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-rw-r--r--sysdeps/ia64/fpu/e_log.S2453
1 files changed, 1539 insertions, 914 deletions
diff --git a/sysdeps/ia64/fpu/e_log.S b/sysdeps/ia64/fpu/e_log.S
index 9ad1e5fe56..c644c6f8f7 100644
--- a/sysdeps/ia64/fpu/e_log.S
+++ b/sysdeps/ia64/fpu/e_log.S
@@ -1,10 +1,10 @@
.file "log.s"
-// Copyright (C) 2000, 2001, Intel Corporation
+
+// Copyright (c) 2000 - 2005, Intel Corporation
// All rights reserved.
-//
-// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
-// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
+//
+// 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
@@ -20,1085 +20,1710 @@
// * 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
+
+// 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
+// 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
+// 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.
-//
+// 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://developer.intel.com/opensource.
+// problem reports or change requests be submitted to it directly at
+// http://www.intel.com/software/products/opensource/libraries/num.htm.
//
// History
//==============================================================
-// 2/02/00 Initial version
-// 4/04/00 Unwind support added
-// 6/16/00 Updated table to be rounded correctly
-// 8/15/00 Bundle added after call to __libm_error_support to properly
+// 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.
-// 8/17/00 Improved speed of main path by 5 cycles
+// 08/17/00 Improved speed of main path by 5 cycles
// Shortened path for x=1.0
-// 1/09/01 Improved speed, fixed flags for neg denormals
-//
+// 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
+// ----------
//
-// Consider x = 2^N 1.f1 f2 f3 f4...f63
-// Log(x) = log(frcpa(x) x/frcpa(x))
-// = log(1/frcpa(x)) + log(frcpa(x) x)
-// = -log(frcpa(x)) + log(frcpa(x) x)
+// 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)
//
-// frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)
+// To calculate log(f) we do following
+// log(f) = log(f * frcpa(f) / frcpa(f)) =
+// = log(f * frcpa(f)) + log(1/frcpa(f))
//
-// -log(frcpa(x)) = -log(C)
-// = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
+// 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
//
-// -log(frcpa(x)) = -log(C)
-// = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
+// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256
//
-// -log(frcpa(x)) = -log(C)
-// = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
+// and
//
-// Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
-
-// Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
-// Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
-// Log(x) = +Nlog2 + T + log(frcpa(x) x)
+// 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.
//
-// Log(x) = +Nlog2 + T + log(C x)
+// Finally we have that log(x) ~ (N*log(2) + T) + P(r)
//
-// Cx = 1 + 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)
//
-// Log(x) = +Nlog2 + T + log(1+r)
-// Log(x) = +Nlog2 + 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.
+// 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
-//===============
-// CASE 1: |x-1| >= 2^-6
-// C = frcpa(x)
-// r = C * x - 1
+// --------------
+// 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)
//
-// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 + P4*r^5 + P5*r^6
+// 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.
//
-// 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
+// Note that both log and log10 use common approximation polynomial
+// it means we need only one set of coefficients of approximation.
//
-// 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
-
-// CASE 2: |x-1| < 2^-6
-// w = x - 1
+// 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 calcutated 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.
//
-// Form wseries = w + Q1*w^2 + Q2*w^3 + ... + Q7*w^8 + Q8*w^9
+// 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.
//
-// result = wseries
-// Special values
+//
+// Special values
//==============================================================
-
-
+//
// log(+0) = -inf
// log(-0) = -inf
-
-// log(+qnan) = +qnan
-// log(-qnan) = -qnan
-// log(+snan) = +qnan
-// log(-snan) = -qnan
-
+//
+// log(+qnan) = +qnan
+// log(-qnan) = -qnan
+// log(+snan) = +qnan
+// log(-snan) = -qnan
+//
// log(-n) = QNAN Indefinite
-// log(-inf) = QNAN Indefinite
-
+// log(-inf) = QNAN Indefinite
+//
// log(+inf) = +inf
-
+//
+//
// Registers used
//==============================================================
