+1/256))/2 |
| data8 0x3f741929f96832f0 //log(1/frcpa(1+2/256))/2 |
| data8 0x3f7c317384c75f06 //log(1/frcpa(1+3/256))/2 |
| data8 0x3f81a6b91ac73386 //log(1/frcpa(1+4/256))/2 |
| data8 0x3f85ba9a5d9ac039 //log(1/frcpa(1+5/256))/2 |
| data8 0x3f89d2a8074325f4 //log(1/frcpa(1+6/256))/2 |
| data8 0x3f8d6b2725979802 //log(1/frcpa(1+7/256))/2 |
| data8 0x3f90c58fa19dfaaa //log(1/frcpa(1+8/256))/2 |
| data8 0x3f92954c78cbce1b //log(1/frcpa(1+9/256))/2 |
| data8 0x3f94a94d2da96c56 //log(1/frcpa(1+10/256))/2 |
| data8 0x3f967c94f2d4bb58 //log(1/frcpa(1+11/256))/2 |
| data8 0x3f985188b630f068 //log(1/frcpa(1+12/256))/2 |
| data8 0x3f9a6b8abe73af4c //log(1/frcpa(1+13/256))/2 |
| data8 0x3f9c441e06f72a9e //log(1/frcpa(1+14/256))/2 |
| data8 0x3f9e1e6713606d07 //log(1/frcpa(1+15/256))/2 |
| data8 0x3f9ffa6911ab9301 //log(1/frcpa(1+16/256))/2 |
| data8 0x3fa0ec139c5da601 //log(1/frcpa(1+17/256))/2 |
| data8 0x3fa1dbd2643d190b //log(1/frcpa(1+18/256))/2 |
| data8 0x3fa2cc7284fe5f1c //log(1/frcpa(1+19/256))/2 |
| data8 0x3fa3bdf5a7d1ee64 //log(1/frcpa(1+20/256))/2 |
| data8 0x3fa4b05d7aa012e0 //log(1/frcpa(1+21/256))/2 |
| data8 0x3fa580db7ceb5702 //log(1/frcpa(1+22/256))/2 |
| data8 0x3fa674f089365a7a //log(1/frcpa(1+23/256))/2 |
| data8 0x3fa769ef2c6b568d //log(1/frcpa(1+24/256))/2 |
| data8 0x3fa85fd927506a48 //log(1/frcpa(1+25/256))/2 |
| data8 0x3fa9335e5d594989 //log(1/frcpa(1+26/256))/2 |
| data8 0x3faa2b0220c8e5f5 //log(1/frcpa(1+27/256))/2 |
| data8 0x3fab0004ac1a86ac //log(1/frcpa(1+28/256))/2 |
| data8 0x3fabf968769fca11 //log(1/frcpa(1+29/256))/2 |
| data8 0x3faccfedbfee13a8 //log(1/frcpa(1+30/256))/2 |
| data8 0x3fada727638446a2 //log(1/frcpa(1+31/256))/2 |
| data8 0x3faea3257fe10f7a //log(1/frcpa(1+32/256))/2 |
| data8 0x3faf7be9fedbfde6 //log(1/frcpa(1+33/256))/2 |
| data8 0x3fb02ab352ff25f4 //log(1/frcpa(1+34/256))/2 |
| data8 0x3fb097ce579d204d //log(1/frcpa(1+35/256))/2 |
| data8 0x3fb1178e8227e47c //log(1/frcpa(1+36/256))/2 |
| data8 0x3fb185747dbecf34 //log(1/frcpa(1+37/256))/2 |
| data8 0x3fb1f3b925f25d41 //log(1/frcpa(1+38/256))/2 |
| data8 0x3fb2625d1e6ddf57 //log(1/frcpa(1+39/256))/2 |
| data8 0x3fb2d1610c86813a //log(1/frcpa(1+40/256))/2 |
| data8 0x3fb340c59741142e //log(1/frcpa(1+41/256))/2 |
| data8 0x3fb3b08b6757f2a9 //log(1/frcpa(1+42/256))/2 |
| data8 0x3fb40dfb08378003 //log(1/frcpa(1+43/256))/2 |
| data8 0x3fb47e74e8ca5f7c //log(1/frcpa(1+44/256))/2 |
| data8 0x3fb4ef51f6466de4 //log(1/frcpa(1+45/256))/2 |
