(CFLAGS-tst-align.c): Add -mpreferred-stack-boundary=4.

1 files changed, 0 insertions, 2757 deletions

diff --git a/sysdeps/ia64/fpu/libm_sincos_large.S b/sysdeps/ia64/fpu/libm_sincos_large.S
deleted file mode 100644
index b09d3693a6..0000000000
--- a/sysdeps/ia64/fpu/libm_sincos_large.S
+++ /dev/null
@@ -1,2757 +0,0 @@
-.file "libm_sincos_large.s"
-
-
-// Copyright (c) 2002 - 2003, Intel Corporation
-// All rights reserved.
-//
-// Contributed 2002 by the Intel Numerics Group, Intel Corporation
-//
-// Redistribution and use in source and binary forms, with or without
-// modification, are permitted provided that the following conditions are
-// met:
-//
-// * Redistributions of source code must retain the above copyright
-// notice, this list of conditions and the following disclaimer.
-//
-// * Redistributions in binary form must reproduce the above copyright
-// notice, this list of conditions and the following disclaimer in the
-// documentation and/or other materials provided with the distribution.
-//
-// * The name of Intel Corporation may not be used to endorse or promote
-// products derived from this software without specific prior written
-// permission.
-
-// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
-// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
-// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
-// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
-// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
-// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
-// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
-// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-//
-// Intel Corporation is the author of this code, and requests that all
-// problem reports or change requests be submitted to it directly at
-// http://www.intel.com/software/products/opensource/libraries/num.htm.
-//
-// History
-//==============================================================
-// 02/15/02 Initial version
-// 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
-// 05/15/03 Reformatted data tables
-//
-//
-// Overview of operation
-//==============================================================
-//
-// These functions calculate the sin and cos for inputs
-// greater than 2^10
-//
-// __libm_sin_large#
-// __libm_cos_large#
-// They accept argument in f8
-// and return result in f8 without final rounding
-//
-// __libm_sincos_large#
-// It accepts argument in f8
-// and returns cos in f8 and sin in f9 without final rounding
-//
-//
-//*********************************************************************
-//
-// Accuracy:       Within .7 ulps for 80-bit floating point values
-//                 Very accurate for double precision values
-//
-//*********************************************************************
-//
-// Resources Used:
-//
-//    Floating-Point Registers: f8 as Input Value, f8 and f9 as Return Values
-//                              f32-f103
-//
-//    General Purpose Registers:
-//      r32-r43
-//      r44-r45 (Used to pass arguments to pi_by_2 reduce routine)
-//
-//    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
-//    (No specialized error handling for this routine)
-//    Inexact raised when appropriate by algorithm
-//
-//    sin(SNaN) = QNaN
-//    sin(QNaN) = QNaN
-//    sin(inf) = QNaN
-//    sin(+/-0) = +/-0
-//    cos(inf) = QNaN
-//    cos(SNaN) = QNaN
-//    cos(QNaN) = QNaN
-//    cos(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
-//  to alpha where
-//
-//  Arg = N pi/2 + alpha, |alpha| <= pi/4.
-//
-//  Since
-//
-//  cos( Arg ) = sin( (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
-//  process.
-//
-//  Let M = N if sine
-//      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
-//  as 2's complement. I = [i_0 i_1]. Then
-//
-//  sin( Arg ) = (-1)^i_0  sin( alpha ) if i_1 = 0,
-//             = (-1)^i_0  cos( alpha )     if i_1 = 1.
-//
-//  For example:
-//       if M = -1, I = 11
-//         sin ((-pi/2 + alpha) = (-1) cos (alpha)
-//       if M = 0, I = 00
-//         sin (alpha) = sin (alpha)
-//       if M = 1, I = 01
-//         sin (pi/2 + alpha) = cos (alpha)
-//       if M = 2, I = 10
-//         sin (pi + alpha) = (-1) sin (alpha)
-//       if M = 3, I = 11
-//         sin ((3/2)pi + alpha) = (-1) cos (alpha)
-//
-//  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, sin(r+c) and cos(r+c) can be
-//  computed very easily by 2 or 3 terms of the Taylor series
-//  expansion as follows:
-//
-//  Case 2:
-//  -------
-//
-//  sin(r + c) = r + c - r^3/6  accurately
-//  cos(r + c) = 1 - 2^(-67)    accurately
-//
-//  Case 4:
-//  -------
-//
-//  sin(r + c) = r + c - r^3/6 + r^5/120    accurately
-//  cos(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
-//  enough to allow the usage of a very short approximation.
-//
-//  The required calculation is either
-//
-//  sin(r + c)  =  sin(r)  +  correction,  or
-//  cos(r + c)  =  cos(r)  +  correction.
-//
-//  Specifically,
-//
-//  sin(r + c) = sin(r) + c sin'(r) + O(c^2)
-//         = sin(r) + c cos (r) + O(c^2)
-//         = sin(r) + c(1 - r^2/2)  accurately.
-//  Similarly,
-//
-//  cos(r + c) = cos(r) - c sin(r) + O(c^2)
-//         = cos(r) - c(r - r^3/6)  accurately.
-//
-//  We therefore concentrate on accurately calculating sin(r) and
-//  cos(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 Taylor series
-//
-//  r - r^3/3! + r^r/5! - ...
-//
-//  and
-//
-//  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
-//  in the accurate computation of sin(r) and cos(r), |r| <= pi/4.
-//
-//  Case small_r: |r| < 2^(-3)
-//  --------------------------
-//
-//  Since Arg = M pi/4 + r + c accurately, and M mod 4 is [i_0 i_1],
-//  we have
-//
-//  sin(Arg) = (-1)^i_0 * sin(r + c)    if i_1 = 0
-//       = (-1)^i_0 * cos(r + c)    if i_1 = 1
-//
-//  can be accurately approximated by
-//
-//  sin(Arg) = (-1)^i_0 * [sin(r) + c]  if i_1 = 0
-//           = (-1)^i_0 * [cos(r) - c*r] if i_1 = 1
-//
-//  because |r| is small and thus the second terms in the correction
-//  are unneccessary.
