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-rw-r--r--sysdeps/ia64/fpu/e_logf.S1786
1 files changed, 993 insertions, 793 deletions
diff --git a/sysdeps/ia64/fpu/e_logf.S b/sysdeps/ia64/fpu/e_logf.S
index 829d0abed0..3d11a296cc 100644
--- a/sysdeps/ia64/fpu/e_logf.S
+++ b/sysdeps/ia64/fpu/e_logf.S
@@ -1,10 +1,10 @@
 .file "logf.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
@@ -20,860 +20,1074 @@
 // * 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
 //==============================================================
-// 3/01/00  Initial version
-// 8/15/00  Bundle added after call to __libm_error_support to properly
+// 03/01/00 Initial version
+// 08/15/00 Bundle added after call to __libm_error_support to properly
 //          set [the previously overwritten] GR_Parameter_RESULT.
-// 1/10/01  Improved speed, fixed flags for neg denormals
-//
+// 01/10/01 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
+// 02/10/03 Reordered header: .section, .global, .proc, .align
+// 03/31/05 Reformatted delimiters between data tables
 //
 // API
 //==============================================================
 // float logf(float)
 // float log10f(float)
 //
+//
 // 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).
 //
-// frcpa(x)       = 2^-N frcpa((1.f1 f2 ... f63)
+// 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)
 //
-// -log(frcpa(x)) = -log(C) 
-//                = -log(2^-N) - log(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) 
-//                = +Nlog2 - 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
+//
+// 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)
 //
-// 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(x) =  +Nlog2 + T                     + log(C x)
+// To compute log10(x) we just use identity:
 //
-// Cx = 1 + r
+//  log10(x) = log(x)/log(10)
 //
-// Log(x) =  +Nlog2 + T  + log(1+r)
-// Log(x) =  +Nlog2 + T  + Series( r - r^2/2 + r^3/3 - r^4/4 ....)
+// 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)
 //
-// 1.f1 f2 ... f8 has 256 entries.
-// They are 1 + k/2^8, k = 0 ... 255
-// These 256 values are the table entries.
 //
 // Implementation
-//===============
-// CASE 1:  |x-1| >= 2^-8
-// 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
+// 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 can be used.
 //
-// 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
+// 1. Computation of log(x) for |x-1| >= 1/256
+//   InvX = frcpa(x)
+//   r = InvX*x - 1
+//   P(r) = r*((1 - A2*r) + r^2*(A3 - A4*r)) = r*P2(r),
+//   A4,A3,A2 are created with setf inctruction.
+//   We use Taylor series and so A4 = 1/4, A3 = 1/3,
+//   A2 = 1/2 rounded to double.
 //
-// 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
-
-// CASE 2:  |x-1| < 2^-6
-// w = x - 1
+//   N = float(n) where n is true unbiased exponent of x
 //
-// Form wseries = w + Q1*w^2 + Q2*w^3 + Q3*w^4
+//   T is tabular value of log(1/frcpa(x)) calculated in quad precision
+//   and rounded to double. To T we get bits from 55 to 62 of register
+//   format significand of x and calculate address
+//     ad_T = table_base_addr + 8 * index
 //
-// result = wseries
-
-// Special values 
+//   L2 (1.0 or 1.0/log(10) depending on function) is calculated in quad
+//   precision and rounded to double; it's loaded from memory
+//
+//   L1 (log(2) or log10(2) depending on function) is calculated in quad
+//   precision and rounded to double; it's created with setf.
+//
+//   And final result = P2(r)*(r*L2) + (T + N*L1)
+//
+//
+// 2. Computation of log(x) for |x-1| < 1/256
+//   r = x - 1
+//   P(r) = r*((1 - A2*r) + r^2*(A3 - A4*r)) = r*P2(r),
+//   A4,A3,A2 are the same as in case |x-1| >= 1/256
+//
+//   And final result = P2(r)*(r*L2)
+//
+// 3. How we define is input argument such that |x-1| < 1/256 or not.
+//
+//    To do it we analyze biased exponent and significand of input argment.
+//
+//      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 register format representation with
+//         0xFFFEFF00000000000000 and 0xFFFF8080000000000000 correspondingly.
+//         As far as biased exponent of x here can be equal only to 0xFFFE or
+//         0xFFFF we need to test only last bit of it. Also signifigand always
+//         has implicit bit set to 1 that can be exluded from comparison.
+//         Thus it's quite enough to generate 64-bit integer bits of that are
+//         ix[63] = biased_exponent_of_x[0] and ix[62-0] = significand_of_x[62-0]
+//         and compare it with 0x7F00000000000000 and 0x80800000000000000 (those
+//         obtained like ix from register representatinos of 255/256 and
+//         257/256). This comparison can be made like in a), using unsigned
+//         version of cmp i.e. ix - 0x7F00000000000000 < 0x0180000000000000.
+//         0x0180000000000000 is difference between 0x80800000000000000 and
+//         0x7F00000000000000.
+//
+//    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
-
+//
+// logf(+0)    = -inf
+// logf(-0)    = -inf
+//
+// logf(+qnan) = +qnan
+// logf(-qnan) = -qnan
+// logf(+snan) = +qnan
+// logf(-snan) = -qnan
+//
+// logf(-n)    = QNAN Indefinite
+// logf(-inf)  = QNAN Indefinite
+//
+// logf(+inf)  = +inf
+//
 // Registers used
 //==============================================================
-// Floating Point registers used: 
+// Floating Point registers used:
 // f8, input
-// f9 -> f15,  f32 -> f47
-
-// General registers used:  
-// r32 -> r51
-
+// f12 -> f14,  f33 -> f39
+//
+// General registers used:
+// r8  -> r11
+// r14 -> r19
+//
 // 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
+// p6 -> p12
 
-// 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_P3           = f11 
-log_P2           = f12 
-log_P1           = f13 
-log_inv_ln10     = f14
-log_log2         = f15 
-
-log_w            = f32
-log_T            = f33 
-log_rp_p32       = f34 
-log_rp_p2        = f35 
-log_rp_p10       = f36
-log_rsq          = f37 
-log_T_plus_Nlog2 = f38 
-log_r            = f39
-log_C            = f40
-log_rp_q32       = f41
-log_rp_q2        = f42
-log_rp_q10       = f43
-log_wsq          = f44
-log_Q            = f45
-log_inv_ln10     = f46
-log_NORM_f8      = f47
-
-// ===================================
-
-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_index                     = r39
-log_AD_1                         = r40
-log_GR_signexp_w                 = r41
-log_GR_fff7                      = 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
+GR_TAG                 = r8
+GR_ad_T                = r8
+GR_N                   = r9
+GR_Exp                 = r10
+GR_Sig                 = r11
+
+GR_025                 = r14
+GR_05                  = r15
+GR_A3                  = r16
+GR_Ind                 = r17
+GR_dx                  = r15
+GR_Ln2                 = r19
