Update.cvs/fedora-glibc-20050106T1443

2004-12-29  Jakub Jelinek  <jakub@redhat.com>

	* sysdeps/ia64/fpu/libm_support.h (__libm_error_support): Use
	libc_hidden_proto instead of HIDDEN_PROTO.
	* sysdeps/ia64/fpu/libm-symbols.h (HIDDEN_PROTO): Remove.
	(__libm_error_support): If ASSEMBLER and in libc, define to
	HIDDEN_JUMPTARGET(__libm_error_support).

2004-12-28  David Mosberger  <davidm@hpl.hp.com>

	* sysdeps/ia64/fpu/Makefile (duplicated-routines): New macro.
	(sysdep_routines): Replace libm_ldexp{,f,l} and libm_scalbn{,f,l}
	with $(duplicated-routines).
	(libm-sysdep_routines): Likewise, but substitute "s_" prefix for
	"m_" prefix.

2004-12-27  David Mosberger  <davidm@hpl.hp.com>

	* sysdeps/ia64/fpu/libm-symbols.h: Add include of <sysdep.h> and
	undefine "ret" macro.  Add __libm_error_support hidden definitions.

	* sysdeps/ia64/fpu/e_lgamma_r.c: Remove CVS-id comment.  Add
	missing portion of copyright statement.
	* sysdeps/ia64/fpu/e_lgammaf_r.c: Likewise.
	* sysdeps/ia64/fpu/e_lgammal_r.c: Likewise.

	* sysdeps/ia64/fpu/w_lgamma.c: Remove CVS-id comment.  Add
	missing portion of copyright statement.
	(__ieee754_lgamma): Rename from lgamma().  Make lgamma() a weak alias.
	(__ieee754_gamma): Likewise.
	* sysdeps/ia64/fpu/w_lgammaf.c: Likewise.
	* sysdeps/ia64/fpu/w_lgammal.c: Likewise.

2004-12-09  H. J. Lu <hjl@lucon.org>

	* sysdeps/ia64/fpu/s_nextafterl.c: Remove.
	* sysdeps/ia64/fpu/s_nexttoward.c: Likewise.
	* sysdeps/ia64/fpu/s_nexttowardf.c: Likewise.
	* sysdeps/ia64/fpu/e_atan2l.S: Remove (duplicate of e_atan2l.c).
	* sysdeps/ia64/fpu/e_expl.S: Likewise.
	* sysdeps/ia64/fpu/e_logl.c: Remove (conflicts with e_logl.S).

2004-11-18  David Mosberger  <davidm@hpl.hp.com>

	* sysdeps/ia64/fpu/README: New file.
	* sysdeps/ia64/fpu/gen_import_file_list: New file.
	* sysdeps/ia64/fpu/import_check: Likewise.
	* sysdeps/ia64/fpu/import_diffs: Likewise.
	* sysdeps/ia64/fpu/import_file.awk: Likewise.
	* sysdeps/ia64/fpu/import_intel_libm: Likewise.
	* sysdeps/ia64/fpu/libm-symbols.h: Likewise.

