2.5-18.1

1 files changed, 2286 insertions, 548 deletions

diff --git a/sysdeps/ia64/fpu/e_asinl.S b/sysdeps/ia64/fpu/e_asinl.S
index 9153832090..ad65a731fc 100644
--- a/sysdeps/ia64/fpu/e_asinl.S
+++ b/sysdeps/ia64/fpu/e_asinl.S
@@ -1,10 +1,10 @@
 .file "asinl.s"
 
-// Copyright (C) 2000, 2001, Intel Corporation
+
+// Copyright (c) 2001 - 2003, 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 2001 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
@@ -20,720 +20,2449 @@
 // * The name of Intel Corporation may not be used to endorse or promote
 // products derived from this software without specific prior written
 // permission.
-//
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS 
-// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT 
+
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS 
+// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
 // CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
-// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, 
-// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR 
-// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY 
+// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
 // OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
-// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS 
-// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 
-// 
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//
 // Intel Corporation is the author of this code, and requests that all
-// problem reports or change requests be submitted to it directly at 
-// http://developer.intel.com/opensource.
+// problem reports or change requests be submitted to it directly at
+// http://www.intel.com/software/products/opensource/libraries/num.htm.
 //
 // History
 //==============================================================
-// 2/02/00  Initial version 
-// 4/04/00  Unwind support added
-// 8/15/00  Bundle added after call to __libm_error_support to properly
-//          set [the previously overwritten] GR_Parameter_RESULT.
+// 08/28/01 New version
+// 05/20/02 Cleaned up namespace and sf0 syntax
+// 02/06/03 Reordered header: .section, .global, .proc, .align
 //
 // API
 //==============================================================
-// long double = asinl(long double)
-// input  floating point f8
-// output floating point f8
+// long double asinl(long double)
 //
-// Registers used
+// Overview of operation
 //==============================================================
+// Background
 //
-// predicate registers used:
-// p6 -> p12
+// Implementation
 //
-// floating-point registers used:
-// f8 has input, then output
-// f32 -> f87, f8 -> f13, f32 -> f87
+// For |s| in [2^{-4}, sqrt(2)/2]:
+// Let t= 2^k*1.b1 b2..b6 1, where s= 2^k*1.b1 b2.. b52
+// asin(s)= asin(t)+asin(r), where r= s*sqrt(1-t^2)-t*sqrt(1-s^2), i.e.
+// r= (s-t)*sqrt(1-t^2)-t*sqrt(1-t^2)*(sqrt((1-s^2)/(1-t^2))-1)
+// asin(r)-r evaluated as 9-degree polynomial (c3*r^3+c5*r^5+c7*r^7+c9*r^9)
+// The 64-bit significands of sqrt(1-t^2), 1/(1-t^2) are read from the table,
+// along with the high and low parts of asin(t) (stored as two double precision
+// values)
 //
-// general registers used:
-// r32 -> r47
+// |s| in (sqrt(2)/2, sqrt(255/256)):
+// Let t= 2^k*1.b1 b2..b6 1, where (1-s^2)*frsqrta(1-s^2)= 2^k*1.b1 b2..b6..
+// asin(|s|)= pi/2-asin(t)+asin(r), r= s*t-sqrt(1-s^2)*sqrt(1-t^2)
+// To minimize accumulated errors, r is computed as
+// r= (t*s)_s-t^2*y*z+z*y*(t^2-1+s^2)_s+z*y*(1-s^2)_s*x+z'*y*(1-s^2)*PS29+
+// +(t*s-(t*s)_s)+z*y*((t^2-1-(t^2-1+s^2)_s)+s^2)+z*y*(1-s^2-(1-s^2)_s)+
+// +ez*z'*y*(1-s^2)*(1-x),
+// where y= frsqrta(1-s^2), z= (sqrt(1-t^2))_s (rounded to 24 significant bits)
+// z'= sqrt(1-t^2), x= ((1-s^2)*y^2-1)/2
+//
+// |s|<2^{-4}: evaluate as 17-degree polynomial
+// (or simply return s, if|s|<2^{-64})
+//
+// |s| in [sqrt(255/256), 1): asin(|s|)= pi/2-asin(sqrt(1-s^2))
+// use 17-degree polynomial for asin(sqrt(1-s^2)),
+// 9-degree polynomial to evaluate sqrt(1-s^2)
+// High order term is (pi/2)_high-(y*(1-s^2))_high
 //
-// Overview of operation
-//==============================================================
-// There are three paths
-// 1. |x| < 2^-40                 ASIN_TINY
-// 2. 2^-40 <= |x| < 1/4          ASIN_POLY
-// 3. 1/4 <= |x| < 1              ASIN_ATAN
 
-#include "libm_support.h"
 
-// Assembly macros
-//==============================================================
-FR_RESULT = f10
-FR_X = f8
-FR_Y = f1
-asin_P79                   = f32
-asin_P59                   = f33
-asin_P39                   = f34
-asin_P19                   = f35
-
-asin_P810                  = f36
-asin_P610                  = f37
-asin_P410                  = f38
-asin_P210                  = f39
-
-asin_A1                    = f41
-asin_A2                    = f42
-asin_A3                    = f43
-asin_A4                    = f44
-asin_A5                    = f45
-asin_A6                    = f46
-asin_A7                    = f47
-asin_A8                    = f48
-asin_A9                    = f49
-asin_A10                   = f50
-
-asin_X2                    = f51
-asin_X4                    = f52
-
-asin_B                     = f53
-asin_Bb                    = f54
-asin_C                     = f55
-asin_Cc                    = f56
-asin_D                     = f57
-
-asin_W                     = f58
-asin_Ww                    = f59
-
-asin_y0                    = f60
-asin_y1                    = f61
-asin_y2                    = f62
-
-asin_H                     = f63
-asin_Hh                    = f64
-
-asin_t1                    = f65
-asin_t2                    = f66
-asin_t3                    = f67
-asin_t4                    = f68
-asin_t5                    = f69
-
-asin_Pseries               = f70
-asin_NORM_f8               = f71
-asin_ABS_NORM_f8           = f72
-
-asin_2m100                 = f73
-asin_P1P2                  = f74
-asin_HALF                  = f75
-asin_1mD                   = f76
-
-asin_1mB                   = f77
-asin_1mBmC                 = f78 
-asin_S                     = f79
-
-asin_BmWW                  = f80 
-asin_BmWWpb                = f81 
-asin_2W                    = f82 
-asin_1d2W                  = f83 
-asin_Dd                    = f84
-
-asin_XWw                   = f85 
-asin_low                   = f86
-
-asin_pi_by_2               = f87
-asin_pi_by_2_lo            = f88
-
-asin_GR_17_ones            = r33
-asin_GR_16_ones            = r34
-asin_GR_signexp_f8         = r35
-asin_GR_exp                = r36
-asin_GR_true_exp           = r37
-asin_GR_ff9b               = r38 
-
-GR_SAVE_B0              = r39
-GR_SAVE_SP              = r40
-GR_SAVE_PFS             = r33 
-// r33 can be used safely.
-// r40 is address of table of coefficients
-// Later it is used to save sp across calls 
-GR_SAVE_GP              = r41
-asin_GR_fffe               = r42 
-asin_GR_retval             = r43 
-
-GR_Parameter_X                 = r44 
-GR_Parameter_Y                 = r45 
-GR_Parameter_RESULT            = r46 
-GR_Parameter_TAG               = r47 
-
-
-// 2^-40:
-// A true exponent of -40 is
-//                    : -40 + register_bias
-//                    : -28 + ffff = ffd7
-
-// A true exponent of -100 is 
-//                    : -100 + register_bias
-//                    : -64 + ffff = ff9b
-
-// Data tables
+
+// Registers used
 //==============================================================
+// f6-f15, f32-f36
+// r2-r3, r23-r23
+// 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
 
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
+       FR_X= f10
+       FR_Y= f1
+       FR_RESULT= f8
+
+
+
+RODATA
 
