2.5-18.1

1 files changed, 711 insertions, 0 deletions

diff --git a/sysdeps/ia64/fpu/e_log2.S b/sysdeps/ia64/fpu/e_log2.S
new file mode 100644
index 0000000000..660a9526b6
--- /dev/null
+++ b/sysdeps/ia64/fpu/e_log2.S
@@ -0,0 +1,711 @@
+.file "log2.s"
+
+
+// Copyright (c) 2000 - 2003, Intel Corporation
+// All rights reserved.
+//
+// Contributed 2000 by the Intel Numerics Group, Intel Corporation
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// met:
+//
+// * Redistributions of source code must retain the above copyright
+// notice, this list of conditions and the following disclaimer.
+//
+// * Redistributions in binary form must reproduce the above copyright
+// notice, this list of conditions and the following disclaimer in the
+// documentation and/or other materials provided with the distribution.
+//
+// * The name of Intel Corporation may not be used to endorse or promote
+// products derived from this software without specific prior written
+// permission.
+
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 
+// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS 
+// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 
+// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 
+// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY 
+// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 
+// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 
+// 
+// Intel Corporation is the author of this code, and requests that all
+// problem reports or change requests be submitted to it directly at 
+// http://www.intel.com/software/products/opensource/libraries/num.htm.
+//
+// History
+//=================================================================
+// 09/11/00 Initial version 
+// 03/19/01 Added one polynomial coefficient, to improve accuracy
+// 05/20/02 Cleaned up namespace and sf0 syntax
+// 02/10/03 Reordered header: .section, .global, .proc, .align
+// 04/18/03 Reformatted T[255]
+//
+// API
+//=================================================================
+// double log2(double)
+//
+// Overview of operation
+//=================================================================
+// Background
+//
+// Implementation
+//
+// Let x = 2^l * m, where     m=1.b1 b2 ... b8 b9 ... b52
+//     y=frcpa(m),   r=m*y-1, f=b1 b2 .. b8 (table index)
+// j=0 if f<128; j=1 if f>=128
+// T is a table that stores log2(1/y) (in entries 1..255) rounded to
+//   double extended precision; f is used as an index; T[255]=0
+// 
