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+.file "tancotl.s"
+
+
+// Copyright (c) 2000 - 2004, Intel Corporation
+// All rights reserved.
+//
+// Contributed 2000 by the Intel Numerics Group, Intel Corporation
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are
+// 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:
+//
+// 02/02/00 (hand-optimized)
+// 04/04/00 Unwind support added
+// 12/28/00 Fixed false invalid flags
+// 02/06/02 Improved speed
+// 05/07/02 Changed interface to __libm_pi_by_2_reduce
+// 05/30/02 Added cotl
+// 02/10/03 Reordered header: .section, .global, .proc, .align;
+//          used data8 for long double table values
+// 05/15/03 Reformatted data tables
+// 10/26/04 Avoided using r14-31 as scratch so not clobbered by dynamic loader
+//
+//*********************************************************************
+//
+// Functions:   tanl(x) = tangent(x), for double-extended precision x values
+//              cotl(x) = cotangent(x), for double-extended precision x values
+//
+//*********************************************************************
+//
+// Resources Used:
+//
+//    Floating-Point Registers: f8 (Input and Return Value)
+//                              f9-f15
+//                              f32-f121
+//
+//    General Purpose Registers:
+//      r32-r70
+//
+//    Predicate Registers:      p6-p15
+//
+//*********************************************************************
+//
+// IEEE Special Conditions for tanl:
+//
+//    Denormal  fault raised on denormal inputs
+//    Overflow exceptions do not occur
+//    Underflow exceptions raised when appropriate for tan
+//    (No specialized error handling for this routine)
+//    Inexact raised when appropriate by algorithm
+//
+//    tanl(SNaN) = QNaN
+//    tanl(QNaN) = QNaN
+//    tanl(inf) = QNaN
+//    tanl(+/-0) = +/-0
+//
+//*********************************************************************
+//
+// IEEE Special Conditions for cotl:
+//
+//    Denormal  fault raised on denormal inputs
+//    Overflow exceptions occur at zero and near zero
+//    Underflow exceptions do not occur
+//    Inexact raised when appropriate by algorithm
+//
+//    cotl(SNaN) = QNaN
+//    cotl(QNaN) = QNaN
+//    cotl(inf) = QNaN
+//    cotl(+/-0) = +/-Inf and error handling is called
+//
+//*********************************************************************
+//
+//    Below are mathematical and algorithmic descriptions for tanl.
+//    For cotl we use next identity cot(x) = -tan(x + Pi/2).
+//    So, to compute cot(x) we just need to increment N (N = N + 1)
+//    and invert sign of the computed result.
+//
+//*********************************************************************
+//
+// Mathematical Description
+//
+// We consider the computation of FPTANL of Arg. Now, given
+//
+//      Arg = N pi/2  + alpha,          |alpha| <= pi/4,
+//
+// basic mathematical relationship shows that
+//
+//      tan( Arg ) =  tan( alpha )     if N is even;
+//                 = -cot( alpha )      otherwise.
+//
+// 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, tan(r+c) and -cot(r+c) can be
+// computed very easily by 2 or 3 terms of the Taylor series
+// expansion as follows:
+//
+// Case 2:
+// -------
+//
+//      tan(r + c) = r + c + r^3/3          ...accurately
+//     -cot(r + c) = -1/(r+c) + r/3          ...accurately
+//
+// Case 4:
+// -------
+//
+//      tan(r + c) = r + c + r^3/3 + 2r^5/15     ...accurately
+//     -cot(r + c) = -1/(r+c) + r/3 + r^3/45     ...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 greatest challenge of this task is that the second terms of
+// the Taylor series for tan(r) and -cot(r)
+//
+//      r + r^3/3 + 2 r^5/15 + ...
+//
+// and
+//
+//      -1/r + r/3 + r^3/45 + ...
+//
+// 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^(-2), however, the second terms will be small
+// enough (5 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 tan(r) and cot(r), |r| <= pi/4.
+//
+// Case small_r: |r| < 2^(-2)
+// --------------------------
+//
+// Since Arg = N pi/4 + r + c accurately, we have
+//
+//      tan(Arg) =  tan(r+c)            for N even,
+//               = -cot(r+c)            otherwise.
+//
+// Here for this case, both tan(r) and -cot(r) can be approximated
+// by simple polynomials:
+//
+//      tan(r) =    r + P1_1 r^3 + P1_2 r^5 + ... + P1_9 r^19
+//     -cot(r) = -1/r + Q1_1 r   + Q1_2 r^3 + ... + Q1_7 r^13
+//
+// accurately. Since |r| is relatively small, tan(r+c) and
+// -cot(r+c) can be accurately approximated by replacing r with
+// r+c only in the first two terms of the corresponding polynomials.
+//
+// Note that P1_1 (and Q1_1 for that matter) approximates 1/3 to
+// almost 64 sig. bits, thus
+//
+//      P1_1 (r+c)^3 =  P1_1 r^3 + c * r^2     accurately.
+//
+// Hence,
+//
+//      tan(r+c) =    r + P1_1 r^3 + P1_2 r^5 + ... + P1_9 r^19
+//                     + c*(1 + r^2)
+//
+//        -cot(r+c) = -1/(r+c) + Q1_1 r   + Q1_2 r^3 + ... + Q1_7 r^13
+//               + Q1_1*c
+//
+//
+// Case normal_r: 2^(-2) <= |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].
+//
+// The required calculation is either
+//
+//      tan(r + c)  =  tan(r)  +  correction,  or
+//     -cot(r + c)  = -cot(r)  +  correction.