 .align 16
 
-asin_coefficients:
-ASM_TYPE_DIRECTIVE(asin_coefficients,@object)
-data8  0xBB08911F2013961E, 0x00003FF8            // A10
-data8  0x981F1095A23A87D3, 0x00003FF8            // A9 
-data8  0xBDF09C6C4177BCC6, 0x00003FF8            // A8 
-data8  0xE4C3A60B049ACCEA, 0x00003FF8            // A7 
-data8  0x8E2789F4E8A8F1AD, 0x00003FF9            // A6 
-data8  0xB745D09B2B0E850B, 0x00003FF9            // A5 
-data8  0xF8E38E3BC4C50920, 0x00003FF9            // A4 
-data8  0xB6DB6DB6D89FCD81, 0x00003FFA            // A3 
-data8  0x99999999999AF376, 0x00003FFB            // A2 
-data8  0xAAAAAAAAAAAAAA71, 0x00003FFC            // A1
-
-data8  0xc90fdaa22168c234, 0x00003FFF            // pi_by_2_hi
-data8  0xc4c6628b80dc1cd1, 0x00003FBF            // pi_by_2_lo
-ASM_SIZE_DIRECTIVE(asin_coefficients)
-
-.align 32
-.global asinl#
+
+
+LOCAL_OBJECT_START(T_table)
+
+// stores 64-bit significand of 1/(1-t^2), 64-bit significand of sqrt(1-t^2),
+// asin(t)_high (double precision), asin(t)_low (double precision)
+
+data8 0x80828692b71c4391, 0xff7ddcec2d87e879
+data8 0x3fb022bc0ae531a0, 0x3c9f599c7bb42af6
+data8 0x80869f0163d0b082, 0xff79cad2247914d3
+data8 0x3fb062dd26afc320, 0x3ca4eff21bd49c5c
+data8 0x808ac7d5a8690705, 0xff75a89ed6b626b9
+data8 0x3fb0a2ff4a1821e0, 0x3cb7e33b58f164cc
+data8 0x808f0112ad8ad2e0, 0xff7176517c2cc0cb
+data8 0x3fb0e32279319d80, 0x3caee31546582c43
+data8 0x80934abba8a1da0a, 0xff6d33e949b1ed31
+data8 0x3fb12346b8101da0, 0x3cb8bfe463d087cd
+data8 0x8097a4d3dbe63d8f, 0xff68e16571015c63
+data8 0x3fb1636c0ac824e0, 0x3c8870a7c5a3556f
+data8 0x809c0f5e9662b3dd, 0xff647ec520bca0f0
+data8 0x3fb1a392756ed280, 0x3c964f1a927461ae
+data8 0x80a08a5f33fadc66, 0xff600c07846a6830
+data8 0x3fb1e3b9fc19e580, 0x3c69eb3576d56332
+data8 0x80a515d91d71acd4, 0xff5b892bc475affa
+data8 0x3fb223e2a2dfbe80, 0x3c6a4e19fd972fb6
+data8 0x80a9b1cfc86ff7cd, 0xff56f631062cf93d
+data8 0x3fb2640c6dd76260, 0x3c62041160e0849e
+data8 0x80ae5e46b78b0d68, 0xff5253166bc17794
+data8 0x3fb2a43761187c80, 0x3cac61651af678c0
+data8 0x80b31b417a4b756b, 0xff4d9fdb14463dc8
+data8 0x3fb2e46380bb6160, 0x3cb06ef23eeba7a1
+data8 0x80b7e8c3ad33c369, 0xff48dc7e1baf6738
+data8 0x3fb32490d0d910c0, 0x3caa05f480b300d5
+data8 0x80bcc6d0f9c784d6, 0xff4408fe9ad13e37
+data8 0x3fb364bf558b3820, 0x3cb01e7e403aaab9
+data8 0x80c1b56d1692492d, 0xff3f255ba75f5f4e
+data8 0x3fb3a4ef12ec3540, 0x3cb4fe8fcdf5f5f1
+data8 0x80c6b49bc72ec446, 0xff3a319453ebd961
+data8 0x3fb3e5200d171880, 0x3caf2dc089b2b7e2
+data8 0x80cbc460dc4e0ae8, 0xff352da7afe64ac6
+data8 0x3fb425524827a720, 0x3cb75a855e7c6053
+data8 0x80d0e4c033bee9c4, 0xff301994c79afb32
+data8 0x3fb46585c83a5e00, 0x3cb3264981c019ab
+data8 0x80d615bdb87556db, 0xff2af55aa431f291
+data8 0x3fb4a5ba916c73c0, 0x3c994251d94427b5
+data8 0x80db575d6291fd8a, 0xff25c0f84bae0cb9
+data8 0x3fb4e5f0a7dbdb20, 0x3cbee2fcc4c786cb
+data8 0x80e0a9a33769e535, 0xff207c6cc0ec09fd
+data8 0x3fb526280fa74620, 0x3c940656e5549b91
+data8 0x80e60c93498e32cd, 0xff1b27b703a19c98
+data8 0x3fb56660ccee2740, 0x3ca7082374d7b2cd
+data8 0x80eb8031b8d4052d, 0xff15c2d6105c72f8
+data8 0x3fb5a69ae3d0b520, 0x3c7c4d46e09ac68a
+data8 0x80f10482b25c6c8a, 0xff104dc8e0813ed4
+data8 0x3fb5e6d6586fec20, 0x3c9aa84ffd9b4958
+data8 0x80f6998a709c7cfb, 0xff0ac88e6a4ab926
+data8 0x3fb627132eed9140, 0x3cbced2cbbbe7d16
+data8 0x80fc3f4d3b657c44, 0xff053325a0c8a2ec
+data8 0x3fb667516b6c34c0, 0x3c6489c5fc68595a
+data8 0x8101f5cf67ed2af8, 0xfeff8d8d73dec2bb
+data8 0x3fb6a791120f33a0, 0x3cbe12acf159dfad
+data8 0x8107bd1558d6291f, 0xfef9d7c4d043df29
+data8 0x3fb6e7d226fabba0, 0x3ca386d099cd0dc7
+data8 0x810d95237e38766a, 0xfef411ca9f80b5f7
+data8 0x3fb72814ae53cc20, 0x3cb9f35731e71dd6
+data8 0x81137dfe55aa0e29, 0xfeee3b9dc7eef009
+data8 0x3fb76858ac403a00, 0x3c74df3dd959141a
+data8 0x811977aa6a479f0f, 0xfee8553d2cb8122c
+data8 0x3fb7a89e24e6b0e0, 0x3ca6034406ee42bc
+data8 0x811f822c54bd5ef8, 0xfee25ea7add46a91
+data8 0x3fb7e8e51c6eb6a0, 0x3cb82f8f78e68ed7
+data8 0x81259d88bb4ffac1, 0xfedc57dc2809fb1d
+data8 0x3fb8292d9700ad60, 0x3cbebb73c0e653f9
+data8 0x812bc9c451e5a257, 0xfed640d974eb6068
+data8 0x3fb8697798c5d620, 0x3ca2feee76a9701b
+data8 0x813206e3da0f3124, 0xfed0199e6ad6b585
+data8 0x3fb8a9c325e852e0, 0x3cb9e88f2f4d0efe
+data8 0x813854ec231172f9, 0xfec9e229dcf4747d
+data8 0x3fb8ea1042932a00, 0x3ca5ff40d81f66fd
+data8 0x813eb3e209ee858f, 0xfec39a7a9b36538b
+data8 0x3fb92a5ef2f247c0, 0x3cb5e3bece4d6b07
+data8 0x814523ca796f56ce, 0xfebd428f72561efe
+data8 0x3fb96aaf3b3281a0, 0x3cb7b9e499436d7c
+data8 0x814ba4aa6a2d3ff9, 0xfeb6da672bd48fe4
+data8 0x3fb9ab011f819860, 0x3cb9168143cc1a7f
+data8 0x81523686e29bbdd7, 0xfeb062008df81f50
+data8 0x3fb9eb54a40e3ac0, 0x3cb6e544197eb1e1
+data8 0x8158d964f7124614, 0xfea9d95a5bcbd65a
+data8 0x3fba2ba9cd080800, 0x3ca9a717be8f7446
+data8 0x815f8d49c9d639e4, 0xfea34073551e1ac8
+data8 0x3fba6c009e9f9260, 0x3c741e989a60938a
+data8 0x8166523a8b24f626, 0xfe9c974a367f785c
+data8 0x3fbaac591d0661a0, 0x3cb2c1290107e57d
+data8 0x816d283c793e0114, 0xfe95ddddb94166cb
+data8 0x3fbaecb34c6ef600, 0x3c9c7d5fbaec405d
+data8 0x81740f54e06d55bd, 0xfe8f142c93750c50
+data8 0x3fbb2d0f310cca00, 0x3cbc09479a9cbcfb
+data8 0x817b07891b15cd5e, 0xfe883a3577e9fceb
+data8 0x3fbb6d6ccf1455e0, 0x3cb9450bff4ee307
+data8 0x818210de91bba6c8, 0xfe814ff7162cf62f
+data8 0x3fbbadcc2abb1180, 0x3c9227fda12a8d24
+data8 0x81892b5abb0f2bf9, 0xfe7a55701a8697b1
+data8 0x3fbbee2d48377700, 0x3cb6fad72acfe356
+data8 0x819057031bf7760e, 0xfe734a9f2dfa1810
+data8 0x3fbc2e902bc10600, 0x3cb4465b588d16ad
+data8 0x819793dd479d4fbe, 0xfe6c2f82f643f68b
+data8 0x3fbc6ef4d9904580, 0x3c8b9ac54823960d
+data8 0x819ee1eedf76367a, 0xfe65041a15d8a92c
+data8 0x3fbcaf5b55dec6a0, 0x3ca2b8d28a954db2
+data8 0x81a6413d934f7a66, 0xfe5dc8632be3477f
+data8 0x3fbcefc3a4e727a0, 0x3c9380da83713ab4
+data8 0x81adb1cf21597d4b, 0xfe567c5cd44431d5
+data8 0x3fbd302dcae51600, 0x3ca995b83421756a
+data8 0x81b533a9563310b8, 0xfe4f2005a78fb50f
+data8 0x3fbd7099cc155180, 0x3caefa2f7a817d5f
+data8 0x81bcc6d20cf4f373, 0xfe47b35c3b0caaeb
+data8 0x3fbdb107acb5ae80, 0x3cb455fc372dd026
+data8 0x81c46b4f2f3d6e68, 0xfe40365f20b316d6
+data8 0x3fbdf177710518c0, 0x3cbee3dcc5b01434
+data8 0x81cc2126b53c1144, 0xfe38a90ce72abf36
+data8 0x3fbe31e91d439620, 0x3cb3e131c950aebd
+data8 0x81d3e85ea5bd8ee2, 0xfe310b6419c9c33a
+data8 0x3fbe725cb5b24900, 0x3c01d3fac6029027
+data8 0x81dbc0fd1637b9c1, 0xfe295d6340932d15
+data8 0x3fbeb2d23e937300, 0x3c6304cc44aeedd1
+data8 0x81e3ab082ad5a0a4, 0xfe219f08e03580b3
+data8 0x3fbef349bc2a77e0, 0x3cac1d2d6abe9c72
+data8 0x81eba6861683cb97, 0xfe19d0537a0946e2
+data8 0x3fbf33c332bbe020, 0x3ca0909dba4e96ca
+data8 0x81f3b37d1afc9979, 0xfe11f1418c0f94e2
+data8 0x3fbf743ea68d5b60, 0x3c937fc12a2a779a
+data8 0x81fbd1f388d4be45, 0xfe0a01d190f09063
+data8 0x3fbfb4bc1be5c340, 0x3cbf51a504b55813
+data8 0x820401efbf87e248, 0xfe020201fff9efea
+data8 0x3fbff53b970d1e80, 0x3ca625444b260078
+data8 0x82106ad2ffdca049, 0xfdf5e3940a49135e
+data8 0x3fc02aff52065460, 0x3c9125d113e22a57
+data8 0x8221343d6ea1d3e2, 0xfde581a45429b0a0