+GR_de                  = r20
+GR_x                   = r21
+GR_xorg                = r22
+
+GR_SAVE_B0             = r33
+GR_SAVE_PFS            = r34
+GR_SAVE_GP             = r35
+GR_SAVE_SP             = r36
+
+GR_Parameter_X         = r37
+GR_Parameter_Y         = r38
+GR_Parameter_RESULT    = r39
+GR_Parameter_TAG       = r40
+
+
+FR_A2                  = f12
+FR_A3                  = f13
+FR_A4                  = f14
+
+FR_RcpX                = f33
+FR_r                   = f34
+FR_r2                  = f35
+FR_tmp                 = f35
+FR_Ln2                 = f36
+FR_T                   = f37
+FR_N                   = f38
+FR_NxLn2pT             = f38
+FR_NormX               = f39
+FR_InvLn10             = f40
+
+
+FR_Y                   = f1
+FR_X                   = f10
+FR_RESULT              = f8
 
 
 // Data tables
 //==============================================================
-
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
-
+RODATA
 .align 16
-
-log_table_1:
-ASM_TYPE_DIRECTIVE(log_table_1,@object)
-data8 0xbfd0001008f39d59    // p3
-data8 0x3fd5556073e0c45a    // p2
-ASM_SIZE_DIRECTIVE(log_table_1)
-
-log_table_2:
-ASM_TYPE_DIRECTIVE(log_table_2,@object)
-data8 0xbfdffffffffaea15    // p1
-data8 0x3fdbcb7b1526e50e    // 1/ln10
-data8 0x3fe62e42fefa39ef    // Log(2)
-data8 0x0                   // pad
-
-data8 0x3F60040155D5889E    //log(1/frcpa(1+   0/256)
-data8 0x3F78121214586B54    //log(1/frcpa(1+   1/256)
-data8 0x3F841929F96832F0    //log(1/frcpa(1+   2/256)
-data8 0x3F8C317384C75F06    //log(1/frcpa(1+   3/256)
-data8 0x3F91A6B91AC73386    //log(1/frcpa(1+   4/256)
-data8 0x3F95BA9A5D9AC039    //log(1/frcpa(1+   5/256)
-data8 0x3F99D2A8074325F4    //log(1/frcpa(1+   6/256)
-data8 0x3F9D6B2725979802    //log(1/frcpa(1+   7/256)
-data8 0x3FA0C58FA19DFAAA    //log(1/frcpa(1+   8/256)
-data8 0x3FA2954C78CBCE1B    //log(1/frcpa(1+   9/256)
-data8 0x3FA4A94D2DA96C56    //log(1/frcpa(1+  10/256)
-data8 0x3FA67C94F2D4BB58    //log(1/frcpa(1+  11/256)
-data8 0x3FA85188B630F068    //log(1/frcpa(1+  12/256)
-data8 0x3FAA6B8ABE73AF4C    //log(1/frcpa(1+  13/256)
-data8 0x3FAC441E06F72A9E    //log(1/frcpa(1+  14/256)
-data8 0x3FAE1E6713606D07    //log(1/frcpa(1+  15/256)
-data8 0x3FAFFA6911AB9301    //log(1/frcpa(1+  16/256)
-data8 0x3FB0EC139C5DA601    //log(1/frcpa(1+  17/256)
-data8 0x3FB1DBD2643D190B    //log(1/frcpa(1+  18/256)
-data8 0x3FB2CC7284FE5F1C    //log(1/frcpa(1+  19/256)
-data8 0x3FB3BDF5A7D1EE64    //log(1/frcpa(1+  20/256)
-data8 0x3FB4B05D7AA012E0    //log(1/frcpa(1+  21/256)
-data8 0x3FB580DB7CEB5702    //log(1/frcpa(1+  22/256)
-data8 0x3FB674F089365A7A    //log(1/frcpa(1+  23/256)
-data8 0x3FB769EF2C6B568D    //log(1/frcpa(1+  24/256)
-data8 0x3FB85FD927506A48    //log(1/frcpa(1+  25/256)
-data8 0x3FB9335E5D594989    //log(1/frcpa(1+  26/256)
-data8 0x3FBA2B0220C8E5F5    //log(1/frcpa(1+  27/256)
-data8 0x3FBB0004AC1A86AC    //log(1/frcpa(1+  28/256)
-data8 0x3FBBF968769FCA11    //log(1/frcpa(1+  29/256)
-data8 0x3FBCCFEDBFEE13A8    //log(1/frcpa(1+  30/256)
-data8 0x3FBDA727638446A2    //log(1/frcpa(1+  31/256)
-data8 0x3FBEA3257FE10F7A    //log(1/frcpa(1+  32/256)
-data8 0x3FBF7BE9FEDBFDE6    //log(1/frcpa(1+  33/256)
-data8 0x3FC02AB352FF25F4    //log(1/frcpa(1+  34/256)
-data8 0x3FC097CE579D204D    //log(1/frcpa(1+  35/256)
-data8 0x3FC1178E8227E47C    //log(1/frcpa(1+  36/256)
-data8 0x3FC185747DBECF34    //log(1/frcpa(1+  37/256)
-data8 0x3FC1F3B925F25D41    //log(1/frcpa(1+  38/256)
-data8 0x3FC2625D1E6DDF57    //log(1/frcpa(1+  39/256)
-data8 0x3FC2D1610C86813A    //log(1/frcpa(1+  40/256)
-data8 0x3FC340C59741142E    //log(1/frcpa(1+  41/256)
-data8 0x3FC3B08B6757F2A9    //log(1/frcpa(1+  42/256)
-data8 0x3FC40DFB08378003    //log(1/frcpa(1+  43/256)
-data8 0x3FC47E74E8CA5F7C    //log(1/frcpa(1+  44/256)
-data8 0x3FC4EF51F6466DE4    //log(1/frcpa(1+  45/256)
-data8 0x3FC56092E02BA516    //log(1/frcpa(1+  46/256)
-data8 0x3FC5D23857CD74D5    //log(1/frcpa(1+  47/256)
-data8 0x3FC6313A37335D76    //log(1/frcpa(1+  48/256)
-data8 0x3FC6A399DABBD383    //log(1/frcpa(1+  49/256)
-data8 0x3FC70337DD3CE41B    //log(1/frcpa(1+  50/256)
-data8 0x3FC77654128F6127    //log(1/frcpa(1+  51/256)
-data8 0x3FC7E9D82A0B022D    //log(1/frcpa(1+  52/256)
-data8 0x3FC84A6B759F512F    //log(1/frcpa(1+  53/256)
-data8 0x3FC8AB47D5F5A310    //log(1/frcpa(1+  54/256)
-data8 0x3FC91FE49096581B    //log(1/frcpa(1+  55/256)
-data8 0x3FC981634011AA75    //log(1/frcpa(1+  56/256)
-data8 0x3FC9F6C407089664    //log(1/frcpa(1+  57/256)
-data8 0x3FCA58E729348F43    //log(1/frcpa(1+  58/256)
-data8 0x3FCABB55C31693AD    //log(1/frcpa(1+  59/256)
-data8 0x3FCB1E104919EFD0    //log(1/frcpa(1+  60/256)
-data8 0x3FCB94EE93E367CB    //log(1/frcpa(1+  61/256)
-data8 0x3FCBF851C067555F    //log(1/frcpa(1+  62/256)
-data8 0x3FCC5C0254BF23A6    //log(1/frcpa(1+  63/256)
-data8 0x3FCCC000C9DB3C52    //log(1/frcpa(1+  64/256)
-data8 0x3FCD244D99C85674    //log(1/frcpa(1+  65/256)
-data8 0x3FCD88E93FB2F450    //log(1/frcpa(1+  66/256)
-data8 0x3FCDEDD437EAEF01    //log(1/frcpa(1+  67/256)
-data8 0x3FCE530EFFE71012    //log(1/frcpa(1+  68/256)
-data8 0x3FCEB89A1648B971    //log(1/frcpa(1+  69/256)
-data8 0x3FCF1E75FADF9BDE    //log(1/frcpa(1+  70/256)
-data8 0x3FCF84A32EAD7C35    //log(1/frcpa(1+  71/256)
-data8 0x3FCFEB2233EA07CD    //log(1/frcpa(1+  72/256)
-data8 0x3FD028F9C7035C1C    //log(1/frcpa(1+  73/256)
-data8 0x3FD05C8BE0D9635A    //log(1/frcpa(1+  74/256)
-data8 0x3FD085EB8F8AE797    //log(1/frcpa(1+  75/256)
-data8 0x3FD0B9C8E32D1911    //log(1/frcpa(1+  76/256)
-data8 0x3FD0EDD060B78081    //log(1/frcpa(1+  77/256)
-data8 0x3FD122024CF0063F    //log(1/frcpa(1+  78/256)
-data8 0x3FD14BE2927AECD4    //log(1/frcpa(1+  79/256)
-data8 0x3FD180618EF18ADF    //log(1/frcpa(1+  80/256)
-data8 0x3FD1B50BBE2FC63B    //log(1/frcpa(1+  81/256)
-data8 0x3FD1DF4CC7CF242D    //log(1/frcpa(1+  82/256)
-data8 0x3FD214456D0EB8D4    //log(1/frcpa(1+  83/256)
-data8 0x3FD23EC5991EBA49    //log(1/frcpa(1+  84/256)
-data8 0x3FD2740D9F870AFB    //log(1/frcpa(1+  85/256)
-data8 0x3FD29ECDABCDFA04    //log(1/frcpa(1+  86/256)
-data8 0x3FD2D46602ADCCEE    //log(1/frcpa(1+  87/256)
-data8 0x3FD2FF66B04EA9D4    //log(1/frcpa(1+  88/256)
-data8 0x3FD335504B355A37    //log(1/frcpa(1+  89/256)
-data8 0x3FD360925EC44F5D    //log(1/frcpa(1+  90/256)
-data8 0x3FD38BF1C3337E75    //log(1/frcpa(1+  91/256)
-data8 0x3FD3C25277333184    //log(1/frcpa(1+  92/256)
-data8 0x3FD3EDF463C1683E    //log(1/frcpa(1+  93/256)
-data8 0x3FD419B423D5E8C7    //log(1/frcpa(1+  94/256)
-data8 0x3FD44591E0539F49    //log(1/frcpa(1+  95/256)
-data8 0x3FD47C9175B6F0AD    //log(1/frcpa(1+  96/256)
-data8 0x3FD4A8B341552B09    //log(1/frcpa(1+  97/256)
-data8 0x3FD4D4F3908901A0    //log(1/frcpa(1+  98/256)
