2.5-18.1

1 files changed, 1303 insertions, 1457 deletions

diff --git a/sysdeps/ia64/fpu/s_cosl.S b/sysdeps/ia64/fpu/s_cosl.S
index 2755580c0d..8d71e50c1a 100644
--- a/sysdeps/ia64/fpu/s_cosl.S
+++ b/sysdeps/ia64/fpu/s_cosl.S
@@ -1,10 +1,10 @@
 .file "sincosl.s"
 
-// Copyright (C) 2000, 2001, Intel Corporation
+
+// Copyright (c) 2000 - 2004, 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
@@ -20,76 +20,82 @@
 // * 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: 
-// 2/02/2000 (hand-optimized)
-// 4/04/00  Unwind support added
+// History:
+// 02/02/00 (hand-optimized)
+// 04/04/00 Unwind support added
+// 07/30/01 Improved speed on all paths
+// 08/20/01 Fixed bundling typo
+// 05/13/02 Changed interface to __libm_pi_by_2_reduce
+// 02/10/03 Reordered header: .section, .global, .proc, .align;
+//          used data8 for long double table values
+// 10/13/03 Corrected final .endp name to match .proc
+// 10/26/04 Avoided using r14-31 as scratch so not clobbered by dynamic loader
 //
-// *********************************************************************
+//*********************************************************************
 //
 // Function:   Combined sinl(x) and cosl(x), where
 //
 //             sinl(x) = sine(x), for double-extended precision x values
 //             cosl(x) = cosine(x), for double-extended precision x values
 //
-// *********************************************************************
+//*********************************************************************
 //
 // Resources Used:
 //
-//    Floating-Point Registers: f8 (Input and Return Value) 
+//    Floating-Point Registers: f8 (Input and Return Value)
 //                              f32-f99
 //
 //    General Purpose Registers:
-//      r32-r43 
-//      r44-r45 (Used to pass arguments to pi_by_2 reduce routine)
+//      r32-r58
 //
 //    Predicate Registers:      p6-p13
 //
-// *********************************************************************
+//*********************************************************************
 //
 //  IEEE Special Conditions:
 //
 //    Denormal  fault raised on denormal inputs
 //    Overflow exceptions do not occur
-//    Underflow exceptions raised when appropriate for sin 
+//    Underflow exceptions raised when appropriate for sin
 //    (No specialized error handling for this routine)
 //    Inexact raised when appropriate by algorithm
 //
 //    sinl(SNaN) = QNaN
 //    sinl(QNaN) = QNaN
-//    sinl(inf) = QNaN 
+//    sinl(inf) = QNaN
 //    sinl(+/-0) = +/-0
-//    cosl(inf) = QNaN 
+//    cosl(inf) = QNaN
 //    cosl(SNaN) = QNaN
 //    cosl(QNaN) = QNaN
 //    cosl(0) = 1
-// 
-// *********************************************************************
+//
+//*********************************************************************
 //
 //  Mathematical Description
 //  ========================
 //
-//  The computation of FSIN and FCOS is best handled in one piece of 
-//  code. The main reason is that given any argument Arg, computation 
-//  of trigonometric functions first calculate N and an approximation 
+//  The computation of FSIN and FCOS is best handled in one piece of
+//  code. The main reason is that given any argument Arg, computation
+//  of trigonometric functions first calculate N and an approximation
 //  to alpha where
 //
 //  Arg = N pi/2 + alpha, |alpha| <= pi/4.
@@ -98,62 +104,62 @@
 //
 //  cosl( Arg ) = sinl( (N+1) pi/2 + alpha ),
 //
-//  therefore, the code for computing sine will produce cosine as long 
-//  as 1 is added to N immediately after the argument reduction 
+//  therefore, the code for computing sine will produce cosine as long
+//  as 1 is added to N immediately after the argument reduction
 //  process.
 //
 //  Let M = N if sine
-//      N+1 if cosine.  
+//      N+1 if cosine.
 //
 //  Now, given
 //
 //  Arg = M pi/2  + alpha, |alpha| <= pi/4,
 //
-//  let I = M mod 4, or I be the two lsb of M when M is represented 
+//  let I = M mod 4, or I be the two lsb of M when M is represented
 //  as 2's complement. I = [i_0 i_1]. Then
 //
-//  sinl( Arg ) = (-1)^i_0  sinl( alpha )	if i_1 = 0,
+//  sinl( Arg ) = (-1)^i_0  sinl( alpha )        if i_1 = 0,
 //             = (-1)^i_0  cosl( alpha )     if i_1 = 1.
 //
 //  For example:
-//       if M = -1, I = 11   
+//       if M = -1, I = 11
 //         sin ((-pi/2 + alpha) = (-1) cos (alpha)
-//       if M = 0, I = 00   
+//       if M = 0, I = 00
 //         sin (alpha) = sin (alpha)
-//       if M = 1, I = 01   
+//       if M = 1, I = 01
 //         sin (pi/2 + alpha) = cos (alpha)
-//       if M = 2, I = 10   
+//       if M = 2, I = 10
 //         sin (pi + alpha) = (-1) sin (alpha)
-//       if M = 3, I = 11   
+//       if M = 3, I = 11
 //         sin ((3/2)pi + alpha) = (-1) cos (alpha)
 //
-//  The value of alpha is obtained by argument reduction and 
+//  The value of alpha is obtained by argument reduction and
 //  represented by two working precision numbers r and c where
 //
 //  alpha =  r  +  c     accurately.
 //
 //  The reduction method is described in a previous write up.
-//  The argument reduction scheme identifies 4 cases. For Cases 2 
-//  and 4, because |alpha| is small, sinl(r+c) and cosl(r+c) can be 
-//  computed very easily by 2 or 3 terms of the Taylor series 
+//  The argument reduction scheme identifies 4 cases. For Cases 2
+//  and 4, because |alpha| is small, sinl(r+c) and cosl(r+c) can be
+//  computed very easily by 2 or 3 terms of the Taylor series
 //  expansion as follows:
 //
 //  Case 2:
 //  -------
 //
-//  sinl(r + c) = r + c - r^3/6	accurately
-//  cosl(r + c) = 1 - 2^(-67)	accurately
+//  sinl(r + c) = r + c - r^3/6        accurately
+//  cosl(r + c) = 1 - 2^(-67)        accurately
 //
 //  Case 4:
 //  -------
 //
-//  sinl(r + c) = r + c - r^3/6 + r^5/120	accurately
-//  cosl(r + c) = 1 - r^2/2 + r^4/24		accurately
+//  sinl(r + c) = r + c - r^3/6 + r^5/120        accurately
+//  cosl(r + c) = 1 - r^2/2 + r^4/24                accurately
 //
-//  The only cases left are Cases 1 and 3 of the argument reduction 
-//  procedure. These two cases will be merged since after the 
-//  argument is reduced in either cases, we have the reduced argument 
-//  represented as r + c and that the magnitude |r + c| is not small 
+//  The only cases left are Cases 1 and 3 of the argument reduction
+//  procedure. These two cases will be merged since after the
+//  argument is reduced in either cases, we have the reduced argument
+//  represented as r + c and that the magnitude |r + c| is not small
 //  enough to allow the usage of a very short approximation.
 //
 //  The required calculation is either
@@ -163,32 +169,32 @@
 //
 //  Specifically,
 //
-//	sinl(r + c) = sinl(r) + c sin'(r) + O(c^2)
-//		   = sinl(r) + c cos (r) + O(c^2)
-//		   = sinl(r) + c(1 - r^2/2)  accurately.
+//        sinl(r + c) = sinl(r) + c sin'(r) + O(c^2)
+//                   = sinl(r) + c cos (r) + O(c^2)
+//                   = sinl(r) + c(1 - r^2/2)  accurately.
 //  Similarly,
 //
-//	cosl(r + c) = cosl(r) - c sinl(r) + O(c^2)
-//		   = cosl(r) - c(r - r^3/6)  accurately.
+//        cosl(r + c) = cosl(r) - c sinl(r) + O(c^2)
+//                   = cosl(r) - c(r - r^3/6)  accurately.
 //
-//  We therefore concentrate on accurately calculating sinl(r) and 
+//  We therefore concentrate on accurately calculating sinl(r) and
 //  cosl(r) for a working-precision number r, |r| <= pi/4 to within
 //  0.1% or so.
 //
-//  The greatest challenge of this task is that the second terms of 
+//  The greatest challenge of this task is that the second terms of
 //  the Taylor series
-//	
-//	r - r^3/3! + r^r/5! - ...
+//
+//        r - r^3/3! + r^r/5! - ...
 //
 //  and
 //
-//	1 - r^2/2! + r^4/4! - ...
+//        1 - r^2/2! + r^4/4! - ...
 //
-//  are not very small when |r| is close to pi/4 and the rounding 
-//  errors will be a concern if simple polynomial accumulation is 
-//  used. When |r| < 2^-3, however, the second terms will be small 
-//  enough (6 bits or so of right shift) that a normal Horner 
-//  recurrence suffices. Hence there are two cases that we consider 
+//  are not very small when |r| is close to pi/4 and the rounding
+//  errors will be a concern if simple polynomial accumulation is
+//  used. When |r| < 2^-3, however, the second terms will be small
+//  enough (6 bits or so of right shift) that a normal Horner
+//  recurrence suffices. Hence there are two cases that we consider
 //  in the accurate computation of sinl(r) and cosl(r), |r| <= pi/4.
 //
 //  Case small_r: |r| < 2^(-3)
@@ -197,88 +203,88 @@
 //  Since Arg = M pi/4 + r + c accurately, and M mod 4 is [i_0 i_1],
 //  we have
 //
-//	sinl(Arg) = (-1)^i_0 * sinl(r + c)	if i_1 = 0
-//		 = (-1)^i_0 * cosl(r + c) 	if i_1 = 1
+//        sinl(Arg) = (-1)^i_0 * sinl(r + c)        if i_1 = 0
+//                 = (-1)^i_0 * cosl(r + c)         if i_1 = 1
 //
 //  can be accurately approximated by
 //
-//  sinl(Arg) = (-1)^i_0 * [sinl(r) + c]	if i_1 = 0
+//  sinl(Arg) = (-1)^i_0 * [sinl(r) + c]        if i_1 = 0
 //           = (-1)^i_0 * [cosl(r) - c*r] if i_1 = 1
 //
-//  because |r| is small and thus the second terms in the correction 
+//  because |r| is small and thus the second terms in the correction
 //  are unneccessary.
 //
-//  Finally, sinl(r) and cosl(r) are approximated by polynomials of 
+//  Finally, sinl(r) and cosl(r) are approximated by polynomials of
 //  moderate lengths.
 //
 //  sinl(r) =  r + S_1 r^3 + S_2 r^5 + ... + S_5 r^11
 //  cosl(r) =  1 + C_1 r^2 + C_2 r^4 + ... + C_5 r^10
 //
-//  We can make use of predicates to selectively calculate 
-//  sinl(r) or cosl(r) based on i_1. 
+//  We can make use of predicates to selectively calculate
+//  sinl(r) or cosl(r) based on i_1.
 //
 //  Case normal_r: 2^(-3) <= |r| <= pi/4
 //  ------------------------------------
 //
 //  This case is more likely than the previous one if one considers
 //  r to be uniformly distributed in [-pi/4 pi/4]. Again,
-// 
-//  sinl(Arg) = (-1)^i_0 * sinl(r + c)	if i_1 = 0
-//           = (-1)^i_0 * cosl(r + c) 	if i_1 = 1.
 //
-//  Because |r| is now larger, we need one extra term in the 
+//  sinl(Arg) = (-1)^i_0 * sinl(r + c)        if i_1 = 0
+//           = (-1)^i_0 * cosl(r + c)         if i_1 = 1.
+//
+//  Because |r| is now larger, we need one extra term in the
 //  correction. sinl(Arg) can be accurately approximated by
 //
 //  sinl(Arg) = (-1)^i_0 * [sinl(r) + c(1-r^2/2)]      if i_1 = 0
 //           = (-1)^i_0 * [cosl(r) - c*r*(1 - r^2/6)]    i_1 = 1.
 //
-//  Finally, sinl(r) and cosl(r) are approximated by polynomials of 
+//  Finally, sinl(r) and cosl(r) are approximated by polynomials of
 //  moderate lengths.
 //
-//	sinl(r) =  r + PP_1_hi r^3 + PP_1_lo r^3 + 
-//	              PP_2 r^5 + ... + PP_8 r^17
+//        sinl(r) =  r + PP_1_hi r^3 + PP_1_lo r^3 +
+//                      PP_2 r^5 + ... + PP_8 r^17
 //
-//	cosl(r) =  1 + QQ_1 r^2 + QQ_2 r^4 + ... + QQ_8 r^16
+//        cosl(r) =  1 + QQ_1 r^2 + QQ_2 r^4 + ... + QQ_8 r^16
 //
-//  where PP_1_hi is only about 16 bits long and QQ_1 is -1/2. 
-//  The crux in accurate computation is to calculate 
+//  where PP_1_hi is only about 16 bits long and QQ_1 is -1/2.
+//  The crux in accurate computation is to calculate
 //
 //  r + PP_1_hi r^3   or  1 + QQ_1 r^2
 //
-//  accurately as two pieces: U_hi and U_lo. The way to achieve this 
-//  is to obtain r_hi as a 10 sig. bit number that approximates r to 
+//  accurately as two pieces: U_hi and U_lo. The way to achieve this
+//  is to obtain r_hi as a 10 sig. bit number that approximates r to
 //  roughly 8 bits or so of accuracy. (One convenient way is
 //
 //  r_hi := frcpa( frcpa( r ) ).)
 //
 //  This way,
 //
-//	r + PP_1_hi r^3 =  r + PP_1_hi r_hi^3 +
-//	                        PP_1_hi (r^3 - r_hi^3)
-//		        =  [r + PP_1_hi r_hi^3]  +  
-//			   [PP_1_hi (r - r_hi) 
-//			      (r^2 + r_hi r + r_hi^2) ]
-//		        =  U_hi  +  U_lo
+//        r + PP_1_hi r^3 =  r + PP_1_hi r_hi^3 +
+//                                PP_1_hi (r^3 - r_hi^3)
+//                        =  [r + PP_1_hi r_hi^3]  +
+//                           [PP_1_hi (r - r_hi)
+//                              (r^2 + r_hi r + r_hi^2) ]
+//                        =  U_hi  +  U_lo
 //
 //  Since r_hi is only 10 bit long and PP_1_hi is only 16 bit long,
-//  PP_1_hi * r_hi^3 is only at most 46 bit long and thus computed 
-//  exactly. Furthermore, r and PP_1_hi r_hi^3 are of opposite sign 
-//  and that there is no more than 8 bit shift off between r and 
-//  PP_1_hi * r_hi^3. Hence the sum, U_hi, is representable and thus 
-//  calculated without any error. Finally, the fact that 
+//  PP_1_hi * r_hi^3 is only at most 46 bit long and thus computed
+//  exactly. Furthermore, r and PP_1_hi r_hi^3 are of opposite sign
+//  and that there is no more than 8 bit shift off between r and
+//  PP_1_hi * r_hi^3. Hence the sum, U_hi, is representable and thus
+//  calculated without any error. Finally, the fact that
 //
-//	|U_lo| <= 2^(-8) |U_hi|
+//        |U_lo| <= 2^(-8) |U_hi|
 //
-//  says that U_hi + U_lo is approximating r + PP_1_hi r^3 to roughly 
+//  says that U_hi + U_lo is approximating r + PP_1_hi r^3 to roughly
 //  8 extra bits of accuracy.
 //
 //  Similarly,
 //
-//	1 + QQ_1 r^2  =  [1 + QQ_1 r_hi^2]  +
-//	                    [QQ_1 (r - r_hi)(r + r_hi)]
-//		      =  U_hi  +  U_lo.
-//		      
-//  Summarizing, we calculate r_hi = frcpa( frcpa( r ) ). 
+//        1 + QQ_1 r^2  =  [1 + QQ_1 r_hi^2]  +
+//                            [QQ_1 (r - r_hi)(r + r_hi)]
+//                      =  U_hi  +  U_lo.
+//
+//  Summarizing, we calculate r_hi = frcpa( frcpa( r ) ).
 //
 //  If i_1 = 0, then
 //
@@ -297,35 +303,35 @@
 //  End
 //
 //  Finally,
-// 
-//	V := poly + ( U_lo + correction )
+//
+//        V := poly + ( U_lo + correction )
 //
 //                 /    U_hi  +  V         if i_0 = 0
-//	result := |
+//        result := |
 //                 \  (-U_hi) -  V         if i_0 = 1
 //
-//  It is important that in the last step, negation of U_hi is 
-//  performed prior to the subtraction which is to be performed in 
-//  the user-set rounding mode. 
+//  It is important that in the last step, negation of U_hi is
+//  performed prior to the subtraction which is to be performed in
+//  the user-set rounding mode.
 //
 //
 //  Algorithmic Description
 //  =======================
 //
-//  The argument reduction algorithm is tightly integrated into FSIN 
-//  and FCOS which share the same code. The following is complete and 
-//  self-contained. The argument reduction description given 
+//  The argument reduction algorithm is tightly integrated into FSIN
+//  and FCOS which share the same code. The following is complete and
+//  self-contained. The argument reduction description given
 //  previously is repeated below.
 //
 //
-//  Step 0. Initialization. 
+//  Step 0. Initialization.
 //
 //   If FSIN is invoked, set N_inc := 0; else if FCOS is invoked,
 //   set N_inc := 1.
 //
 //  Step 1. Check for exceptional and special cases.
 //
-//   * If Arg is +-0, +-inf, NaN, NaT, go to Step 10 for special 
+//   * If Arg is +-0, +-inf, NaN, NaT, go to Step 10 for special
 //     handling.
 //   * If |Arg| < 2^24, go to Step 2 for reduction of moderate
 //     arguments. This is the most likely case.
@@ -335,18 +341,18 @@
 //
 //  Step 2. Reduction of moderate arguments.
 //
-//  If |Arg| < pi/4 	...quick branch
-//     N_fix := N_inc	(integer)
+//  If |Arg| < pi/4         ...quick branch
+//     N_fix := N_inc        (integer)
 //     r     := Arg
 //     c     := 0.0
 //     Branch to Step 4, Case_1_complete
-//  Else 		...cf. argument reduction
-//     N     := Arg * two_by_PI	(fp)
-//     N_fix := fcvt.fx( N )	(int)
+//  Else                 ...cf. argument reduction
+//     N     := Arg * two_by_PI        (fp)
+//     N_fix := fcvt.fx( N )        (int)
 //     N     := fcvt.xf( N_fix )
 //     N_fix := N_fix + N_inc
-//     s     := Arg - N * P_1	(first piece of pi/2)
-//     w     := -N * P_2	(second piece of pi/2)
+//     s     := Arg - N * P_1        (first piece of pi/2)
+//     w     := -N * P_2        (second piece of pi/2)
 //
 //     If |s| >= 2^(-33)
 //        go to Step 3, Case_1_reduce
@@ -358,8 +364,8 @@
 //  Step 3. Case_1_reduce.
 //
 //  r := s + w
-//  c := (s - r) + w	...observe order
-//   
+//  c := (s - r) + w        ...observe order
+//
 //  Step 4. Case_1_complete
 //
 //  ...At this point, the reduced argument alpha is
@@ -375,17 +381,17 @@
 //
 //  If i_1 = 0, then
 //    poly := r*FR_rsq*(PP_1_lo + FR_rsq*(PP_2 + ... FR_rsq*PP_8))
-//    U_hi := r + PP_1_hi*r_hi*r_hi*r_hi	...any order
+//    U_hi := r + PP_1_hi*r_hi*r_hi*r_hi        ...any order
 //    U_lo := PP_1_hi*r_lo*(r*r + r*r_hi + r_hi*r_hi)
-//    correction := c + c*C_1*FR_rsq		...any order
+//    correction := c + c*C_1*FR_rsq                ...any order
 //  Else
 //    poly := FR_rsq*FR_rsq*(QQ_2 + FR_rsq*(QQ_3 + ... + FR_rsq*QQ_8))
-//    U_hi := 1 + QQ_1 * r_hi * r_hi		...any order
+//    U_hi := 1 + QQ_1 * r_hi * r_hi                ...any order
 //    U_lo := QQ_1 * r_lo * (r + r_hi)
-//    correction := -c*(r + S_1*FR_rsq*r)	...any order
+//    correction := -c*(r + S_1*FR_rsq*r)        ...any order
 //  Endif
 //
-//  V := poly + (U_lo + correction)	...observe order
+//  V := poly + (U_lo + correction)        ...observe order
 //
 //  result := (i_0 == 0?   1.0 : -1.0)
 //
@@ -397,7 +403,7 @@
 //  Return
 //
 //  Step 6. Small_r.
-// 
+//
 //  ...Use flush to zero mode without causing exception
 //    Let [i_0 i_1] be the two lsb of N_fix.
 //
@@ -412,7 +418,7 @@
 //  Else
 //     z := FR_rsq*FR_rsq; z := FR_rsq*z
 //     poly_lo := C_3 + FR_rsq*(C_4 + FR_rsq*C_5)
-//     poly_hi := FR_rsq*(C_1 + FR_rsq*C_2) 
+//     poly_hi := FR_rsq*(C_1 + FR_rsq*C_2)
 //     correction := -c*r
 //     result := 1
 //  Endif
@@ -429,15 +435,15 @@
 //
 //  Step 7. Case_2_reduce.
 //
-//  ...Refer to the write up for argument reduction for 
+//  ...Refer to the write up for argument reduction for
 //  ...rationale. The reduction algorithm below is taken from
 //  ...argument reduction description and integrated this.
 //
 //  w := N*P_3
-//  U_1 := N*P_2 + w		...FMA
-//  U_2 := (N*P_2 - U_1) + w	...2 FMA
+//  U_1 := N*P_2 + w                ...FMA
+//  U_2 := (N*P_2 - U_1) + w        ...2 FMA
 //  ...U_1 + U_2 is  N*(P_2+P_3) accurately
-//   
+//
 //  r := s - U_1
 //  c := ( (s - r) - U_1 ) - U_2
 //
@@ -446,29 +452,29 @@
 //  ...Case 1, this case requires much more work to reduce
 //  ...the argument, the subsequent calculation needed for
 //  ...any of the trigonometric function is very little because
-//  ...|alpha| < 1.01*2^(-33) and thus two terms of the 
+//  ...|alpha| < 1.01*2^(-33) and thus two terms of the
 //  ...Taylor series expansion suffices.
 //
 //  If i_1 = 0 then
-//     poly := c + S_1 * r * r * r	...any order
+//     poly := c + S_1 * r * r * r        ...any order
 //     result := r
 //  Else
 //     poly := -2^(-67)
 //     result := 1.0
 //  Endif
-//   
+//
 //  If i_0 = 1, result := -result
 //
 //  Last operation. Perform in user-set rounding mode
 //
 //  result := (i_0 == 0?     result + poly :
 //                           result - poly )
-//   
+//
 //  Return
 //
-//  
+//
 //  Step 8. Pre-reduction of large arguments.
-// 
+//
 //  ...Again, the following reduction procedure was described
 //  ...in the separate write up for argument reduction, which
 //  ...is tightly integrated here.
@@ -476,13 +482,13 @@
 //  N_0 := Arg * Inv_P_0
 //  N_0_fix := fcvt.fx( N_0 )
 //  N_0 := fcvt.xf( N_0_fix)
-   
+
 //  Arg' := Arg - N_0 * P_0
 //  w := N_0 * d_1
 //  N := Arg' * two_by_PI
 //  N_fix := fcvt.fx( N )
 //  N := fcvt.xf( N_fix )
-//  N_fix := N_fix + N_inc 
+//  N_fix := N_fix + N_inc
 //
 //  s := Arg' - N * P_1
 //  w := w - N * P_2
@@ -494,15 +500,15 @@
 //  Endif
 //
 //  Step 9. Case_4_reduce.
-// 
+//
 //    ...first obtain N_0*d_1 and -N*P_2 accurately
-//   U_hi := N_0 * d_1		V_hi := -N*P_2
-//   U_lo := N_0 * d_1 - U_hi	V_lo := -N*P_2 - U_hi	...FMAs
+//   U_hi := N_0 * d_1                V_hi := -N*P_2
+//   U_lo := N_0 * d_1 - U_hi        V_lo := -N*P_2 - U_hi        ...FMAs
 //
 //   ...compute the contribution from N_0*d_1 and -N*P_3
 //   w := -N*P_3
 //   w := w + N_0*d_2
-//   t := U_lo + V_lo + w		...any order
+//   t := U_lo + V_lo + w                ...any order
 //
 //   ...at this point, the mathematical value
 //   ...s + U_hi + V_hi  + t approximates the true reduced argument
@@ -517,12 +523,12 @@
 //   endif
 //   ...order in computing "a" must be observed. This branch is
 //   ...best implemented by predicates.
-//   ...A + a  is U_hi + V_hi accurately. Moreover, "a" is 
+//   ...A + a  is U_hi + V_hi accurately. Moreover, "a" is
 //   ...much smaller than A: |a| <= (1/2)ulp(A).
 //
 //   ...Just need to calculate   s + A + a + t
-//   C_hi := s + A		t := t + a
-//   C_lo := (s - C_hi) + A	
+//   C_hi := s + A                t := t + a
+//   C_lo := (s - C_hi) + A
 //   C_lo := C_lo + t
 //
 //   ...Final steps for reduction
@@ -548,156 +554,192 @@
 //   result := (i_0 == 0?     result + poly :
 //                            result - poly )
 //   Return
-//  
+//
 //   Large Arguments: For arguments above 2**63, a Payne-Hanek
 //   style argument reduction is used and pi_by_2 reduce is called.
 //
 