+// If f=0 and b9=0, r is set to 2^{-8}* 0.b9 b10 ... b52 = m-1 (fractional part of m),
+//                  and 0 is used instead of T[0] 
+//                  (polynomial evaluation only, for m=1+r, 0<=r<2^{-9})
+// If f=255, r is set to (m-2)/2  (T[255]=0, and only polynomial evaluation is used
+//                                 for m=2(1-r'), 0<=r'<2^{-9})
+//
+// log2(x) is approximated as
+//     (l-j) + T[f] + (c1*r+c2*r^2+...+c7*r^7), if f>0
+// 
+
+
+// Special values 
+//=================================================================
+//  log2(0)=-inf, raises Divide by Zero
+//  log2(+inf)=inf
+//  log2(x)=NaN,  raises Invalid if x<0
+//
+
+
+// Registers used
+//==============================================================
+//   f6-f15, f32-f33
+//   r2-r3, r23-r30
+//   p6,p7,p8,p12
+//
+
+
+GR_SAVE_B0                    = r33
+GR_SAVE_PFS                   = r34
+GR_SAVE_GP                    = r35 // This reg. can safely be used 
+GR_SAVE_SP                    = r36
+
+GR_Parameter_X                = r37
+GR_Parameter_Y                = r38
+GR_Parameter_RESULT           = r39
+GR_Parameter_TAG              = r40
+
+FR_X             = f10
+FR_Y             = f1
+FR_RESULT        = f8
+
+
+
+
+// Data tables
+//==============================================================
+
+RODATA
+
+.align 16
+
+LOCAL_OBJECT_START(poly_coeffs)
+
+data8 0xbfd0000000000000, 0x3fc999999999999a //C_4, C_5
+data8 0xbfc5555555555555, 0x3fc2492492492492 //C_6, C_7
+data8 0xb8aa3b295c17f0bc, 0x00003fff  // C_1
+data8 0xaaaaaaaaaaaaaaab, 0x00003ffd  // C_3=1/3
+LOCAL_OBJECT_END(poly_coeffs)
+
+
+LOCAL_OBJECT_START(T_table)
+
+data8 0xb8d8752172fed131, 0x00003ff6
+data8 0x8ae7f475764180a3, 0x00003ff8
+data8 0xe7f73862e72ee35d, 0x00003ff8
+data8 0xa2b25310c941a2f2, 0x00003ff9
+data8 0xcbb91d671abb2e85, 0x00003ff9
+data8 0xfac91e34daa50483, 0x00003ff9
+data8 0x9504a5042eb495c5, 0x00003ffa
+data8 0xa9c4a0bbb580ee02, 0x00003ffa
+data8 0xc19264dc8a5e3bf9, 0x00003ffa
+data8 0xd67aa6703ebf4a77, 0x00003ffa
+data8 0xee76cac6d6e08ce7, 0x00003ffa
+data8 0x81c3f7de5434ed04, 0x00003ffb
+data8 0x8c563033a3ce01e4, 0x00003ffb
+data8 0x9876e9f09a98661c, 0x00003ffb
+data8 0xa31e0ac9b2326ce2, 0x00003ffb
+data8 0xadcf09e1fd10e4a5, 0x00003ffb
+data8 0xb889f992cf03cdb6, 0x00003ffb
+data8 0xc34eec68d901a714, 0x00003ffb
+data8 0xce1df524e9909ed9, 0x00003ffb
+data8 0xd8f726bcb0b80ad0, 0x00003ffb
+data8 0xe3da945b878e27d1, 0x00003ffb
+data8 0xeec851633b76a320, 0x00003ffb
