2.5-18.1

1 files changed, 325 insertions, 413 deletions

diff --git a/sysdeps/ia64/fpu/e_atan2.S b/sysdeps/ia64/fpu/e_atan2.S
index 38dd2f749a..7a17fbfed4 100644
--- a/sysdeps/ia64/fpu/e_atan2.S
+++ b/sysdeps/ia64/fpu/e_atan2.S
@@ -1,10 +1,10 @@
 .file "atan2.s"
 
-// Copyright (C) 2000, 2001, Intel Corporation
+
+// Copyright (c) 2000 - 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 2000 by the Intel Numerics Group, Intel Corporation
 //
 // Redistribution and use in source and binary forms, with or without
 // modification, are permitted provided that the following conditions are
@@ -20,33 +20,39 @@
 // * 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.
-// 8/17/00  Changed predicate register macro-usage to direct predicate
-//          names due to an assembler bug.
-// 9/28/00  Updated to set invalid on SNaN inputs
-// 1/19/01  Fixed flags for small results
+// 02/02/00  Initial version
+// 04/04/00  Unwind support added
+// 08/15/00  Bundle added after call to __libm_error_support to properly
+//           set [the previously overwritten] GR_Parameter_RESULT.
+// 08/17/00  Changed predicate register macro-usage to direct predicate
+//           names due to an assembler bug.
+// 09/28/00  Updated to set invalid on SNaN inputs
+// 01/19/01  Fixed flags for small results
+// 04/13/01  Rescheduled to make all paths faster
+// 05/20/02  Cleaned up namespace and sf0 syntax
+// 08/20/02  Corrected inexact flag and directed rounding symmetry bugs
+// 02/06/03  Reordered header: .section, .global, .proc, .align
+// 04/17/03  Added missing mutex directive
+// 12/23/03  atan2(NaN1,NaN2) now QNaN1, for consistency with atan2f, atan2l
 //
 // API
 //==============================================================
@@ -55,10 +61,12 @@
 // Overview of operation
 //==============================================================
 //
+// The atan2 function returns values in the interval [-pi,+pi].
+//
 // There are two basic paths: swap true and swap false.
 // atan2(Y,X) ==> atan2(V/U) where U >= V. If Y > X, we must swap.
 //
-// p6  swap True    |Y| > |X| 
+// p6  swap True    |Y| > |X|
 // p7  swap False   |Y| <= |X|
 // p8  X+   (If swap=True p8=p9=0)
 // p9  X-
@@ -66,21 +74,21 @@
 // all the other predicates p10 thru p15 are false for the main path
 //
 // Simple trigonometric identities show
-//   Region 1 (-45 to +45 degrees):  
+//   Region 1 (-45 to +45 degrees):
 //         X>0, |Y|<=X, V=Y, U=X     atan2(Y,X) = sgnY * (0 + atan(V/U))
 //
-//   Region 2 (-90 to -45 degrees, and +45 to +90 degrees):  
+//   Region 2 (-90 to -45 degrees, and +45 to +90 degrees):
 //         X>0, |Y|>X, V=X, U=Y      atan2(Y,X) = sgnY * (pi/2 - atan(V/U))
 //
-//   Region 3 (-135 to -90 degrees, and +90 to +135 degrees):  
+//   Region 3 (-135 to -90 degrees, and +90 to +135 degrees):
 //         X<0, |Y|>X, V=X, U=Y      atan2(Y,X) = sgnY * (pi/2 + atan(V/U))
 //
-//   Region 4 (-180 to -135 degrees, and +135 to +180 degrees):  
+//   Region 4 (-180 to -135 degrees, and +135 to +180 degrees):
 //         X<0, |Y|<=X, V=Y, U=X      atan2(Y,X) = sgnY * (pi - atan(V/U))
 //
 // So the result is always of the form atan2(Y,X) = P + sgnXY * atan(V/U)
 //
-// We compute atan(V/U) from the identity 
+// We compute atan(V/U) from the identity
 //      atan(z) + atan([(V/U)-z] / [1+(V/U)z])
 //      where z is a limited precision approximation (16 bits) to V/U
 //
@@ -124,30 +132,40 @@
 //             +number           -0          +pi/2
 //             -number           -0          -pi/2
 //
-//             +0                +number     +0 
-//             -0                +number     -0 
+//             +0                +number     +0
+//             -0                +number     -0
 //             +0                -number     +pi
 //             -0                -number     -pi
 //
-//             +0                +0          +0 
-//             -0                +0          -0 
+//             +0                +0          +0
+//             -0                +0          -0
 //             +0                -0          +pi
 //             -0                -0          -pi
 //
 //            Nan             anything      quiet Y
-//            anything        NaN           quiet X
+//            Not NaN         NaN           quiet X
 
 // atan2(+-0/+-0) sets double error tag to 37
-// atan2(+-0/+-0) sets single error tag to 38
 
-#include "libm_support.h"
+// Registers used
+//==============================================================
+
+// predicate registers used:
+// p6 -> p15
+
+// floating-point registers used:
+// f8, f9 input
+// f32 -> f119
+
+// general registers used
+// r32 -> r41
 
 // Assembly macros
 //==============================================================
 
 EXP_AD_P1                    = r33
 EXP_AD_P2                    = r34
-atan2_GR_sml_exp             = r35
+rsig_near_one                = r35
 
 
 GR_SAVE_B0                   = r35
@@ -159,22 +177,23 @@ GR_Parameter_Y               = r39
 GR_Parameter_RESULT          = r40
 atan2_GR_tag                 = r41
 
-
-atan2_X                      = f9
 atan2_Y                      = f8
+atan2_X                      = f9
 
 atan2_u1_X                   = f32
 atan2_u1_Y                   = f33
-atan2_Umax                   = f34
-atan2_Vmin                   = f35
+atan2_z2_X                   = f34
+atan2_z2_Y                   = f35
+
 atan2_two                    = f36
-atan2_absX                   = f37
+atan2_B1sq_Y                 = f37
 atan2_z1_X                   = f38
 atan2_z1_Y                   = f39
 atan2_B1X                    = f40
+
 atan2_B1Y                    = f41
-atan2_wp                     = f42
-atan2_B1sq                   = f43
+atan2_wp_X                   = f42
+atan2_B1sq_X                 = f43
 atan2_z                      = f44
 atan2_w                      = f45
 
