e_atanh.s

glibc 2.9,最新版的C语言库函数

.file "atanh.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
// ==============================================================
// 05/03/01  Initial version
// 05/20/02  Cleaned up namespace and sf0 syntax
// 02/06/03  Reordered header: .section, .global, .proc, .align
// 05/26/03  Improved performance, fixed to handle unorms
// 03/31/05  Reformatted delimiters between data tables
//
// API
// ==============================================================
// double atanh(double)
//
// Overview of operation
// ==============================================================
//
// There are 7 paths:
// 1. x = +/-0.0
//    Return atanh(x) = +/-0.0
//
// 2. 0.0 < |x| < 1/4
//    Return atanh(x) = Po2l(x),
//    where Po2l(x) = (((((((((C9*x^2 + C8)*x^2 + C7)*x^2 + C6)*x^2 +
//          C5)*x^2 + C4)*x^2 + C3)*x^2 + C2)*x^2 + C1)* x^2 + C0)*x^3 + x
// 3. 1/4 <= |x| < 1
//    Return atanh(x) = sign(x) * log((1 + |x|)/(1 - |x|))
//    To compute (1 + |x|)/(1 - |x|) modified Newton Raphson method is used
//    (3 iterations)
//    Algorithm description for log function see below.
//
// 4. |x| = 1
//    Return atanh(x) = sign(x) * +INF
//
// 5. 1 < |x| <= +INF
//    Return atanh(x) = QNaN
//
// 6. x = [S,Q]NaN
//    Return atanh(x) = QNaN
//
// 7. x = denormal
//    Return atanh(x) = x
//
//==============================================================
// Algorithm Description for log(x) function
// Below we are using the fact that inequality x - 1.0 > 2^(-6) is always true
// for this atanh implementation
//
// 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 - 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
// f32 -> f77

// General registers used:
// r14 -> r27, r33 -> r39

// Predicate registers used:
// p6 -> p14

// p10, p11      to indicate is argument positive or negative
// p12           to filter out case when x = [Q,S]NaN or +/-0
// p13           to filter out case when x = denormal
// p6, p7        to filter out case when |x| >= 1
// p8            to filter out case when |x| < 1/4

// Assembly macros
//==============================================================
Data2Ptr              = r14
Data3Ptr              = r15
RcpTablePtr           = r16
rExpbMask             = r17
rBias                 = r18
rNearZeroBound        = r19
rArgSExpb             = r20
rArgExpb              = r21
rSExpb                = r22
rExpb                 = r23
rSig                  = r24
rN                    = r25
rInd                  = r26
DataPtr               = r27

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

//==============================================================
fAbsX                 = f32
fOneMx                = f33
fOnePx                = f34
fY                    = f35
fR                    = f36
fR2                   = f37
fR3                   = f38
fRcp                  = f39
fY4Rcp                = f40
fRcp0                 = f41
fRcp0n                = f42
fRcp1                 = f43
fRcp2                 = f44
fRcp3                 = f45
fN4Cvt                = f46
fN                    = f47
fY2                   = f48
fLog2                 = f49
fLogT                 = f50
fLogT_N               = f51
fX2                   = f52
fX3                   = f53
fX4                   = f54
fX8                   = f55
fP0                   = f56
fP5                   = f57
fP4                   = f58
fP3                   = f59
fP2                   = f60
fP1                   = f61
fNormX                = f62
fC9                   = f63
fC8                   = f64
fC7                   = f65
fC6                   = f66
fC5                   = f67
fC4                   = f68
fC3                   = f69
fC2                   = f70
fC1                   = f71
fC0                   = f72
fP98                  = f73
fP76                  = f74
fP54                  = f75
fP32                  = f76
fP10                  = f77

// Data tables
//==============================================================
RODATA
.align 16

LOCAL_OBJECT_START(atanh_data)
data8 0xBFC5555DA7212371              //   P5
data8 0x3FC999A19EEF5826              //   P4
data8 0xBFCFFFFFFFFEF009              //   P3
data8 0x3FD555555554ECB2              //   P2
data8 0xBFE0000000000000              //   P1 = -0.5
data8 0x0000000000000000              //   pad
data8 0xb17217f7d1cf79ac , 0x00003ffd //   0.5*log(2)
data8 0x0000000000000000 , 0x00000000 //   pad to eliminate bank conflicts
LOCAL_OBJECT_END(atanh_data)

LOCAL_OBJECT_START(atanh_data_2)
data8 0x8649FB89D3AD51FB , 0x00003FFB //   C9
data8 0xCC10AABEF160077A , 0x00003FFA //   C8
data8 0xF1EDB99AC0819CE2 , 0x00003FFA //   C7
data8 0x8881E53A809AD24D , 0x00003FFB //   C6
data8 0x9D8A116EF212F271 , 0x00003FFB //   C5
data8 0xBA2E8A6D1D756453 , 0x00003FFB //   C4
data8 0xE38E38E7A0945692 , 0x00003FFB //   C3
data8 0x924924924536891A , 0x00003FFC //   C2
data8 0xCCCCCCCCCCD08D51 , 0x00003FFC //   C1
data8 0xAAAAAAAAAAAAAA0C , 0x00003FFD //   C0
LOCAL_OBJECT_END(atanh_data_2)