+data8 0xf82ea4bb6101421a, 0x00003ffb
+data8 0x8197ddd7736b2864, 0x00003ffc
+data8 0x871dad4f994253f0, 0x00003ffc
+data8 0x8ca8cae3e892d549, 0x00003ffc
+data8 0x916d6e1559a4b697, 0x00003ffc
+data8 0x97028118efabeb7d, 0x00003ffc
+data8 0x9bcfbce1592ad5d5, 0x00003ffc
+data8 0xa16ee95d0da54a91, 0x00003ffc
+data8 0xa644dcf3403fa5d0, 0x00003ffc
+data8 0xab1ee14ffd659064, 0x00003ffc
+data8 0xb0cd12faebcc6757, 0x00003ffc
+data8 0xb5affdf9b3b221e0, 0x00003ffc
+data8 0xba970fb307c6ade1, 0x00003ffc
+data8 0xbf824f3a9f3e7561, 0x00003ffc
+data8 0xc544c055fde99333, 0x00003ffc
+data8 0xca39266532bdf26c, 0x00003ffc
+data8 0xcf31d124b8fa2f56, 0x00003ffc
+data8 0xd42ec7f59017b6ab, 0x00003ffc
+data8 0xd930124bea9a2c67, 0x00003ffc
+data8 0xde35b7af70e4dab3, 0x00003ffc
+data8 0xe33fbfbb8533ef03, 0x00003ffc
+data8 0xe77625911a7dcef3, 0x00003ffc
+data8 0xec884bd689cc12e3, 0x00003ffc
+data8 0xf19eeabf9e99a40a, 0x00003ffc
+data8 0xf6ba0a35e3d88051, 0x00003ffc
+data8 0xfbd9b237f7b4192b, 0x00003ffc
+data8 0x80111d4a1ee0c79e, 0x00003ffd
+data8 0x82a523a5f875bbfc, 0x00003ffd
+data8 0x84ccecdc92cd0815, 0x00003ffd
+data8 0x87653369d92c057a, 0x00003ffd
+data8 0x89ffd1742da3aa21, 0x00003ffd
+data8 0x8c2d2227d053d9b6, 0x00003ffd
+data8 0x8e5c189793f7f798, 0x00003ffd
+data8 0x90fd0a20e72f3c96, 0x00003ffd
+data8 0x932fa937301e59ae, 0x00003ffd
+data8 0x95d5061a5f0f5f7f, 0x00003ffd
+data8 0x980b5a2ef10e7023, 0x00003ffd
+data8 0x9a4361c5514d3c27, 0x00003ffd
+data8 0x9c7d1f7d541313fd, 0x00003ffd
+data8 0x9f2b16040b500d04, 0x00003ffd
+data8 0xa168a0fa9db22c98, 0x00003ffd
+data8 0xa3a7eaa1f9116293, 0x00003ffd
+data8 0xa5e8f5b4072a3d44, 0x00003ffd
+data8 0xa82bc4f11a5e88aa, 0x00003ffd
+data8 0xaa705b2001db8317, 0x00003ffd
+data8 0xacb6bb0e1e0f8005, 0x00003ffd
+data8 0xaefee78f75707221, 0x00003ffd
+data8 0xb148e37ec994dd99, 0x00003ffd
+data8 0xb394b1bdaca0bc17, 0x00003ffd
+data8 0xb5e255349707e496, 0x00003ffd
+data8 0xb831d0d2fda791cc, 0x00003ffd
+data8 0xba83278f6838ab20, 0x00003ffd
+data8 0xbcd65c67881c7d47, 0x00003ffd
+data8 0xbeb3e0f21d72dc92, 0x00003ffd
+data8 0xc10a7a03457d35dc, 0x00003ffd
+data8 0xc362f9b6f51eddd3, 0x00003ffd
+data8 0xc5bd6326ebfce656, 0x00003ffd
+data8 0xc7a0b3d0637c8f97, 0x00003ffd
+data8 0xc9fe96af0df8e4b5, 0x00003ffd
+data8 0xcc5e6c214b4a2cd7, 0x00003ffd
+data8 0xce46199f374d29cf, 0x00003ffd
+data8 0xd0a978a14c0d9ebe, 0x00003ffd
+data8 0xd293fecafec7f9b5, 0x00003ffd
+data8 0xd4faf1f6f5cf32e6, 0x00003ffd
+data8 0xd6e8595abaad34d1, 0x00003ffd
+data8 0xd952eb7a8ffc1593, 0x00003ffd