| data8 0x3fb56092e02ba516 //log(1/frcpa(1+46/256))/2 |
| data8 0x3fb5d23857cd74d5 //log(1/frcpa(1+47/256))/2 |
| data8 0x3fb6313a37335d76 //log(1/frcpa(1+48/256))/2 |
| data8 0x3fb6a399dabbd383 //log(1/frcpa(1+49/256))/2 |
| data8 0x3fb70337dd3ce41b //log(1/frcpa(1+50/256))/2 |
| data8 0x3fb77654128f6127 //log(1/frcpa(1+51/256))/2 |
| data8 0x3fb7e9d82a0b022d //log(1/frcpa(1+52/256))/2 |
| data8 0x3fb84a6b759f512f //log(1/frcpa(1+53/256))/2 |
| data8 0x3fb8ab47d5f5a310 //log(1/frcpa(1+54/256))/2 |
| data8 0x3fb91fe49096581b //log(1/frcpa(1+55/256))/2 |
| data8 0x3fb981634011aa75 //log(1/frcpa(1+56/256))/2 |
| data8 0x3fb9f6c407089664 //log(1/frcpa(1+57/256))/2 |
| data8 0x3fba58e729348f43 //log(1/frcpa(1+58/256))/2 |
| data8 0x3fbabb55c31693ad //log(1/frcpa(1+59/256))/2 |
| data8 0x3fbb1e104919efd0 //log(1/frcpa(1+60/256))/2 |
| data8 0x3fbb94ee93e367cb //log(1/frcpa(1+61/256))/2 |
| data8 0x3fbbf851c067555f //log(1/frcpa(1+62/256))/2 |
| data8 0x3fbc5c0254bf23a6 //log(1/frcpa(1+63/256))/2 |
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| data8 0x3fbd88e93fb2f450 //log(1/frcpa(1+66/256))/2 |
| data8 0x3fbdedd437eaef01 //log(1/frcpa(1+67/256))/2 |
| data8 0x3fbe530effe71012 //log(1/frcpa(1+68/256))/2 |
| data8 0x3fbeb89a1648b971 //log(1/frcpa(1+69/256))/2 |
| data8 0x3fbf1e75fadf9bde //log(1/frcpa(1+70/256))/2 |
| data8 0x3fbf84a32ead7c35 //log(1/frcpa(1+71/256))/2 |
| data8 0x3fbfeb2233ea07cd //log(1/frcpa(1+72/256))/2 |
| data8 0x3fc028f9c7035c1c //log(1/frcpa(1+73/256))/2 |
| data8 0x3fc05c8be0d9635a //log(1/frcpa(1+74/256))/2 |
| data8 0x3fc085eb8f8ae797 //log(1/frcpa(1+75/256))/2 |
| data8 0x3fc0b9c8e32d1911 //log(1/frcpa(1+76/256))/2 |
| data8 0x3fc0edd060b78081 //log(1/frcpa(1+77/256))/2 |
| data8 0x3fc122024cf0063f //log(1/frcpa(1+78/256))/2 |
| data8 0x3fc14be2927aecd4 //log(1/frcpa(1+79/256))/2 |
| data8 0x3fc180618ef18adf //log(1/frcpa(1+80/256))/2 |
| data8 0x3fc1b50bbe2fc63b //log(1/frcpa(1+81/256))/2 |
| data8 0x3fc1df4cc7cf242d //log(1/frcpa(1+82/256))/2 |
| data8 0x3fc214456d0eb8d4 //log(1/frcpa(1+83/256))/2 |
| data8 0x3fc23ec5991eba49 //log(1/frcpa(1+84/256))/2 |
| data8 0x3fc2740d9f870afb //log(1/frcpa(1+85/256))/2 |
| data8 0x3fc29ecdabcdfa04 //log(1/frcpa(1+86/256))/2 |
| data8 0x3fc2d46602adccee //log(1/frcpa(1+87/256))/2 |
| data8 0x3fc2ff66b04ea9d4 //log(1/frcpa(1+88/256))/2 |
| data8 0x3fc335504b355a37 //log(1/frcpa(1+89/256))/2 |
| data8 0x3fc360925ec44f5d //log(1/frcpa(1+90/256))/2 |