+data8 0x3fc06b84f8e03220, 0x3caccf362295894b
+data8 0x82324434adbf99c2, 0xfdd4de1a001fb775
+data8 0x3fc0ac0ed1fe7240, 0x3cc22f676096b0af
+data8 0x82439aee8d0c7747, 0xfdc3f8e8269d1f03
+data8 0x3fc0ec9cee9e4820, 0x3cca147e2886a628
+data8 0x825538a1d0fcb2f0, 0xfdb2d201a9b1ba66
+data8 0x3fc12d2f6006f0a0, 0x3cc72b36633bc2d4
+data8 0x82671d86345c5cee, 0xfda1695934d723e7
+data8 0x3fc16dc63789de60, 0x3cb11f9c47c7b83f
+data8 0x827949d46a121770, 0xfd8fbee13cbbb823
+data8 0x3fc1ae618682e620, 0x3cce1b59020cef8e
+data8 0x828bbdc61eeab9ba, 0xfd7dd28bff0c9f34
+data8 0x3fc1ef015e586c40, 0x3cafec043e0225ee
+data8 0x829e7995fb6de9e1, 0xfd6ba44b823ee1ca
+data8 0x3fc22fa5d07b90c0, 0x3cba905409caf8e3
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+data8 0x3fe6bdd49bea05c0, 0x3cdc6b29937c575d
+data8 0xe2df5765854ccdb0, 0xc049f1c2d1b8014b
+data8 0x3fe712a6b76c6e80, 0x3ce1ddc6f2922321
+data8 0xe71f7a9b94fcb4c3, 0xbe833105ec291e91
+data8 0x3fe76840418978a0, 0x3ccda46e85432c3d
+data8 0xeb96b72d3374b91e, 0xbcb2bb61493b28b3
+data8 0x3fe7bea9496d5a40, 0x3ce37b42ec6e17d3
+data8 0xf049183c3f53c39b, 0xbad848720223d3a8
+data8 0x3fe815ea59dab0a0, 0x3cb03ad41bfc415b
+data8 0xf53b11ec7f415f15, 0xb8f38b57c53c9c48
+data8 0x3fe86e0c84010760, 0x3cc03bfcfb17fe1f
+data8 0xfa718f05adbf2c33, 0xb70432500286b185
+data8 0x3fe8c7196b9225c0, 0x3ced99fcc6866ba9
+data8 0xfff200c3f5489608, 0xb509e6454dca33cc
+data8 0x3fe9211b54441080, 0x3cb789cb53515688
+// The following table entries are not used
+//data8 0x82e138a0fac48700, 0xb3044a513a8e6132
+//data8 0x3fe97c1d30f5b7c0, 0x3ce1eb765612d1d0
+//data8 0x85f4cc7fc670d021, 0xb0f2fb2ea6cbbc88
+//data8 0x3fe9d82ab4b5fde0, 0x3ced3fe6f27e8039
+//data8 0x89377c1387d5b908, 0xaed58e9a09014d5c
+//data8 0x3fea355065f87fa0, 0x3cbef481d25f5b58
+//data8 0x8cad7a2c98dec333, 0xacab929ce114d451
+//data8 0x3fea939bb451e2a0, 0x3c8e92b4fbf4560f
+//data8 0x905b7dfc99583025, 0xaa748cc0dbbbc0ec
+//data8 0x3feaf31b11270220, 0x3cdced8c61bd7bd5
+//data8 0x9446d8191f80dd42, 0xa82ff92687235baf
+//data8 0x3feb53de0bcffc20, 0x3cbe1722fb47509e
+//data8 0x98758ba086e4000a, 0xa5dd497a9c184f58
+//data8 0x3febb5f571cb0560, 0x3ce0c7774329a613
+//data8 0x9cee6c7bf18e4e24, 0xa37be3c3cd1de51b
+//data8 0x3fec197373bc7be0, 0x3ce08ebdb55c3177
+//data8 0xa1b944000a1b9440, 0xa10b2101b4f27e03
+//data8 0x3fec7e6bd023da60, 0x3ce5fc5fd4995959
+//data8 0xa6defd8ba04d3e38, 0x9e8a4b93cad088ec
+//data8 0x3fece4f404e29b20, 0x3cea3413401132b5
+//data8 0xac69dd408a10c62d, 0x9bf89d5d17ddae8c
+//data8 0x3fed4d2388f63600, 0x3cd5a7fb0d1d4276
+//data8 0xb265c39cbd80f97a, 0x99553d969fec7beb
+//data8 0x3fedb714101e0a00, 0x3cdbda21f01193f2
+//data8 0xb8e081a16ae4ae73, 0x969f3e3ed2a0516c
+//data8 0x3fee22e1da97bb00, 0x3ce7231177f85f71
+//data8 0xbfea427678945732, 0x93d5990f9ee787af
+//data8 0x3fee90ac13b18220, 0x3ce3c8a5453363a5
+//data8 0xc79611399b8c90c5, 0x90f72bde80febc31
+//data8 0x3fef009542b712e0, 0x3ce218fd79e8cb56
+//data8 0xcffa8425040624d7, 0x8e02b4418574ebed
+//data8 0x3fef72c3d2c57520, 0x3cd32a717f82203f
+//data8 0xd93299cddcf9cf23, 0x8af6ca48e9c44024
+//data8 0x3fefe762b77744c0, 0x3ce53478a6bbcf94
+//data8 0xe35eda760af69ad9, 0x87d1da0d7f45678b
+//data8 0x3ff02f511b223c00, 0x3ced6e11782c28fc
+//data8 0xeea6d733421da0a6, 0x84921bbe64ae029a
+//data8 0x3ff06c5c6f8ce9c0, 0x3ce71fc71c1ffc02
+//data8 0xfb3b2c73fc6195cc, 0x813589ba3a5651b6
+//data8 0x3ff0aaf2613700a0, 0x3cf2a72d2fd94ef3
+//data8 0x84ac1fcec4203245, 0xfb73a828893df19e
+//data8 0x3ff0eb367c3fd600, 0x3cf8054c158610de
+//data8 0x8ca50621110c60e6, 0xf438a14c158d867c
+//data8 0x3ff12d51caa6b580, 0x3ce6bce9748739b6
+//data8 0x95b8c2062d6f8161, 0xecb3ccdd37b369da
+//data8 0x3ff1717418520340, 0x3ca5c2732533177c
+//data8 0xa0262917caab4ad1, 0xe4dde4ddc81fd119
+//data8 0x3ff1b7d59dd40ba0, 0x3cc4c7c98e870ff5
+//data8 0xac402c688b72f3f4, 0xdcae469be46d4c8d
+//data8 0x3ff200b93cc5a540, 0x3c8dd6dc1bfe865a
+//data8 0xba76968b9eabd9ab, 0xd41a8f3df1115f7f
+//data8 0x3ff24c6f8f6affa0, 0x3cf1acb6d2a7eff7
+//data8 0xcb63c87c23a71dc5, 0xcb161074c17f54ec
+//data8 0x3ff29b5b338b7c80, 0x3ce9b5845f6ec746
+//data8 0xdfe323b8653af367, 0xc19107d99ab27e42
+//data8 0x3ff2edf6fac7f5a0, 0x3cf77f961925fa02
+//data8 0xf93746caaba3e1f1, 0xb777744a9df03bff
+//data8 0x3ff344df237486c0, 0x3cf6ddf5f6ddda43
+//data8 0x8ca77052f6c340f0, 0xacaf476f13806648
+//data8 0x3ff3a0dfa4bb4ae0, 0x3cfee01bbd761bff
+//data8 0xa1a48604a81d5c62, 0xa11575d30c0aae50
+//data8 0x3ff4030b73c55360, 0x3cf1cf0e0324d37c
+//data8 0xbe45074b05579024, 0x9478e362a07dd287
+//data8 0x3ff46ce4c738c4e0, 0x3ce3179555367d12
+//data8 0xe7a08b5693d214ec, 0x8690e3575b8a7c3b
+//data8 0x3ff4e0a887c40a80, 0x3cfbd5d46bfefe69
+//data8 0x94503d69396d91c7, 0xedd2ce885ff04028
+//data8 0x3ff561ebd9c18cc0, 0x3cf331bd176b233b
+//data8 0xced1d96c5bb209e6, 0xc965278083808702
+//data8 0x3ff5f71d7ff42c80, 0x3ce3301cc0b5a48c
+//data8 0xabac2cee0fc24e20, 0x9c4eb1136094cbbd
+//data8 0x3ff6ae4c63222720, 0x3cf5ff46874ee51e
+//data8 0x8040201008040201, 0xb4d7ac4d9acb1bf4
+//data8 0x3ff7b7d33b928c40, 0x3cfacdee584023bb
+LOCAL_OBJECT_END(T_table)
+
+
+
+.align 16
+
+LOCAL_OBJECT_START(poly_coeffs)
+       // C_3
+data8 0xaaaaaaaaaaaaaaab, 0x0000000000003ffc
+       // C_5
+data8 0x999999999999999a, 0x0000000000003ffb
+       // C_7, C_9
+data8 0x3fa6db6db6db6db7, 0x3f9f1c71c71c71c8
+       // pi/2 (low, high)
+data8 0x3C91A62633145C07, 0x3FF921FB54442D18
+       // C_11, C_13
+data8 0x3f96e8ba2e8ba2e9, 0x3f91c4ec4ec4ec4e
+       // C_15, C_17
+data8 0x3f8c99999999999a, 0x3f87a87878787223
+LOCAL_OBJECT_END(poly_coeffs)
+
+
+R_DBL_S = r21
+R_EXP0 = r22
+R_EXP = r15
+R_SGNMASK = r23
+R_TMP = r24
+R_TMP2 = r25
+R_INDEX = r26
+R_TMP3 = r27
+R_TMP03 = r27
+R_TMP4 = r28
+R_TMP5 = r23
+R_TMP6 = r22
+R_TMP7 = r21
+R_T = r29
+R_BIAS = r20
+
+F_T = f6
+F_1S2 = f7
+F_1S2_S = f9
+F_INV_1T2 = f10
+F_SQRT_1T2 = f11
+F_S2T2 = f12
+F_X = f13
+F_D = f14
+F_2M64 = f15
+
+F_CS2 = f32
+F_CS3 = f33
+F_CS4 = f34
+F_CS5 = f35
+F_CS6 = f36
+F_CS7 = f37
+F_CS8 = f38
+F_CS9 = f39
+F_S23 = f40 
+F_S45 = f41 
+F_S67 = f42 
+F_S89 = f43 
+F_S25 = f44 
+F_S69 = f45 
+F_S29 = f46 
+F_X2 = f47 
+F_X4 = f48 
+F_TSQRT = f49 
+F_DTX = f50 
+F_R = f51 
+F_R2 = f52 
+F_R3 = f53 
+F_R4 = f54 
+
+F_C3 = f55 
+F_C5 = f56 
+F_C7 = f57 
+F_C9 = f58 
+F_P79 = f59 
+F_P35 = f60 
+F_P39 = f61 
+
+F_ATHI = f62 
+F_ATLO = f63 
+
+F_T1 = f64 
+F_Y = f65 
+F_Y2 = f66 
+F_ANDMASK = f67 
+F_ORMASK = f68 
+F_S = f69 
+F_05 = f70 
+F_SQRT_1S2 = f71 
+F_DS = f72 
+F_Z = f73 
+F_1T2 = f74 
+F_DZ = f75 
+F_ZE = f76 
+F_YZ = f77 
+F_Y1S2 = f78 
+F_Y1S2X = f79 
+F_1X = f80 
+F_ST = f81 
+F_1T2_ST = f82 
+F_TSS = f83 
+F_Y1S2X2 = f84 
+F_DZ_TERM = f85 
+F_DTS = f86 
+F_DS2X = f87 
+F_T2 = f88 
+F_ZY1S2S = f89 
+F_Y1S2_1X = f90 
+F_TS = f91
+F_PI2_LO = f92 
+F_PI2_HI = f93 
+F_S19 = f94 
+F_INV1T2_2 = f95 
+F_CORR = f96 
+F_DZ0 = f97 
+
+F_C11 = f98 
+F_C13 = f99 
+F_C15 = f100
+F_C17 = f101
+F_P1113 = f102
+F_P1517 = f103
+F_P1117 = f104
+F_P317 = f105
+F_R8 = f106
+F_HI = f107
+F_1S2_HI = f108
+F_DS2 = f109
+F_Y2_2 = f110
+F_S2 = f111
+F_S_DS2 = f112
+F_S_1S2S = f113
+F_XL = f114
+F_2M128 = f115
+
 