-#include "libm_support.h" 
-
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
-.align 64 
-
-FSINCOSL_CONSTANTS:
-ASM_TYPE_DIRECTIVE(FSINCOSL_CONSTANTS,@object)
-data4 0x4B800000, 0xCB800000, 0x00000000,0x00000000 // two**24, -two**24
-data4 0x4E44152A, 0xA2F9836E, 0x00003FFE,0x00000000 // Inv_pi_by_2
-data4 0xCE81B9F1, 0xC84D32B0, 0x00004016,0x00000000 // P_0 
-data4 0x2168C235, 0xC90FDAA2, 0x00003FFF,0x00000000 // P_1 
-data4 0xFC8F8CBB, 0xECE675D1, 0x0000BFBD,0x00000000 // P_2 
-data4 0xACC19C60, 0xB7ED8FBB, 0x0000BF7C,0x00000000 // P_3 
-data4 0x5F000000, 0xDF000000, 0x00000000,0x00000000 // two_to_63, -two_to_63
-data4 0x6EC6B45A, 0xA397E504, 0x00003FE7,0x00000000 // Inv_P_0 
-data4 0xDBD171A1, 0x8D848E89, 0x0000BFBF,0x00000000 // d_1 
-data4 0x18A66F8E, 0xD5394C36, 0x0000BF7C,0x00000000 // d_2 
-data4 0x2168C234, 0xC90FDAA2, 0x00003FFE,0x00000000 // pi_by_4 
-data4 0x2168C234, 0xC90FDAA2, 0x0000BFFE,0x00000000 // neg_pi_by_4 
-data4 0x3E000000, 0xBE000000, 0x00000000,0x00000000 // two**-3, -two**-3
-data4 0x2F000000, 0xAF000000, 0x9E000000,0x00000000 // two**-33, -two**-33, -two**-67
-data4 0xA21C0BC9, 0xCC8ABEBC, 0x00003FCE,0x00000000 // PP_8 
-data4 0x720221DA, 0xD7468A05, 0x0000BFD6,0x00000000 // PP_7 
-data4 0x640AD517, 0xB092382F, 0x00003FDE,0x00000000 // PP_6 
-data4 0xD1EB75A4, 0xD7322B47, 0x0000BFE5,0x00000000 // PP_5 
-data4 0xFFFFFFFE, 0xFFFFFFFF, 0x0000BFFD,0x00000000 // C_1 
-data4 0x00000000, 0xAAAA0000, 0x0000BFFC,0x00000000 // PP_1_hi 
-data4 0xBAF69EEA, 0xB8EF1D2A, 0x00003FEC,0x00000000 // PP_4 
-data4 0x0D03BB69, 0xD00D00D0, 0x0000BFF2,0x00000000 // PP_3 
-data4 0x88888962, 0x88888888, 0x00003FF8,0x00000000 // PP_2
-data4 0xAAAB0000, 0xAAAAAAAA, 0x0000BFEC,0x00000000 // PP_1_lo 
-data4 0xC2B0FE52, 0xD56232EF, 0x00003FD2,0x00000000 // QQ_8
-data4 0x2B48DCA6, 0xC9C99ABA, 0x0000BFDA,0x00000000 // QQ_7
-data4 0x9C716658, 0x8F76C650, 0x00003FE2,0x00000000 // QQ_6
-data4 0xFDA8D0FC, 0x93F27DBA, 0x0000BFE9,0x00000000 // QQ_5
-data4 0xAAAAAAAA, 0xAAAAAAAA, 0x0000BFFC,0x00000000 // S_1 
-data4 0x00000000, 0x80000000, 0x0000BFFE,0x00000000 // QQ_1 
-data4 0x0C6E5041, 0xD00D00D0, 0x00003FEF,0x00000000 // QQ_4 
-data4 0x0B607F60, 0xB60B60B6, 0x0000BFF5,0x00000000 // QQ_3 
-data4 0xAAAAAA9B, 0xAAAAAAAA, 0x00003FFA,0x00000000 // QQ_2 
-data4 0xFFFFFFFE, 0xFFFFFFFF, 0x0000BFFD,0x00000000 // C_1 
-data4 0xAAAA719F, 0xAAAAAAAA, 0x00003FFA,0x00000000 // C_2 
-data4 0x0356F994, 0xB60B60B6, 0x0000BFF5,0x00000000 // C_3
-data4 0xB2385EA9, 0xD00CFFD5, 0x00003FEF,0x00000000 // C_4 
-data4 0x292A14CD, 0x93E4BD18, 0x0000BFE9,0x00000000 // C_5
-data4 0xAAAAAAAA, 0xAAAAAAAA, 0x0000BFFC,0x00000000 // S_1 
-data4 0x888868DB, 0x88888888, 0x00003FF8,0x00000000 // S_2 
-data4 0x055EFD4B, 0xD00D00D0, 0x0000BFF2,0x00000000 // S_3 
-data4 0x839730B9, 0xB8EF1C5D, 0x00003FEC,0x00000000 // S_4
-data4 0xE5B3F492, 0xD71EA3A4, 0x0000BFE5,0x00000000 // S_5
-data4 0x38800000, 0xB8800000, 0x00000000            // two**-14, -two**-14
-ASM_SIZE_DIRECTIVE(FSINCOSL_CONSTANTS)
-
-FR_Input_X        = f8 
-FR_Neg_Two_to_M3  = f32 
-FR_Two_to_63      = f32 
-FR_Two_to_24      = f33 
-FR_Pi_by_4        = f33 
-FR_Two_to_M14     = f34 
-FR_Two_to_M33     = f35 
-FR_Neg_Two_to_24  = f36 
-FR_Neg_Pi_by_4    = f36 
-FR_Neg_Two_to_M14 = f37 
-FR_Neg_Two_to_M33 = f38 
-FR_Neg_Two_to_M67 = f39 
-FR_Inv_pi_by_2    = f40 
-FR_N_float        = f41 
-FR_N_fix          = f42 
-FR_P_1            = f43 
-FR_P_2            = f44 
-FR_P_3            = f45 
-FR_s              = f46 
-FR_w              = f47 
-FR_c              = f48 
-FR_r              = f49 
-FR_Z              = f50 
-FR_A              = f51 
-FR_a              = f52 
-FR_t              = f53 
-FR_U_1            = f54 
-FR_U_2            = f55 
-FR_C_1            = f56 
-FR_C_2            = f57 
-FR_C_3            = f58 
-FR_C_4            = f59 
-FR_C_5            = f60 
-FR_S_1            = f61 
-FR_S_2            = f62 
-FR_S_3            = f63 
-FR_S_4            = f64 
-FR_S_5            = f65 
-FR_poly_hi        = f66 
-FR_poly_lo        = f67 
-FR_r_hi           = f68 
-FR_r_lo           = f69 
-FR_rsq            = f70 
-FR_r_cubed        = f71 
-FR_C_hi           = f72 
-FR_N_0            = f73 
-FR_d_1            = f74 
-FR_V              = f75 
-FR_V_hi           = f75 
-FR_V_lo           = f76 
-FR_U_hi           = f77 
-FR_U_lo           = f78 
-FR_U_hiabs        = f79 
-FR_V_hiabs        = f80 
-FR_PP_8           = f81 
-FR_QQ_8           = f81 
-FR_PP_7           = f82 
-FR_QQ_7           = f82 
-FR_PP_6           = f83 
-FR_QQ_6           = f83 
-FR_PP_5           = f84 
-FR_QQ_5           = f84 
-FR_PP_4           = f85 
-FR_QQ_4           = f85 
-FR_PP_3           = f86 
-FR_QQ_3           = f86 
-FR_PP_2           = f87 
-FR_QQ_2           = f87 
-FR_QQ_1           = f88 
-FR_N_0_fix        = f89 
-FR_Inv_P_0        = f90 
-FR_corr           = f91 
-FR_poly           = f92 
-FR_d_2            = f93 
-FR_Two_to_M3      = f94 
-FR_Neg_Two_to_63  = f94 
-FR_P_0            = f95 
-FR_C_lo           = f96 
-FR_PP_1           = f97 
-FR_PP_1_lo        = f98 
-FR_ArgPrime       = f99 
-
-GR_Table_Base  = r32 
-GR_Table_Base1 = r33 
-GR_i_0         = r34
-GR_i_1         = r35
-GR_N_Inc       = r36 
-GR_Sin_or_Cos  = r37 
+
+RODATA
+.align 16
+
+LOCAL_OBJECT_START(FSINCOSL_CONSTANTS)
+
+sincosl_table_p:
+data8 0xA2F9836E4E44152A, 0x00003FFE // Inv_pi_by_2
+data8 0xC84D32B0CE81B9F1, 0x00004016 // P_0
+data8 0xC90FDAA22168C235, 0x00003FFF // P_1
+data8 0xECE675D1FC8F8CBB, 0x0000BFBD // P_2
+data8 0xB7ED8FBBACC19C60, 0x0000BF7C // P_3
+data8 0x8D848E89DBD171A1, 0x0000BFBF // d_1
+data8 0xD5394C3618A66F8E, 0x0000BF7C // d_2
+LOCAL_OBJECT_END(FSINCOSL_CONSTANTS)
+
+LOCAL_OBJECT_START(sincosl_table_d)
+data8 0xC90FDAA22168C234, 0x00003FFE // pi_by_4
+data8 0xA397E5046EC6B45A, 0x00003FE7 // Inv_P_0
+data4 0x3E000000, 0xBE000000         // 2^-3 and -2^-3
+data4 0x2F000000, 0xAF000000         // 2^-33 and -2^-33
+data4 0x9E000000, 0x00000000         // -2^-67
+data4 0x00000000, 0x00000000         // pad
+LOCAL_OBJECT_END(sincosl_table_d)
+
+LOCAL_OBJECT_START(sincosl_table_pp)
+data8 0xCC8ABEBCA21C0BC9, 0x00003FCE // PP_8
+data8 0xD7468A05720221DA, 0x0000BFD6 // PP_7
+data8 0xB092382F640AD517, 0x00003FDE // PP_6
+data8 0xD7322B47D1EB75A4, 0x0000BFE5 // PP_5
+data8 0xFFFFFFFFFFFFFFFE, 0x0000BFFD // C_1
+data8 0xAAAA000000000000, 0x0000BFFC // PP_1_hi
+data8 0xB8EF1D2ABAF69EEA, 0x00003FEC // PP_4
+data8 0xD00D00D00D03BB69, 0x0000BFF2 // PP_3
+data8 0x8888888888888962, 0x00003FF8 // PP_2
+data8 0xAAAAAAAAAAAB0000, 0x0000BFEC // PP_1_lo
+LOCAL_OBJECT_END(sincosl_table_pp)
+
+LOCAL_OBJECT_START(sincosl_table_qq)
+data8 0xD56232EFC2B0FE52, 0x00003FD2 // QQ_8
+data8 0xC9C99ABA2B48DCA6, 0x0000BFDA // QQ_7
+data8 0x8F76C6509C716658, 0x00003FE2 // QQ_6
+data8 0x93F27DBAFDA8D0FC, 0x0000BFE9 // QQ_5
+data8 0xAAAAAAAAAAAAAAAA, 0x0000BFFC // S_1
+data8 0x8000000000000000, 0x0000BFFE // QQ_1
+data8 0xD00D00D00C6E5041, 0x00003FEF // QQ_4
+data8 0xB60B60B60B607F60, 0x0000BFF5 // QQ_3
+data8 0xAAAAAAAAAAAAAA9B, 0x00003FFA // QQ_2
+LOCAL_OBJECT_END(sincosl_table_qq)
+
+LOCAL_OBJECT_START(sincosl_table_c)
+data8 0xFFFFFFFFFFFFFFFE, 0x0000BFFD // C_1
+data8 0xAAAAAAAAAAAA719F, 0x00003FFA // C_2
+data8 0xB60B60B60356F994, 0x0000BFF5 // C_3
+data8 0xD00CFFD5B2385EA9, 0x00003FEF // C_4
+data8 0x93E4BD18292A14CD, 0x0000BFE9 // C_5
+LOCAL_OBJECT_END(sincosl_table_c)
+
+LOCAL_OBJECT_START(sincosl_table_s)
+data8 0xAAAAAAAAAAAAAAAA, 0x0000BFFC // S_1
+data8 0x88888888888868DB, 0x00003FF8 // S_2
+data8 0xD00D00D0055EFD4B, 0x0000BFF2 // S_3
+data8 0xB8EF1C5D839730B9, 0x00003FEC // S_4
+data8 0xD71EA3A4E5B3F492, 0x0000BFE5 // S_5
+data4 0x38800000, 0xB8800000                        // two**-14 and -two**-14
+LOCAL_OBJECT_END(sincosl_table_s)
+
+FR_Input_X        = f8
+FR_Result         = f8
+
+FR_r              = f8
+FR_c              = f9
+
+FR_norm_x         = f9
+FR_inv_pi_2to63   = f10
+FR_rshf_2to64     = f11
+FR_2tom64         = f12
+FR_rshf           = f13
+FR_N_float_signif = f14
+FR_abs_x          = f15
+FR_Pi_by_4        = f34
+FR_Two_to_M14     = f35
+FR_Neg_Two_to_M14 = f36
+FR_Two_to_M33     = f37
+FR_Neg_Two_to_M33 = f38
+FR_Neg_Two_to_M67 = f39
+FR_Inv_pi_by_2    = f40
+FR_N_float        = f41
+FR_N_fix          = f42
+FR_P_1            = f43
+FR_P_2            = f44
+FR_P_3            = f45
+FR_s              = f46
+FR_w              = f47
+FR_d_2            = f48
+FR_tmp_result     = f49
+FR_Z              = f50
+FR_A              = f51
+FR_a              = f52
+FR_t              = f53
+FR_U_1            = f54
+FR_U_2            = f55
+FR_C_1            = f56
+FR_C_2            = f57
+FR_C_3            = f58
+FR_C_4            = f59
+FR_C_5            = f60
+FR_S_1            = f61
+FR_S_2            = f62
+FR_S_3            = f63
+FR_S_4            = f64
+FR_S_5            = f65
+FR_poly_hi        = f66
+FR_poly_lo        = f67
+FR_r_hi           = f68
+FR_r_lo           = f69
+FR_rsq            = f70
+FR_r_cubed        = f71
+FR_C_hi           = f72
+FR_N_0            = f73
+FR_d_1            = f74
+FR_V              = f75
+FR_V_hi           = f75
+FR_V_lo           = f76
+FR_U_hi           = f77
+FR_U_lo           = f78
+FR_U_hiabs        = f79
+FR_V_hiabs        = f80
+FR_PP_8           = f81
+FR_QQ_8           = f101
+FR_PP_7           = f82
+FR_QQ_7           = f102
+FR_PP_6           = f83
+FR_QQ_6           = f103
+FR_PP_5           = f84
+FR_QQ_5           = f104
+FR_PP_4           = f85
+FR_QQ_4           = f105
+FR_PP_3           = f86
+FR_QQ_3           = f106
+FR_PP_2           = f87
+FR_QQ_2           = f107
+FR_QQ_1           = f108
+FR_r_hi_sq        = f88
+FR_N_0_fix        = f89
+FR_Inv_P_0        = f90
+FR_corr           = f91
+FR_poly           = f92
+FR_Neg_Two_to_M3  = f93
+FR_Two_to_M3      = f94
+FR_P_0            = f95
+FR_C_lo           = f96
+FR_PP_1           = f97
+FR_PP_1_lo        = f98
+FR_ArgPrime       = f99
+FR_inexact        = f100
+
+GR_exp_m2_to_m3= r36
+GR_N_Inc       = r37
+GR_Sin_or_Cos  = r38
+GR_signexp_x   = r40
+GR_exp_x       = r40
+GR_exp_mask    = r41
+GR_exp_2_to_63 = r42
+GR_exp_2_to_m3 = r43
+GR_exp_2_to_24 = r44
+
+GR_sig_inv_pi  = r45
+GR_rshf_2to64  = r46
+GR_exp_2tom64  = r47
+GR_rshf        = r48
+GR_ad_p        = r49
+GR_ad_d        = r50
+GR_ad_pp       = r51
+GR_ad_qq       = r52
+GR_ad_c        = r53
+GR_ad_s        = r54
+GR_ad_ce       = r55
+GR_ad_se       = r56
+GR_ad_m14      = r57
+GR_ad_s1       = r58
 
