mirror of
https://sourceware.org/git/glibc.git
synced 2024-12-30 14:31:14 +00:00
ee6189855a
equivalent, but shorter instructions. * sysdeps/unix/sysv/linux/x86_64/sysdep.h: Likewise. * sysdeps/unix/sysv/linux/x86_64/setcontext.S: Likewise. * sysdeps/unix/sysv/linux/x86_64/clone.S: Likewise. * sysdeps/unix/sysv/linux/x86_64/swapcontext.S: Likewise. * sysdeps/unix/x86_64/sysdep.S: Likewise. * sysdeps/x86_64/strchr.S: Likewise. * sysdeps/x86_64/memset.S: Likewise. * sysdeps/x86_64/strcspn.S: Likewise. * sysdeps/x86_64/strcmp.S: Likewise. * sysdeps/x86_64/elf/start.S: Likewise. * sysdeps/x86_64/strspn.S: Likewise. * sysdeps/x86_64/dl-machine.h: Likewise. * sysdeps/x86_64/bsd-_setjmp.S: Likewise. * sysdeps/x86_64/bsd-setjmp.S: Likewise. * sysdeps/x86_64/strtok.S: Likewise.
790 lines
22 KiB
ArmAsm
790 lines
22 KiB
ArmAsm
.file "log1pf.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
|
|
//==============================================================
|
|
// 02/02/00 Initial version
|
|
// 04/04/00 Unwind support added
|
|
// 08/15/00 Bundle added after call to __libm_error_support to properly
|
|
// set [the previously overwritten] GR_Parameter_RESULT.
|
|
// 06/29/01 Improved speed of all paths
|
|
// 05/20/02 Cleaned up namespace and sf0 syntax
|
|
// 10/02/02 Improved performance by basing on log algorithm
|
|
// 02/10/03 Reordered header: .section, .global, .proc, .align
|
|
// 04/18/03 Eliminate possible WAW dependency warning
|
|
// 12/16/03 Fixed parameter passing to/from error handling routine
|
|
//
|
|
// API
|
|
//==============================================================
|
|
// float log1pf(float)
|
|
//
|
|
// log1p(x) = log(x+1)
|
|
//
|
|
// Overview of operation
|
|
//==============================================================
|
|
// Background
|
|
// ----------
|
|
//
|
|
// This algorithm is based on fact that
|
|
// log1p(x) = log(1+x) and
|
|
// log(a b) = log(a) + log(b).
|
|
// In our case we have 1+x = 2^N f, where 1 <= f < 2.
|
|
// So
|
|
// log(1+x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f)
|
|
//
|
|
// To calculate log(f) we do following
|
|
// log(f) = log(f * frcpa(f) / frcpa(f)) =
|
|
// = log(f * frcpa(f)) + log(1/frcpa(f))
|
|
//
|
|
// According to definition of IA-64's frcpa instruction it's a
|
|
// floating point that approximates 1/f using a lookup on the
|
|
// top of 8 bits of the input number's + 1 significand with relative
|
|
// error < 2^(-8.886). So we have following
|
|
//
|
|
// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256
|
|
//
|
|
// and
|
|
//
|
|
// log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) =
|
|
// = log(1 + r) + T
|
|
//
|
|
// The first value can be computed by polynomial P(r) approximating
|
|
// log(1 + r) on |r| < 1/256 and the second is precomputed tabular
|
|
// value defined by top 8 bit of f.
|
|
//
|
|
// Finally we have that log(1+x) ~ (N*log(2) + T) + P(r)
|
|
//
|
|
// Note that if input argument is close to 0.0 (in our case it means
|
|
// that |x| < 1/256) we can use just polynomial approximation
|
|
// because 1+x = 2^0 * f = f = 1 + r and
|
|
// log(1+x) = log(1 + r) ~ P(r)
|
|
//
|
|
//
|
|
// Implementation
|
|
// --------------
|
|
//
|
|
// 1. |x| >= 2^(-8), and x > -1
|
|
// InvX = frcpa(x+1)
|
|
// r = InvX*(x+1) - 1
|
|
// P(r) = r*((1 - A2*4) + r^2*(A3 - A4*r)) = r*P2(r),
|
|
// A4,A3,A2 are created with setf instruction.