LOCAL_OBJECT_START(atanh_data_3)
data8 0x80200aaeac44ef38 , 0x00003ff5 //   log(1/frcpa(1+0/2^-8))/2
//
data8 0xc09090a2c35aa070 , 0x00003ff6 //   log(1/frcpa(1+1/2^-8))/2
data8 0xa0c94fcb41977c75 , 0x00003ff7 //   log(1/frcpa(1+2/2^-8))/2
data8 0xe18b9c263af83301 , 0x00003ff7 //   log(1/frcpa(1+3/2^-8))/2
data8 0x8d35c8d6399c30ea , 0x00003ff8 //   log(1/frcpa(1+4/2^-8))/2
data8 0xadd4d2ecd601cbb8 , 0x00003ff8 //   log(1/frcpa(1+5/2^-8))/2
//
data8 0xce95403a192f9f01 , 0x00003ff8 //   log(1/frcpa(1+6/2^-8))/2
data8 0xeb59392cbcc01096 , 0x00003ff8 //   log(1/frcpa(1+7/2^-8))/2
data8 0x862c7d0cefd54c5d , 0x00003ff9 //   log(1/frcpa(1+8/2^-8))/2
data8 0x94aa63c65e70d499 , 0x00003ff9 //   log(1/frcpa(1+9/2^-8))/2
data8 0xa54a696d4b62b382 , 0x00003ff9 //   log(1/frcpa(1+10/2^-8))/2
//
data8 0xb3e4a796a5dac208 , 0x00003ff9 //   log(1/frcpa(1+11/2^-8))/2
data8 0xc28c45b1878340a9 , 0x00003ff9 //   log(1/frcpa(1+12/2^-8))/2
data8 0xd35c55f39d7a6235 , 0x00003ff9 //   log(1/frcpa(1+13/2^-8))/2
data8 0xe220f037b954f1f5 , 0x00003ff9 //   log(1/frcpa(1+14/2^-8))/2
data8 0xf0f3389b036834f3 , 0x00003ff9 //   log(1/frcpa(1+15/2^-8))/2
//
data8 0xffd3488d5c980465 , 0x00003ff9 //   log(1/frcpa(1+16/2^-8))/2
data8 0x87609ce2ed300490 , 0x00003ffa //   log(1/frcpa(1+17/2^-8))/2
data8 0x8ede9321e8c85927 , 0x00003ffa //   log(1/frcpa(1+18/2^-8))/2
data8 0x96639427f2f8e2f4 , 0x00003ffa //   log(1/frcpa(1+19/2^-8))/2
data8 0x9defad3e8f73217b , 0x00003ffa //   log(1/frcpa(1+20/2^-8))/2
//
data8 0xa582ebd50097029c , 0x00003ffa //   log(1/frcpa(1+21/2^-8))/2
data8 0xac06dbe75ab80fee , 0x00003ffa //   log(1/frcpa(1+22/2^-8))/2
data8 0xb3a78449b2d3ccca , 0x00003ffa //   log(1/frcpa(1+23/2^-8))/2
data8 0xbb4f79635ab46bb2 , 0x00003ffa //   log(1/frcpa(1+24/2^-8))/2
data8 0xc2fec93a83523f3f , 0x00003ffa //   log(1/frcpa(1+25/2^-8))/2
//
data8 0xc99af2eaca4c4571 , 0x00003ffa //   log(1/frcpa(1+26/2^-8))/2
data8 0xd1581106472fa653 , 0x00003ffa //   log(1/frcpa(1+27/2^-8))/2
data8 0xd8002560d4355f2e , 0x00003ffa //   log(1/frcpa(1+28/2^-8))/2
data8 0xdfcb43b4fe508632 , 0x00003ffa //   log(1/frcpa(1+29/2^-8))/2
data8 0xe67f6dff709d4119 , 0x00003ffa //   log(1/frcpa(1+30/2^-8))/2
//
data8 0xed393b1c22351280 , 0x00003ffa //   log(1/frcpa(1+31/2^-8))/2
data8 0xf5192bff087bcc35 , 0x00003ffa //   log(1/frcpa(1+32/2^-8))/2
data8 0xfbdf4ff6dfef2fa3 , 0x00003ffa //   log(1/frcpa(1+33/2^-8))/2
data8 0x81559a97f92f9cc7 , 0x00003ffb //   log(1/frcpa(1+34/2^-8))/2
data8 0x84be72bce90266e8 , 0x00003ffb //   log(1/frcpa(1+35/2^-8))/2
//
data8 0x88bc74113f23def2 , 0x00003ffb //   log(1/frcpa(1+36/2^-8))/2
data8 0x8c2ba3edf6799d11 , 0x00003ffb //   log(1/frcpa(1+37/2^-8))/2
data8 0x8f9dc92f92ea08b1 , 0x00003ffb //   log(1/frcpa(1+38/2^-8))/2
data8 0x9312e8f36efab5a7 , 0x00003ffb //   log(1/frcpa(1+39/2^-8))/2