-// Floating Point registers used:
+// Floating Point registers used:
// f8, input
-// f9 -> f15, f32 -> f68
-
-// General registers used:
-// r32 -> r51
-
+// f7 -> f15, f32 -> f42
+//
+// General registers used:
+// r8 -> r11
+// r14 -> r23
+//
// Predicate registers used:
// p6 -> p15
-// p8 log base e
-// p6 log base e special
-// p9 used in the frcpa
-// p13 log base e large W
-// p14 log base e small w
-
-// p7 log base 10
-// p10 log base 10 large W
-// p11 log base 10 small w
-// p12 log base 10 special
-
-#include "libm_support.h"
-
// Assembly macros
//==============================================================
-
-log_int_Nfloat = f9
-log_Nfloat = f10
-
-log_P5 = f11
-log_P4 = f12
-log_P3 = f13
-log_P2 = f14
-log_half = f15
-
-log_log2 = f32
-log_T = f33
-
-log_rp_p4 = f34
-log_rp_p32 = f35
-log_rp_p2 = f36
-log_w6 = f37
-log_rp_p10 = f38
-log_rcube = f39
-log_rsq = f40
-
-log_T_plus_Nlog2 = f41
-log_w3 = f42
-
-log_r = f43
-log_C = f44
-
-log_w = f45
-log_Q8 = f46
-log_Q7 = f47
-log_Q4 = f48
-log_Q3 = f49
-log_Q6 = f50
-log_Q5 = f51
-log_Q2 = f52
-log_Q1 = f53
-log_P1 = f53
-
-log_rp_q7 = f54
-log_rp_q65 = f55
-log_Qlo = f56
-
-log_rp_q3 = f57
-log_rp_q21 = f58
-log_Qhi = f59
-
-log_wsq = f60
-log_w4 = f61
-log_Q = f62
-
-log_inv_ln10 = f63
-log_log10_hi = f64
-log_log10_lo = f65
-log_rp_q10 = f66
-log_NORM_f8 = f67
-log_r2P_r = f68
-
-// ===================================
-
-log_GR_exp_17_ones = r33
-log_GR_exp_16_ones = r34
-log_GR_exp_f8 = r35
-log_GR_signexp_f8 = r36
-log_GR_true_exp_f8 = r37
-log_GR_significand_f8 = r38
-log_GR_half_exp = r39
-log_GR_index = r39
-log_AD_1 = r40
-log_GR_signexp_w = r41
-log_GR_fff9 = r42
-log_AD_2 = r43
-log_GR_exp_w = r44
-
-GR_SAVE_B0 = r45
-GR_SAVE_GP = r46
-GR_SAVE_PFS = r47
-
-GR_Parameter_X = r48
-GR_Parameter_Y = r49
-GR_Parameter_RESULT = r50
-log_GR_tag = r51
-
-
-// Data tables
+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
//==============================================================
-
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
-
+RODATA
.align 16
-log_table_1:
-ASM_TYPE_DIRECTIVE(log_table_1,@object)
-data8 0xBFC5555DA7212371 // P5
-data8 0x3FC999A19EEF5826 // P4
-data8 0x3FBC756AC654273B // Q8
-data8 0xBFC001A42489AB4D // Q7
-data8 0x3FC99999999A169B // Q4
-data8 0xBFD00000000019AC // Q3
-ASM_SIZE_DIRECTIVE(log_table_1)
-log_table_2:
-ASM_TYPE_DIRECTIVE(log_table_2,@object)
-data8 0xBFCFFFFFFFFEF009 // P3
-data8 0x3FD555555554ECB2 // P2
-data8 0x3FC2492479AA0DF8 // Q6
-data8 0xBFC5555544986F52 // Q5
-data8 0x3FD5555555555555 // Q2
-data8 0xBFE0000000000000 // Q1, P1 = -0.5
-
-
-data8 0xde5bd8a937287195, 0x00003ffd // double-extended 1/ln(10)
-data8 0xb17217f7d1cf79ac, 0x00003ffe // log2
-// b17217f7d1cf79ab c9e3b39803f2f6a
-
-
-data8 0x80200aaeac44ef38 , 0x00003ff6 // log(1/frcpa(1+ 0/2^-8))
-
-data8 0xc09090a2c35aa070 , 0x00003ff7 // log(1/frcpa(1+ 1/2^-8))
-data8 0xa0c94fcb41977c75 , 0x00003ff8 // log(1/frcpa(1+ 2/2^-8))
-data8 0xe18b9c263af83301 , 0x00003ff8 // log(1/frcpa(1+ 3/2^-8))
-data8 0x8d35c8d6399c30ea , 0x00003ff9 // log(1/frcpa(1+ 4/2^-8))
-data8 0xadd4d2ecd601cbb8 , 0x00003ff9 // log(1/frcpa(1+ 5/2^-8))
-
-data8 0xce95403a192f9f01 , 0x00003ff9 // log(1/frcpa(1+ 6/2^-8))
-data8 0xeb59392cbcc01096 , 0x00003ff9 // log(1/frcpa(1+ 7/2^-8))
-data8 0x862c7d0cefd54c5d , 0x00003ffa // log(1/frcpa(1+ 8/2^-8))
-data8 0x94aa63c65e70d499 , 0x00003ffa // log(1/frcpa(1+ 9/2^-8))
-data8 0xa54a696d4b62b382 , 0x00003ffa // log(1/frcpa(1+ 10/2^-8))
-
-data8 0xb3e4a796a5dac208 , 0x00003ffa // log(1/frcpa(1+ 11/2^-8))
-data8 0xc28c45b1878340a9 , 0x00003ffa // log(1/frcpa(1+ 12/2^-8))
-data8 0xd35c55f39d7a6235 , 0x00003ffa // log(1/frcpa(1+ 13/2^-8))
-data8 0xe220f037b954f1f5 , 0x00003ffa // log(1/frcpa(1+ 14/2^-8))
-data8 0xf0f3389b036834f3 , 0x00003ffa // log(1/frcpa(1+ 15/2^-8))
-
-data8 0xffd3488d5c980465 , 0x00003ffa // log(1/frcpa(1+ 16/2^-8))
-data8 0x87609ce2ed300490 , 0x00003ffb // log(1/frcpa(1+ 17/2^-8))
-data8 0x8ede9321e8c85927 , 0x00003ffb // log(1/frcpa(1+ 18/2^-8))
-data8 0x96639427f2f8e2f4 , 0x00003ffb // log(1/frcpa(1+ 19/2^-8))
-data8 0x9defad3e8f73217b , 0x00003ffb // log(1/frcpa(1+ 20/2^-8))
-
-data8 0xa582ebd50097029c , 0x00003ffb // log(1/frcpa(1+ 21/2^-8))
-data8 0xac06dbe75ab80fee , 0x00003ffb // log(1/frcpa(1+ 22/2^-8))
-data8 0xb3a78449b2d3ccca , 0x00003ffb // log(1/frcpa(1+ 23/2^-8))
-data8 0xbb4f79635ab46bb2 , 0x00003ffb // log(1/frcpa(1+ 24/2^-8))
-data8 0xc2fec93a83523f3f , 0x00003ffb // log(1/frcpa(1+ 25/2^-8))
-