@@ -183,178 +202,149 @@ atan2_P1                     = f47
 atan2_P2                     = f48
 atan2_P3                     = f49
 atan2_P4                     = f50
+
 atan2_P5                     = f51
 atan2_P6                     = f52
 atan2_P7                     = f53
 atan2_P8                     = f54
 atan2_P9                     = f55
+
 atan2_P10                    = f56
 atan2_P11                    = f57
 atan2_P12                    = f58
 atan2_P13                    = f59
 atan2_P14                    = f60
+
 atan2_P15                    = f61
 atan2_P16                    = f62
 atan2_P17                    = f63
 atan2_P18                    = f64
 atan2_P19                    = f65
+
 atan2_P20                    = f66
 atan2_P21                    = f67
 atan2_P22                    = f68
-atan2_Pi_by_2                = f69
-
+atan2_tmp                    = f68
+atan2_pi_by_2                = f69
+atan2_sgn_pi_by_2            = f69
 atan2_V13                    = f70
+
 atan2_W11                    = f71
 atan2_E                      = f72
-atan2_gamma                  = f73
+atan2_wp_Y                   = f73
 atan2_V11                    = f74
 atan2_V12                    = f75
+
 atan2_V7                     = f76
 atan2_V8                     = f77
 atan2_W7                     = f78
 atan2_W8                     = f79
 atan2_W3                     = f80
+
 atan2_W4                     = f81
 atan2_V3                     = f82
 atan2_V4                     = f83
 atan2_F                      = f84
 atan2_gV                     = f85
+
 atan2_V10                    = f86
 atan2_zcub                   = f87
 atan2_V6                     = f88
 atan2_V9                     = f89
 atan2_W10                    = f90
+
 atan2_W6                     = f91
 atan2_W2                     = f92
 atan2_V2                     = f93
-
 atan2_alpha                  = f94
 atan2_alpha_1                = f95
+
 atan2_gVF                    = f96
 atan2_V5                     = f97
 atan2_W12                    = f98
 atan2_W5                     = f99
 atan2_alpha_sq               = f100
+
 atan2_Cp                     = f101
 atan2_V1                     = f102
-
-atan2_sml_norm               = f103
-atan2_FR_tmp                 = f103
-
+atan2_ysq                    = f103
 atan2_W1                     = f104
 atan2_alpha_cub              = f105
+
 atan2_C                      = f106
-atan2_P                      = f107
+atan2_xsq                    = f107
 atan2_d                      = f108
 atan2_A_hi                   = f109
 atan2_dsq                    = f110
+
 atan2_pd                     = f111
 atan2_A_lo                   = f112
 atan2_A                      = f113
-
 atan2_Pp                     = f114
+atan2_sgnY                   = f115
 
-atan2_sgnY                   = f116
+atan2_sig_near_one           = f116
+atan2_near_one               = f116
 atan2_pi                     = f117
-atan2_sgnX                   = f118
-atan2_sgnXY                  = f119
-
-atan2_3pi_by_4               = f120
-atan2_pi_by_4                = f121
-
-//atan2_sF                     = p7
-//atan2_sT                     = p6
+atan2_sgn_pi                 = f117
+atan2_3pi_by_4               = f118
+atan2_pi_by_4                = f119
 
-// These coefficients are for atan2. 
-// You can also use this set to substitute those used in the |X| <= 1 case for atan; 
-// BUT NOT vice versa.
 
 /////////////////////////////////////////////////////////////
 
 
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
+RODATA
 
 .align 16
 
-atan2_tb1:
-ASM_TYPE_DIRECTIVE(atan2_tb1,@object)
-data8 0xB199DD6D2675C40F ,  0x0000BFFA // P10
+LOCAL_OBJECT_START(atan2_tb1)
 data8 0xA21922DC45605EA1 ,  0x00003FFA // P11
-data8 0xD78F28FC2A592781 ,  0x0000BFFA // P8
+data8 0xB199DD6D2675C40F ,  0x0000BFFA // P10
 data8 0xC2F01E5DDD100DBE ,  0x00003FFA // P9
-data8 0x9D89D7D55C3287A5 ,  0x00003FFB // P5
+data8 0xD78F28FC2A592781 ,  0x0000BFFA // P8
 data8 0xF0F03ADB3FC930D3 ,  0x00003FFA // P7
-data8 0xF396268151CFB11C ,  0x00003FF7 // P17 
-data8 0x9D3436AABE218776 ,  0x00003FF5 // P19
-data8 0x80D601879218B53A ,  0x00003FFA // P13
-data8 0xA2270D30A90AA220 ,  0x00003FF9 // P15
-data8 0xCCCCCCCCCCC906CD ,  0x00003FFC // P1
+data8 0x88887EBB209E3543 ,  0x0000BFFB // P6
+data8 0x9D89D7D55C3287A5 ,  0x00003FFB // P5
+data8 0xBA2E8B9793955C77 ,  0x0000BFFB // P4
 data8 0xE38E38E320A8A098 ,  0x00003FFB // P3
-data8 0xFE7E52D2A89995B3 ,  0x0000BFEC // P22
-data8 0xC90FDAA22168C235 ,  0x00003FFE // pi/4
-ASM_SIZE_DIRECTIVE(atan2_tb1)
+data8 0x9249249247E37913 ,  0x0000BFFC // P2
+data8 0xCCCCCCCCCCC906CD ,  0x00003FFC // P1
+data8 0xAAAAAAAAAAAAA8A9 ,  0x0000BFFD // P0
+data8 0xC90FDAA22168C235 ,  0x00004000 // pi
+LOCAL_OBJECT_END(atan2_tb1)
 