+data8 0xdb433ccd805f171e, 0x00003ffd
+data8 0xddb178dc43e6bd84, 0x00003ffd
+data8 0xdfa4bcfb333342a4, 0x00003ffd
+data8 0xe19953741ccea015, 0x00003ffd
+data8 0xe40cee16a2ff21c5, 0x00003ffd
+data8 0xe6048470cdbde8ea, 0x00003ffd
+data8 0xe7fd7308d6895b14, 0x00003ffd
+data8 0xe9f7bbb6a1ff9f87, 0x00003ffd
+data8 0xec7280138809433d, 0x00003ffd
+data8 0xee6fda4365cd051f, 0x00003ffd
+data8 0xf06e94a122ff1f12, 0x00003ffd
+data8 0xf26eb1151441fce5, 0x00003ffd
+data8 0xf470318b88a77e2f, 0x00003ffd
+data8 0xf67317f4d4c8aa58, 0x00003ffd
+data8 0xf8f8b250a9c4cde6, 0x00003ffd
+data8 0xfafec54831f1a484, 0x00003ffd
+data8 0xfd06449bf3eaea1e, 0x00003ffd
+data8 0xff0f324ddb19ab67, 0x00003ffd
+data8 0x808cc8320a9acf15, 0x00003ffe
+data8 0x8192b0748f2cef06, 0x00003ffe
+data8 0x829952f5e6a24ee5, 0x00003ffe
+data8 0x83a0b0bfafe1424e, 0x00003ffe
+data8 0x8466b29f9c41caea, 0x00003ffe
+data8 0x856f5aae0881d857, 0x00003ffe
+data8 0x8678c0eae8ee8190, 0x00003ffe
+data8 0x8782e6685676b9d7, 0x00003ffe
+data8 0x888dcc3abc4554ec, 0x00003ffe
+data8 0x89997378de7b98b8, 0x00003ffe
+data8 0x8aa5dd3be1044279, 0x00003ffe
+data8 0x8b6facdfd0360ab8, 0x00003ffe
+data8 0x8c7d6db7169e0cdb, 0x00003ffe
+data8 0x8d8bf424d6e130b2, 0x00003ffe
+data8 0x8e575b506f409fa6, 0x00003ffe
+data8 0x8f673e418776492c, 0x00003ffe
+data8 0x9077e9ed700ef9ba, 0x00003ffe
+data8 0x9144ef1baec80b20, 0x00003ffe
+data8 0x9256fcdb537f035f, 0x00003ffe
+data8 0x9369d68d75e7e1d6, 0x00003ffe
+data8 0x943880613b8f9f1e, 0x00003ffe
+data8 0x954cc1d9e0d94206, 0x00003ffe
+data8 0xd3c70a37bdf7a294, 0x0000bffd
+data8 0xd19bb053fb0284ec, 0x0000bffd
+data8 0xcffa1a3b7dafb8bf, 0x0000bffd
+data8 0xcdcbe1e2776479ee, 0x0000bffd
+data8 0xcc282218b8bfdda2, 0x0000bffd
+data8 0xc9f703a9afcb38ac, 0x0000bffd
+data8 0xc851146ab89593c6, 0x0000bffd
+data8 0xc61d08265927a860, 0x0000bffd
+data8 0xc474e39705912d26, 0x0000bffd
+data8 0xc23de19ec30c6e3e, 0x0000bffd
+data8 0xc09381cc45db45b4, 0x0000bffd
+data8 0xbee82b4e025ff90c, 0x0000bffd
+data8 0xbcace101149788ec, 0x0000bffd
+data8 0xbaff46962ea47964, 0x0000bffd
+data8 0xb950b1be5e0c14a2, 0x0000bffd
+data8 0xb7110e6ce866f2bc, 0x0000bffd
+data8 0xb5602ccc2a81db52, 0x0000bffd
+data8 0xb3ae4ce740fc8ef1, 0x0000bffd
+data8 0xb1fb6d92c8240ccc, 0x0000bffd
+data8 0xafb609c09b244abc, 0x0000bffd
+data8 0xae00d1cfdeb43cfd, 0x0000bffd
+data8 0xac4a967a8c8c9bd0, 0x0000bffd
+data8 0xaa93568c249e6c52, 0x0000bffd
+data8 0xa8db10cdff375343, 0x0000bffd
+data8 0xa68e6fc5a42376e3, 0x0000bffd