| data8 0x3fc38bf1c3337e75 //log(1/frcpa(1+91/256))/2 |
| data8 0x3fc3c25277333184 //log(1/frcpa(1+92/256))/2 |
| data8 0x3fc3edf463c1683e //log(1/frcpa(1+93/256))/2 |
| data8 0x3fc419b423d5e8c7 //log(1/frcpa(1+94/256))/2 |
| data8 0x3fc44591e0539f49 //log(1/frcpa(1+95/256))/2 |
| data8 0x3fc47c9175b6f0ad //log(1/frcpa(1+96/256))/2 |
| data8 0x3fc4a8b341552b09 //log(1/frcpa(1+97/256))/2 |
| data8 0x3fc4d4f3908901a0 //log(1/frcpa(1+98/256))/2 |
| data8 0x3fc501528da1f968 //log(1/frcpa(1+99/256))/2 |
| data8 0x3fc52dd06347d4f6 //log(1/frcpa(1+100/256))/2 |
| data8 0x3fc55a6d3c7b8a8a //log(1/frcpa(1+101/256))/2 |
| data8 0x3fc5925d2b112a59 //log(1/frcpa(1+102/256))/2 |
| data8 0x3fc5bf406b543db2 //log(1/frcpa(1+103/256))/2 |
| data8 0x3fc5ec433d5c35ae //log(1/frcpa(1+104/256))/2 |
| data8 0x3fc61965cdb02c1f //log(1/frcpa(1+105/256))/2 |
| data8 0x3fc646a84935b2a2 //log(1/frcpa(1+106/256))/2 |
| data8 0x3fc6740add31de94 //log(1/frcpa(1+107/256))/2 |
| data8 0x3fc6a18db74a58c5 //log(1/frcpa(1+108/256))/2 |
| data8 0x3fc6cf31058670ec //log(1/frcpa(1+109/256))/2 |
| data8 0x3fc6f180e852f0ba //log(1/frcpa(1+110/256))/2 |
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| data8 0x3fc7a9b9889f19e2 //log(1/frcpa(1+114/256))/2 |
| data8 0x3fc7d81b037eb6a6 //log(1/frcpa(1+115/256))/2 |
| data8 0x3fc8069e33827231 //log(1/frcpa(1+116/256))/2 |
| data8 0x3fc82996d3ef8bcb //log(1/frcpa(1+117/256))/2 |
| data8 0x3fc85855776dcbfb //log(1/frcpa(1+118/256))/2 |
| data8 0x3fc8873658327ccf //log(1/frcpa(1+119/256))/2 |
| data8 0x3fc8aa75973ab8cf //log(1/frcpa(1+120/256))/2 |
| data8 0x3fc8d992dc8824e5 //log(1/frcpa(1+121/256))/2 |
| data8 0x3fc908d2ea7d9512 //log(1/frcpa(1+122/256))/2 |
| data8 0x3fc92c59e79c0e56 //log(1/frcpa(1+123/256))/2 |
| data8 0x3fc95bd750ee3ed3 //log(1/frcpa(1+124/256))/2 |
| data8 0x3fc98b7811a3ee5b //log(1/frcpa(1+125/256))/2 |
| data8 0x3fc9af47f33d406c //log(1/frcpa(1+126/256))/2 |
| data8 0x3fc9df270c1914a8 //log(1/frcpa(1+127/256))/2 |
| data8 0x3fca0325ed14fda4 //log(1/frcpa(1+128/256))/2 |
| data8 0x3fca33440224fa79 //log(1/frcpa(1+129/256))/2 |
| data8 0x3fca57725e80c383 //log(1/frcpa(1+130/256))/2 |
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| data8 0x3fcd490246defa6b //log(1/frcpa(1+148/256))/2 |
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| data8 0x3fcd9509707ae52f //log(1/frcpa(1+150/256))/2 |
| data8 0x3fcdbb2efe92c554 //log(1/frcpa(1+151/256))/2 |