-//
-//  Finally, sin(r) and cos(r) are approximated by polynomials of
-//  moderate lengths.
-//
-//  sin(r) =  r + S_1 r^3 + S_2 r^5 + ... + S_5 r^11
-//  cos(r) =  1 + C_1 r^2 + C_2 r^4 + ... + C_5 r^10
-//
-//  We can make use of predicates to selectively calculate
-//  sin(r) or cos(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,
-//
-//  sin(Arg) = (-1)^i_0 * sin(r + c)    if i_1 = 0
-//           = (-1)^i_0 * cos(r + c)    if i_1 = 1.
-//
-//  Because |r| is now larger, we need one extra term in the
-//  correction. sin(Arg) can be accurately approximated by
-//
-//  sin(Arg) = (-1)^i_0 * [sin(r) + c(1-r^2/2)]      if i_1 = 0
-//           = (-1)^i_0 * [cos(r) - c*r*(1 - r^2/6)]    i_1 = 1.
-//
-//  Finally, sin(r) and cos(r) are approximated by polynomials of
-//  moderate lengths.
-//
-//  sin(r) =  r + PP_1_hi r^3 + PP_1_lo r^3 +
-//                PP_2 r^5 + ... + PP_8 r^17
-//
-//  cos(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
-//
-//  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
-//  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
-//
-//  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
-//
-//  |U_lo| <= 2^(-8) |U_hi|
-//
-//  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 ) ).
-//
-//  If i_1 = 0, then
-//
-//    U_hi := r + PP_1_hi * r_hi^3
-//    U_lo := PP_1_hi * (r - r_hi) * (r^2 + r*r_hi + r_hi^2)
-//    poly := PP_1_lo r^3 + PP_2 r^5 + ... + PP_8 r^17
-//    correction := c * ( 1 + C_1 r^2 )
-//
-//  Else ...i_1 = 1
-//
-//    U_hi := 1 + QQ_1 * r_hi * r_hi
-//    U_lo := QQ_1 * (r - r_hi) * (r + r_hi)
-//    poly := QQ_2 * r^4 + QQ_3 * r^6 + ... + QQ_8 r^16
-//    correction := -c * r * (1 + S_1 * r^2)
-//
-//  End
-//
-//  Finally,
-//
-//  V := poly + ( U_lo + correction )
-//
-//                 /    U_hi  +  V         if i_0 = 0
-//  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.
-//
-//
-//  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
-//  previously is repeated below.
-//
-//
-//  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
-//     handling.
-//   * If |Arg| < 2^24, go to Step 2 for reduction of moderate
-//     arguments. This is the most likely case.
-//   * If |Arg| < 2^63, go to Step 8 for pre-reduction of large
-//     arguments.
-//   * If |Arg| >= 2^63, go to Step 10 for special handling.
-//
-//  Step 2. Reduction of moderate arguments.
-//
-//  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)
-//     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)
-//
-//     If |s| >= 2^(-33)
-//        go to Step 3, Case_1_reduce
-//     Else
-//        go to Step 7, Case_2_reduce
-//     Endif
-//  Endif
-//
-//  Step 3. Case_1_reduce.
-//
-//  r := s + w
-//  c := (s - r) + w    ...observe order
-//
-//  Step 4. Case_1_complete
-//
-//  ...At this point, the reduced argument alpha is
-//  ...accurately represented as r + c.
-//  If |r| < 2^(-3), go to Step 6, small_r.
-//
-//  Step 5. Normal_r.
-//
-//  Let [i_0 i_1] by the 2 lsb of N_fix.
-//  FR_rsq  := r * r
-//  r_hi := frcpa( frcpa( r ) )
-//  r_lo := r - r_hi
-//
-//  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_lo := PP_1_hi*r_lo*(r*r + r*r_hi + r_hi*r_hi)
-//    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_lo := QQ_1 * r_lo * (r + r_hi)
-//    correction := -c*(r + S_1*FR_rsq*r)   ...any order
-//  Endif
-//
-//  V := poly + (U_lo + correction) ...observe order
-//
-//  result := (i_0 == 0?   1.0 : -1.0)
-//
-//  Last instruction in user-set rounding mode
-//
-//  result := (i_0 == 0?   result*U_hi + V :
-//                        result*U_hi - V)
-//
-//  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.
-//
-//  FR_rsq := r * r
-//
-//  If i_1 = 0 then
-//     z := FR_rsq*FR_rsq; z := FR_rsq*z *r
-//     poly_lo := S_3 + FR_rsq*(S_4 + FR_rsq*S_5)
-//     poly_hi := r*FR_rsq*(S_1 + FR_rsq*S_2)
-//     correction := c
-//     result := r
-//  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)
-//     correction := -c*r
-//     result := 1
-//  Endif
-//
-//  poly := poly_hi + (z * poly_lo + correction)
-//
-//  If i_0 = 1, result := -result
-//
-//  Last operation. Perform in user-set rounding mode
-//
-//  result := (i_0 == 0?     result + poly :
-//                          result - poly )
-//  Return
-//
-//  Step 7. Case_2_reduce.
-//
-//  ...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 + U_2 is  N*(P_2+P_3) accurately
-//
-//  r := s - U_1
-//  c := ( (s - r) - U_1 ) - U_2
-//
-//  ...The mathematical sum r + c approximates the reduced
-//  ...argument accurately. Note that although compared to
-//  ...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
-//  ...Taylor series expansion suffices.
