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glibc/sysdeps/ia64/fpu/e_log.S
Szabolcs Nagy f29b7c492d Remove the error handling wrapper from log 
Introduce new log symbol version that doesn't do SVID compatible error
handling.  The standard errno and fp exception based error handling is
inline in the new code and does not have significant overhead.

The wrapper is disabled for sysdeps/ieee754/dbl-64 by using empty
w_log.c and enabled for targets with their own log implementation by
including math/w_log.c.

The compatibility symbol version still uses the wrapper with SVID error
handling around the new code.  There is no new symbol version nor
compatibility code on !LIBM_SVID_COMPAT targets (e.g. riscv).

On targets where previously logl was an alias of log, now it points to
the compatibility symbol with the wrapper, because it still need the
SVID compatible error handling.  This affects NO_LONG_DOUBLE (e.g. arm)
and LONG_DOUBLE_COMPAT (e.g. alpha) targets as well.

The __log_finite symbol is now an alias of log.  Both __log_finite and
log set errno and thus not const functions.

The ia64 asm is changed so the compat and new symbol versions map to the
same address.

On x86_64 #include <math.h> was added before macro definitions that may
affect that header.

Tested with build-many-glibcs.py.

	* math/Versions (GLIBC_2.29): Add log.
	* math/w_log_compat.c (__log_compat): Change to versioned compat
	symbol.
	* math/w_log.c: New file.
	* sysdeps/i386/fpu/w_log.c: New file.
	* sysdeps/ia64/fpu/e_log.S: Update.
	* sysdeps/ieee754/dbl-64/e_log.c (__ieee754_log): Rename to __log
	and add necessary aliases.
	* sysdeps/ieee754/dbl-64/w_log.c: New file.
	* sysdeps/m68k/m680x0/fpu/w_log.c: New file.
	* sysdeps/mach/hurd/i386/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/aarch64/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/alpha/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/arm/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/hppa/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/i386/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/ia64/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/m68k/coldfire/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/m68k/m680x0/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/microblaze/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/mips/mips32/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/mips/mips64/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/nios2/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/powerpc/powerpc32/fpu/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/powerpc/powerpc32/nofpu/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/powerpc/powerpc64/libm-le.abilist: Update.
	* sysdeps/unix/sysv/linux/powerpc/powerpc64/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/s390/s390-32/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/s390/s390-64/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/sh/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/sparc/sparc32/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/sparc/sparc64/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/x86_64/64/libm.abilist: Update.
	* sysdeps/unix/sysv/linux/x86_64/x32/libm.abilist: Update.
	* sysdeps/x86_64/fpu/multiarch/e_log-avx.c (__ieee754_log): Rename to
	__log.
	* sysdeps/x86_64/fpu/multiarch/e_log-fma.c (__ieee754_log): Likewise.
	* sysdeps/x86_64/fpu/multiarch/e_log-fma4.c (__ieee754_log): Likewise.
	* sysdeps/x86_64/fpu/multiarch/e_log.c (__ieee754_log): Likewise.
	* sysdeps/x86_64/fpu/multiarch/w_log.c: New file.
2018-11-21 09:56:27 +00:00

1737 lines
49 KiB
ArmAsm
Raw Blame History

.file "log.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
//==============================================================
// 02/02/00 Initial version
// 04/04/00 Unwind support added
// 06/16/00 Updated table to be rounded correctly
// 08/15/00 Bundle added after call to __libm_error_support to properly
// set [the previously overwritten] GR_Parameter_RESULT.
// 08/17/00 Improved speed of main path by 5 cycles
// Shortened path for x=1.0
// 01/09/01 Improved speed, fixed flags for neg denormals
// 05/20/02 Cleaned up namespace and sf0 syntax
// 05/23/02 Modified algorithm. Now only one polynomial is used
// for |x-1| >= 1/256 and for |x-1| < 1/256
// 12/11/02 Improved performance for Itanium 2
// 03/31/05 Reformatted delimiters between data tables
//
// API
//==============================================================
// double log(double)
// double log10(double)
//
//
// Overview of operation
//==============================================================
// Background
// ----------
//
// This algorithm is based on fact that
// log(a b) = log(a) + log(b).
// In our case we have x = 2^N f, where 1 <= f < 2.
// So
// log(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 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(x) ~ (N*log(2) + T) + P(r)
//
// Note that if input argument is close to 1.0 (in our case it means
// that |1 - x| < 1/256) we can use just polynomial approximation
// because x = 2^0 * f = f = 1 + r and
// log(x) = log(1 + r) ~ P(r)
//
//
// To compute log10(x) we use the simple identity
//
// log10(x) = log(x)/log(10)
//
// so we have that
//
// log10(x) = (N*log(2) + T + log(1+r)) / log(10) =
// = N*(log(2)/log(10)) + (T/log(10)) + log(1 + r)/log(10)
//
//
// Implementation
// --------------
// It can be seen that formulas for log and log10 differ from one another
// only by coefficients and tabular values. Namely as log as log10 are
// calculated as (N*L1 + T) + L2*Series(r) where in case of log
// L1 = log(2)
// T = log(1/frcpa(x))
// L2 = 1.0
// and in case of log10
// L1 = log(2)/log(10)
// T = log(1/frcpa(x))/log(10)
// L2 = 1.0/log(10)
//
// So common code with two different entry points those set pointers
// to the base address of coresponding data sets containing values
// of L2,T and prepare integer representation of L1 needed for following
// setf instruction.
//
// Note that both log and log10 use common approximation polynomial
// it means we need only one set of coefficients of approximation.
//
//
// 1. |x-1| >= 1/256
// InvX = frcpa(x)
// r = InvX*x - 1
// P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)),
// all coefficients are calculated in quad and rounded to double
// precision. A7,A6,A5,A4 are stored in memory whereas A3 and A2
// created with setf.
//
// 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 represented by two floating-point numbers 64-bit Thi and 32-bit Tlo.
// To load Thi,Tlo we get bits from 55 to 62 of register format significand
// as index and calculate two addresses
// ad_Thi = Thi_table_base_addr + 8 * index
// ad_Tlo = Tlo_table_base_addr + 4 * index
//
// L2 (1.0 or 1.0/log(10) depending on function) is calculated in quad
// precision and rounded to double extended; it's loaded from memory.
//
// L1 (log(2) or log10(2) depending on function) is calculated in quad
// precision and represented by two floating-point 64-bit numbers L1hi,L1lo
// stored in memory.
//
// And final result = ((L1hi*N + Thi) + (N*L1lo + Tlo)) + L2*P(r)
//
//
// 2. |x-1| < 1/256
// r = x - 1
// P(r) = r*((r*A3 - A2) + r^4*((A4 + r*A5) + r^2*(A6 + r*A7)),
// A7,A6,A5A4,A3,A2 are the same as in case |x-1| >= 1/256
//
// And final results
// log(x) = P(r)
// log10(x) = L2*P(r)
//
// 3. How we define is input argument such that |x-1| < 1/256 or not.
//
// To do it we analyze biased exponent and integer representation of
// input argument
//
// a) First we test is biased exponent equal to 0xFFFE or 0xFFFF (i.e.
// we test is 0.5 <= x < 2). This comparison can be performed using
// unsigned version of cmp instruction in such a way
// biased_exponent_of_x - 0xFFFE < 2
//
//
// b) Second (in case when result of a) is true) we need to compare x
// with 1-1/256 and 1+1/256 or in double precision memory representation
// with 0x3FEFE00000000000 and 0x3FF0100000000000 correspondingly.
// This comparison can be made like in a), using unsigned
// version of cmp i.e. ix - 0x3FEFE00000000000 < 0x0000300000000000.
// 0x0000300000000000 is difference between 0x3FF0100000000000 and
// 0x3FEFE00000000000
//
// Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are
// filtered and processed on special branches.