|
|
// We use Taylor series and so A4 = 1/4, A3 = 1/3,
|
|
// A2 = 1/2 rounded to double.
|
|
//
|
|
// N = float(n) where n is true unbiased exponent of x
|
|
//
|
|
// T is tabular value of log(1/frcpa(x)) calculated in quad precision
|
|
// and rounded to double. To load T we get bits from 55 to 62 of register
|
|
// format significand as index and calculate address
|
|
// ad_T = table_base_addr + 8 * index
|
|
//
|
|
// L1 (log(2)) is calculated in quad precision and rounded to double;
|
|
// it's created with setf
|
|
//
|
|
// And final result = P2(r)*r + (T + N*L1)
|
|
//
|
|
//
|
|
// 2. 2^(-40) <= |x| < 2^(-8)
|
|
// r = x
|
|
// P(r) = r*((1 - A2*4) + r^2*(A3 - A4*r)) = r*P2(r),
|
|
// A4,A3,A2 are the same as in case |x| >= 1/256
|
|
//
|
|
// And final result = P2(r)*r
|
|
//
|
|
// 3. 0 < |x| < 2^(-40)
|
|
// Although log1p(x) is basically x, we would like to preserve the inexactness
|
|
// nature as well as consistent behavior under different rounding modes.
|
|
// We can do this by computing the result as
|
|
//
|
|
// log1p(x) = x - x*x
|
|
//
|
|
//
|
|
// Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are
|
|
// filtered and processed on special branches.
|
|
//
|
|
|
|
//
|
|
// Special values
|
|
//==============================================================
|
|
//
|
|
// log1p(-1) = -inf // Call error support
|
|
//
|
|
// log1p(+qnan) = +qnan
|
|
// log1p(-qnan) = -qnan
|
|
// log1p(+snan) = +qnan
|
|
// log1p(-snan) = -qnan
|
|
//
|
|
// log1p(x),x<-1= QNAN Indefinite // Call error support
|
|
// log1p(-inf) = QNAN Indefinite
|
|
// log1p(+inf) = +inf
|
|
// log1p(+/-0) = +/-0
|
|
//
|
|
//
|
|
// Registers used
|
|
//==============================================================
|
|
// Floating Point registers used:
|
|
// f8, input
|
|
// f7 -> f15, f32 -> f36
|
|
//
|
|
// General registers used:
|
|
// r8 -> r11
|
|
// r14 -> r22
|
|
//
|
|
// Predicate registers used:
|
|
// p6 -> p12
|
|
|
|
// Assembly macros
|
|
//==============================================================
|
|
GR_TAG = r8
|
|
GR_ad_T = r9
|
|
GR_Exp = r10
|
|
GR_N = r11
|
|
|
|
GR_signexp_x = r14
|
|
GR_exp_mask = r15
|
|
GR_exp_bias = r16
|
|
GR_05 = r17
|
|
GR_A3 = r18
|
|
GR_Sig = r19
|
|
GR_Ind = r19
|
|
GR_exp_x = r20
|
|
GR_Ln2 = r21
|
|
GR_025 = r22
|
|
|
|
|
|
GR_SAVE_B0 = r33
|
|
GR_SAVE_PFS = r34
|
|