 .section .text
-.proc  asinl#
-.align 32
+GLOBAL_LIBM_ENTRY(asinl)
+
+{.mfi
+       // get exponent, mantissa (rounded to double precision) of s
+       getf.d R_DBL_S = f8
+       // 1-s^2
+       fnma.s1 F_1S2 = f8, f8, f1
+       // r2 = pointer to T_table
+       addl r2 = @ltoff(T_table), gp
+}
 
+{.mfi
+       // sign mask
+       mov R_SGNMASK = 0x20000
+       nop.f 0
+       // bias-63-1
+       mov R_TMP03 = 0xffff-64;;
+}
 
-asinl: 
 
-{ .mfi
-      alloc r32 = ar.pfs,1,11,4,0                        
-(p0)  fnorm      asin_NORM_f8 = f8                       
-(p0)  mov        asin_GR_17_ones = 0x1ffff               
+{.mfi
+       // get exponent of s
+       getf.exp R_EXP = f8
+       nop.f 0
+       // R_TMP4 = 2^45
+       shl R_TMP4 = R_SGNMASK, 45-17
 }
 
-{ .mii
-(p0)  mov        asin_GR_16_ones = 0xffff                
-(p0)  mov        asin_GR_ff9b = 0xff9b ;;                   
-      nop.i 999
+{.mlx
+       // load bias-4
+       mov R_TMP = 0xffff-4
+       // load RU(sqrt(2)/2) to integer register (in double format, shifted left by 1)
+       movl R_TMP2 = 0x7fcd413cccfe779a;;
 }
 
 
-{ .mmi
-(p0)  setf.exp  asin_2m100 = asin_GR_ff9b                                      
-(p0)  addl           r40   = @ltoff(asin_coefficients), gp
-      nop.i 999
+{.mfi
+       // load 2^{-64} in FP register
+       setf.exp F_2M64 = R_TMP03
+       nop.f 0
+       // index = (0x7-exponent)|b1 b2.. b6
+       extr.u R_INDEX = R_DBL_S, 46, 9
 }
-;;
 
-{ .mmi
-      ld8 r40 = [r40]
-      nop.m 999
-      nop.i 999
+{.mfi
+       // get t = sign|exponent|b1 b2.. b6 1 x.. x
+       or R_T = R_DBL_S, R_TMP4
+       nop.f 0
+       // R_TMP4 = 2^45-1
+       sub R_TMP4 = R_TMP4, r0, 1;;
 }
-;;
 
 
+{.mfi
+       // get t = sign|exponent|b1 b2.. b6 1 0.. 0
+       andcm R_T = R_T, R_TMP4
+       nop.f 0
+       // eliminate sign from R_DBL_S (shift left by 1)
+       shl R_TMP3 = R_DBL_S, 1
+}
 
-// Load the constants
+{.mfi
+       // R_BIAS = 3*2^6
+       mov R_BIAS = 0xc0
+       nop.f 0
+       // eliminate sign from R_EXP
+       andcm R_EXP0 = R_EXP, R_SGNMASK;;
+}
 
-{ .mmi
-(p0) ldfe       asin_A10 = [r40],16 ;;      
-(p0) ldfe       asin_A9  = [r40],16      
-      nop.i 999 ;;
+
+
+{.mfi
+       // load start address for T_table
+       ld8 r2 = [r2]
+       nop.f 0
+       // p8 = 1 if |s|> = sqrt(2)/2
+       cmp.geu p8, p0 = R_TMP3, R_TMP2
 }
 
-{ .mmi
-(p0) ldfe       asin_A8  = [r40],16 ;;      
-(p0) ldfe       asin_A7  = [r40],16      
-      nop.i 999 ;;
+{.mlx
+       // p7 = 1 if |s|<2^{-4} (exponent of s<bias-4)
+       cmp.lt p7, p0 = R_EXP0, R_TMP
+       // sqrt coefficient cs8 = -33*13/128
+       movl R_TMP2 = 0xc0568000;;
 }
 
-{ .mmi
-(p0) ldfe       asin_A6  = [r40],16 ;;      
-(p0)  getf.exp   asin_GR_signexp_f8  = asin_NORM_f8                            
-      nop.i 999
+
+
+{.mbb
+       // load t in FP register
+       setf.d F_T = R_T
+       // if |s|<2^{-4}, take alternate path
+ (p7) br.cond.spnt SMALL_S
+       // if |s|> = sqrt(2)/2, take alternate path
+ (p8) br.cond.sptk LARGE_S
 }
 
-{ .mmi
-(p0) ldfe       asin_A5  = [r40],16 ;;      
-(p0) ldfe       asin_A4  = [r40],16      
-      nop.i 999 ;;
+{.mlx
+       // index = (4-exponent)|b1 b2.. b6
+       sub R_INDEX = R_INDEX, R_BIAS
+       // sqrt coefficient cs9 = 55*13/128
+       movl R_TMP = 0x40b2c000;;
 }
 
-{ .mfi
-      nop.m 999
-(p0) fmerge.s   asin_ABS_NORM_f8 = f0, asin_NORM_f8            
-(p0)  and        asin_GR_exp         = asin_GR_signexp_f8, asin_GR_17_ones ;;     
+
+{.mfi
+       // sqrt coefficient cs8 = -33*13/128
+       setf.s F_CS8 = R_TMP2
+       nop.f 0
+       // shift R_INDEX by 5
+       shl R_INDEX = R_INDEX, 5
+}
+
+{.mfi
+       // sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
+       mov R_TMP4 = 0xffff - 1
+       nop.f 0
+       // sqrt coefficient cs6 = -21/16
+       mov R_TMP6 = 0xbfa8;;
 }
 
-// case 1: |x| < 2^-40         ==> p6 (includes x = +-0)
-// case 2: 2^-40 <= |x| < 2^-2 ==> p8
-// case 3: 2^-2  <= |x| < 1    ==> p9
-// case 4: 1  <= |x|           ==> p11
-//   In case 4, we pick up the special case x = +-1 and return +-pi/2
 
-{ .mii
-(p0) ldfe       asin_A3  = [r40],16      
-(p0)  sub        asin_GR_true_exp    = asin_GR_exp, asin_GR_16_ones ;;            
-(p0)  cmp.ge.unc p6, p7    = -41, asin_GR_true_exp ;;             
+{.mlx
+       // table index
+       add r2 = r2, R_INDEX
+       // sqrt coefficient cs7 = 33/16
+       movl R_TMP2 = 0x40040000;;
 }
 
-{ .mii
-(p0) ldfe       asin_A2  = [r40],16      
-(p7)  cmp.ge.unc p8, p9    = -3,  asin_GR_true_exp ;;             
-(p9)  cmp.ge.unc p10, p11  = -1,  asin_GR_true_exp              
+
+{.mmi
+       // load cs9 = 55*13/128
+       setf.s F_CS9 = R_TMP
+       // sqrt coefficient cs5 = 7/8
+       mov R_TMP3 = 0x3f60
+       // sqrt coefficient cs6 = 21/16
+       shl R_TMP6 = R_TMP6, 16;;
 }
 
-{ .mmi
-(p0) ldfe       asin_A1  = [r40],16 ;;      
-(p0) ldfe       asin_pi_by_2  = [r40],16 
-      nop.i 999
+
+{.mmi
+       // load significand of 1/(1-t^2)
+       ldf8 F_INV_1T2 = [r2], 8
+       // sqrt coefficient cs7 = 33/16
+       setf.s F_CS7 = R_TMP2
+       // sqrt coefficient cs4 = -5/8
+       mov R_TMP5 = 0xbf20;;
 }
 
-// case 4: |x| >= 1
-{ .mib
-      nop.m 999
-      nop.i 999
-(p11) br.spnt         L(ASIN_ERROR_RETURN) ;;                         
+
+{.mmi
+       // load significand of sqrt(1-t^2)
+       ldf8 F_SQRT_1T2 = [r2], 8
+       // sqrt coefficient cs6 = 21/16
+       setf.s F_CS6 = R_TMP6
+       // sqrt coefficient cs5 = 7/8
+       shl R_TMP3 = R_TMP3, 16;;
 }
 
-// case 1: |x| < 2^-40
-{ .mfb
-      nop.m 999
-(p6)  fma.s0         f8 = asin_2m100,f8,f8                       
-(p6)  br.ret.spnt   b0 ;;                                          
+
+{.mmi
+       // sqrt coefficient cs3 = 0.5 (set exponent = bias-1)
+       setf.exp F_CS3 = R_TMP4
+       // r3 = pointer to polynomial coefficients
+       addl r3 = @ltoff(poly_coeffs), gp
+       // sqrt coefficient cs4 = -5/8
+       shl R_TMP5 = R_TMP5, 16;;
 }
 
 
-// case 2: 2^-40 <= |x| < 2^-2 ==> p8
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_X2   = f8,f8, f0                       
-      nop.i 999 ;;
+{.mfi
+       // sqrt coefficient cs5 = 7/8
+       setf.s F_CS5 = R_TMP3
+       // d = s-t
+       fms.s1 F_D = f8, f1, F_T
+       // set p6 = 1 if s<0, p11 = 1 if s> = 0
+       cmp.ge p6, p11 = R_EXP, R_DBL_S
 }
 