-//
-//  If i_1 = 0 then
-//     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.
-
-//  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
-//
-//  s := Arg' - N * P_1
-//  w := w - N * P_2
-//
-//  If |s| >= 2^(-14)
-//     go to Step 3
-//  Else
-//     go to Step 9
-//  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
-//
-//   ...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
-//
-//   ...at this point, the mathematical value
-//   ...s + U_hi + V_hi  + t approximates the true reduced argument
-//   ...accurately. Just need to compute this accurately.
-//
-//   ...Calculate U_hi + V_hi accurately:
-//   A := U_hi + V_hi
-//   if |U_hi| >= |V_hi| then
-//      a := (U_hi - A) + V_hi
-//   else
-//      a := (V_hi - A) + U_hi
-//   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
-//   ...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_lo := C_lo + t
-//
-//   ...Final steps for reduction
-//   r := C_hi + C_lo
-//   c := (C_hi - r) + C_lo
-//
-//   ...At this point, we have r and c
-//   ...And all we need is a couple of terms of the corresponding
-//   ...Taylor series.
-//
-//   If i_1 = 0
-//      poly := c + r*FR_rsq*(S_1 + FR_rsq*S_2)
-//      result := r
-//   Else
-//      poly := FR_rsq*(C_1 + FR_rsq*C_2)
-//      result := 1
-//   Endif
-//
-//   If i_0 = 1, result := -result
-//
-//   Last operation. Perform in user-set rounding mode
-//
-//   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.
-//
-
-
-RODATA
-.align 16
-
-LOCAL_OBJECT_START(FSINCOS_CONSTANTS)
-
-data4 0x4B800000 // two**24
-data4 0xCB800000 // -two**24
-data4 0x00000000 // pad
-data4 0x00000000 // pad
-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
-data4 0x5F000000 // two**63
-data4 0xDF000000 // -two**63
-data4 0x00000000 // pad
-data4 0x00000000 // pad
-data8 0xA397E5046EC6B45A, 0x00003FE7 // Inv_P_0
-data8 0x8D848E89DBD171A1, 0x0000BFBF // d_1
-data8 0xD5394C3618A66F8E, 0x0000BF7C // d_2
-data8 0xC90FDAA22168C234, 0x00003FFE // pi_by_4
-data8 0xC90FDAA22168C234, 0x0000BFFE // neg_pi_by_4
-data4 0x3E000000 // two**-3
-data4 0xBE000000 // -two**-3
-data4 0x00000000 // pad
-data4 0x00000000 // pad
-data4 0x2F000000 // two**-33
-data4 0xAF000000 // -two**-33
-data4 0x9E000000 // -two**-67
-data4 0x00000000 // pad
-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
-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
-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
-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 // two**-14
-data4 0xB8800000 // -two**-14
-LOCAL_OBJECT_END(FSINCOS_CONSTANTS)
-
-// sin and cos registers
-
-// FR
-FR_Input_X        = f8
-
-FR_r              = f8
-FR_c              = f9
-
-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_d_2            = f48
-FR_prelim         = 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_Neg_Two_to_M3  = 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
-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
-
-GR_SAVE_B0        = r39
-GR_SAVE_GP        = r40
-GR_SAVE_PFS       = r41
-
-// sincos combined routine registers
-
-// GR
-GR_SINCOS_SAVE_PFS    = r32
-GR_SINCOS_SAVE_B0     = r33
-GR_SINCOS_SAVE_GP     = r34
-
-// FR
-FR_SINCOS_ARG         = f100
-FR_SINCOS_RES_SIN     = f101
-
-
-.section .text
-
-
-GLOBAL_LIBM_ENTRY(__libm_sincos_large)
-
-{ .mfi
-        alloc GR_SINCOS_SAVE_PFS = ar.pfs,0,3,0,0
-        fma.s1 FR_SINCOS_ARG     = f8, f1, f0  // Save argument for sin and cos
-        mov GR_SINCOS_SAVE_B0    = b0
-};;
-
-{ .mfb
-        mov GR_SINCOS_SAVE_GP    = gp
-        nop.f  0
-        br.call.sptk b0          = __libm_sin_large // Call sin
-};;
-
-{ .mfi
-        nop.m  0
-        fma.s1 FR_SINCOS_RES_SIN = f8, f1, f0 // Save sin result
-        nop.i  0
-};;
-
-{ .mfb
-        nop.m  0
-        fma.s1 f8                = FR_SINCOS_ARG, f1, f0 // Arg for cos
-        br.call.sptk b0          = __libm_cos_large // Call cos
-};;
-
-{ .mfi
-        mov    gp                = GR_SINCOS_SAVE_GP
-        fma.s1 f9                = FR_SINCOS_RES_SIN, f1, f0 // Out sin result
-        mov    b0                = GR_SINCOS_SAVE_B0
-};;
-
-{ .mib
-        nop.m  0
-        mov ar.pfs               = GR_SINCOS_SAVE_PFS
-        br.ret.sptk                b0 // sincos_large exit
-};;
-
-GLOBAL_LIBM_END(__libm_sincos_large)
-
-
-
-
-GLOBAL_LIBM_ENTRY(__libm_sin_large)
-
-{ .mlx
-alloc GR_Table_Base = ar.pfs,0,12,2,0
-       movl GR_Sin_or_Cos = 0x0 ;;
-}
-
-{ .mmi
-      nop.m 999
-      addl           GR_Table_Base   = @ltoff(FSINCOS_CONSTANTS#), gp
-      nop.i 999
-}
-;;
-
-{ .mmi
-      ld8 GR_Table_Base = [GR_Table_Base]
-      nop.m 999
-      nop.i 999
-}
-;;
-
-
-{ .mib
-      nop.m 999
-      nop.i 999
-       br.cond.sptk SINCOS_CONTINUE ;;
-}
-
-GLOBAL_LIBM_END(__libm_sin_large)
-
-GLOBAL_LIBM_ENTRY(__libm_cos_large)
-
-{ .mlx
-alloc GR_Table_Base= ar.pfs,0,12,2,0
-       movl GR_Sin_or_Cos = 0x1 ;;
-}
-
-{ .mmi
-      nop.m 999
-      addl           GR_Table_Base   = @ltoff(FSINCOS_CONSTANTS#), gp
-      nop.i 999
-}
-;;
-
-{ .mmi
-      ld8 GR_Table_Base = [GR_Table_Base]
-      nop.m 999
-      nop.i 999
-}
-;;
-
-//
-//     Load Table Address
-//
-SINCOS_CONTINUE:
-
-{ .mmi
-       add GR_Table_Base1 = 96, GR_Table_Base
-       ldfs FR_Two_to_24 = [GR_Table_Base], 4
-       nop.i 999
-}
-;;
-
-{ .mmi
-      nop.m 999
-//
-//     Load 2**24, load 2**63.