+//
+// Specifically,
+//
+//      tan(r + c) =  tan(r) + c tan'(r)  + O(c^2)
+//                 =  tan(r) + c sec^2(r) + O(c^2)
+//                 =  tan(r) + c SEC_sq     ...accurately
+//                as long as SEC_sq approximates sec^2(r)
+//                to, say, 5 bits or so.
+//
+// Similarly,
+//
+//     -cot(r + c) = -cot(r) - c cot'(r)  + O(c^2)
+//                 = -cot(r) + c csc^2(r) + O(c^2)
+//                 = -cot(r) + c CSC_sq     ...accurately
+//                as long as CSC_sq approximates csc^2(r)
+//                to, say, 5 bits or so.
+//
+// We therefore concentrate on accurately calculating tan(r) and
+// cot(r) for a working-precision number r, |r| <= pi/4 to within
+// 0.1% or so.
+//
+// We will employ a table-driven approach. Let
+//
+//      r = sgn_r * 2^k * 1.b_1 b_2 ... b_5 ... b_63
+//        = sgn_r * ( B + x )
+//
+// where
+//
+//      B = 2^k * 1.b_1 b_2 ... b_5 1
+//      x = |r| - B
+//
+// Now,
+//                   tan(B)  +   tan(x)
+//      tan( B + x ) =  ------------------------
+//                   1 -  tan(B)*tan(x)
+//
+//               /                         \
+//               |   tan(B)  +   tan(x)          |
+
+//      = tan(B) +  | ------------------------ - tan(B) |
+//               |     1 -  tan(B)*tan(x)          |
+//               \                         /
+//
+//                 sec^2(B) * tan(x)
+//      = tan(B) + ------------------------
+//                 1 -  tan(B)*tan(x)
+//
+//                (1/[sin(B)*cos(B)]) * tan(x)
+//      = tan(B) + --------------------------------
+//                      cot(B)  -  tan(x)
+//
+//
+// Clearly, the values of tan(B), cot(B) and 1/(sin(B)*cos(B)) are
+// calculated beforehand and stored in a table. Since
+//
+//      |x| <= 2^k * 2^(-6)  <= 2^(-7)  (because k = -1, -2)
+//
+// a very short polynomial will be sufficient to approximate tan(x)
+// accurately. The details involved in computing the last expression
+// will be given in the next section on algorithm description.
+//
+//
+// Now, we turn to the case where cot( B + x ) is needed.
+//
+//
+//                   1 - tan(B)*tan(x)
+//      cot( B + x ) =  ------------------------
+//                   tan(B)  +  tan(x)
+//
+//               /                           \
+//               |   1 - tan(B)*tan(x)              |
+
+//      = cot(B) +  | ----------------------- - cot(B) |
+//               |     tan(B)  +  tan(x)            |
+//               \                           /
+//
+//               [tan(B) + cot(B)] * tan(x)
+//      = cot(B) - ----------------------------
+//                   tan(B)  +  tan(x)
+//
+//                (1/[sin(B)*cos(B)]) * tan(x)
+//      = cot(B) - --------------------------------
+//                      tan(B)  +  tan(x)
+//
+//
+// Note that the values of tan(B), cot(B) and 1/(sin(B)*cos(B)) that
+// are needed are the same set of values needed in the previous
+// case.
+//
+// Finally, we can put all the ingredients together as follows:
+//
+//      Arg = N * pi/2 +  r + c          ...accurately
+//
+//      tan(Arg) =  tan(r) + correction    if N is even;
+//               = -cot(r) + correction    otherwise.
+//
+// For Cases 2 and 4,
+//
+//     Case 2:
+//     tan(Arg) =  tan(r + c) = r + c + r^3/3           N even
+//              = -cot(r + c) = -1/(r+c) + r/3           N odd
+//     Case 4:
+//     tan(Arg) =  tan(r + c) = r + c + r^3/3 + 2r^5/15  N even
+//              = -cot(r + c) = -1/(r+c) + r/3 + r^3/45  N odd
+//
+//
+// For Cases 1 and 3,
+//
+//     Case small_r: |r| < 2^(-2)
+//
+//      tan(Arg) =  r + P1_1 r^3 + P1_2 r^5 + ... + P1_9 r^19
+//                     + c*(1 + r^2)               N even
+//
+//               = -1/(r+c) + Q1_1 r   + Q1_2 r^3 + ... + Q1_7 r^13
+//                     + Q1_1*c                    N odd
+//
+//     Case normal_r: 2^(-2) <= |r| <= pi/4
+//
+//      tan(Arg) =  tan(r) + c * sec^2(r)     N even
+//               = -cot(r) + c * csc^2(r)     otherwise
+//
+//     For N even,
+//
+//      tan(Arg) = tan(r) + c*sec^2(r)
+//               = tan( sgn_r * (B+x) ) + c * sec^2(|r|)
+//               = sgn_r * ( tan(B+x)  + sgn_r*c*sec^2(|r|) )
+//               = sgn_r * ( tan(B+x)  + sgn_r*c*sec^2(B) )
+//
+// since B approximates |r| to 2^(-6) in relative accuracy.
+//
+//                 /            (1/[sin(B)*cos(B)]) * tan(x)
+//    tan(Arg) = sgn_r * | tan(B) + --------------------------------
+//                 \                     cot(B)  -  tan(x)
+//                                        \
+//                       + CORR  |
+
+//                                     /
+// where
+//
+//    CORR = sgn_r*c*tan(B)*SC_inv(B);  SC_inv(B) = 1/(sin(B)*cos(B)).