 // Added for unwind support
 
@@ -706,386 +748,377 @@ GR_SAVE_GP     = r40
 GR_SAVE_PFS    = r41
 
 
-.global sinl#
-.global cosl#
-#ifdef _LIBC
-.global __sinl#
-.global __cosl#
-#endif
-
 .section .text
-.proc sinl#
-#ifdef _LIBC
-.proc __sinl#
-#endif
-.align 64 
-sinl:
-#ifdef _LIBC
-__sinl:
-#endif
+
+GLOBAL_IEEE754_ENTRY(sinl)
 { .mlx
-alloc GR_Table_Base = ar.pfs,0,12,2,0
-(p0)   movl GR_Sin_or_Cos = 0x0 ;;
+      alloc r32 = ar.pfs,0,27,2,0
+      movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi
 }
-
-{ .mmi
-      nop.m 999
-(p0)  addl           GR_Table_Base   = @ltoff(FSINCOSL_CONSTANTS#), gp
-      nop.i 999
+{ .mlx
+      mov GR_Sin_or_Cos = 0x0
+      movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64)
 }
 ;;
 
-{ .mmb
-      ld8 GR_Table_Base = [GR_Table_Base]
+{ .mfi
+      addl           GR_ad_p   = @ltoff(FSINCOSL_CONSTANTS#), gp
+      fclass.m p6, p0 =  FR_Input_X, 0x1E3 // Test x natval, nan, inf
+      mov GR_exp_2_to_m3 = 0xffff - 3      // Exponent of 2^-3
+}
+{ .mfb
       nop.m 999
-(p0)   br.cond.sptk L(SINCOSL_CONTINUE) ;;
+      fnorm.s1 FR_norm_x = FR_Input_X      // Normalize x
+      br.cond.sptk SINCOSL_CONTINUE
 }
 ;;
 
+GLOBAL_IEEE754_END(sinl)
 
-.endp sinl#
-ASM_SIZE_DIRECTIVE(sinl#)
-
-.section .text
-.proc cosl#
-cosl:
-#ifdef _LIBC
-.proc __cosl#
-__cosl:
-#endif
+GLOBAL_IEEE754_ENTRY(cosl)
+{ .mlx
+      alloc r32 = ar.pfs,0,27,2,0
+      movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi
+}
 { .mlx
-alloc GR_Table_Base= ar.pfs,0,12,2,0
-(p0)   movl GR_Sin_or_Cos = 0x1 ;;
+      mov GR_Sin_or_Cos = 0x1
+      movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64)
 }
 ;;
 
-{ .mmi
+{ .mfi
+      addl           GR_ad_p   = @ltoff(FSINCOSL_CONSTANTS#), gp
+      fclass.m p6, p0 =  FR_Input_X, 0x1E3 // Test x natval, nan, inf
+      mov GR_exp_2_to_m3 = 0xffff - 3      // Exponent of 2^-3
+}
+{ .mfi
       nop.m 999
-(p0)  addl           GR_Table_Base   = @ltoff(FSINCOSL_CONSTANTS#), gp
+      fnorm.s1 FR_norm_x = FR_Input_X      // Normalize x
       nop.i 999
 }
 ;;
 
-{ .mmb
-      ld8 GR_Table_Base = [GR_Table_Base]
-      nop.m 999
-      nop.b 999
+SINCOSL_CONTINUE:
+{ .mfi
+      setf.sig FR_inv_pi_2to63 = GR_sig_inv_pi // Form 1/pi * 2^63
+      nop.f 999
+      mov GR_exp_2tom64 = 0xffff - 64      // Scaling constant to compute N
+}
+{ .mlx
+      setf.d FR_rshf_2to64 = GR_rshf_2to64    // Form const 1.1000 * 2^(63+64)
+      movl GR_rshf = 0x43e8000000000000       // Form const 1.1000 * 2^63
 }
 ;;
 
+{ .mfi
+      ld8 GR_ad_p = [GR_ad_p]              // Point to Inv_pi_by_2
+      fclass.m p7, p0 = FR_Input_X, 0x0b   // Test x denormal
+      nop.i 999
+}
+;;
 