//
//
// Special values
//==============================================================
//
// log(+0) = -inf
// log(-0) = -inf
//
// log(+qnan) = +qnan
// log(-qnan) = -qnan
// log(+snan) = +qnan
// log(-snan) = -qnan
//
// log(-n) = QNAN Indefinite
// log(-inf) = QNAN Indefinite
//
// log(+inf) = +inf
//
//
// Registers used
//==============================================================
// Floating Point registers used:
// f8, input
// f7 -> f15, f32 -> f42
//
// General registers used:
// r8 -> r11
// r14 -> r23
//
// Predicate registers used:
// p6 -> p15
// Assembly macros
//==============================================================
GR_TAG = r8
GR_ad_1 = r8
GR_ad_2 = r9
GR_Exp = r10
GR_N = r11
GR_x = r14
GR_dx = r15
GR_NearOne = r15
GR_xorg = r16
GR_mask = r16
GR_05 = r17
GR_A3 = r18
GR_Sig = r19
GR_Ind = r19
GR_Nm1 = r20
GR_bias = r21
GR_ad_3 = r22
GR_rexp = r23
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_tmp = f9
FR_r = f10
FR_r2 = f11
FR_r4 = f12
FR_N = f13
FR_Ln2hi = f14
FR_Ln2lo = f15
FR_A7 = f32
FR_A6 = f33
FR_A5 = f34
FR_A4 = f35
FR_A3 = f36
FR_A2 = f37
FR_Thi = f38
FR_NxLn2hipThi = f38
FR_NxLn2pT = f38
FR_Tlo = f39
FR_NxLn2lopTlo = f39
FR_InvLn10 = f40
FR_A32 = f41
FR_A321 = f42
FR_Y = f1
FR_X = f10
FR_RESULT = f8
// Data
//==============================================================
RODATA
.align 16
LOCAL_OBJECT_START(log_data)
// coefficients of polynomial approximation
data8 0x3FC2494104381A8E // A7
data8 0xBFC5556D556BBB69 // A6
//
// two parts of ln(2)
data8 0x3FE62E42FEF00000,0x3DD473DE6AF278ED
//
data8 0x8000000000000000,0x3FFF // 1.0
//
data8 0x3FC999999988B5E9 // A5
data8 0xBFCFFFFFFFF6FFF5 // A4
//
// hi parts of ln(1/frcpa(1+i/256)), i=0...255
data8 0x3F60040155D5889D // 0
data8 0x3F78121214586B54 // 1
data8 0x3F841929F96832EF // 2
data8 0x3F8C317384C75F06 // 3
data8 0x3F91A6B91AC73386 // 4
data8 0x3F95BA9A5D9AC039 // 5
data8 0x3F99D2A8074325F3 // 6
data8 0x3F9D6B2725979802 // 7
data8 0x3FA0C58FA19DFAA9 // 8
data8 0x3FA2954C78CBCE1A // 9
data8 0x3FA4A94D2DA96C56 // 10
data8 0x3FA67C94F2D4BB58 // 11
data8 0x3FA85188B630F068 // 12
data8 0x3FAA6B8ABE73AF4C // 13
data8 0x3FAC441E06F72A9E // 14
data8 0x3FAE1E6713606D06 // 15
data8 0x3FAFFA6911AB9300 // 16
data8 0x3FB0EC139C5DA600 // 17
data8 0x3FB1DBD2643D190B // 18
data8 0x3FB2CC7284FE5F1C // 19
data8 0x3FB3BDF5A7D1EE64 // 20
data8 0x3FB4B05D7AA012E0 // 21
data8 0x3FB580DB7CEB5701 // 22
data8 0x3FB674F089365A79 // 23
data8 0x3FB769EF2C6B568D // 24
data8 0x3FB85FD927506A47 // 25
data8 0x3FB9335E5D594988 // 26
data8 0x3FBA2B0220C8E5F4 // 27
data8 0x3FBB0004AC1A86AB // 28
data8 0x3FBBF968769FCA10 // 29
data8 0x3FBCCFEDBFEE13A8 // 30
data8 0x3FBDA727638446A2 // 31
data8 0x3FBEA3257FE10F79 // 32
data8 0x3FBF7BE9FEDBFDE5 // 33
data8 0x3FC02AB352FF25F3 // 34
data8 0x3FC097CE579D204C // 35
data8 0x3FC1178E8227E47B // 36
data8 0x3FC185747DBECF33 // 37
data8 0x3FC1F3B925F25D41 // 38
data8 0x3FC2625D1E6DDF56 // 39
data8 0x3FC2D1610C868139 // 40
data8 0x3FC340C59741142E // 41
data8 0x3FC3B08B6757F2A9 // 42
data8 0x3FC40DFB08378003 // 43
data8 0x3FC47E74E8CA5F7C // 44
data8 0x3FC4EF51F6466DE4 // 45
data8 0x3FC56092E02BA516 // 46
data8 0x3FC5D23857CD74D4 // 47
data8 0x3FC6313A37335D76 // 48
data8 0x3FC6A399DABBD383 // 49
data8 0x3FC70337DD3CE41A // 50
data8 0x3FC77654128F6127 // 51
data8 0x3FC7E9D82A0B022D // 52
data8 0x3FC84A6B759F512E // 53
data8 0x3FC8AB47D5F5A30F // 54
data8 0x3FC91FE49096581B // 55
data8 0x3FC981634011AA75 // 56
data8 0x3FC9F6C407089664 // 57
data8 0x3FCA58E729348F43 // 58
data8 0x3FCABB55C31693AC // 59
data8 0x3FCB1E104919EFD0 // 60
data8 0x3FCB94EE93E367CA // 61
data8 0x3FCBF851C067555E // 62
data8 0x3FCC5C0254BF23A5 // 63
data8 0x3FCCC000C9DB3C52 // 64
data8 0x3FCD244D99C85673 // 65
data8 0x3FCD88E93FB2F450 // 66
data8 0x3FCDEDD437EAEF00 // 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 0x3FD0EDD060B78080 // 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 0x3FD29ECDABCDFA03 // 86
data8 0x3FD2D46602ADCCEE // 87
data8 0x3FD2FF66B04EA9D4 // 88
data8 0x3FD335504B355A37 // 89
data8 0x3FD360925EC44F5C // 90
data8 0x3FD38BF1C3337E74 // 91
data8 0x3FD3C25277333183 // 92
data8 0x3FD3EDF463C1683E // 93
data8 0x3FD419B423D5E8C7 // 94
data8 0x3FD44591E0539F48 // 95
data8 0x3FD47C9175B6F0AD // 96
data8 0x3FD4A8B341552B09 // 97
data8 0x3FD4D4F39089019F // 98
data8 0x3FD501528DA1F967 // 99
data8 0x3FD52DD06347D4F6 // 100
data8 0x3FD55A6D3C7B8A89 // 101
data8 0x3FD5925D2B112A59 // 102
data8 0x3FD5BF406B543DB1 // 103
data8 0x3FD5EC433D5C35AD // 104
data8 0x3FD61965CDB02C1E // 105
data8 0x3FD646A84935B2A1 // 106
data8 0x3FD6740ADD31DE94 // 107
data8 0x3FD6A18DB74A58C5 // 108
data8 0x3FD6CF31058670EC // 109
data8 0x3FD6F180E852F0B9 // 110
data8 0x3FD71F5D71B894EF // 111
data8 0x3FD74D5AEFD66D5C // 112
data8 0x3FD77B79922BD37D // 113
data8 0x3FD7A9B9889F19E2 // 114
data8 0x3FD7D81B037EB6A6 // 115
data8 0x3FD8069E33827230 // 116
data8 0x3FD82996D3EF8BCA // 117
data8 0x3FD85855776DCBFA // 118
data8 0x3FD8873658327CCE // 119
data8 0x3FD8AA75973AB8CE // 120
data8 0x3FD8D992DC8824E4 // 121
data8 0x3FD908D2EA7D9511 // 122
data8 0x3FD92C59E79C0E56 // 123
data8 0x3FD95BD750EE3ED2 // 124
data8 0x3FD98B7811A3EE5B // 125
data8 0x3FD9AF47F33D406B // 126
data8 0x3FD9DF270C1914A7 // 127