-//
-       ldfs FR_Neg_Two_to_24 = [GR_Table_Base], 12
-       mov   r41 = ar.pfs ;;
-}
-
-{ .mfi
-       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
-//
-       fclass.m.unc  p6, p8 =  FR_Input_X, 0x1E3
-       mov   r40 = gp ;;
-}
-
-{ .mfi
-      nop.m 999
-       fclass.nm.unc p8, p0 =  FR_Input_X, 0x1FF
-// GR_Sin_or_Cos denotes
-       mov   r39 = b0
-}
-
-{ .mfb
-       ldfs FR_Neg_Two_to_63 = [GR_Table_Base1], 12
-       fclass.m.unc p10, p0 = FR_Input_X, 0x007
-(p6)   br.cond.spnt SINCOS_SPECIAL ;;
-}
-
-{ .mib
-      nop.m 999
-      nop.i 999
-(p8)   br.cond.spnt SINCOS_SPECIAL ;;
-}
-
-{ .mib
-      nop.m 999
-      nop.i 999
-//
-//     Branch if +/- NaN, Inf.
-//     Load -2**24, load -2**63.
-//
-(p10)  br.cond.spnt SINCOS_ZERO ;;
-}
-
-{ .mmb
-       ldfe FR_Inv_pi_by_2 = [GR_Table_Base], 16
-       ldfe FR_Inv_P_0 = [GR_Table_Base1], 16
-      nop.b 999 ;;
-}
-
-{ .mmb
-      nop.m 999
-       ldfe     FR_d_1 = [GR_Table_Base1], 16
-      nop.b 999 ;;
-}
-//
-//     Raise possible denormal operand flag with useful fcmp
-//     Is x <= -2**63
-//     Load Inv_P_0 for pre-reduction
-//     Load Inv_pi_by_2
-//
-
-{ .mmb
-       ldfe     FR_P_0 = [GR_Table_Base], 16
-       ldfe FR_d_2 = [GR_Table_Base1], 16
-      nop.b 999 ;;
-}
-//
-//     Load P_0
-//     Load d_1
-//     Is x >= 2**63
-//     Is x <= -2**24?
-//
-
-{ .mmi
-       ldfe FR_P_1 = [GR_Table_Base], 16 ;;
-//
-//     Load P_1
-//     Load d_2
-//     Is x >= 2**24?
-//
-       ldfe FR_P_2 = [GR_Table_Base], 16
-      nop.i 999 ;;
-}
-
-{ .mmf
-      nop.m 999
-       ldfe FR_P_3 = [GR_Table_Base], 16
-       fcmp.le.unc.s1   p7, p8 = FR_Input_X, FR_Neg_Two_to_24
-}
-
-{ .mfi
-      nop.m 999
-//
-//     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
-//
-       fcmp.le.unc.s1   p10, p11 = FR_Input_X, FR_Neg_Two_to_63
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p8)   fcmp.ge.s1 p7, p0 = FR_Input_X, FR_Two_to_24
-      nop.i 999
-}
-
-{ .mfi
-       ldfe FR_Pi_by_4 = [GR_Table_Base1], 16
-(p11)  fcmp.ge.s1   p10, p0 = FR_Input_X, FR_Two_to_63
-      nop.i 999 ;;
-}
-
-{ .mmi
-       ldfe FR_Neg_Pi_by_4 = [GR_Table_Base1], 16 ;;
-       ldfs FR_Two_to_M3 = [GR_Table_Base1], 4
-      nop.i 999 ;;
-}
-
-{ .mib
-       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 SINCOS_ARG_TOO_LARGE ;;
-}
-
-{ .mib
-      nop.m 999
-      nop.i 999
-//
-//     Branch out if x >= 2**63. Use Payne-Hanek Reduction
-//
-(p7)   br.cond.spnt SINCOS_LARGER_ARG ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     Branch if Arg <= -2**24 or Arg >= 2**24 and use pre-reduction.
-//
-       fma.s1   FR_N_float = FR_Input_X, FR_Inv_pi_by_2, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-       fcmp.lt.unc.s1   p6, p7 = FR_Input_X, FR_Pi_by_4
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     Select the case when |Arg| < pi/4
-//     Else Select the case when |Arg| >= pi/4
-//
-       fcvt.fx.s1 FR_N_fix = FR_N_float
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 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
-//     lf |x| < pi/4, is x < 2**(-3).
-//     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 ;;
-}
-
-{ .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
-//     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 SINCOS_SMALL_R ;;
-}
-
-{ .mib
-      nop.m 999
-      nop.i 999
-(p6)   br.cond.sptk SINCOS_NORMAL_R ;;
-}
-//
-//     if |x| < pi/4, branch based on |x| < 2**(-3) or otherwise.