-data8 0xc99af2eaca4c4571 , 0x00003ffb // log(1/frcpa(1+ 26/2^-8))
-data8 0xd1581106472fa653 , 0x00003ffb // log(1/frcpa(1+ 27/2^-8))
-data8 0xd8002560d4355f2e , 0x00003ffb // log(1/frcpa(1+ 28/2^-8))
-data8 0xdfcb43b4fe508632 , 0x00003ffb // log(1/frcpa(1+ 29/2^-8))
-data8 0xe67f6dff709d4119 , 0x00003ffb // log(1/frcpa(1+ 30/2^-8))
-
-data8 0xed393b1c22351280 , 0x00003ffb // log(1/frcpa(1+ 31/2^-8))
-data8 0xf5192bff087bcc35 , 0x00003ffb // log(1/frcpa(1+ 32/2^-8))
-data8 0xfbdf4ff6dfef2fa3 , 0x00003ffb // log(1/frcpa(1+ 33/2^-8))
-data8 0x81559a97f92f9cc7 , 0x00003ffc // log(1/frcpa(1+ 34/2^-8))
-data8 0x84be72bce90266e8 , 0x00003ffc // log(1/frcpa(1+ 35/2^-8))
-
-data8 0x88bc74113f23def2 , 0x00003ffc // log(1/frcpa(1+ 36/2^-8))
-data8 0x8c2ba3edf6799d11 , 0x00003ffc // log(1/frcpa(1+ 37/2^-8))
-data8 0x8f9dc92f92ea08b1 , 0x00003ffc // log(1/frcpa(1+ 38/2^-8))
-data8 0x9312e8f36efab5a7 , 0x00003ffc // log(1/frcpa(1+ 39/2^-8))
-data8 0x968b08643409ceb6 , 0x00003ffc // log(1/frcpa(1+ 40/2^-8))
-
-data8 0x9a062cba08a1708c , 0x00003ffc // log(1/frcpa(1+ 41/2^-8))
-data8 0x9d845b3abf95485c , 0x00003ffc // log(1/frcpa(1+ 42/2^-8))
-data8 0xa06fd841bc001bb4 , 0x00003ffc // log(1/frcpa(1+ 43/2^-8))
-data8 0xa3f3a74652fbe0db , 0x00003ffc // log(1/frcpa(1+ 44/2^-8))
-data8 0xa77a8fb2336f20f5 , 0x00003ffc // log(1/frcpa(1+ 45/2^-8))
-
-data8 0xab0497015d28b0a0 , 0x00003ffc // log(1/frcpa(1+ 46/2^-8))
-data8 0xae91c2be6ba6a615 , 0x00003ffc // log(1/frcpa(1+ 47/2^-8))
-data8 0xb189d1b99aebb20b , 0x00003ffc // log(1/frcpa(1+ 48/2^-8))
-data8 0xb51cced5de9c1b2c , 0x00003ffc // log(1/frcpa(1+ 49/2^-8))
-data8 0xb819bee9e720d42f , 0x00003ffc // log(1/frcpa(1+ 50/2^-8))
-
-data8 0xbbb2a0947b093a5d , 0x00003ffc // log(1/frcpa(1+ 51/2^-8))
-data8 0xbf4ec1505811684a , 0x00003ffc // log(1/frcpa(1+ 52/2^-8))
-data8 0xc2535bacfa8975ff , 0x00003ffc // log(1/frcpa(1+ 53/2^-8))
-data8 0xc55a3eafad187eb8 , 0x00003ffc // log(1/frcpa(1+ 54/2^-8))
-data8 0xc8ff2484b2c0da74 , 0x00003ffc // log(1/frcpa(1+ 55/2^-8))
-
-data8 0xcc0b1a008d53ab76 , 0x00003ffc // log(1/frcpa(1+ 56/2^-8))
-data8 0xcfb6203844b3209b , 0x00003ffc // log(1/frcpa(1+ 57/2^-8))
-data8 0xd2c73949a47a19f5 , 0x00003ffc // log(1/frcpa(1+ 58/2^-8))
-data8 0xd5daae18b49d6695 , 0x00003ffc // log(1/frcpa(1+ 59/2^-8))
-data8 0xd8f08248cf7e8019 , 0x00003ffc // log(1/frcpa(1+ 60/2^-8))
-
-data8 0xdca7749f1b3e540e , 0x00003ffc // log(1/frcpa(1+ 61/2^-8))
-data8 0xdfc28e033aaaf7c7 , 0x00003ffc // log(1/frcpa(1+ 62/2^-8))
-data8 0xe2e012a5f91d2f55 , 0x00003ffc // log(1/frcpa(1+ 63/2^-8))
-data8 0xe600064ed9e292a8 , 0x00003ffc // log(1/frcpa(1+ 64/2^-8))
-data8 0xe9226cce42b39f60 , 0x00003ffc // log(1/frcpa(1+ 65/2^-8))
-
-data8 0xec4749fd97a28360 , 0x00003ffc // log(1/frcpa(1+ 66/2^-8))
-data8 0xef6ea1bf57780495 , 0x00003ffc // log(1/frcpa(1+ 67/2^-8))
-data8 0xf29877ff38809091 , 0x00003ffc // log(1/frcpa(1+ 68/2^-8))
-data8 0xf5c4d0b245cb89be , 0x00003ffc // log(1/frcpa(1+ 69/2^-8))
-data8 0xf8f3afd6fcdef3aa , 0x00003ffc // log(1/frcpa(1+ 70/2^-8))
-
-data8 0xfc2519756be1abc7 , 0x00003ffc // log(1/frcpa(1+ 71/2^-8))
-data8 0xff59119f503e6832 , 0x00003ffc // log(1/frcpa(1+ 72/2^-8))
-data8 0x8147ce381ae0e146 , 0x00003ffd // log(1/frcpa(1+ 73/2^-8))
-data8 0x82e45f06cb1ad0f2 , 0x00003ffd // log(1/frcpa(1+ 74/2^-8))
-data8 0x842f5c7c573cbaa2 , 0x00003ffd // log(1/frcpa(1+ 75/2^-8))
-
-data8 0x85ce471968c8893a , 0x00003ffd // log(1/frcpa(1+ 76/2^-8))
-data8 0x876e8305bc04066d , 0x00003ffd // log(1/frcpa(1+ 77/2^-8))
-data8 0x891012678031fbb3 , 0x00003ffd // log(1/frcpa(1+ 78/2^-8))
-data8 0x8a5f1493d766a05f , 0x00003ffd // log(1/frcpa(1+ 79/2^-8))
-data8 0x8c030c778c56fa00 , 0x00003ffd // log(1/frcpa(1+ 80/2^-8))
-
-data8 0x8da85df17e31d9ae , 0x00003ffd // log(1/frcpa(1+ 81/2^-8))
-data8 0x8efa663e7921687e , 0x00003ffd // log(1/frcpa(1+ 82/2^-8))
-data8 0x90a22b6875c6a1f8 , 0x00003ffd // log(1/frcpa(1+ 83/2^-8))
-data8 0x91f62cc8f5d24837 , 0x00003ffd // log(1/frcpa(1+ 84/2^-8))
-data8 0x93a06cfc3857d980 , 0x00003ffd // log(1/frcpa(1+ 85/2^-8))
-
-data8 0x94f66d5e6fd01ced , 0x00003ffd // log(1/frcpa(1+ 86/2^-8))
-data8 0x96a330156e6772f2 , 0x00003ffd // log(1/frcpa(1+ 87/2^-8))
-data8 0x97fb3582754ea25b , 0x00003ffd // log(1/frcpa(1+ 88/2^-8))
-data8 0x99aa8259aad1bbf2 , 0x00003ffd // log(1/frcpa(1+ 89/2^-8))
-data8 0x9b0492f6227ae4a8 , 0x00003ffd // log(1/frcpa(1+ 90/2^-8))
-
-data8 0x9c5f8e199bf3a7a5 , 0x00003ffd // log(1/frcpa(1+ 91/2^-8))
-data8 0x9e1293b9998c1daa , 0x00003ffd // log(1/frcpa(1+ 92/2^-8))
-data8 0x9f6fa31e0b41f308 , 0x00003ffd // log(1/frcpa(1+ 93/2^-8))