+//
+// For N odd,
+//
+//      tan(Arg) = -cot(r) + c*csc^2(r)
+//               = -cot( sgn_r * (B+x) ) + c * csc^2(|r|)
+//               = sgn_r * ( -cot(B+x)  + sgn_r*c*csc^2(|r|) )
+//               = sgn_r * ( -cot(B+x)  + sgn_r*c*csc^2(B) )
+//
+// since B approximates |r| to 2^(-6) in relative accuracy.
+//
+//                 /            (1/[sin(B)*cos(B)]) * tan(x)
+//    tan(Arg) = sgn_r * | -cot(B) + --------------------------------
+//                 \                     tan(B)  +  tan(x)
+//                                        \
+//                       + CORR  |
+
+//                                     /
+// where
+//
+//    CORR = sgn_r*c*cot(B)*SC_inv(B);  SC_inv(B) = 1/(sin(B)*cos(B)).
+//
+//
+// The actual algorithm prescribes how all the mathematical formulas
+// are calculated.
+//
+//
+// 2. Algorithmic Description
+// ==========================
+//
+// 2.1 Computation for Cases 2 and 4.
+// ----------------------------------
+//
+// For Case 2, we use two-term polynomials.
+//
+//    For N even,
+//
+//    rsq := r * r
+//    Poly := c + r * rsq * P1_1
+//    Result := r + Poly          ...in user-defined rounding
+//
+//    For N odd,
+//    S_hi  := -frcpa(r)               ...8 bits
+//    S_hi  := S_hi + S_hi*(1 + S_hi*r)     ...16 bits
+//    S_hi  := S_hi + S_hi*(1 + S_hi*r)     ...32 bits
+//    S_hi  := S_hi + S_hi*(1 + S_hi*r)     ...64 bits
+//    S_lo  := S_hi*( (1 + S_hi*r) + S_hi*c )
+//    ...S_hi + S_lo is -1/(r+c) to extra precision
+//    S_lo  := S_lo + Q1_1*r
+//
+//    Result := S_hi + S_lo     ...in user-defined rounding
+//
+// For Case 4, we use three-term polynomials
+//
+//    For N even,
+//
+//    rsq := r * r
+//    Poly := c + r * rsq * (P1_1 + rsq * P1_2)
+//    Result := r + Poly          ...in user-defined rounding
+//
+//    For N odd,
+//    S_hi  := -frcpa(r)               ...8 bits
+//    S_hi  := S_hi + S_hi*(1 + S_hi*r)     ...16 bits
+//    S_hi  := S_hi + S_hi*(1 + S_hi*r)     ...32 bits
+//    S_hi  := S_hi + S_hi*(1 + S_hi*r)     ...64 bits
+//    S_lo  := S_hi*( (1 + S_hi*r) + S_hi*c )
+//    ...S_hi + S_lo is -1/(r+c) to extra precision
+//    rsq   := r * r
+//    P      := Q1_1 + rsq*Q1_2
+//    S_lo  := S_lo + r*P
+//
+//    Result := S_hi + S_lo     ...in user-defined rounding
+//
+//
+// Note that the coefficients P1_1, P1_2, Q1_1, and Q1_2 are
+// the same as those used in the small_r case of Cases 1 and 3
+// below.
+//
+//
+// 2.2 Computation for Cases 1 and 3.
+// ----------------------------------
+// This is further divided into the case of small_r,
+// where |r| < 2^(-2), and the case of normal_r, where |r| lies between
+// 2^(-2) and pi/4.
+//
+// Algorithm for the case of small_r
+// ---------------------------------
+//
+// For N even,
+//      rsq   := r * r
+//      Poly1 := rsq*(P1_1 + rsq*(P1_2 + rsq*P1_3))
+//      r_to_the_8    := rsq * rsq
+//      r_to_the_8    := r_to_the_8 * r_to_the_8
+//      Poly2 := P1_4 + rsq*(P1_5 + rsq*(P1_6 + ... rsq*P1_9))
+//      CORR  := c * ( 1 + rsq )
+//      Poly  := Poly1 + r_to_the_8*Poly2
+//      Poly := r*Poly + CORR
+//      Result := r + Poly     ...in user-defined rounding
+//      ...note that Poly1 and r_to_the_8 can be computed in parallel
+//      ...with Poly2 (Poly1 is intentionally set to be much
+//      ...shorter than Poly2 so that r_to_the_8 and CORR can be hidden)
+//
+// For N odd,
+//      S_hi  := -frcpa(r)               ...8 bits
+//      S_hi  := S_hi + S_hi*(1 + S_hi*r)     ...16 bits
+//      S_hi  := S_hi + S_hi*(1 + S_hi*r)     ...32 bits
+//      S_hi  := S_hi + S_hi*(1 + S_hi*r)     ...64 bits
+//      S_lo  := S_hi*( (1 + S_hi*r) + S_hi*c )
+//      ...S_hi + S_lo is -1/(r+c) to extra precision
+//      S_lo  := S_lo + Q1_1*c
+//
+//      ...S_hi and S_lo are computed in parallel with
+//      ...the following
+//      rsq := r*r
+//      P   := Q1_1 + rsq*(Q1_2 + rsq*(Q1_3 + ... + rsq*Q1_7))
+//
+//      Poly :=  r*P + S_lo
+//      Result :=  S_hi  +  Poly      ...in user-defined rounding
+//
+//
+// Algorithm for the case of normal_r
+// ----------------------------------
+//
+// Here, we first consider the computation of tan( r + c ). As
+// presented in the previous section,
+//
+//      tan( r + c )  =  tan(r) + c * sec^2(r)
+//                 =  sgn_r * [ tan(B+x) + CORR ]
+//      CORR = sgn_r * c * tan(B) * 1/[sin(B)*cos(B)]
+//
+// because sec^2(r) = sec^(|r|), and B approximate |r| to 6.5 bits.