-
-//
-//     Load Table Address
-//
-
-L(SINCOSL_CONTINUE): 
-{ .mmi
-(p0)   add GR_Table_Base1 = 96, GR_Table_Base
-(p0)   ldfs	FR_Two_to_24 = [GR_Table_Base], 4
-// GR_Sin_or_Cos denotes 
-(p0)   mov   r39 = b0 ;;
+{ .mfi
+      getf.exp GR_signexp_x = FR_Input_X   // Get sign and exponent of x
+      fclass.m p10, p0 = FR_Input_X, 0x007 // Test x zero
+      nop.i 999
 }
-{ .mmi
-       nop.m 0
-//
-//     Load 2**24, load 2**63.
-//
-(p0)   ldfs	FR_Neg_Two_to_24 = [GR_Table_Base], 12
-       nop.i 0
+{ .mib
+      mov GR_exp_mask = 0x1ffff            // Exponent mask
+      nop.i 999
+(p6)  br.cond.spnt SINCOSL_SPECIAL         // Branch if x natval, nan, inf
 }
+;;
+
 { .mfi
-(p0)   ldfs	FR_Two_to_63 = [GR_Table_Base1], 4
-//
-//     Check for unnormals - unsupported operands. We do not want
-//     to generate denormal exception
-//     Check for NatVals, QNaNs, SNaNs, +/-Infs
-//     Check for EM unsupporteds
-//     Check for Zero 
-//
-(p0)   fclass.m.unc  p6, p0 =  FR_Input_X, 0x1E3
-       nop.i 0
-};;
-{ .mmf
-        nop.m 999
-(p0)   ldfs	FR_Neg_Two_to_63 = [GR_Table_Base1], 12
-(p0)   fclass.nm.unc p8, p0 =  FR_Input_X, 0x1FF
-}
-{ .mfb
-	nop.m 999
-(p0)   fclass.m.unc p10, p0 = FR_Input_X, 0x007
-(p6)   br.cond.spnt L(SINCOSL_SPECIAL) ;;
+      setf.exp FR_2tom64 = GR_exp_2tom64   // Form 2^-64 for scaling N_float
+      nop.f 0
+      add GR_ad_d = 0x70, GR_ad_p          // Point to constant table d
 }
 { .mib
-	nop.m 999
-	nop.i 999
-(p8)   br.cond.spnt L(SINCOSL_SPECIAL) ;;
+      setf.d FR_rshf = GR_rshf         // Form right shift const 1.1000 * 2^63
+      mov  GR_exp_m2_to_m3 = 0x2fffc       // Form -(2^-3)
+(p7)  br.cond.spnt SINCOSL_DENORMAL        // Branch if x denormal
 }
-{ .mib
-	nop.m 999
-	nop.i 999
-//
-//     Branch if +/- NaN, Inf.
-//     Load -2**24, load -2**63.
-//
-(p10)  br.cond.spnt L(SINCOSL_ZERO) ;;
+;;
+
+SINCOSL_COMMON:
+{ .mfi
+      and GR_exp_x = GR_exp_mask, GR_signexp_x // Get exponent of x
+      fclass.nm p8, p0 = FR_Input_X, 0x1FF // Test x unsupported type
+      mov GR_exp_2_to_63 = 0xffff + 63     // Exponent of 2^63
 }
-{ .mmb
-(p0)   ldfe	FR_Inv_pi_by_2 = [GR_Table_Base], 16
-(p0)   ldfe	FR_Inv_P_0 = [GR_Table_Base1], 16
-	nop.b 999 ;;
+{ .mib
+      add GR_ad_pp = 0x40, GR_ad_d         // Point to constant table pp
+      mov GR_exp_2_to_24 = 0xffff + 24     // Exponent of 2^24
+(p10) br.cond.spnt SINCOSL_ZERO            // Branch if x zero
 }
-{ .mmb
-(p0)   ldfe		FR_d_1 = [GR_Table_Base1], 16
-//
-//     Raise possible denormal operand flag with useful fcmp
-//     Is x <= -2**63
-//     Load Inv_P_0 for pre-reduction
-//     Load Inv_pi_by_2
-//
-(p0)   ldfe		FR_P_0 = [GR_Table_Base], 16
-	nop.b 999 ;;
+;;
+
+{ .mfi
+      ldfe FR_Inv_pi_by_2 = [GR_ad_p], 16  // Load 2/pi
+      fcmp.eq.s0 p15, p0 = FR_Input_X, f0  // Dummy to set denormal
+      add GR_ad_qq = 0xa0, GR_ad_pp        // Point to constant table qq
 }
-{ .mmb
-(p0)   ldfe	FR_d_2 = [GR_Table_Base1], 16
-//
-//     Load P_0
-//     Load d_1
-//     Is x >= 2**63
-//     Is x <= -2**24?
-//
-(p0)   ldfe	FR_P_1 = [GR_Table_Base], 16
-	nop.b 999 ;;
+{ .mfi
+      ldfe FR_Pi_by_4 = [GR_ad_d], 16      // Load pi/4 for range test
+      nop.f 999
+      cmp.ge p10,p0 = GR_exp_x, GR_exp_2_to_63   // Is |x| >= 2^63
 }
-//
-//     Load P_1
-//     Load d_2
-//     Is x >= 2**24?
-//
+;;
+
 { .mfi
-(p0)   ldfe	FR_P_2 = [GR_Table_Base], 16
-(p0)   fcmp.le.unc.s1	p7, p8 = FR_Input_X, FR_Neg_Two_to_24
-	nop.i 999 ;;
+      ldfe FR_P_0 = [GR_ad_p], 16          // Load P_0 for pi/4 <= |x| < 2^63
+      fmerge.s FR_abs_x = f1, FR_norm_x    // |x|
+      add GR_ad_c = 0x90, GR_ad_qq         // Point to constant table c
 }
-{ .mbb
-(p0)   ldfe	FR_P_3 = [GR_Table_Base], 16
-	nop.b 999
-	nop.b 999 ;;
+{ .mfi
+      ldfe FR_Inv_P_0 = [GR_ad_d], 16      // Load 1/P_0 for pi/4 <= |x| < 2^63
+      nop.f 999
+      cmp.ge p7,p0 = GR_exp_x, GR_exp_2_to_24   // Is |x| >= 2^24
 }
+;;
+
 { .mfi
-	nop.m 999
-(p8)   fcmp.ge.s1 p7, p0 = FR_Input_X, FR_Two_to_24
-	nop.i 999
+      ldfe FR_P_1 = [GR_ad_p], 16          // Load P_1 for pi/4 <= |x| < 2^63
+      nop.f 999
+      add GR_ad_s = 0x50, GR_ad_c          // Point to constant table s
 }
 { .mfi
-(p0)   ldfe	FR_Pi_by_4 = [GR_Table_Base1], 16
-//
-//     Branch if +/- zero.
-//     Decide about the paths to take:
-//     If -2**24 < FR_Input_X < 2**24 - CASE 1 OR 2 
-//     OTHERWISE - CASE 3 OR 4 
-//
-(p0)   fcmp.le.unc.s0	p10, p11 = FR_Input_X, FR_Neg_Two_to_63
-	nop.i 999 ;;
+      ldfe FR_PP_8 = [GR_ad_pp], 16        // Load PP_8 for 2^-3 < |r| < pi/4
+      nop.f 999
+      nop.i 999
 }
-{ .mmi
-(p0)   ldfe	FR_Neg_Pi_by_4 = [GR_Table_Base1], 16 ;;
-(p0)   ldfs	FR_Two_to_M3 = [GR_Table_Base1], 4
-	nop.i 999
+;;
+
+{ .mfi
+      ldfe FR_P_2 = [GR_ad_p], 16          // Load P_2 for pi/4 <= |x| < 2^63
+      nop.f 999
+      add GR_ad_ce = 0x40, GR_ad_c         // Point to end of constant table c
 }
 { .mfi
-	nop.m 999
-(p11)  fcmp.ge.s1	p10, p0 = FR_Input_X, FR_Two_to_63
-	nop.i 999 ;;
+      ldfe FR_QQ_8 = [GR_ad_qq], 16        // Load QQ_8 for 2^-3 < |r| < pi/4
+      nop.f 999
+      nop.i 999
 }
-{ .mib
-(p0)   ldfs	FR_Neg_Two_to_M3 = [GR_Table_Base1], 12
-	nop.i 999
-//
-//     Load P_2
-//     Load P_3
-//     Load pi_by_4
-//     Load neg_pi_by_4
-//     Load 2**(-3)
-//     Load -2**(-3).
-//
-(p10)  br.cond.spnt L(SINCOSL_ARG_TOO_LARGE) ;;
+;;
+
+{ .mfi
+      ldfe FR_QQ_7 = [GR_ad_qq], 16        // Load QQ_7 for 2^-3 < |r| < pi/4
+      fma.s1        FR_N_float_signif = FR_Input_X, FR_inv_pi_2to63, FR_rshf_2to64
+      add GR_ad_se = 0x40, GR_ad_s         // Point to end of constant table s
 }
 { .mib
-	nop.m 999
-	nop.i 999
-//
-//     Branch out if x >= 2**63. Use Payne-Hanek Reduction
-//
-(p7)   br.cond.spnt L(SINCOSL_LARGER_ARG) ;;
+      ldfe FR_PP_7 = [GR_ad_pp], 16        // Load PP_7 for 2^-3 < |r| < pi/4
+      mov GR_ad_s1 = GR_ad_s               // Save pointer to S_1
+(p10) br.cond.spnt SINCOSL_ARG_TOO_LARGE   // Branch if |x| >= 2^63
+                                           // Use Payne-Hanek Reduction
 }
+;;
+
 { .mfi
-	nop.m 999
-// 
-//     Branch if Arg <= -2**24 or Arg >= 2**24 and use pre-reduction.
-//
-(p0)   fma.s1	FR_N_float = FR_Input_X, FR_Inv_pi_by_2, f0
-	nop.i 999 ;;
+      ldfe FR_P_3 = [GR_ad_p], 16          // Load P_3 for pi/4 <= |x| < 2^63
+      fmerge.se FR_r = FR_norm_x, FR_norm_x // r = x, in case |x| < pi/4
+      add GR_ad_m14 = 0x50, GR_ad_s        // Point to constant table m14
 }
-{ .mfi
-	nop.m 999
-(p0)   fcmp.lt.unc.s1	p6, p7 = FR_Input_X, FR_Pi_by_4
-	nop.i 999 ;;
+{ .mfb
+      ldfps FR_Two_to_M3, FR_Neg_Two_to_M3 = [GR_ad_d], 8
+      fma.s1 FR_rsq = FR_norm_x, FR_norm_x, f0 // rsq = x*x, in case |x| < pi/4
+(p7)  br.cond.spnt SINCOSL_LARGER_ARG      // Branch if 2^24 <= |x| < 2^63
+                                           // Use pre-reduction
+}
+;;
+
+{ .mmf
+      ldfe FR_PP_6 = [GR_ad_pp], 16       // Load PP_6 for normal path
+      ldfe FR_QQ_6 = [GR_ad_qq], 16       // Load QQ_6 for normal path
+      fmerge.se FR_c = f0, f0             // c = 0 in case |x| < pi/4
 }
+;;
+
+{ .mmf
+      ldfe FR_PP_5 = [GR_ad_pp], 16       // Load PP_5 for normal path
+      ldfe FR_QQ_5 = [GR_ad_qq], 16       // Load QQ_5 for normal path
+      nop.f 999
+}
+;;
+
+// Here if 0 < |x| < 2^24
 { .mfi
-	nop.m 999
-// 
-//     Select the case when |Arg| < pi/4 
-//     Else Select the case when |Arg| >= pi/4 
-//
-(p0)   fcvt.fx.s1 FR_N_fix = FR_N_float
-	nop.i 999 ;;
+      ldfe FR_S_5 = [GR_ad_se], -16       // Load S_5 if i_1=0
+      fcmp.lt.s1  p6, p7 = FR_abs_x, FR_Pi_by_4  // Test |x| < pi/4
+      nop.i 999
 }
 { .mfi
-	nop.m 999
+      ldfe FR_C_5 = [GR_ad_ce], -16       // Load C_5 if i_1=1
+      fms.s1 FR_N_float = FR_N_float_signif, FR_2tom64, FR_rshf
+      nop.i 999
+}
+;;
+
+{ .mmi
+      ldfe FR_S_4 = [GR_ad_se], -16       // Load S_4 if i_1=0
+      ldfe FR_C_4 = [GR_ad_ce], -16       // Load C_4 if i_1=1
+      nop.i 999
+}
+;;
+
 //
 //     N  = Arg * 2/pi
 //     Check if Arg < pi/4
 //
-(p6)   fcmp.gt.s1 p6, p7 = FR_Input_X, FR_Neg_Pi_by_4
-	nop.i 999 ;;
-}
 //
 //     Case 2: Convert integer N_fix back to normalized floating-point value.
 //     Case 1: p8 is only affected  when p6 is set
 //
-{ .mfi
-(p7)   ldfs FR_Two_to_M33 = [GR_Table_Base1], 4
 //
 //     Grab the integer part of N and call it N_fix
 //
-(p6)   fmerge.se FR_r = FR_Input_X, FR_Input_X
-//     If |x| < pi/4, r = x and c = 0 
+{ .mfi
+(p7)  ldfps FR_Two_to_M33, FR_Neg_Two_to_M33 = [GR_ad_d], 8
+(p6)  fma.s1 FR_r_cubed = FR_r, FR_rsq, f0        // r^3 if |x| < pi/4
+(p6)  mov GR_N_Inc = GR_Sin_or_Cos                // N_Inc if |x| < pi/4
+}
+;;
+
+//     If |x| < pi/4, r = x and c = 0
 //     lf |x| < pi/4, is x < 2**(-3).
-//     r = Arg 
+//     r = Arg
 //     c = 0
-(p6)   mov GR_N_Inc = GR_Sin_or_Cos ;;
-}
-{ .mmf
-	nop.m 999
-(p7)   ldfs FR_Neg_Two_to_M33 = [GR_Table_Base1], 4
-(p6)   fmerge.se FR_c = f0, f0
-}
-{ .mfi
-	nop.m 999
-(p6)   fcmp.lt.unc.s1	p8, p9 = FR_Input_X, FR_Two_to_M3
-	nop.i 999 ;;
+{ .mmi
+(p7)  getf.sig        GR_N_Inc = FR_N_float_signif
+(p6)  cmp.lt.unc p8,p0 = GR_exp_x, GR_exp_2_to_m3   // Is |x| < 2^-3
+(p6)  tbit.z p9,p10 = GR_N_Inc, 0         // p9  if i_1=0, N mod 4 = 0,1
+                                          // p10 if i_1=1, N mod 4 = 2,3
 }
-{ .mfi
-	nop.m 999
+;;
+
 //
 //     lf |x| < pi/4, is -2**(-3)< x < 2**(-3) - set p8.
-//     If |x| >= pi/4, 
-//     Create the right N for |x| < pi/4 and otherwise 
+//     If |x| >= pi/4,
+//     Create the right N for |x| < pi/4 and otherwise
 //     Case 2: Place integer part of N in GP register
 //
-(p7)   fcvt.xf FR_N_float = FR_N_fix
-	nop.i 999 ;;
-}
-{ .mmf
-	nop.m 999
-(p7)   getf.sig	GR_N_Inc = FR_N_fix
-(p8)   fcmp.gt.s1 p8, p0 = FR_Input_X, FR_Neg_Two_to_M3 ;;
-}
-{ .mib
-	nop.m 999
-	nop.i 999
-//
-//     Load 2**(-33), -2**(-33)
-//
-(p8)   br.cond.spnt L(SINCOSL_SMALL_R) ;;
+
+
+{ .mbb
+      nop.m 999
+(p8)  br.cond.spnt SINCOSL_SMALL_R_0    // Branch if 0 < |x| < 2^-3
+(p6)  br.cond.spnt SINCOSL_NORMAL_R_0   // Branch if 2^-3 <= |x| < pi/4
 }
-{ .mib
-	nop.m 999
-	nop.i 999
-(p6)   br.cond.sptk L(SINCOSL_NORMAL_R) ;;
+;;
+
+// Here if pi/4 <= |x| < 2^24
+{ .mfi
+      ldfs FR_Neg_Two_to_M67 = [GR_ad_d], 8     // Load -2^-67
+      fnma.s1 FR_s = FR_N_float, FR_P_1, FR_Input_X // s = -N * P_1  + Arg
+      add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos    // Adjust N_Inc for sin/cos
 }
-//
-//     if |x| < pi/4, branch based on |x| < 2**(-3) or otherwise.
-//
-//
-//     In this branch, |x| >= pi/4.
-// 
 { .mfi
-(p0)   ldfs FR_Neg_Two_to_M67 = [GR_Table_Base1], 8
-//
-//     Load -2**(-67)
-// 
-(p0)   fnma.s1	FR_s = FR_N_float, FR_P_1, FR_Input_X
-//
-//     w = N * P_2
-//     s = -N * P_1  + Arg
-//
-(p0)   add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos
+      nop.m 999
+      fma.s1 FR_w = FR_N_float, FR_P_2, f0      // w = N * P_2
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p0)   fma.s1	FR_w = FR_N_float, FR_P_2, f0
-	nop.i 999 ;;
+      nop.m 999
+      fms.s1 FR_r = FR_s, f1, FR_w        // r = s - w, assume |s| >= 2^-33
+      tbit.z p9,p10 = GR_N_Inc, 0         // p9  if i_1=0, N mod 4 = 0,1
+                                          // p10 if i_1=1, N mod 4 = 2,3
 }
+;;
+
 { .mfi
-	nop.m 999
-// 
-//     Adjust N_fix by N_inc to determine whether sine or
-//     cosine is being calculated
-//
-(p0)   fcmp.lt.unc.s1 p7, p6 = FR_s, FR_Two_to_M33
-	nop.i 999 ;;
+      nop.m 999
+      fcmp.lt.s1 p7, p6 = FR_s, FR_Two_to_M33
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p7)   fcmp.gt.s1 p7, p6 = FR_s, FR_Neg_Two_to_M33
-	nop.i 999 ;;
+      nop.m 999
+(p7)  fcmp.gt.s1 p7, p6 = FR_s, FR_Neg_Two_to_M33 // p6 if |s| >= 2^-33, else p7
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//     Remember x >= pi/4.
-//     Is s <= -2**(-33) or s >= 2**(-33) (p6)
-//     or -2**(-33) < s < 2**(-33) (p7)
-(p6)   fms.s1 FR_r = FR_s, f1, FR_w
-	nop.i 999
+      nop.m 999
+      fms.s1 FR_c = FR_s, f1, FR_r             // c = s - r, for |s| >= 2^-33
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-(p7)   fma.s1 FR_w = FR_N_float, FR_P_3, f0
-	nop.i 999 ;;
+      nop.m 999
+      fma.s1 FR_rsq = FR_r, FR_r, f0           // rsq = r * r, for |s| >= 2^-33
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p7)   fma.s1 FR_U_1 = FR_N_float, FR_P_2, FR_w
-	nop.i 999
+      nop.m 999
+(p7)  fma.s1 FR_w = FR_N_float, FR_P_3, f0
+      nop.i 999
 }
+;;
+
+{ .mmf
+(p9)  ldfe FR_C_1 = [GR_ad_pp], 16     // Load C_1 if i_1=0
+(p10) ldfe FR_S_1 = [GR_ad_qq], 16     // Load S_1 if i_1=1
+      frcpa.s1 FR_r_hi, p15 = f1, FR_r  // r_hi = frcpa(r)
+}
+;;
+
 { .mfi
-	nop.m 999
-(p6)   fms.s1 FR_c = FR_s, f1, FR_r
-	nop.i 999 ;;
+      nop.m 999
+(p6)  fcmp.lt.unc.s1 p8, p13 = FR_r, FR_Two_to_M3 // If big s, test r with 2^-3
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-// 
-//     For big s: r = s - w: No futher reduction is necessary 
+      nop.m 999
+(p7)  fma.s1 FR_U_1 = FR_N_float, FR_P_2, FR_w
+      nop.i 999
+}
+;;
+
+//
+//     For big s: r = s - w: No futher reduction is necessary
 //     For small s: w = N * P_3 (change sign) More reduction
 //
-(p6)   fcmp.lt.unc.s1 p8, p9 = FR_r, FR_Two_to_M3
-	nop.i 999 ;;
+{ .mfi
+        nop.m 999
+(p8)   fcmp.gt.s1 p8, p13 = FR_r, FR_Neg_Two_to_M3 // If big s, p8 if |r| < 2^-3
+        nop.i 999 ;;
 }
+
 { .mfi
-	nop.m 999
-(p8)   fcmp.gt.s1 p8, p9 = FR_r, FR_Neg_Two_to_M3
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_poly = FR_rsq, FR_PP_8, FR_PP_7 // poly = rsq*PP_8+PP_7 if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
+      nop.m 999
+(p10) fma.s1 FR_poly = FR_rsq, FR_QQ_8, FR_QQ_7 // poly = rsq*QQ_8+QQ_7 if i_1=1
+      nop.i 999
+}
+;;
+
+{ .mfi
+        nop.m 999
 (p7)   fms.s1 FR_r = FR_s, f1, FR_U_1
-	nop.i 999
+        nop.i 999
 }
-{ .mfb
-	nop.m 999
+;;
+
+{ .mfi
+      nop.m 999
+(p6)  fma.s1 FR_r_cubed = FR_r, FR_rsq, f0  // rcubed = r * rsq
+      nop.i 999
+}
+;;
+
+{ .mfi
 //
 //     For big s: Is |r| < 2**(-3)?
 //     For big s: c = S - r
@@ -1095,355 +1128,356 @@ L(SINCOSL_CONTINUE):
 //     If p9 is set, prepare to branch to Normal_R.
 //     For big s,  r is complete here.
 //
-(p6)   fms.s1 FR_c = FR_c, f1, FR_w
-// 
+//
 //     For big s: c = c + w (w has not been negated.)
 //     For small s: r = S - U_1
 //
-(p8)   br.cond.spnt	L(SINCOSL_SMALL_R) ;;
+      nop.m 999
+(p6)  fms.s1 FR_c = FR_c, f1, FR_w
+      nop.i 999
 }
-{ .mib
-	nop.m 999
-	nop.i 999
-(p9)   br.cond.sptk	L(SINCOSL_NORMAL_R) ;;
+{ .mbb
+      nop.m 999
+(p8)  br.cond.spnt    SINCOSL_SMALL_R_1  // Branch if |s|>=2^-33, |r| < 2^-3,
+                                         // and pi/4 <= |x| < 2^24
+(p13) br.cond.sptk    SINCOSL_NORMAL_R_1 // Branch if |s|>=2^-33, |r| >= 2^-3,
+                                         // and pi/4 <= |x| < 2^24
 }
-{ .mfi
-(p7)   add GR_Table_Base1 = 224, GR_Table_Base1
+;;
+
+SINCOSL_S_TINY:
 //
-//     Branch to SINCOSL_SMALL_R or SINCOSL_NORMAL_R
+// Here if |s| < 2^-33, and pi/4 <= |x| < 2^24
+//
+{ .mfi
+       fms.s1 FR_U_2 = FR_N_float, FR_P_2, FR_U_1
 //
-(p7)   fms.s1 FR_U_2 = FR_N_float, FR_P_2, FR_U_1
-// 
 //     c = S - U_1
 //     r = S_1 * r
 //
 //
-(p7)   extr.u	GR_i_1 = GR_N_Inc, 0, 1 ;;
 }
+;;
+
 { .mmi
-	nop.m 999
+        nop.m 999
 //
 //     Get [i_0,i_1] - two lsb of N_fix_gr.
 //     Do dummy fmpy so inexact is always set.
 //
-(p7)   cmp.eq.unc p9, p10 = 0x0, GR_i_1
-(p7)   extr.u	GR_i_0 = GR_N_Inc, 1, 1 ;;
+      tbit.z p9,p10 = GR_N_Inc, 0      // p9  if i_1=0, N mod 4 = 0,1
+                                       // p10 if i_1=1, N mod 4 = 2,3
 }
-// 
+;;
+
+//
 //     For small s: U_2 = N * P_2 - U_1
 //     S_1 stored constant - grab the one stored with the
 //     coefficients.
-// 
+//
 { .mfi
-(p7)   ldfe FR_S_1 = [GR_Table_Base1], 16
+       ldfe FR_S_1 = [GR_ad_s1], 16
 //
 //     Check if i_1 and i_0  != 0
 //
-(p10)  fma.s1	FR_poly = f0, f1, FR_Neg_Two_to_M67
-(p7)   cmp.eq.unc p11, p12 = 0x0, GR_i_0 ;;
+(p10)  fma.s1        FR_poly = f0, f1, FR_Neg_Two_to_M67
+      tbit.z p11,p12 = GR_N_Inc, 1     // p11 if i_0=0, N mod 4 = 0,2
+                                       // p12 if i_0=1, N mod 4 = 1,3
 }
+;;
+
 { .mfi
-	nop.m 999
-(p7)   fms.s1	FR_s = FR_s, f1, FR_r
-	nop.i 999
+        nop.m 999
+       fms.s1        FR_s = FR_s, f1, FR_r
+        nop.i 999
 }
 { .mfi
-	nop.m 999
-// 
+        nop.m 999
+//
 //     S = S - r
 //     U_2 = U_2 + w
 //     load S_1
 //
-(p7)   fma.s1	FR_rsq = FR_r, FR_r, f0
-	nop.i 999 ;;
+       fma.s1        FR_rsq = FR_r, FR_r, f0
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-(p7)   fma.s1	FR_U_2 = FR_U_2, f1, FR_w
-	nop.i 999
+        nop.m 999
+       fma.s1        FR_U_2 = FR_U_2, f1, FR_w
+        nop.i 999
 }
 { .mfi
-	nop.m 999
-(p7)   fmerge.se FR_Input_X = FR_r, FR_r
-	nop.i 999 ;;
+        nop.m 999
+       fmerge.se FR_tmp_result = FR_r, FR_r
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-(p10)  fma.s1 FR_Input_X = f0, f1, f1
-	nop.i 999 ;;
+        nop.m 999
+(p10)  fma.s1 FR_tmp_result = f0, f1, f1
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-// 
+        nop.m 999
+//
 //     FR_rsq = r * r
 //     Save r as the result.
 //
-(p7)   fms.s1	FR_c = FR_s, f1, FR_U_1
-	nop.i 999 ;;
+       fms.s1        FR_c = FR_s, f1, FR_U_1
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-// 
+        nop.m 999
+//
 //     if ( i_1 ==0) poly = c + S_1*r*r*r
 //     else Result = 1
 //
-(p12)  fnma.s1 FR_Input_X = FR_Input_X, f1, f0
-	nop.i 999
+(p12)  fnma.s1 FR_tmp_result = FR_tmp_result, f1, f0
+        nop.i 999
 }
 { .mfi
-	nop.m 999
-(p7)   fma.s1	FR_r = FR_S_1, FR_r, f0
-	nop.i 999 ;;
+        nop.m 999
+       fma.s1        FR_r = FR_S_1, FR_r, f0
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-(p7)   fma.s0	FR_S_1 = FR_S_1, FR_S_1, f0
-	nop.i 999 ;;
+        nop.m 999
+       fma.s0        FR_S_1 = FR_S_1, FR_S_1, f0
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     If i_1 != 0, poly = 2**(-67)
 //
-(p7)   fms.s1 FR_c = FR_c, f1, FR_U_2
-	nop.i 999 ;;
+       fms.s1 FR_c = FR_c, f1, FR_U_2
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-// 
+        nop.m 999
+//
 //     c = c - U_2
-// 
+//
 (p9)   fma.s1 FR_poly = FR_r, FR_rsq, FR_c
-	nop.i 999 ;;
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     i_0 != 0, so Result = -Result
 //
-(p11)  fma.s0 FR_Input_X = FR_Input_X, f1, FR_poly
-	nop.i 999 ;;
+(p11)  fma.s0 FR_Result = FR_tmp_result, f1, FR_poly
+        nop.i 999 ;;
 }
 { .mfb
-	nop.m 999
-(p12)  fms.s0 FR_Input_X = FR_Input_X, f1, FR_poly
+        nop.m 999
+(p12)  fms.s0 FR_Result = FR_tmp_result, f1, FR_poly
 //
 //     if (i_0 == 0),  Result = Result + poly
 //     else            Result = Result - poly
 //
-(p0)    br.ret.sptk   b0 ;;
-}
-L(SINCOSL_LARGER_ARG): 
-{ .mfi
-	nop.m 999
-(p0)   fma.s1 FR_N_0 = FR_Input_X, FR_Inv_P_0, f0
-	nop.i 999
+        br.ret.sptk   b0         // Exit if |s| < 2^-33, and pi/4 <= |x| < 2^24
 }
 ;;
 