-//
-//
-//     In this branch, |x| >= pi/4.
-//
-
-{ .mfi
-       ldfs FR_Neg_Two_to_M67 = [GR_Table_Base1], 8
-//
-//     Load -2**(-67)
-//
-       fnma.s1  FR_s = FR_N_float, FR_P_1, FR_Input_X
-//
-//     w = N * P_2
-//     s = -N * P_1  + Arg
-//
-       add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos
-}
-
-{ .mfi
-      nop.m 999
-       fma.s1   FR_w = FR_N_float, FR_P_2, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     Adjust N_fix by N_inc to determine whether sine or
-//     cosine is being calculated
-//
-       fcmp.lt.unc.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 ;;
-}
-
-{ .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
-}
-
-{ .mfi
-      nop.m 999
-(p7)   fma.s1 FR_w = FR_N_float, FR_P_3, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p7)   fma.s1 FR_U_1 = FR_N_float, FR_P_2, FR_w
-      nop.i 999
-}
-
-{ .mfi
-      nop.m 999
-(p6)   fms.s1 FR_c = FR_s, f1, FR_r
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 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, p9 = FR_r, FR_Neg_Two_to_M3
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p7)   fms.s1 FR_r = FR_s, f1, FR_U_1
-      nop.i 999
-}
-
-{ .mfb
-      nop.m 999
-//
-//     For big s: Is |r| < 2**(-3)?
-//     For big s: c = S - r
-//     For small s: U_1 = N * P_2 + w
-//
-//     If p8 is set, prepare to branch to Small_R.
-//     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 SINCOS_SMALL_R ;;
-}
-
-{ .mib
-      nop.m 999
-      nop.i 999
-(p9)   br.cond.sptk SINCOS_NORMAL_R ;;
-}
-
-{ .mfi
-(p7)   add GR_Table_Base1 = 224, GR_Table_Base1
-//
-//     Branch to SINCOS_SMALL_R or SINCOS_NORMAL_R
-//
-(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 ;;
-//
-//     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 ;;
-}
-//
-//     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
-//
-//     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 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p7)   fms.s1   FR_s = FR_s, f1, FR_r
-      nop.i 999
-}
-
-{ .mfi
-      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 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p7)   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
-(p7)   fmerge.se FR_prelim = FR_r, FR_r
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//(p10)  fma.s1 FR_Input_X = f0, f1, f1
-(p10)  fma.s1 FR_prelim = f0, f1, f1
-      nop.i 999 ;;
-}
-
-{ .mfi
-      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 ;;
-}
-
-{ .mfi
-      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
-(p12)  fnma.s1 FR_prelim = FR_prelim, f1, f0
-      nop.i 999
-}
-
-{ .mfi
-      nop.m 999
-(p7)   fma.s1   FR_r = FR_S_1, FR_r, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p7)   fma.d.s1 FR_S_1 = FR_S_1, FR_S_1, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     If i_1 != 0, poly = 2**(-67)
-//
-(p7)   fms.s1 FR_c = FR_c, f1, FR_U_2
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     c = c - U_2
-//
-(p9)   fma.s1 FR_poly = FR_r, FR_rsq, FR_c
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     i_0 != 0, so Result = -Result
-//
-(p11)  fma.s1 FR_Input_X = FR_prelim, f1, FR_poly
-      nop.i 999 ;;
-}
-
-{ .mfb
-      nop.m 999
-(p12)  fms.s1 FR_Input_X = FR_prelim, f1, FR_poly
-//
-//     if (i_0 == 0),  Result = Result + poly
-//     else            Result = Result - poly
-//
-       br.ret.sptk   b0 ;;
-}
-SINCOS_LARGER_ARG:
-
-{ .mfi
-      nop.m 999
-       fma.s1 FR_N_0 = FR_Input_X, FR_Inv_P_0, f0
-      nop.i 999
-}
-;;
-
-//     This path for argument > 2*24
-//     Adjust table_ptr1 to beginning of table.
-//
-
-{ .mmi
-      nop.m 999
-      addl           GR_Table_Base   = @ltoff(FSINCOS_CONSTANTS#), gp
-      nop.i 999
-}
-;;
-
-{ .mmi
-      ld8 GR_Table_Base = [GR_Table_Base]
-      nop.m 999
-      nop.i 999
-}
-;;
-
-
-//
-//     Point to  2*-14
-//     N_0 = Arg * Inv_P_0
-//
-
-{ .mmi
-       add GR_Table_Base = 688, GR_Table_Base ;;
-       ldfs FR_Two_to_M14 = [GR_Table_Base], 4
-      nop.i 999 ;;
-}
-
-{ .mfi
-       ldfs FR_Neg_Two_to_M14 = [GR_Table_Base], 0
-      nop.f 999
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     Load values 2**(-14) and -2**(-14)
-//
-       fcvt.fx.s1 FR_N_0_fix = FR_N_0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     N_0_fix  = integer part of N_0
-//
-       fcvt.xf FR_N_0 = FR_N_0_fix
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     Make N_0 the integer part
-//
-       fnma.s1 FR_ArgPrime = FR_N_0, FR_P_0, FR_Input_X
-      nop.i 999
-}
-
-{ .mfi
-      nop.m 999
-       fma.s1 FR_w = FR_N_0, FR_d_1, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     Arg' = -N_0 * P_0 + Arg
-//     w  = N_0 * d_1
-//
-       fma.s1 FR_N_float = FR_ArgPrime, FR_Inv_pi_by_2, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     N = A' * 2/pi
-//
-       fcvt.fx.s1 FR_N_fix = FR_N_float
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     N_fix is the integer part
-//
-       fcvt.xf FR_N_float = FR_N_fix
-      nop.i 999 ;;
-}
-
-{ .mfi
-       getf.sig GR_N_Inc = FR_N_fix
-      nop.f 999
-      nop.i 999 ;;
-}
-
-{ .mii
-      nop.m 999
-      nop.i 999 ;;
-       add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     N is the integer part of the reduced-reduced argument.