data8 0x3FDA0325ED14FDA4 // 128
data8 0x3FDA33440224FA78 // 129
data8 0x3FDA57725E80C382 // 130
data8 0x3FDA87D0165DD199 // 131
data8 0x3FDAAC2E6C03F895 // 132
data8 0x3FDADCCC6FDF6A81 // 133
data8 0x3FDB015B3EB1E790 // 134
data8 0x3FDB323A3A635948 // 135
data8 0x3FDB56FA04462909 // 136
data8 0x3FDB881AA659BC93 // 137
data8 0x3FDBAD0BEF3DB164 // 138
data8 0x3FDBD21297781C2F // 139
data8 0x3FDC039236F08818 // 140
data8 0x3FDC28CB1E4D32FC // 141
data8 0x3FDC4E19B84723C1 // 142
data8 0x3FDC7FF9C74554C9 // 143
data8 0x3FDCA57B64E9DB05 // 144
data8 0x3FDCCB130A5CEBAF // 145
data8 0x3FDCF0C0D18F326F // 146
data8 0x3FDD232075B5A201 // 147
data8 0x3FDD490246DEFA6B // 148
data8 0x3FDD6EFA918D25CD // 149
data8 0x3FDD9509707AE52F // 150
data8 0x3FDDBB2EFE92C554 // 151
data8 0x3FDDEE2F3445E4AE // 152
data8 0x3FDE148A1A2726CD // 153
data8 0x3FDE3AFC0A49FF3F // 154
data8 0x3FDE6185206D516D // 155
data8 0x3FDE882578823D51 // 156
data8 0x3FDEAEDD2EAC990C // 157
data8 0x3FDED5AC5F436BE2 // 158
data8 0x3FDEFC9326D16AB8 // 159
data8 0x3FDF2391A21575FF // 160
data8 0x3FDF4AA7EE03192C // 161
data8 0x3FDF71D627C30BB0 // 162
data8 0x3FDF991C6CB3B379 // 163
data8 0x3FDFC07ADA69A90F // 164
data8 0x3FDFE7F18EB03D3E // 165
data8 0x3FE007C053C5002E // 166
data8 0x3FE01B942198A5A0 // 167
data8 0x3FE02F74400C64EA // 168
data8 0x3FE04360BE7603AC // 169
data8 0x3FE05759AC47FE33 // 170
data8 0x3FE06B5F1911CF51 // 171
data8 0x3FE078BF0533C568 // 172
data8 0x3FE08CD9687E7B0E // 173
data8 0x3FE0A10074CF9019 // 174
data8 0x3FE0B5343A234476 // 175
data8 0x3FE0C974C89431CD // 176
data8 0x3FE0DDC2305B9886 // 177
data8 0x3FE0EB524BAFC918 // 178
data8 0x3FE0FFB54213A475 // 179
data8 0x3FE114253DA97D9F // 180
data8 0x3FE128A24F1D9AFF // 181
data8 0x3FE1365252BF0864 // 182
data8 0x3FE14AE558B4A92D // 183
data8 0x3FE15F85A19C765B // 184
data8 0x3FE16D4D38C119FA // 185
data8 0x3FE18203C20DD133 // 186
data8 0x3FE196C7BC4B1F3A // 187
data8 0x3FE1A4A738B7A33C // 188
data8 0x3FE1B981C0C9653C // 189
data8 0x3FE1CE69E8BB106A // 190
data8 0x3FE1DC619DE06944 // 191
data8 0x3FE1F160A2AD0DA3 // 192
data8 0x3FE2066D7740737E // 193
data8 0x3FE2147DBA47A393 // 194
data8 0x3FE229A1BC5EBAC3 // 195
data8 0x3FE237C1841A502E // 196
data8 0x3FE24CFCE6F80D9A // 197
data8 0x3FE25B2C55CD5762 // 198
data8 0x3FE2707F4D5F7C40 // 199
data8 0x3FE285E0842CA383 // 200
data8 0x3FE294294708B773 // 201
data8 0x3FE2A9A2670AFF0C // 202
data8 0x3FE2B7FB2C8D1CC0 // 203
data8 0x3FE2C65A6395F5F5 // 204
data8 0x3FE2DBF557B0DF42 // 205
data8 0x3FE2EA64C3F97654 // 206
data8 0x3FE3001823684D73 // 207
data8 0x3FE30E97E9A8B5CC // 208
data8 0x3FE32463EBDD34E9 // 209
data8 0x3FE332F4314AD795 // 210
data8 0x3FE348D90E7464CF // 211
data8 0x3FE35779F8C43D6D // 212
data8 0x3FE36621961A6A99 // 213
data8 0x3FE37C299F3C366A // 214
data8 0x3FE38AE2171976E7 // 215
data8 0x3FE399A157A603E7 // 216
data8 0x3FE3AFCCFE77B9D1 // 217
data8 0x3FE3BE9D503533B5 // 218
data8 0x3FE3CD7480B4A8A2 // 219
data8 0x3FE3E3C43918F76C // 220
data8 0x3FE3F2ACB27ED6C6 // 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 0x3FE489445EFFFCCB // 230
data8 0x3FE4A018BCB69835 // 231
data8 0x3FE4AF5A0C9D65D7 // 232
data8 0x3FE4BEA2A5BDBE87 // 233
data8 0x3FE4CDF28F10AC46 // 234
data8 0x3FE4DD49CF994058 // 235
data8 0x3FE4ECA86E64A683 // 236
data8 0x3FE503C43CD8EB68 // 237
data8 0x3FE513356667FC57 // 238
data8 0x3FE522AE0738A3D7 // 239
data8 0x3FE5322E26867857 // 240
data8 0x3FE541B5CB979809 // 241
data8 0x3FE55144FDBCBD62 // 242
data8 0x3FE560DBC45153C6 // 243
data8 0x3FE5707A26BB8C66 // 244
data8 0x3FE587F60ED5B8FF // 245
data8 0x3FE597A7977C8F31 // 246
data8 0x3FE5A760D634BB8A // 247
data8 0x3FE5B721D295F10E // 248
data8 0x3FE5C6EA94431EF9 // 249
data8 0x3FE5D6BB22EA86F5 // 250
data8 0x3FE5E6938645D38F // 251
data8 0x3FE5F673C61A2ED1 // 252
data8 0x3FE6065BEA385926 // 253
data8 0x3FE6164BFA7CC06B // 254
data8 0x3FE62643FECF9742 // 255
//
// lo parts of ln(1/frcpa(1+i/256)), i=0...255
data4 0x20E70672 // 0
data4 0x1F60A5D0 // 1
data4 0x218EABA0 // 2
data4 0x21403104 // 3
data4 0x20E9B54E // 4
data4 0x21EE1382 // 5
data4 0x226014E3 // 6
data4 0x2095E5C9 // 7
data4 0x228BA9D4 // 8
data4 0x22932B86 // 9
data4 0x22608A57 // 10
data4 0x220209F3 // 11
data4 0x212882CC // 12
data4 0x220D46E2 // 13
data4 0x21FA4C28 // 14
data4 0x229E5BD9 // 15
data4 0x228C9838 // 16
data4 0x2311F954 // 17
data4 0x221365DF // 18
data4 0x22BD0CB3 // 19
data4 0x223D4BB7 // 20
data4 0x22A71BBE // 21
data4 0x237DB2FA // 22
data4 0x23194C9D // 23
data4 0x22EC639E // 24
data4 0x2367E669 // 25
data4 0x232E1D5F // 26
data4 0x234A639B // 27
data4 0x2365C0E0 // 28
data4 0x234646C1 // 29
data4 0x220CBF9C // 30
data4 0x22A00FD4 // 31
data4 0x2306A3F2 // 32
data4 0x23745A9B // 33
data4 0x2398D756 // 34
data4 0x23DD0B6A // 35
data4 0x23DE338B // 36
data4 0x23A222DF // 37
data4 0x223164F8 // 38
data4 0x23B4E87B // 39
data4 0x23D6CCB8 // 40
data4 0x220C2099 // 41
data4 0x21B86B67 // 42
data4 0x236D14F1 // 43
data4 0x225A923F // 44
data4 0x22748723 // 45
data4 0x22200D13 // 46
data4 0x23C296EA // 47
data4 0x2302AC38 // 48
data4 0x234B1996 // 49
data4 0x2385E298 // 50
data4 0x23175BE5 // 51
data4 0x2193F482 // 52
data4 0x23BFEA90 // 53
data4 0x23D70A0C // 54
data4 0x231CF30A // 55
data4 0x235D9E90 // 56
data4 0x221AD0CB // 57
data4 0x22FAA08B // 58
data4 0x23D29A87 // 59