+//
+//      tan( r + c ) =
+//           /           (1/[sin(B)*cos(B)]) * tan(x)
+//      sgn_r * | tan(B) + --------------------------------  +
+//           \                     cot(B)  -  tan(x)
+//                                \
+//                          CORR  |
+
+//                                /
+//
+// The values of tan(B), cot(B) and 1/(sin(B)*cos(B)) are
+// calculated beforehand and stored in a table. Specifically,
+// the table values are
+//
+//      tan(B)             as  T_hi  +  T_lo;
+//      cot(B)             as  C_hi  +  C_lo;
+//      1/[sin(B)*cos(B)]  as  SC_inv
+//
+// T_hi, C_hi are in  double-precision  memory format;
+// T_lo, C_lo are in  single-precision  memory format;
+// SC_inv     is  in extended-precision memory format.
+//
+// The value of tan(x) will be approximated by a short polynomial of
+// the form
+//
+//      tan(x)  as  x  +  x * P, where
+//           P  =   x^2 * (P2_1 + x^2 * (P2_2 + x^2 * P2_3))
+//
+// Because |x| <= 2^(-7), cot(B) - x approximates cot(B) - tan(x)
+// to a relative accuracy better than 2^(-20). Thus, a good
+// initial guess of 1/( cot(B) - tan(x) ) to initiate the iterative
+// division is:
+//
+//      1/(cot(B) - tan(x))      is approximately
+//      1/(cot(B) -   x)         is
+//      tan(B)/(1 - x*tan(B))    is approximately
+//      T_hi / ( 1 - T_hi * x )  is approximately
+//
+//      T_hi * [ 1 + (Thi * x) + (T_hi * x)^2 ]
+//
+// The calculation of tan(r+c) therefore proceed as follows:
+//
+//      Tx     := T_hi * x
+//      xsq     := x * x
+//
+//      V_hi     := T_hi*(1 + Tx*(1 + Tx))
+//      P     := xsq * (P1_1 + xsq*(P1_2 + xsq*P1_3))
+//      ...V_hi serves as an initial guess of 1/(cot(B) - tan(x))
+//         ...good to about 20 bits of accuracy
+//
+//      tanx     := x + x*P
+//      D     := C_hi - tanx
+//      ...D is a double precision denominator: cot(B) - tan(x)
+//
+//      V_hi     := V_hi + V_hi*(1 - V_hi*D)
+//      ....V_hi approximates 1/(cot(B)-tan(x)) to 40 bits
+//
+//      V_lo     := V_hi * ( [ (1 - V_hi*C_hi) + V_hi*tanx ]
+//                           - V_hi*C_lo )   ...observe all order
+//         ...V_hi + V_lo approximates 1/(cot(B) - tan(x))
+//      ...to extra accuracy
+//
+//      ...               SC_inv(B) * (x + x*P)
+//      ...   tan(B) +      ------------------------- + CORR
+//         ...                cot(B) - (x + x*P)
+//      ...
+//      ... = tan(B) + SC_inv(B)*(x + x*P)*(V_hi + V_lo) + CORR
+//      ...
+//
+//      Sx     := SC_inv * x
+//      CORR     := sgn_r * c * SC_inv * T_hi
+//
+//      ...put the ingredients together to compute
+//      ...               SC_inv(B) * (x + x*P)
+//      ...   tan(B) +      ------------------------- + CORR
+//         ...                cot(B) - (x + x*P)
+//      ...
+//      ... = tan(B) + SC_inv(B)*(x + x*P)*(V_hi + V_lo) + CORR
+//      ...
+//      ... = T_hi + T_lo + CORR +
+//      ...    Sx * V_hi + Sx * V_lo + Sx * P *(V_hi + V_lo)
+//
+//      CORR := CORR + T_lo
+//      tail := V_lo + P*(V_hi + V_lo)
+//         tail := Sx * tail  +  CORR
+//      tail := Sx * V_hi  +  tail
+//         T_hi := sgn_r * T_hi
+//
+//         ...T_hi + sgn_r*tail  now approximate
+//      ...sgn_r*(tan(B+x) + CORR) accurately
+//
+//      Result :=  T_hi + sgn_r*tail  ...in user-defined
+//                           ...rounding control
+//      ...It is crucial that independent paths be fully
+//      ...exploited for performance's sake.
+//
+//
+// Next, we consider the computation of -cot( r + c ). As
+// presented in the previous section,
+//
+//        -cot( r + c )  =  -cot(r) + c * csc^2(r)
+//                 =  sgn_r * [ -cot(B+x) + CORR ]
+//      CORR = sgn_r * c * cot(B) * 1/[sin(B)*cos(B)]
+//
+// because csc^2(r) = csc^(|r|), and B approximate |r| to 6.5 bits.
+//
+//        -cot( r + c ) =
+//           /             (1/[sin(B)*cos(B)]) * tan(x)
+//      sgn_r * | -cot(B) + --------------------------------  +
+//           \                     tan(B)  +  tan(x)
+//                                \
+//                          CORR  |
+
+//                                /
+//
+// The values of tan(B), cot(B) and 1/(sin(B)*cos(B)) are
+// calculated beforehand and stored in a table. Specifically,
+// the table values are
+//
+//      tan(B)             as  T_hi  +  T_lo;
+//      cot(B)             as  C_hi  +  C_lo;
+//      1/[sin(B)*cos(B)]  as  SC_inv
+//
+// T_hi, C_hi are in  double-precision  memory format;
+// T_lo, C_lo are in  single-precision  memory format;
+// SC_inv     is  in extended-precision memory format.