| data8 0x3fcdee2f3445e4af //log(1/frcpa(1+152/256))/2 |
| data8 0x3fce148a1a2726ce //log(1/frcpa(1+153/256))/2 |
| data8 0x3fce3afc0a49ff40 //log(1/frcpa(1+154/256))/2 |
| data8 0x3fce6185206d516e //log(1/frcpa(1+155/256))/2 |
| data8 0x3fce882578823d52 //log(1/frcpa(1+156/256))/2 |
| data8 0x3fceaedd2eac990c //log(1/frcpa(1+157/256))/2 |
| data8 0x3fced5ac5f436be3 //log(1/frcpa(1+158/256))/2 |
| data8 0x3fcefc9326d16ab9 //log(1/frcpa(1+159/256))/2 |
| data8 0x3fcf2391a2157600 //log(1/frcpa(1+160/256))/2 |
| data8 0x3fcf4aa7ee03192d //log(1/frcpa(1+161/256))/2 |
| data8 0x3fcf71d627c30bb0 //log(1/frcpa(1+162/256))/2 |
| data8 0x3fcf991c6cb3b379 //log(1/frcpa(1+163/256))/2 |
| data8 0x3fcfc07ada69a910 //log(1/frcpa(1+164/256))/2 |
| data8 0x3fcfe7f18eb03d3e //log(1/frcpa(1+165/256))/2 |
| data8 0x3fd007c053c5002e //log(1/frcpa(1+166/256))/2 |
| data8 0x3fd01b942198a5a1 //log(1/frcpa(1+167/256))/2 |
| data8 0x3fd02f74400c64eb //log(1/frcpa(1+168/256))/2 |
| data8 0x3fd04360be7603ad //log(1/frcpa(1+169/256))/2 |
| data8 0x3fd05759ac47fe34 //log(1/frcpa(1+170/256))/2 |
| data8 0x3fd06b5f1911cf52 //log(1/frcpa(1+171/256))/2 |
| data8 0x3fd078bf0533c568 //log(1/frcpa(1+172/256))/2 |
| data8 0x3fd08cd9687e7b0e //log(1/frcpa(1+173/256))/2 |
| data8 0x3fd0a10074cf9019 //log(1/frcpa(1+174/256))/2 |
| data8 0x3fd0b5343a234477 //log(1/frcpa(1+175/256))/2 |
| data8 0x3fd0c974c89431ce //log(1/frcpa(1+176/256))/2 |
| data8 0x3fd0ddc2305b9886 //log(1/frcpa(1+177/256))/2 |
| data8 0x3fd0eb524bafc918 //log(1/frcpa(1+178/256))/2 |
| data8 0x3fd0ffb54213a476 //log(1/frcpa(1+179/256))/2 |
| data8 0x3fd114253da97d9f //log(1/frcpa(1+180/256))/2 |
| data8 0x3fd128a24f1d9aff //log(1/frcpa(1+181/256))/2 |
| data8 0x3fd1365252bf0865 //log(1/frcpa(1+182/256))/2 |
| data8 0x3fd14ae558b4a92d //log(1/frcpa(1+183/256))/2 |
| data8 0x3fd15f85a19c765b //log(1/frcpa(1+184/256))/2 |
| data8 0x3fd16d4d38c119fa //log(1/frcpa(1+185/256))/2 |
| data8 0x3fd18203c20dd133 //log(1/frcpa(1+186/256))/2 |
| data8 0x3fd196c7bc4b1f3b //log(1/frcpa(1+187/256))/2 |
| data8 0x3fd1a4a738b7a33c //log(1/frcpa(1+188/256))/2 |
| data8 0x3fd1b981c0c9653d //log(1/frcpa(1+189/256))/2 |
| data8 0x3fd1ce69e8bb106b //log(1/frcpa(1+190/256))/2 |
| data8 0x3fd1dc619de06944 //log(1/frcpa(1+191/256))/2 |
| data8 0x3fd1f160a2ad0da4 //log(1/frcpa(1+192/256))/2 |
| data8 0x3fd2066d7740737e //log(1/frcpa(1+193/256))/2 |
| data8 0x3fd2147dba47a394 //log(1/frcpa(1+194/256))/2 |