+data8 0xa4d3c25e68dc57f2, 0x0000bffd
+data8 0xa3180b0c192a3816, 0x0000bffd
+data8 0xa15b488e7aa329a0, 0x0000bffd
+data8 0x9f9d79a30f0e1d5f, 0x0000bffd
+data8 0x9dde9d050ee7d4ac, 0x0000bffd
+data8 0x9c1eb16d63d7356c, 0x0000bffd
+data8 0x9a5db592a310c36a, 0x0000bffd
+data8 0x989ba82907a9016f, 0x0000bffd
+data8 0x96d887e26cd57b79, 0x0000bffd
+data8 0x9514536e481c3a4f, 0x0000bffd
+data8 0x934f0979a3715fc9, 0x0000bffd
+data8 0x9188a8af1742a9d5, 0x0000bffd
+data8 0x8fc12fb6c470995f, 0x0000bffd
+data8 0x8df89d364e34f8f1, 0x0000bffd
+data8 0x8c2eefd0d3f67dd6, 0x0000bffd
+data8 0x8a642626eb093d54, 0x0000bffd
+data8 0x88983ed6985bae58, 0x0000bffd
+data8 0x86cb387b4a0feec6, 0x0000bffd
+data8 0x84fd11add101024b, 0x0000bffd
+data8 0x83c856dd81804b78, 0x0000bffd
+data8 0x81f84c2c62afd6f1, 0x0000bffd
+data8 0x80271d3e4be5ea5a, 0x0000bffd
+data8 0xfca991447e7b485d, 0x0000bffc
+data8 0xf90299c904793a3c, 0x0000bffc
+data8 0xf559511d2dc1ed69, 0x0000bffc
+data8 0xf2e72afee9bd2aee, 0x0000bffc
+data8 0xef39ff1d8a40770e, 0x0000bffc
+data8 0xeb8a7a2311c935dc, 0x0000bffc
+data8 0xe7d8990dc620012f, 0x0000bffc
+data8 0xe560b1e3b86e44b6, 0x0000bffc
+data8 0xe1aadb38caee80c4, 0x0000bffc
+data8 0xddf2a051f81b76a4, 0x0000bffc
+data8 0xdb7678bafcaf4b5f, 0x0000bffc
+data8 0xd7ba3a8f0df19bfc, 0x0000bffc
+data8 0xd3fb8fdbdd5cebdb, 0x0000bffc
+data8 0xd17b191905c35652, 0x0000bffc
+data8 0xcdb85d29cefd7121, 0x0000bffc
+data8 0xc9f32c3c88221ef6, 0x0000bffc
+data8 0xc76e5741a95b5dae, 0x0000bffc
+data8 0xc3a506d80d38c718, 0x0000bffc
+data8 0xbfd938ccef8b68c1, 0x0000bffc
+data8 0xbd4ff63e82eef78c, 0x0000bffc
+data8 0xb97ffa2b563865bd, 0x0000bffc
+data8 0xb6f3eb3011eddcea, 0x0000bffc
+data8 0xb31fb7d64898b3e6, 0x0000bffc
+data8 0xb090d63a409e7880, 0x0000bffc
+data8 0xacb8623c7ffa4f39, 0x0000bffc
+data8 0xa8dd5c83d2e45246, 0x0000bffc
+data8 0xa649e998a8d91f2e, 0x0000bffc
+data8 0xa26a93fed6faa94f, 0x0000bffc
+data8 0x9fd43df079d0db1f, 0x0000bffc
+data8 0x9d3cbe69aecac4c2, 0x0000bffc
+data8 0x99574f13c570d0fb, 0x0000bffc
+data8 0x96bce349bf7ee6c7, 0x0000bffc
+data8 0x92d30c9b86cee18e, 0x0000bffc
+data8 0x9035adef17c5bd5c, 0x0000bffc
+data8 0x8c4765e8e8b5f251, 0x0000bffc
+data8 0x89a70da448316ffa, 0x0000bffc
+data8 0x85b44a24474af78a, 0x0000bffc
+data8 0x8310f17aab5adf70, 0x0000bffc
+data8 0x806c6388d0965f29, 0x0000bffc
+data8 0xf8e69092bf0c5ead, 0x0000bffb
+data8 0xf397608bfd2d90e6, 0x0000bffb
+data8 0xee45be24d0eedbc4, 0x0000bffb
+data8 0xe646af233db881e9, 0x0000bffb
+data8 0xe0eee4e1ce3d06fb, 0x0000bffb