	* sysdeps/ia64/fpu/e_acos.S: Update from Intel libm v2.1+.
	* sysdeps/ia64/fpu/e_acosf.S: Likewise.
	* sysdeps/ia64/fpu/e_acosl.S: Likewise.
	* sysdeps/ia64/fpu/e_asin.S: Likewise.
	* sysdeps/ia64/fpu/e_asinf.S: Likewise.
	* sysdeps/ia64/fpu/e_asinl.S: Likewise.
	* sysdeps/ia64/fpu/e_atan2.S: Likewise.
	* sysdeps/ia64/fpu/e_atan2f.S: Likewise.
	* sysdeps/ia64/fpu/e_cosh.S: Likewise.
	* sysdeps/ia64/fpu/e_coshf.S: Likewise.
	* sysdeps/ia64/fpu/e_coshl.S: Likewise.
	* sysdeps/ia64/fpu/e_exp.S: Likewise.
	* sysdeps/ia64/fpu/e_expf.S: Likewise.
	* sysdeps/ia64/fpu/e_fmod.S: Likewise.
	* sysdeps/ia64/fpu/e_fmodf.S: Likewise.
	* sysdeps/ia64/fpu/e_fmodl.S: Likewise.
	* sysdeps/ia64/fpu/e_hypot.S: Likewise.
	* sysdeps/ia64/fpu/e_hypotf.S: Likewise.
	* sysdeps/ia64/fpu/e_hypotl.S: Likewise.
	* sysdeps/ia64/fpu/e_log.S: Likewise.
	* sysdeps/ia64/fpu/e_log2.S: Likewise.
	* sysdeps/ia64/fpu/e_log2f.S: Likewise.
	* sysdeps/ia64/fpu/e_log2l.S: Likewise.
	* sysdeps/ia64/fpu/e_logf.S: Likewise.
	* sysdeps/ia64/fpu/e_pow.S: Likewise.
	* sysdeps/ia64/fpu/e_powf.S: Likewise.
	* sysdeps/ia64/fpu/e_powl.S: Likewise.
	* sysdeps/ia64/fpu/e_remainder.S: Likewise.
	* sysdeps/ia64/fpu/e_remainderf.S: Likewise.
	* sysdeps/ia64/fpu/e_remainderl.S: Likewise.
	* sysdeps/ia64/fpu/e_scalb.S: Likewise.
	* sysdeps/ia64/fpu/e_scalbf.S: Likewise.
	* sysdeps/ia64/fpu/e_scalbl.S: Likewise.
	* sysdeps/ia64/fpu/e_sinh.S: Likewise.
	* sysdeps/ia64/fpu/e_sinhf.S: Likewise.
	* sysdeps/ia64/fpu/e_sinhl.S: Likewise.
	* sysdeps/ia64/fpu/e_sqrt.S: Likewise.
	* sysdeps/ia64/fpu/e_sqrtf.S: Likewise.
	* sysdeps/ia64/fpu/e_sqrtl.S: Likewise.
	* sysdeps/ia64/fpu/libm_error.c: Likewise.
	* sysdeps/ia64/fpu/libm_reduce.c: Likewise.
	* sysdeps/ia64/fpu/libm_support.h: Likewise.
	* sysdeps/ia64/fpu/s_atan.S: Likewise.
	* sysdeps/ia64/fpu/s_atanf.S: Likewise.
	* sysdeps/ia64/fpu/s_atanl.S: Likewise.
	* sysdeps/ia64/fpu/s_cbrt.S: Likewise.
	* sysdeps/ia64/fpu/s_cbrtf.S: Likewise.
	* sysdeps/ia64/fpu/s_cbrtl.S: Likewise.
	* sysdeps/ia64/fpu/s_ceil.S: Likewise.
	* sysdeps/ia64/fpu/s_ceilf.S: Likewise.
	* sysdeps/ia64/fpu/s_ceill.S: Likewise.
	* sysdeps/ia64/fpu/s_cos.S: Likewise.
	* sysdeps/ia64/fpu/s_cosf.S: Likewise.
	* sysdeps/ia64/fpu/s_cosl.S: Likewise.
	* sysdeps/ia64/fpu/s_expm1.S: Likewise.
	* sysdeps/ia64/fpu/s_expm1f.S: Likewise.
	* sysdeps/ia64/fpu/s_expm1l.S: Likewise.
	* sysdeps/ia64/fpu/s_fabs.S: Likewise.
	* sysdeps/ia64/fpu/s_fabsf.S: Likewise.
	* sysdeps/ia64/fpu/s_fabsl.S: Likewise.
	* sysdeps/ia64/fpu/s_floor.S: Likewise.
	* sysdeps/ia64/fpu/s_floorf.S: Likewise.
	* sysdeps/ia64/fpu/s_floorl.S: Likewise.
	* sysdeps/ia64/fpu/s_frexp.c: Likewise.
	* sysdeps/ia64/fpu/s_frexpf.c: Likewise.
	* sysdeps/ia64/fpu/s_frexpl.c: Likewise.
	* sysdeps/ia64/fpu/s_ilogb.S: Likewise.
	* sysdeps/ia64/fpu/s_ilogbf.S: Likewise.
	* sysdeps/ia64/fpu/s_ilogbl.S: Likewise.
	* sysdeps/ia64/fpu/s_log1p.S: Likewise.
	* sysdeps/ia64/fpu/s_log1pf.S: Likewise.
	* sysdeps/ia64/fpu/s_log1pl.S: Likewise.
	* sysdeps/ia64/fpu/s_logb.S: Likewise.
	* sysdeps/ia64/fpu/s_logbf.S: Likewise.
	* sysdeps/ia64/fpu/s_logbl.S: Likewise.
	* sysdeps/ia64/fpu/s_modf.S: Likewise.
	* sysdeps/ia64/fpu/s_modff.S: Likewise.
	* sysdeps/ia64/fpu/s_modfl.S: Likewise.
	* sysdeps/ia64/fpu/s_nearbyint.S: Likewise.
	* sysdeps/ia64/fpu/s_nearbyintf.S: Likewise.
	* sysdeps/ia64/fpu/s_nearbyintl.S: Likewise.
	* sysdeps/ia64/fpu/s_rint.S: Likewise.
	* sysdeps/ia64/fpu/s_rintf.S: Likewise.
	* sysdeps/ia64/fpu/s_rintl.S: Likewise.
	* sysdeps/ia64/fpu/s_round.S: Likewise.
	* sysdeps/ia64/fpu/s_roundf.S: Likewise.
	* sysdeps/ia64/fpu/s_roundl.S: Likewise.
	* sysdeps/ia64/fpu/s_significand.S: Likewise.
	* sysdeps/ia64/fpu/s_significandf.S: Likewise.
	* sysdeps/ia64/fpu/s_significandl.S: Likewise.
	* sysdeps/ia64/fpu/s_tan.S: Likewise.
	* sysdeps/ia64/fpu/s_tanf.S: Likewise.
	* sysdeps/ia64/fpu/s_tanl.S: Likewise.
	* sysdeps/ia64/fpu/s_trunc.S: Likewise.
	* sysdeps/ia64/fpu/s_truncf.S: Likewise.
	* sysdeps/ia64/fpu/s_truncl.S: Likewise.