GR_SAVE_GP = r35
|
|
GR_SAVE_SP = r36
|
|
|
|
GR_Parameter_X = r37
|
|
GR_Parameter_Y = r38
|
|
GR_Parameter_RESULT = r39
|
|
GR_Parameter_TAG = r40
|
|
|
|
|
|
|
|
FR_NormX = f7
|
|
FR_RcpX = f9
|
|
FR_r = f10
|
|
FR_r2 = f11
|
|
FR_r4 = f12
|
|
FR_N = f13
|
|
FR_Ln2 = f14
|
|
FR_Xp1 = f15
|
|
|
|
FR_A4 = f33
|
|
FR_A3 = f34
|
|
FR_A2 = f35
|
|
|
|
FR_T = f36
|
|
FR_NxLn2pT = f36
|
|
|
|
|
|
|
|
FR_Y = f1
|
|
FR_X = f10
|
|
FR_RESULT = f8
|
|
|
|
|
|
// Data
|
|
//==============================================================
|
|
RODATA
|
|
.align 16
|
|
|
|
LOCAL_OBJECT_START(log_data)
|
|
// ln(1/frcpa(1+i/256)), i=0...255
|
|
data8 0x3F60040155D5889E // 0
|
|
data8 0x3F78121214586B54 // 1
|
|
data8 0x3F841929F96832F0 // 2
|
|
data8 0x3F8C317384C75F06 // 3
|
|
data8 0x3F91A6B91AC73386 // 4
|
|
data8 0x3F95BA9A5D9AC039 // 5
|
|
data8 0x3F99D2A8074325F4 // 6
|
|
data8 0x3F9D6B2725979802 // 7
|
|
data8 0x3FA0C58FA19DFAAA // 8
|
|
data8 0x3FA2954C78CBCE1B // 9
|
|
data8 0x3FA4A94D2DA96C56 // 10
|
|
data8 0x3FA67C94F2D4BB58 // 11
|
|
data8 0x3FA85188B630F068 // 12
|
|
data8 0x3FAA6B8ABE73AF4C // 13
|
|
data8 0x3FAC441E06F72A9E // 14
|
|
data8 0x3FAE1E6713606D07 // 15
|
|
data8 0x3FAFFA6911AB9301 // 16
|
|
data8 0x3FB0EC139C5DA601 // 17
|
|
data8 0x3FB1DBD2643D190B // 18
|
|
data8 0x3FB2CC7284FE5F1C // 19
|
|
data8 0x3FB3BDF5A7D1EE64 // 20
|
|
data8 0x3FB4B05D7AA012E0 // 21
|
|
data8 0x3FB580DB7CEB5702 // 22
|
|
data8 0x3FB674F089365A7A // 23
|
|
data8 0x3FB769EF2C6B568D // 24
|
|
data8 0x3FB85FD927506A48 // 25
|
|
data8 0x3FB9335E5D594989 // 26
|
|
data8 0x3FBA2B0220C8E5F5 // 27
|
|
data8 0x3FBB0004AC1A86AC // 28
|
|
data8 0x3FBBF968769FCA11 // 29
|
|
data8 0x3FBCCFEDBFEE13A8 // 30
|
|
data8 0x3FBDA727638446A2 // 31
|
|
data8 0x3FBEA3257FE10F7A // 32
|
|
data8 0x3FBF7BE9FEDBFDE6 // 33
|
|
data8 0x3FC02AB352FF25F4 // 34
|
|
data8 0x3FC097CE579D204D // 35
|
|
data8 0x3FC1178E8227E47C // 36
|
|
data8 0x3FC185747DBECF34 // 37
|
|
data8 0x3FC1F3B925F25D41 // 38
|
|
data8 0x3FC2625D1E6DDF57 // 39
|
|
data8 0x3FC2D1610C86813A // 40
|
|
data8 0x3FC340C59741142E // 41
|
|
data8 0x3FC3B08B6757F2A9 // 42
|
|
data8 0x3FC40DFB08378003 // 43
|
|
data8 0x3FC47E74E8CA5F7C // 44
|
|
data8 0x3FC4EF51F6466DE4 // 45
|
|
data8 0x3FC56092E02BA516 // 46
|
|
data8 0x3FC5D23857CD74D5 // 47
|
|
data8 0x3FC6313A37335D76 // 48
|
|
data8 0x3FC6A399DABBD383 // 49