+//
+// The value of tan(x) will be approximated by a short polynomial of
+// the form
+//
+//      tan(x)  as  x  +  x * P, where
+//           P  =   x^2 * (P2_1 + x^2 * (P2_2 + x^2 * P2_3))
+//
+// Because |x| <= 2^(-7), tan(B) + x approximates tan(B) + tan(x)
+// to a relative accuracy better than 2^(-18). Thus, a good
+// initial guess of 1/( tan(B) + tan(x) ) to initiate the iterative
+// division is:
+//
+//      1/(tan(B) + tan(x))      is approximately
+//      1/(tan(B) +   x)         is
+//      cot(B)/(1 + x*cot(B))    is approximately
+//      C_hi / ( 1 + C_hi * x )  is approximately
+//
+//      C_hi * [ 1 - (C_hi * x) + (C_hi * x)^2 ]
+//
+// The calculation of -cot(r+c) therefore proceed as follows:
+//
+//      Cx     := C_hi * x
+//      xsq     := x * x
+//
+//      V_hi     := C_hi*(1 - Cx*(1 - Cx))
+//      P     := xsq * (P1_1 + xsq*(P1_2 + xsq*P1_3))
+//      ...V_hi serves as an initial guess of 1/(tan(B) + tan(x))
+//         ...good to about 18 bits of accuracy
+//
+//      tanx     := x + x*P
+//      D     := T_hi + tanx
+//      ...D is a double precision denominator: tan(B) + tan(x)
+//
+//      V_hi     := V_hi + V_hi*(1 - V_hi*D)
+//      ....V_hi approximates 1/(tan(B)+tan(x)) to 40 bits
+//
+//      V_lo     := V_hi * ( [ (1 - V_hi*T_hi) - V_hi*tanx ]
+//                           - V_hi*T_lo )   ...observe all order
+//         ...V_hi + V_lo approximates 1/(tan(B) + tan(x))
+//      ...to extra accuracy
+//
+//      ...               SC_inv(B) * (x + x*P)
+//      ...  -cot(B) +      ------------------------- + CORR
+//         ...                tan(B) + (x + x*P)
+//      ...
+//      ... =-cot(B) + SC_inv(B)*(x + x*P)*(V_hi + V_lo) + CORR
+//      ...
+//
+//      Sx     := SC_inv * x
+//      CORR     := sgn_r * c * SC_inv * C_hi
+//
+//      ...put the ingredients together to compute
+//      ...               SC_inv(B) * (x + x*P)
+//      ...  -cot(B) +      ------------------------- + CORR
+//         ...                tan(B) + (x + x*P)
+//      ...
+//      ... =-cot(B) + SC_inv(B)*(x + x*P)*(V_hi + V_lo) + CORR
+//      ...
+//      ... =-C_hi - C_lo + CORR +
+//      ...    Sx * V_hi + Sx * V_lo + Sx * P *(V_hi + V_lo)
+//
+//      CORR := CORR - C_lo
+//      tail := V_lo + P*(V_hi + V_lo)
+//         tail := Sx * tail  +  CORR
+//      tail := Sx * V_hi  +  tail
+//         C_hi := -sgn_r * C_hi
+//
+//         ...C_hi + sgn_r*tail now approximates
+//      ...sgn_r*(-cot(B+x) + CORR) accurately
+//
+//      Result :=  C_hi + sgn_r*tail   in user-defined rounding control
+//      ...It is crucial that independent paths be fully
+//      ...exploited for performance's sake.
+//
+// 3. Implementation Notes
+// =======================
+//
+//   Table entries T_hi, T_lo; C_hi, C_lo; SC_inv
+//
+//   Recall that 2^(-2) <= |r| <= pi/4;
+//
+//      r = sgn_r * 2^k * 1.b_1 b_2 ... b_63
+//
+//   and
+//
+//        B = 2^k * 1.b_1 b_2 b_3 b_4 b_5 1
+//
+//   Thus, for k = -2, possible values of B are
+//
+//          B = 2^(-2) * ( 1 + index/32  +  1/64 ),
+//      index ranges from 0 to 31
+//
+//   For k = -1, however, since |r| <= pi/4 = 0.78...
+//   possible values of B are
+//
+//        B = 2^(-1) * ( 1 + index/32  +  1/64 )
+//      index ranges from 0 to 19.