-data8 0x3FD501528DA1F968    //log(1/frcpa(1+  99/256)
-data8 0x3FD52DD06347D4F6    //log(1/frcpa(1+ 100/256)
-data8 0x3FD55A6D3C7B8A8A    //log(1/frcpa(1+ 101/256)
-data8 0x3FD5925D2B112A59    //log(1/frcpa(1+ 102/256)
-data8 0x3FD5BF406B543DB2    //log(1/frcpa(1+ 103/256)
-data8 0x3FD5EC433D5C35AE    //log(1/frcpa(1+ 104/256)
-data8 0x3FD61965CDB02C1F    //log(1/frcpa(1+ 105/256)
-data8 0x3FD646A84935B2A2    //log(1/frcpa(1+ 106/256)
-data8 0x3FD6740ADD31DE94    //log(1/frcpa(1+ 107/256)
-data8 0x3FD6A18DB74A58C5    //log(1/frcpa(1+ 108/256)
-data8 0x3FD6CF31058670EC    //log(1/frcpa(1+ 109/256)
-data8 0x3FD6F180E852F0BA    //log(1/frcpa(1+ 110/256)
-data8 0x3FD71F5D71B894F0    //log(1/frcpa(1+ 111/256)
-data8 0x3FD74D5AEFD66D5C    //log(1/frcpa(1+ 112/256)
-data8 0x3FD77B79922BD37E    //log(1/frcpa(1+ 113/256)
-data8 0x3FD7A9B9889F19E2    //log(1/frcpa(1+ 114/256)
-data8 0x3FD7D81B037EB6A6    //log(1/frcpa(1+ 115/256)
-data8 0x3FD8069E33827231    //log(1/frcpa(1+ 116/256)
-data8 0x3FD82996D3EF8BCB    //log(1/frcpa(1+ 117/256)
-data8 0x3FD85855776DCBFB    //log(1/frcpa(1+ 118/256)
-data8 0x3FD8873658327CCF    //log(1/frcpa(1+ 119/256)
-data8 0x3FD8AA75973AB8CF    //log(1/frcpa(1+ 120/256)
-data8 0x3FD8D992DC8824E5    //log(1/frcpa(1+ 121/256)
-data8 0x3FD908D2EA7D9512    //log(1/frcpa(1+ 122/256)
-data8 0x3FD92C59E79C0E56    //log(1/frcpa(1+ 123/256)
-data8 0x3FD95BD750EE3ED3    //log(1/frcpa(1+ 124/256)
-data8 0x3FD98B7811A3EE5B    //log(1/frcpa(1+ 125/256)
-data8 0x3FD9AF47F33D406C    //log(1/frcpa(1+ 126/256)
-data8 0x3FD9DF270C1914A8    //log(1/frcpa(1+ 127/256)
-data8 0x3FDA0325ED14FDA4    //log(1/frcpa(1+ 128/256)
-data8 0x3FDA33440224FA79    //log(1/frcpa(1+ 129/256)
-data8 0x3FDA57725E80C383    //log(1/frcpa(1+ 130/256)
-data8 0x3FDA87D0165DD199    //log(1/frcpa(1+ 131/256)
-data8 0x3FDAAC2E6C03F896    //log(1/frcpa(1+ 132/256)
-data8 0x3FDADCCC6FDF6A81    //log(1/frcpa(1+ 133/256)
-data8 0x3FDB015B3EB1E790    //log(1/frcpa(1+ 134/256)
-data8 0x3FDB323A3A635948    //log(1/frcpa(1+ 135/256)
-data8 0x3FDB56FA04462909    //log(1/frcpa(1+ 136/256)
-data8 0x3FDB881AA659BC93    //log(1/frcpa(1+ 137/256)
-data8 0x3FDBAD0BEF3DB165    //log(1/frcpa(1+ 138/256)
-data8 0x3FDBD21297781C2F    //log(1/frcpa(1+ 139/256)
-data8 0x3FDC039236F08819    //log(1/frcpa(1+ 140/256)
-data8 0x3FDC28CB1E4D32FD    //log(1/frcpa(1+ 141/256)
-data8 0x3FDC4E19B84723C2    //log(1/frcpa(1+ 142/256)
-data8 0x3FDC7FF9C74554C9    //log(1/frcpa(1+ 143/256)
-data8 0x3FDCA57B64E9DB05    //log(1/frcpa(1+ 144/256)
-data8 0x3FDCCB130A5CEBB0    //log(1/frcpa(1+ 145/256)
-data8 0x3FDCF0C0D18F326F    //log(1/frcpa(1+ 146/256)
-data8 0x3FDD232075B5A201    //log(1/frcpa(1+ 147/256)
-data8 0x3FDD490246DEFA6B    //log(1/frcpa(1+ 148/256)
-data8 0x3FDD6EFA918D25CD    //log(1/frcpa(1+ 149/256)
-data8 0x3FDD9509707AE52F    //log(1/frcpa(1+ 150/256)
-data8 0x3FDDBB2EFE92C554    //log(1/frcpa(1+ 151/256)
-data8 0x3FDDEE2F3445E4AF    //log(1/frcpa(1+ 152/256)
-data8 0x3FDE148A1A2726CE    //log(1/frcpa(1+ 153/256)
-data8 0x3FDE3AFC0A49FF40    //log(1/frcpa(1+ 154/256)
-data8 0x3FDE6185206D516E    //log(1/frcpa(1+ 155/256)
-data8 0x3FDE882578823D52    //log(1/frcpa(1+ 156/256)
-data8 0x3FDEAEDD2EAC990C    //log(1/frcpa(1+ 157/256)
-data8 0x3FDED5AC5F436BE3    //log(1/frcpa(1+ 158/256)
-data8 0x3FDEFC9326D16AB9    //log(1/frcpa(1+ 159/256)
-data8 0x3FDF2391A2157600    //log(1/frcpa(1+ 160/256)
-data8 0x3FDF4AA7EE03192D    //log(1/frcpa(1+ 161/256)
-data8 0x3FDF71D627C30BB0    //log(1/frcpa(1+ 162/256)
-data8 0x3FDF991C6CB3B379    //log(1/frcpa(1+ 163/256)
-data8 0x3FDFC07ADA69A910    //log(1/frcpa(1+ 164/256)
-data8 0x3FDFE7F18EB03D3E    //log(1/frcpa(1+ 165/256)
-data8 0x3FE007C053C5002E    //log(1/frcpa(1+ 166/256)
-data8 0x3FE01B942198A5A1    //log(1/frcpa(1+ 167/256)
-data8 0x3FE02F74400C64EB    //log(1/frcpa(1+ 168/256)
-data8 0x3FE04360BE7603AD    //log(1/frcpa(1+ 169/256)
-data8 0x3FE05759AC47FE34    //log(1/frcpa(1+ 170/256)
-data8 0x3FE06B5F1911CF52    //log(1/frcpa(1+ 171/256)
-data8 0x3FE078BF0533C568    //log(1/frcpa(1+ 172/256)
-data8 0x3FE08CD9687E7B0E    //log(1/frcpa(1+ 173/256)
-data8 0x3FE0A10074CF9019    //log(1/frcpa(1+ 174/256)
-data8 0x3FE0B5343A234477    //log(1/frcpa(1+ 175/256)
-data8 0x3FE0C974C89431CE    //log(1/frcpa(1+ 176/256)
-data8 0x3FE0DDC2305B9886    //log(1/frcpa(1+ 177/256)
-data8 0x3FE0EB524BAFC918    //log(1/frcpa(1+ 178/256)
-data8 0x3FE0FFB54213A476    //log(1/frcpa(1+ 179/256)
-data8 0x3FE114253DA97D9F    //log(1/frcpa(1+ 180/256)
-data8 0x3FE128A24F1D9AFF    //log(1/frcpa(1+ 181/256)
-data8 0x3FE1365252BF0865    //log(1/frcpa(1+ 182/256)
-data8 0x3FE14AE558B4A92D    //log(1/frcpa(1+ 183/256)
-data8 0x3FE15F85A19C765B    //log(1/frcpa(1+ 184/256)
-data8 0x3FE16D4D38C119FA    //log(1/frcpa(1+ 185/256)
-data8 0x3FE18203C20DD133    //log(1/frcpa(1+ 186/256)
-data8 0x3FE196C7BC4B1F3B    //log(1/frcpa(1+ 187/256)
-data8 0x3FE1A4A738B7A33C    //log(1/frcpa(1+ 188/256)
-data8 0x3FE1B981C0C9653D    //log(1/frcpa(1+ 189/256)
-data8 0x3FE1CE69E8BB106B    //log(1/frcpa(1+ 190/256)
-data8 0x3FE1DC619DE06944    //log(1/frcpa(1+ 191/256)
-data8 0x3FE1F160A2AD0DA4    //log(1/frcpa(1+ 192/256)
-data8 0x3FE2066D7740737E    //log(1/frcpa(1+ 193/256)
-data8 0x3FE2147DBA47A394    //log(1/frcpa(1+ 194/256)
-data8 0x3FE229A1BC5EBAC3    //log(1/frcpa(1+ 195/256)
-data8 0x3FE237C1841A502E    //log(1/frcpa(1+ 196/256)
-data8 0x3FE24CFCE6F80D9A    //log(1/frcpa(1+ 197/256)
-data8 0x3FE25B2C55CD5762    //log(1/frcpa(1+ 198/256)
-data8 0x3FE2707F4D5F7C41    //log(1/frcpa(1+ 199/256)
-data8 0x3FE285E0842CA384    //log(1/frcpa(1+ 200/256)
-data8 0x3FE294294708B773    //log(1/frcpa(1+ 201/256)
-data8 0x3FE2A9A2670AFF0C    //log(1/frcpa(1+ 202/256)
-data8 0x3FE2B7FB2C8D1CC1    //log(1/frcpa(1+ 203/256)
-data8 0x3FE2C65A6395F5F5    //log(1/frcpa(1+ 204/256)
-data8 0x3FE2DBF557B0DF43    //log(1/frcpa(1+ 205/256)
-data8 0x3FE2EA64C3F97655    //log(1/frcpa(1+ 206/256)
-data8 0x3FE3001823684D73    //log(1/frcpa(1+ 207/256)
-data8 0x3FE30E97E9A8B5CD    //log(1/frcpa(1+ 208/256)
-data8 0x3FE32463EBDD34EA    //log(1/frcpa(1+ 209/256)
-data8 0x3FE332F4314AD796    //log(1/frcpa(1+ 210/256)
-data8 0x3FE348D90E7464D0    //log(1/frcpa(1+ 211/256)
-data8 0x3FE35779F8C43D6E    //log(1/frcpa(1+ 212/256)
-data8 0x3FE36621961A6A99    //log(1/frcpa(1+ 213/256)
-data8 0x3FE37C299F3C366A    //log(1/frcpa(1+ 214/256)
-data8 0x3FE38AE2171976E7    //log(1/frcpa(1+ 215/256)
-data8 0x3FE399A157A603E7    //log(1/frcpa(1+ 216/256)
-data8 0x3FE3AFCCFE77B9D1    //log(1/frcpa(1+ 217/256)
-data8 0x3FE3BE9D503533B5    //log(1/frcpa(1+ 218/256)
-data8 0x3FE3CD7480B4A8A3    //log(1/frcpa(1+ 219/256)
-data8 0x3FE3E3C43918F76C    //log(1/frcpa(1+ 220/256)
-data8 0x3FE3F2ACB27ED6C7    //log(1/frcpa(1+ 221/256)
-data8 0x3FE4019C2125CA93    //log(1/frcpa(1+ 222/256)