-data8 0xa0cda11eaf46390e , 0x00003ffd // log(1/frcpa(1+ 94/2^-8))
-data8 0xa22c8f029cfa45aa , 0x00003ffd // log(1/frcpa(1+ 95/2^-8))
-
-data8 0xa3e48badb7856b34 , 0x00003ffd // log(1/frcpa(1+ 96/2^-8))
-data8 0xa5459a0aa95849f9 , 0x00003ffd // log(1/frcpa(1+ 97/2^-8))
-data8 0xa6a79c84480cfebd , 0x00003ffd // log(1/frcpa(1+ 98/2^-8))
-data8 0xa80a946d0fcb3eb2 , 0x00003ffd // log(1/frcpa(1+ 99/2^-8))
-data8 0xa96e831a3ea7b314 , 0x00003ffd // log(1/frcpa(1+100/2^-8))
-
-data8 0xaad369e3dc544e3b , 0x00003ffd // log(1/frcpa(1+101/2^-8))
-data8 0xac92e9588952c815 , 0x00003ffd // log(1/frcpa(1+102/2^-8))
-data8 0xadfa035aa1ed8fdc , 0x00003ffd // log(1/frcpa(1+103/2^-8))
-data8 0xaf6219eae1ad6e34 , 0x00003ffd // log(1/frcpa(1+104/2^-8))
-data8 0xb0cb2e6d8160f753 , 0x00003ffd // log(1/frcpa(1+105/2^-8))
-
-data8 0xb2354249ad950f72 , 0x00003ffd // log(1/frcpa(1+106/2^-8))
-data8 0xb3a056e98ef4a3b4 , 0x00003ffd // log(1/frcpa(1+107/2^-8))
-data8 0xb50c6dba52c6292a , 0x00003ffd // log(1/frcpa(1+108/2^-8))
-data8 0xb679882c33876165 , 0x00003ffd // log(1/frcpa(1+109/2^-8))
-data8 0xb78c07429785cedc , 0x00003ffd // log(1/frcpa(1+110/2^-8))
-
-data8 0xb8faeb8dc4a77d24 , 0x00003ffd // log(1/frcpa(1+111/2^-8))
-data8 0xba6ad77eb36ae0d6 , 0x00003ffd // log(1/frcpa(1+112/2^-8))
-data8 0xbbdbcc915e9bee50 , 0x00003ffd // log(1/frcpa(1+113/2^-8))
-data8 0xbd4dcc44f8cf12ef , 0x00003ffd // log(1/frcpa(1+114/2^-8))
-data8 0xbec0d81bf5b531fa , 0x00003ffd // log(1/frcpa(1+115/2^-8))
-
-data8 0xc034f19c139186f4 , 0x00003ffd // log(1/frcpa(1+116/2^-8))
-data8 0xc14cb69f7c5e55ab , 0x00003ffd // log(1/frcpa(1+117/2^-8))
-data8 0xc2c2abbb6e5fd56f , 0x00003ffd // log(1/frcpa(1+118/2^-8))
-data8 0xc439b2c193e6771e , 0x00003ffd // log(1/frcpa(1+119/2^-8))
-data8 0xc553acb9d5c67733 , 0x00003ffd // log(1/frcpa(1+120/2^-8))
-
-data8 0xc6cc96e441272441 , 0x00003ffd // log(1/frcpa(1+121/2^-8))
-data8 0xc8469753eca88c30 , 0x00003ffd // log(1/frcpa(1+122/2^-8))
-data8 0xc962cf3ce072b05c , 0x00003ffd // log(1/frcpa(1+123/2^-8))
-data8 0xcadeba8771f694aa , 0x00003ffd // log(1/frcpa(1+124/2^-8))
-data8 0xcc5bc08d1f72da94 , 0x00003ffd // log(1/frcpa(1+125/2^-8))
-
-data8 0xcd7a3f99ea035c29 , 0x00003ffd // log(1/frcpa(1+126/2^-8))
-data8 0xcef93860c8a53c35 , 0x00003ffd // log(1/frcpa(1+127/2^-8))
-data8 0xd0192f68a7ed23df , 0x00003ffd // log(1/frcpa(1+128/2^-8))
-data8 0xd19a201127d3c645 , 0x00003ffd // log(1/frcpa(1+129/2^-8))
-data8 0xd2bb92f4061c172c , 0x00003ffd // log(1/frcpa(1+130/2^-8))
-
-data8 0xd43e80b2ee8cc8fc , 0x00003ffd // log(1/frcpa(1+131/2^-8))
-data8 0xd56173601fc4ade4 , 0x00003ffd // log(1/frcpa(1+132/2^-8))
-data8 0xd6e6637efb54086f , 0x00003ffd // log(1/frcpa(1+133/2^-8))
-data8 0xd80ad9f58f3c8193 , 0x00003ffd // log(1/frcpa(1+134/2^-8))
-data8 0xd991d1d31aca41f8 , 0x00003ffd // log(1/frcpa(1+135/2^-8))
-
-data8 0xdab7d02231484a93 , 0x00003ffd // log(1/frcpa(1+136/2^-8))
-data8 0xdc40d532cde49a54 , 0x00003ffd // log(1/frcpa(1+137/2^-8))
-data8 0xdd685f79ed8b265e , 0x00003ffd // log(1/frcpa(1+138/2^-8))
-data8 0xde9094bbc0e17b1d , 0x00003ffd // log(1/frcpa(1+139/2^-8))
-data8 0xe01c91b78440c425 , 0x00003ffd // log(1/frcpa(1+140/2^-8))
-
-data8 0xe14658f26997e729 , 0x00003ffd // log(1/frcpa(1+141/2^-8))
-data8 0xe270cdc2391e0d23 , 0x00003ffd // log(1/frcpa(1+142/2^-8))
-data8 0xe3ffce3a2aa64922 , 0x00003ffd // log(1/frcpa(1+143/2^-8))
-data8 0xe52bdb274ed82887 , 0x00003ffd // log(1/frcpa(1+144/2^-8))
-data8 0xe6589852e75d7df6 , 0x00003ffd // log(1/frcpa(1+145/2^-8))
-
-data8 0xe786068c79937a7d , 0x00003ffd // log(1/frcpa(1+146/2^-8))
-data8 0xe91903adad100911 , 0x00003ffd // log(1/frcpa(1+147/2^-8))
-data8 0xea481236f7d35bb0 , 0x00003ffd // log(1/frcpa(1+148/2^-8))
-data8 0xeb77d48c692e6b14 , 0x00003ffd // log(1/frcpa(1+149/2^-8))
-data8 0xeca84b83d7297b87 , 0x00003ffd // log(1/frcpa(1+150/2^-8))
-
-data8 0xedd977f4962aa158 , 0x00003ffd // log(1/frcpa(1+151/2^-8))
-data8 0xef7179a22f257754 , 0x00003ffd // log(1/frcpa(1+152/2^-8))
-data8 0xf0a450d139366ca7 , 0x00003ffd // log(1/frcpa(1+153/2^-8))
-data8 0xf1d7e0524ff9ffdb , 0x00003ffd // log(1/frcpa(1+154/2^-8))
-data8 0xf30c29036a8b6cae , 0x00003ffd // log(1/frcpa(1+155/2^-8))
-
-data8 0xf4412bc411ea8d92 , 0x00003ffd // log(1/frcpa(1+156/2^-8))
-data8 0xf576e97564c8619d , 0x00003ffd // log(1/frcpa(1+157/2^-8))
-data8 0xf6ad62fa1b5f172f , 0x00003ffd // log(1/frcpa(1+158/2^-8))
-data8 0xf7e499368b55c542 , 0x00003ffd // log(1/frcpa(1+159/2^-8))
-data8 0xf91c8d10abaffe22 , 0x00003ffd // log(1/frcpa(1+160/2^-8))
-