data4 0x20C4B2FE // 60
data4 0x2381B8B7 // 61
data4 0x23F8D9FC // 62
data4 0x23EAAE7B // 63
data4 0x2329E8AA // 64
data4 0x23EC0322 // 65
data4 0x2357FDCB // 66
data4 0x2392A9AD // 67
data4 0x22113B02 // 68
data4 0x22DEE901 // 69
data4 0x236A6D14 // 70
data4 0x2371D33E // 71
data4 0x2146F005 // 72
data4 0x23230B06 // 73
data4 0x22F1C77D // 74
data4 0x23A89FA3 // 75
data4 0x231D1241 // 76
data4 0x244DA96C // 77
data4 0x23ECBB7D // 78
data4 0x223E42B4 // 79
data4 0x23801BC9 // 80
data4 0x23573263 // 81
data4 0x227C1158 // 82
data4 0x237BD749 // 83
data4 0x21DDBAE9 // 84
data4 0x23401735 // 85
data4 0x241D9DEE // 86
data4 0x23BC88CB // 87
data4 0x2396D5F1 // 88
data4 0x23FC89CF // 89
data4 0x2414F9A2 // 90
data4 0x2474A0F5 // 91
data4 0x24354B60 // 92
data4 0x23C1EB40 // 93
data4 0x2306DD92 // 94
data4 0x24353B6B // 95
data4 0x23CD1701 // 96
data4 0x237C7A1C // 97
data4 0x245793AA // 98
data4 0x24563695 // 99
data4 0x23C51467 // 100
data4 0x24476B68 // 101
data4 0x212585A9 // 102
data4 0x247B8293 // 103
data4 0x2446848A // 104
data4 0x246A53F8 // 105
data4 0x246E496D // 106
data4 0x23ED1D36 // 107
data4 0x2314C258 // 108
data4 0x233244A7 // 109
data4 0x245B7AF0 // 110
data4 0x24247130 // 111
data4 0x22D67B38 // 112
data4 0x2449F620 // 113
data4 0x23BBC8B8 // 114
data4 0x237D3BA0 // 115
data4 0x245E8F13 // 116
data4 0x2435573F // 117
data4 0x242DE666 // 118
data4 0x2463BC10 // 119
data4 0x2466587D // 120
data4 0x2408144B // 121
data4 0x2405F0E5 // 122
data4 0x22381CFF // 123
data4 0x24154F9B // 124
data4 0x23A4E96E // 125
data4 0x24052967 // 126
data4 0x2406963F // 127
data4 0x23F7D3CB // 128
data4 0x2448AFF4 // 129
data4 0x24657A21 // 130
data4 0x22FBC230 // 131
data4 0x243C8DEA // 132
data4 0x225DC4B7 // 133
data4 0x23496EBF // 134
data4 0x237C2B2B // 135
data4 0x23A4A5B1 // 136
data4 0x2394E9D1 // 137
data4 0x244BC950 // 138
data4 0x23C7448F // 139
data4 0x2404A1AD // 140
data4 0x246511D5 // 141
data4 0x24246526 // 142
data4 0x23111F57 // 143
data4 0x22868951 // 144
data4 0x243EB77F // 145
data4 0x239F3DFF // 146
data4 0x23089666 // 147
data4 0x23EBFA6A // 148
data4 0x23C51312 // 149
data4 0x23E1DD5E // 150
data4 0x232C0944 // 151
data4 0x246A741F // 152
data4 0x2414DF8D // 153
data4 0x247B5546 // 154
data4 0x2415C980 // 155
data4 0x24324ABD // 156
data4 0x234EB5E5 // 157
data4 0x2465E43E // 158
data4 0x242840D1 // 159
data4 0x24444057 // 160
data4 0x245E56F0 // 161
data4 0x21AE30F8 // 162
data4 0x23FB3283 // 163
data4 0x247A4D07 // 164
data4 0x22AE314D // 165
data4 0x246B7727 // 166
data4 0x24EAD526 // 167
data4 0x24B41DC9 // 168
data4 0x24EE8062 // 169
data4 0x24A0C7C4 // 170
data4 0x24E8DA67 // 171
data4 0x231120F7 // 172
data4 0x24401FFB // 173
data4 0x2412DD09 // 174
data4 0x248C131A // 175
data4 0x24C0A7CE // 176
data4 0x243DD4C8 // 177
data4 0x24457FEB // 178
data4 0x24DEEFBB // 179
data4 0x243C70AE // 180
data4 0x23E7A6FA // 181
data4 0x24C2D311 // 182
data4 0x23026255 // 183
data4 0x2437C9B9 // 184
data4 0x246BA847 // 185
data4 0x2420B448 // 186
data4 0x24C4CF5A // 187
data4 0x242C4981 // 188
data4 0x24DE1525 // 189
data4 0x24F5CC33 // 190
data4 0x235A85DA // 191
data4 0x24A0B64F // 192
data4 0x244BA0A4 // 193
data4 0x24AAF30A // 194
data4 0x244C86F9 // 195
data4 0x246D5B82 // 196
data4 0x24529347 // 197
data4 0x240DD008 // 198
data4 0x24E98790 // 199
data4 0x2489B0CE // 200
data4 0x22BC29AC // 201
data4 0x23F37C7A // 202
data4 0x24987FE8 // 203
data4 0x22AFE20B // 204
data4 0x24C8D7C2 // 205
data4 0x24B28B7D // 206
data4 0x23B6B271 // 207
data4 0x24C77CB6 // 208
data4 0x24EF1DCA // 209
data4 0x24A4F0AC // 210
data4 0x24CF113E // 211
data4 0x2496BBAB // 212
data4 0x23C7CC8A // 213
data4 0x23AE3961 // 214
data4 0x2410A895 // 215
data4 0x23CE3114 // 216
data4 0x2308247D // 217
data4 0x240045E9 // 218
data4 0x24974F60 // 219
data4 0x242CB39F // 220
data4 0x24AB8D69 // 221
data4 0x23436788 // 222
data4 0x24305E9E // 223
data4 0x243E71A9 // 224
data4 0x23C2A6B3 // 225
data4 0x23FFE6CF // 226
data4 0x2322D801 // 227
data4 0x24515F21 // 228
data4 0x2412A0D6 // 229
data4 0x24E60D44 // 230
data4 0x240D9251 // 231
data4 0x247076E2 // 232
data4 0x229B101B // 233
data4 0x247B12DE // 234
data4 0x244B9127 // 235
data4 0x2499EC42 // 236
data4 0x21FC3963 // 237
data4 0x23E53266 // 238
data4 0x24CE102D // 239
data4 0x23CC45D2 // 240
data4 0x2333171D // 241
data4 0x246B3533 // 242
data4 0x24931129 // 243
data4 0x24405FFA // 244
data4 0x24CF464D // 245
data4 0x237095CD // 246
data4 0x24F86CBD // 247
data4 0x24E2D84B // 248
data4 0x21ACBB44 // 249
data4 0x24F43A8C // 250
data4 0x249DB931 // 251
data4 0x24A385EF // 252
data4 0x238B1279 // 253
data4 0x2436213E // 254
data4 0x24F18A3B // 255
LOCAL_OBJECT_END(log_data)
LOCAL_OBJECT_START(log10_data)
// coefficients of polynoimal approximation
data8 0x3FC2494104381A8E // A7
data8 0xBFC5556D556BBB69 // A6
//
// two parts of ln(2)/ln(10)
data8 0x3FD3441350900000, 0x3DCEF3FDE623E256
//
data8 0xDE5BD8A937287195,0x3FFD // 1/ln(10)
//
data8 0x3FC999999988B5E9 // A5
data8 0xBFCFFFFFFFF6FFF5 // A4
//
// Hi parts of ln(1/frcpa(1+i/256))/ln(10), i=0...255
data8 0x3F4BD27045BFD024 // 0
data8 0x3F64E84E793A474A // 1
data8 0x3F7175085AB85FF0 // 2
data8 0x3F787CFF9D9147A5 // 3
data8 0x3F7EA9D372B89FC8 // 4
data8 0x3F82DF9D95DA961C // 5
data8 0x3F866DF172D6372B // 6
