e_log.s

Glibc 2.3.2源代码(解压后有100多M)

.file "log.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
//==============================================================
// 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
//          set [the previously overwritten] GR_Parameter_RESULT.
// 8/17/00  Improved speed of main path by 5 cycles
//          Shortened path for x=1.0
// 1/09/01  Improved speed, fixed flags for neg denormals
//
//
// 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)
//
// 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^-6
// C = frcpa(x)
// r = C * x - 1
//
// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 + P4*r^5 + P5*r^6
//
// 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-extended

// CASE 2:  |x-1| < 2^-6
// w = x - 1
//
// Form wseries = w + Q1*w^2 + Q2*w^3 + ... + Q7*w^8 + Q8*w^9
//
// 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 -> f68

// 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_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
//==============================================================

#ifdef _LIBC
.rodata
#else
.data
#endif

.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))