-data8 0x3FE4181061389722    //log(1/frcpa(1+ 223/256)
-data8 0x3FE42711518DF545    //log(1/frcpa(1+ 224/256)
-data8 0x3FE436194E12B6BF    //log(1/frcpa(1+ 225/256)
-data8 0x3FE445285D68EA69    //log(1/frcpa(1+ 226/256)
-data8 0x3FE45BCC464C893A    //log(1/frcpa(1+ 227/256)
-data8 0x3FE46AED21F117FC    //log(1/frcpa(1+ 228/256)
-data8 0x3FE47A1527E8A2D3    //log(1/frcpa(1+ 229/256)
-data8 0x3FE489445EFFFCCC    //log(1/frcpa(1+ 230/256)
-data8 0x3FE4A018BCB69835    //log(1/frcpa(1+ 231/256)
-data8 0x3FE4AF5A0C9D65D7    //log(1/frcpa(1+ 232/256)
-data8 0x3FE4BEA2A5BDBE87    //log(1/frcpa(1+ 233/256)
-data8 0x3FE4CDF28F10AC46    //log(1/frcpa(1+ 234/256)
-data8 0x3FE4DD49CF994058    //log(1/frcpa(1+ 235/256)
-data8 0x3FE4ECA86E64A684    //log(1/frcpa(1+ 236/256)
-data8 0x3FE503C43CD8EB68    //log(1/frcpa(1+ 237/256)
-data8 0x3FE513356667FC57    //log(1/frcpa(1+ 238/256)
-data8 0x3FE522AE0738A3D8    //log(1/frcpa(1+ 239/256)
-data8 0x3FE5322E26867857    //log(1/frcpa(1+ 240/256)
-data8 0x3FE541B5CB979809    //log(1/frcpa(1+ 241/256)
-data8 0x3FE55144FDBCBD62    //log(1/frcpa(1+ 242/256)
-data8 0x3FE560DBC45153C7    //log(1/frcpa(1+ 243/256)
-data8 0x3FE5707A26BB8C66    //log(1/frcpa(1+ 244/256)
-data8 0x3FE587F60ED5B900    //log(1/frcpa(1+ 245/256)
-data8 0x3FE597A7977C8F31    //log(1/frcpa(1+ 246/256)
-data8 0x3FE5A760D634BB8B    //log(1/frcpa(1+ 247/256)
-data8 0x3FE5B721D295F10F    //log(1/frcpa(1+ 248/256)
-data8 0x3FE5C6EA94431EF9    //log(1/frcpa(1+ 249/256)
-data8 0x3FE5D6BB22EA86F6    //log(1/frcpa(1+ 250/256)
-data8 0x3FE5E6938645D390    //log(1/frcpa(1+ 251/256)
-data8 0x3FE5F673C61A2ED2    //log(1/frcpa(1+ 252/256)
-data8 0x3FE6065BEA385926    //log(1/frcpa(1+ 253/256)
-data8 0x3FE6164BFA7CC06B    //log(1/frcpa(1+ 254/256)
-data8 0x3FE62643FECF9743    //log(1/frcpa(1+ 255/256)
-ASM_SIZE_DIRECTIVE(log_table_2)
-
-   
-.align 32
-.global logf#
-.global log10f#
-
-// log10 has p7 true, p8 false
-// log   has p8 true, p7 false
-
+LOCAL_OBJECT_START(logf_data)
+data8 0x3FF0000000000000 // 1.0
+//
+// ln(1/frcpa(1+i/256)), i=0...255
+data8 0x3F60040155D5889E // 0
+data8 0x3F78121214586B54 // 1
+data8 0x3F841929F96832F0 // 2
+data8 0x3F8C317384C75F06 // 3
+data8 0x3F91A6B91AC73386 // 4
+data8 0x3F95BA9A5D9AC039 // 5
+data8 0x3F99D2A8074325F4 // 6
+data8 0x3F9D6B2725979802 // 7
+data8 0x3FA0C58FA19DFAAA // 8
+data8 0x3FA2954C78CBCE1B // 9
+data8 0x3FA4A94D2DA96C56 // 10
+data8 0x3FA67C94F2D4BB58 // 11
+data8 0x3FA85188B630F068 // 12
+data8 0x3FAA6B8ABE73AF4C // 13
+data8 0x3FAC441E06F72A9E // 14
+data8 0x3FAE1E6713606D07 // 15
+data8 0x3FAFFA6911AB9301 // 16
+data8 0x3FB0EC139C5DA601 // 17
+data8 0x3FB1DBD2643D190B // 18
+data8 0x3FB2CC7284FE5F1C // 19
+data8 0x3FB3BDF5A7D1EE64 // 20
+data8 0x3FB4B05D7AA012E0 // 21
+data8 0x3FB580DB7CEB5702 // 22
+data8 0x3FB674F089365A7A // 23
+data8 0x3FB769EF2C6B568D // 24
+data8 0x3FB85FD927506A48 // 25
+data8 0x3FB9335E5D594989 // 26
+data8 0x3FBA2B0220C8E5F5 // 27
+data8 0x3FBB0004AC1A86AC // 28
+data8 0x3FBBF968769FCA11 // 29
+data8 0x3FBCCFEDBFEE13A8 // 30
+data8 0x3FBDA727638446A2 // 31
+data8 0x3FBEA3257FE10F7A // 32
+data8 0x3FBF7BE9FEDBFDE6 // 33
+data8 0x3FC02AB352FF25F4 // 34
+data8 0x3FC097CE579D204D // 35
+data8 0x3FC1178E8227E47C // 36
+data8 0x3FC185747DBECF34 // 37
+data8 0x3FC1F3B925F25D41 // 38
+data8 0x3FC2625D1E6DDF57 // 39
+data8 0x3FC2D1610C86813A // 40
+data8 0x3FC340C59741142E // 41
+data8 0x3FC3B08B6757F2A9 // 42
+data8 0x3FC40DFB08378003 // 43
+data8 0x3FC47E74E8CA5F7C // 44
+data8 0x3FC4EF51F6466DE4 // 45
+data8 0x3FC56092E02BA516 // 46
+data8 0x3FC5D23857CD74D5 // 47
+data8 0x3FC6313A37335D76 // 48
+data8 0x3FC6A399DABBD383 // 49
+data8 0x3FC70337DD3CE41B // 50
+data8 0x3FC77654128F6127 // 51
+data8 0x3FC7E9D82A0B022D // 52
+data8 0x3FC84A6B759F512F // 53
+data8 0x3FC8AB47D5F5A310 // 54
+data8 0x3FC91FE49096581B // 55
+data8 0x3FC981634011AA75 // 56
+data8 0x3FC9F6C407089664 // 57
+data8 0x3FCA58E729348F43 // 58
+data8 0x3FCABB55C31693AD // 59
+data8 0x3FCB1E104919EFD0 // 60
+data8 0x3FCB94EE93E367CB // 61
+data8 0x3FCBF851C067555F // 62
+data8 0x3FCC5C0254BF23A6 // 63
+data8 0x3FCCC000C9DB3C52 // 64
+data8 0x3FCD244D99C85674 // 65
+data8 0x3FCD88E93FB2F450 // 66
+data8 0x3FCDEDD437EAEF01 // 67
+data8 0x3FCE530EFFE71012 // 68
+data8 0x3FCEB89A1648B971 // 69
+data8 0x3FCF1E75FADF9BDE // 70
+data8 0x3FCF84A32EAD7C35 // 71
+data8 0x3FCFEB2233EA07CD // 72
+data8 0x3FD028F9C7035C1C // 73
+data8 0x3FD05C8BE0D9635A // 74
+data8 0x3FD085EB8F8AE797 // 75
+data8 0x3FD0B9C8E32D1911 // 76
+data8 0x3FD0EDD060B78081 // 77
+data8 0x3FD122024CF0063F // 78
+data8 0x3FD14BE2927AECD4 // 79
+data8 0x3FD180618EF18ADF // 80
+data8 0x3FD1B50BBE2FC63B // 81
+data8 0x3FD1DF4CC7CF242D // 82
+data8 0x3FD214456D0EB8D4 // 83
+data8 0x3FD23EC5991EBA49 // 84
+data8 0x3FD2740D9F870AFB // 85
+data8 0x3FD29ECDABCDFA04 // 86
+data8 0x3FD2D46602ADCCEE // 87
+data8 0x3FD2FF66B04EA9D4 // 88
+data8 0x3FD335504B355A37 // 89
+data8 0x3FD360925EC44F5D // 90
+data8 0x3FD38BF1C3337E75 // 91
+data8 0x3FD3C25277333184 // 92
+data8 0x3FD3EDF463C1683E // 93
+data8 0x3FD419B423D5E8C7 // 94
+data8 0x3FD44591E0539F49 // 95
+data8 0x3FD47C9175B6F0AD // 96
+data8 0x3FD4A8B341552B09 // 97
+data8 0x3FD4D4F3908901A0 // 98
+data8 0x3FD501528DA1F968 // 99
+data8 0x3FD52DD06347D4F6 // 100
+data8 0x3FD55A6D3C7B8A8A // 101
+data8 0x3FD5925D2B112A59 // 102
+data8 0x3FD5BF406B543DB2 // 103
+data8 0x3FD5EC433D5C35AE // 104
+data8 0x3FD61965CDB02C1F // 105
+data8 0x3FD646A84935B2A2 // 106
+data8 0x3FD6740ADD31DE94 // 107
+data8 0x3FD6A18DB74A58C5 // 108
+data8 0x3FD6CF31058670EC // 109
+data8 0x3FD6F180E852F0BA // 110
+data8 0x3FD71F5D71B894F0 // 111
+data8 0x3FD74D5AEFD66D5C // 112
+data8 0x3FD77B79922BD37E // 113
+data8 0x3FD7A9B9889F19E2 // 114
+data8 0x3FD7D81B037EB6A6 // 115
+data8 0x3FD8069E33827231 // 116
+data8 0x3FD82996D3EF8BCB // 117
+data8 0x3FD85855776DCBFB // 118
+data8 0x3FD8873658327CCF // 119
+data8 0x3FD8AA75973AB8CF // 120
+data8 0x3FD8D992DC8824E5 // 121
+data8 0x3FD908D2EA7D9512 // 122
+data8 0x3FD92C59E79C0E56 // 123
+data8 0x3FD95BD750EE3ED3 // 124
+data8 0x3FD98B7811A3EE5B // 125
+data8 0x3FD9AF47F33D406C // 126
+data8 0x3FD9DF270C1914A8 // 127
+data8 0x3FDA0325ED14FDA4 // 128
+data8 0x3FDA33440224FA79 // 129
+data8 0x3FDA57725E80C383 // 130
+data8 0x3FDA87D0165DD199 // 131
+data8 0x3FDAAC2E6C03F896 // 132
+data8 0x3FDADCCC6FDF6A81 // 133
+data8 0x3FDB015B3EB1E790 // 134
+data8 0x3FDB323A3A635948 // 135
+data8 0x3FDB56FA04462909 // 136
+data8 0x3FDB881AA659BC93 // 137
+data8 0x3FDBAD0BEF3DB165 // 138
+data8 0x3FDBD21297781C2F // 139
+data8 0x3FDC039236F08819 // 140
+data8 0x3FDC28CB1E4D32FD // 141
+data8 0x3FDC4E19B84723C2 // 142
+data8 0x3FDC7FF9C74554C9 // 143
+data8 0x3FDCA57B64E9DB05 // 144
+data8 0x3FDCCB130A5CEBB0 // 145
+data8 0x3FDCF0C0D18F326F // 146