+//
+//
+
+RODATA
+.align 16
+
+LOCAL_OBJECT_START(TANL_BASE_CONSTANTS)
+
+tanl_table_1:
+data8    0xA2F9836E4E44152A, 0x00003FFE // two_by_pi
+data8    0xC84D32B0CE81B9F1, 0x00004016 // P_0
+data8    0xC90FDAA22168C235, 0x00003FFF // P_1
+data8    0xECE675D1FC8F8CBB, 0x0000BFBD // P_2
+data8    0xB7ED8FBBACC19C60, 0x0000BF7C // P_3
+LOCAL_OBJECT_END(TANL_BASE_CONSTANTS)
+
+LOCAL_OBJECT_START(tanl_table_2)
+data8    0xC90FDAA22168C234, 0x00003FFE // PI_BY_4
+data8    0xA397E5046EC6B45A, 0x00003FE7 // Inv_P_0
+data8    0x8D848E89DBD171A1, 0x0000BFBF // d_1
+data8    0xD5394C3618A66F8E, 0x0000BF7C // d_2
+data4    0x3E800000 // two**-2
+data4    0xBE800000 // -two**-2
+data4    0x00000000 // pad
+data4    0x00000000 // pad
+LOCAL_OBJECT_END(tanl_table_2)
+
+LOCAL_OBJECT_START(tanl_table_p1)
+data8    0xAAAAAAAAAAAAAABD, 0x00003FFD // P1_1
+data8    0x8888888888882E6A, 0x00003FFC // P1_2
+data8    0xDD0DD0DD0F0177B6, 0x00003FFA // P1_3
+data8    0xB327A440646B8C6D, 0x00003FF9 // P1_4
+data8    0x91371B251D5F7D20, 0x00003FF8 // P1_5
+data8    0xEB69A5F161C67914, 0x00003FF6 // P1_6
+data8    0xBEDD37BE019318D2, 0x00003FF5 // P1_7
+data8    0x9979B1463C794015, 0x00003FF4 // P1_8
+data8    0x8EBD21A38C6EB58A, 0x00003FF3 // P1_9
+LOCAL_OBJECT_END(tanl_table_p1)
+
+LOCAL_OBJECT_START(tanl_table_q1)
+data8    0xAAAAAAAAAAAAAAB4, 0x00003FFD // Q1_1
+data8    0xB60B60B60B5FC93E, 0x00003FF9 // Q1_2
+data8    0x8AB355E00C9BBFBF, 0x00003FF6 // Q1_3
+data8    0xDDEBBC89CBEE3D4C, 0x00003FF2 // Q1_4
+data8    0xB3548A685F80BBB6, 0x00003FEF // Q1_5
+data8    0x913625604CED5BF1, 0x00003FEC // Q1_6
+data8    0xF189D95A8EE92A83, 0x00003FE8 // Q1_7
+LOCAL_OBJECT_END(tanl_table_q1)
+
+LOCAL_OBJECT_START(tanl_table_p2)
+data8    0xAAAAAAAAAAAB362F, 0x00003FFD // P2_1
+data8    0x88888886E97A6097, 0x00003FFC // P2_2
+data8    0xDD108EE025E716A1, 0x00003FFA // P2_3
+LOCAL_OBJECT_END(tanl_table_p2)
+
+LOCAL_OBJECT_START(tanl_table_tm2)
+//
+//  Entries T_hi   double-precision memory format
+//  Index = 0,1,...,31  B = 2^(-2)*(1+Index/32+1/64)
+//  Entries T_lo  single-precision memory format
+//  Index = 0,1,...,31  B = 2^(-2)*(1+Index/32+1/64)
+//
+data8 0x3FD09BC362400794
+data4 0x23A05C32, 0x00000000
+data8 0x3FD124A9DFFBC074
+data4 0x240078B2, 0x00000000
+data8 0x3FD1AE235BD4920F
+data4 0x23826B8E, 0x00000000
+data8 0x3FD2383515E2701D
+data4 0x22D31154, 0x00000000
+data8 0x3FD2C2E463739C2D
+data4 0x2265C9E2, 0x00000000
+data8 0x3FD34E36AFEEA48B
+data4 0x245C05EB, 0x00000000
+data8 0x3FD3DA317DBB35D1
+data4 0x24749F2D, 0x00000000
+data8 0x3FD466DA67321619
+data4 0x2462CECE, 0x00000000
+data8 0x3FD4F4371F94A4D5
+data4 0x246D0DF1, 0x00000000
+data8 0x3FD5824D740C3E6D
+data4 0x240A85B5, 0x00000000
+data8 0x3FD611234CB1E73D
+data4 0x23F96E33, 0x00000000
+data8 0x3FD6A0BEAD9EA64B
+data4 0x247C5393, 0x00000000
+data8 0x3FD73125B804FD01
+data4 0x241F3B29, 0x00000000
+data8 0x3FD7C25EAB53EE83
+data4 0x2479989B, 0x00000000
+data8 0x3FD8546FE6640EED
+data4 0x23B343BC, 0x00000000
+data8 0x3FD8E75FE8AF1892
+data4 0x241454D1, 0x00000000
+data8 0x3FD97B3553928BDA
+data4 0x238613D9, 0x00000000
+data8 0x3FDA0FF6EB9DE4DE
+data4 0x22859FA7, 0x00000000
+data8 0x3FDAA5AB99ECF92D
+data4 0x237A6D06, 0x00000000
+data8 0x3FDB3C5A6D8F1796
+data4 0x23952F6C, 0x00000000
+data8 0x3FDBD40A9CFB8BE4
+data4 0x2280FC95, 0x00000000
+data8 0x3FDC6CC387943100
+data4 0x245D2EC0, 0x00000000
+data8 0x3FDD068CB736C500
+data4 0x23C4AD7D, 0x00000000
+data8 0x3FDDA16DE1DDBC31
+data4 0x23D076E6, 0x00000000
+data8 0x3FDE3D6EEB515A93
+data4 0x244809A6, 0x00000000
+data8 0x3FDEDA97E6E9E5F1
+data4 0x220856C8, 0x00000000
+data8 0x3FDF78F11963CE69
+data4 0x244BE993, 0x00000000
+data8 0x3FE00C417D635BCE
+data4 0x23D21799, 0x00000000