data8 0x968b08643409ceb6 , 0x00003ffb //   log(1/frcpa(1+40/2^-8))/2
//
data8 0x9a062cba08a1708c , 0x00003ffb //   log(1/frcpa(1+41/2^-8))/2
data8 0x9d845b3abf95485c , 0x00003ffb //   log(1/frcpa(1+42/2^-8))/2
data8 0xa06fd841bc001bb4 , 0x00003ffb //   log(1/frcpa(1+43/2^-8))/2
data8 0xa3f3a74652fbe0db , 0x00003ffb //   log(1/frcpa(1+44/2^-8))/2
data8 0xa77a8fb2336f20f5 , 0x00003ffb //   log(1/frcpa(1+45/2^-8))/2
//
data8 0xab0497015d28b0a0 , 0x00003ffb //   log(1/frcpa(1+46/2^-8))/2
data8 0xae91c2be6ba6a615 , 0x00003ffb //   log(1/frcpa(1+47/2^-8))/2
data8 0xb189d1b99aebb20b , 0x00003ffb //   log(1/frcpa(1+48/2^-8))/2
data8 0xb51cced5de9c1b2c , 0x00003ffb //   log(1/frcpa(1+49/2^-8))/2
data8 0xb819bee9e720d42f , 0x00003ffb //   log(1/frcpa(1+50/2^-8))/2
//
data8 0xbbb2a0947b093a5d , 0x00003ffb //   log(1/frcpa(1+51/2^-8))/2
data8 0xbf4ec1505811684a , 0x00003ffb //   log(1/frcpa(1+52/2^-8))/2
data8 0xc2535bacfa8975ff , 0x00003ffb //   log(1/frcpa(1+53/2^-8))/2
data8 0xc55a3eafad187eb8 , 0x00003ffb //   log(1/frcpa(1+54/2^-8))/2
data8 0xc8ff2484b2c0da74 , 0x00003ffb //   log(1/frcpa(1+55/2^-8))/2
//
data8 0xcc0b1a008d53ab76 , 0x00003ffb //   log(1/frcpa(1+56/2^-8))/2
data8 0xcfb6203844b3209b , 0x00003ffb //   log(1/frcpa(1+57/2^-8))/2
data8 0xd2c73949a47a19f5 , 0x00003ffb //   log(1/frcpa(1+58/2^-8))/2
data8 0xd5daae18b49d6695 , 0x00003ffb //   log(1/frcpa(1+59/2^-8))/2
data8 0xd8f08248cf7e8019 , 0x00003ffb //   log(1/frcpa(1+60/2^-8))/2
//
data8 0xdca7749f1b3e540e , 0x00003ffb //   log(1/frcpa(1+61/2^-8))/2
data8 0xdfc28e033aaaf7c7 , 0x00003ffb //   log(1/frcpa(1+62/2^-8))/2
data8 0xe2e012a5f91d2f55 , 0x00003ffb //   log(1/frcpa(1+63/2^-8))/2
data8 0xe600064ed9e292a8 , 0x00003ffb //   log(1/frcpa(1+64/2^-8))/2
data8 0xe9226cce42b39f60 , 0x00003ffb //   log(1/frcpa(1+65/2^-8))/2
//
data8 0xec4749fd97a28360 , 0x00003ffb //   log(1/frcpa(1+66/2^-8))/2
data8 0xef6ea1bf57780495 , 0x00003ffb //   log(1/frcpa(1+67/2^-8))/2
data8 0xf29877ff38809091 , 0x00003ffb //   log(1/frcpa(1+68/2^-8))/2
data8 0xf5c4d0b245cb89be , 0x00003ffb //   log(1/frcpa(1+69/2^-8))/2
data8 0xf8f3afd6fcdef3aa , 0x00003ffb //   log(1/frcpa(1+70/2^-8))/2
//
data8 0xfc2519756be1abc7 , 0x00003ffb //   log(1/frcpa(1+71/2^-8))/2
data8 0xff59119f503e6832 , 0x00003ffb //   log(1/frcpa(1+72/2^-8))/2
data8 0x8147ce381ae0e146 , 0x00003ffc //   log(1/frcpa(1+73/2^-8))/2
data8 0x82e45f06cb1ad0f2 , 0x00003ffc //   log(1/frcpa(1+74/2^-8))/2
data8 0x842f5c7c573cbaa2 , 0x00003ffc //   log(1/frcpa(1+75/2^-8))/2
//
data8 0x85ce471968c8893a , 0x00003ffc //   log(1/frcpa(1+76/2^-8))/2
data8 0x876e8305bc04066d , 0x00003ffc //   log(1/frcpa(1+77/2^-8))/2
data8 0x891012678031fbb3 , 0x00003ffc //   log(1/frcpa(1+78/2^-8))/2
data8 0x8a5f1493d766a05f , 0x00003ffc //   log(1/frcpa(1+79/2^-8))/2
data8 0x8c030c778c56fa00 , 0x00003ffc //   log(1/frcpa(1+80/2^-8))/2
//