|
|
data8 0x3FC70337DD3CE41B // 50
|
|
data8 0x3FC77654128F6127 // 51
|
|
data8 0x3FC7E9D82A0B022D // 52
|
|
data8 0x3FC84A6B759F512F // 53
|
|
data8 0x3FC8AB47D5F5A310 // 54
|
|
data8 0x3FC91FE49096581B // 55
|
|
data8 0x3FC981634011AA75 // 56
|
|
data8 0x3FC9F6C407089664 // 57
|
|
data8 0x3FCA58E729348F43 // 58
|
|
data8 0x3FCABB55C31693AD // 59
|
|
data8 0x3FCB1E104919EFD0 // 60
|
|
data8 0x3FCB94EE93E367CB // 61
|
|
data8 0x3FCBF851C067555F // 62
|
|
data8 0x3FCC5C0254BF23A6 // 63
|
|
data8 0x3FCCC000C9DB3C52 // 64
|
|
data8 0x3FCD244D99C85674 // 65
|
|
data8 0x3FCD88E93FB2F450 // 66
|
|
data8 0x3FCDEDD437EAEF01 // 67
|
|
data8 0x3FCE530EFFE71012 // 68
|
|
data8 0x3FCEB89A1648B971 // 69
|
|
data8 0x3FCF1E75FADF9BDE // 70
|
|
data8 0x3FCF84A32EAD7C35 // 71
|
|
data8 0x3FCFEB2233EA07CD // 72
|
|
data8 0x3FD028F9C7035C1C // 73
|
|
data8 0x3FD05C8BE0D9635A // 74
|
|
data8 0x3FD085EB8F8AE797 // 75
|
|
data8 0x3FD0B9C8E32D1911 // 76
|
|
data8 0x3FD0EDD060B78081 // 77
|
|
data8 0x3FD122024CF0063F // 78
|
|
data8 0x3FD14BE2927AECD4 // 79
|
|
data8 0x3FD180618EF18ADF // 80
|
|
data8 0x3FD1B50BBE2FC63B // 81
|
|
data8 0x3FD1DF4CC7CF242D // 82
|
|
data8 0x3FD214456D0EB8D4 // 83
|
|
data8 0x3FD23EC5991EBA49 // 84
|
|
data8 0x3FD2740D9F870AFB // 85
|
|
data8 0x3FD29ECDABCDFA04 // 86
|
|
data8 0x3FD2D46602ADCCEE // 87
|
|
data8 0x3FD2FF66B04EA9D4 // 88
|
|
data8 0x3FD335504B355A37 // 89
|
|
data8 0x3FD360925EC44F5D // 90
|
|
data8 0x3FD38BF1C3337E75 // 91
|
|
data8 0x3FD3C25277333184 // 92
|
|
data8 0x3FD3EDF463C1683E // 93
|
|
data8 0x3FD419B423D5E8C7 // 94
|
|
data8 0x3FD44591E0539F49 // 95
|
|
data8 0x3FD47C9175B6F0AD // 96
|
|
data8 0x3FD4A8B341552B09 // 97
|
|
data8 0x3FD4D4F3908901A0 // 98
|
|
data8 0x3FD501528DA1F968 // 99
|
|
data8 0x3FD52DD06347D4F6 // 100
|
|
data8 0x3FD55A6D3C7B8A8A // 101
|
|
data8 0x3FD5925D2B112A59 // 102
|
|
data8 0x3FD5BF406B543DB2 // 103
|
|
data8 0x3FD5EC433D5C35AE // 104
|
|
data8 0x3FD61965CDB02C1F // 105
|
|
data8 0x3FD646A84935B2A2 // 106
|
|
data8 0x3FD6740ADD31DE94 // 107
|
|
data8 0x3FD6A18DB74A58C5 // 108
|
|
data8 0x3FD6CF31058670EC // 109
|
|
data8 0x3FD6F180E852F0BA // 110
|
|
data8 0x3FD71F5D71B894F0 // 111
|
|
data8 0x3FD74D5AEFD66D5C // 112
|
|
data8 0x3FD77B79922BD37E // 113
|
|
data8 0x3FD7A9B9889F19E2 // 114
|
|
data8 0x3FD7D81B037EB6A6 // 115
|
|
data8 0x3FD8069E33827231 // 116