-data8 0xfa553f7018c966f3 , 0x00003ffd // log(1/frcpa(1+161/2^-8))
-data8 0xfb8eb13e185d802c , 0x00003ffd // log(1/frcpa(1+162/2^-8))
-data8 0xfcc8e3659d9bcbed , 0x00003ffd // log(1/frcpa(1+163/2^-8))
-data8 0xfe03d6d34d487fd2 , 0x00003ffd // log(1/frcpa(1+164/2^-8))
-data8 0xff3f8c7581e9f0ae , 0x00003ffd // log(1/frcpa(1+165/2^-8))
-
-data8 0x803e029e280173ae , 0x00003ffe // log(1/frcpa(1+166/2^-8))
-data8 0x80dca10cc52d0757 , 0x00003ffe // log(1/frcpa(1+167/2^-8))
-data8 0x817ba200632755a1 , 0x00003ffe // log(1/frcpa(1+168/2^-8))
-data8 0x821b05f3b01d6774 , 0x00003ffe // log(1/frcpa(1+169/2^-8))
-data8 0x82bacd623ff19d06 , 0x00003ffe // log(1/frcpa(1+170/2^-8))
-
-data8 0x835af8c88e7a8f47 , 0x00003ffe // log(1/frcpa(1+171/2^-8))
-data8 0x83c5f8299e2b4091 , 0x00003ffe // log(1/frcpa(1+172/2^-8))
-data8 0x8466cb43f3d87300 , 0x00003ffe // log(1/frcpa(1+173/2^-8))
-data8 0x850803a67c80ca4b , 0x00003ffe // log(1/frcpa(1+174/2^-8))
-data8 0x85a9a1d11a23b461 , 0x00003ffe // log(1/frcpa(1+175/2^-8))
-
-data8 0x864ba644a18e6e05 , 0x00003ffe // log(1/frcpa(1+176/2^-8))
-data8 0x86ee1182dcc432f7 , 0x00003ffe // log(1/frcpa(1+177/2^-8))
-data8 0x875a925d7e48c316 , 0x00003ffe // log(1/frcpa(1+178/2^-8))
-data8 0x87fdaa109d23aef7 , 0x00003ffe // log(1/frcpa(1+179/2^-8))
-data8 0x88a129ed4becfaf2 , 0x00003ffe // log(1/frcpa(1+180/2^-8))
-
-data8 0x89451278ecd7f9cf , 0x00003ffe // log(1/frcpa(1+181/2^-8))
-data8 0x89b29295f8432617 , 0x00003ffe // log(1/frcpa(1+182/2^-8))
-data8 0x8a572ac5a5496882 , 0x00003ffe // log(1/frcpa(1+183/2^-8))
-data8 0x8afc2d0ce3b2dadf , 0x00003ffe // log(1/frcpa(1+184/2^-8))
-data8 0x8b6a69c608cfd3af , 0x00003ffe // log(1/frcpa(1+185/2^-8))
-
-data8 0x8c101e106e899a83 , 0x00003ffe // log(1/frcpa(1+186/2^-8))
-data8 0x8cb63de258f9d626 , 0x00003ffe // log(1/frcpa(1+187/2^-8))
-data8 0x8d2539c5bd19e2b1 , 0x00003ffe // log(1/frcpa(1+188/2^-8))
-data8 0x8dcc0e064b29e6f1 , 0x00003ffe // log(1/frcpa(1+189/2^-8))
-data8 0x8e734f45d88357ae , 0x00003ffe // log(1/frcpa(1+190/2^-8))
-
-data8 0x8ee30cef034a20db , 0x00003ffe // log(1/frcpa(1+191/2^-8))
-data8 0x8f8b0515686d1d06 , 0x00003ffe // log(1/frcpa(1+192/2^-8))
-data8 0x90336bba039bf32f , 0x00003ffe // log(1/frcpa(1+193/2^-8))
-data8 0x90a3edd23d1c9d58 , 0x00003ffe // log(1/frcpa(1+194/2^-8))
-data8 0x914d0de2f5d61b32 , 0x00003ffe // log(1/frcpa(1+195/2^-8))
-
-data8 0x91be0c20d28173b5 , 0x00003ffe // log(1/frcpa(1+196/2^-8))
-data8 0x9267e737c06cd34a , 0x00003ffe // log(1/frcpa(1+197/2^-8))
-data8 0x92d962ae6abb1237 , 0x00003ffe // log(1/frcpa(1+198/2^-8))
-data8 0x9383fa6afbe2074c , 0x00003ffe // log(1/frcpa(1+199/2^-8))
-data8 0x942f0421651c1c4e , 0x00003ffe // log(1/frcpa(1+200/2^-8))
-
-data8 0x94a14a3845bb985e , 0x00003ffe // log(1/frcpa(1+201/2^-8))
-data8 0x954d133857f861e7 , 0x00003ffe // log(1/frcpa(1+202/2^-8))
-data8 0x95bfd96468e604c4 , 0x00003ffe // log(1/frcpa(1+203/2^-8))
-data8 0x9632d31cafafa858 , 0x00003ffe // log(1/frcpa(1+204/2^-8))
-data8 0x96dfaabd86fa1647 , 0x00003ffe // log(1/frcpa(1+205/2^-8))
-
-data8 0x9753261fcbb2a594 , 0x00003ffe // log(1/frcpa(1+206/2^-8))
-data8 0x9800c11b426b996d , 0x00003ffe // log(1/frcpa(1+207/2^-8))
-data8 0x9874bf4d45ae663c , 0x00003ffe // log(1/frcpa(1+208/2^-8))
-data8 0x99231f5ee9a74f79 , 0x00003ffe // log(1/frcpa(1+209/2^-8))
-data8 0x9997a18a56bcad28 , 0x00003ffe // log(1/frcpa(1+210/2^-8))
-
-data8 0x9a46c873a3267e79 , 0x00003ffe // log(1/frcpa(1+211/2^-8))
-data8 0x9abbcfc621eb6cb6 , 0x00003ffe // log(1/frcpa(1+212/2^-8))
-data8 0x9b310cb0d354c990 , 0x00003ffe // log(1/frcpa(1+213/2^-8))
-data8 0x9be14cf9e1b3515c , 0x00003ffe // log(1/frcpa(1+214/2^-8))
-data8 0x9c5710b8cbb73a43 , 0x00003ffe // log(1/frcpa(1+215/2^-8))
-
-data8 0x9ccd0abd301f399c , 0x00003ffe // log(1/frcpa(1+216/2^-8))
-data8 0x9d7e67f3bdce8888 , 0x00003ffe // log(1/frcpa(1+217/2^-8))
-data8 0x9df4ea81a99daa01 , 0x00003ffe // log(1/frcpa(1+218/2^-8))
-data8 0x9e6ba405a54514ba , 0x00003ffe // log(1/frcpa(1+219/2^-8))
-data8 0x9f1e21c8c7bb62b3 , 0x00003ffe // log(1/frcpa(1+220/2^-8))
-
-data8 0x9f956593f6b6355c , 0x00003ffe // log(1/frcpa(1+221/2^-8))
-data8 0xa00ce1092e5498c3 , 0x00003ffe // log(1/frcpa(1+222/2^-8))
-data8 0xa0c08309c4b912c1 , 0x00003ffe // log(1/frcpa(1+223/2^-8))
-data8 0xa1388a8c6faa2afa , 0x00003ffe // log(1/frcpa(1+224/2^-8))
-data8 0xa1b0ca7095b5f985 , 0x00003ffe // log(1/frcpa(1+225/2^-8))
-
-data8 0xa22942eb47534a00 , 0x00003ffe // log(1/frcpa(1+226/2^-8))
-data8 0xa2de62326449d0a3 , 0x00003ffe // log(1/frcpa(1+227/2^-8))
-data8 0xa357690f88bfe345 , 0x00003ffe // log(1/frcpa(1+228/2^-8))