| data8 0x3fd229a1bc5ebac3 //log(1/frcpa(1+195/256))/2 |
| data8 0x3fd237c1841a502e //log(1/frcpa(1+196/256))/2 |
| data8 0x3fd24cfce6f80d9a //log(1/frcpa(1+197/256))/2 |
| data8 0x3fd25b2c55cd5762 //log(1/frcpa(1+198/256))/2 |
| data8 0x3fd2707f4d5f7c41 //log(1/frcpa(1+199/256))/2 |
| data8 0x3fd285e0842ca384 //log(1/frcpa(1+200/256))/2 |
| data8 0x3fd294294708b773 //log(1/frcpa(1+201/256))/2 |
| data8 0x3fd2a9a2670aff0c //log(1/frcpa(1+202/256))/2 |
| data8 0x3fd2b7fb2c8d1cc1 //log(1/frcpa(1+203/256))/2 |
| data8 0x3fd2c65a6395f5f5 //log(1/frcpa(1+204/256))/2 |
| data8 0x3fd2dbf557b0df43 //log(1/frcpa(1+205/256))/2 |
| data8 0x3fd2ea64c3f97655 //log(1/frcpa(1+206/256))/2 |
| data8 0x3fd3001823684d73 //log(1/frcpa(1+207/256))/2 |
| data8 0x3fd30e97e9a8b5cd //log(1/frcpa(1+208/256))/2 |
| data8 0x3fd32463ebdd34ea //log(1/frcpa(1+209/256))/2 |
| data8 0x3fd332f4314ad796 //log(1/frcpa(1+210/256))/2 |
| data8 0x3fd348d90e7464d0 //log(1/frcpa(1+211/256))/2 |
| data8 0x3fd35779f8c43d6e //log(1/frcpa(1+212/256))/2 |
| data8 0x3fd36621961a6a99 //log(1/frcpa(1+213/256))/2 |
| data8 0x3fd37c299f3c366a //log(1/frcpa(1+214/256))/2 |
| data8 0x3fd38ae2171976e7 //log(1/frcpa(1+215/256))/2 |
| data8 0x3fd399a157a603e7 //log(1/frcpa(1+216/256))/2 |
| data8 0x3fd3afccfe77b9d1 //log(1/frcpa(1+217/256))/2 |
| data8 0x3fd3be9d503533b5 //log(1/frcpa(1+218/256))/2 |
| data8 0x3fd3cd7480b4a8a3 //log(1/frcpa(1+219/256))/2 |
| data8 0x3fd3e3c43918f76c //log(1/frcpa(1+220/256))/2 |
| data8 0x3fd3f2acb27ed6c7 //log(1/frcpa(1+221/256))/2 |
| data8 0x3fd4019c2125ca93 //log(1/frcpa(1+222/256))/2 |
| data8 0x3fd4181061389722 //log(1/frcpa(1+223/256))/2 |
| data8 0x3fd42711518df545 //log(1/frcpa(1+224/256))/2 |
| data8 0x3fd436194e12b6bf //log(1/frcpa(1+225/256))/2 |
| data8 0x3fd445285d68ea69 //log(1/frcpa(1+226/256))/2 |
| data8 0x3fd45bcc464c893a //log(1/frcpa(1+227/256))/2 |
| data8 0x3fd46aed21f117fc //log(1/frcpa(1+228/256))/2 |
| data8 0x3fd47a1527e8a2d3 //log(1/frcpa(1+229/256))/2 |
| data8 0x3fd489445efffccc //log(1/frcpa(1+230/256))/2 |
| data8 0x3fd4a018bcb69835 //log(1/frcpa(1+231/256))/2 |
| data8 0x3fd4af5a0c9d65d7 //log(1/frcpa(1+232/256))/2 |
| data8 0x3fd4bea2a5bdbe87 //log(1/frcpa(1+233/256))/2 |
| data8 0x3fd4cdf28f10ac46 //log(1/frcpa(1+234/256))/2 |
| data8 0x3fd4dd49cf994058 //log(1/frcpa(1+235/256))/2 |
| data8 0x3fd4eca86e64a684 //log(1/frcpa(1+236/256))/2 |
| data8 0x3fd503c43cd8eb68 //log(1/frcpa(1+237/256))/2 |
