e_logf.s

Glibc 2.3.2源代码(解压后有100多M)

.file "logf.s"

// Copyright (C) 2000, 2001, 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.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
//
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
//
// * The name of Intel Corporation may not be used to endorse or promote
// products derived from this software without specific prior written
// permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS 
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY 
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 
// 
// Intel Corporation is the author of this code, and requests that all
// problem reports or change requests be submitted to it directly at 
// http://developer.intel.com/opensource.
//
// History
//==============================================================
// 3/01/00  Initial version
// 8/15/00  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
//
//
// 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)
//
// frcpa(x)       = 2^-N frcpa((1.f1 f2 ... f63)
//
// -log(frcpa(x)) = -log(C) 
//                = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
//
// -log(frcpa(x)) = -log(C) 
//                = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
//
// -log(frcpa(x)) = -log(C) 
//                = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
//
// 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)
//
// Cx = 1 + 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.
//
// Implementation
//===============
// CASE 1:  |x-1| >= 2^-8
// C = frcpa(x)
// r = C * x - 1
//
// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4
//
// x = f * 2*n where f is 1.f_1f_2f_3....f_63
// Nfloat = float(n)  where n is the true unbiased exponent
// pre-index = f_1f_2....f_8
// index = pre_index * 16
// get the dxt table entry at index + offset = T
//
// result = (T + Nfloat * log(2)) + rseries
//
// The T table is calculated as follows
// Form x_k = 1 + k/2^8 where k goes from 0... 255
//      y_k = frcpa(x_k)
//      log(1/y_k)  in quad and round to double

// CASE 2:  |x-1| < 2^-6
// w = x - 1
//
// Form wseries = w + Q1*w^2 + Q2*w^3 + Q3*w^4
//
// result = wseries

// Special values 
//==============================================================


// log(+0)    = -inf
// log(-0)    = -inf

// log(+qnan) = +qnan 
// log(-qnan) = -qnan 
// log(+snan) = +qnan 
// log(-snan) = -qnan 

// log(-n)    = QNAN Indefinite
// log(-inf)  = QNAN Indefinite 

// log(+inf)  = +inf

// Registers used
//==============================================================
// Floating Point registers used: 
// f8, input
// f9 -> f15,  f32 -> f47

// General registers used:  
// r32 -> r51

// 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_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


// Data tables
//==============================================================

#ifdef _LIBC
.rodata
#else
.data
#endif

.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)