-//     This path for argument > 2*24 
-//     Adjust table_ptr1 to beginning of table.
+SINCOSL_LARGER_ARG:
 //
-
-{ .mmi
-      nop.m 999
-(p0)  addl           GR_Table_Base   = @ltoff(FSINCOSL_CONSTANTS#), gp
-      nop.i 999
-}
-;;
-
-{ .mmi
-      ld8 GR_Table_Base = [GR_Table_Base]
-      nop.m 999
-      nop.i 999
+// Here if 2^24 <= |x| < 2^63
+//
+{ .mfi
+      ldfe FR_d_1 = [GR_ad_p], 16          // Load d_1 for |x| >= 2^24 path
+       fma.s1 FR_N_0 = FR_Input_X, FR_Inv_P_0, f0
+        nop.i 999
 }
 ;;
 
-
-// 
-//     Point to  2*-14 
+//
 //     N_0 = Arg * Inv_P_0
 //
+//     Load values 2**(-14) and -2**(-14)
 { .mmi
-(p0)   add GR_Table_Base = 688, GR_Table_Base ;;
-(p0)   ldfs FR_Two_to_M14 = [GR_Table_Base], 4
-	nop.i 999 ;;
+       ldfps FR_Two_to_M14, FR_Neg_Two_to_M14 = [GR_ad_m14]
+        nop.i 999 ;;
 }
 { .mfi
-(p0)   ldfs FR_Neg_Two_to_M14 = [GR_Table_Base], 0
-	nop.f 999
-	nop.i 999 ;;
+      ldfe FR_d_2 = [GR_ad_p], 16          // Load d_2 for |x| >= 2^24 path
+        nop.f 999
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
-//     Load values 2**(-14) and -2**(-14)
 //
-(p0)   fcvt.fx.s1 FR_N_0_fix = FR_N_0
-	nop.i 999 ;;
+       fcvt.fx.s1 FR_N_0_fix = FR_N_0
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     N_0_fix  = integer part of N_0
 //
-(p0)   fcvt.xf FR_N_0 = FR_N_0_fix 
-	nop.i 999 ;;
+       fcvt.xf FR_N_0 = FR_N_0_fix
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     Make N_0 the integer part
 //
-(p0)   fnma.s1 FR_ArgPrime = FR_N_0, FR_P_0, FR_Input_X
-	nop.i 999
+       fnma.s1 FR_ArgPrime = FR_N_0, FR_P_0, FR_Input_X
+        nop.i 999
 }
 { .mfi
-	nop.m 999
-(p0)   fma.s1 FR_w = FR_N_0, FR_d_1, f0
-	nop.i 999 ;;
+        nop.m 999
+       fma.s1 FR_w = FR_N_0, FR_d_1, f0
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     Arg' = -N_0 * P_0 + Arg
 //     w  = N_0 * d_1
 //
-(p0)   fma.s1 FR_N_float = FR_ArgPrime, FR_Inv_pi_by_2, f0
-	nop.i 999 ;;
+       fma.s1 FR_N_float = FR_ArgPrime, FR_Inv_pi_by_2, f0
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
-//     N = A' * 2/pi	
+//     N = A' * 2/pi
 //
-(p0)   fcvt.fx.s1 FR_N_fix = FR_N_float
-	nop.i 999 ;;
+       fcvt.fx.s1 FR_N_fix = FR_N_float
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
-//     N_fix is the integer part	
+//     N_fix is the integer part
 //
-(p0)   fcvt.xf FR_N_float = FR_N_fix 
-	nop.i 999 ;;
+       fcvt.xf FR_N_float = FR_N_fix
+        nop.i 999 ;;
 }
 { .mfi
-(p0)   getf.sig GR_N_Inc = FR_N_fix
-	nop.f 999
-	nop.i 999 ;;
+       getf.sig GR_N_Inc = FR_N_fix
+        nop.f 999
+        nop.i 999 ;;
 }
 { .mii
-	nop.m 999
-	nop.i 999 ;;
-(p0)   add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos ;;
+        nop.m 999
+        nop.i 999 ;;
+       add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     N is the integer part of the reduced-reduced argument.
 //     Put the integer in a GP register
 //
-(p0)   fnma.s1 FR_s = FR_N_float, FR_P_1, FR_ArgPrime
-	nop.i 999
+       fnma.s1 FR_s = FR_N_float, FR_P_1, FR_ArgPrime
+        nop.i 999
 }
 { .mfi
-	nop.m 999
-(p0)   fnma.s1 FR_w = FR_N_float, FR_P_2, FR_w
-	nop.i 999 ;;
+        nop.m 999
+       fnma.s1 FR_w = FR_N_float, FR_P_2, FR_w
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     s = -N*P_1 + Arg'
 //     w = -N*P_2 + w
 //     N_fix_gr = N_fix_gr + N_inc
 //
-(p0)   fcmp.lt.unc.s1 p9, p8 = FR_s, FR_Two_to_M14
-	nop.i 999 ;;
+       fcmp.lt.unc.s1 p9, p8 = FR_s, FR_Two_to_M14
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-(p9)   fcmp.gt.s1 p9, p8 = FR_s, FR_Neg_Two_to_M14
-	nop.i 999 ;;
+        nop.m 999
+(p9)   fcmp.gt.s1 p9, p8 = FR_s, FR_Neg_Two_to_M14  // p9 if |s| < 2^-14
+        nop.i 999 ;;
 }
+
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     For |s|  > 2**(-14) r = S + w (r complete)
 //     Else       U_hi = N_0 * d_1
 //
 (p9)   fma.s1 FR_V_hi = FR_N_float, FR_P_2, f0
-	nop.i 999
+        nop.i 999
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 (p9)   fma.s1 FR_U_hi = FR_N_0, FR_d_1, f0
-	nop.i 999 ;;
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     Either S <= -2**(-14) or S >= 2**(-14)
 //     or -2**(-14) < s < 2**(-14)
 //
 (p8)   fma.s1 FR_r = FR_s, f1, FR_w
-	nop.i 999
+        nop.i 999
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 (p9)   fma.s1 FR_w = FR_N_float, FR_P_3, f0
-	nop.i 999 ;;
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     We need abs of both U_hi and V_hi - don't
 //     worry about switched sign of V_hi.
 //
 (p9)   fms.s1 FR_A = FR_U_hi, f1, FR_V_hi
-	nop.i 999
+        nop.i 999
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
-//     Big s: finish up c = (S - r) + w (c complete)	
+//     Big s: finish up c = (S - r) + w (c complete)
 //     Case 4: A =  U_hi + V_hi
 //     Note: Worry about switched sign of V_hi, so subtract instead of add.
 //
 (p9)   fnma.s1 FR_V_lo = FR_N_float, FR_P_2, FR_V_hi
-	nop.i 999 ;;
+        nop.i 999 ;;
 }
 { .mmf
-	nop.m 999
-	nop.m 999
+        nop.m 999
+        nop.m 999
 (p9)   fms.s1 FR_U_lo = FR_N_0, FR_d_1, FR_U_hi
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 (p9)   fmerge.s FR_V_hiabs = f0, FR_V_hi
-	nop.i 999 ;;
+        nop.i 999 ;;
 }
+//{ .mfb
+//(p9)   fmerge.s f8= FR_V_lo,FR_V_lo
+//(p9)   br.ret.sptk b0
+//}
+//;;
 { .mfi
-	nop.m 999
+        nop.m 999
 //     For big s: c = S - r
 //     For small s do more work: U_lo = N_0 * d_1 - U_hi
 //
 (p9)   fmerge.s FR_U_hiabs = f0, FR_U_hi
-	nop.i 999
+        nop.i 999
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
-//     For big s: Is |r| < 2**(-3)	
+//     For big s: Is |r| < 2**(-3)
 //     For big s: if p12 set, prepare to branch to Small_R.
 //     For big s: If p13 set, prepare to branch to Normal_R.
 //
-(p8)   fms.s1 FR_c = FR_s, f1, FR_r 
-	nop.i 999 ;;
+(p8)   fms.s1 FR_c = FR_s, f1, FR_r
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     For small S: V_hi = N * P_2
 //                  w = N * P_3
@@ -1451,104 +1485,99 @@ L(SINCOSL_LARGER_ARG):
 //     so (-) missing for V_hi and w.
 //
 (p8)   fcmp.lt.unc.s1 p12, p13 = FR_r, FR_Two_to_M3
-	nop.i 999 ;;
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 (p12)  fcmp.gt.s1 p12, p13 = FR_r, FR_Neg_Two_to_M3
-	nop.i 999 ;;
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 (p8)   fma.s1 FR_c = FR_c, f1, FR_w
-	nop.i 999
+        nop.i 999
 }
 { .mfb
-	nop.m 999
+        nop.m 999
 (p9)   fms.s1 FR_w = FR_N_0, FR_d_2, FR_w
-(p12)  br.cond.spnt L(SINCOSL_SMALL_R) ;;
+(p12)  br.cond.spnt SINCOSL_SMALL_R      // Branch if |r| < 2^-3
+                                         // and 2^24 <= |x| < 2^63
 }
+;;
+
 { .mib
-	nop.m 999
-	nop.i 999
-(p13)  br.cond.sptk L(SINCOSL_NORMAL_R) ;;
+        nop.m 999
+        nop.i 999
+(p13)  br.cond.sptk SINCOSL_NORMAL_R     // Branch if |r| >= 2^-3
+                                         // and 2^24 <= |x| < 2^63
 }
+;;
+
+SINCOSL_LARGER_S_TINY:
+//
+// Here if |s| < 2^-14, and 2^24 <= |x| < 2^63
+//
 { .mfi
-	nop.m 999
-// 
-//     Big s: Vector off when |r| < 2**(-3).  Recall that p8 will be true. 
+        nop.m 999
+//
+//     Big s: Vector off when |r| < 2**(-3).  Recall that p8 will be true.
 //     The remaining stuff is for Case 4.
 //     Small s: V_lo = N * P_2 + U_hi (U_hi is in place of V_hi in writeup)
 //     Note: the (-) is still missing for V_lo.
 //     Small s: w = w + N_0 * d_2
 //     Note: the (-) is now incorporated in w.
 //
-(p9)   fcmp.ge.unc.s1 p10, p11 = FR_U_hiabs, FR_V_hiabs
-(p0)   extr.u	GR_i_1 = GR_N_Inc, 0, 1
+       fcmp.ge.unc.s1 p7, p8 = FR_U_hiabs, FR_V_hiabs
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     C_hi = S + A
 //
-(p9)   fma.s1 FR_t = FR_U_lo, f1, FR_V_lo
-(p0)   extr.u	GR_i_0 = GR_N_Inc, 1, 1 ;;
+       fma.s1 FR_t = FR_U_lo, f1, FR_V_lo
 }
+;;
+
 { .mfi
-	nop.m 999
+        nop.m 999
 //
-//     t = U_lo + V_lo 
+//     t = U_lo + V_lo
 //
 //
-(p10)  fms.s1 FR_a = FR_U_hi, f1, FR_A
-	nop.i 999 ;;
+(p7)  fms.s1 FR_a = FR_U_hi, f1, FR_A
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-(p11)  fma.s1 FR_a = FR_V_hi, f1, FR_A
-	nop.i 999
-}
-;;
-
-{ .mmi
-      nop.m 999
-(p0)  addl           GR_Table_Base   = @ltoff(FSINCOSL_CONSTANTS#), gp
-      nop.i 999
-}
-;;
-
-{ .mmi
-      ld8 GR_Table_Base = [GR_Table_Base]
-      nop.m 999
-      nop.i 999
+        nop.m 999
+(p8)  fma.s1 FR_a = FR_V_hi, f1, FR_A
+        nop.i 999
 }
 ;;
 