+data8 0x3FDD232075B5A201 // 147
+data8 0x3FDD490246DEFA6B // 148
+data8 0x3FDD6EFA918D25CD // 149
+data8 0x3FDD9509707AE52F // 150
+data8 0x3FDDBB2EFE92C554 // 151
+data8 0x3FDDEE2F3445E4AF // 152
+data8 0x3FDE148A1A2726CE // 153
+data8 0x3FDE3AFC0A49FF40 // 154
+data8 0x3FDE6185206D516E // 155
+data8 0x3FDE882578823D52 // 156
+data8 0x3FDEAEDD2EAC990C // 157
+data8 0x3FDED5AC5F436BE3 // 158
+data8 0x3FDEFC9326D16AB9 // 159
+data8 0x3FDF2391A2157600 // 160
+data8 0x3FDF4AA7EE03192D // 161
+data8 0x3FDF71D627C30BB0 // 162
+data8 0x3FDF991C6CB3B379 // 163
+data8 0x3FDFC07ADA69A910 // 164
+data8 0x3FDFE7F18EB03D3E // 165
+data8 0x3FE007C053C5002E // 166
+data8 0x3FE01B942198A5A1 // 167
+data8 0x3FE02F74400C64EB // 168
+data8 0x3FE04360BE7603AD // 169
+data8 0x3FE05759AC47FE34 // 170
+data8 0x3FE06B5F1911CF52 // 171
+data8 0x3FE078BF0533C568 // 172
+data8 0x3FE08CD9687E7B0E // 173
+data8 0x3FE0A10074CF9019 // 174
+data8 0x3FE0B5343A234477 // 175
+data8 0x3FE0C974C89431CE // 176
+data8 0x3FE0DDC2305B9886 // 177
+data8 0x3FE0EB524BAFC918 // 178
+data8 0x3FE0FFB54213A476 // 179
+data8 0x3FE114253DA97D9F // 180
+data8 0x3FE128A24F1D9AFF // 181
+data8 0x3FE1365252BF0865 // 182
+data8 0x3FE14AE558B4A92D // 183
+data8 0x3FE15F85A19C765B // 184
+data8 0x3FE16D4D38C119FA // 185
+data8 0x3FE18203C20DD133 // 186
+data8 0x3FE196C7BC4B1F3B // 187
+data8 0x3FE1A4A738B7A33C // 188
+data8 0x3FE1B981C0C9653D // 189
+data8 0x3FE1CE69E8BB106B // 190
+data8 0x3FE1DC619DE06944 // 191
+data8 0x3FE1F160A2AD0DA4 // 192
+data8 0x3FE2066D7740737E // 193
+data8 0x3FE2147DBA47A394 // 194
+data8 0x3FE229A1BC5EBAC3 // 195
+data8 0x3FE237C1841A502E // 196
+data8 0x3FE24CFCE6F80D9A // 197
+data8 0x3FE25B2C55CD5762 // 198
+data8 0x3FE2707F4D5F7C41 // 199
+data8 0x3FE285E0842CA384 // 200
+data8 0x3FE294294708B773 // 201
+data8 0x3FE2A9A2670AFF0C // 202
+data8 0x3FE2B7FB2C8D1CC1 // 203
+data8 0x3FE2C65A6395F5F5 // 204
+data8 0x3FE2DBF557B0DF43 // 205
+data8 0x3FE2EA64C3F97655 // 206
+data8 0x3FE3001823684D73 // 207
+data8 0x3FE30E97E9A8B5CD // 208
+data8 0x3FE32463EBDD34EA // 209
+data8 0x3FE332F4314AD796 // 210
+data8 0x3FE348D90E7464D0 // 211
+data8 0x3FE35779F8C43D6E // 212
+data8 0x3FE36621961A6A99 // 213
+data8 0x3FE37C299F3C366A // 214
+data8 0x3FE38AE2171976E7 // 215
+data8 0x3FE399A157A603E7 // 216
+data8 0x3FE3AFCCFE77B9D1 // 217
+data8 0x3FE3BE9D503533B5 // 218
+data8 0x3FE3CD7480B4A8A3 // 219
+data8 0x3FE3E3C43918F76C // 220
+data8 0x3FE3F2ACB27ED6C7 // 221
+data8 0x3FE4019C2125CA93 // 222
+data8 0x3FE4181061389722 // 223
+data8 0x3FE42711518DF545 // 224
+data8 0x3FE436194E12B6BF // 225
+data8 0x3FE445285D68EA69 // 226
+data8 0x3FE45BCC464C893A // 227
+data8 0x3FE46AED21F117FC // 228
+data8 0x3FE47A1527E8A2D3 // 229
+data8 0x3FE489445EFFFCCC // 230
+data8 0x3FE4A018BCB69835 // 231
+data8 0x3FE4AF5A0C9D65D7 // 232
+data8 0x3FE4BEA2A5BDBE87 // 233
+data8 0x3FE4CDF28F10AC46 // 234
+data8 0x3FE4DD49CF994058 // 235
+data8 0x3FE4ECA86E64A684 // 236
+data8 0x3FE503C43CD8EB68 // 237
+data8 0x3FE513356667FC57 // 238
+data8 0x3FE522AE0738A3D8 // 239
+data8 0x3FE5322E26867857 // 240
+data8 0x3FE541B5CB979809 // 241
+data8 0x3FE55144FDBCBD62 // 242
+data8 0x3FE560DBC45153C7 // 243
+data8 0x3FE5707A26BB8C66 // 244
+data8 0x3FE587F60ED5B900 // 245
+data8 0x3FE597A7977C8F31 // 246
+data8 0x3FE5A760D634BB8B // 247
+data8 0x3FE5B721D295F10F // 248
+data8 0x3FE5C6EA94431EF9 // 249
+data8 0x3FE5D6BB22EA86F6 // 250
+data8 0x3FE5E6938645D390 // 251
+data8 0x3FE5F673C61A2ED2 // 252
+data8 0x3FE6065BEA385926 // 253
+data8 0x3FE6164BFA7CC06B // 254
+data8 0x3FE62643FECF9743 // 255
+LOCAL_OBJECT_END(logf_data)
+
+LOCAL_OBJECT_START(log10f_data)
+data8 0x3FDBCB7B1526E50E // 1/ln(10)
+//
+// ln(1/frcpa(1+i/256))/ln(10), i=0...255
+data8 0x3F4BD27045BFD025 // 0
+data8 0x3F64E84E793A474A // 1
+data8 0x3F7175085AB85FF0 // 2
+data8 0x3F787CFF9D9147A5 // 3
+data8 0x3F7EA9D372B89FC8 // 4
+data8 0x3F82DF9D95DA961C // 5
+data8 0x3F866DF172D6372C // 6
+data8 0x3F898D79EF5EEDF0 // 7
+data8 0x3F8D22ADF3F9579D // 8
+data8 0x3F9024231D30C398 // 9
+data8 0x3F91F23A98897D4A // 10
+data8 0x3F93881A7B818F9E // 11
+data8 0x3F951F6E1E759E35 // 12
+data8 0x3F96F2BCE7ADC5B4 // 13
+data8 0x3F988D362CDF359E // 14
+data8 0x3F9A292BAF010982 // 15
+data8 0x3F9BC6A03117EB97 // 16
+data8 0x3F9D65967DE3AB09 // 17
+data8 0x3F9F061167FC31E8 // 18
+data8 0x3FA05409E4F7819C // 19
+data8 0x3FA125D0432EA20E // 20
+data8 0x3FA1F85D440D299B // 21
+data8 0x3FA2AD755749617D // 22
+data8 0x3FA381772A00E604 // 23
+data8 0x3FA45643E165A70B // 24
+data8 0x3FA52BDD034475B8 // 25
+data8 0x3FA5E3966B7E9295 // 26
+data8 0x3FA6BAAF47C5B245 // 27
+data8 0x3FA773B3E8C4F3C8 // 28
+data8 0x3FA84C51EBEE8D15 // 29
+data8 0x3FA906A6786FC1CB // 30
+data8 0x3FA9C197ABF00DD7 // 31
+data8 0x3FAA9C78712191F7 // 32
+data8 0x3FAB58C09C8D637C // 33
+data8 0x3FAC15A8BCDD7B7E // 34
+data8 0x3FACD331E2C2967C // 35
+data8 0x3FADB11ED766ABF4 // 36
+data8 0x3FAE70089346A9E6 // 37
+data8 0x3FAF2F96C6754AEE // 38
+data8 0x3FAFEFCA8D451FD6 // 39
+data8 0x3FB0585283764178 // 40
+data8 0x3FB0B913AAC7D3A7 // 41
+data8 0x3FB11A294F2569F6 // 42
+data8 0x3FB16B51A2696891 // 43
+data8 0x3FB1CD03ADACC8BE // 44
+data8 0x3FB22F0BDD7745F5 // 45
+data8 0x3FB2916ACA38D1E8 // 46
+data8 0x3FB2F4210DF7663D // 47
+data8 0x3FB346A6C3C49066 // 48
+data8 0x3FB3A9FEBC60540A // 49
+data8 0x3FB3FD0C10A3AA54 // 50
+data8 0x3FB46107D3540A82 // 51
+data8 0x3FB4C55DD16967FE // 52
+data8 0x3FB51940330C000B // 53
+data8 0x3FB56D620EE7115E // 54
+data8 0x3FB5D2ABCF26178E // 55
+data8 0x3FB6275AA5DEBF81 // 56
+data8 0x3FB68D4EAF26D7EE // 57
+data8 0x3FB6E28C5C54A28D // 58
+data8 0x3FB7380B9665B7C8 // 59
+data8 0x3FB78DCCC278E85B // 60
+data8 0x3FB7F50C2CF2557A // 61
+data8 0x3FB84B5FD5EAEFD8 // 62
+data8 0x3FB8A1F6BAB2B226 // 63
+data8 0x3FB8F8D144557BDF // 64
+data8 0x3FB94FEFDCD61D92 // 65
+data8 0x3FB9A752EF316149 // 66
+data8 0x3FB9FEFAE7611EE0 // 67
+data8 0x3FBA56E8325F5C87 // 68
+data8 0x3FBAAF1B3E297BB4 // 69
+data8 0x3FBB079479C372AD // 70
+data8 0x3FBB6054553B12F7 // 71
+data8 0x3FBBB95B41AB5CE6 // 72
+data8 0x3FBC12A9B13FE079 // 73
+data8 0x3FBC6C4017382BEA // 74
+data8 0x3FBCB41FBA42686D // 75
+data8 0x3FBD0E38CE73393F // 76
+data8 0x3FBD689B2193F133 // 77
+data8 0x3FBDC3472B1D2860 // 78
+data8 0x3FBE0C06300D528B // 79
+data8 0x3FBE6738190E394C // 80
+data8 0x3FBEC2B50D208D9B // 81
+data8 0x3FBF0C1C2B936828 // 82
+data8 0x3FBF68216C9CC727 // 83
+data8 0x3FBFB1F6381856F4 // 84
+data8 0x3FC00742AF4CE5F8 // 85
+data8 0x3FC02C64906512D2 // 86
+data8 0x3FC05AF1E63E03B4 // 87
+data8 0x3FC0804BEA723AA9 // 88
+data8 0x3FC0AF1FD6711527 // 89
+data8 0x3FC0D4B2A8805A00 // 90
+data8 0x3FC0FA5EF136A06C // 91
+data8 0x3FC1299A4FB3E306 // 92
+data8 0x3FC14F806253C3ED // 93
+data8 0x3FC175805D1587C1 // 94
+data8 0x3FC19B9A637CA295 // 95
+data8 0x3FC1CB5FC26EDE17 // 96