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_X4   = asin_X2,asin_X2, f0             
-      nop.i 999 ;;
+{.mfi
+       // r3 = load start address to polynomial coefficients
+       ld8 r3 = [r3]
+       // s+t
+       fma.s1 F_S2T2 = f8, f1, F_T
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_P810 = asin_X4, asin_A10, asin_A8      
-      nop.i 999
+
+{.mfi
+       // sqrt coefficient cs4 = -5/8
+       setf.s F_CS4 = R_TMP5
+       // s^2-t^2
+       fma.s1 F_S2T2 = F_S2T2, F_D, f0
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_P79  = asin_X4, asin_A9, asin_A7       
-      nop.i 999 ;;
+
+{.mfi
+       // load C3
+       ldfe F_C3 = [r3], 16
+       // 0.5/(1-t^2) = 2^{-64}*(2^63/(1-t^2))
+       fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_P610 = asin_X4, asin_P810, asin_A6     
-      nop.i 999
+{.mfi
+       // load C_5
+       ldfe F_C5 = [r3], 16
+       // set correct exponent for sqrt(1-t^2)
+       fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_P59  = asin_X4, asin_P79, asin_A5      
-      nop.i 999 ;;
+
+{.mfi
+       // load C_7, C_9
+       ldfpd F_C7, F_C9 = [r3]
+       // x = -(s^2-t^2)/(1-t^2)/2
+       fnma.s1 F_X = F_INV_1T2, F_S2T2, f0
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_P410 = asin_X4, asin_P610, asin_A4     
-      nop.i 999
+
+{.mfi
+       // load asin(t)_high, asin(t)_low
+       ldfpd F_ATHI, F_ATLO = [r2]
+       // t*sqrt(1-t^2)
+       fma.s1 F_TSQRT = F_T, F_SQRT_1T2, f0
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_P39  = asin_X4, asin_P59, asin_A3      
-      nop.i 999 ;;
+
+{.mfi
+       nop.m 0
+       // cs9*x+cs8
+       fma.s1 F_S89 = F_CS9, F_X, F_CS8
+       nop.i 0
 }
 
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_P210 = asin_X4, asin_P410, asin_A2     
-      nop.i 999
+{.mfi
+       nop.m 0
+       // cs7*x+cs6
+       fma.s1 F_S67 = F_CS7, F_X, F_CS6
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_P19  = asin_X4, asin_P39, asin_A1      
-      nop.i 999 ;;
+{.mfi
+       nop.m 0
+       // cs5*x+cs4
+       fma.s1 F_S45 = F_CS5, F_X, F_CS4
+       nop.i 0
 }
 
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_P1P2    = asin_X2, asin_P210, asin_P19 
-      nop.i 999 ;;
+{.mfi
+       nop.m 0
+       // x*x
+       fma.s1 F_X2 = F_X, F_X, f0
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p8)  fma.s1        asin_P1P2    = asin_X2, asin_P1P2, f0       
-      nop.i 999 ;;
+
+{.mfi
+       nop.m 0
+       // (s-t)-t*x
+       fnma.s1 F_DTX = F_T, F_X, F_D
+       nop.i 0
 }
 
-{ .mfb
-      nop.m 999
-(p8)  fma.s0        f8 = asin_NORM_f8, asin_P1P2, asin_NORM_f8  
-(p8)  br.ret.spnt   b0 ;;                                          
+{.mfi
+       nop.m 0
+       // cs3*x+cs2 (cs2 = -0.5 = -cs3)
+       fms.s1 F_S23 = F_CS3, F_X, F_CS3
+       nop.i 0;;
 }
 
-// case 3: 2^-2  <= |x| < 1    
-// 1- X*X is computed as B + b
-// Step 1.1:     Get B and b
 
-// atan2 will return
-//   f8  = Z_hi
-//   f10 = Z_lo
-//   f11 = s_lo
+{.mfi
+       nop.m 0
+       // cs9*x^3+cs8*x^2+cs7*x+cs6
+       fma.s1 F_S69 = F_S89, F_X2, F_S67
+       nop.i 0
+}
 
+{.mfi
+       nop.m 0
+       // x^4
+       fma.s1 F_X4 = F_X2, F_X2, f0
+       nop.i 0;;
+}
 
-{ .mfi
-(p0)  mov            asin_GR_fffe = 0xfffe                      
-(p0)   fmerge.se f8 = asin_ABS_NORM_f8, asin_ABS_NORM_f8                                   
-nop.i 0
-};;
 
-{ .mmf
-nop.m 0
-(p0)   setf.exp       asin_HALF = asin_GR_fffe                   
-(p0)   fmerge.se f12 = asin_NORM_f8, asin_NORM_f8 ;;                         
+{.mfi
+       nop.m 0
+       // t*sqrt(1-t^2)*x^2
+       fma.s1 F_TSQRT = F_TSQRT, F_X2, f0
+       nop.i 0
 }
 
+{.mfi
+       nop.m 0
+       // cs5*x^3+cs4*x^2+cs3*x+cs2
+       fma.s1 F_S25 = F_S45, F_X2, F_S23
+       nop.i 0;;
+}
 
-{ .mfi
-      nop.m 999
-(p0)  fcmp.lt.unc.s1 p6,p7 = asin_ABS_NORM_f8, asin_HALF        
-      nop.i 999 ;;
+
+{.mfi
+       nop.m 0
+       // ((s-t)-t*x)*sqrt(1-t^2)
+       fma.s1 F_DTX = F_DTX, F_SQRT_1T2, f0
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p7)  fma.s1         asin_D   = f1,f1,asin_ABS_NORM_f8          
-      nop.i 999
+
+{.mfi
+       nop.m 0
+       // if sign is negative, negate table values: asin(t)_low
+ (p6) fnma.s1 F_ATLO = F_ATLO, f1, f0
+       nop.i 0
 }
 
-{ .mfi
-      nop.m 999
-(p7)  fms.s1         asin_C   = f1,f1,asin_ABS_NORM_f8          
-      nop.i 999 ;;
+{.mfi
+       nop.m 0
+       // PS29 = cs9*x^7+..+cs5*x^3+cs4*x^2+cs3*x+cs2
+       fma.s1 F_S29 = F_S69, F_X4, F_S25
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p7)  fma.s1         asin_B   = asin_C, asin_D, f0              
-      nop.i 999
+
+{.mfi
+       nop.m 0
+       // if sign is negative, negate table values: asin(t)_high
+ (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0
+       nop.i 0
 }
 
-{ .mfi
-      nop.m 999
-(p7)  fms.s1         asin_1mD = f1,f1,asin_D                    
-      nop.i 999 ;;
+{.mfi
+       nop.m 0
+       // R = ((s-t)-t*x)*sqrt(1-t^2)-t*sqrt(1-t^2)*x^2*PS29
+       fnma.s1 F_R = F_S29, F_TSQRT, F_DTX
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p7)  fma.s1         asin_Dd  = asin_1mD,f1, asin_ABS_NORM_f8   
-      nop.i 999
+
+{.mfi
+       nop.m 0
+       // R^2
+       fma.s1 F_R2 = F_R, F_R, f0
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p7)  fms.s1         asin_Bb  = asin_C, asin_D, asin_B          
-      nop.i 999 ;;
+
+{.mfi
+       nop.m 0
+       // c7+c9*R^2
+       fma.s1 F_P79 = F_C9, F_R2, F_C7
+       nop.i 0
 }
 
-{ .mfi
-      nop.m 999
-(p7)  fma.s1         asin_Bb  = asin_C, asin_Dd, asin_Bb        
-      nop.i 999
+{.mfi
+       nop.m 0
+       // c3+c5*R^2
+       fma.s1 F_P35 = F_C5, F_R2, F_C3
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p6)  fma.s1         asin_C   = asin_ABS_NORM_f8, asin_ABS_NORM_f8, f0     
-      nop.i 999 ;;
+{.mfi
+       nop.m 0
+       // R^3
+       fma.s1 F_R4 = F_R2, F_R2, f0
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p6)  fms.s1         asin_B   = f1, f1, asin_C                             
-      nop.i 999
+{.mfi
+       nop.m 0
+       // R^3
+       fma.s1 F_R3 = F_R2, F_R, f0
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p6)  fms.s1         asin_Cc  = asin_ABS_NORM_f8, asin_ABS_NORM_f8, asin_C 
-      nop.i 999 ;;
+
+
+{.mfi
+       nop.m 0
+       // c3+c5*R^2+c7*R^4+c9*R^6
+       fma.s1 F_P39 = F_P79, F_R4, F_P35
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_Hh     = asin_HALF, asin_B, f0                   
-      nop.i 999
+
+{.mfi
+       nop.m 0
+       // asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
+       fma.s1 F_P39 = F_P39, F_R3, F_ATLO
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p6)  fms.s1         asin_1mB = f1, f1, asin_B                             
-      nop.i 999 ;;
+
+{.mfi
+       nop.m 0
+       // R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
+       fma.s1 F_P39 = F_P39, f1, F_R
+       nop.i 0;;
 }
 
-// Step 1.2: 
-// sqrt(B + b) is computed as W + w
-// Get W
 
-{ .mfi
-      nop.m 999
-(p0)  frsqrta.s1     asin_y0,p8  = asin_B                                  
-      nop.i 999 ;;
+{.mfb
+       nop.m 0
+       // result = asin(t)_high+R+asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
+       fma.s0 f8 = F_ATHI, f1, F_P39
+       // return
+       br.ret.sptk b0;;
 }
 
-{ .mfi
-      nop.m 999
-(p6)  fms.s1         asin_1mBmC = asin_1mB, f1, asin_C                     
-      nop.i 999 ;;
+
+
+
+LARGE_S:
+
+{.mfi
+       // bias-1
+       mov R_TMP3 = 0xffff - 1
+       // y ~ 1/sqrt(1-s^2)
+       frsqrta.s1 F_Y, p7 = F_1S2
+       // c9 = 55*13*17/128
+       mov R_TMP4 = 0x10af7b
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_t1     = asin_y0, asin_y0, f0                    
-      nop.i 999 ;;
+{.mlx
+       // c8 = -33*13*15/128
+       mov R_TMP5 = 0x184923
+       movl R_TMP2 = 0xff00000000000000;;
 }
 