-
 { .mfi
-(p0)   add GR_Table_Base = 528, GR_Table_Base
 //
 //     Is U_hiabs >= V_hiabs?
 //
-(p9)   fma.s1 FR_C_hi = FR_s, f1, FR_A
-	nop.i 999 ;;
+        nop.m 999
+       fma.s1 FR_C_hi = FR_s, f1, FR_A
+        nop.i 999 ;;
 }
 { .mmi
-(p0)   ldfe FR_C_1 = [GR_Table_Base], 16 ;;
-(p0)   ldfe FR_C_2 = [GR_Table_Base], 64
-	nop.i 999 ;;
+       ldfe FR_C_1 = [GR_ad_c], 16 ;;
+       ldfe FR_C_2 = [GR_ad_c], 64
+        nop.i 999 ;;
 }
 //
 //     c = c + C_lo  finished.
 //     Load  C_2
 //
 { .mfi
-(p0)   ldfe	FR_S_1 = [GR_Table_Base], 16
+       ldfe        FR_S_1 = [GR_ad_s], 16
 //
-//     C_lo = S - C_hi 
+//     C_lo = S - C_hi
 //
-(p0)   fma.s1 FR_t = FR_t, f1, FR_w
-	nop.i 999 ;;
+       fma.s1 FR_t = FR_t, f1, FR_w
+        nop.i 999 ;;
 }
 //
 //     r and c have been computed.
@@ -1558,855 +1587,695 @@ L(SINCOSL_LARGER_ARG):
 //     Load S_1
 //
 { .mfi
-(p0)   ldfe FR_S_2 = [GR_Table_Base], 64
+       ldfe FR_S_2 = [GR_ad_s], 64
 //
-//     t = t + w	
+//     t = t + w
 //
-(p10)  fms.s1 FR_a = FR_a, f1, FR_V_hi
-(p0)   cmp.eq.unc p9, p10 = 0x0, GR_i_0 ;;
+(p7)  fms.s1 FR_a = FR_a, f1, FR_V_hi
+      tbit.z p9,p10 = GR_N_Inc, 0      // p9  if i_1=0, N mod 4 = 0,1
+                                       // p10 if i_1=1, N mod 4 = 2,3
 }
+;;
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     For larger u than v: a = U_hi - A
 //     Else a = V_hi - A (do an add to account for missing (-) on V_hi
 //
-(p0)   fms.s1 FR_C_lo = FR_s, f1, FR_C_hi
-	nop.i 999 ;;
+       fms.s1 FR_C_lo = FR_s, f1, FR_C_hi
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-(p11)  fms.s1 FR_a = FR_U_hi, f1, FR_a
-(p0)   cmp.eq.unc p11, p12 = 0x0, GR_i_1 ;;
+        nop.m 999
+(p8)  fms.s1 FR_a = FR_U_hi, f1, FR_a
+      tbit.z p11,p12 = GR_N_Inc, 1     // p11 if i_0=0, N mod 4 = 0,2
+                                       // p12 if i_0=1, N mod 4 = 1,3
 }
+;;
+
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     If u > v: a = (U_hi - A)  + V_hi
 //     Else      a = (V_hi - A)  + U_hi
 //     In each case account for negative missing from V_hi.
 //
-(p0)   fma.s1 FR_C_lo = FR_C_lo, f1, FR_A
-	nop.i 999 ;;
+       fma.s1 FR_C_lo = FR_C_lo, f1, FR_A
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
-//     C_lo = (S - C_hi) + A	
+//     C_lo = (S - C_hi) + A
 //
-(p0)   fma.s1 FR_t = FR_t, f1, FR_a
-	nop.i 999 ;;
+       fma.s1 FR_t = FR_t, f1, FR_a
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
-//     t = t + a 
+//     t = t + a
 //
-(p0)   fma.s1 FR_C_lo = FR_C_lo, f1, FR_t
-	nop.i 999 ;;
+       fma.s1 FR_C_lo = FR_C_lo, f1, FR_t
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     C_lo = C_lo + t
-//     Adjust Table_Base to beginning of table
 //
-(p0)   fma.s1 FR_r = FR_C_hi, f1, FR_C_lo
-	nop.i 999 ;;
+       fma.s1 FR_r = FR_C_hi, f1, FR_C_lo
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     Load S_2
 //
-(p0)   fma.s1 FR_rsq = FR_r, FR_r, f0
-	nop.i 999
+       fma.s1 FR_rsq = FR_r, FR_r, f0
+        nop.i 999
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
-//     Table_Base points to C_1
 //     r = C_hi + C_lo
 //
-(p0)   fms.s1 FR_c = FR_C_hi, f1, FR_r
-	nop.i 999 ;;
+       fms.s1 FR_c = FR_C_hi, f1, FR_r
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     if i_1 ==0: poly = S_2 * FR_rsq + S_1
 //     else        poly = C_2 * FR_rsq + C_1
 //
-(p11)  fma.s1 FR_Input_X = f0, f1, FR_r
-	nop.i 999 ;;
+(p9)  fma.s1 FR_tmp_result = f0, f1, FR_r
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-(p12)  fma.s1 FR_Input_X = f0, f1, f1
-	nop.i 999 ;;
+        nop.m 999
+(p10)  fma.s1 FR_tmp_result = f0, f1, f1
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
-//     Compute r_cube = FR_rsq * r	
+//     Compute r_cube = FR_rsq * r
 //
-(p11)  fma.s1 FR_poly = FR_rsq, FR_S_2, FR_S_1
-	nop.i 999 ;;
+(p9)  fma.s1 FR_poly = FR_rsq, FR_S_2, FR_S_1
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-(p12)  fma.s1 FR_poly = FR_rsq, FR_C_2, FR_C_1
-	nop.i 999
+        nop.m 999
+(p10)  fma.s1 FR_poly = FR_rsq, FR_C_2, FR_C_1
+        nop.i 999
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     Compute FR_rsq = r * r
 //     Is i_1 == 0 ?
 //
-(p0)   fma.s1 FR_r_cubed = FR_rsq, FR_r, f0
-	nop.i 999 ;;
+       fma.s1 FR_r_cubed = FR_rsq, FR_r, f0
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     c = C_hi - r
 //     Load  C_1
 //
-(p0)   fma.s1 FR_c = FR_c, f1, FR_C_lo
-	nop.i 999
+       fma.s1 FR_c = FR_c, f1, FR_C_lo
+        nop.i 999
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     if i_1 ==0: poly = r_cube * poly + c
 //     else        poly = FR_rsq * poly
 //
-(p10)  fms.s1 FR_Input_X = f0, f1, FR_Input_X
-	nop.i 999 ;;
+(p12)  fms.s1 FR_tmp_result = f0, f1, FR_tmp_result
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
 //     if i_1 ==0: Result = r
 //     else        Result = 1.0
 //
-(p11)  fma.s1 FR_poly = FR_r_cubed, FR_poly, FR_c
-	nop.i 999 ;;
+(p9)  fma.s1 FR_poly = FR_r_cubed, FR_poly, FR_c
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
-(p12)  fma.s1 FR_poly = FR_rsq, FR_poly, f0
-	nop.i 999 ;;
+        nop.m 999
+(p10)  fma.s1 FR_poly = FR_rsq, FR_poly, f0
+        nop.i 999 ;;
 }
 { .mfi
-	nop.m 999
+        nop.m 999
 //
-//     if i_0 !=0: Result = -Result 
+//     if i_0 !=0: Result = -Result
 //
-(p9)   fma.s0 FR_Input_X = FR_Input_X, f1, FR_poly
-	nop.i 999 ;;
+(p11)   fma.s0 FR_Result = FR_tmp_result, f1, FR_poly
+        nop.i 999 ;;
 }
 { .mfb
-	nop.m 999
-(p10)  fms.s0 FR_Input_X = FR_Input_X, f1, FR_poly
+        nop.m 999
+(p12)  fms.s0 FR_Result = FR_tmp_result, f1, FR_poly
 //
 //     if i_0 == 0: Result = Result + poly
 //     else         Result = Result - poly
 //
-(p0)    br.ret.sptk   b0 ;;
+      br.ret.sptk   b0         // Exit for |s| < 2^-14, and 2^24 <= |x| < 2^63
 }
-L(SINCOSL_SMALL_R): 
-{ .mii
-	nop.m 999
-(p0)  	extr.u	GR_i_1 = GR_N_Inc, 0, 1 ;;
+;;
+
+
+SINCOSL_SMALL_R:
+//
+// Here if |r| < 2^-3
 //
+// Enter with r, c, and N_Inc computed
 //
 //      Compare both i_1 and i_0 with 0.
 //      if i_1 == 0, set p9.
 //      if i_0 == 0, set p11.
 //
-(p0)  	cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;;
-}
-{ .mfi
-	nop.m 999
-(p0)  	fma.s1 FR_rsq = FR_r, FR_r, f0
-(p0)  	extr.u	GR_i_0 = GR_N_Inc, 1, 1 ;;
-}
+
 { .mfi
-	nop.m 999
-//
-// 	Z = Z * FR_rsq 
-//
-(p10)	fnma.s1	FR_c = FR_c, FR_r, f0
-(p0)  	cmp.eq.unc p11, p12 = 0x0, GR_i_0
+      nop.m 999
+      fma.s1 FR_rsq = FR_r, FR_r, f0   // rsq = r * r
+      tbit.z p9,p10 = GR_N_Inc, 0      // p9  if i_1=0, N mod 4 = 0,1
+                                       // p10 if i_1=1, N mod 4 = 2,3
 }
 ;;
 
-// ******************************************************************
-// ******************************************************************
-// ******************************************************************
-//      r and c have been computed.
-//      We know whether this is the sine or cosine routine.
-//      Make sure ftz mode is set - should be automatic when using wre
-//      |r| < 2**(-3)
-//
-//      Set table_ptr1 to beginning of constant table.
-//      Get [i_0,i_1] - two lsb of N_fix_gr.
-//
-
 { .mmi
-      nop.m 999
-(p0)  addl           GR_Table_Base   = @ltoff(FSINCOSL_CONSTANTS#), gp
+(p9)  ldfe FR_S_5 = [GR_ad_se], -16    // Load S_5 if i_1=0
+(p10) ldfe FR_C_5 = [GR_ad_ce], -16    // Load C_5 if i_1=1
       nop.i 999
 }
 ;;
 
 { .mmi
-      ld8 GR_Table_Base = [GR_Table_Base]
-      nop.m 999
+(p9)  ldfe FR_S_4 = [GR_ad_se], -16    // Load S_4 if i_1=0
+(p10) ldfe FR_C_4 = [GR_ad_ce], -16    // Load C_4 if i_1=1
       nop.i 999
 }
 ;;
 