-//     Put the integer in a GP register
-//
-       fnma.s1 FR_s = FR_N_float, FR_P_1, FR_ArgPrime
-      nop.i 999
-}
-
-{ .mfi
-      nop.m 999
-       fnma.s1 FR_w = FR_N_float, FR_P_2, FR_w
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     s = -N*P_1 + Arg'
-//     w = -N*P_2 + w
-//     N_fix_gr = N_fix_gr + N_inc
-//
-       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 ;;
-}
-
-{ .mfi
-      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
-}
-
-{ .mfi
-      nop.m 999
-(p9)   fma.s1 FR_U_hi = FR_N_0, FR_d_1, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      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
-}
-
-{ .mfi
-      nop.m 999
-(p9)   fma.s1 FR_w = FR_N_float, FR_P_3, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      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
-}
-
-{ .mfi
-      nop.m 999
-//
-//     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 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p9)   fms.s1 FR_U_lo = FR_N_0, FR_d_1, FR_U_hi
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p9)   fmerge.s FR_V_hiabs = f0, FR_V_hi
-      nop.i 999
-}
-
-{ .mfi
-      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 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     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
-}
-
-{ .mfi
-      nop.m 999
-//
-//     For small S: V_hi = N * P_2
-//                  w = N * P_3
-//     Note the product does not include the (-) as in the writeup
-//     so (-) missing for V_hi and w.
-//
-(p8)   fcmp.lt.unc.s1 p12, p13 = FR_r, FR_Two_to_M3
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p12)  fcmp.gt.s1 p12, p13 = FR_r, FR_Neg_Two_to_M3
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p8)   fma.s1 FR_c = FR_c, f1, FR_w
-      nop.i 999
-}
-
-{ .mfb
-      nop.m 999
-(p9)   fms.s1 FR_w = FR_N_0, FR_d_2, FR_w
-(p12)  br.cond.spnt SINCOS_SMALL_R ;;
-}
-
-{ .mib
-      nop.m 999
-      nop.i 999
-(p13)  br.cond.sptk SINCOS_NORMAL_R ;;
-}
-
-{ .mfi
-      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
-       extr.u   GR_i_1 = GR_N_Inc, 0, 1 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     C_hi = S + A
-//
-(p9)   fma.s1 FR_t = FR_U_lo, f1, FR_V_lo
-       extr.u   GR_i_0 = GR_N_Inc, 1, 1 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     t = U_lo + V_lo
-//
-//
-(p10)  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
-      addl           GR_Table_Base   = @ltoff(FSINCOS_CONSTANTS#), gp
-      nop.i 999
-}
-;;
-
-{ .mmi
-      ld8 GR_Table_Base = [GR_Table_Base]
-      nop.m 999
-      nop.i 999
-}
-;;
-
-
-{ .mfi
-       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 ;;
-}
-
-{ .mmi
-       ldfe FR_C_1 = [GR_Table_Base], 16 ;;
-       ldfe FR_C_2 = [GR_Table_Base], 64
-      nop.i 999 ;;
-}
-
-{ .mmf
-      nop.m 999
-//
-//     c = c + C_lo  finished.
-//     Load  C_2
-//
-       ldfe FR_S_1 = [GR_Table_Base], 16
-//
-//     C_lo = S - C_hi
-//
-       fma.s1 FR_t = FR_t, f1, FR_w ;;
-}
-//
-//     r and c have been computed.
-//     Make sure ftz mode is set - should be automatic when using wre
-//     |r| < 2**(-3)
-//     Get [i_0,i_1] - two lsb of N_fix.
-//     Load S_1
-//
-
-{ .mfi
-       ldfe FR_S_2 = [GR_Table_Base], 64
-//
-//     t = t + w
-//
-(p10)  fms.s1 FR_a = FR_a, f1, FR_V_hi
-       cmp.eq.unc p9, p10 = 0x0, GR_i_0
-}
-
-{ .mfi
-      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
-//
-       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
-       cmp.eq.unc p11, p12 = 0x0, GR_i_1
-}
-
-{ .mfi
-      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.
-//
-       fma.s1 FR_C_lo = FR_C_lo, f1, FR_A
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     C_lo = (S - C_hi) + A
-//
-       fma.s1 FR_t = FR_t, f1, FR_a
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     t = t + a
-//
-       fma.s1 FR_C_lo = FR_C_lo, f1, FR_t
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     C_lo = C_lo + t
-//     Adjust Table_Base to beginning of table
-//
-       fma.s1 FR_r = FR_C_hi, f1, FR_C_lo
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     Load S_2
-//
-       fma.s1 FR_rsq = FR_r, FR_r, f0
-      nop.i 999
-}
-
-{ .mfi
-      nop.m 999
-//
-//     Table_Base points to C_1
-//     r = C_hi + C_lo
-//
-       fms.s1 FR_c = FR_C_hi, f1, FR_r
-      nop.i 999 ;;
-}
-
-{ .mfi
-      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
-(p11)  fma.s1 FR_prelim = f0, f1, FR_r
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//(p12)  fma.s1 FR_Input_X = f0, f1, f1
-(p12)  fma.s1 FR_prelim = f0, f1, f1
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     Compute r_cube = FR_rsq * r
-//
-(p11)  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
-}
-
-{ .mfi
-      nop.m 999
-//
-//     Compute FR_rsq = r * r
-//     Is i_1 == 0 ?
