mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-23 05:20:06 +00:00
30891f35fa
We stopped adding "Contributed by" or similar lines in sources in 2012 in favour of git logs and keeping the Contributors section of the glibc manual up to date. Removing these lines makes the license header a bit more consistent across files and also removes the possibility of error in attribution when license blocks or files are copied across since the contributed-by lines don't actually reflect reality in those cases. Move all "Contributed by" and similar lines (Written by, Test by, etc.) into a new file CONTRIBUTED-BY to retain record of these contributions. These contributors are also mentioned in manual/contrib.texi, so we just maintain this additional record as a courtesy to the earlier developers. The following scripts were used to filter a list of files to edit in place and to clean up the CONTRIBUTED-BY file respectively. These were not added to the glibc sources because they're not expected to be of any use in future given that this is a one time task: https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02 Reviewed-by: Carlos O'Donell <carlos@redhat.com>
846 lines
29 KiB
ArmAsm
846 lines
29 KiB
ArmAsm
.file "atanhf.s"
|
|
|
|
|
|
// Copyright (c) 2000 - 2003, Intel Corporation
|
|
// All rights reserved.
|
|
//
|
|
//
|
|
// 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
|
|
data8 0x3fbcc000c9db3c52 //log(1/frcpa(1+64/256))/2
|
|
data8 0x3fbd244d99c85674 //log(1/frcpa(1+65/256))/2
|
|
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
|
|
data8 0x3fc71f5d71b894f0 //log(1/frcpa(1+111/256))/2
|
|
data8 0x3fc74d5aefd66d5c //log(1/frcpa(1+112/256))/2
|
|
data8 0x3fc77b79922bd37e //log(1/frcpa(1+113/256))/2
|
|
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
|
|
data8 0x3fca87d0165dd199 //log(1/frcpa(1+131/256))/2
|
|
data8 0x3fcaac2e6c03f896 //log(1/frcpa(1+132/256))/2
|
|
data8 0x3fcadccc6fdf6a81 //log(1/frcpa(1+133/256))/2
|
|
data8 0x3fcb015b3eb1e790 //log(1/frcpa(1+134/256))/2
|
|
data8 0x3fcb323a3a635948 //log(1/frcpa(1+135/256))/2
|
|
data8 0x3fcb56fa04462909 //log(1/frcpa(1+136/256))/2
|
|
data8 0x3fcb881aa659bc93 //log(1/frcpa(1+137/256))/2
|
|
data8 0x3fcbad0bef3db165 //log(1/frcpa(1+138/256))/2
|
|
data8 0x3fcbd21297781c2f //log(1/frcpa(1+139/256))/2
|
|
data8 0x3fcc039236f08819 //log(1/frcpa(1+140/256))/2
|
|
data8 0x3fcc28cb1e4d32fd //log(1/frcpa(1+141/256))/2
|
|
data8 0x3fcc4e19b84723c2 //log(1/frcpa(1+142/256))/2
|
|
data8 0x3fcc7ff9c74554c9 //log(1/frcpa(1+143/256))/2
|
|
data8 0x3fcca57b64e9db05 //log(1/frcpa(1+144/256))/2
|
|
data8 0x3fcccb130a5cebb0 //log(1/frcpa(1+145/256))/2
|
|
data8 0x3fccf0c0d18f326f //log(1/frcpa(1+146/256))/2
|
|
data8 0x3fcd232075b5a201 //log(1/frcpa(1+147/256))/2
|
|
data8 0x3fcd490246defa6b //log(1/frcpa(1+148/256))/2
|
|
data8 0x3fcd6efa918d25cd //log(1/frcpa(1+149/256))/2
|
|
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)
|
|
libm_alias_float_other (atanh, atanh)
|
|
|
|
|
|
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#
|