|
|
data8 0x3FD82996D3EF8BCB // 117
|
|
data8 0x3FD85855776DCBFB // 118
|
|
data8 0x3FD8873658327CCF // 119
|
|
data8 0x3FD8AA75973AB8CF // 120
|
|
data8 0x3FD8D992DC8824E5 // 121
|
|
data8 0x3FD908D2EA7D9512 // 122
|
|
data8 0x3FD92C59E79C0E56 // 123
|
|
data8 0x3FD95BD750EE3ED3 // 124
|
|
data8 0x3FD98B7811A3EE5B // 125
|
|
data8 0x3FD9AF47F33D406C // 126
|
|
data8 0x3FD9DF270C1914A8 // 127
|
|
data8 0x3FDA0325ED14FDA4 // 128
|
|
data8 0x3FDA33440224FA79 // 129
|
|
data8 0x3FDA57725E80C383 // 130
|
|
data8 0x3FDA87D0165DD199 // 131
|
|
data8 0x3FDAAC2E6C03F896 // 132
|
|
data8 0x3FDADCCC6FDF6A81 // 133
|
|
data8 0x3FDB015B3EB1E790 // 134
|
|
data8 0x3FDB323A3A635948 // 135
|
|
data8 0x3FDB56FA04462909 // 136
|
|
data8 0x3FDB881AA659BC93 // 137
|
|
data8 0x3FDBAD0BEF3DB165 // 138
|
|
data8 0x3FDBD21297781C2F // 139
|
|
data8 0x3FDC039236F08819 // 140
|
|
data8 0x3FDC28CB1E4D32FD // 141
|
|
data8 0x3FDC4E19B84723C2 // 142
|
|
data8 0x3FDC7FF9C74554C9 // 143
|
|
data8 0x3FDCA57B64E9DB05 // 144
|
|
data8 0x3FDCCB130A5CEBB0 // 145
|
|
data8 0x3FDCF0C0D18F326F // 146
|
|
data8 0x3FDD232075B5A201 // 147
|
|
data8 0x3FDD490246DEFA6B // 148
|
|
data8 0x3FDD6EFA918D25CD // 149
|
|
data8 0x3FDD9509707AE52F // 150
|
|
data8 0x3FDDBB2EFE92C554 // 151
|
|
data8 0x3FDDEE2F3445E4AF // 152
|
|
data8 0x3FDE148A1A2726CE // 153
|
|
data8 0x3FDE3AFC0A49FF40 // 154
|
|
data8 0x3FDE6185206D516E // 155
|
|
data8 0x3FDE882578823D52 // 156
|
|
data8 0x3FDEAEDD2EAC990C // 157
|
|
data8 0x3FDED5AC5F436BE3 // 158
|
|
data8 0x3FDEFC9326D16AB9 // 159
|
|
data8 0x3FDF2391A2157600 // 160
|
|
data8 0x3FDF4AA7EE03192D // 161
|
|
data8 0x3FDF71D627C30BB0 // 162
|
|
data8 0x3FDF991C6CB3B379 // 163
|
|
data8 0x3FDFC07ADA69A910 // 164
|
|
data8 0x3FDFE7F18EB03D3E // 165
|
|
data8 0x3FE007C053C5002E // 166
|
|
data8 0x3FE01B942198A5A1 // 167
|
|
data8 0x3FE02F74400C64EB // 168
|
|
data8 0x3FE04360BE7603AD // 169
|
|
data8 0x3FE05759AC47FE34 // 170
|
|
data8 0x3FE06B5F1911CF52 // 171
|
|
data8 0x3FE078BF0533C568 // 172
|
|
data8 0x3FE08CD9687E7B0E // 173
|
|
data8 0x3FE0A10074CF9019 // 174
|
|
data8 0x3FE0B5343A234477 // 175
|
|
data8 0x3FE0C974C89431CE // 176
|
|
data8 0x3FE0DDC2305B9886 // 177
|
|
data8 0x3FE0EB524BAFC918 // 178
|
|
data8 0x3FE0FFB54213A476 // 179
|
|
data8 0x3FE114253DA97D9F // 180
|
|
data8 0x3FE128A24F1D9AFF // 181
|
|