+data8 0xdb94a049e6e87a4f, 0x0000bffb
+data8 0xd3888ef9a4249f5a, 0x0000bffb
+data8 0xce280e6fbac39194, 0x0000bffb
+data8 0xc8c50b72319ad574, 0x0000bffb
+data8 0xc0abcd39f41e329b, 0x0000bffb
+data8 0xbb4279cfa7f9667b, 0x0000bffb
+data8 0xb5d69bac77ec398a, 0x0000bffb
+data8 0xb068306bf20d6233, 0x0000bffb
+data8 0xa83dc1b019ddb6a8, 0x0000bffb
+data8 0xa2c8eb1886c2d024, 0x0000bffb
+data8 0x9d517ee93f8e16c0, 0x0000bffb
+data8 0x97d77aae659b92fb, 0x0000bffb
+data8 0x8f9b91da5736d415, 0x0000bffb
+data8 0x8a1b06b09b7fd1d1, 0x0000bffb
+data8 0x8497daca0a2e077a, 0x0000bffb
+data8 0xfe241745a453f10c, 0x0000bffa
+data8 0xf3132d6708d723c5, 0x0000bffa
+data8 0xe7fcf2e21a0e7d77, 0x0000bffa
+data8 0xd75198b04afb8da9, 0x0000bffa
+data8 0xcc2dfe1a4a8ca305, 0x0000bffa
+data8 0xc10500d63aa65882, 0x0000bffa
+data8 0xb5d69bac77ec398a, 0x0000bffa
+data8 0xaaa2c95dc66abcde, 0x0000bffa
+data8 0x9f6984a342d13101, 0x0000bffa
+data8 0x942ac82e5387ac51, 0x0000bffa
+data8 0x88e68ea899a0976c, 0x0000bffa
+data8 0xefebc4409ccf872e, 0x0000bff9
+data8 0xd947b0c6642ef69e, 0x0000bff9
+data8 0xc2987d51e043d407, 0x0000bff9
+data8 0xabde1eeee6bfd257, 0x0000bff9
+data8 0x95188a9917cf2e01, 0x0000bff9
+data8 0xfc8f6a777c1b7f1e, 0x0000bff8
+data8 0xced727635c59725c, 0x0000bff8
+data8 0xa108358a4c904615, 0x0000bff8
+data8 0xe644fcbeb3ac9c90, 0x0000bff7
+data8 0x8a4bd667bf08e7de, 0x0000bff7
+data8 0x0000000000000000 // T[255] Low
+data8 0x0000000000000000 // T[255] High
+LOCAL_OBJECT_END(T_table)
+
+
+
+.section .text
+GLOBAL_LIBM_ENTRY(log2)
+
+{ .mfi
+  alloc r32=ar.pfs,1,4,4,0     
+  // y=frcpa(x)  
+  frcpa.s1 f6,p0=f1,f8
+  // will form significand of 1.5 (to test whether the index is 128 or above) 
+  mov r24=0xc
+}
+{.mfi
+  nop.m 0
+  // normalize x 
+  fma.s1 f7=f8,f1,f0
+  // r2 = pointer to C_1...C_6 followed by T_table
+  addl r2 = @ltoff(poly_coeffs), gp;;
+}
+{.mfi
+  // get significand
+  getf.sig r25=f8
+  // f8 denormal ?
+  fclass.m p8,p10=f8,0x9
+  // will form significand of 1.5 (to test whether the index is 128 or above) 
+  shl r24=r24,60
+}
+{.mfi
+  mov r26=0x804
+  nop.f 0
+  // r23=bias-1
+  mov r23=0xfffe;;
+}
+
+{.mmf
+  getf.exp r29=f8
+  // load start address for C_1...C_6 followed by T_table
+  ld8 r2=[r2]
+  // will continue only for positive normal/denormal numbers          
+  fclass.nm.unc p12,p7 = f8, 0x19 ;;
+}
+
+.pred.rel "mutex",p8,p10
+{.mfi
+  // denormal input, repeat get significand (after normalization)
+  (p8) getf.sig r25=f7
+  // x=1 ?