-atan2_tb2:
-ASM_TYPE_DIRECTIVE(atan2_tb2,@object)
-data8 0x9F90FB984D8E39D0 ,  0x0000BFF3 // P20
+LOCAL_OBJECT_START(atan2_tb2)
 data8 0xCE585A259BD8374C ,  0x00003FF0 // P21
-data8 0xBA2E8B9793955C77 ,  0x0000BFFB // P4
-data8 0x88887EBB209E3543 ,  0x0000BFFB // P6
-data8 0xD818B4BB43D84BF2 ,  0x0000BFF8 // P16
+data8 0x9F90FB984D8E39D0 ,  0x0000BFF3 // P20
+data8 0x9D3436AABE218776 ,  0x00003FF5 // P19
 data8 0xDEC343E068A6D2A8 ,  0x0000BFF6 // P18
-data8 0x9297B23CCFFB291F ,  0x0000BFFA // P12
+data8 0xF396268151CFB11C ,  0x00003FF7 // P17
+data8 0xD818B4BB43D84BF2 ,  0x0000BFF8 // P16
+data8 0xA2270D30A90AA220 ,  0x00003FF9 // P15
 data8 0xD5F4F2182E7A8725 ,  0x0000BFF9 // P14
-data8 0xAAAAAAAAAAAAA8A9 ,  0x0000BFFD // P0
-data8 0x9249249247E37913 ,  0x0000BFFC // P2
+data8 0x80D601879218B53A ,  0x00003FFA // P13
+data8 0x9297B23CCFFB291F ,  0x0000BFFA // P12
+data8 0xFE7E52D2A89995B3 ,  0x0000BFEC // P22
 data8 0xC90FDAA22168C235 ,  0x00003FFF // pi/2
-data8 0xC90FDAA22168C235 ,  0x00004000 // pi
+data8 0xC90FDAA22168C235 ,  0x00003FFE // pi/4
 data8 0x96cbe3f9990e91a8 ,  0x00004000 // 3pi/4
-ASM_SIZE_DIRECTIVE(atan2_tb2)
-
-
+LOCAL_OBJECT_END(atan2_tb2)
 
 
-.align 32
-.global atan2#
-#ifdef _LIBC
-.global __atan2#
-.global __ieee754_atan2#
-#endif
 
-////////////////////////////////////////////////////////
 
 .section .text
-.align 32
-
-.proc  atan2#
-atan2:
-#ifdef _LIBC
-.proc  __atan2#
-__atan2:
-.proc  __ieee754_atan2#
-__ieee754_atan2:
-#endif
-// qnan snan inf norm     unorm 0 -+
-// 0    0    1   0        0     0 11
-
-
-//         Y NAN?     p10 p11
-// p10 ==> quiet Y and return
-// p11     X NAN?     p12, p13 
-// p12 ==> quiet X and return
+GLOBAL_IEEE754_ENTRY(atan2)
 
 { .mfi
            alloc        r32           = ar.pfs,1,5,4,0
            frcpa.s1     atan2_u1_X,p6 = f1,atan2_X
-           addl         EXP_AD_P2   = @ltoff(atan2_tb2), gp
+           nop.i 999
 }
 { .mfi
            addl         EXP_AD_P1   = @ltoff(atan2_tb1), gp
-           fclass.m.unc p10,p11 = f8, 0xc3
+           fma.s1       atan2_two  = f1,f1,f1
            nop.i 999
 ;;
 }
@@ -366,256 +356,233 @@ __ieee754_atan2:
 }
 { .mfi
            nop.m 999
-           fma.s1       atan2_two  = f1,f1,f1 
+           fma.s1       atan2_xsq  = atan2_X,atan2_X,f0
            nop.i 999
 ;;
 }
 
-
 { .mfi
-           ld8 EXP_AD_P2 = [ EXP_AD_P2]
-           famax.s1     atan2_Umax =  f8,f9
+           nop.m 999
+           fclass.m p10,p0 = atan2_Y, 0xc3     // Test for y=nan
            nop.i 999
 }
-;;
-
 { .mfi
            nop.m 999
-           fmerge.s     atan2_absX = f0,atan2_X
+           fma.s1       atan2_ysq  = atan2_Y,atan2_Y,f0
            nop.i 999
 }
 ;;
 
-// p10 Y NAN, quiet and return
 { .mfi
-           ldfe         atan2_P10  = [EXP_AD_P1],16
-           fmerge.s     atan2_sgnY = atan2_Y,f1
+           add  EXP_AD_P2 = 0xd0,EXP_AD_P1
+           fclass.m p12,p0 = atan2_X, 0xc3     // Test for x nan
            nop.i 999
 }
-{ .mfb
-           nop.m 999
-(p10)      fma.d f8 = f8,f9,f0 
-(p10)      br.ret.spnt b0
 ;;
-}
 
 
-{ .mmf
+// p10 Y NAN, quiet and return
+{ .mfi
            ldfe         atan2_P11  = [EXP_AD_P1],16
-           ldfe         atan2_P20  = [EXP_AD_P2],16
-           fmerge.s     atan2_sgnX = atan2_X,f1
+           fmerge.s     atan2_sgnY = atan2_Y,f1
+           nop.i 999
+}
+{ .mfb
+           ldfe         atan2_P21  = [EXP_AD_P2],16
+(p10)      fma.d.s0 f8 = atan2_X,atan2_Y,f0   // If y=nan, result quietized y
+(p10)      br.ret.spnt b0        // Exit if y=nan
 ;;
 }
 
 
-{ .mfi 
-           ldfe         atan2_P8   = [EXP_AD_P1],16
+{ .mfi
+           ldfe         atan2_P10  = [EXP_AD_P1],16
            fma.s1       atan2_z1_X = atan2_u1_X, atan2_Y, f0
            nop.i 999
 }
-{ .mfi 
-
-           ldfe         atan2_P21  = [EXP_AD_P2],16
-           fma.s1       atan2_z1_Y = atan2_u1_Y, atan2_X, f0
+{ .mfi
+           ldfe         atan2_P20  = [EXP_AD_P2],16
+           fnma.s1      atan2_B1X  = atan2_u1_X, atan2_X, atan2_two
            nop.i 999
 ;;
 }
 
-{ .mfi 
+{ .mfi
            ldfe         atan2_P9   = [EXP_AD_P1],16
-           fnma.s1      atan2_B1X  = atan2_u1_X, atan2_X, atan2_two
+           fma.s1       atan2_z1_Y = atan2_u1_Y, atan2_X, f0
            nop.i 999
 }
-{ .mfi 
-
-           ldfe         atan2_P4   = [EXP_AD_P2],16
+{ .mfi
+           ldfe         atan2_P19  = [EXP_AD_P2],16
            fnma.s1      atan2_B1Y  = atan2_u1_Y, atan2_Y, atan2_two
            nop.i 999
-;;
 }
-
-// p6 (atan2_sT) true if swap
-// p7 (atan2_sF) true if no swap
-// p11 ==> Y !NAN;  X NAN?
+;;
 