-
-// 
-//      Set table_ptr1 to point to S_5.
-//      Set table_ptr1 to point to C_5.
-//      Compute FR_rsq = r * r
-//
-{ .mfi
-(p9)  	add GR_Table_Base = 672, GR_Table_Base
-(p10)	fmerge.s FR_r = f1, f1
-(p10) 	add GR_Table_Base = 592, GR_Table_Base ;;
+SINCOSL_SMALL_R_0:
+// Entry point for 2^-3 < |x| < pi/4
+.pred.rel "mutex",p9,p10
+SINCOSL_SMALL_R_1:
+// Entry point for pi/4 < |x| < 2^24 and |r| < 2^-3
+.pred.rel "mutex",p9,p10
+{ .mfi
+(p9)  ldfe FR_S_3 = [GR_ad_se], -16    // Load S_3 if i_1=0
+      fma.s1 FR_Z = FR_rsq, FR_rsq, f0 // Z = rsq * rsq
+      nop.i 999
 }
-// 
-//      Set table_ptr1 to point to S_5.
-//      Set table_ptr1 to point to C_5.
-//
-{ .mmi
-(p9)  	ldfe FR_S_5 = [GR_Table_Base], -16 ;;
-//
-//      if (i_1 == 0) load S_5
-//      if (i_1 != 0) load C_5
-//
-(p9)  	ldfe FR_S_4 = [GR_Table_Base], -16
-	nop.i 999 ;;
+{ .mfi
+(p10) ldfe FR_C_3 = [GR_ad_ce], -16    // Load C_3 if i_1=1
+(p10) fnma.s1 FR_c = FR_c, FR_r, f0    // c = -c * r if i_1=0
+      nop.i 999
 }
+;;
+
 { .mmf
-(p10) 	ldfe FR_C_5 = [GR_Table_Base], -16
-// 
-//      Z = FR_rsq * FR_rsq
-//
-(p9)  	ldfe FR_S_3 = [GR_Table_Base], -16
-//
-//      Compute FR_rsq = r * r
-//      if (i_1 == 0) load S_4
-//      if (i_1 != 0) load C_4
-//
-(p0)   	fma.s1 FR_Z = FR_rsq, FR_rsq, f0 ;;
-}
-//
-//      if (i_1 == 0) load S_3
-//      if (i_1 != 0) load C_3
-//
-{ .mmi
-(p9)  	ldfe FR_S_2 = [GR_Table_Base], -16 ;;
-//
-//      if (i_1 == 0) load S_2
-//      if (i_1 != 0) load C_2
-//
-(p9)  	ldfe FR_S_1 = [GR_Table_Base], -16
-	nop.i 999
-}
-{ .mmi
-(p10) 	ldfe FR_C_4 = [GR_Table_Base], -16 ;;
-(p10)  	ldfe FR_C_3 = [GR_Table_Base], -16
-	nop.i 999 ;;
+(p9)  ldfe FR_S_2 = [GR_ad_se], -16    // Load S_2 if i_1=0
+(p10) ldfe FR_C_2 = [GR_ad_ce], -16    // Load C_2 if i_1=1
+(p10) fmerge.s FR_r = f1, f1
 }
+;;
+
 { .mmi
-(p10) 	ldfe FR_C_2 = [GR_Table_Base], -16 ;;
-(p10) 	ldfe FR_C_1 = [GR_Table_Base], -16
-	nop.i 999
-}
-{ .mfi
-	nop.m 999
-//
-//      if (i_1 != 0):
-//      poly_lo = FR_rsq * C_5 + C_4
-//      poly_hi = FR_rsq * C_2 + C_1
-//
-(p9)  	fma.s1 FR_Z = FR_Z, FR_r, f0
-	nop.i 999 ;;
+(p9)  ldfe FR_S_1 = [GR_ad_se], -16    // Load S_1 if i_1=0
+(p10) ldfe FR_C_1 = [GR_ad_ce], -16    // Load C_1 if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      if (i_1 == 0) load S_1
-//      if (i_1 != 0) load C_1
-//
-(p9)  	fma.s1 FR_poly_lo = FR_rsq, FR_S_5, FR_S_4
-	nop.i 999
+      nop.m 999
+(p9)  fma.s1 FR_Z = FR_Z, FR_r, f0     // Z = Z * r if i_1=0
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      c = -c * r
-//      dummy fmpy's to flag inexact.
-//
-(p9)	fma.s0 FR_S_4 = FR_S_4, FR_S_4, f0
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_poly_lo = FR_rsq, FR_S_5, FR_S_4 // poly_lo=rsq*S_5+S_4 if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-//
-//      poly_lo = FR_rsq * poly_lo + C_3
-//      poly_hi = FR_rsq * poly_hi
-//
-(p0)    fma.s1	FR_Z = FR_Z, FR_rsq, f0
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s1 FR_poly_lo = FR_rsq, FR_C_5, FR_C_4 // poly_lo=rsq*C_5+C_4 if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p9)  	fma.s1 FR_poly_hi = FR_rsq, FR_S_2, FR_S_1
-	nop.i 999
+      nop.m 999
+(p9)  fma.s1 FR_poly_hi = FR_rsq, FR_S_2, FR_S_1 // poly_hi=rsq*S_2+S_1 if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-//
-//      if (i_1 == 0):
-//      poly_lo = FR_rsq * S_5 + S_4
-//      poly_hi = FR_rsq * S_2 + S_1
-//
-(p10) 	fma.s1 FR_poly_lo = FR_rsq, FR_C_5, FR_C_4
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s1 FR_poly_hi = FR_rsq, FR_C_2, FR_C_1 // poly_hi=rsq*C_2+C_1 if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      if (i_1 == 0):
-//      Z = Z * r  for only one of the small r cases - not there
-//      in original implementation notes.
-// 
-(p9)  	fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_S_3
-	nop.i 999 ;;
+      nop.m 999
+      fma.s1 FR_Z = FR_Z, FR_rsq, f0             // Z = Z * rsq
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10) 	fma.s1 FR_poly_hi = FR_rsq, FR_C_2, FR_C_1
-	nop.i 999
+      nop.m 999
+(p9)  fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_S_3 // p_lo=p_lo*rsq+S_3, i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-(p10)	fma.s0 FR_C_1 = FR_C_1, FR_C_1, f0
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_C_3 // p_lo=p_lo*rsq+C_3, i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p9)  	fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0
-	nop.i 999
+      nop.m 999
+(p9)  fma.s0 FR_inexact = FR_S_4, FR_S_4, f0     // Dummy op to set inexact
+      tbit.z p11,p12 = GR_N_Inc, 1     // p11 if i_0=0, N mod 4 = 0,2
+                                       // p12 if i_0=1, N mod 4 = 1,3
 }
 { .mfi
-	nop.m 999
-//
-//      poly_lo = FR_rsq * poly_lo + S_3
-//      poly_hi = FR_rsq * poly_hi
-//
-(p10) 	fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_C_3
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s0 FR_inexact = FR_C_1, FR_C_1, f0     // Dummy op to set inexact
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10) 	fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0     // p_hi=p_hi*rsq if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-//
-// 	if (i_1 == 0): dummy fmpy's to flag inexact
-// 	r = 1
-//
-(p9)	fma.s1 FR_poly_hi = FR_r, FR_poly_hi, f0
-	nop.i 999
+      nop.m 999
+(p10) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0     // p_hi=p_hi*rsq if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-// 	poly_hi = r * poly_hi 
-//
-(p0)    fma.s1	FR_poly = FR_Z, FR_poly_lo, FR_c
-	nop.i 999 ;;
+      nop.m 999
+      fma.s1 FR_poly = FR_Z, FR_poly_lo, FR_c        // poly=Z*poly_lo+c
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p12)	fms.s1	FR_r = f0, f1, FR_r
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_poly_hi = FR_r, FR_poly_hi, f0       // p_hi=r*p_hi if i_1=0
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      poly_hi = Z * poly_lo + c	
-// 	if i_0 == 1: r = -r     
-//
-(p0) 	fma.s1	FR_poly = FR_poly, f1, FR_poly_hi
-	nop.i 999 ;;
+      nop.m 999
+(p12) fms.s1 FR_r = f0, f1, FR_r                     // r = -r if i_0=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p12)	fms.s0 FR_Input_X = FR_r, f1, FR_poly
-	nop.i 999
+      nop.m 999
+      fma.s1 FR_poly = FR_poly, f1, FR_poly_hi       // poly=poly+poly_hi
+      nop.i 999
 }
-{ .mfb
-	nop.m 999
-//
-//      poly = poly + poly_hi	
-//
-(p11)	fma.s0 FR_Input_X = FR_r, f1, FR_poly
+;;
+
 //
 //      if (i_0 == 0) Result = r + poly
 //      if (i_0 != 0) Result = r - poly
 //
-(p0)    br.ret.sptk   b0 ;;
-}
-L(SINCOSL_NORMAL_R): 
-{ .mii
-	nop.m 999
-(p0)	extr.u	GR_i_1 = GR_N_Inc, 0, 1 ;;
-//
-//      Set table_ptr1 and table_ptr2 to base address of
-//      constant table.
-(p0)	cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;;
-}
 { .mfi
-	nop.m 999
-(p0)	fma.s1	FR_rsq = FR_r, FR_r, f0
-(p0)	extr.u	GR_i_0 = GR_N_Inc, 1, 1 ;;
+      nop.m 999
+(p11) fma.s0 FR_Result = FR_r, f1, FR_poly
+      nop.i 999
 }
-{ .mfi
-	nop.m 999
-(p0)	frcpa.s1 FR_r_hi, p6 = f1, FR_r
-(p0)	cmp.eq.unc p11, p12 = 0x0, GR_i_0
+{ .mfb
+      nop.m 999
+(p12) fms.s0 FR_Result = FR_r, f1, FR_poly
+      br.ret.sptk   b0                               // Exit for |r| < 2^-3
 }
 ;;
 
-// ******************************************************************
-// ******************************************************************
-// ******************************************************************
+
+SINCOSL_NORMAL_R:
 //
-//      r and c have been computed.
-//      We known whether this is the sine or cosine routine.
-//      Make sure ftz mode is set - should be automatic when using wre
-//      Get [i_0,i_1] - two lsb of N_fix_gr alone.
+// Here if 2^-3 <= |r| < pi/4
+// THIS IS THE MAIN PATH
 //
-
-{ .mmi
-      nop.m 999
-(p0)  addl           GR_Table_Base   = @ltoff(FSINCOSL_CONSTANTS#), gp
+// Enter with r, c, and N_Inc having been computed
+//
+{ .mfi
+      ldfe FR_PP_6 = [GR_ad_pp], 16    // Load PP_6
+      fma.s1 FR_rsq = FR_r, FR_r, f0   // rsq = r * r
+      tbit.z p9,p10 = GR_N_Inc, 0      // p9  if i_1=0, N mod 4 = 0,1
+                                       // p10 if i_1=1, N mod 4 = 2,3
+}
+{ .mfi
+      ldfe FR_QQ_6 = [GR_ad_qq], 16    // Load QQ_6
+      nop.f 999
       nop.i 999
 }
 ;;
 
 { .mmi
-      ld8 GR_Table_Base = [GR_Table_Base]
-      nop.m 999
+(p9)  ldfe FR_PP_5 = [GR_ad_pp], 16    // Load PP_5 if i_1=0
+(p10) ldfe FR_QQ_5 = [GR_ad_qq], 16    // Load QQ_5 if i_1=1
       nop.i 999
 }
 ;;
 
+SINCOSL_NORMAL_R_0:
+// Entry for 2^-3 < |x| < pi/4
+.pred.rel "mutex",p9,p10
+{ .mmf
+(p9)  ldfe FR_C_1 = [GR_ad_pp], 16     // Load C_1 if i_1=0
+(p10) ldfe FR_S_1 = [GR_ad_qq], 16     // Load S_1 if i_1=1
+      frcpa.s1 FR_r_hi, p6 = f1, FR_r  // r_hi = frcpa(r)
+}
+;;
 