	* sysdeps/ia64/fpu/e_acosh.S: New file from Intel libm v2.1+.
	* sysdeps/ia64/fpu/e_acoshf.S: Likewise.
	* sysdeps/ia64/fpu/e_acoshl.S: Likewise.
	* sysdeps/ia64/fpu/e_atanh.S: Likewise.
	* sysdeps/ia64/fpu/e_atanhf.S: Likewise.
	* sysdeps/ia64/fpu/e_atanhl.S: Likewise.
	* sysdeps/ia64/fpu/e_exp10.S: Likewise.
	* sysdeps/ia64/fpu/e_exp10f.S: Likewise.
	* sysdeps/ia64/fpu/e_exp10l.S: Likewise.
	* sysdeps/ia64/fpu/e_exp2.S: Likewise.
	* sysdeps/ia64/fpu/e_exp2f.S: Likewise.
	* sysdeps/ia64/fpu/e_exp2l.S: Likewise.
	* sysdeps/ia64/fpu/e_lgamma_r.S: Likewise.
	* sysdeps/ia64/fpu/e_lgammaf_r.S: Likewise.
	* sysdeps/ia64/fpu/e_lgammal_r.S: Likewise.
	* sysdeps/ia64/fpu/e_logl.S: Likewise.
	* sysdeps/ia64/fpu/libm_frexp.S: Likewise.
	* sysdeps/ia64/fpu/libm_frexpf.S: Likewise.
	* sysdeps/ia64/fpu/libm_frexpl.S: Likewise.
	* sysdeps/ia64/fpu/s_libm_ldexp.S: Likewise.
	* sysdeps/ia64/fpu/s_libm_ldexpf.S: Likewise.
	* sysdeps/ia64/fpu/s_libm_ldexpl.S: Likewise.
	* sysdeps/ia64/fpu/s_libm_scalbn.S: Likewise.
	* sysdeps/ia64/fpu/s_libm_scalbnf.S: Likewise.
	* sysdeps/ia64/fpu/s_libm_scalbnl.S: Likewise.
	* sysdeps/ia64/fpu/libm_lgamma.S: Likewise.
	* sysdeps/ia64/fpu/libm_lgammaf.S: Likewise.
	* sysdeps/ia64/fpu/libm_lgammal.S: Likewise.
	* sysdeps/ia64/fpu/libm_sincos.S: Likewise.
	* sysdeps/ia64/fpu/libm_sincos_large.S: Likewise.
	* sysdeps/ia64/fpu/libm_sincosf.S: Likewise.
	* sysdeps/ia64/fpu/libm_sincosl.S: Likewise.
	* sysdeps/ia64/fpu/libm_scalblnf.S: Likewise.
	* sysdeps/ia64/fpu/s_asinh.S: Likewise.
	* sysdeps/ia64/fpu/s_asinhf.S: Likewise.
	* sysdeps/ia64/fpu/s_asinhl.S: Likewise.
	* sysdeps/ia64/fpu/s_erf.S: Likewise.
	* sysdeps/ia64/fpu/s_erfc.S: Likewise.
	* sysdeps/ia64/fpu/s_erfcf.S: Likewise.
	* sysdeps/ia64/fpu/s_erfcl.S: Likewise.
	* sysdeps/ia64/fpu/s_erff.S: Likewise.
	* sysdeps/ia64/fpu/s_erfl.S: Likewise.
	* sysdeps/ia64/fpu/s_fdim.S: Likewise.
	* sysdeps/ia64/fpu/s_fdimf.S: Likewise.
	* sysdeps/ia64/fpu/s_fdiml.S: Likewise.
	* sysdeps/ia64/fpu/s_fma.S: Likewise.
	* sysdeps/ia64/fpu/s_fmaf.S: Likewise.
	* sysdeps/ia64/fpu/s_fmal.S: Likewise.
	* sysdeps/ia64/fpu/s_fmax.S: Likewise.
	* sysdeps/ia64/fpu/s_fmaxf.S: Likewise.
	* sysdeps/ia64/fpu/s_fmaxl.S: Likewise.
	* sysdeps/ia64/fpu/s_ldexp.c: Likewise.
	* sysdeps/ia64/fpu/s_ldexpf.c: Likewise.
	* sysdeps/ia64/fpu/s_ldexpl.c: Likewise.
	* sysdeps/ia64/fpu/s_nextafter.S: Likewise.
	* sysdeps/ia64/fpu/s_nextafterf.S: Likewise.
	* sysdeps/ia64/fpu/s_nextafterl.S: Likewise.
	* sysdeps/ia64/fpu/s_nexttoward.S: Likewise.
	* sysdeps/ia64/fpu/s_nexttowardf.S: Likewise.
	* sysdeps/ia64/fpu/s_nexttowardl.S: Likewise.
	* sysdeps/ia64/fpu/s_tanh.S: Likewise.
	* sysdeps/ia64/fpu/s_tanhf.S: Likewise.
	* sysdeps/ia64/fpu/s_tanhl.S: Likewise.
	* sysdeps/ia64/fpu/s_scalblnf.c: Likewise.
	* sysdeps/ia64/fpu/w_lgamma.c: Likewise.
	* sysdeps/ia64/fpu/w_lgammaf.c: Likewise.
	* sysdeps/ia64/fpu/w_lgammal.c: Likewise.
	* sysdeps/ia64/fpu/w_tgamma.S: Likewise.
	* sysdeps/ia64/fpu/w_tgammaf.S: Likewise.
	* sysdeps/ia64/fpu/w_tgammal.S: Likewise.