 { .mfi
-           ldfe         atan2_P5   = [EXP_AD_P1],16
-//           fcmp.eq.unc.s1 atan2_sF,atan2_sT    = atan2_Umax, atan2_X
-           fcmp.eq.unc.s1 p7,p6    = atan2_Umax, atan2_X
+           ldfe         atan2_P8   = [EXP_AD_P1],16
+           fma.s1       atan2_z2_X = atan2_u1_X, atan2_ysq, f0
            nop.i 999
 }
 { .mfi
-           ldfe         atan2_P6   = [EXP_AD_P2],16
-(p11)      fclass.m.unc p12,p13    = f9, 0xc3
+           ldfe         atan2_P18  = [EXP_AD_P2],16
+           fma.s1       atan2_z2_Y = atan2_u1_Y, atan2_xsq, f0
            nop.i 999
-;;
 }
-
-{ .mmf
-           ldfe         atan2_P7   = [EXP_AD_P1],16
-           ldfe         atan2_P16  = [EXP_AD_P2],16
-           famin.s1     atan2_Vmin =  f8,f9
 ;;
-}
 
-// p8 true if X positive
-// p9 true if X negative
-// both are false is swap is true
+// p10 ==> x  inf     y ?
+// p11 ==> x !inf     y ?
 { .mfi
-           ldfe         atan2_P17  = [EXP_AD_P1],16
-//(atan2_sF) fcmp.eq.unc.s1 p8,p9    = atan2_sgnX,f1
-(p7) fcmp.eq.unc.s1 p8,p9    = atan2_sgnX,f1
+           ldfe         atan2_P7   = [EXP_AD_P1],16
+           fclass.m p10,p11 = atan2_X, 0x23    // test for x inf
            nop.i 999
 }
-{ .mfi
-           ldfe         atan2_P18  = [EXP_AD_P2],16
-           fma.s1       atan2_sgnXY     = atan2_sgnX, atan2_sgnY, f0 
-           nop.i 999
+{ .mfb
+           ldfe         atan2_P17  = [EXP_AD_P2],16
+(p12)      fma.d.s0        f8 = atan2_X,atan2_Y,f0     // If x nan, result quiet x
+(p12)      br.ret.spnt b0                 // Exit for x nan
 ;;
 }
 
+// p6 true if swap,    means |y| >  |x|    or ysq > xsq
+// p7 true if no swap, means |x| >= |y|    or xsq >= ysq
+{ .mmf
+           ldfe         atan2_P6   = [EXP_AD_P1],16
+           ldfe         atan2_P16  = [EXP_AD_P2],16
+           fcmp.ge.s1 p7,p6    = atan2_xsq, atan2_ysq
+;;
+}
 
 { .mfi
-           ldfe         atan2_P19  = [EXP_AD_P1],16
-//(atan2_sF) fma.s1       atan2_wp   = atan2_z1_X, atan2_z1_X, f0
-(p7) fma.s1       atan2_wp   = atan2_z1_X, atan2_z1_X, f0
+           ldfe         atan2_P5   = [EXP_AD_P1],16
+           fma.s1       atan2_wp_X   = atan2_z1_X, atan2_z1_X, f0
            nop.i 999
 }
 { .mfi
-           ldfe         atan2_P12  = [EXP_AD_P2],16
-//(atan2_sT) fma.s1       atan2_wp   = atan2_z1_Y, atan2_z1_Y, f0
-(p6) fma.s1       atan2_wp   = atan2_z1_Y, atan2_z1_Y, f0
+           ldfe         atan2_P15       = [EXP_AD_P2],16
+           fma.s1       atan2_B1sq_X = atan2_B1X, atan2_B1X, f0
            nop.i 999
 ;;
 }
 
-
 { .mfi
-           ldfe         atan2_P13  = [EXP_AD_P1],16
-//(atan2_sF) fma.s1       atan2_z         = atan2_z1_X, atan2_B1X, f0
-(p7) fma.s1       atan2_z         = atan2_z1_X, atan2_B1X, f0
+           ldfe         atan2_P4   = [EXP_AD_P1],16
+(p6)       fma.s1       atan2_wp_Y   = atan2_z1_Y, atan2_z1_Y, f0
            nop.i 999
 }
 { .mfi
            ldfe         atan2_P14  = [EXP_AD_P2],16
-//(atan2_sT) fma.s1       atan2_z         = atan2_z1_Y, atan2_B1Y, f0
-(p6) fma.s1       atan2_z         = atan2_z1_Y, atan2_B1Y, f0
+(p6)       fma.s1       atan2_B1sq_Y = atan2_B1Y, atan2_B1Y, f0
            nop.i 999
 ;;
 }
 
-
 { .mfi
-           ldfe         atan2_P15       = [EXP_AD_P1],16
-//(atan2_sF) fma.s1       atan2_B1sq = atan2_B1X, atan2_B1X, f0
-(p7) fma.s1       atan2_B1sq = atan2_B1X, atan2_B1X, f0
+           ldfe         atan2_P3        = [EXP_AD_P1],16
+(p6)       fma.s1       atan2_E         = atan2_z2_Y, atan2_B1Y, atan2_Y
            nop.i 999
 }
 { .mfi
-           ldfe         atan2_P0        = [EXP_AD_P2],16
-//(atan2_sT) fma.s1       atan2_B1sq = atan2_B1Y, atan2_B1Y, f0
-(p6) fma.s1       atan2_B1sq = atan2_B1Y, atan2_B1Y, f0
+           ldfe         atan2_P13  = [EXP_AD_P2],16
+(p7)       fma.s1       atan2_E         = atan2_z2_X, atan2_B1X, atan2_X
            nop.i 999
 ;;
 }
 
 
-// p12 ==> X NAN, quiet and return
 { .mfi
-           ldfe         atan2_P1        = [EXP_AD_P1],16
-           fmerge.s     atan2_Umax      = f0,atan2_Umax
+           ldfe         atan2_P2        = [EXP_AD_P1],16
+(p6)       fma.s1       atan2_z         = atan2_z1_Y, atan2_B1Y, f0
            nop.i 999
 }
-{ .mfb
-           ldfe         atan2_P2        = [EXP_AD_P2],16
-(p12)      fma.d        f8 = f9,f8,f0
-(p12)      br.ret.spnt b0
+{ .mfi
+           ldfe         atan2_P12  = [EXP_AD_P2],16
+(p7)       fma.s1       atan2_z         = atan2_z1_X, atan2_B1X, f0
+           nop.i 999
 ;;
 }
 