+data8 0x3FE05CAB1C302CD3
+data4 0x248A1B1D, 0x00000000
+data8 0x3FE0ADB9DB6A1FA0
+data4 0x23D53E33, 0x00000000
+data8 0x3FE0FF724A20BA81
+data4 0x24DB9ED5, 0x00000000
+data8 0x3FE151D9153FA6F5
+data4 0x24E9E451, 0x00000000
+LOCAL_OBJECT_END(tanl_table_tm2)
+
+LOCAL_OBJECT_START(tanl_table_tm1)
+//
+//  Entries T_hi   double-precision memory format
+//  Index = 0,1,...,19  B = 2^(-1)*(1+Index/32+1/64)
+//  Entries T_lo  single-precision memory format
+//  Index = 0,1,...,19  B = 2^(-1)*(1+Index/32+1/64)
+//
+data8 0x3FE1CEC4BA1BE39E
+data4 0x24B60F9E, 0x00000000
+data8 0x3FE277E45ABD9B2D
+data4 0x248C2474, 0x00000000
+data8 0x3FE324180272B110
+data4 0x247B8311, 0x00000000
+data8 0x3FE3D38B890E2DF0
+data4 0x24C55751, 0x00000000
+data8 0x3FE4866D46236871
+data4 0x24E5BC34, 0x00000000
+data8 0x3FE53CEE45E044B0
+data4 0x24001BA4, 0x00000000
+data8 0x3FE5F74282EC06E4
+data4 0x24B973DC, 0x00000000
+data8 0x3FE6B5A125DF43F9
+data4 0x24895440, 0x00000000
+data8 0x3FE77844CAFD348C
+data4 0x240021CA, 0x00000000
+data8 0x3FE83F6BCEED6B92
+data4 0x24C45372, 0x00000000
+data8 0x3FE90B58A34F3665
+data4 0x240DAD33, 0x00000000
+data8 0x3FE9DC522C1E56B4
+data4 0x24F846CE, 0x00000000
+data8 0x3FEAB2A427041578
+data4 0x2323FB6E, 0x00000000
+data8 0x3FEB8E9F9DD8C373
+data4 0x24B3090B, 0x00000000
+data8 0x3FEC709B65C9AA7B
+data4 0x2449F611, 0x00000000
+data8 0x3FED58F4ACCF8435
+data4 0x23616A7E, 0x00000000
+data8 0x3FEE480F97635082
+data4 0x24C2FEAE, 0x00000000
+data8 0x3FEF3E57F0ACC544
+data4 0x242CE964, 0x00000000
+data8 0x3FF01E20F7E06E4B
+data4 0x2480D3EE, 0x00000000
+data8 0x3FF0A1258A798A69
+data4 0x24DB8967, 0x00000000
+LOCAL_OBJECT_END(tanl_table_tm1)
+
+LOCAL_OBJECT_START(tanl_table_cm2)
+//
+//  Entries C_hi   double-precision memory format
+//  Index = 0,1,...,31  B = 2^(-2)*(1+Index/32+1/64)
+//  Entries C_lo  single-precision memory format
+//  Index = 0,1,...,31  B = 2^(-2)*(1+Index/32+1/64)
+//
+data8 0x400ED3E2E63EFBD0
+data4 0x259D94D4, 0x00000000
+data8 0x400DDDB4C515DAB5
+data4 0x245F0537, 0x00000000
+data8 0x400CF57ABE19A79F
+data4 0x25D4EA9F, 0x00000000
+data8 0x400C1A06D15298ED
+data4 0x24AE40A0, 0x00000000
+data8 0x400B4A4C164B2708
+data4 0x25A5AAB6, 0x00000000
+data8 0x400A855A5285B068
+data4 0x25524F18, 0x00000000
+data8 0x4009CA5A3FFA549F
+data4 0x24C999C0, 0x00000000
+data8 0x4009188A646AF623
+data4 0x254FD801, 0x00000000
+data8 0x40086F3C6084D0E7
+data4 0x2560F5FD, 0x00000000
+data8 0x4007CDD2A29A76EE
+data4 0x255B9D19, 0x00000000
+data8 0x400733BE6C8ECA95
+data4 0x25CB021B, 0x00000000
+data8 0x4006A07E1F8DDC52
+data4 0x24AB4722, 0x00000000
+data8 0x4006139BC298AD58
+data4 0x252764E2, 0x00000000
+data8 0x40058CABBAD7164B
+data4 0x24DAF5DB, 0x00000000
+data8 0x40050B4BAE31A5D3
+data4 0x25EA20F4, 0x00000000
+data8 0x40048F2189F85A8A
+data4 0x2583A3E8, 0x00000000
+data8 0x400417DAA862380D
+data4 0x25DCC4CC, 0x00000000
+data8 0x4003A52B1088FCFE
+data4 0x2430A492, 0x00000000
+data8 0x400336CCCD3527D5
+data4 0x255F77CF, 0x00000000
+data8 0x4002CC7F5760766D
+data4 0x25DA0BDA, 0x00000000
+data8 0x4002660711CE02E3
+data4 0x256FF4A2, 0x00000000
+data8 0x4002032CD37BBE04
+data4 0x25208AED, 0x00000000
+data8 0x4001A3BD7F050775
+data4 0x24B72DD6, 0x00000000
+data8 0x40014789A554848A
+data4 0x24AB4DAA, 0x00000000
+data8 0x4000EE65323E81B7
+data4 0x2584C440, 0x00000000
+data8 0x4000982721CF1293
+data4 0x25C9428D, 0x00000000
+data8 0x400044A93D415EEB
+data4 0x25DC8482, 0x00000000
+data8 0x3FFFE78FBD72C577
+data4 0x257F5070, 0x00000000
+data8 0x3FFF4AC375EFD28E
+data4 0x23EBBF7A, 0x00000000
+data8 0x3FFEB2AF60B52DDE
+data4 0x22EECA07, 0x00000000
+data8 0x3FFE1F1935204180
+data4 0x24191079, 0x00000000
+data8 0x3FFD8FCA54F7E60A
+data4 0x248D3058, 0x00000000