-//
-       fma.s1 FR_r_cubed = FR_rsq, FR_r, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     c = C_hi - r
-//     Load  C_1
-//
-       fma.s1 FR_c = FR_c, f1, FR_C_lo
-      nop.i 999
-}
-
-{ .mfi
-      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
-(p10)  fms.s1 FR_prelim = f0, f1, FR_prelim
-      nop.i 999 ;;
-}
-
-{ .mfi
-      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 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p12)  fma.s1 FR_poly = FR_rsq, FR_poly, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//     if i_0 !=0: Result = -Result
-//
-(p9)   fma.s1 FR_Input_X = FR_prelim, f1, FR_poly
-      nop.i 999 ;;
-}
-
-{ .mfb
-      nop.m 999
-(p10)  fms.s1 FR_Input_X = FR_prelim, f1, FR_poly
-//
-//     if i_0 == 0: Result = Result + poly
-//     else         Result = Result - poly
-//
-       br.ret.sptk   b0 ;;
-}
-SINCOS_SMALL_R:
-
-{ .mii
-      nop.m 999
-        extr.u  GR_i_1 = GR_N_Inc, 0, 1 ;;
-//
-//
-//      Compare both i_1 and i_0 with 0.
-//      if i_1 == 0, set p9.
-//      if i_0 == 0, set p11.
-//
-        cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;;
-}
-
-{ .mfi
-      nop.m 999
-        fma.s1 FR_rsq = FR_r, FR_r, f0
-        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
-        cmp.eq.unc p11, p12 = 0x0, GR_i_0
-}
-;;
-
-// ******************************************************************
-// ******************************************************************
-// ******************************************************************
-//      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
-      addl           GR_Table_Base   = @ltoff(FSINCOS_CONSTANTS#), gp
-      nop.i 999
-}
-;;
-
-{ .mmi
-      ld8 GR_Table_Base = [GR_Table_Base]
-      nop.m 999
-      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 ;;
-}
-//
-//      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 ;;
-}
-
-{ .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
-//
-        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 ;;
-}
-
-{ .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 ;;
-}
-
-{ .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
-}
-
-{ .mfi
-      nop.m 999
-//
-//      c = -c * r
-//      dummy fmpy's to flag inexact.
-//
-(p9)    fma.d.s1 FR_S_4 = FR_S_4, FR_S_4, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//      poly_lo = FR_rsq * poly_lo + C_3
-//      poly_hi = FR_rsq * poly_hi
-//
-        fma.s1  FR_Z = FR_Z, FR_rsq, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p9)    fma.s1 FR_poly_hi = FR_rsq, FR_S_2, FR_S_1
-      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 ;;
-}
-
-{ .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 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_poly_hi = FR_rsq, FR_C_2, FR_C_1
-      nop.i 999
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.d.s1 FR_C_1 = FR_C_1, FR_C_1, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p9)    fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0
-      nop.i 999
-}
-
-{ .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 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0
-      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
-}
-
-{ .mfi
-      nop.m 999
-//
-//  poly_hi = r * poly_hi
-//
-        fma.s1  FR_poly = FR_Z, FR_poly_lo, FR_c
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p12)   fms.s1  FR_r = f0, f1, FR_r
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//      poly_hi = Z * poly_lo + c
-//  if i_0 == 1: r = -r
-//
-        fma.s1  FR_poly = FR_poly, f1, FR_poly_hi
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p12)   fms.s1 FR_Input_X = FR_r, f1, FR_poly
-      nop.i 999
-}
-
-{ .mfb
-      nop.m 999
-//
-//      poly = poly + poly_hi
-//
-(p11)   fma.s1 FR_Input_X = FR_r, f1, FR_poly
-//
-//      if (i_0 == 0) Result = r + poly
-//      if (i_0 != 0) Result = r - poly
-//
-       br.ret.sptk   b0 ;;
-}
-SINCOS_NORMAL_R:
-
-{ .mii
-      nop.m 999
-        extr.u  GR_i_1 = GR_N_Inc, 0, 1 ;;
-//
-//      Set table_ptr1 and table_ptr2 to base address of
-//      constant table.
-        cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;;
-}
-
-{ .mfi
-      nop.m 999
-        fma.s1  FR_rsq = FR_r, FR_r, f0
-        extr.u  GR_i_0 = GR_N_Inc, 1, 1 ;;
-}
-
-{ .mfi
-      nop.m 999
-        frcpa.s1 FR_r_hi, p6 = f1, FR_r
-        cmp.eq.unc p11, p12 = 0x0, GR_i_0
-}
-;;
-
-// ******************************************************************
-// ******************************************************************
-// ******************************************************************
-//
-//      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.
-//
-
-{ .mmi
-      nop.m 999
-      addl           GR_Table_Base   = @ltoff(FSINCOS_CONSTANTS#), gp
-      nop.i 999
-}
-;;
-
-{ .mmi
-      ld8 GR_Table_Base = [GR_Table_Base]
-      nop.m 999
-      nop.i 999
-}
-;;
-
-
-{ .mfi
-(p10)   add GR_Table_Base = 384, GR_Table_Base
-//(p12)   fms.s1 FR_Input_X = f0, f1, f1
-(p12)   fms.s1 FR_prelim = f0, f1, f1
-(p9)    add GR_Table_Base = 224, GR_Table_Base ;;
-}
-
-{ .mmf
-      nop.m 999
-(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 ;;
-(p11)   fma.s1 FR_prelim = f0, f1, f1 ;;
-}
-
-{ .mmf
-(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
-        fma.s1 FR_r_cubed = FR_r, FR_rsq, f0 ;;
-}
-
-{ .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
-//
-        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 ;;
-}
-
-{ .mmi
-(p10)   ldfe FR_QQ_4 = [GR_Table_Base], 16 ;;
-(p9)    ldfe FR_PP_1 = [GR_Table_Base], 16
-      nop.i 999 ;;
-}
-
-{ .mmf
-(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
-(p10)   fma.s1 FR_poly = FR_rsq, FR_QQ_8, FR_QQ_7 ;;
-}
-//
-//      if (i_1=0) poly = rsq * poly + PP_5
-//      else       poly = rsq * poly + QQ_5
-//      Load PP_4 or QQ_4
-//
-
-{ .mmf
-(p9)    ldfe FR_PP_3 = [GR_Table_Base], 16
-(p10)   ldfe FR_QQ_2 = [GR_Table_Base], 16
-//
-//      r_hi =   frcpa(frcpa(r)).