	* sysdeps/ia64/fpu/e_gamma_r.c: New empty dummy-file.
	* sysdeps/ia64/fpu/e_gammaf_r.c: Likewise.
	* sysdeps/ia64/fpu/e_gammal_r.c: Likewise.
	* sysdeps/ia64/fpu/w_acosh.c: Likewise.
	* sysdeps/ia64/fpu/w_acoshf.c: Likewise.
	* sysdeps/ia64/fpu/w_acoshl.c: Likewise.
	* sysdeps/ia64/fpu/w_atanh.c: Likewise.
	* sysdeps/ia64/fpu/w_atanhf.c: Likewise.
	* sysdeps/ia64/fpu/w_atanhl.c: Likewise.
	* sysdeps/ia64/fpu/w_exp10.c: Likewise.
	* sysdeps/ia64/fpu/w_exp10f.c: Likewise.
	* sysdeps/ia64/fpu/w_exp10l.c: Likewise.
	* sysdeps/ia64/fpu/w_exp2.c: Likewise.
	* sysdeps/ia64/fpu/w_exp2f.c: Likewise.
	* sysdeps/ia64/fpu/w_exp2l.c: Likewise.
	* sysdeps/ia64/fpu/w_expl.c: Likewise.
	* sysdeps/ia64/fpu/e_expl.S: Likewise.
	* sysdeps/ia64/fpu/w_lgamma_r.c: Likewise.
	* sysdeps/ia64/fpu/w_lgammaf_r.c: Likewise.
	* sysdeps/ia64/fpu/w_lgammal_r.c: Likewise.
	* sysdeps/ia64/fpu/w_log2.c: Likewise.
	* sysdeps/ia64/fpu/w_log2f.c: Likewise.
	* sysdeps/ia64/fpu/w_log2l.c: Likewise.
	* sysdeps/ia64/fpu/w_sinh.c: Likewise.
	* sysdeps/ia64/fpu/w_sinhf.c: Likewise.
	* sysdeps/ia64/fpu/w_sinhl.c: Likewise.