+data8 0x3FC1F1B4E65F2590 // 97
+data8 0x3FC218248B5DC3E5 // 98
+data8 0x3FC23EAED62ADC76 // 99
+data8 0x3FC26553EBD337BD // 100
+data8 0x3FC28C13F1B11900 // 101
+data8 0x3FC2BCAA14381386 // 102
+data8 0x3FC2E3A740B7800F // 103
+data8 0x3FC30ABFD8F333B6 // 104
+data8 0x3FC331F403985097 // 105
+data8 0x3FC35943E7A60690 // 106
+data8 0x3FC380AFAC6E7C07 // 107
+data8 0x3FC3A8377997B9E6 // 108
+data8 0x3FC3CFDB771C9ADB // 109
+data8 0x3FC3EDA90D39A5DF // 110
+data8 0x3FC4157EC09505CD // 111
+data8 0x3FC43D7113FB04C1 // 112
+data8 0x3FC4658030AD1CCF // 113
+data8 0x3FC48DAC404638F6 // 114
+data8 0x3FC4B5F56CBBB869 // 115
+data8 0x3FC4DE5BE05E7583 // 116
+data8 0x3FC4FCBC0776FD85 // 117
+data8 0x3FC525561E9256EE // 118
+data8 0x3FC54E0DF3198865 // 119
+data8 0x3FC56CAB7112BDE2 // 120
+data8 0x3FC59597BA735B15 // 121
+data8 0x3FC5BEA23A506FDA // 122
+data8 0x3FC5DD7E08DE382F // 123
+data8 0x3FC606BDD3F92355 // 124
+data8 0x3FC6301C518A501F // 125
+data8 0x3FC64F3770618916 // 126
+data8 0x3FC678CC14C1E2D8 // 127
+data8 0x3FC6981005ED2947 // 128
+data8 0x3FC6C1DB5F9BB336 // 129
+data8 0x3FC6E1488ECD2881 // 130
+data8 0x3FC70B4B2E7E41B9 // 131
+data8 0x3FC72AE209146BF9 // 132
+data8 0x3FC7551C81BD8DCF // 133
+data8 0x3FC774DD76CC43BE // 134
+data8 0x3FC79F505DB00E88 // 135
+data8 0x3FC7BF3BDE099F30 // 136
+data8 0x3FC7E9E7CAC437F9 // 137
+data8 0x3FC809FE4902D00D // 138
+data8 0x3FC82A2757995CBE // 139
+data8 0x3FC85525C625E098 // 140
+data8 0x3FC8757A79831887 // 141
+data8 0x3FC895E2058D8E03 // 142
+data8 0x3FC8C13437695532 // 143
+data8 0x3FC8E1C812EF32BE // 144
+data8 0x3FC9026F112197E8 // 145
+data8 0x3FC923294888880B // 146
+data8 0x3FC94EEA4B8334F3 // 147
+data8 0x3FC96FD1B639FC09 // 148
+data8 0x3FC990CCA66229AC // 149
+data8 0x3FC9B1DB33334843 // 150
+data8 0x3FC9D2FD740E6607 // 151
+data8 0x3FC9FF49EEDCB553 // 152
+data8 0x3FCA209A84FBCFF8 // 153
+data8 0x3FCA41FF1E43F02B // 154
+data8 0x3FCA6377D2CE9378 // 155
+data8 0x3FCA8504BAE0D9F6 // 156
+data8 0x3FCAA6A5EEEBEFE3 // 157
+data8 0x3FCAC85B878D7879 // 158
+data8 0x3FCAEA259D8FFA0B // 159
+data8 0x3FCB0C0449EB4B6B // 160
+data8 0x3FCB2DF7A5C50299 // 161
+data8 0x3FCB4FFFCA70E4D1 // 162
+data8 0x3FCB721CD17157E3 // 163
+data8 0x3FCB944ED477D4ED // 164
+data8 0x3FCBB695ED655C7D // 165
+data8 0x3FCBD8F2364AEC0F // 166
+data8 0x3FCBFB63C969F4FF // 167
+data8 0x3FCC1DEAC134D4E9 // 168
+data8 0x3FCC4087384F4F80 // 169
+data8 0x3FCC6339498F09E2 // 170
+data8 0x3FCC86010FFC076C // 171
+data8 0x3FCC9D3D065C5B42 // 172
+data8 0x3FCCC029375BA07A // 173
+data8 0x3FCCE32B66978BA4 // 174
+data8 0x3FCD0643AFD51404 // 175
+data8 0x3FCD29722F0DEA45 // 176
+data8 0x3FCD4CB70070FE44 // 177
+data8 0x3FCD6446AB3F8C96 // 178
+data8 0x3FCD87B0EF71DB45 // 179
+data8 0x3FCDAB31D1FE99A7 // 180
+data8 0x3FCDCEC96FDC888F // 181
+data8 0x3FCDE6908876357A // 182
+data8 0x3FCE0A4E4A25C200 // 183
+data8 0x3FCE2E2315755E33 // 184
+data8 0x3FCE461322D1648A // 185
+data8 0x3FCE6A0E95C7787B // 186
+data8 0x3FCE8E216243DD60 // 187
+data8 0x3FCEA63AF26E007C // 188
+data8 0x3FCECA74ED15E0B7 // 189
+data8 0x3FCEEEC692CCD25A // 190
+data8 0x3FCF070A36B8D9C1 // 191
+data8 0x3FCF2B8393E34A2D // 192
+data8 0x3FCF5014EF538A5B // 193
+data8 0x3FCF68833AF1B180 // 194
+data8 0x3FCF8D3CD9F3F04F // 195
+data8 0x3FCFA5C61ADD93E9 // 196
+data8 0x3FCFCAA8567EBA7A // 197
+data8 0x3FCFE34CC8743DD8 // 198
+data8 0x3FD0042BFD74F519 // 199
+data8 0x3FD016BDF6A18017 // 200
+data8 0x3FD023262F907322 // 201
+data8 0x3FD035CCED8D32A1 // 202
+data8 0x3FD042430E869FFC // 203
+data8 0x3FD04EBEC842B2E0 // 204
+data8 0x3FD06182E84FD4AC // 205
+data8 0x3FD06E0CB609D383 // 206
+data8 0x3FD080E60BEC8F12 // 207
+data8 0x3FD08D7E0D894735 // 208
+data8 0x3FD0A06CC96A2056 // 209
+data8 0x3FD0AD131F3B3C55 // 210
+data8 0x3FD0C01771E775FB // 211
+data8 0x3FD0CCCC3CAD6F4B // 212
+data8 0x3FD0D986D91A34A9 // 213
+data8 0x3FD0ECA9B8861A2D // 214
+data8 0x3FD0F972F87FF3D6 // 215
+data8 0x3FD106421CF0E5F7 // 216
+data8 0x3FD11983EBE28A9D // 217
+data8 0x3FD12661E35B785A // 218
+data8 0x3FD13345D2779D3B // 219
+data8 0x3FD146A6F597283A // 220
+data8 0x3FD15399E81EA83D // 221
+data8 0x3FD16092E5D3A9A6 // 222
+data8 0x3FD17413C3B7AB5E // 223
+data8 0x3FD1811BF629D6FB // 224
+data8 0x3FD18E2A47B46686 // 225
+data8 0x3FD19B3EBE1A4418 // 226
+data8 0x3FD1AEE9017CB450 // 227
+data8 0x3FD1BC0CED7134E2 // 228
+data8 0x3FD1C93712ABC7FF // 229
+data8 0x3FD1D66777147D3F // 230
+data8 0x3FD1EA3BD1286E1C // 231
+data8 0x3FD1F77BED932C4C // 232
+data8 0x3FD204C25E1B031F // 233
+data8 0x3FD2120F28CE69B1 // 234
+data8 0x3FD21F6253C48D01 // 235
+data8 0x3FD22CBBE51D60AA // 236
+data8 0x3FD240CE4C975444 // 237
+data8 0x3FD24E37F8ECDAE8 // 238
+data8 0x3FD25BA8215AF7FC // 239
+data8 0x3FD2691ECC29F042 // 240
+data8 0x3FD2769BFFAB2E00 // 241
+data8 0x3FD2841FC23952C9 // 242
+data8 0x3FD291AA1A384978 // 243
+data8 0x3FD29F3B0E15584B // 244
+data8 0x3FD2B3A0EE479DF7 // 245
+data8 0x3FD2C142842C09E6 // 246
+data8 0x3FD2CEEACCB7BD6D // 247
+data8 0x3FD2DC99CE82FF21 // 248
+data8 0x3FD2EA4F902FD7DA // 249
+data8 0x3FD2F80C186A25FD // 250
+data8 0x3FD305CF6DE7B0F7 // 251
+data8 0x3FD3139997683CE7 // 252
+data8 0x3FD3216A9BB59E7C // 253
+data8 0x3FD32F4281A3CEFF // 254
+data8 0x3FD33D2150110092 // 255
+LOCAL_OBJECT_END(log10f_data)
+
+
+// Code
+//==============================================================
 .section .text
-.proc  log10f#
-.align 32
 
-log10f: 
-#ifdef _LIBC
-.global __ieee754_log10f
-.type __ieee754_log10f,@function
-__ieee754_log10f:
-#endif
-{ .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) 
-}
-;;
-
-.endp log10f
-ASM_SIZE_DIRECTIVE(log10f)
-ASM_SIZE_DIRECTIVE(__ieee754_log10f)
+// logf   has p13 true, p14 false
+// log10f has p14 true, p13 false
 
-
-
-.section .text
-.proc  logf#
-.align 32
-logf: 
-#ifdef _LIBC
-.global __ieee754_logf
-.type __ieee754_logf,@function
-__ieee754_logf:
-#endif
-
-{ .mfi
-     alloc     r32=ar.pfs,1,15,4,0                    
-     frcpa.s1  log_C,p9 = f1,f8                 
-     cmp.eq.unc     p8,p7         = r0, r0 
-}
+GLOBAL_IEEE754_ENTRY(log10f)
 { .mfi
-     addl           log_AD_1   = @ltoff(log_table_1), gp
-     fnorm.s1 log_NORM_f8 = f8 
-     nop.i 999
+      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
 }
-;;
-
-L(LOG_LOG10_X):
-
+{ .mlx
+      addl          GR_ad_T = @ltoff(log10f_data),gp
+      movl          GR_A3 = 0x3FD5555555555555 // double precision memory
+                                               // representation of A3
+};;
 { .mfi
-     getf.exp   log_GR_signexp_f8 = f8 // If x unorm then must recompute
-     fclass.m.unc p15,p0 = f8, 0x0b            // Test for x=unorm
-     mov        log_GR_fff7 = 0xfff7
+      getf.sig      GR_Sig = f8 // if x is unorm then must recompute
+      fclass.m      p8,p0 = f8,9 // is x positive unorm?