-//      r_cube = r * FR_rsq.
-//
-(p9)    fma.s1 FR_poly = FR_rsq, FR_PP_8, FR_PP_7 ;;
-}
-//
-//      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 ;;
-}
-
-{ .mmf
-      nop.m 999
-(p9)    ldfe FR_PP_1_lo = [GR_Table_Base], 16
-(p10)   fma.s1 FR_corr = FR_S_1, FR_r_cubed, FR_r
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_6
-      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 ;;
-}
-
-{ .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
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_U_lo = FR_r_hi, f1, FR_r
-      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
-}
-
-{ .mfi
-      nop.m 999
-//
-//      U_hi = r_hi * r_hi
-//
-        fms.s1 FR_r_lo = FR_r, f1, FR_r_hi
-      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
-//
-        fma.s1 FR_U_hi = FR_r_hi, FR_r_hi, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_5
-      nop.i 999
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fnma.s1 FR_corr = FR_corr, FR_c, f0
-      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 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p9)    fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_5
-      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.d.s1 FR_PP_5 = FR_PP_5, FR_PP_4, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p9)    fma.s1 FR_U_lo = FR_r, FR_r, FR_U_lo
-      nop.i 999
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0
-      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 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_4
-      nop.i 999
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_U_hi = FR_QQ_1, FR_U_hi, f1
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.d.s1 FR_QQ_5 = FR_QQ_5, FR_QQ_5, f0
-      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 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p9)    fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0
-      nop.i 999
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_U_lo = FR_QQ_1,FR_U_lo, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p9)    fma.s1 FR_U_hi = FR_PP_1, FR_U_hi, f0
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_3
-      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 ;;
-}
-
-{ .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 ;;
-}
-
-{ .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 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_2
-      nop.i 999 ;;
-}
-
-{ .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 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//      if (i_0==0)  Result = 1
-//      else         Result = -1
-//
-        fma.s1 FR_V = FR_U_lo, f1, FR_corr
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_poly = FR_rsq, FR_poly, f0
-      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 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p10)   fma.s1 FR_poly = FR_rsq, FR_poly, f0
-      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 ;;
-}
-
-{ .mfi
-      nop.m 999
-//
-//      if (i_1==0) poly = r_cube * poly
-//      else        poly = FR_rsq * poly
-//
-        fma.s1  FR_V = FR_poly, f1, FR_V
-      nop.i 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-//(p12)   fms.s1 FR_Input_X = FR_Input_X, FR_U_hi, FR_V
-(p12)   fms.s1 FR_Input_X = FR_prelim, FR_U_hi, FR_V
-      nop.i 999
-}
-
-{ .mfb
-      nop.m 999
-//
-//      V = V + poly
-//
-//(p11)   fma.s1 FR_Input_X = FR_Input_X, FR_U_hi, FR_V
-(p11)   fma.s1 FR_Input_X = FR_prelim, FR_U_hi, FR_V
-//
-//      if (i_0==0) Result = Result * U_hi + V
-//      else        Result = Result * U_hi - V
-//
-       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
-//
-SINCOS_ZERO:
-
-{ .mmb
-        cmp.eq.unc p6, p7 = 0x1, GR_Sin_or_Cos
-      nop.m 999
-      nop.b 999 ;;
-}
-
-{ .mfi
-      nop.m 999
-(p7)    fmerge.s FR_Input_X = FR_Input_X, FR_Input_X
-      nop.i 999
-}
-
-{ .mfb
-      nop.m 999
-(p6)    fmerge.s FR_Input_X = f1, f1
-       br.ret.sptk   b0 ;;
-}
-
-SINCOS_SPECIAL:
-
-//
-//      Path for Arg = +/- QNaN, SNaN, Inf
-//      Invalid can be raised. SNaNs
-//      become QNaNs
-//
-
-{ .mfb
-      nop.m 999
-        fmpy.s1 FR_Input_X = FR_Input_X, f0
-        br.ret.sptk   b0 ;;
-}
-GLOBAL_LIBM_END(__libm_cos_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 r49-50. 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_2)
-SINCOS_ARG_TOO_LARGE:
-
-.prologue
-//      Readjust Table ptr
-{ .mfi
-        adds  GR_Table_Base1 = -16, GR_Table_Base1
-        nop.f 999
-.save   ar.pfs,GR_SAVE_PFS
-        mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
-};;
-
-{ .mmi
-        ldfs FR_Two_to_M3 = [GR_Table_Base1],4
-        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
-        ldfs FR_Neg_Two_to_M3 = [GR_Table_Base1],0
-        nop.i 0
-        br.call.sptk b0=__libm_pi_by_2_reduce#
-};;
-
-{ .mfi
-        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
-};;
-
-{ .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
-};;
-
-{ .mbb
-        nop.m 999
-(p6)    br.cond.spnt SINCOS_SMALL_R            // Branch if |r| < 1/4
-        br.cond.sptk SINCOS_NORMAL_R ;;        // Branch if 1/4 <= |r| < pi/4
-}
-
-LOCAL_LIBM_END(__libm_callout_2)
-
-.type   __libm_pi_by_2_reduce#,@function
-.global __libm_pi_by_2_reduce#
-