data8 0x3FE1365252BF0865 // 182
|
|
data8 0x3FE14AE558B4A92D // 183
|
|
data8 0x3FE15F85A19C765B // 184
|
|
data8 0x3FE16D4D38C119FA // 185
|
|
data8 0x3FE18203C20DD133 // 186
|
|
data8 0x3FE196C7BC4B1F3B // 187
|
|
data8 0x3FE1A4A738B7A33C // 188
|
|
data8 0x3FE1B981C0C9653D // 189
|
|
data8 0x3FE1CE69E8BB106B // 190
|
|
data8 0x3FE1DC619DE06944 // 191
|
|
data8 0x3FE1F160A2AD0DA4 // 192
|
|
data8 0x3FE2066D7740737E // 193
|
|
data8 0x3FE2147DBA47A394 // 194
|
|
data8 0x3FE229A1BC5EBAC3 // 195
|
|
data8 0x3FE237C1841A502E // 196
|
|
data8 0x3FE24CFCE6F80D9A // 197
|
|
data8 0x3FE25B2C55CD5762 // 198
|
|
data8 0x3FE2707F4D5F7C41 // 199
|
|
data8 0x3FE285E0842CA384 // 200
|
|
data8 0x3FE294294708B773 // 201
|
|
data8 0x3FE2A9A2670AFF0C // 202
|
|
data8 0x3FE2B7FB2C8D1CC1 // 203
|
|
data8 0x3FE2C65A6395F5F5 // 204
|
|
data8 0x3FE2DBF557B0DF43 // 205
|
|
data8 0x3FE2EA64C3F97655 // 206
|
|
data8 0x3FE3001823684D73 // 207
|
|
data8 0x3FE30E97E9A8B5CD // 208
|
|
data8 0x3FE32463EBDD34EA // 209
|
|
data8 0x3FE332F4314AD796 // 210
|
|
data8 0x3FE348D90E7464D0 // 211
|
|
data8 0x3FE35779F8C43D6E // 212
|
|
data8 0x3FE36621961A6A99 // 213
|
|
data8 0x3FE37C299F3C366A // 214
|
|
data8 0x3FE38AE2171976E7 // 215
|
|
data8 0x3FE399A157A603E7 // 216
|
|
data8 0x3FE3AFCCFE77B9D1 // 217
|
|
data8 0x3FE3BE9D503533B5 // 218
|
|
data8 0x3FE3CD7480B4A8A3 // 219
|
|
data8 0x3FE3E3C43918F76C // 220
|
|
data8 0x3FE3F2ACB27ED6C7 // 221
|
|
data8 0x3FE4019C2125CA93 // 222
|
|
data8 0x3FE4181061389722 // 223
|
|
data8 0x3FE42711518DF545 // 224
|
|
data8 0x3FE436194E12B6BF // 225
|
|
data8 0x3FE445285D68EA69 // 226
|
|
data8 0x3FE45BCC464C893A // 227
|
|
data8 0x3FE46AED21F117FC // 228
|
|
data8 0x3FE47A1527E8A2D3 // 229
|
|
data8 0x3FE489445EFFFCCC // 230
|
|
data8 0x3FE4A018BCB69835 // 231
|
|
data8 0x3FE4AF5A0C9D65D7 // 232
|
|
data8 0x3FE4BEA2A5BDBE87 // 233
|
|
data8 0x3FE4CDF28F10AC46 // 234
|
|
data8 0x3FE4DD49CF994058 // 235
|
|
data8 0x3FE4ECA86E64A684 // 236
|
|
data8 0x3FE503C43CD8EB68 // 237
|
|
data8 0x3FE513356667FC57 // 238
|
|
data8 0x3FE522AE0738A3D8 // 239
|
|
data8 0x3FE5322E26867857 // 240
|
|
data8 0x3FE541B5CB979809 // 241
|
|
data8 0x3FE55144FDBCBD62 // 242
|
|
data8 0x3FE560DBC45153C7 // 243
|
|
data8 0x3FE5707A26BB8C66 // 244
|
|
data8 0x3FE587F60ED5B900 // 245
|
|
data8 0x3FE597A7977C8F31 // 246
|
|
data8 0x3FE5A760D634BB8B // 247
|
|