 
-// p10 ==> x  inf     y ?
-// p11 ==> x !inf     y ?
 { .mfi
-           ldfe         atan2_P3        = [EXP_AD_P1],16
-           fmerge.s     atan2_Vmin      = f0,atan2_Vmin
+           ldfe         atan2_P1        = [EXP_AD_P1],16
+           fcmp.eq.s0  p14,p15=atan2_X,atan2_Y  // Dummy for denorm and invalid
            nop.i 999
 }
-{ .mfi
-           ldfe         atan2_Pi_by_2   = [EXP_AD_P2],16
-           fclass.m.unc p10,p11 = f9, 0x23
-           nop.i 999
+{ .mlx
+           ldfe         atan2_P22       = [EXP_AD_P2],16
+           movl         rsig_near_one = 0x8000000000000001 // signif near 1.0
 ;;
 }
 
 
+// p12 ==> x  inf     y inf
+// p13 ==> x  inf     y !inf
 { .mmf
-           ldfe         atan2_P22       = [EXP_AD_P1],16
-           ldfe         atan2_pi        = [EXP_AD_P2],16
-           nop.f 999
+           ldfe         atan2_P0        = [EXP_AD_P1],16
+           ldfe         atan2_pi_by_2   = [EXP_AD_P2],16
+(p10)      fclass.m.unc p12,p13 = atan2_Y, 0x23  // x inf, test if y inf
 ;;
 }
 
 { .mfi
-           nop.m 999 
-           fcmp.eq.s0  p12,p13=f9,f8   // Dummy to catch denormal and invalid
+           ldfe         atan2_pi        = [EXP_AD_P1],16
+(p6)       fma.s1       atan2_w         = atan2_wp_Y, atan2_B1sq_Y,f0
            nop.i 999
-;;
 }
-
-
 { .mfi
-           ldfe         atan2_pi_by_4       = [EXP_AD_P1],16
-//(atan2_sT) fmerge.ns    atan2_sgnXY     = atan2_sgnXY, atan2_sgnXY
-(p6) fmerge.ns    atan2_sgnXY     = atan2_sgnXY, atan2_sgnXY
+           ldfe         atan2_pi_by_4       = [EXP_AD_P2],16
+(p7)       fma.s1       atan2_w         = atan2_wp_X, atan2_B1sq_X,f0
            nop.i 999
+;;
 }
+
 { .mfi
            ldfe         atan2_3pi_by_4       = [EXP_AD_P2],16
-           fma.s1       atan2_w         = atan2_wp, atan2_B1sq,f0
+(p11)      fclass.m.unc p9,p0 = atan2_Y, 0x23  // x not inf, test if y inf
            nop.i 999
 ;;
 }
 
-// p12 ==> x  inf     y inf
-// p13 ==> x  inf     y !inf
+{ .mfi
+           setf.sig      atan2_sig_near_one = rsig_near_one
+(p12)      fcmp.gt.unc.s1 p10,p11 = atan2_X,f0 // x inf, y inf, test if x +inf
+           nop.i 999
+}
 { .mfi
            nop.m 999
-           fmerge.s     atan2_z         = f0, atan2_z
+(p6)       fnma.s1       atan2_gV        = atan2_Y, atan2_z, atan2_X
            nop.i 999
 ;;
 }
 
 { .mfi
-           nop.m 99
-(p10)      fclass.m.unc p12,p13 = f8, 0x23
+           nop.m 999
+           frcpa.s1     atan2_F,p0     = f1, atan2_E
            nop.i 999
 }
 { .mfi
-           nop.m 99
-(p11)      fclass.m.unc p14,p15 = f8, 0x23
+           nop.m 999
+(p7)       fnma.s1       atan2_gV        = atan2_X, atan2_z, atan2_Y
            nop.i 999
 ;;
 }
 
+// p13 ==> x  inf     y !inf
 { .mfi
            nop.m 999
-(p12)      fcmp.eq.unc.s1 p10,p11       = atan2_sgnX,f1
-           nop.i 99
-;;
+(p13)      fcmp.gt.unc.s1 p14,p15 = atan2_X,f0 // x inf, y !inf, test if x +inf
+           nop.i 999
 }
-
-
 { .mfb
-           mov atan2_GR_sml_exp = 0x1  // Small exponent for making small norm
-(p14)      fma.d       f8 = atan2_sgnY, atan2_Pi_by_2, f0
-(p14)      br.ret.spnt b0
+           nop.m 999
+(p9)       fma.d.s0  f8 = atan2_sgnY, atan2_pi_by_2, f0  // +-pi/2 if x !inf, y inf
+(p9)       br.ret.spnt b0      // exit if x not inf, y inf, result is +-pi/2
 ;;
 }
 
-// Make a very small normal in case need to force inexact and underflow
 { .mfi
-           setf.exp atan2_sml_norm = atan2_GR_sml_exp
+           nop.m 999
            fma.s1       atan2_V13       = atan2_w, atan2_P11, atan2_P10
            nop.i 999
 }
@@ -626,58 +593,58 @@ __ieee754_atan2:
 ;;
 }
 
-
 { .mfi
            nop.m 999
-           fma.s1       atan2_E         = atan2_Vmin, atan2_z, atan2_Umax
+           fma.s1       atan2_V11       = atan2_w, atan2_P9, atan2_P8
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fnma.s1      atan2_gamma     = atan2_Umax, atan2_z, f1
+           fma.s1       atan2_V12       = atan2_w, atan2_w, f0
            nop.i 999
 ;;
 }
 
 { .mfi
            nop.m 999
-           fma.s1       atan2_V11       = atan2_w, atan2_P9, atan2_P8
+           fma.s1       atan2_V8        = atan2_w, atan2_P7 , atan2_P6
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fma.s1       atan2_V12       = atan2_w, atan2_w, f0
+           fma.s1       atan2_W8        = atan2_w, atan2_P19, atan2_P18
            nop.i 999
 ;;
 }
 
 { .mfi
            nop.m 999
-           fma.s1       atan2_V7        = atan2_w, atan2_P5 , atan2_P4 
+           fnma.s1      atan2_alpha     = atan2_E, atan2_F, f1
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fma.s1       atan2_V8        = atan2_w, atan2_P7 , atan2_P6 
+           fnma.s1      atan2_alpha_1   = atan2_E, atan2_F, atan2_two
            nop.i 999
 ;;
 }
 