-{ .mfi
-      nop.m 999
-(p6)  fms.s1         asin_Bb  = asin_1mBmC, f1, asin_Cc                    
-      nop.i 999 ;;
+{.mfi
+       // set p6 = 1 if s<0, p11 = 1 if s>0
+       cmp.ge p6, p11 = R_EXP, R_DBL_S
+       // 1-s^2
+       fnma.s1 F_1S2 = f8, f8, f1
+       // set p9 = 1
+       cmp.eq p9, p0 = r0, r0;;
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fnma.s1        asin_t2     = asin_t1, asin_Hh, asin_HALF             
-      nop.i 999 ;;
+
+{.mfi
+       // load 0.5
+       setf.exp F_05 = R_TMP3
+       // (1-s^2) rounded to single precision
+       fnma.s.s1 F_1S2_S = f8, f8, f1
+       // c9 = 55*13*17/128
+       shl R_TMP4 = R_TMP4, 10
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_y1     = asin_t2, asin_y0, asin_y0               
-      nop.i 999 ;;
+{.mlx
+       // AND mask for getting t ~ sqrt(1-s^2)
+       setf.sig F_ANDMASK = R_TMP2
+       // OR mask
+       movl R_TMP2 = 0x0100000000000000;;
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_t3     = asin_y1, asin_Hh, f0                    
-      nop.i 999 ;;
+
+{.mfi
+       nop.m 0
+       // (s^2)_s
+       fma.s.s1 F_S2 = f8, f8, f0
+       nop.i 0;;
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fnma.s1        asin_t4     = asin_t3, asin_y1, asin_HALF             
-      nop.i 999 ;;
+
+{.mmi
+       // c9 = 55*13*17/128
+       setf.s F_CS9 = R_TMP4
+       // c7 = 33*13/16
+       mov R_TMP4 = 0x41d68
+       // c8 = -33*13*15/128
+       shl R_TMP5 = R_TMP5, 11;;
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_y2     = asin_t4, asin_y1, asin_y1               
-      nop.i 999 ;;
+
+{.mfi
+       setf.sig F_ORMASK = R_TMP2
+       // y^2
+       fma.s1 F_Y2 = F_Y, F_Y, f0
+       // c7 = 33*13/16
+       shl R_TMP4 = R_TMP4, 12
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_S      = asin_B, asin_y2, f0                     
-      nop.i 999
+{.mfi
+       // c6 = -33*7/16
+       mov R_TMP6 = 0xc1670
+       // y' ~ sqrt(1-s^2)
+       fma.s1 F_T1 = F_Y, F_1S2, f0
+       // c5 = 63/8
+       mov R_TMP7 = 0x40fc;;
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_H      = asin_y2, asin_HALF, f0                  
-      nop.i 999 ;;
+
+{.mlx
+       // load c8 = -33*13*15/128
+       setf.s F_CS8 = R_TMP5
+       // c4 = -35/8
+       movl R_TMP5 = 0xc08c0000;;
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_t5     = asin_Hh, asin_y2, f0                    
-      nop.i 999 ;;
+{.mfi
+       // r3 = pointer to polynomial coefficients
+       addl r3 = @ltoff(poly_coeffs), gp
+       // 1-(1-s^2)_s
+       fnma.s1 F_DS = F_1S2_S, f1, f1
+       // p9 = 0 if p7 = 1 (p9 = 1 for special cases only)
+ (p7) cmp.ne p9, p0 = r0, r0
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fnma.s1        asin_Dd     = asin_S, asin_S, asin_B                  
-      nop.i 999 ;;
+{.mlx
+       // load c7 = 33*13/16
+       setf.s F_CS7 = R_TMP4
+       // c3 = 5/2
+       movl R_TMP4 = 0x40200000;;
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_W      = asin_Dd, asin_H, asin_S                 
-      nop.i 999 ;;
+
+{.mfi
+       nop.m 0
+       // 1-(s^2)_s
+       fnma.s1 F_S_1S2S = F_S2, f1, f1
+       nop.i 0
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_2W       = asin_W, f1, asin_W                    
-      nop.i 999
+{.mlx
+       // load c4 = -35/8
+       setf.s F_CS4 = R_TMP5
+       // c2 = -3/2
+       movl R_TMP5 = 0xbfc00000;;
 }
 
-// Step 1.3
-// Get w
-{ .mfi
-      nop.m 999
-(p0)  fnma.s1        asin_BmWW     = asin_W, asin_W, asin_B                
-      nop.i 999 ;;
+
+{.mfi
+       // load c3 = 5/2
+       setf.s F_CS3 = R_TMP4
+       // x = (1-s^2)_s*y^2-1
+       fms.s1 F_X = F_1S2_S, F_Y2, f1
+       // c6 = -33*7/16
+       shl R_TMP6 = R_TMP6, 12
 }
 
-// Step 2
-// asin(x) = atan2(X,sqrt(1-X*X))
-//         = atan2(X, W) -Xw
-// corr = Xw
-// asin(x) = Z_hi + (s_lo*Z_lo - corr)
-// Call atan2(X, W)
-// Save W in f9 
-// Save X in f12 
-// Save w in f13
+{.mfi
+       nop.m 0
+       // y^2/2
+       fma.s1 F_Y2_2 = F_Y2, F_05, f0
+       nop.i 0;;
+}
 
-{ .mfi
-      nop.m 999
-(p0)   fmerge.se f9 = asin_W, asin_W                                      
-      nop.i 999 ;;
+
+{.mfi
+       // load c6 = -33*7/16
+       setf.s F_CS6 = R_TMP6
+       // eliminate lower bits from y'
+       fand F_T = F_T1, F_ANDMASK
+       // c5 = 63/8
+       shl R_TMP7 = R_TMP7, 16
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_BmWWpb   = asin_BmWW, f1, asin_Bb                
-      nop.i 999 ;;
+{.mfb
+       // r3 = load start address to polynomial coefficients
+       ld8 r3 = [r3]
+       // 1-(1-s^2)_s-s^2
+       fnma.s1 F_DS = f8, f8, F_DS
+       // p9 = 1 if s is a special input (NaN, or |s|> = 1)
+ (p9) br.cond.spnt ASINL_SPECIAL_CASES;;
 }
 
-{ .mfi
-      nop.m 999
-(p0)  frcpa.s1       asin_1d2W,p9  = f1, asin_2W                           
-      nop.i 999 ;;
+{.mmf
+       // get exponent, significand of y' (in single prec.)
+       getf.s R_TMP = F_T1
+       // load c3 = -3/2
+       setf.s F_CS2 = R_TMP5
+       // y*(1-s^2)
+       fma.s1 F_Y1S2 = F_Y, F_1S2, f0;;
 }
 
-{ .mfi
-      nop.m 999
-(p0)  fma.s1         asin_Ww       = asin_BmWWpb, asin_1d2W, f0            
-      nop.i 999 ;;
+
+{.mfi
+       nop.m 0
+       // x' = (y^2/2)*(1-(s^2)_s)-0.5
+       fms.s1 F_XL = F_Y2_2, F_S_1S2S, F_05
+       nop.i 0
 }
-.endp asinl
-ASM_SIZE_DIRECTIVE(asinl)
 
-.proc __libm_callout
-__libm_callout:
-.prologue
-{ .mfi
-        nop.m 0
-        nop.f 0
-.save   ar.pfs,GR_SAVE_PFS
-        mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
-};;
-{ .mfi
-        mov GR_SAVE_GP=gp                       // Save gp
-        nop.f 0
-.save   b0, GR_SAVE_B0
-        mov GR_SAVE_B0=b0                       // Save b0
+{.mfi
+       nop.m 0
+       // s^2-(s^2)_s
+       fms.s1 F_S_DS2 = f8, f8, F_S2
+       nop.i 0;;
 }
-.body
+
+
+{.mfi
+       nop.m 0
+       // if s<0, set s = -s
+ (p6) fnma.s1 f8 = f8, f1, f0
+       nop.i 0;;
+}
+
+{.mfi
+       // load c5 = 63/8
+       setf.s F_CS5 = R_TMP7
+       // x = (1-s^2)_s*y^2-1+(1-(1-s^2)_s-s^2)*y^2
+       fma.s1 F_X = F_DS, F_Y2, F_X
+       // for t = 2^k*1.b1 b2.., get 7-k|b1.. b6
+       extr.u R_INDEX = R_TMP, 17, 9;;
+}
+
+
+{.mmi
+       // index = (4-exponent)|b1 b2.. b6
+       sub R_INDEX = R_INDEX, R_BIAS
+       nop.m 0
+       // get exponent of y
+       shr.u R_TMP2 = R_TMP, 23;;
+}
+
+{.mmi
+       // load C3
+       ldfe F_C3 = [r3], 16
+       // set p8 = 1 if y'<2^{-4}
+       cmp.gt p8, p0 = 0x7b, R_TMP2
+       // shift R_INDEX by 5
+       shl R_INDEX = R_INDEX, 5;;
+}
+
+
 {.mfb
-        nop.m 0
-(p0)    fmerge.se f13 = asin_Ww, asin_Ww                                   
-(p0)    br.call.sptk.many  b0=__libm_atan2_reg#                  
-};;
-{ .mfi
-        mov   gp = GR_SAVE_GP                  // Restore gp
-(p0)    fma.s1  asin_XWw  = asin_ABS_NORM_f8,f13,f0             
-        mov   b0 = GR_SAVE_B0                  // Restore return address
-};;
-// asin_XWw = Xw = corr
-// asin_low = (s_lo * Z_lo - corr)
-// f8       = Z_hi + (s_lo * Z_lo - corr)
+       // get table index for sqrt(1-t^2)
+       add r2 = r2, R_INDEX
+       // get t = 2^k*1.b1 b2.. b7 1
+       for F_T = F_T, F_ORMASK
+ (p8) br.cond.spnt VERY_LARGE_INPUT;;
+}
 
-{ .mfi
-        nop.m 999
-(p0)    fms.s1  asin_low  = f11, f10, asin_XWw                                
-        mov   ar.pfs = GR_SAVE_PFS             // Restore ar.pfs
-};;
 
-{ .mfi
-      nop.m 999
-(p0)   fma.s0  f8        = f8, f1, asin_low                                
-      nop.i 999 ;;
+
+{.mmf
+       // load C5
+       ldfe F_C5 = [r3], 16
+       // load 1/(1-t^2)
+       ldfp8 F_INV_1T2, F_SQRT_1T2 = [r2], 16
+       // x = ((1-s^2)*y^2-1)/2
+       fma.s1 F_X = F_X, F_05, f0;;
 }
 
-{ .mfb
-      nop.m 999
-(p0)   fmerge.s f8 = f12,f8 
-(p0)  br.ret.sptk   b0 ;;                                                    
+
+
+{.mmf
+       nop.m 0
+       // C7, C9
+       ldfpd F_C7, F_C9 = [r3], 16
+       // set correct exponent for t
+       fmerge.se F_T = F_T1, F_T;;
 }
-.endp __libm_callout
-ASM_SIZE_DIRECTIVE(__libm_callout)
 
-.proc SPECIAL
-SPECIAL:
-L(ASIN_ERROR_RETURN): 
 
-// If X is 1, return (sign of X)pi/2
 
-{ .mfi
-      nop.m 999
-(p0)  fcmp.eq.unc p6,p7 = asin_ABS_NORM_f8,f1   
-      nop.i 999 ;;
+{.mfi
+       // pi/2 (low, high)
+       ldfpd F_PI2_LO, F_PI2_HI = [r3]
+       // c9*x+c8
+       fma.s1 F_S89 = F_X, F_CS9, F_CS8
+       nop.i 0
 }
 
-{ .mfb
-(p6) ldfe          asin_pi_by_2_lo  = [r40] 
-(p6) fmerge.s      asin_pi_by_2 = f8,asin_pi_by_2          
-     nop.b 0;;
+{.mfi
+       nop.m 0
+       // x^2
+       fma.s1 F_X2 = F_X, F_X, f0
+       nop.i 0;;
 }
 