-data8 0xa3d0a93f45169a4b , 0x00003ffe // log(1/frcpa(1+229/2^-8))
-data8 0xa44a22f7ffe65f30 , 0x00003ffe // log(1/frcpa(1+230/2^-8))
-
-data8 0xa500c5e5b4c1aa36 , 0x00003ffe // log(1/frcpa(1+231/2^-8))
-data8 0xa57ad064eb2ebbc2 , 0x00003ffe // log(1/frcpa(1+232/2^-8))
-data8 0xa5f5152dedf4384e , 0x00003ffe // log(1/frcpa(1+233/2^-8))
-data8 0xa66f9478856233ec , 0x00003ffe // log(1/frcpa(1+234/2^-8))
-data8 0xa6ea4e7cca02c32e , 0x00003ffe // log(1/frcpa(1+235/2^-8))
-
-data8 0xa765437325341ccf , 0x00003ffe // log(1/frcpa(1+236/2^-8))
-data8 0xa81e21e6c75b4020 , 0x00003ffe // log(1/frcpa(1+237/2^-8))
-data8 0xa899ab333fe2b9ca , 0x00003ffe // log(1/frcpa(1+238/2^-8))
-data8 0xa9157039c51ebe71 , 0x00003ffe // log(1/frcpa(1+239/2^-8))
-data8 0xa991713433c2b999 , 0x00003ffe // log(1/frcpa(1+240/2^-8))
-
-data8 0xaa0dae5cbcc048b3 , 0x00003ffe // log(1/frcpa(1+241/2^-8))
-data8 0xaa8a27ede5eb13ad , 0x00003ffe // log(1/frcpa(1+242/2^-8))
-data8 0xab06de228a9e3499 , 0x00003ffe // log(1/frcpa(1+243/2^-8))
-data8 0xab83d135dc633301 , 0x00003ffe // log(1/frcpa(1+244/2^-8))
-data8 0xac3fb076adc7fe7a , 0x00003ffe // log(1/frcpa(1+245/2^-8))
-
-data8 0xacbd3cbbe47988f1 , 0x00003ffe // log(1/frcpa(1+246/2^-8))
-data8 0xad3b06b1a5dc57c3 , 0x00003ffe // log(1/frcpa(1+247/2^-8))
-data8 0xadb90e94af887717 , 0x00003ffe // log(1/frcpa(1+248/2^-8))
-data8 0xae3754a218f7c816 , 0x00003ffe // log(1/frcpa(1+249/2^-8))
-data8 0xaeb5d9175437afa2 , 0x00003ffe // log(1/frcpa(1+250/2^-8))
-
-data8 0xaf349c322e9c7cee , 0x00003ffe // log(1/frcpa(1+251/2^-8))
-data8 0xafb39e30d1768d1c , 0x00003ffe // log(1/frcpa(1+252/2^-8))
-data8 0xb032df51c2c93116 , 0x00003ffe // log(1/frcpa(1+253/2^-8))
-data8 0xb0b25fd3e6035ad9 , 0x00003ffe // log(1/frcpa(1+254/2^-8))
-data8 0xb1321ff67cba178c , 0x00003ffe // log(1/frcpa(1+255/2^-8))
-ASM_SIZE_DIRECTIVE(log_table_2)
-
-
-.align 32
-.global log#
-.global log10#
+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
+//==============================================================
-// log10 has p7 true, p8 false
-// log has p8 true, p7 false
+// log has p13 true, p14 false
+// log10 has p14 true, p13 false
.section .text
-.proc log10#
-.align 32
-
-log10:
-#ifdef _LIBC
-.global __ieee754_log10
-.type __ieee754_log10,@function
-__ieee754_log10:
-#endif
+GLOBAL_IEEE754_ENTRY(log10)
{ .mfi
- alloc r32=ar.pfs,1,15,4,0
- frcpa.s1 log_C,p9 = f1,f8
- cmp.eq.unc p7,p8 = r0, r0
-}
-{ .mfb
- addl log_AD_1 = @ltoff(log_table_1), gp
- fnorm.s1 log_NORM_f8 = f8
- br.sptk L(LOG_LOG10_X)
+ 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
}
-;;
-
-.endp log10
-ASM_SIZE_DIRECTIVE(log10)
-ASM_SIZE_DIRECTIVE(__ieee754_log10)
-
-
-.section .text
-.proc log#
-.align 32
-log:
-#ifdef _LIBC
-.global __ieee754_log
-.type __ieee754_log,@function
-__ieee754_log:
-#endif
+{ .mlx
+ addl GR_ad_1 = @ltoff(log10_data),gp
+ movl GR_A3 = 0x3fd5555555555557 // double precision memory
+ // representation of A3
+};;
{ .mfi
- alloc r32=ar.pfs,1,15,4,0
- frcpa.s1 log_C,p9 = f1,f8
- cmp.eq.unc p8,p7 = r0, r0
-}
-{ .mfi
- addl log_AD_1 = @ltoff(log_table_1), gp
- fnorm.s1 log_NORM_f8 = f8
- nop.i 999
+ 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)
-L(LOG_LOG10_X):
+GLOBAL_IEEE754_ENTRY(log)
{ .mfi
- ld8 log_AD_1 = [log_AD_1]
- fclass.m.unc p15,p0 = f8, 0x0b // Test for x=unorm
- mov log_GR_fff9 = 0xfff9
-}
-{ .mfi
- mov log_GR_half_exp = 0x0fffe
- fms.s1 log_w = f8,f1,f1
- mov log_GR_exp_17_ones = 0x1ffff
-}
-;;
-
-{ .mmi
- getf.exp log_GR_signexp_f8 = f8 // If x unorm then must recompute
- setf.exp log_half = log_GR_half_exp // Form 0.5 = -Q1
- nop.i 999
-}
-;;
-
-{ .mmb
- adds log_AD_2 = 0x30, log_AD_1
- mov log_GR_exp_16_ones = 0xffff
-(p15) br.cond.spnt L(LOG_DENORM)
-}
-;;
-
-L(LOG_COMMON):
-{.mfi
- ldfpd log_P5,log_P4 = [log_AD_1],16
- fclass.m.unc p6,p0 = f8, 0xc3 // Test for x=nan
- and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
+ getf.exp GR_Exp = f8 // if x is unorm then must recompute
+ frcpa.s1 FR_RcpX,p0 = f1,f8
+ mov GR_05 = 0xfffe
}
-{.mfi
- ldfpd log_P3,log_P2 = [log_AD_2],16
- nop.f 999
- nop.i 999
-}
-;;
+{ .mlx
+ addl GR_ad_1 = @ltoff(log_data),gp
+ movl GR_A3 = 0x3fd5555555555557 // double precision memory
+ // representation of A3
+};;
{ .mfi
- ldfpd log_Q8,log_Q7 = [log_AD_1],16
- fclass.m.unc p11,p0 = f8, 0x21 // Test for x=+inf
- sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
+ 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
- ldfpd log_Q6,log_Q5 = [log_AD_2],16
- nop.f 999
- nop.i 999
-}
-;;
-