+  fcmp.eq.s0 p6,p0=f8,f1
+  // get T_index
+  (p10) shr.u r28=r25,63-8
+}
+{.mfi
+  // f32=0.5
+  setf.exp f32=r23
+  nop.f 0
+  // r27=bias
+  mov r27=0xffff;;
+}
+
+{.mmi
+  // denormal input, repeat get exponent (after normalization)
+  (p8) getf.exp r29=f7
+  mov r23=0xff
+  // r26=0x80400...0 (threshold for using polynomial approximation)
+  shl r26=r26,64-12;;
+}
+
+{.mfb
+  add r3=48,r2
+  // r=1-x*y
+  fms.s1 f6=f6,f8,f1
+  (p12) br.cond.spnt SPECIAL_LOG2
+}
+{.mfi
+  // load C_4, C_5
+  ldfpd f10,f11=[r2],16
+  nop.f 0
+  cmp.geu p12,p0=r25,r24;;
+}
+
+{.mmi
+  // load C_6, C_7
+  ldfpd f12,f13=[r2],16
+  // r27=bias-1 (if index >=128, will add exponent+1) 
+  (p12) mov r27=0xfffe
+  (p8) shr.u r28=r25,63-8;;
+}
+
+
+{.mfi
+  // load C_1
+  ldfe f14=[r2],32
+  fmerge.se f7=f1,f7
+  // if first 9 bits after leading 1 are all zero, then p8=1
+  cmp.ltu p8,p12=r25,r26
+}
+{.mfi
+  // load C_3
+  ldfe f15=[r3]
+  nop.f 0
+  // get T_index
+  and r28=r28,r23;;
+}
+{.mfi
+  // r29=exponent-bias
+  sub r29=r29,r27
+  // x=1, return 0
+  (p6) fma.d.s0 f8=f0,f0,f0
+  // get T address
+  shladd r2=r28,4,r2
+}
+{.mfb
+  // first 8 bits after leading 1 are all ones ?
+  cmp.eq p10,p0=r23,r28
+  // if first 8 bits after leading bit are 0, use polynomial approx. only
+  (p8) fms.s1 f6=f7,f1,f1
+  // x=1, return
+  (p6) br.ret.spnt b0;;
+}
+{.mfi
+  // r26=1
+  mov r26=1
+  // if first 8 bits after leading 1 are all ones, use polynomial approx. only
+  (p10) fms.s1 f6=f7,f32,f1
+  nop.i 0;;
+}
+
+.pred.rel "mutex",p8,p12
+{.mmf
+  // load T (unless first 9 bits after leading 1 are 0)
+  (p12) ldfe f33=[r2]
+  // f8=expon - bias 
+  setf.sig f8=r29
+  // set T=0 (if first 9 bits after leading 1 are 0)
+  (p8) fma.s1 f33=f0,f0,f0;;
+}
+
+{.mfi
+  nop.m 0
+  // P12=1-0.5*r
+  fnma.s1 f32=f32,f6,f1
+  // r26=2^{63}
+  shl r26=r26,63
+}
+{.mfi
+  nop.m 0
+  // r2=r*r
+  fma.s1 f7=f6,f6,f0
+  nop.i 0;;
+}
+{.mfi
+  // significand(x)=1 ?
+  cmp.eq p0,p6=r26,r25
+  // P67=C_6+C_7*r
+  fma.s1 f13=f13,f6,f12
+  nop.i 0
+}
+{.mfi
+  nop.m 0
+  // P45=C_4+C_5*r
+  fma.s1 f10=f11,f6,f10
+  nop.i 0;;
+}
+
+{.mfi
+  nop.m 0
+  // C_1*r
+  (p6) fma.s1 f14=f14,f6,f0
+  nop.i 0;;
+}
+{.mfi
+  nop.m 0
+  // normalize additive term (l=exponent of x)
+  fcvt.xf f8=f8
+  nop.i 0
+}
+{.mfi
+  nop.m 0
+  // P13=1-0.5*r+C_3*r^2
+  (p6) fma.s1 f15=f15,f7,f32
+  nop.i 0;;
+}
+
+{.mfi
+  nop.m 0
+  // P47=P45+r2*P67
+  (p6) fma.s1 f13=f13,f7,f10
+  // if significand(x)=1, return exponent (l)
+  nop.i 0
+}
+{.mfi
+  nop.m 0
+  // r3=r^3
+  (p6) fma.s1 f7=f7,f6,f0
+  nop.i 0;;
+}
+
+{.mfi
+  nop.m 0
+  // add T+l
+  (p6) fma.s1 f8=f8,f1,f33
+  nop.i 0
+}
+{.mfi
+  nop.m 0
+  // P17=P13+r3*P47
+  (p6) fma.s1 f13=f13,f7,f15
+  nop.i 0;;
+}
+
+{.mfb
+  nop.m 0
+  // result=T+l+(C_1*r)*P16
+  (p6) fma.d.s0 f8=f13,f14,f8
+  // return
+  br.ret.sptk b0;;
+}
+
+
+SPECIAL_LOG2:
+{.mfi 
+  nop.m 0
+  // x=+Infinity ?