data8 0x3F898D79EF5EEDEF // 7
data8 0x3F8D22ADF3F9579C // 8
data8 0x3F9024231D30C398 // 9
data8 0x3F91F23A98897D49 // 10
data8 0x3F93881A7B818F9E // 11
data8 0x3F951F6E1E759E35 // 12
data8 0x3F96F2BCE7ADC5B4 // 13
data8 0x3F988D362CDF359E // 14
data8 0x3F9A292BAF010981 // 15
data8 0x3F9BC6A03117EB97 // 16
data8 0x3F9D65967DE3AB08 // 17
data8 0x3F9F061167FC31E7 // 18
data8 0x3FA05409E4F7819B // 19
data8 0x3FA125D0432EA20D // 20
data8 0x3FA1F85D440D299B // 21
data8 0x3FA2AD755749617C // 22
data8 0x3FA381772A00E603 // 23
data8 0x3FA45643E165A70A // 24
data8 0x3FA52BDD034475B8 // 25
data8 0x3FA5E3966B7E9295 // 26
data8 0x3FA6BAAF47C5B244 // 27
data8 0x3FA773B3E8C4F3C7 // 28
data8 0x3FA84C51EBEE8D15 // 29
data8 0x3FA906A6786FC1CA // 30
data8 0x3FA9C197ABF00DD6 // 31
data8 0x3FAA9C78712191F7 // 32
data8 0x3FAB58C09C8D637C // 33
data8 0x3FAC15A8BCDD7B7E // 34
data8 0x3FACD331E2C2967B // 35
data8 0x3FADB11ED766ABF4 // 36
data8 0x3FAE70089346A9E6 // 37
data8 0x3FAF2F96C6754AED // 38
data8 0x3FAFEFCA8D451FD5 // 39
data8 0x3FB0585283764177 // 40
data8 0x3FB0B913AAC7D3A6 // 41
data8 0x3FB11A294F2569F5 // 42
data8 0x3FB16B51A2696890 // 43
data8 0x3FB1CD03ADACC8BD // 44
data8 0x3FB22F0BDD7745F5 // 45
data8 0x3FB2916ACA38D1E7 // 46
data8 0x3FB2F4210DF7663C // 47
data8 0x3FB346A6C3C49065 // 48
data8 0x3FB3A9FEBC605409 // 49
data8 0x3FB3FD0C10A3AA54 // 50
data8 0x3FB46107D3540A81 // 51
data8 0x3FB4C55DD16967FE // 52
data8 0x3FB51940330C000A // 53
data8 0x3FB56D620EE7115E // 54
data8 0x3FB5D2ABCF26178D // 55
data8 0x3FB6275AA5DEBF81 // 56
data8 0x3FB68D4EAF26D7EE // 57
data8 0x3FB6E28C5C54A28D // 58
data8 0x3FB7380B9665B7C7 // 59
data8 0x3FB78DCCC278E85B // 60
data8 0x3FB7F50C2CF25579 // 61
data8 0x3FB84B5FD5EAEFD7 // 62
data8 0x3FB8A1F6BAB2B226 // 63
data8 0x3FB8F8D144557BDF // 64
data8 0x3FB94FEFDCD61D92 // 65
data8 0x3FB9A752EF316149 // 66
data8 0x3FB9FEFAE7611EDF // 67
data8 0x3FBA56E8325F5C86 // 68
data8 0x3FBAAF1B3E297BB3 // 69
data8 0x3FBB079479C372AC // 70
data8 0x3FBB6054553B12F7 // 71
data8 0x3FBBB95B41AB5CE5 // 72
data8 0x3FBC12A9B13FE079 // 73
data8 0x3FBC6C4017382BEA // 74
data8 0x3FBCB41FBA42686C // 75
data8 0x3FBD0E38CE73393E // 76
data8 0x3FBD689B2193F132 // 77
data8 0x3FBDC3472B1D285F // 78
data8 0x3FBE0C06300D528B // 79
data8 0x3FBE6738190E394B // 80
data8 0x3FBEC2B50D208D9A // 81
data8 0x3FBF0C1C2B936827 // 82
data8 0x3FBF68216C9CC726 // 83
data8 0x3FBFB1F6381856F3 // 84
data8 0x3FC00742AF4CE5F8 // 85
data8 0x3FC02C64906512D2 // 86
data8 0x3FC05AF1E63E03B4 // 87
data8 0x3FC0804BEA723AA8 // 88
data8 0x3FC0AF1FD6711526 // 89
data8 0x3FC0D4B2A88059FF // 90
data8 0x3FC0FA5EF136A06C // 91
data8 0x3FC1299A4FB3E305 // 92
data8 0x3FC14F806253C3EC // 93
data8 0x3FC175805D1587C1 // 94
data8 0x3FC19B9A637CA294 // 95
data8 0x3FC1CB5FC26EDE16 // 96
data8 0x3FC1F1B4E65F2590 // 97
data8 0x3FC218248B5DC3E5 // 98
data8 0x3FC23EAED62ADC76 // 99
data8 0x3FC26553EBD337BC // 100
data8 0x3FC28C13F1B118FF // 101
data8 0x3FC2BCAA14381385 // 102
data8 0x3FC2E3A740B7800E // 103
data8 0x3FC30ABFD8F333B6 // 104
data8 0x3FC331F403985096 // 105
data8 0x3FC35943E7A6068F // 106
data8 0x3FC380AFAC6E7C07 // 107
data8 0x3FC3A8377997B9E5 // 108
data8 0x3FC3CFDB771C9ADB // 109
data8 0x3FC3EDA90D39A5DE // 110
data8 0x3FC4157EC09505CC // 111
data8 0x3FC43D7113FB04C0 // 112
data8 0x3FC4658030AD1CCE // 113
data8 0x3FC48DAC404638F5 // 114
data8 0x3FC4B5F56CBBB869 // 115
data8 0x3FC4DE5BE05E7582 // 116
data8 0x3FC4FCBC0776FD85 // 117
data8 0x3FC525561E9256EE // 118
data8 0x3FC54E0DF3198865 // 119
data8 0x3FC56CAB7112BDE2 // 120
data8 0x3FC59597BA735B15 // 121
data8 0x3FC5BEA23A506FD9 // 122
data8 0x3FC5DD7E08DE382E // 123
data8 0x3FC606BDD3F92355 // 124
data8 0x3FC6301C518A501E // 125
data8 0x3FC64F3770618915 // 126
data8 0x3FC678CC14C1E2D7 // 127
data8 0x3FC6981005ED2947 // 128
data8 0x3FC6C1DB5F9BB335 // 129
data8 0x3FC6E1488ECD2880 // 130
data8 0x3FC70B4B2E7E41B8 // 131
data8 0x3FC72AE209146BF8 // 132
data8 0x3FC7551C81BD8DCF // 133
data8 0x3FC774DD76CC43BD // 134
data8 0x3FC79F505DB00E88 // 135
data8 0x3FC7BF3BDE099F30 // 136
data8 0x3FC7E9E7CAC437F8 // 137
data8 0x3FC809FE4902D00D // 138
data8 0x3FC82A2757995CBD // 139
data8 0x3FC85525C625E098 // 140
data8 0x3FC8757A79831887 // 141
data8 0x3FC895E2058D8E02 // 142
data8 0x3FC8C13437695531 // 143
data8 0x3FC8E1C812EF32BE // 144
data8 0x3FC9026F112197E8 // 145
data8 0x3FC923294888880A // 146
data8 0x3FC94EEA4B8334F2 // 147
data8 0x3FC96FD1B639FC09 // 148
data8 0x3FC990CCA66229AB // 149
data8 0x3FC9B1DB33334842 // 150
data8 0x3FC9D2FD740E6606 // 151
data8 0x3FC9FF49EEDCB553 // 152
data8 0x3FCA209A84FBCFF7 // 153
data8 0x3FCA41FF1E43F02B // 154
data8 0x3FCA6377D2CE9377 // 155
data8 0x3FCA8504BAE0D9F5 // 156
data8 0x3FCAA6A5EEEBEFE2 // 157
data8 0x3FCAC85B878D7878 // 158
data8 0x3FCAEA259D8FFA0B // 159
data8 0x3FCB0C0449EB4B6A // 160
data8 0x3FCB2DF7A5C50299 // 161
data8 0x3FCB4FFFCA70E4D1 // 162
data8 0x3FCB721CD17157E2 // 163
data8 0x3FCB944ED477D4EC // 164
data8 0x3FCBB695ED655C7C // 165
data8 0x3FCBD8F2364AEC0F // 166
data8 0x3FCBFB63C969F4FF // 167
data8 0x3FCC1DEAC134D4E9 // 168
data8 0x3FCC4087384F4F80 // 169
data8 0x3FCC6339498F09E1 // 170
data8 0x3FCC86010FFC076B // 171
data8 0x3FCC9D3D065C5B41 // 172
data8 0x3FCCC029375BA079 // 173
data8 0x3FCCE32B66978BA4 // 174