+ 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
- ldfpd log_Q4,log_Q3 = [log_AD_1],16
- fma.s1 log_wsq = log_w, log_w, f0
- nop.i 999
-}
-{ .mfb
- ldfpd log_Q2,log_Q1 = [log_AD_2],16
-(p6) fma.d.s0 f8 = f8,f1,f0 // quietize nan result if x=nan
-(p6) br.ret.spnt b0 // Exit for x=nan
+ 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.sig log_int_Nfloat = log_GR_true_exp_f8
- fcmp.eq.s1 p10,p0 = log_NORM_f8, f1 // Test for x=+1.0
- nop.i 999
-}
-{ .mfb
- nop.m 999
- fms.s1 log_r = log_C,f8,f1
-(p11) br.ret.spnt b0 // Exit for x=+inf
-}
-;;
-
-
-{ .mmf
- getf.sig log_GR_significand_f8 = log_NORM_f8
- ldfe log_inv_ln10 = [log_AD_2],16
- fclass.m.unc p6,p0 = f8, 0x07 // Test for x=0
-}
-;;
-
-
-{ .mfb
- nop.m 999
-(p10) fmerge.s f8 = f0, f0
-(p10) br.ret.spnt b0 // Exit for x=1.0
-;;
-}
-
+ setf.exp FR_A2 = GR_05 // create A2
+ fnorm.s1 FR_NormX = f8
+ mov GR_bias = 0xffff
+};;
+
{ .mfi
- getf.exp log_GR_signexp_w = log_w
- fclass.m.unc p12,p0 = f8, 0x3a // Test for x neg norm, unorm, inf
- shl log_GR_index = log_GR_significand_f8,1
+ 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
- ldfe log_log2 = [log_AD_2],16
- fnma.s1 log_rp_q10 = log_half, log_wsq, log_w
- shr.u log_GR_index = log_GR_index,56
+ 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
}
-{ .mfb
- nop.m 999
- fma.s1 log_w3 = log_wsq, log_w, f0
-(p6) br.cond.spnt L(LOG_ZERO_NEG) // Branch if x=0
-;;
-}
-
-
{ .mfi
- and log_GR_exp_w = log_GR_exp_17_ones, log_GR_signexp_w
- fma.s1 log_w4 = log_wsq, log_wsq, f0
- nop.i 999
-}
-{ .mfb
- shladd log_AD_2 = log_GR_index,4,log_AD_2
- fma.s1 log_rsq = log_r, log_r, f0
-(p12) br.cond.spnt L(LOG_ZERO_NEG) // Branch if x<0
-;;
-}
+ 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
- ldfe log_T = [log_AD_2]
- fma.s1 log_rp_p4 = log_P5, log_r, log_P4
- nop.i 999
+ 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
}
-{ .mfi
- nop.m 999
- fma.s1 log_rp_p32 = log_P3, log_r, log_P2
- nop.i 999
-;;
-}
-
+{ .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
- nop.m 999
- fma.s1 log_rp_q7 = log_Q8, log_w, log_Q7
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 log_rp_q65 = log_Q6, log_w, log_Q5
- nop.i 999
-;;
+ 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
+};;
-// p13 <== large w log
-// p14 <== small w log
+// p6 is true if |x-1| < 1/256
+// p7 is true if |x-1| >= 1/256
{ .mfi
-(p8) cmp.ge.unc p13,p14 = log_GR_exp_w, log_GR_fff9
- fma.s1 log_rp_q3 = log_Q4, log_w, log_Q3
- nop.i 999
-;;
-}
+ ldfd FR_Thi = [GR_ad_2]
+(p6) fms.s1 FR_r = f8,f1,f1 // range reduction for |x-1|<1/256
+ nop.i 0
+};;
-// p10 <== large w log10
-// p11 <== small w log10
-{ .mfi
-(p7) cmp.ge.unc p10,p11 = log_GR_exp_w, log_GR_fff9
- fcvt.xf log_Nfloat = log_int_Nfloat
- nop.i 999
+{ .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
- nop.m 999
- fma.s1 log_rp_q21 = log_Q2, log_w3, log_rp_q10
- nop.i 999 ;;
+(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 999
- fma.s1 log_rcube = log_rsq, log_r, f0
- nop.i 999
+ nop.m 0
+ fma.s1 FR_A6 = FR_A7,FR_r,FR_A6 // A7*r+A6
+ nop.i 0
}
{ .mfi
- nop.m 999
- fma.s1 log_rp_p10 = log_rsq, log_P1, log_r
- nop.i 999
-;;
-}
+(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
- nop.m 999
- fcmp.eq.s0 p6,p0 = f8,f0 // Sets flag on +denormal input
- nop.i 999
-}
-{ .mfi
- nop.m 999
- fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32
- nop.i 999
-;;
-}
-
+(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 999
- fma.s1 log_w6 = log_w3, log_w3, f0
- nop.i 999
+ nop.m 0
+ fma.s1 FR_r4 = FR_r2,FR_r2,f0 // r^4
+ nop.i 0
}
{ .mfi
- nop.m 999
- fma.s1 log_Qlo = log_rp_q7, log_wsq, log_rp_q65
- nop.i 999
-}
-;;
+ nop.m 0
+(p8) fma.s1 FR_NxLn2pT = f0,f0,f0 // Clear NxLn2pT if log10 near 1
+ nop.i 0
+};;
{ .mfi
- nop.m 999
- fma.s1 log_Qhi = log_rp_q3, log_w4, log_rp_q21
- nop.i 999 ;;
+ 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 999
- fma.s1 log_T_plus_Nlog2 = log_Nfloat,log_log2, log_T
- nop.i 999 ;;
-}
+ 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
- nop.m 999
- fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10
- nop.i 999 ;;
+(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
+};;
-
-// small w, log <== p14
{ .mfi
- nop.m 999
-(p14) fma.d f8 = log_Qlo, log_w6, log_Qhi
- nop.i 999
+(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 999
- fma.s1 log_Q = log_Qlo, log_w6, log_Qhi
- nop.i 999 ;;
-}
-
+ nop.m 0
+ // (N*Ln2hi+Thi) + (N*Ln2lo+Tlo)
+(p7) fma.s1 FR_NxLn2pT = FR_NxLn2hipThi,f1,FR_NxLn2lopTlo
+ nop.i 0
+};;
{ .mfi
- nop.m 999
-(p10) fma.s1 log_log10_hi = log_T_plus_Nlog2, log_inv_ln10,f0