-// If X is a NAN, leave
-// qnan snan inf norm     unorm 0 -+
-// 1    1    0   0        0     0 11
-{ .mfb
-      nop.m 999
-(p6)  fma.s0     f8 = f8,asin_pi_by_2_lo,asin_pi_by_2              
-(p6)  br.ret.spnt   b0                           
+
+{.mfi
+       nop.m 0
+       // y*(1-s^2)*x
+       fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
+       nop.i 0
 }
-{ .mfi
-      nop.m 999
-(p0)  fclass.m.unc p12,p0 = f8, 0xc3            
-      nop.i 999 ;;
+
+{.mfi
+       nop.m 0
+       // c7*x+c6
+       fma.s1 F_S67 = F_X, F_CS7, F_CS6
+       nop.i 0;;
 }
 
-{ .mfb
-      nop.m 999
-(p12) fma.s0 f8 = f8,f1,f0                       
-(p12) br.ret.spnt   b0 ;;                          
+
+{.mfi
+       nop.m 0
+       // 1-x
+       fnma.s1 F_1X = F_X, f1, f1
+       nop.i 0
 }
-{ .mfi
-(p0)   mov   GR_Parameter_TAG = 60                   
-(p0)   frcpa f10, p6 = f0, f0                   
-nop.i 0
-};;
-.endp SPECIAL
-ASM_SIZE_DIRECTIVE(SPECIAL)
 