data8 0x3FCD0643AFD51404 // 175
data8 0x3FCD29722F0DEA45 // 176
data8 0x3FCD4CB70070FE43 // 177
data8 0x3FCD6446AB3F8C95 // 178
data8 0x3FCD87B0EF71DB44 // 179
data8 0x3FCDAB31D1FE99A6 // 180
data8 0x3FCDCEC96FDC888E // 181
data8 0x3FCDE69088763579 // 182
data8 0x3FCE0A4E4A25C1FF // 183
data8 0x3FCE2E2315755E32 // 184
data8 0x3FCE461322D1648A // 185
data8 0x3FCE6A0E95C7787B // 186
data8 0x3FCE8E216243DD60 // 187
data8 0x3FCEA63AF26E007C // 188
data8 0x3FCECA74ED15E0B7 // 189
data8 0x3FCEEEC692CCD259 // 190
data8 0x3FCF070A36B8D9C0 // 191
data8 0x3FCF2B8393E34A2D // 192
data8 0x3FCF5014EF538A5A // 193
data8 0x3FCF68833AF1B17F // 194
data8 0x3FCF8D3CD9F3F04E // 195
data8 0x3FCFA5C61ADD93E9 // 196
data8 0x3FCFCAA8567EBA79 // 197
data8 0x3FCFE34CC8743DD8 // 198
data8 0x3FD0042BFD74F519 // 199
data8 0x3FD016BDF6A18017 // 200
data8 0x3FD023262F907322 // 201
data8 0x3FD035CCED8D32A1 // 202
data8 0x3FD042430E869FFB // 203
data8 0x3FD04EBEC842B2DF // 204
data8 0x3FD06182E84FD4AB // 205
data8 0x3FD06E0CB609D383 // 206
data8 0x3FD080E60BEC8F12 // 207
data8 0x3FD08D7E0D894735 // 208
data8 0x3FD0A06CC96A2055 // 209
data8 0x3FD0AD131F3B3C55 // 210
data8 0x3FD0C01771E775FB // 211
data8 0x3FD0CCCC3CAD6F4B // 212
data8 0x3FD0D986D91A34A8 // 213
data8 0x3FD0ECA9B8861A2D // 214
data8 0x3FD0F972F87FF3D5 // 215
data8 0x3FD106421CF0E5F7 // 216
data8 0x3FD11983EBE28A9C // 217
data8 0x3FD12661E35B7859 // 218
data8 0x3FD13345D2779D3B // 219
data8 0x3FD146A6F597283A // 220
data8 0x3FD15399E81EA83D // 221
data8 0x3FD16092E5D3A9A6 // 222
data8 0x3FD17413C3B7AB5D // 223
data8 0x3FD1811BF629D6FA // 224
data8 0x3FD18E2A47B46685 // 225
data8 0x3FD19B3EBE1A4418 // 226
data8 0x3FD1AEE9017CB450 // 227
data8 0x3FD1BC0CED7134E1 // 228
data8 0x3FD1C93712ABC7FF // 229
data8 0x3FD1D66777147D3E // 230
data8 0x3FD1EA3BD1286E1C // 231
data8 0x3FD1F77BED932C4C // 232
data8 0x3FD204C25E1B031F // 233
data8 0x3FD2120F28CE69B1 // 234
data8 0x3FD21F6253C48D00 // 235
data8 0x3FD22CBBE51D60A9 // 236
data8 0x3FD240CE4C975444 // 237
data8 0x3FD24E37F8ECDAE7 // 238
data8 0x3FD25BA8215AF7FC // 239
data8 0x3FD2691ECC29F042 // 240
data8 0x3FD2769BFFAB2DFF // 241
data8 0x3FD2841FC23952C9 // 242
data8 0x3FD291AA1A384978 // 243
data8 0x3FD29F3B0E15584A // 244
data8 0x3FD2B3A0EE479DF7 // 245
data8 0x3FD2C142842C09E5 // 246
data8 0x3FD2CEEACCB7BD6C // 247
data8 0x3FD2DC99CE82FF20 // 248
data8 0x3FD2EA4F902FD7D9 // 249
data8 0x3FD2F80C186A25FC // 250
data8 0x3FD305CF6DE7B0F6 // 251
data8 0x3FD3139997683CE7 // 252
data8 0x3FD3216A9BB59E7C // 253
data8 0x3FD32F4281A3CEFE // 254
data8 0x3FD33D2150110091 // 255
//
// Lo parts of ln(1/frcpa(1+i/256))/ln(10), i=0...255
data4 0x1FB0EB5A // 0
data4 0x206E5EE3 // 1
data4 0x208F3609 // 2
data4 0x2070EB03 // 3
data4 0x1F314BAE // 4
data4 0x217A889D // 5
data4 0x21E63650 // 6
data4 0x21C2F4A3 // 7
data4 0x2192A10C // 8
data4 0x1F84B73E // 9
data4 0x2243FBCA // 10
data4 0x21BD9C51 // 11
data4 0x213C542B // 12
data4 0x21047386 // 13
data4 0x21217D8F // 14
data4 0x226791B7 // 15
data4 0x204CCE66 // 16
data4 0x2234CE9F // 17
data4 0x220675E2 // 18
data4 0x22B8E5BA // 19
data4 0x22C12D14 // 20
data4 0x211D41F0 // 21
data4 0x228507F3 // 22
data4 0x22F7274B // 23
data4 0x22A7FDD1 // 24
data4 0x2244A06E // 25
data4 0x215DCE69 // 26
data4 0x22F5C961 // 27
data4 0x22EBEF29 // 28
data4 0x222A2CB6 // 29
data4 0x22B9FE00 // 30
data4 0x22E79EB7 // 31
data4 0x222F9607 // 32
data4 0x2189D87F // 33
data4 0x2236DB45 // 34
data4 0x22ED77FB // 35
data4 0x21CB70F0 // 36
data4 0x21B8ACE8 // 37
data4 0x22EC58C1 // 38
data4 0x22CFCC1C // 39
data4 0x2343E77A // 40
data4 0x237FBC7F // 41
data4 0x230D472E // 42
data4 0x234686FB // 43
data4 0x23770425 // 44
data4 0x223977EC // 45
data4 0x2345800A // 46
data4 0x237BC351 // 47
data4 0x23191502 // 48
data4 0x232BAC12 // 49
data4 0x22692421 // 50
data4 0x234D409D // 51
data4 0x22EC3214 // 52
data4 0x2376C916 // 53
data4 0x22B00DD1 // 54
data4 0x2309D910 // 55
data4 0x22F925FD // 56
data4 0x22A63A7B // 57
data4 0x2106264A // 58
data4 0x234227F9 // 59
data4 0x1ECB1978 // 60
data4 0x23460A62 // 61
data4 0x232ED4B1 // 62
data4 0x226DDC38 // 63
data4 0x1F101A73 // 64
data4 0x21B1F82B // 65
data4 0x22752F19 // 66
data4 0x2320BC15 // 67
data4 0x236EEC5E // 68
data4 0x23404D3E // 69
data4 0x2304C517 // 70
data4 0x22F7441A // 71
data4 0x230D3D7A // 72
data4 0x2264A9DF // 73
data4 0x22410CC8 // 74
data4 0x2342CCCB // 75
data4 0x23560BD4 // 76
data4 0x237BBFFE // 77
data4 0x2373A206 // 78
data4 0x22C871B9 // 79
data4 0x2354B70C // 80
data4 0x232EDB33 // 81
data4 0x235DB680 // 82
data4 0x230EF422 // 83
data4 0x235316CA // 84
data4 0x22EEEE8B // 85
data4 0x2375C88C // 86
data4 0x235ABD21 // 87
data4 0x23A0D232 // 88
data4 0x23F5FFB5 // 89
data4 0x23D3CEC8 // 90
data4 0x22A92204 // 91
data4 0x238C64DF // 92
data4 0x23B82896 // 93
data4 0x22D633B8 // 94
data4 0x23861E93 // 95
data4 0x23CB594B // 96
data4 0x2330387E // 97
data4 0x21CD4702 // 98
data4 0x2284C505 // 99
data4 0x23D6995C // 100
data4 0x23F6C807 // 101
data4 0x239CEF5C // 102
data4 0x239442B0 // 103
data4 0x22B35EE5 // 104
data4 0x2391E9A4 // 105
data4 0x23A390F5 // 106
data4 0x2349AC9C // 107
data4 0x23FA5535 // 108
data4 0x21E3A46A // 109
data4 0x23B44ABA // 110
data4 0x23CEA8E0 // 111
data4 0x23F647DC // 112
data4 0x2390D1A8 // 113