 { .mfi
-(p10)	add GR_Table_Base = 384, GR_Table_Base
-(p12)	fms.s1 FR_Input_X = f0, f1, f1
-(p9)	add GR_Table_Base = 224, GR_Table_Base ;;
+      nop.m 999
+(p9)  fma.s1 FR_poly = FR_rsq, FR_PP_8, FR_PP_7 // poly = rsq*PP_8+PP_7 if i_1=0
+      nop.i 999
 }
 { .mfi
-(p10)	ldfe FR_QQ_8 = [GR_Table_Base], 16
-//
-//      if (i_1==0) poly = poly * FR_rsq + PP_1_lo
-//      else        poly = FR_rsq * poly
-//
-(p11)	fma.s1 FR_Input_X = f0, f1, f1
-	nop.i 999 ;;
-}
-{ .mmb
-(p10)	ldfe FR_QQ_7 = [GR_Table_Base], 16
-//
-// 	Adjust table pointers based on i_0 
-//      Compute rsq = r * r
-//
-(p9)	ldfe FR_PP_8 = [GR_Table_Base], 16
-	nop.b 999 ;;
+      nop.m 999
+(p10) fma.s1 FR_poly = FR_rsq, FR_QQ_8, FR_QQ_7 // poly = rsq*QQ_8+QQ_7 if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p0)	fma.s1 FR_r_cubed = FR_r, FR_rsq, f0
-	nop.i 999 ;;
+      nop.m 999
+      fma.s1 FR_r_cubed = FR_r, FR_rsq, f0  // rcubed = r * rsq
+      nop.i 999
 }
+;;
+
+
+SINCOSL_NORMAL_R_1:
+// Entry for pi/4 <= |x| < 2^24
+.pred.rel "mutex",p9,p10
 { .mmf
-(p9)	ldfe FR_PP_7 = [GR_Table_Base], 16
-(p10)	ldfe FR_QQ_6 = [GR_Table_Base], 16
-//
-//      Load PP_8 and QQ_8; PP_7 and QQ_7
-//
-(p0)	frcpa.s1 FR_r_hi, p6 = f1, FR_r_hi ;;
-}
-//
-//      if (i_1==0) poly =   PP_7 + FR_rsq * PP_8.
-//      else        poly =   QQ_7 + FR_rsq * QQ_8.
-//
-{ .mmb
-(p9)	ldfe FR_PP_6 = [GR_Table_Base], 16
-(p10)	ldfe FR_QQ_5 = [GR_Table_Base], 16
-	nop.b 999 ;;
-}
-{ .mmb
-(p9)	ldfe FR_PP_5 = [GR_Table_Base], 16
-(p10)	ldfe FR_S_1 = [GR_Table_Base], 16
-	nop.b 999 ;;
-}
-{ .mmb
-(p10)	ldfe FR_QQ_1 = [GR_Table_Base], 16
-(p9)	ldfe FR_C_1 = [GR_Table_Base], 16
-	nop.b 999 ;;
-}
-{ .mmb
-(p10)	ldfe FR_QQ_4 = [GR_Table_Base], 16
-(p9)	ldfe FR_PP_1 = [GR_Table_Base], 16
-	nop.b 999 ;;
-}
-{ .mmb
-(p10)	ldfe FR_QQ_3 = [GR_Table_Base], 16
-//
-//      if (i_1=0) corr = corr + c*c
-//      else       corr = corr * c 
-//
-(p9)	ldfe FR_PP_4 = [GR_Table_Base], 16
-	nop.b 999 ;;
-}
-{ .mfi
-	nop.m 999
-(p10)	fma.s1 FR_poly = FR_rsq, FR_QQ_8, FR_QQ_7
-	nop.i 999 ;;
-}
-//
-//      if (i_1=0) poly = rsq * poly + PP_5 
-//      else       poly = rsq * poly + QQ_5 
-//      Load PP_4 or QQ_4
-//
-{ .mmi
-(p9)	ldfe FR_PP_3 = [GR_Table_Base], 16 ;;
-(p10)	ldfe FR_QQ_2 = [GR_Table_Base], 16
-	nop.i 999
+(p9)  ldfe FR_PP_1 = [GR_ad_pp], 16             // Load PP_1_hi if i_1=0
+(p10) ldfe FR_QQ_1 = [GR_ad_qq], 16             // Load QQ_1    if i_1=1
+      frcpa.s1 FR_r_hi, p6 = f1, FR_r_hi        // r_hi = frpca(frcpa(r))
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      r_hi =   frcpa(frcpa(r)).
-//      r_cube = r * FR_rsq.
-//
-(p9)	fma.s1 FR_poly = FR_rsq, FR_PP_8, FR_PP_7
-	nop.i 999 ;;
+(p9)  ldfe FR_PP_4 = [GR_ad_pp], 16             // Load PP_4 if i_1=0
+(p9)  fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_6 // poly = rsq*poly+PP_6 if i_1=0
+      nop.i 999
 }
-//
-//      Do dummy multiplies so inexact is always set. 
-//
 { .mfi
-(p9)	ldfe FR_PP_2 = [GR_Table_Base], 16
-//
-//      r_lo = r - r_hi	
-//
-(p9)	fma.s1 FR_U_lo = FR_r_hi, FR_r_hi, f0
-	nop.i 999 ;;
-}
-{ .mbb
-(p9)	ldfe FR_PP_1_lo = [GR_Table_Base], 16
-	nop.b 999
-	nop.b 999 ;;
+(p10) ldfe FR_QQ_4 = [GR_ad_qq], 16             // Load QQ_4 if i_1=1
+(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_6 // poly = rsq*poly+QQ_6 if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_corr = FR_S_1, FR_r_cubed, FR_r
-	nop.i 999
+      nop.m 999
+(p9)  fma.s1 FR_corr = FR_C_1, FR_rsq, f0       // corr = C_1 * rsq if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_6
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s1 FR_corr = FR_S_1, FR_r_cubed, FR_r // corr = S_1 * r^3 + r if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      if (i_1=0) U_lo = r_hi * r_hi
-//      else       U_lo = r_hi + r
-//
-(p9)	fma.s1 FR_corr = FR_C_1, FR_rsq, f0
-	nop.i 999 ;;
+(p9)  ldfe FR_PP_3 = [GR_ad_pp], 16             // Load PP_3 if i_1=0
+      fma.s1 FR_r_hi_sq = FR_r_hi, FR_r_hi, f0  // r_hi_sq = r_hi * r_hi
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-//
-//      if (i_1=0) corr = C_1 * rsq
-//      else       corr = S_1 * r_cubed + r
-//
-(p9)	fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_6
-	nop.i 999 ;;
+(p10) ldfe FR_QQ_3 = [GR_ad_qq], 16             // Load QQ_3 if i_1=1
+      fms.s1 FR_r_lo = FR_r, f1, FR_r_hi        // r_lo = r - r_hi
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_U_lo = FR_r_hi, f1, FR_r
-	nop.i 999
+(p9)  ldfe FR_PP_2 = [GR_ad_pp], 16             // Load PP_2 if i_1=0
+(p9)  fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_5 // poly = rsq*poly+PP_5 if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-//
-//      if (i_1=0) U_hi = r_hi + U_hi 
-//      else       U_hi = QQ_1 * U_hi + 1
-//
-(p9)	fma.s1 FR_U_lo = FR_r, FR_r_hi, FR_U_lo
-	nop.i 999 ;;
+(p10) ldfe FR_QQ_2 = [GR_ad_qq], 16             // Load QQ_2 if i_1=1
+(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_5 // poly = rsq*poly+QQ_5 if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      U_hi = r_hi * r_hi	
-//
-(p0)	fms.s1 FR_r_lo = FR_r, f1, FR_r_hi
-	nop.i 999
+(p9)  ldfe FR_PP_1_lo = [GR_ad_pp], 16          // Load PP_1_lo if i_1=0
+(p9)  fma.s1 FR_corr = FR_corr, FR_c, FR_c      // corr = corr * c + c if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-//
-//      Load PP_1, PP_6, PP_5, and C_1
-//      Load QQ_1, QQ_6, QQ_5, and S_1
-//
-(p0)	fma.s1 FR_U_hi = FR_r_hi, FR_r_hi, f0
-	nop.i 999 ;;
+      nop.m 999
+(p10) fnma.s1 FR_corr = FR_corr, FR_c, f0       // corr = -corr * c if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_5
-	nop.i 999
+      nop.m 999
+(p9)  fma.s1 FR_U_lo = FR_r, FR_r_hi, FR_r_hi_sq // U_lo = r*r_hi+r_hi_sq, i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-(p10)	fnma.s1	FR_corr = FR_corr, FR_c, f0
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s1 FR_U_lo = FR_r_hi, f1, FR_r        // U_lo = r_hi + r if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      if (i_1=0) U_lo = r * r_hi + U_lo 
-//      else       U_lo = r_lo * U_lo
-//
-(p9)	fma.s1 FR_corr = FR_corr, FR_c, FR_c
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_U_hi = FR_r_hi, FR_r_hi_sq, f0  // U_hi = r_hi*r_hi_sq if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-(p9)	fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_5
-	nop.i 999
+      nop.m 999
+(p10) fma.s1 FR_U_hi = FR_QQ_1, FR_r_hi_sq, f1  // U_hi = QQ_1*r_hi_sq+1, i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      if (i_1 =0) U_hi = r + U_hi
-//      if (i_1 =0) U_lo = r_lo * U_lo 
-//      
-//
-(p9)	fma.s0 FR_PP_5 = FR_PP_5, FR_PP_4, f0
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_4 // poly = poly*rsq+PP_4 if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-(p9)	fma.s1 FR_U_lo = FR_r, FR_r, FR_U_lo
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_4 // poly = poly*rsq+QQ_4 if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_U_lo = FR_r, FR_r, FR_U_lo      // U_lo = r * r + U_lo if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-//
-//      if (i_1=0) poly = poly * rsq + PP_6
-//      else       poly = poly * rsq + QQ_6 
-//
-(p9)	fma.s1 FR_U_hi = FR_r_hi, FR_U_hi, f0
-	nop.i 999
+      nop.m 999
+(p10) fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0     // U_lo = r_lo * U_lo if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_4
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_U_hi = FR_PP_1, FR_U_hi, f0     // U_hi = PP_1 * U_hi if i_1=0
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_U_hi = FR_QQ_1, FR_U_hi, f1
-	nop.i 999
+      nop.m 999
+(p9)  fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_3 // poly = poly*rsq+PP_3 if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-(p10)	fma.s0 FR_QQ_5 = FR_QQ_5, FR_QQ_5, f0
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_3 // poly = poly*rsq+QQ_3 if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      if (i_1!=0) U_hi = PP_1 * U_hi  
-//      if (i_1!=0) U_lo = r * r  + U_lo  
-//      Load PP_3 or QQ_3
-//
-(p9)	fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_4
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0     // U_lo = r_lo * U_lo if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-(p9)	fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s1 FR_U_lo = FR_QQ_1,FR_U_lo, f0      // U_lo = QQ_1 * U_lo if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_U_lo = FR_QQ_1,FR_U_lo, f0
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_U_hi = FR_r, f1, FR_U_hi        // U_hi = r + U_hi if i_1=0
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p9)	fma.s1 FR_U_hi = FR_PP_1, FR_U_hi, f0
-	nop.i 999
+      nop.m 999
+(p9)  fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_2 // poly = poly*rsq+PP_2 if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_3
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_2 // poly = poly*rsq+QQ_2 if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      Load PP_2, QQ_2
-//
-(p9)	fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_3
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_U_lo = FR_PP_1, FR_U_lo, f0     // U_lo = PP_1 * U_lo if i_1=0
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      if (i_1==0) poly = FR_rsq * poly  + PP_3
-//      else        poly = FR_rsq * poly  + QQ_3
-//      Load PP_1_lo
-//
-(p9)	fma.s1 FR_U_lo = FR_PP_1, FR_U_lo, f0
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_1_lo // poly =poly*rsq+PP1lo i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-//
-//      if (i_1 =0) poly = poly * rsq + pp_r4
-//      else        poly = poly * rsq + qq_r4
-//
-(p9)	fma.s1 FR_U_hi = FR_r, f1, FR_U_hi
-	nop.i 999
+      nop.m 999
+(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0      // poly = poly*rsq if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_2
-	nop.i 999 ;;
+      nop.m 999
+      fma.s1 FR_V = FR_U_lo, f1, FR_corr        // V = U_lo + corr
+      tbit.z p11,p12 = GR_N_Inc, 1              // p11 if i_0=0, N mod 4 = 0,2
+                                                // p12 if i_0=1, N mod 4 = 1,3
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      if (i_1==0) U_lo =  PP_1_hi * U_lo
-//      else        U_lo =  QQ_1 * U_lo
-//
-(p9)	fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_2
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s0 FR_inexact = FR_PP_5, FR_PP_4, f0  // Dummy op to set inexact
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-//
-//      if (i_0==0)  Result = 1
-//      else         Result = -1
-//
-(p0) 	fma.s1 FR_V = FR_U_lo, f1, FR_corr
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s0 FR_inexact = FR_QQ_5, FR_QQ_5, f0  // Dummy op to set inexact
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_poly = FR_rsq, FR_poly, f0
-	nop.i 999 ;;
+      nop.m 999
+(p9)  fma.s1 FR_poly = FR_r_cubed, FR_poly, f0  // poly = poly*r^3 if i_1=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-//
-//      if (i_1==0) poly =  FR_rsq * poly + PP_2
-//      else poly =  FR_rsq * poly + QQ_2
-// 
-(p9)	fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_1_lo
-	nop.i 999 ;;
+      nop.m 999
+(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0      // poly = poly*rsq if i_1=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-(p10)	fma.s1 FR_poly = FR_rsq, FR_poly, f0
-	nop.i 999 ;;
+      nop.m 999
+(p11) fma.s1 FR_tmp_result = f0, f1, f1// tmp_result=+1.0 if i_0=0
+      nop.i 999
 }
 { .mfi
-	nop.m 999
-//
-//      V = U_lo + corr
-//
-(p9)	fma.s1 FR_poly = FR_r_cubed, FR_poly, f0
-	nop.i 999 ;;
+      nop.m 999
+(p12) fms.s1 FR_tmp_result = f0, f1, f1// tmp_result=-1.0 if i_0=1
+      nop.i 999
 }
+;;
+
 { .mfi
-	nop.m 999
-//
-//      if (i_1==0) poly = r_cube * poly
-//      else        poly = FR_rsq * poly
-//
-(p0)	fma.s1	FR_V = FR_poly, f1, FR_V
-	nop.i 999 ;;
+      nop.m 999
+      fma.s1 FR_V = FR_poly, f1, FR_V           // V = poly + V
+      nop.i 999
 }
+;;
+
+// If i_0 = 0  Result =  U_hi + V
+// If i_0 = 1  Result = -U_hi - V
 { .mfi
-	nop.m 999
-(p12)	fms.s0 FR_Input_X = FR_Input_X, FR_U_hi, FR_V
-	nop.i 999
+        nop.m 999
+(p11)        fma.s0 FR_Result = FR_tmp_result, FR_U_hi, FR_V
+        nop.i 999
 }
 { .mfb
-	nop.m 999
-//
-//      V = V + poly	
-//
-(p11)	fma.s0 FR_Input_X = FR_Input_X, FR_U_hi, FR_V
-//
-//      if (i_0==0) Result = Result * U_hi + V
-//      else        Result = Result * U_hi - V
-//
-(p0)    br.ret.sptk   b0 
-};;
-
-//
-//    	If cosine, FR_Input_X = 1
-//    	If sine, FR_Input_X = +/-Zero (Input FR_Input_X)
-//    	Results are exact, no exceptions
-//
+        nop.m 999
+(p12)        fms.s0 FR_Result = FR_tmp_result, FR_U_hi, FR_V
+        br.ret.sptk   b0                     // Exit for 2^-3 <= |r| < pi/4
+}
+;;
 
-L(SINCOSL_ZERO):
-{ .mbb
-(p0)    cmp.eq.unc p6, p7 = 0x1, GR_Sin_or_Cos
-        nop.b 999
-        nop.b 999 ;;
+SINCOSL_ZERO:
+// Here if x = 0
+{ .mfi
+      cmp.eq.unc p6, p7 = 0x1, GR_Sin_or_Cos
+      nop.f 999
+      nop.i 999
 }
+;;
+
 { .mfi
-        nop.m 999
-(p7)    fmerge.s FR_Input_X = FR_Input_X, FR_Input_X
-        nop.i 999
+      nop.m 999
+(p7)  fmerge.s FR_Result = FR_Input_X, FR_Input_X // If sin, result = input
+      nop.i 999
 }
 { .mfb
-        nop.m 999
-(p6)    fmerge.s FR_Input_X = f1, f1
-(p0)    br.ret.sptk   b0 ;;
+      nop.m 999
+(p6)  fma.s0 FR_Result = f1, f1, f0    // If cos, result=1.0
+      br.ret.sptk   b0                  // Exit for x=0
+}
+;;
+
+
+SINCOSL_DENORMAL:
+{ .mmb
+      getf.exp GR_signexp_x = FR_norm_x   // Get sign and exponent of x
+      nop.m 999
+      br.cond.sptk  SINCOSL_COMMON        // Return to common code
 }
-L(SINCOSL_SPECIAL):
+;;
+
+SINCOSL_SPECIAL:
 { .mfb
         nop.m 999
 //
@@ -2414,106 +2283,83 @@ L(SINCOSL_SPECIAL):
 //      Invalid can be raised. SNaNs
 //      become QNaNs
 //
-(p0)    fmpy.s0 FR_Input_X = FR_Input_X, f0
-(p0)    br.ret.sptk   b0 ;;
+        fmpy.s0 FR_Result = FR_Input_X, f0
+        br.ret.sptk   b0 ;;
 }
-.endp cosl#
-ASM_SIZE_DIRECTIVE(cosl#)
 
-//      Call int pi_by_2_reduce(double* x, double *y)
-//      for |arguments| >= 2**63
-//      Address to save r and c as double 
-//
-//             sp+32  -> f0
-//      r45    sp+16  -> f0
-//      r44 -> sp     -> InputX  
-//      
+GLOBAL_IEEE754_END(cosl)
 
-.proc __libm_callout
-__libm_callout:
-L(SINCOSL_ARG_TOO_LARGE): 
+// *******************************************************************
+// *******************************************************************
+// *******************************************************************
+//
+//     Special Code to handle very large argument case.
+//     Call int __libm_pi_by_2_reduce(x,r,c) for |arguments| >= 2**63
+//     The interface is custom:
+//       On input:
+//         (Arg or x) is in f8
+//       On output:
+//         r is in f8
+//         c is in f9
+//         N is in r8
+//     Be sure to allocate at least 2 GP registers as output registers for
+//     __libm_pi_by_2_reduce.  This routine uses r59-60. These are used as
+//     scratch registers within the __libm_pi_by_2_reduce routine (for speed).
+//
+//     We know also that __libm_pi_by_2_reduce preserves f10-15, f71-127.  We
+//     use this to eliminate save/restore of key fp registers in this calling
+//     function.
+//
+// *******************************************************************
+// *******************************************************************
+// *******************************************************************
+
+LOCAL_LIBM_ENTRY(__libm_callout)
+SINCOSL_ARG_TOO_LARGE:
 .prologue
 { .mfi
-        add   r45=-32,sp                        // Parameter: r address 
         nop.f 0
 .save   ar.pfs,GR_SAVE_PFS
         mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
-}
-{ .mfi
-.fframe 64
-        add sp=-64,sp                           // Create new stack
-        nop.f 0
-        mov GR_SAVE_GP=gp                       // Save gp
 };;
+
 { .mmi
-        stfe [r45] = f0,16                      // Clear Parameter r on stack
-        add  r44 = 16,sp                        // Parameter x address
+        setf.exp FR_Two_to_M3 = GR_exp_2_to_m3  // Form 2^-3
+        mov GR_SAVE_GP=gp                       // Save gp
 .save   b0, GR_SAVE_B0
         mov GR_SAVE_B0=b0                       // Save b0
 };;
+
 .body
+//
+//     Call argument reduction with x in f8
+//     Returns with N in r8, r in f8, c in f9
+//     Assumes f71-127 are preserved across the call
+//
 { .mib
-        stfe [r45] = f0,-16                     // Clear Parameter c on stack 
-        nop.i 0
-        nop.b 0
-}
-{ .mib
-        stfe [r44] = FR_Input_X                 // Store Parameter x on stack
+        setf.exp FR_Neg_Two_to_M3 = GR_exp_m2_to_m3 // Form -(2^-3)
         nop.i 0
-(p0)    br.call.sptk b0=__libm_pi_by_2_reduce# ;;
+        br.call.sptk b0=__libm_pi_by_2_reduce#
 };;
-{ .mii
-(p0)    ldfe  FR_Input_X =[r44],16
-//
-//      Get r and c off stack
-//
-(p0)    adds  GR_Table_Base1 = -16, GR_Table_Base1
-//
-//      Get r and c off stack
-//
-(p0)    add   GR_N_Inc = GR_Sin_or_Cos,r8 ;;
-}
-{ .mmb
-(p0)    ldfe  FR_r =[r45],16
-//
-//      Get X off the stack
-//      Readjust Table ptr
-//
-(p0)    ldfs FR_Two_to_M3 = [GR_Table_Base1],4
-	nop.b 999 ;;
-}
-{ .mmb
-(p0)    ldfs FR_Neg_Two_to_M3 = [GR_Table_Base1],0
-(p0)    ldfe  FR_c =[r45]
-	nop.b 999 ;;
-}
+
 { .mfi
-.restore sp
-        add   sp = 64,sp                       // Restore stack pointer
-(p0)    fcmp.lt.unc.s1	p6, p0 = FR_r, FR_Two_to_M3
+        add   GR_N_Inc = GR_Sin_or_Cos,r8
+        fcmp.lt.unc.s1        p6, p0 = FR_r, FR_Two_to_M3
         mov   b0 = GR_SAVE_B0                  // Restore return address
 };;
-{ .mib
+
+{ .mfi
         mov   gp = GR_SAVE_GP                  // Restore gp
+(p6)    fcmp.gt.unc.s1        p6, p0 = FR_r, FR_Neg_Two_to_M3
         mov   ar.pfs = GR_SAVE_PFS             // Restore ar.pfs
-        nop.b 0
 };;
-{ .mfi
-	nop.m 999
-(p6)    fcmp.gt.unc.s1	p6, p0 = FR_r, FR_Neg_Two_to_M3
-	nop.i 999 ;;
-}
-{ .mib
-	nop.m 999
-	nop.i 999
-(p6)    br.cond.spnt L(SINCOSL_SMALL_R) ;;
-}
-{ .mib
-	nop.m 999
-	nop.i 999
-(p0)    br.cond.sptk L(SINCOSL_NORMAL_R) ;;
-}
-.endp __libm_callout
-ASM_SIZE_DIRECTIVE(__libm_callout)
+
+{ .mbb
+        nop.m 999
+(p6)    br.cond.spnt SINCOSL_SMALL_R     // Branch if |r|< 2^-3 for |x| >= 2^63
+        br.cond.sptk SINCOSL_NORMAL_R    // Branch if |r|>=2^-3 for |x| >= 2^63
+};;
+
+LOCAL_LIBM_END(__libm_callout)
 .type   __libm_pi_by_2_reduce#,@function
 .global __libm_pi_by_2_reduce#