+      sub           GR_025 = GR_05,r0,1 // biased exponent of A4=0.25
 }
+{ .mlx
+      ld8           GR_ad_T = [GR_ad_T]
+      movl          GR_Ln2 = 0x3FD34413509F79FF // double precision memory
+                                                // representation of
+                                                // log(2)/ln(10)
+};;
 { .mfi
-     ld8 log_AD_1 = [log_AD_1]
-     fms.s1     log_w = f8,f1,f1              
-     mov       log_GR_exp_17_ones = 0x1ffff
-}
-;;
-
-{ .mmi
-     getf.sig   log_GR_significand_f8 = f8 // If x unorm then must recompute
-     mov       log_GR_exp_16_ones = 0xffff
-     nop.i 999
-}
-;;
-
-{ .mmb
-     adds log_AD_2 = 0x10, log_AD_1
-     and        log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones  
-(p15) br.cond.spnt L(LOG_DENORM)     
-}
-;;
-
-L(LOG_COMMON):
-{.mfi
-     ldfpd      log_P3,log_P2 = [log_AD_1],16           
-     fclass.m.unc p6,p0 = f8, 0xc3             // Test for x=nan
-     shl        log_GR_index = log_GR_significand_f8,1            
-}
-{.mfi
-     sub       log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones 
-     nop.f 999
-     nop.i 999
+      setf.d        FR_A3 = GR_A3 // create A3
+      fcmp.eq.s1    p14,p13 = f0,f0 // set p14 to 1 for log10f
+      dep.z         GR_xorg = GR_05,55,8 // 0x7F00000000000000 integer number
+                                         // bits of that are
+                                         // GR_xorg[63]   = last bit of biased
+                                         //            exponent of 255/256
+                                         // GR_xorg[62-0] = bits from 62 to 0
+                                         //            of significand of 255/256
 }
-;;
+{ .mib
+      setf.exp      FR_A2 = GR_05 // create A2
+      sub           GR_de = GR_Exp,GR_05 // biased_exponent_of_x - 0xFFFE
+                                         // needed to comparion with 0.5 and 2.0
+      br.cond.sptk  logf_log10f_common
+};;
+GLOBAL_IEEE754_END(log10f)
 
+GLOBAL_IEEE754_ENTRY(logf)
 { .mfi
-     ldfpd      log_P1,log_inv_ln10 = [log_AD_2],16           
-     fclass.m.unc p11,p0 = f8, 0x21            // Test for x=+inf
-     shr.u     log_GR_index = log_GR_index,56
+      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_T = @ltoff(logf_data),gp
+      movl          GR_A3 = 0x3FD5555555555555 // double precision memory
+                                               // representation of A3
+};;
 { .mfi
-     setf.sig  log_int_Nfloat = log_GR_true_exp_f8
-     nop.f 999
-     nop.i 999
+      getf.sig      GR_Sig = f8 // if x is unorm then must recompute
+      fclass.m      p8,p0 = f8,9 // is x positive unorm?
+      dep.z         GR_xorg = GR_05,55,8 // 0x7F00000000000000 integer number
+                                         // bits of that are
+                                         // GR_xorg[63]   = last bit of biased
+                                         //            exponent of 255/256
+                                         // GR_xorg[62-0] = bits from 62 to 0
+                                         //            of significand of 255/256
 }
-;;
-
-
 { .mfi
-     ldfd       log_log2 = [log_AD_2],16   
-     fma.s1     log_wsq     = log_w, log_w, f0
-     nop.i 999
-}
-{ .mfb
-     nop.m 999
-(p6) fma.s.s0   f8 = f8,f1,f0      // quietize nan result if x=nan
-(p6) br.ret.spnt b0                // Exit for x=nan
-}
-;;
-
-
+      ld8           GR_ad_T = [GR_ad_T]
+      nop.f         0
+      sub           GR_025 = GR_05,r0,1 // biased exponent of A4=0.25
+};;
 { .mfi
-     shladd log_AD_2 = log_GR_index,3,log_AD_2
-     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
-     nop.m 999
-     nop.m 999
-     fclass.m.unc p6,p0 = f8, 0x07        // Test for x=0
-}
-;;
-
-
-{ .mfb
-     ldfd       log_T = [log_AD_2]
-(p10) fmerge.s f8 = f0, f0
-(p10) br.ret.spnt b0                // Exit for x=1.0
-;;
+      setf.d        FR_A3 = GR_A3 // create A3
+      fcmp.eq.s1    p13,p14 = f0,f0 // p13 - true for logf
+      sub           GR_de = GR_Exp,GR_05 // biased_exponent_of_x - 0xFFFE
+                                         // needed to comparion with 0.5 and 2.0
 }
-
+{ .mlx
+      setf.exp      FR_A2 = GR_05 // create A2
+      movl          GR_Ln2 = 0x3FE62E42FEFA39EF // double precision memory
+                                                // representation of log(2)
+};;
+logf_log10f_common:
 { .mfi
-     getf.exp   log_GR_signexp_w = log_w
-     fclass.m.unc p12,p0 = f8, 0x3a       // Test for x neg norm, unorm, inf
-     nop.i 999
-}
-;;
-
-{ .mmb
-     nop.m 999
-     nop.m 999
-(p6) br.cond.spnt L(LOG_ZERO_NEG)      // Branch if x=0
-;;
+      setf.exp      FR_A4 = GR_025 // create A4=0.25
+      fclass.m      p9,p0 = f8,0x3A // is x < 0 (including negateve unnormals)?
+      dep           GR_x = GR_Exp,GR_Sig,63,1 // produce integer that bits are
+                                              // GR_x[63] = GR_Exp[0]
+                                              // GR_x[62-0] = GR_Sig[62-0]
 }
- 
-
+{ .mib
+      sub           GR_N = GR_Exp,GR_05,1 // unbiased exponent of x
+      cmp.gtu       p6,p7 = 2,GR_de // is 0.5 <= x < 2.0?
+(p8)  br.cond.spnt  logf_positive_unorm
+};;
+logf_core:
 { .mfi
-     and log_GR_exp_w = log_GR_exp_17_ones, log_GR_signexp_w
-     nop.f 999
-     nop.i 999
+      setf.sig      FR_N = GR_N // copy unbiased exponent of x to the
+                                // significand field of FR_N
+      fclass.m      p10,p0 = f8,0x1E1 // is x NaN, NaT or +Inf?
+      dep.z         GR_dx = GR_05,54,3 // 0x0180000000000000 - difference
+                                       // between our integer representations
+                                       // of 257/256 and 255/256
 }
-{ .mfb
-     nop.m 999
-     fma.s1     log_rsq     = log_r, log_r, f0                   
-(p12) br.cond.spnt L(LOG_ZERO_NEG)     // Branch if x<0
-;;
-}
-
 { .mfi
-     nop.m 999
-     fma.s1      log_rp_p32 = log_P3, log_r, log_P2
-     nop.i 999
-}
+      nop.m         0
+      nop.f         0
+      sub           GR_x = GR_x,GR_xorg // difference between representations
+                                        // of x and 255/256
+};;
 { .mfi
-     nop.m 999
-     fma.s1    log_rp_q32   = log_P3, log_w, log_P2
-     nop.i 999
-;;
+      ldfd          FR_InvLn10 = [GR_ad_T],8
+      fcmp.eq.s1    p11,p0 = f8,f1 // is x equal to 1.0?