data4 0x23D0CFA2 // 114
data4 0x236E0872 // 115
data4 0x23B88B91 // 116
data4 0x2283C359 // 117
data4 0x232F647F // 118
data4 0x23122CD7 // 119
data4 0x232CF564 // 120
data4 0x232630FD // 121
data4 0x23BEE1C8 // 122
data4 0x23B2BD30 // 123
data4 0x2301F1C0 // 124
data4 0x23CE4D67 // 125
data4 0x23A353C9 // 126
data4 0x238086E8 // 127
data4 0x22D0D29E // 128
data4 0x23A3B3C8 // 129
data4 0x23F69F4B // 130
data4 0x23EA3C21 // 131
data4 0x23951C88 // 132
data4 0x2372AFFC // 133
data4 0x23A6D1A8 // 134
data4 0x22BBBAF4 // 135
data4 0x227FA3DD // 136
data4 0x23804D9B // 137
data4 0x232D771F // 138
data4 0x239CB57B // 139
data4 0x2303CF34 // 140
data4 0x22218C2A // 141
data4 0x23991BEE // 142
data4 0x23EB3596 // 143
data4 0x230487FA // 144
data4 0x2135DF4C // 145
data4 0x2380FD2D // 146
data4 0x23EB75E9 // 147
data4 0x211C62C8 // 148
data4 0x23F518F1 // 149
data4 0x23FEF882 // 150
data4 0x239097C7 // 151
data4 0x223E2BDA // 152
data4 0x23988F89 // 153
data4 0x22E4A4AD // 154
data4 0x23F03D9C // 155
data4 0x23F5018F // 156
data4 0x23E1E250 // 157
data4 0x23FD3D90 // 158
data4 0x22DEE2FF // 159
data4 0x238342AB // 160
data4 0x22E6736F // 161
data4 0x233AFC28 // 162
data4 0x2395F661 // 163
data4 0x23D8B991 // 164
data4 0x23CD58D5 // 165
data4 0x21941FD6 // 166
data4 0x23352915 // 167
data4 0x235D09EE // 168
data4 0x22DC7EF9 // 169
data4 0x238BC9F3 // 170
data4 0x2397DF8F // 171
data4 0x2380A7BB // 172
data4 0x23EFF48C // 173
data4 0x21E67408 // 174
data4 0x236420F7 // 175
data4 0x22C8DFB5 // 176
data4 0x239B5D35 // 177
data4 0x23BDC09D // 178
data4 0x239E822C // 179
data4 0x23984F0A // 180
data4 0x23EF2119 // 181
data4 0x23F738B8 // 182
data4 0x23B66187 // 183
data4 0x23B06AD7 // 184
data4 0x2369140F // 185
data4 0x218DACE6 // 186
data4 0x21DF23F1 // 187
data4 0x235D8B34 // 188
data4 0x23460333 // 189
data4 0x23F11D62 // 190
data4 0x23C37147 // 191
data4 0x22B2AE2A // 192
data4 0x23949211 // 193
data4 0x23B69799 // 194
data4 0x23DBEC75 // 195
data4 0x229A6FB3 // 196
data4 0x23FC6C60 // 197
data4 0x22D01FFC // 198
data4 0x235985F0 // 199
data4 0x23F7ECA5 // 200
data4 0x23F924D3 // 201
data4 0x2381B92F // 202
data4 0x243A0FBE // 203
data4 0x24712D72 // 204
data4 0x24594E2F // 205
data4 0x220CD12A // 206
data4 0x23D87FB0 // 207
data4 0x2338288A // 208
data4 0x242BB2CC // 209
data4 0x220F6265 // 210
data4 0x23BB7FE3 // 211
data4 0x2301C0A2 // 212
data4 0x246709AB // 213
data4 0x23A619E2 // 214
data4 0x24030E3B // 215
data4 0x233C36CC // 216
data4 0x241AAB77 // 217
data4 0x243D41A3 // 218
data4 0x23834A60 // 219
data4 0x236AC7BF // 220
data4 0x23B6D597 // 221
data4 0x210E9474 // 222
data4 0x242156E6 // 223
data4 0x243A1D68 // 224
data4 0x2472187C // 225
data4 0x23834E86 // 226
data4 0x23CA0807 // 227
data4 0x24745887 // 228
data4 0x23E2B0E1 // 229
data4 0x2421EB67 // 230
data4 0x23DCC64E // 231
data4 0x22DF71D1 // 232
data4 0x238D5ECA // 233
data4 0x23CDE86F // 234
data4 0x24131F45 // 235
data4 0x240FE4E2 // 236
data4 0x2317731A // 237
data4 0x24015C76 // 238
data4 0x2301A4E8 // 239
data4 0x23E52A6D // 240
data4 0x247D8A0D // 241
data4 0x23DFEEBA // 242
data4 0x22139FEC // 243
data4 0x2454A112 // 244
data4 0x23C21E28 // 245
data4 0x2460D813 // 246
data4 0x24258924 // 247
data4 0x2425680F // 248
data4 0x24194D1E // 249
data4 0x24242C2F // 250
data4 0x243DDE5E // 251
data4 0x23DEB388 // 252
data4 0x23E0E6EB // 253
data4 0x24393E74 // 254
data4 0x241B1863 // 255
LOCAL_OBJECT_END(log10_data)
// Code
//==============================================================
// log has p13 true, p14 false
// log10 has p14 true, p13 false
.section .text
GLOBAL_IEEE754_ENTRY(log10)
{ .mfi
getf.exp GR_Exp = f8 // if x is unorm then must recompute
frcpa.s1 FR_RcpX,p0 = f1,f8
mov GR_05 = 0xFFFE // biased exponent of A2=0.5
}
{ .mlx
addl GR_ad_1 = @ltoff(log10_data),gp
movl GR_A3 = 0x3fd5555555555557 // double precision memory
// representation of A3
};;
{ .mfi
getf.sig GR_Sig = f8 // get significand to calculate index
fclass.m p8,p0 = f8,9 // is x positive unorm?
mov GR_xorg = 0x3fefe // double precision memory msb of 255/256
}
{ .mib
ld8 GR_ad_1 = [GR_ad_1]
cmp.eq p14,p13 = r0,r0 // set p14 to 1 for log10
br.cond.sptk log_log10_common
};;
GLOBAL_IEEE754_END(log10)
libm_alias_double_other (__log10, log10)
GLOBAL_IEEE754_ENTRY(log)
{ .mfi
getf.exp GR_Exp = f8 // if x is unorm then must recompute
frcpa.s1 FR_RcpX,p0 = f1,f8
mov GR_05 = 0xfffe
}
{ .mlx
addl GR_ad_1 = @ltoff(log_data),gp
movl GR_A3 = 0x3fd5555555555557 // double precision memory
// representation of A3
};;
{ .mfi
getf.sig GR_Sig = f8 // get significand to calculate index
fclass.m p8,p0 = f8,9 // is x positive unorm?
mov GR_xorg = 0x3fefe // double precision memory msb of 255/256
}
{ .mfi
ld8 GR_ad_1 = [GR_ad_1]
nop.f 0
cmp.eq p13,p14 = r0,r0 // set p13 to 1 for log
};;
log_log10_common:
{ .mfi
getf.d GR_x = f8 // double precision memory representation of x
fclass.m p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf?
dep.z GR_dx = 3, 44, 2 // Create 0x0000300000000000
// Difference between double precision
// memory representations of 257/256 and
// 255/256
}
{ .mfi
setf.exp FR_A2 = GR_05 // create A2
fnorm.s1 FR_NormX = f8
mov GR_bias = 0xffff
};;
{ .mfi
setf.d FR_A3 = GR_A3 // create A3
fcmp.eq.s1 p12,p0 = f1,f8 // is x equal to 1.0?