| data8 0x3fd513356667fc57 //log(1/frcpa(1+238/256))/2 |
| data8 0x3fd522ae0738a3d8 //log(1/frcpa(1+239/256))/2 |
| data8 0x3fd5322e26867857 //log(1/frcpa(1+240/256))/2 |
| data8 0x3fd541b5cb979809 //log(1/frcpa(1+241/256))/2 |
| data8 0x3fd55144fdbcbd62 //log(1/frcpa(1+242/256))/2 |
| data8 0x3fd560dbc45153c7 //log(1/frcpa(1+243/256))/2 |
| data8 0x3fd5707a26bb8c66 //log(1/frcpa(1+244/256))/2 |
| data8 0x3fd587f60ed5b900 //log(1/frcpa(1+245/256))/2 |
| data8 0x3fd597a7977c8f31 //log(1/frcpa(1+246/256))/2 |
| data8 0x3fd5a760d634bb8b //log(1/frcpa(1+247/256))/2 |
| data8 0x3fd5b721d295f10f //log(1/frcpa(1+248/256))/2 |
| data8 0x3fd5c6ea94431ef9 //log(1/frcpa(1+249/256))/2 |
| data8 0x3fd5d6bb22ea86f6 //log(1/frcpa(1+250/256))/2 |
| data8 0x3fd5e6938645d390 //log(1/frcpa(1+251/256))/2 |
| data8 0x3fd5f673c61a2ed2 //log(1/frcpa(1+252/256))/2 |
| data8 0x3fd6065bea385926 //log(1/frcpa(1+253/256))/2 |
| data8 0x3fd6164bfa7cc06b //log(1/frcpa(1+254/256))/2 |
| data8 0x3fd62643fecf9743 //log(1/frcpa(1+255/256))/2 |
| LOCAL_OBJECT_END(atanhf_data2) |
| |
| |
| .section .text |
| GLOBAL_LIBM_ENTRY(atanhf) |
| |
| { .mfi |
| getf.exp rArgSExpb = f8 |
| fclass.m p9,p0 = f8, 0x0b // is arg denormal ? |
| mov rExpbMask = 0x1ffff |
| } |
| { .mfi |
| addl DataPtr = @ltoff(atanhf_data), gp |
| fnma.s1 fOneMx = f8, f1, f1 // 1 - x |
| mov rBias = 0xffff |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fclass.m p7,p0 = f8, 0xc7 // is arg NaN or +/-0 ? |
| mov rNearZeroBound = 0xffeb // 2^(-20) |
| } |
| { .mfi |
| ld8 DataPtr = [DataPtr] |
| fma.s1 fOnePx = f8, f1, f1 // 1 + x |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 0 |
| fnorm.s1 fNormX = f8 // Normalize x |
| (p9) br.cond.spnt ATANH_UNORM // Branch if x=unorm |
| } |
| ;; |
| |
| ATANH_COMMON: |
| // Return here if x=unorm and not denorm |
| { .mfi |
| ldfpd fP3, fP2 = [DataPtr], 16 |
| fma.s1 fX2 = f8, f8, f0 // x^2 |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| (p7) fma.s.s0 f8 = f8,f1,f8 // NaN or +/-0 |
| (p7) br.ret.spnt b0 |
| } |
| ;; |
| |
| { .mfi |
| ldfpd fP1, fHalf = [DataPtr], 16 |
| frcpa.s1 fRcpM, p9 = f1, fOneMx // rcpm = frcpa(1 - x) |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| getf.exp rExpbm = fOneMx |
| frcpa.s1 fRcpP, p0 = f1, fOnePx // rcpp = frcpa(1 + x) |
| // biased exponent |
| and rArgExpb = rArgSExpb, rExpbMask |
| } |
| ;; |
| |
| { .mmi |
| getf.exp rExpbp = fOnePx |
| // is |x| < 2^(-20) ? |