+
 { .mfi
            nop.m 999
-           fma.s1       atan2_W7        = atan2_w, atan2_P17, atan2_P16 
+           fma.s1       atan2_V7        = atan2_w, atan2_P5 , atan2_P4
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fma.s1       atan2_W8        = atan2_w, atan2_P19, atan2_P18
+           fma.s1       atan2_W7        = atan2_w, atan2_P17, atan2_P16
            nop.i 999
 ;;
 }
 
 { .mfi
            nop.m 999
-           fma.s1       atan2_W3        = atan2_w, atan2_P13, atan2_P12 
+           fma.s1       atan2_V4        = atan2_w, atan2_P3 , atan2_P2
            nop.i 999
 }
 { .mfi
@@ -689,55 +656,55 @@ __ieee754_atan2:
 
 { .mfi
            nop.m 999
-           fma.s1       atan2_V3        = atan2_w, atan2_P1 , atan2_P0 
+           fma.s1       atan2_V3        = atan2_w, atan2_P1 , atan2_P0
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fma.s1       atan2_V4        = atan2_w, atan2_P3 , atan2_P2
+           fma.s1       atan2_W3        = atan2_w, atan2_P13, atan2_P12
            nop.i 999
 ;;
 }
 
 { .mfi
            nop.m 999
-           fma.s1       atan2_zcub      = atan2_z, atan2_w, f0
+           fma.s1       atan2_V10       = atan2_V12, atan2_V13, atan2_V11
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fnma.s1       atan2_gV        = atan2_Umax, atan2_z, atan2_Vmin 
+           fma.s1       atan2_gVF       = atan2_gV, atan2_F, f0
            nop.i 999
 ;;
 }
 
 { .mfi
            nop.m 999
-           frcpa.s1     atan2_F,p15     = f1, atan2_E
+           fma.s1       atan2_alpha_sq  = atan2_alpha, atan2_alpha, f0
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fma.s1       atan2_V10       = atan2_V12, atan2_V13, atan2_V11
+           fma.s1       atan2_Cp        = atan2_alpha, atan2_alpha_1, f1
            nop.i 999
 ;;
 }
 
 { .mfi
            nop.m 999
-           fma.s1       atan2_V6        = atan2_V12, atan2_V8 , atan2_V7 
+           fma.s1       atan2_V9        = atan2_V12, atan2_V12, f0
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fma.s1       atan2_V9        = atan2_V12, atan2_V12, f0
+           fma.s1       atan2_W10       = atan2_V12, atan2_P22 , atan2_W11
            nop.i 999
 ;;
 }
 
 { .mfi
            nop.m 999
-           fma.s1       atan2_W10       = atan2_V12, atan2_P22 , atan2_W11
+           fma.s1       atan2_V6        = atan2_V12, atan2_V8 , atan2_V7
            nop.i 999
 }
 { .mfi
@@ -749,65 +716,47 @@ __ieee754_atan2:
 
 { .mfi
            nop.m 999
-           fma.s1       atan2_W2        = atan2_V12, atan2_W4  , atan2_W3
+           fma.s1       atan2_V2        = atan2_V12, atan2_V4 , atan2_V3
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fma.s1       atan2_V2        = atan2_V12, atan2_V4 , atan2_V3
+           fma.s1       atan2_W2        = atan2_V12, atan2_W4  , atan2_W3
            nop.i 999
 ;;
 }
 
-
-// Both X and Y are INF
-// p10 ==> X +
-// p11 ==> X -
-.pred.rel "mutex",p10,p11
-{ .mfb
-           nop.m 999
-(p10)      fma.d       f8              = atan2_sgnY, atan2_pi_by_4, f0
-(p10)      br.ret.spnt b0
-}
-{ .mfb
-           nop.m 999
-(p11)      fma.d       f8              = atan2_sgnY, atan2_3pi_by_4, f0
-(p11)      br.ret.spnt b0
-;;
-}
-
-
-.pred.rel "mutex",p8,p9,p6
+// p8 ==> y   0     x?
+// p9 ==> y  !0     x?
 { .mfi
            nop.m 999
-           fnma.s1      atan2_alpha     = atan2_E, atan2_F, f1
+           fclass.m p8,p9 = atan2_Y, 0x07  // Test for y=0
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fnma.s1      atan2_alpha_1   = atan2_E, atan2_F, atan2_two
+           fma.s1       atan2_zcub      = atan2_z, atan2_w, f0
            nop.i 999
 ;;
 }
 
-
 { .mfi
            nop.m 999
-//(atan2_sT) fmerge.s     atan2_P         = atan2_Y, atan2_Pi_by_2
-(p6) fmerge.s     atan2_P         = atan2_Y, atan2_Pi_by_2
+           fma.s1       atan2_alpha_cub = atan2_alpha, atan2_alpha_sq, f0
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fma.s1       atan2_gVF       = atan2_gV, atan2_F, f0
+           fma.s1       atan2_C         = atan2_gVF, atan2_Cp, f0
            nop.i 999
 ;;
 }
 
-
+// p12 ==>  y0     x0
+// p13 ==>  y0     x!0
 { .mfi
            nop.m 999
-           fma.s1       atan2_V5        = atan2_V9, atan2_V10, atan2_V6
+(p8)       fclass.m.unc p12,p13 = atan2_X, 0x07  // y=0, test if x is 0
            nop.i 999
 }
 { .mfi
@@ -817,11 +766,9 @@ __ieee754_atan2:
 ;;
 }
 
-
-
 { .mfi
            nop.m 999
-(p8)       fmerge.s     atan2_P         = atan2_sgnY, f0
+           fma.s1       atan2_V5        = atan2_V9, atan2_V10, atan2_V6
            nop.i 999
 }
 { .mfi
@@ -832,249 +779,215 @@ __ieee754_atan2:
 }
 
 
-
-
+// p9 ==>  y!0    x0
 { .mfi
            nop.m 999
-(p9)       fmerge.s     atan2_P         = atan2_sgnY, atan2_pi
+(p9)       fclass.m.unc p9,p0 = atan2_X, 0x07  // y not 0, test if x is 0
            nop.i 999
+}
+// p10 ==> X +INF, Y +-INF
+{ .mfb
+           nop.m 999
+(p10)      fma.d.s0       f8 = atan2_sgnY, atan2_pi_by_4, f0 // x=+inf, y=inf
+(p10)      br.ret.spnt b0          // Exit for x=+inf, y=inf, result is +-pi/4
 ;;
 }
 