+      extr.u        GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index
 }
-
+{ .mib
+      setf.d        FR_Ln2 = GR_Ln2 // create log(2) or log10(2)
+(p6)  cmp.gtu       p6,p7 = GR_dx,GR_x // set p6 if 255/256 <= x < 257/256
+(p9)  br.cond.spnt  logf_negatives // jump if input argument is negative number
+};;
+// p6 is true if |x-1| < 1/256
+// p7 is true if |x-1| >= 1/256
+.pred.rel "mutex",p6,p7
 { .mfi
-     nop.m 999
-     fcvt.xf   log_Nfloat = log_int_Nfloat
-     nop.i 999 ;;
+      shladd        GR_ad_T = GR_Ind,3,GR_ad_T // calculate address of T
+(p7)  fms.s1        FR_r = FR_RcpX,f8,f1 // range reduction for |x-1|>=1/256
+      extr.u        GR_Exp = GR_Exp,0,17 // exponent without sign
 }
-
+{ .mfb
+      nop.m         0
+(p6)  fms.s1        FR_r = f8,f1,f1 // range reduction for |x-1|<1/256
+(p10) br.cond.spnt  logf_nan_nat_pinf // exit for NaN, NaT or +Inf
+};;
+{ .mfb
+      ldfd          FR_T = [GR_ad_T] // load T
+(p11) fma.s.s0      f8 = f0,f0,f0
+(p11) br.ret.spnt   b0 // exit for x = 1.0
+};;
+{ .mib
+      nop.m         0
+      cmp.eq        p12,p0 = r0,GR_Exp // is x +/-0? (here it's quite enough
+                                       // only to compare exponent with 0
+                                       // because all unnormals already
+                                       // have been filtered)
+(p12) br.cond.spnt  logf_zeroes        // Branch if input argument is +/-0
+};;
 { .mfi
-     nop.m 999
-     fma.s1    log_rp_p10   = log_P1, log_r, f1
-     nop.i 999
+      nop.m         0
+      fnma.s1       FR_A2 = FR_A2,FR_r,f1 // A2*r+1
+      nop.i         0
 }
 { .mfi
-     nop.m 999
-     fma.s1    log_rp_q10  = log_P1, log_w, f1
-     nop.i 999
-;;
-}
-
-//    p13 <== large w log
-//    p14 <== small w log
+      nop.m         0
+      fma.s1        FR_r2 = FR_r,FR_r,f0  // r^2
+      nop.i         0
+};;
 { .mfi
-(p8) cmp.ge.unc p13,p14 = log_GR_exp_w, log_GR_fff7
-     fcmp.eq.s0 p6,p0 = f8,f0         // Sets flag on +denormal input
-     nop.i 999
-;;
+      nop.m         0
+      fcvt.xf       FR_N = FR_N // convert integer N in significand of FR_N
+                                // to floating-point representation
+      nop.i         0
 }
-
-//    p10 <== large w log10
-//    p11 <== small w log10
 { .mfi
-(p7) cmp.ge.unc p10,p11 = log_GR_exp_w, log_GR_fff7
-     nop.f 999
-     nop.i 999 ;;
-}
-
+      nop.m         0
+      fnma.s1       FR_A3 = FR_A4,FR_r,FR_A3 // A4*r+A3
+      nop.i         0
+};;
 { .mfi
-     nop.m 999
-     fma.s1        log_T_plus_Nlog2 = log_Nfloat,log_log2, log_T    
-     nop.i 999 ;;
+      nop.m         0
+      fma.s1        FR_r = FR_r,FR_InvLn10,f0 // For log10f we have r/log(10)
+      nop.i         0
 }
-
-
 { .mfi
-     nop.m 999
-     fma.s1     log_rp_p2   = log_rp_p32, log_rsq, log_rp_p10
-     nop.i 999
-}
+      nop.m         0
+      nop.f         0
+      nop.i         0
+};;
 { .mfi
-     nop.m 999
-     fma.s1     log_rp_q2   = log_rp_q32, log_wsq, log_rp_q10
-     nop.i 999
-;;
+      nop.m         0
+      fma.s1        FR_A2 = FR_A3,FR_r2,FR_A2 // (A4*r+A3)*r^2+(A2*r+1)
+      nop.i         0
 }
-
-
-//    small w, log   <== p14
 { .mfi
-     nop.m 999
-(p14) fma.s        f8       = log_rp_q2, log_w, f0
-     nop.i 999
-}
+      nop.m         0
+      fma.s1        FR_NxLn2pT = FR_N,FR_Ln2,FR_T // N*Ln2+T
+      nop.i         0
+};;
+.pred.rel "mutex",p6,p7
 { .mfi
-     nop.m 999
-(p11) fma.s1        log_Q       = log_rp_q2, log_w, f0
-     nop.i 999 ;;
+      nop.m         0
+(p7)  fma.s.s0      f8 = FR_A2,FR_r,FR_NxLn2pT // result for |x-1|>=1/256
+      nop.i         0
 }
+{ .mfb
+      nop.m         0
+(p6)  fma.s.s0      f8 = FR_A2,FR_r,f0 // result for |x-1|<1/256
+      br.ret.sptk   b0
+};;
 
-
-//    large w, log   <== p13
-.pred.rel "mutex",p13,p10
+.align 32
+logf_positive_unorm:
 { .mfi
-      nop.m 999
-(p13) fma.s        f8        = log_rp_p2, log_r, log_T_plus_Nlog2
-      nop.i 999 
-}
+      nop.m         0
+(p8)  fma.s0        f8 = f8,f1,f0 // Normalize & set D-flag
+      nop.i         0
+};;
 { .mfi
-      nop.m 999
-(p10) fma.s1     log_Q     = log_rp_p2, log_r, log_T_plus_Nlog2
-      nop.i 999  ;;
-}
-
-
-//    log10
-{ .mfb
-      nop.m 999
-(p7)  fma.s      f8 = log_inv_ln10,log_Q,f0                         
-      br.ret.sptk     b0 
-;;
-}
-
-
-L(LOG_DENORM):
-{ .mmi
-     getf.exp   log_GR_signexp_f8 = log_NORM_f8 
-     nop.m 999
-     nop.i 999
-}
-;;
-{ .mmb
-     getf.sig   log_GR_significand_f8 = log_NORM_f8 
-     and        log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones  
-     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
+      getf.exp      GR_Exp = f8    // recompute biased exponent
+      nop.f         0
+      cmp.ne        p6,p7 = r0,r0  // p6 <- 0, p7 <- 1 because
+                                   // in case of unorm we are out
+                                   // interval [255/256; 257/256]
+};;
 { .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(-)
-
+      getf.sig      GR_Sig = f8 // recompute significand
+      nop.f         0
+      nop.i         0
+};;
+{ .mib
+      sub           GR_N = GR_Exp,GR_05,1 // unbiased exponent N
+      nop.i         0
+      br.cond.sptk  logf_core // return into main path
+};;
 
+.align 32
+logf_nan_nat_pinf:
 { .mfi
-     nop.m 999
-     fmerge.ns   f6 = f1,f1            // Form -1.0
-     nop.i 999  ;;
+      nop.m         0
+      fma.s.s0      f8 = f8,f1,f0 // set V-flag
+      nop.i         0
 }
+{ .mfb
+      nop.m         0
+      nop.f         0
+      br.ret.sptk   b0 // exit for NaN, NaT or +Inf
+};;
 
-// p9  means  ln(+-0)  = -inf
-// p10 means  log(+-0) = -inf
-// Log(+-0) = -inf 
-
-{ .mfi
-	nop.m 999
-(p8)  fclass.m.unc  p9,p0 = f10, 0x07           
-	nop.i 999
-}
+.align 32
+logf_zeroes:
 { .mfi
-	nop.m 999
-(p7)  fclass.m.unc  p10,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
 }
-
-
-// p13  ln(-)
-// p14  log(-)
-
-// Log(-inf, -normal, -unnormal) = QNAN indefinite
 { .mfi
-	nop.m 999
-(p8)  fclass.m.unc  p13,p0 = f10, 0x3a           
-	nop.i 999 
-}
+(p13) mov           GR_TAG = 4 // set libm error in case of logf
+      fms.s1        FR_tmp = f0,f0,f1 // -1.0
+      nop.i         0
+};;
 { .mfi
-	nop.m 999
-(p7)  fclass.m.unc  p14,p0 = f10, 0x3a           
-	nop.i 999  ;;
+      nop.m         0
+      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 = 10 // set libm error in case of log10f
+      nop.i         0
+      br.cond.sptk  logf_libm_err
+};;
 
-
-.pred.rel "mutex",p9,p10
+.align 32
+logf_negatives:
 { .mfi
-(p9)     mov        log_GR_tag = 4       
-(p9)    frcpa f8,p11 = f6,f0                   
-            nop.i 999
-}
+(p13) mov           GR_TAG = 5 // set libm error in case of logf
+      fmerge.s      FR_X = f8,f8 // keep input argument for subsequent
+                                 // call of __libm_error_support#
+      nop.i         0
+};;
 { .mfi
-(p10)    mov        log_GR_tag = 10       
-(p10)   frcpa f8,p12 = f6,f0                   
-            nop.i 999 ;;
-}
+(p14) mov           GR_TAG = 11 // set libm error in case of log10f
+      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.
+      nop.i         0
+};;
 
-.pred.rel "mutex",p13,p14
-{ .mfi
-(p13)    mov        log_GR_tag = 5       
-(p13)    frcpa f8,p11 = f0,f0                   
-            nop.i 999
-}
-{ .mfb
-(p14)    mov        log_GR_tag = 11       
-(p14)   frcpa f8,p12 = f0,f0                   
-        br.cond.sptk __libm_error_region ;; 
-}
-.endp logf
-ASM_SIZE_DIRECTIVE(logf)
-ASM_SIZE_DIRECTIVE(__ieee754_logf)
+.align 32
+logf_libm_err:
+{ .mmi
+      alloc         r32 = ar.pfs,1,4,4,0
+      mov           GR_Parameter_TAG = GR_TAG
+      nop.i         0
+};;
+GLOBAL_IEEE754_END(logf)
 
 
 // Stack operations when calling error support.
@@ -890,70 +1104,56 @@ ASM_SIZE_DIRECTIVE(__ieee754_logf)
 //    save ar.pfs          save b0                                               restore gp
 //    save gp                                                                    restore ar.pfs
 
-
-
-.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
-        nop.f 0
-.save   ar.pfs,GR_SAVE_PFS
-        mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
+      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
+      add sp=-64,sp                           // Create new stack
+      nop.f 0
+      mov GR_SAVE_GP=gp                       // Save gp
 };;
-
-
-// (2)
 { .mmi
-        stfs [GR_Parameter_Y] = f1,16         // STORE Parameter 2 on stack
-        add GR_Parameter_X = 16,sp            // Parameter 1 address
+      stfs [GR_Parameter_Y] = FR_Y,16         // STORE Parameter 2 on stack
+      add GR_Parameter_X = 16,sp              // Parameter 1 address
 .save   b0, GR_SAVE_B0
-        mov GR_SAVE_B0=b0                     // Save b0
+      mov GR_SAVE_B0=b0                       // Save b0
 };;
-
 .body
-// (3)
 { .mib
-        stfs [GR_Parameter_X] = f10                   // STORE Parameter 1 on stack
-        add   GR_Parameter_RESULT = 0,GR_Parameter_Y  // Parameter 3 address
-        nop.b 0                             
+      stfs [GR_Parameter_X] = FR_X                  // STORE Parameter 1 on stack
+      add   GR_Parameter_RESULT = 0,GR_Parameter_Y  // Parameter 3 address
+      nop.b 0
 }
 { .mib
-        stfs [GR_Parameter_Y] = f8                    // STORE Parameter 3 on stack
-        add   GR_Parameter_Y = -16,GR_Parameter_Y
-        br.call.sptk b0=__libm_error_support#         // Call error handling function
+      stfs [GR_Parameter_Y] = FR_RESULT             // STORE Parameter 3 on stack
+      add   GR_Parameter_Y = -16,GR_Parameter_Y
+      br.call.sptk b0=__libm_error_support#         // Call error handling function
 };;
-
 { .mmi
-        nop.m 0
-        nop.m 0
-        add   GR_Parameter_RESULT = 48,sp
+      nop.m 0
+      nop.m 0
+      add   GR_Parameter_RESULT = 48,sp
 };;
-
-// (4)
 { .mmi
-        ldfs  f8 = [GR_Parameter_RESULT]       // Get return result off stack
+      ldfs  f8 = [GR_Parameter_RESULT]       // Get return result off stack
 .restore sp
-        add   sp = 64,sp                       // Restore stack pointer
-        mov   b0 = GR_SAVE_B0                  // Restore return address
+      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#
+