| cmp.gt p8,p0 = rNearZeroBound, rArgExpb |
| cmp.ge p6,p0 = rArgExpb, rBias // is |x| >= 1 ? |
| } |
| ;; |
| |
| { .mmb |
| getf.sig rSigm = fOneMx |
| nop.m 0 |
| (p6) br.cond.spnt atanhf_ge_one |
| } |
| ;; |
| |
| { .mfb |
| getf.sig rSigp = fOnePx |
| (p8) fma.s.s0 f8 = fX2, f8, f8 // x + x^3 |
| (p8) br.ret.spnt b0 // Exit for MAX_DENORM_ABS < |x| < 2^-20 |
| } |
| ;; |
| |
| { .mfi |
| ldfd fLog2 = [DataPtr], 16 |
| fms.s1 fRm = fRcpM, fOneMx, f1 // rm = rcpm * (1 - x) - 1 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mmf |
| // (1 - x) is always positive here and we need not mask sign bit |
| sub rNm = rExpbm, rBias |
| // (1 + x) is always positive here and we need not mask sign bit |
| sub rNp = rExpbp, rBias |
| fms.s1 fRp = fRcpP, fOnePx, f1 // rp = rcpp * (1 + x) - 1 |
| } |
| ;; |
| |
| { .mmi |
| setf.sig fN4CvtM = rNm |
| setf.sig fN4CvtP = rNp |
| extr.u rIndm = rSigm,55,8 // Extract 8 bits |
| } |
| ;; |
| |
| { .mmi |
| shladd RcpTablePtrM = rIndm, 3, DataPtr |
| nop.m 0 |
| extr.u rIndp = rSigp,55,8 // Extract 8 bits |
| } |
| ;; |
| |
| { .mmi |
| ldfd fLogTm = [RcpTablePtrM] |
| shladd RcpTablePtrP = rIndp, 3, DataPtr |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| ldfd fLogTp = [RcpTablePtrP] |
| fma.s1 fRm2 = fRm, fRm, f0 // rm^2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fP32m = fP3, fRm, fP2 // P3*rm + P2 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 fRp2 = fRp, fRp, f0 // rp^2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fP10m = fP1, fRm, fHalf // P1*rm + 1 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fma.s1 fP32p = fP3, fRp, fP2 // P3*rp + P2 |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fma.s1 fP10p = fP1, fRp, fHalf // P1*rp + 1 |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fcvt.xf fNm = fN4CvtM |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| fcvt.xf fNp = fN4CvtP |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| // (P3*rm + P2)*rm^2 + (P1*rm + 1) |
| fma.s1 fP32m = fP32m, fRm2, fP10m |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| // (P3*rp + P2)*rp^2 + (P1*rp + 1) |
| fma.s1 fP32p = fP32p, fRp2, fP10p |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| // Nm*ln(2)/2 + Tm/2 |
| fma.s1 fLogTm = fNm, fLog2, fLogTm |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| // Np*ln(2)/2 + Tp/2 |
| fma.s1 fLogTp = fNp, fLog2, fLogTp |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| // ((P3*rm + P2)*rm^2 + (P3*rm + 1))*0.5*rm + (Nm*ln(2)/2 + Tm/2) |