	* sysdeps/ia64/fpu/libm_atan2_reg.S: Remove.
	* sysdeps/ia64/fpu/s_ldexp.S: Likewise.
	* sysdeps/ia64/fpu/s_ldexpf.S: Likewise.
	* sysdeps/ia64/fpu/s_ldexpl.S: Likewise.
	* sysdeps/ia64/fpu/s_scalbn.S: Likewise.
	* sysdeps/ia64/fpu/s_scalbnf.S: Likewise.
	* sysdeps/ia64/fpu/s_scalbnl.S: Likewise.

	* sysdeps/ia64/fpu/s_sincos.c: Make it an empty dummy-file.
	* sysdeps/ia64/fpu/s_sincosf.c: Likewise.
	* sysdeps/ia64/fpu/s_sincosl.c: Likewise.

	* sysdeps/ia64/fpu/e_atan2l.S: Add "Not needed" comment.

	* sysdeps/ia64/fpu/s_copysign.S: Add __libm_copysign{,f,l}
	alias for use by libm_error.c

	* sysdeps/ia64/fpu/Makefile (libm-sysdep_routines): Remove
	libm_atan2_reg, libm_tan, libm_frexp4{f,l}.
	Mention s_erfc{,f,l}, libm_frexp{,f,l}, libm_ldexp{,f,l},
	libm_sincos{,f,l}, libm_sincos_large, libm_lgamma{,f,l},
	libm_scalbn{,f,l}, libm_scalblnf.
	(sysdep_routines): Remove libm_frexp4{,f,l}.
	Mention libm_frexp{,f,l}, libm_ldexp{,f,l}, and libm_scalbn{,f,l}.
	(sysdep-CPPFLAGS): Add -include libm-symbols.h, -D__POSIX__,
	_D_LIB_VERSIONIMF=_LIB_VERSION, -DSIZE_LONG_INT_64, and
	-DSIZE_LONG_LONG_INT_64.

1 files changed, 2754 insertions, 0 deletions

diff --git a/sysdeps/ia64/fpu/libm_sincos_large.S b/sysdeps/ia64/fpu/libm_sincos_large.S
new file mode 100644
index 0000000000..42cf0940f0
--- /dev/null
+++ b/sysdeps/ia64/fpu/libm_sincos_large.S
@@ -0,0 +1,2754 @@
+.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#
+