dep.z GR_xorg = GR_xorg, 44, 19 // 0x3fefe00000000000
// double precision memory
// representation of 255/256
}
{ .mib
add GR_ad_2 = 0x30,GR_ad_1 // address of A5,A4
add GR_ad_3 = 0x840,GR_ad_1 // address of ln(1/frcpa) lo parts
(p8) br.cond.spnt log_positive_unorms
};;
log_core:
{ .mfi
ldfpd FR_A7,FR_A6 = [GR_ad_1],16
fclass.m p10,p0 = f8,0x3A // is x < 0?
sub GR_Nm1 = GR_Exp,GR_05 // unbiased_exponent_of_x - 1
}
{ .mfi
ldfpd FR_A5,FR_A4 = [GR_ad_2],16
(p9) fma.d.s0 f8 = f8,f1,f0 // set V-flag
sub GR_N = GR_Exp,GR_bias // unbiased_exponent_of_x
};;
{ .mfi
setf.sig FR_N = GR_N // copy unbiased exponent of x to significand
fms.s1 FR_r = FR_RcpX,f8,f1 // range reduction for |x-1|>=1/256
extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index
}
{ .mib
sub GR_x = GR_x, GR_xorg // get diff between x and 255/256
cmp.gtu p6, p7 = 2, GR_Nm1 // p6 true if 0.5 <= x < 2
(p9) br.ret.spnt b0 // exit for NaN, NaT and +Inf
};;
{ .mfi
ldfpd FR_Ln2hi,FR_Ln2lo = [GR_ad_1],16
fclass.m p11,p0 = f8,0x07 // is x = 0?
shladd GR_ad_3 = GR_Ind,2,GR_ad_3 // address of Tlo
}
{ .mib
shladd GR_ad_2 = GR_Ind,3,GR_ad_2 // address of Thi
(p6) cmp.leu p6, p7 = GR_x, GR_dx // 255/256 <= x <= 257/256
(p10) br.cond.spnt log_negatives // jump if x is negative
};;
// p6 is true if |x-1| < 1/256
// p7 is true if |x-1| >= 1/256
{ .mfi
ldfd FR_Thi = [GR_ad_2]
(p6) fms.s1 FR_r = f8,f1,f1 // range reduction for |x-1|<1/256
nop.i 0
};;
{ .mmi
(p7) ldfs FR_Tlo = [GR_ad_3]
nop.m 0
nop.i 0
}
{ .mfb
nop.m 0
(p12) fma.d.s0 f8 = f0,f0,f0
(p12) br.ret.spnt b0 // exit for +1.0
};;
.pred.rel "mutex",p6,p7
{ .mfi
(p6) mov GR_NearOne = 1
fms.s1 FR_A32 = FR_A3,FR_r,FR_A2 // A3*r-A2
(p7) mov GR_NearOne = 0
}
{ .mfb
ldfe FR_InvLn10 = [GR_ad_1],16
fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2
(p11) br.cond.spnt log_zeroes // jump if x is zero
};;
{ .mfi
nop.m 0
fma.s1 FR_A6 = FR_A7,FR_r,FR_A6 // A7*r+A6
nop.i 0
}
{ .mfi
(p7) cmp.eq.unc p9,p0 = r0,r0 // set p9 if |x-1| > 1/256
fma.s1 FR_A4 = FR_A5,FR_r,FR_A4 // A5*r+A4
(p14) cmp.eq.unc p8,p0 = 1,GR_NearOne // set p8 to 1 if it's log10
// and argument near 1.0
};;
{ .mfi
(p6) getf.exp GR_rexp = FR_r // Get signexp of x-1
(p7) fcvt.xf FR_N = FR_N
(p8) cmp.eq p9,p6 = r0,r0 // Also set p9 and clear p6 if log10
// and arg near 1
};;
{ .mfi
nop.m 0
fma.s1 FR_r4 = FR_r2,FR_r2,f0 // r^4
nop.i 0
}
{ .mfi
nop.m 0
(p8) fma.s1 FR_NxLn2pT = f0,f0,f0 // Clear NxLn2pT if log10 near 1
nop.i 0
};;
{ .mfi
nop.m 0
// (A3*r+A2)*r^2+r
fma.s1 FR_A321 = FR_A32,FR_r2,FR_r
mov GR_mask = 0x1ffff
}
{ .mfi
nop.m 0
// (A7*r+A6)*r^2+(A5*r+A4)
fma.s1 FR_A4 = FR_A6,FR_r2,FR_A4
nop.i 0
};;
{ .mfi
(p6) and GR_rexp = GR_rexp, GR_mask
// N*Ln2hi+Thi
(p7) fma.s1 FR_NxLn2hipThi = FR_N,FR_Ln2hi,FR_Thi
nop.i 0
}
{ .mfi
nop.m 0
// N*Ln2lo+Tlo
(p7) fma.s1 FR_NxLn2lopTlo = FR_N,FR_Ln2lo,FR_Tlo
nop.i 0
};;
{ .mfi
(p6) sub GR_rexp = GR_rexp, GR_bias // unbiased exponent of x-1
(p9) fma.s1 f8 = FR_A4,FR_r4,FR_A321 // P(r) if |x-1| >= 1/256 or
// log10 and |x-1| < 1/256
nop.i 0
}
{ .mfi
nop.m 0
// (N*Ln2hi+Thi) + (N*Ln2lo+Tlo)
(p7) fma.s1 FR_NxLn2pT = FR_NxLn2hipThi,f1,FR_NxLn2lopTlo
nop.i 0
};;
{ .mfi
(p6) cmp.gt.unc p10, p6 = -40, GR_rexp // Test |x-1| < 2^-40
nop.f 0
nop.i 0
};;
{ .mfi
nop.m 0
(p10) fma.d.s0 f8 = FR_A32,FR_r2,FR_r // log(x) if |x-1| < 2^-40
nop.i 0
};;
.pred.rel "mutex",p6,p9
{ .mfi
nop.m 0
(p6) fma.d.s0 f8 = FR_A4,FR_r4,FR_A321 // log(x) if 2^-40 <= |x-1| < 1/256
nop.i 0
}
{ .mfb
nop.m 0
(p9) fma.d.s0 f8 = f8,FR_InvLn10,FR_NxLn2pT // result if |x-1| >= 1/256
// or log10 and |x-1| < 1/256
br.ret.sptk b0
};;
.align 32
log_positive_unorms:
{ .mmf
getf.exp GR_Exp = FR_NormX // recompute biased exponent
getf.d GR_x = FR_NormX // recompute double precision x
fcmp.eq.s1 p12,p0 = f1,FR_NormX // is x equal to 1.0?
};;
{ .mfb
getf.sig GR_Sig = FR_NormX // recompute significand
fcmp.eq.s0 p15, p0 = f8, f0 // set denormal flag
br.cond.sptk log_core
};;
.align 32
log_zeroes:
{ .mfi
nop.m 0
fmerge.s FR_X = f8,f8 // keep input argument for subsequent
// call of __libm_error_support#
nop.i 0
}
{ .mfi
nop.m 0
fms.s1 FR_tmp = f0,f0,f1 // -1.0
nop.i 0
};;
.pred.rel "mutex",p13,p14
{ .mfi
(p13) mov GR_TAG = 2 // set libm error in case of log
frcpa.s0 f8,p0 = FR_tmp,f0 // log(+/-0) should be equal to -INF.
// We can get it using frcpa because it
// sets result to the IEEE-754 mandated
// quotient of FR_tmp/f0.
// As far as FR_tmp is -1 it'll be -INF
nop.i 0
}
{ .mib
(p14) mov GR_TAG = 8 // set libm error in case of log10
nop.i 0
br.cond.sptk log_libm_err
};;
.align 32
log_negatives:
{ .mfi
nop.m 0
fmerge.s FR_X = f8,f8
nop.i 0
};;
.pred.rel "mutex",p13,p14
{ .mfi
(p13) mov GR_TAG = 3 // set libm error in case of log
frcpa.s0 f8,p0 = f0,f0 // log(negatives) 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.
(p14) mov GR_TAG = 9 // set libm error in case of log10
};;
.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(log)
libm_alias_double_other (__log, log)
#ifdef SHARED
.symver log,log@@GLIBC_2.29
.weak __log_compat
.set __log_compat,__log
.symver __log_compat,log@GLIBC_2.2
#endif
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
stfd [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
stfd [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
stfd [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
ldfd 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#
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