-
+.pred.rel "mutex",p11,p14
 { .mfi
            nop.m 999
-           fma.s1       atan2_alpha_sq  = atan2_alpha, atan2_alpha, f0  
+(p14)      fmerge.s    f8 = atan2_sgnY, f0 // x=+inf, y !inf, result +-0
            nop.i 999
 }
-{ .mfi
+// p11 ==> X -INF, Y +-INF
+{ .mfb
            nop.m 999
-           fma.s1       atan2_Cp        = atan2_alpha, atan2_alpha_1, f1  
-           nop.i 999
+(p11)      fma.d.s0       f8 = atan2_sgnY, atan2_3pi_by_4, f0 // x=-inf, y=inf
+(p11)      br.ret.spnt b0          // Exit for x=-inf, y=inf, result is +-3pi/4
 ;;
 }
 
-
 { .mfi
            nop.m 999
-           fma.s1       atan2_V1        = atan2_V9, atan2_V5, atan2_V2
+(p13)      fcmp.gt.unc.s1 p10,p11 = atan2_X,f0 // x not 0, y=0, test if x>0
            nop.i 999
 }
-{ .mfi
+{ .mfb
            nop.m 999
-           fma.s1       atan2_W12       = atan2_V9, atan2_W12, f0
-           nop.i 999
+           fma.s1       atan2_d         = atan2_alpha_cub, atan2_C, atan2_C
+(p14)      br.ret.spnt b0         // Exit if x=+inf, y !inf, result +-0
 ;;
 }
 
-
-// p13 ==> x  inf     y !inf
 { .mfi
            nop.m 999
-           fma.s1       atan2_W1        = atan2_V9, atan2_W5, atan2_W2
+           fma.s1       atan2_W12       = atan2_V9, atan2_W12, f0
            nop.i 999
 }
-{ .mfi
+{ .mfb
            nop.m 999
-(p13)      fcmp.eq.unc.s1 p10,p11       = atan2_sgnX,f1
-           nop.i 999
+(p9)       fma.d.s0       f8 = atan2_sgnY, atan2_pi_by_2, f0 // x=0, y not 0
+(p9)       br.ret.spnt b0      // Exit if x=0 and y not 0, result is +-pi/2
 ;;
 }
 
-
 { .mfi
            nop.m 999
-           fma.s1       atan2_alpha_cub = atan2_alpha, atan2_alpha_sq, f0
+           fma.s1       atan2_V1        = atan2_V9, atan2_V5, atan2_V2
            nop.i 999
 }
-{ .mfi
+{ .mfb
            nop.m 999
-           fma.s1       atan2_C         = atan2_gVF, atan2_Cp, f0
-           nop.i 999
+           fma.s1       atan2_W1        = atan2_V9, atan2_W5, atan2_W2
+(p12)      br.spnt ATAN2_ERROR            // Branch if x=0 and y=0
 ;;
 }
 
-.pred.rel "mutex",p10,p11 
-// x inf y !inf
-{ .mfb
+{ .mfi
            nop.m 999
-(p10)      fmerge.s     f8              = atan2_sgnY, f0
-(p10)      br.ret.spnt b0
+(p10)      fmerge.s     f8              = atan2_sgnY, f0  // +-0 if x>0, y=0
+           nop.i 999
 }
 { .mfb
            nop.m 999
-(p11)      fma.d        f8              = atan2_sgnY, atan2_pi, f0
-(p11)      br.ret.spnt b0
+(p11)      fma.d.s0        f8 = atan2_sgnY, atan2_pi, f0 // +-pi if x<0, y=0
+(p13)      br.ret.spnt b0      // Exit if x!0 and y=0
 ;;
 }
 
 
-
-// p10 ==> y   0     x?
-// p11 ==> y  !0     x?
 { .mfi
            nop.m 999
-           fclass.m.unc p10,p11 = f8, 0x07
+           fma.s1       atan2_pd        = atan2_P0, atan2_d, f0
            nop.i 999
-;;
 }
-
 { .mfi
            nop.m 999
-(p8)       fmerge.s     atan2_sml_norm  = atan2_sgnY, atan2_sml_norm
+           fma.s1       atan2_dsq       = atan2_d, atan2_d, f0
            nop.i 999
 ;;
 }
 
+
 { .mfi
            nop.m 999
-           fma.s1       atan2_Pp        = atan2_W12, atan2_W1, atan2_V1
+           fmerge.se    atan2_near_one = f1, atan2_sig_near_one // Const ~1.0
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fma.s1       atan2_d         = atan2_alpha_cub, atan2_C, atan2_C
+           fma.s1       atan2_Pp        = atan2_W12, atan2_W1, atan2_V1
            nop.i 999
 ;;
 }
 
-// p12 ==>  y0     x0
-// p13 ==>  y0     x!0
-// p14 ==>  y!0    x0
-// p15 ==>  y!0    x!0
-{ .mfi
-           nop.m 999
-(p10)      fclass.m.unc p12,p13 = f9, 0x07 
-           nop.i 999
-}
+// p8 true if no swap and X positive
+// p9 true if no swap and X negative
+// both are false is swap is true
 { .mfi
            nop.m 999
-(p11)      fclass.m.unc p14,p15 = f9, 0x07 
+(p7)       fcmp.ge.unc.s1 p8,p9    = atan2_X,f0
            nop.i 999
-;;
 }
-
-
-
-
 { .mfb
            nop.m 999
-(p13)      fcmp.eq.unc.s1 p10,p11       = atan2_sgnX,f1
-(p12)      br.spnt ATAN2_ERROR
+(p15)      fma.d.s0        f8              = atan2_sgnY, atan2_pi, f0
+(p15)      br.ret.spnt b0         // Exit if x=-inf, y !inf, result +-pi
 ;;
 }
 
-
-
 { .mfi
            nop.m 999
-           fma.s1       atan2_pd        = atan2_P0, atan2_d, f0
+           fma.s1       atan2_sgn_pi_by_2 = atan2_pi_by_2, atan2_sgnY, f0
            nop.i 999
 }
 { .mfi
            nop.m 999
-           fma.s1       atan2_dsq       = atan2_d, atan2_d, f0
+           fma.s1       atan2_A_lo      = atan2_pd, atan2_dsq, atan2_d
            nop.i 999
 ;;
 }
 