+  fclass.m p7,p0=f8,0x21
+  nop.i 0;;
+}
+{.mfi
+  nop.m 0
+  // x=+/-Zero ?
+  fclass.m p8,p0=f8,0x7
+  nop.i 0;;
+}
+{.mfi
+  nop.m 0
+  // x=-Infinity, -normal, -denormal ?
+  fclass.m p6,p0=f8,0x3a
+  nop.i 0;;
+}
+{.mfb
+  nop.m 0
+  // log2(+Infinity)=+Infinity
+  nop.f 0
+  (p7) br.ret.spnt b0;;
+}
+{.mfi
+  (p8) mov GR_Parameter_TAG = 170                          
+  // log2(+/-0)=-infinity, raises Divide by Zero
+  // set f8=-0
+  (p8) fmerge.ns f8=f0,f8
+  nop.i 0;;
+}
+{.mfb
+  nop.m 0
+  (p8) frcpa.s0 f8,p0=f1,f8
+  (p8) br.cond.sptk __libm_error_region;;
+}
+{.mfb
+  (p6) mov GR_Parameter_TAG = 171 
+  // x<0: return NaN, raise Invalid
+  (p6) frcpa.s0 f8,p0=f0,f0
+  (p6) br.cond.sptk __libm_error_region;;
+}                          
+  
+
+{.mfb
+  nop.m 0
+  // Remaining cases: NaNs
+  fma.d.s0 f8=f8,f1,f0
+  br.ret.sptk b0;;
+}
+
+GLOBAL_LIBM_END(log2)
+
+
+LOCAL_LIBM_ENTRY(__libm_error_region)
+.prologue
+{ .mfi
+        add   GR_Parameter_Y=-32,sp             // Parameter 2 value
+        nop.f 0
+.save   ar.pfs,GR_SAVE_PFS
+        mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs 
+}
+{ .mfi
+.fframe 64 
+        add sp=-64,sp                           // Create new stack
+        nop.f 0
+        mov GR_SAVE_GP=gp                       // Save gp
+};;
+{ .mmi
+        stfd [GR_Parameter_Y] = FR_Y,16         // STORE Parameter 2 on stack
+        add GR_Parameter_X = 16,sp              // Parameter 1 address
+.save   b0, GR_SAVE_B0                      
+        mov GR_SAVE_B0=b0                       // Save b0 
+};;
+.body
+{ .mib
+        stfd [GR_Parameter_X] = FR_X                  // STORE Parameter 1 on stack 
+        add   GR_Parameter_RESULT = 0,GR_Parameter_Y  // Parameter 3 address 
+	nop.b 0                                      
+}
+{ .mib
+        stfd [GR_Parameter_Y] = FR_RESULT             // STORE Parameter 3 on stack
+        add   GR_Parameter_Y = -16,GR_Parameter_Y  
+        br.call.sptk b0=__libm_error_support#         // Call error handling function
+};;
+{ .mmi
+        nop.m 0
+        nop.m 0
+        add   GR_Parameter_RESULT = 48,sp
+};;
+{ .mmi
+        ldfd  f8 = [GR_Parameter_RESULT]       // Get return result off stack
+.restore sp
+        add   sp = 64,sp                       // Restore stack pointer
+        mov   b0 = GR_SAVE_B0                  // Restore return address
+};;
+{ .mib
+        mov   gp = GR_SAVE_GP                  // Restore gp 
+        mov   ar.pfs = GR_SAVE_PFS             // Restore ar.pfs
+        br.ret.sptk     b0                     // Return
+};; 
+
+LOCAL_LIBM_END(__libm_error_region)
+.type   __libm_error_support#,@function
+.global __libm_error_support#
+
+