data8 0x3FE5B721D295F10F // 248
|
|
data8 0x3FE5C6EA94431EF9 // 249
|
|
data8 0x3FE5D6BB22EA86F6 // 250
|
|
data8 0x3FE5E6938645D390 // 251
|
|
data8 0x3FE5F673C61A2ED2 // 252
|
|
data8 0x3FE6065BEA385926 // 253
|
|
data8 0x3FE6164BFA7CC06B // 254
|
|
data8 0x3FE62643FECF9743 // 255
|
|
LOCAL_OBJECT_END(log_data)
|
|
|
|
|
|
// Code
|
|
//==============================================================
|
|
|
|
.section .text
|
|
GLOBAL_IEEE754_ENTRY(log1pf)
|
|
{ .mfi
|
|
getf.exp GR_signexp_x = f8 // if x is unorm then must recompute
|
|
fadd.s1 FR_Xp1 = f8, f1 // Form 1+x
|
|
mov GR_05 = 0xfffe
|
|
}
|
|
{ .mlx
|
|
addl GR_ad_T = @ltoff(log_data),gp
|
|
movl GR_A3 = 0x3fd5555555555555 // double precision memory
|
|
// representation of A3
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ld8 GR_ad_T = [GR_ad_T]
|
|
fclass.m p8,p0 = f8,0xb // Is x unorm?
|
|
mov GR_exp_mask = 0x1ffff
|
|
}
|
|
{ .mfi
|
|
mov GR_025 = 0xfffd // Exponent of 0.25
|
|
fnorm.s1 FR_NormX = f8 // Normalize x
|
|
mov GR_exp_bias = 0xffff
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
setf.exp FR_A2 = GR_05 // create A2 = 0.5
|
|
fclass.m p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf?
|
|
nop.i 0
|
|
}
|
|
{ .mib
|
|
setf.d FR_A3 = GR_A3 // create A3
|
|
nop.i 0
|
|
(p8) br.cond.spnt log1p_unorm // Branch if x=unorm
|
|
}
|
|
;;
|
|
|
|
log1p_common:
|
|
{ .mfi
|
|
setf.exp FR_A4 = GR_025 // create A4 = 0.25
|
|
frcpa.s1 FR_RcpX,p0 = f1,FR_Xp1
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p9) fma.s.s0 f8 = f8,f1,f0 // set V-flag
|
|
(p9) br.ret.spnt b0 // exit for NaN, NaT and +Inf
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
getf.exp GR_Exp = FR_Xp1 // signexp of x+1
|
|
fclass.m p10,p0 = FR_Xp1,0x3A // is 1+x < 0?
|
|
and GR_exp_x = GR_exp_mask, GR_signexp_x // biased exponent of x
|
|
}
|
|
{ .mlx
|
|
nop.m 0
|
|
movl GR_Ln2 = 0x3FE62E42FEFA39EF // double precision memory
|
|
// representation of log(2)
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
getf.sig GR_Sig = FR_Xp1 // get significand to calculate index
|
|
// for T if |x| >= 2^-8
|
|
fcmp.eq.s1 p12,p0 = f8,f0 // is x equal to 0?
|
|
sub GR_exp_x = GR_exp_x, GR_exp_bias // true exponent of x
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
sub GR_N = GR_Exp,GR_exp_bias // true exponent of x+1
|
|
fcmp.eq.s1 p11,p0 = FR_Xp1,f0 // is x = -1?