+
 { .mfi
            nop.m 999
-           fma.s1       atan2_A_hi      = atan2_zcub, atan2_Pp, atan2_z
+           fma.s1       atan2_sgn_pi = atan2_pi, atan2_sgnY, f0
            nop.i 999
 }
-{ .mfb
+{ .mfi
            nop.m 999
-(p14)      fma.d       f8 = atan2_sgnY, atan2_Pi_by_2, f0
-(p14)      br.ret.spnt b0                
+           fma.s1       atan2_A_hi      = atan2_zcub, atan2_Pp, atan2_z
+           nop.i 999
 ;;
 }
 
 
-
-{ .mfb
-           nop.m 999
-(p10)      fmerge.s     f8              = atan2_sgnY, f0
-(p10)      br.ret.spnt b0
-}
-{ .mfb
+// For |Y| <= |X| and X > 0, force inexact in case A_lo is zero
+{ .mfi
            nop.m 999
-(p11)      fma.d        f8              = atan2_sgnY, atan2_pi, f0
-(p11)      br.ret.spnt b0
+(p8)       fmpy.s0      atan2_tmp       = atan2_P22, atan2_P22
+           nop.i 999
 ;;
 }
 
-
-
 { .mfi
            nop.m 999
-           fma.s1       atan2_A_lo      = atan2_pd, atan2_dsq, atan2_d
+           fma.s1       atan2_A         = atan2_A_hi, f1, atan2_A_lo
            nop.i 999
-;;
 }
-
-
+// For |Y| <= |X| and X > 0, result is A_hi + A_lo
 { .mfi
            nop.m 999
-           fma.s1       atan2_A         = atan2_A_hi, f1, atan2_A_lo
+(p8)       fma.d.s0       f8         = atan2_A_hi, f1, atan2_A_lo
            nop.i 999
 ;;
 }
 
-// Force inexact and possibly underflow if very small results
+.pred.rel "mutex",p6,p9
+// We perturb A by multiplying by 1.0+1ulp as we produce the result
+// in order to get symmetrically rounded results in directed rounding modes.
+// If we don't do this, there are a few cases where the trailing 11 bits of
+// the significand of the result, before converting to double, are zero.  These
+// cases do not round symmetrically in round to +infinity or round to -infinity.
+// The perturbation also insures that the inexact flag is set.
+// For |Y| > |X|, result is  +- pi/2 - (A_hi + A_lo)
 { .mfi
            nop.m 999
-(p8)       fma.d        atan2_FR_tmp    = atan2_sgnXY, atan2_A, atan2_sml_norm
+(p6)       fnma.d.s0      f8        = atan2_A, atan2_near_one, atan2_sgn_pi_by_2
            nop.i 999
 }
+// For |Y| <= |X|, and X < 0, result is  +- pi + (A_hi + A_lo)
 { .mfb
            nop.m 999
-           fma.d        f8              = atan2_sgnXY, atan2_A, atan2_P
-           br.ret.sptk  b0     
+(p9)       fma.d.s0        f8        = atan2_A, atan2_near_one, atan2_sgn_pi
+           br.ret.sptk  b0
 ;;
 }
 
 ATAN2_ERROR:
-
+// Here if x=0 and y=0
 { .mfi
           nop.m 999
-          fcmp.eq.unc.s1 p10,p11       = atan2_sgnX,f1
+          fclass.m p10,p11       = atan2_X,0x05  // Test if x=+0
           nop.i 999
 }
 ;;
 
 { .mfi
-          mov        atan2_GR_tag     = 37 
-(p10)     fmerge.s     f10             = atan2_sgnY, f0
-          nop.i 999 
+          mov        atan2_GR_tag     = 37
+(p10)     fmerge.s     f10             = atan2_sgnY, f0 // x=+0, y=0
+          nop.i 999
 }
 { .mfi
           nop.m 999
-(p11)     fma.d        f10            = atan2_sgnY, atan2_pi, f0
+(p11)     fma.d.s0        f10            = atan2_sgnY, atan2_pi, f0 // x=-0, y=0
           nop.i 999
 ;;
 }
-.endp atan2#
-ASM_SIZE_DIRECTIVE(atan2#)
-
+GLOBAL_IEEE754_END(atan2)
 
-// Stack operations when calling error support.
-//       (1)               (2)                          (3) (call)              (4)
-//   sp   -> +          psp -> +                     psp -> +                   sp -> +
-//           |                 |                            |                         |
-//           |                 | <- GR_Y               R3 ->| <- GR_RESULT            | -> f8
-//           |                 |                            |                         |
-//           | <-GR_Y      Y2->|                       Y2 ->| <- GR_Y                 |
-//           |                 |                            |                         |
-//           |                 | <- GR_X               X1 ->|                         |
-//           |                 |                            |                         |
-//  sp-64 -> +          sp ->  +                     sp ->  +                         +
-//    save ar.pfs          save b0                                               restore gp
-//    save gp                                                                    restore ar.pfs
 
-
-.proc __libm_error_region
-__libm_error_region:
+LOCAL_LIBM_ENTRY(__libm_error_region)
 .prologue
 // (1)
 { .mfi
@@ -1102,19 +1015,19 @@ __libm_error_region:
 .body
 // (3)
 { .mib
-        stfd [GR_Parameter_X] = f9                   // STORE Parameter 1 on stack
+        stfd [GR_Parameter_X] = f9            // STORE Parameter 1 on stack
         add   GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
-        nop.b 0                                 
+        nop.b 0
 }
 { .mib
-        stfd [GR_Parameter_Y] = f10                  // STORE Parameter 3 on stack
+        stfd [GR_Parameter_Y] = f10           // STORE Parameter 3 on stack
         add   GR_Parameter_Y = -16,GR_Parameter_Y
-        br.call.sptk b0=__libm_error_support#        // Call error handling function
+        br.call.sptk b0=__libm_error_support# // Call error handling function
 };;
 { .mmi
-        nop.m 0
-        nop.m 0
         add   GR_Parameter_RESULT = 48,sp
+        nop.m 0
+        nop.i 0
 };;
 
 // (4)
@@ -1130,8 +1043,7 @@ __libm_error_region:
         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#