-.proc __libm_error_region
-__libm_error_region:
+{.mfi
+       nop.m 0
+       // c3*x+c2
+       fma.s1 F_S23 = F_X, F_CS3, F_CS2
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // 1-t^2
+       fnma.s1 F_1T2 = F_T, F_T, f1
+       nop.i 0
+}
+
+{.mfi
+       // load asin(t)_high, asin(t)_low
+       ldfpd F_ATHI, F_ATLO = [r2]
+       // c5*x+c4
+       fma.s1 F_S45 = F_X, F_CS5, F_CS4
+       nop.i 0;;
+}
+
+
+
+{.mfi
+       nop.m 0
+       // t*s
+       fma.s1 F_TS = F_T, f8, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // 0.5/(1-t^2)
+       fma.s1 F_INV_1T2 = F_INV_1T2, F_2M64, f0
+       nop.i 0;;
+}
+
+{.mfi
+       nop.m 0
+       // z~sqrt(1-t^2), rounded to 24 significant bits
+       fma.s.s1 F_Z = F_SQRT_1T2, F_2M64, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // sqrt(1-t^2)
+       fma.s1 F_SQRT_1T2 = F_SQRT_1T2, F_2M64, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // y*(1-s^2)*x^2
+       fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // x^4
+       fma.s1 F_X4 = F_X2, F_X2, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // s*t rounded to 24 significant bits
+       fma.s.s1 F_TSS = F_T, f8, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // c9*x^3+..+c6
+       fma.s1 F_S69 = F_X2, F_S89, F_S67
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // ST = (t^2-1+s^2) rounded to 24 significant bits
+       fms.s.s1 F_ST = f8, f8, F_1T2
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // c5*x^3+..+c2
+       fma.s1 F_S25 = F_X2, F_S45, F_S23
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // 0.25/(1-t^2)
+       fma.s1 F_INV1T2_2 = F_05, F_INV_1T2, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // t*s-sqrt(1-t^2)*(1-s^2)*y
+       fnma.s1 F_TS = F_Y1S2, F_SQRT_1T2, F_TS
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // z*0.5/(1-t^2)
+       fma.s1 F_ZE = F_INV_1T2, F_SQRT_1T2, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // z^2+t^2-1
+       fms.s1 F_DZ0 = F_Z, F_Z, F_1T2
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (1-s^2-(1-s^2)_s)*x
+       fma.s1 F_DS2X = F_X, F_DS, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // t*s-(t*s)_s
+       fms.s1 F_DTS = F_T, f8, F_TSS
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // c9*x^7+..+c2
+       fma.s1 F_S29 = F_X4, F_S69, F_S25
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // y*z
+       fma.s1 F_YZ = F_Z, F_Y, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // t^2
+       fma.s1 F_T2 = F_T, F_T, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // 1-t^2+ST
+       fma.s1 F_1T2_ST = F_ST, f1, F_1T2
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // y*(1-s^2)(1-x)
+       fma.s1 F_Y1S2_1X = F_Y1S2, F_1X, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // dz ~ sqrt(1-t^2)-z
+       fma.s1 F_DZ = F_DZ0, F_ZE, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // -1+correction for sqrt(1-t^2)-z
+       fnma.s1 F_CORR = F_INV1T2_2, F_DZ0, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (PS29*x^2+x)*y*(1-s^2)
+       fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // z*y*(1-s^2)_s
+       fma.s1 F_ZY1S2S = F_YZ, F_1S2_S, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // s^2-(1-t^2+ST)
+       fms.s1 F_1T2_ST = f8, f8, F_1T2_ST
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x
+       fma.s1 F_DTS = F_YZ, F_DS2X, F_DTS
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // dz*y*(1-s^2)*(1-x)
+       fma.s1 F_DZ_TERM = F_DZ, F_Y1S2_1X, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // R = t*s-sqrt(1-t^2)*(1-s^2)*y+sqrt(1-t^2)*(1-s^2)*y*PS19
+       // (used for polynomial evaluation)
+       fma.s1 F_R = F_S19, F_SQRT_1T2, F_TS
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (PS29*x^2)*y*(1-s^2)
+       fma.s1 F_S29 = F_Y1S2X2, F_S29, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // apply correction to dz*y*(1-s^2)*(1-x)
+       fma.s1 F_DZ_TERM = F_DZ_TERM, F_CORR, F_DZ_TERM
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // R^2
+       fma.s1 F_R2 = F_R, F_R, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (t*s-(t*s)_s)+z*y*(1-s^2-(1-s^2)_s)*x+dz*y*(1-s^2)*(1-x)
+       fma.s1 F_DZ_TERM = F_DZ_TERM, f1, F_DTS
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c7+c9*R^2
+       fma.s1 F_P79 = F_C9, F_R2, F_C7
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // c3+c5*R^2
+       fma.s1 F_P35 = F_C5, F_R2, F_C3
+       nop.i 0;;
+}
+
+{.mfi
+       nop.m 0
+       // asin(t)_low-(pi/2)_low
+       fms.s1 F_ATLO = F_ATLO, f1, F_PI2_LO
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // R^4
+       fma.s1 F_R4 = F_R2, F_R2, f0
+       nop.i 0;;
+}
+
+{.mfi
+       nop.m 0
+       // R^3
+       fma.s1 F_R3 = F_R2, F_R, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (t*s)_s-t^2*y*z
+       fnma.s1 F_TSS = F_T2, F_YZ, F_TSS
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)
+       fma.s1 F_DZ_TERM = F_YZ, F_1T2_ST, F_DZ_TERM
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (pi/2)_hi-asin(t)_hi
+       fms.s1 F_ATHI = F_PI2_HI, f1, F_ATHI
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // c3+c5*R^2+c7*R^4+c9*R^6
+       fma.s1 F_P39 = F_P79, F_R4, F_P35
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST)+
+       // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29
+       fma.s1 F_DZ_TERM = F_SQRT_1T2, F_S29, F_DZ_TERM
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (t*s)_s-t^2*y*z+z*y*ST
+       fma.s1 F_TSS = F_YZ, F_ST, F_TSS
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // -asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
+       fms.s1 F_P39 = F_P39, F_R3, F_ATLO
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // if s<0, change sign of F_ATHI
+ (p6) fnma.s1 F_ATHI = F_ATHI, f1, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
+       // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 +
+       // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
+       fma.s1 F_DZ_TERM = F_P39, f1, F_DZ_TERM
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
+       // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x +
+       // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6)
+       fma.s1 F_DZ_TERM = F_ZY1S2S, F_X, F_DZ_TERM
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // d(ts)+z*y*d(1-s^2)*x+dz*y*(1-s^2)*(1-x)+z*y*(s^2-1+t^2-ST) +
+       // + sqrt(1-t^2)*y*(1-s^2)*x^2*PS29 + z*y*(1-s^2)_s*x +
+       // - asin(t)_low+R^3*(c3+c5*R^2+c7*R^4+c9*R^6) +
+       // + (t*s)_s-t^2*y*z+z*y*ST
+       fma.s1 F_DZ_TERM = F_TSS, f1, F_DZ_TERM
+       nop.i 0;;
+}
+
+
+.pred.rel "mutex", p6, p11
+{.mfi
+       nop.m 0
+       // result: add high part of pi/2-table value
+       // s>0 in this case
+ (p11) fma.s0 f8 = F_DZ_TERM, f1, F_ATHI
+       nop.i 0
+}
+
+{.mfb
+       nop.m 0
+       // result: add high part of pi/2-table value
+       // if s<0
+ (p6) fnma.s0 f8 = F_DZ_TERM, f1, F_ATHI
+       br.ret.sptk b0;;
+}
+
+
+
+
+
+
+SMALL_S:
+
+       // use 15-term polynomial approximation
+
+{.mmi
+       // r3 = pointer to polynomial coefficients
+       addl r3 = @ltoff(poly_coeffs), gp;;
+       // load start address for coefficients
+       ld8 r3 = [r3]
+       mov R_TMP = 0x3fbf;;
+}
+
+
+{.mmi
+       add r2 = 64, r3
+       ldfe F_C3 = [r3], 16
+       // p7 = 1 if |s|<2^{-64} (exponent of s<bias-64)
+       cmp.lt p7, p0 = R_EXP0, R_TMP;;
+}
+
+{.mmf
+       ldfe F_C5 = [r3], 16
+       ldfpd F_C11, F_C13 = [r2], 16
+	   // 2^{-128}
+       fma.s1 F_2M128 = F_2M64, F_2M64, f0;;
+}
+
+{.mmf
+       ldfpd F_C7, F_C9 = [r3]
+       ldfpd F_C15, F_C17 = [r2]
+       // if |s|<2^{-64}, return s+2^{-128}*s
+ (p7) fma.s0 f8 = f8, F_2M128, f8;;
+}
+
+
+
+{.mfb
+       nop.m 0
+       // s^2
+       fma.s1 F_R2 = f8, f8, f0
+       // if |s|<2^{-64}, return s
+ (p7) br.ret.spnt b0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // s^3
+       fma.s1 F_R3 = f8, F_R2, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // s^4
+       fma.s1 F_R4 = F_R2, F_R2, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c3+c5*s^2
+       fma.s1 F_P35 = F_C5, F_R2, F_C3
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // c11+c13*s^2
+       fma.s1 F_P1113 = F_C13, F_R2, F_C11
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c7+c9*s^2
+       fma.s1 F_P79 = F_C9, F_R2, F_C7
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // c15+c17*s^2
+       fma.s1 F_P1517 = F_C17, F_R2, F_C15
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // s^8
+       fma.s1 F_R8 = F_R4, F_R4, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c3+c5*s^2+c7*s^4+c9*s^6
+       fma.s1 F_P39 = F_P79, F_R4, F_P35
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // c11+c13*s^2+c15*s^4+c17*s^6
+       fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c3+..+c17*s^14
+       fma.s1 F_P317 = F_R8, F_P1117, F_P39
+       nop.i 0;;
+}
+
+
+{.mfb
+       nop.m 0
+       // result
+       fma.s0 f8 = F_P317, F_R3, f8
+       br.ret.sptk b0;;
+}
+
+
+{.mfb
+       nop.m 0
+       fma.s0 f8 = F_P317, F_R3, f0//F_P317, F_R3, F_S29
+       // nop.f 0//fma.s0 f8 = f13, f6, f0
+       br.ret.sptk b0;;
+}
+
+
+
+
+
+       VERY_LARGE_INPUT:
+
+{.mfi
+       nop.m 0
+       // s rounded to 24 significant bits
+       fma.s.s1 F_S = f8, f1, f0
+       nop.i 0
+}
+
+{.mfi
+       // load C5
+       ldfe F_C5 = [r3], 16
+       // x = ((1-(s^2)_s)*y^2-1)/2-(s^2-(s^2)_s)*y^2/2
+       fnma.s1 F_X = F_S_DS2, F_Y2_2, F_XL
+       nop.i 0;;
+}
+
+
+
+{.mmf
+       nop.m 0
+       // C7, C9
+       ldfpd F_C7, F_C9 = [r3], 16
+       nop.f 0;;
+}
+
+
+
+{.mfi
+       // pi/2 (low, high)
+       ldfpd F_PI2_LO, F_PI2_HI = [r3], 16
+       // c9*x+c8
+       fma.s1 F_S89 = F_X, F_CS9, F_CS8
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // x^2
+       fma.s1 F_X2 = F_X, F_X, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // y*(1-s^2)*x
+       fma.s1 F_Y1S2X = F_Y1S2, F_X, f0
+       nop.i 0
+}
+
+{.mfi
+       // C11, C13
+       ldfpd F_C11, F_C13 = [r3], 16
+       // c7*x+c6
+       fma.s1 F_S67 = F_X, F_CS7, F_CS6
+       nop.i 0;;
+}
+
+
+{.mfi
+       // C15, C17
+       ldfpd F_C15, F_C17 = [r3], 16
+       // c3*x+c2
+       fma.s1 F_S23 = F_X, F_CS3, F_CS2
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c5*x+c4
+       fma.s1 F_S45 = F_X, F_CS5, F_CS4
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (s_s)^2
+       fma.s1 F_DS = F_S, F_S, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // 1-(s_s)^2
+       fnma.s1 F_1S2_S = F_S, F_S, f1
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // y*(1-s^2)*x^2
+       fma.s1 F_Y1S2X2 = F_Y1S2, F_X2, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // x^4
+       fma.s1 F_X4 = F_X2, F_X2, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c9*x^3+..+c6
+       fma.s1 F_S69 = F_X2, F_S89, F_S67
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c5*x^3+..+c2
+       fma.s1 F_S25 = F_X2, F_S45, F_S23
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // ((s_s)^2-s^2)
+       fnma.s1 F_DS = f8, f8, F_DS
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // (pi/2)_high-y*(1-(s_s)^2)
+       fnma.s1 F_HI = F_Y, F_1S2_S, F_PI2_HI
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c9*x^7+..+c2
+       fma.s1 F_S29 = F_X4, F_S69, F_S25
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // -(y*(1-(s_s)^2))_high
+       fms.s1 F_1S2_HI = F_HI, f1, F_PI2_HI
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (PS29*x^2+x)*y*(1-s^2)
+       fma.s1 F_S19 = F_Y1S2X2, F_S29, F_Y1S2X
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // y*(1-(s_s)^2)-(y*(1-s^2))_high
+       fma.s1 F_DS2 = F_Y, F_1S2_S, F_1S2_HI
+       nop.i 0;;
+}
+
+
+
+{.mfi
+       nop.m 0
+       // R ~ sqrt(1-s^2)
+       // (used for polynomial evaluation)
+       fnma.s1 F_R = F_S19, f1, F_Y1S2
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // y*(1-s^2)-(y*(1-s^2))_high
+       fma.s1 F_DS2 = F_Y, F_DS, F_DS2
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // (pi/2)_low+(PS29*x^2)*y*(1-s^2)
+       fma.s1 F_S29 = F_Y1S2X2, F_S29, F_PI2_LO
+       nop.i 0;;
+}
+
+
+
+{.mfi
+       nop.m 0
+       // R^2
+       fma.s1 F_R2 = F_R, F_R, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (pi/2)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)
+       fms.s1 F_S29 = F_S29, f1, F_DS2
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c7+c9*R^2
+       fma.s1 F_P79 = F_C9, F_R2, F_C7
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // c3+c5*R^2
+       fma.s1 F_P35 = F_C5, F_R2, F_C3
+       nop.i 0;;
+}
+
+
+
+{.mfi
+       nop.m 0
+       // R^4
+       fma.s1 F_R4 = F_R2, F_R2, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // R^3
+       fma.s1 F_R3 = F_R2, F_R, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c11+c13*R^2
+       fma.s1 F_P1113 = F_C13, F_R2, F_C11
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // c15+c17*R^2
+       fma.s1 F_P1517 = F_C17, F_R2, F_C15
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (pi/2)_low+(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-(y*(1-s^2))_high)+y*(1-s^2)*x
+       fma.s1 F_S29 = F_Y1S2, F_X, F_S29
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c11+c13*R^2+c15*R^4+c17*R^6
+       fma.s1 F_P1117 = F_P1517, F_R4, F_P1113
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // c3+c5*R^2+c7*R^4+c9*R^6
+       fma.s1 F_P39 = F_P79, F_R4, F_P35
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // R^8
+       fma.s1 F_R8 = F_R4, F_R4, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // c3+c5*R^2+c7*R^4+c9*R^6+..+c17*R^14
+       fma.s1 F_P317 = F_P1117, F_R8, F_P39
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // (pi/2)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
+       // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
+       fnma.s1 F_S29 = F_P317, F_R3, F_S29
+       nop.i 0;;
+}
+
+{.mfi
+       nop.m 0
+       // set sign
+  (p6) fnma.s1 F_S29 = F_S29, f1, f0
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+  (p6) fnma.s1 F_HI = F_HI, f1, f0
+       nop.i 0;;
+}
+
+
+{.mfb
+       nop.m 0
+       // Result:
+       // (pi/2)_low-(PS29*x^2)*y*(1-s^2)-(y*(1-s^2)-
+       // -(y*(1-s^2))_high)+y*(1-s^2)*x - P3, 17
+       // +(pi/2)_high-(y*(1-s^2))_high
+       fma.s0 f8 = F_S29, f1, F_HI
+       br.ret.sptk b0;;
+}
+
+
+
+
+
+
+
+
+
+       ASINL_SPECIAL_CASES:
+
+{.mfi
+       alloc r32 = ar.pfs, 1, 4, 4, 0
+       // check if the input is a NaN, or unsupported format
+       // (i.e. not infinity or normal/denormal)
+       fclass.nm p7, p8 = f8, 0x3f
+       // pointer to pi/2
+       add r3 = 48, r3;;
+}
+
+
+{.mfi
+       // load pi/2
+       ldfpd F_PI2_HI, F_PI2_LO = [r3]
+       // get |s|
+       fmerge.s F_S = f0, f8
+       nop.i 0
+}
+
+{.mfb
+       nop.m 0
+       // if NaN, quietize it, and return
+ (p7) fma.s0 f8 = f8, f1, f0
+ (p7) br.ret.spnt b0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // |s| = 1 ?
+       fcmp.eq.s0 p9, p0 = F_S, f1
+       nop.i 0
+}
+
+{.mfi
+       nop.m 0
+       // load FR_X
+       fma.s1 FR_X = f8, f1, f0
+       // load error tag
+       mov GR_Parameter_TAG = 60;;
+}
+
+
+{.mfb
+       nop.m 0
+       // change sign if s = -1
+ (p6)  fnma.s1 F_PI2_HI = F_PI2_HI, f1, f0
+       nop.b 0
+}
+
+{.mfb
+       nop.m 0
+       // change sign if s = -1
+ (p6)  fnma.s1 F_PI2_LO = F_PI2_LO, f1, f0
+       nop.b 0;;
+}
+
+{.mfb
+       nop.m 0
+       // if s = 1, result is pi/2
+ (p9) fma.s0 f8 = F_PI2_HI, f1, F_PI2_LO
+       // return if |s| = 1
+ (p9) br.ret.sptk b0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // get Infinity
+       frcpa.s1 FR_RESULT, p0 = f1, f0
+       nop.i 0;;
+}
+
+
+{.mfi
+       nop.m 0
+       // return QNaN indefinite (0*Infinity)
+       fma.s0 FR_RESULT = f0, FR_RESULT, f0
+       nop.i 0;;
+}
+
+
+GLOBAL_LIBM_END(asinl)
+
+
+
+LOCAL_LIBM_ENTRY(__libm_error_region)
 .prologue
+// (1)
 { .mfi
         add   GR_Parameter_Y=-32,sp             // Parameter 2 value
         nop.f 0
@@ -742,24 +2471,29 @@ __libm_error_region:
 }
 { .mfi
 .fframe 64
-        add sp=-64,sp                           // Create new stack
+        add sp=-64,sp                          // Create new stack
         nop.f 0
-        mov GR_SAVE_GP=gp                       // Save gp
+        mov GR_SAVE_GP=gp                      // Save gp
 };;
+
+
+// (2)
 { .mmi
-        stfe [GR_Parameter_Y] = FR_Y,16         // Store Parameter 2 on stack
-        add GR_Parameter_X = 16,sp              // Parameter 1 address
+        stfe [GR_Parameter_Y] = f1,16         // 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
-        stfe [GR_Parameter_X] = FR_X            // Store Parameter 1 on stack
+        stfe [GR_Parameter_X] = FR_X              // Store Parameter 1 on stack
         add   GR_Parameter_RESULT = 0,GR_Parameter_Y
         nop.b 0                                 // Parameter 3 address
 }
 { .mib
-        stfe [GR_Parameter_Y] = FR_RESULT       // Store Parameter 3 on stack
+        stfe [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
 };;
@@ -768,23 +2502,27 @@ __libm_error_region:
         nop.m 0
         add   GR_Parameter_RESULT = 48,sp
 };;
+
+// (4)
 { .mmi
         ldfe  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   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#
 
-.type   __libm_atan2_reg#,@function
-.global __libm_atan2_reg#
+
+
+
+