|
|
cmp.gt p6,p7 = -8, GR_exp_x // Is |x| < 2^-8
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
nop.f 0
|
|
(p10) br.cond.spnt log1p_lt_minus_1 // jump if x < -1
|
|
}
|
|
;;
|
|
|
|
// p6 is true if |x| < 1/256
|
|
// p7 is true if |x| >= 1/256
|
|
.pred.rel "mutex",p6,p7
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fms.s1 FR_r = f8,f1,f0 // range reduction for |x|<1/256
|
|
(p6) cmp.gt.unc p10,p0 = -40, GR_exp_x // Is |x| < 2^-40
|
|
}
|
|
{ .mfb
|
|
(p7) setf.sig FR_N = GR_N // copy unbiased exponent of x to the
|
|
// significand field of FR_N
|
|
(p7) fms.s1 FR_r = FR_RcpX,FR_Xp1,f1 // range reduction for |x|>=1/256
|
|
(p12) br.ret.spnt b0 // exit for x=0, return x
|
|
}
|
|
;;
|
|
|
|
{ .mib
|
|
setf.d FR_Ln2 = GR_Ln2 // create log(2)
|
|
(p7) extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index
|
|
(p11) br.cond.spnt log1p_eq_minus_1 // jump if x = -1
|
|
}
|
|
;;
|
|
|
|
{ .mmf
|
|
(p7) shladd GR_ad_T = GR_Ind,3,GR_ad_T // address of T
|
|
nop.m 0
|
|
(p10) fnma.s.s0 f8 = f8,f8,f8 // If |x| very small, result=x-x*x
|
|
}
|
|
;;
|
|
|
|
{ .mmb
|
|
(p7) ldfd FR_T = [GR_ad_T]
|
|
nop.m 0
|
|
(p10) br.ret.spnt b0 // Exit if |x| < 2^-40
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_A2 = FR_A2,FR_r,f1 // 1.0 - A2*r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_A3 = FR_A4,FR_r,FR_A3 // A3 - A4*r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fcvt.xf FR_N = FR_N
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// (A3*r+A2)*r^2+r
|
|
fma.s1 FR_A2 = FR_A3,FR_r2,FR_A2 // (A4*r+A3)*r^2+(A2*r+1)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// N*Ln2hi+T
|
|
(p7) fma.s1 FR_NxLn2pT = FR_N,FR_Ln2,FR_T
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
.pred.rel "mutex",p6,p7
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fma.s.s0 f8 = FR_A2,FR_r,f0 // result if 2^(-40) <= |x| < 1/256
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p7) fma.s.s0 f8 = FR_A2,FR_r,FR_NxLn2pT // result if |x| >= 1/256
|
|
br.ret.sptk b0 // Exit if |x| >= 2^(-40)
|
|
}
|
|
;;
|
|
|
|
.align 32
|
|
log1p_unorm:
|
|
// Here if x=unorm
|
|
{ .mfb
|
|
getf.exp GR_signexp_x = FR_NormX // recompute biased exponent
|
|
nop.f 0
|
|
br.cond.sptk log1p_common
|
|
}
|
|
;;
|
|
|
|
.align 32
|
|
log1p_eq_minus_1:
|
|
// Here if x=-1
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.s FR_X = f8,f8 // keep input argument for subsequent
|
|
// call of __libm_error_support#
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
mov GR_TAG = 142 // set libm error in case of log1p(-1).
|
|
frcpa.s0 f8,p0 = f8,f0 // log1p(-1) should be equal to -INF.
|
|
// We can get it using frcpa because it
|
|
// sets result to the IEEE-754 mandated
|
|
// quotient of f8/f0.
|
|
nop.i 0
|
|
}
|
|
{ .mib
|
|
nop.m 0
|
|
nop.i 0
|
|
br.cond.sptk log_libm_err
|
|
}
|
|
;;
|
|
|
|
.align 32
|
|
log1p_lt_minus_1:
|
|
// Here if x < -1
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.s FR_X = f8,f8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
mov GR_TAG = 143 // set libm error in case of x < -1.
|
|
frcpa.s0 f8,p0 = f0,f0 // log1p(x) x < -1 should be equal to NaN.
|
|
// We can get it using frcpa because it
|
|
// sets result to the IEEE-754 mandated
|
|
// quotient of f0/f0 i.e. NaN.
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
.align 32
|
|
log_libm_err:
|
|
{ .mmi
|
|
alloc r32 = ar.pfs,1,4,4,0
|
|
mov GR_Parameter_TAG = GR_TAG
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
GLOBAL_IEEE754_END(log1pf)
|
|
|
|
|
|
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] = FR_Y,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] = FR_X // STORE Parameter 1 on stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
|
|
nop.b 0
|
|
}
|
|
{ .mib
|
|
stfs [GR_Parameter_Y] = FR_RESULT // 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#
|
|
|