| fma.d.s1 fP32m = fP32m, fRm, fLogTm |
| nop.i 0 |
| } |
| { .mfi |
| nop.m 0 |
| // ((P3*rp + P2)*rp^2 + (P3*rp + 1))*0.5*rp + (Np*ln(2)/2 + Tp/2) |
| fma.d.s1 fP32p = fP32p, fRp, fLogTp |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 0 |
| // atanhf(x) = 0.5 * (log(1 + x) - log(1 - x)) |
| fnma.s.s0 f8 = fP32m, f1, fP32p |
| br.ret.sptk b0 // Exit for 2^(-20) <= |x| < 1.0 |
| } |
| ;; |
| |
| |
| ATANH_UNORM: |
| // Here if x=unorm |
| { .mfi |
| getf.exp rArgSExpb = fNormX // Recompute if x unorm |
| fclass.m p0,p9 = fNormX, 0x0b // Test x denorm |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfb |
| nop.m 0 |
| fcmp.lt.s0 p10,p11 = f8, f0 // Set denormal flag |
| (p9) br.cond.sptk ATANH_COMMON // Continue if x unorm and not denorm |
| } |
| ;; |
| |
| .pred.rel "mutex",p6,p7 |
| { .mfi |
| nop.m 0 |
| (p6) fnma.s.s0 f8 = f8,f8,f8 // Result x-x^2 if x=-denorm |
| nop.i 0 |
| } |
| { .mfb |
| nop.m 0 |
| (p7) fma.s.s0 f8 = f8,f8,f8 // Result x+x^2 if x=+denorm |
| br.ret.spnt b0 // Exit if denorm |
| } |
| ;; |
| |
| // Here if |x| >= 1.0 |
| atanhf_ge_one: |
| { .mfi |
| alloc r32 = ar.pfs,1,3,4,0 |
| fmerge.s fArgAbs = f0, f8 // Form |x| |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fmerge.s f10 = f8, f8 // Save input for error call |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfi |
| nop.m 0 |
| fcmp.eq.s1 p6,p7 = fArgAbs, f1 // Test for |x| = 1.0 |
| nop.i 0 |
| } |
| ;; |
| |
| // Set error tag and result, and raise invalid flag if |x| > 1.0 |
| { .mfi |
| (p7) mov atanh_GR_tag = 133 |
| (p7) frcpa.s0 f8, p0 = f0, f0 // Get QNaN, and raise invalid |
| nop.i 0 |
| } |
| ;; |
| |
| // Set error tag and result, and raise Z flag if |x| = 1.0 |
| { .mfi |
| nop.m 0 |
| (p6) frcpa.s0 fRm, p0 = f1, f0 // Get inf, and raise Z flag |
| nop.i 0 |
| } |
| ;; |
| |
| { .mfb |
| (p6) mov atanh_GR_tag = 134 |
| (p6) fmerge.s f8 = f8, fRm // result is +-inf |
| br.cond.sptk __libm_error_region // Exit if |x| >= 1.0 |
| } |
| ;; |
| |
| GLOBAL_LIBM_END(atanhf) |
| |
| |
| 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] = 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 |
| { .mib |
| stfs [GR_Parameter_X] = f10 // STORE Parameter 1 on stack |
| // Parameter 3 address |
| add GR_Parameter_RESULT = 0,GR_Parameter_Y |
| 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 |
| 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# |