- nop.i 999 ;;
-}
+(p6) cmp.gt.unc p10, p6 = -40, GR_rexp // Test |x-1| < 2^-40
+ nop.f 0
+ nop.i 0
+};;
-// large w, log <== p13
-.pred.rel "mutex",p13,p10
{ .mfi
- nop.m 999
-(p13) fadd.d f8 = log_T_plus_Nlog2, log_r2P_r
- nop.i 999
-}
-{ .mfi
- nop.m 999
-(p10) fma.s1 log_log10_lo = log_inv_ln10, log_r2P_r,f0
- nop.i 999 ;;
-}
-
+ nop.m 0
+(p10) fma.d.s0 f8 = FR_A32,FR_r2,FR_r // log(x) if |x-1| < 2^-40
+ nop.i 0
+};;
-// small w, log10 <== p11
+.pred.rel "mutex",p6,p9
{ .mfi
- nop.m 999
-(p11) fma.d f8 = log_inv_ln10,log_Q,f0
- nop.i 999 ;;
-}
-
-// large w, log10 <== p10
-{ .mfb
- nop.m 999
-(p10) fma.d f8 = log_log10_hi, f1, log_log10_lo
- br.ret.sptk b0
-;;
+ 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
}
-
-L(LOG_DENORM):
{ .mfb
- getf.exp log_GR_signexp_f8 = log_NORM_f8
- nop.f 999
- br.cond.sptk L(LOG_COMMON)
-}
-;;
-
-L(LOG_ZERO_NEG):
-
-// qnan snan inf norm unorm 0 -+
-// 0 0 0 0 0 1 11 0x7
-// 0 0 1 1 1 0 10 0x3a
-
-// Save x (f8) in f10
-{ .mfi
- nop.m 999
- fmerge.s f10 = f8,f8
- nop.i 999 ;;
-}
-
-// p8 p9 means ln(+-0) = -inf
-// p7 p10 means log(+-0) = -inf
-
-// p13 means ln(-)
-// p14 means log(-)
-
+ 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
+};;
-{ .mfi
- nop.m 999
- fmerge.ns f6 = f1,f1 // Form -1.0
- nop.i 999 ;;
-}
+.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?
+};;
-// p9 means ln(+-0) = -inf
-// p10 means log(+-0) = -inf
-// Log(+-0) = -inf
+{ .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 999
-(p8) fclass.m.unc p9,p0 = f10, 0x07
- nop.i 999
+ 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 999
-(p7) fclass.m.unc p10,p0 = f10, 0x07
- nop.i 999 ;;
-}
-
-
-// p13 ln(-)
-// p14 log(-)
+ nop.m 0
+ fms.s1 FR_tmp = f0,f0,f1 // -1.0
+ nop.i 0
+};;
-// Log(-inf, -normal, -unnormal) = QNAN indefinite
-{ .mfi
- nop.m 999
-(p8) fclass.m.unc p13,p0 = f10, 0x3a
- nop.i 999
-}
+.pred.rel "mutex",p13,p14
{ .mfi
- nop.m 999
-(p7) fclass.m.unc p14,p0 = f10, 0x3a
- nop.i 999 ;;
+(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
+};;
-
-.pred.rel "mutex",p9,p10
-{ .mfi
-(p9) mov log_GR_tag = 2
-(p9) frcpa f8,p11 = f6,f0
- nop.i 999
-}
+.align 32
+log_negatives:
{ .mfi
-(p10) mov log_GR_tag = 8
-(p10) frcpa f8,p12 = f6,f0
- nop.i 999 ;;
-}
+ nop.m 0
+ fmerge.s FR_X = f8,f8
+ nop.i 0
+};;
.pred.rel "mutex",p13,p14
{ .mfi
-(p13) mov log_GR_tag = 3
-(p13) frcpa f8,p11 = f0,f0
- nop.i 999
-}
-{ .mfb
-(p14) mov log_GR_tag = 9
-(p14) frcpa f8,p12 = f0,f0
- br.cond.sptk __libm_error_region ;;
-}
-.endp log
-ASM_SIZE_DIRECTIVE(log)
-ASM_SIZE_DIRECTIVE(__ieee754_log)
-
-
-// Stack operations when calling error support.
-// (1) (2) (3) (call) (4)
-// sp -> + psp -> + psp -> + sp -> +
-// | | | |
-// | | <- GR_Y R3 ->| <- GR_RESULT | -> f8
-// | | | |
-// | <-GR_Y Y2->| Y2 ->| <- GR_Y |
-// | | | |
-// | | <- GR_X X1 ->| |
-// | | | |
-// sp-64 -> + sp -> + sp -> + +
-// save ar.pfs save b0 restore gp
-// save gp restore ar.pfs
+(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)
-.proc __libm_error_region
-__libm_error_region:
+LOCAL_LIBM_ENTRY(__libm_error_region)
.prologue
-
-// (1)
{ .mfi
- add GR_Parameter_Y=-32,sp // Parameter 2 value
+ 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
+ mov GR_SAVE_PFS = ar.pfs // Save ar.pfs
}
{ .mfi
.fframe 64
- add sp=-64,sp // Create new stack
+ add sp = -64,sp // Create new stack
nop.f 0
- mov GR_SAVE_GP=gp // Save gp
+ mov GR_SAVE_GP = gp // Save gp
};;
-
-// (2)
{ .mmi
- stfd [GR_Parameter_Y] = f1,16 // STORE Parameter 2 on stack
+ 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
+ mov GR_SAVE_B0 = b0 // Save b0
};;
.body
-// (3)
{ .mib
- stfd [GR_Parameter_X] = f10 // STORE Parameter 1 on stack
- add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
- nop.b 0
+ 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] = f8 // STORE Parameter 3 on stack
+ 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
+ br.call.sptk b0=__libm_error_support# // Call error handling function
};;
{ .mmi
- nop.m 0
- nop.m 0
add GR_Parameter_RESULT = 48,sp
+ nop.m 0
+ nop.i 0
};;
-// (4)
{ .mmi
- ldfd f8 = [GR_Parameter_RESULT] // Get return result off stack
+ 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
+ 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
+ mov gp = GR_SAVE_GP // Restore gp
+ mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
+ br.ret.sptk b0 // Return
};;
-
-.endp __libm_error_region
-ASM_SIZE_DIRECTIVE(__libm_error_region)
-
+LOCAL_LIBM_END(__libm_error_region)
.type __libm_error_support#,@function
.global __libm_error_support#
+