+LOCAL_OBJECT_END(tanl_table_cm2)
+
+LOCAL_OBJECT_START(tanl_table_cm1)
+//
+//  Entries C_hi   double-precision memory format
+//  Index = 0,1,...,19  B = 2^(-1)*(1+Index/32+1/64)
+//  Entries C_lo  single-precision memory format
+//  Index = 0,1,...,19  B = 2^(-1)*(1+Index/32+1/64)
+//
+data8 0x3FFCC06A79F6FADE
+data4 0x239C7886, 0x00000000
+data8 0x3FFBB91F891662A6
+data4 0x250BD191, 0x00000000
+data8 0x3FFABFB6529F155D
+data4 0x256CC3E6, 0x00000000
+data8 0x3FF9D3002E964AE9
+data4 0x250843E3, 0x00000000
+data8 0x3FF8F1EF89DCB383
+data4 0x2277C87E, 0x00000000
+data8 0x3FF81B937C87DBD6
+data4 0x256DA6CF, 0x00000000
+data8 0x3FF74F141042EDE4
+data4 0x2573D28A, 0x00000000
+data8 0x3FF68BAF1784B360
+data4 0x242E489A, 0x00000000
+data8 0x3FF5D0B57C923C4C
+data4 0x2532D940, 0x00000000
+data8 0x3FF51D88F418EF20
+data4 0x253C7DD6, 0x00000000
+data8 0x3FF4719A02F88DAE
+data4 0x23DB59BF, 0x00000000
+data8 0x3FF3CC6649DA0788
+data4 0x252B4756, 0x00000000
+data8 0x3FF32D770B980DB8
+data4 0x23FE585F, 0x00000000
+data8 0x3FF2945FE56C987A
+data4 0x25378A63, 0x00000000
+data8 0x3FF200BDB16523F6
+data4 0x247BB2E0, 0x00000000
+data8 0x3FF172358CE27778
+data4 0x24446538, 0x00000000
+data8 0x3FF0E873FDEFE692
+data4 0x2514638F, 0x00000000
+data8 0x3FF0632C33154062
+data4 0x24A7FC27, 0x00000000
+data8 0x3FEFC42EB3EF115F
+data4 0x248FD0FE, 0x00000000
+data8 0x3FEEC9E8135D26F6
+data4 0x2385C719, 0x00000000
+LOCAL_OBJECT_END(tanl_table_cm1)
+
+LOCAL_OBJECT_START(tanl_table_scim2)
+//
+//  Entries SC_inv in Swapped IEEE format (extended)
+//  Index = 0,1,...,31  B = 2^(-2)*(1+Index/32+1/64)
+//
+data8    0x839D6D4A1BF30C9E, 0x00004001
+data8    0x80092804554B0EB0, 0x00004001
+data8    0xF959F94CA1CF0DE9, 0x00004000
+data8    0xF3086BA077378677, 0x00004000
+data8    0xED154515CCD4723C, 0x00004000
+data8    0xE77909441C27CF25, 0x00004000
+data8    0xE22D037D8DDACB88, 0x00004000
+data8    0xDD2B2D8A89C73522, 0x00004000
+data8    0xD86E1A23BB2C1171, 0x00004000
+data8    0xD3F0E288DFF5E0F9, 0x00004000
+data8    0xCFAF16B1283BEBD5, 0x00004000
+data8    0xCBA4AFAA0D88DD53, 0x00004000
+data8    0xC7CE03CCCA67C43D, 0x00004000
+data8    0xC427BC820CA0DDB0, 0x00004000
+data8    0xC0AECD57F13D8CAB, 0x00004000
+data8    0xBD606C3871ECE6B1, 0x00004000
+data8    0xBA3A0A96A44C4929, 0x00004000
+data8    0xB7394F6FE5CCCEC1, 0x00004000
+data8    0xB45C12039637D8BC, 0x00004000
+data8    0xB1A0552892CB051B, 0x00004000
+data8    0xAF04432B6BA2FFD0, 0x00004000
+data8    0xAC862A237221235F, 0x00004000
+data8    0xAA2478AF5F00A9D1, 0x00004000
+data8    0xA7DDBB0C81E082BF, 0x00004000
+data8    0xA5B0987D45684FEE, 0x00004000
+data8    0xA39BD0F5627A8F53, 0x00004000
+data8    0xA19E3B036EC5C8B0, 0x00004000
+data8    0x9FB6C1F091CD7C66, 0x00004000
+data8    0x9DE464101FA3DF8A, 0x00004000
+data8    0x9C263139A8F6B888, 0x00004000
+data8    0x9A7B4968C27B0450, 0x00004000
+data8    0x98E2DB7E5EE614EE, 0x00004000
+LOCAL_OBJECT_END(tanl_table_scim2)
+
+LOCAL_OBJECT_START(tanl_table_scim1)
+//
+//  Entries SC_inv in Swapped IEEE format (extended)
+//  Index = 0,1,...,19  B = 2^(-1)*(1+Index/32+1/64)
+//
+data8    0x969F335C13B2B5BA, 0x00004000
+data8    0x93D446D9D4C0F548, 0x00004000
+data8    0x9147094F61B798AF, 0x00004000
+data8    0x8EF317CC758787AC, 0x00004000
+data8    0x8CD498B3B99EEFDB, 0x00004000
+data8    0x8AE82A7DDFF8BC37, 0x00004000
+data8    0x892AD546E3C55D42, 0x00004000
+data8    0x8799FEA9D15573C1, 0x00004000
+data8    0x86335F88435A4B4C, 0x00004000
+data8    0x84F4FB6E3E93A87B, 0x00004000
+data8    0x83DD195280A382FB, 0x00004000
+data8    0x82EA3D7FA4CB8C9E, 0x00004000
+data8    0x821B247C6861D0A8, 0x00004000
+data8    0x816EBED163E8D244, 0x00004000
+data8    0x80E42D9127E4CFC6, 0x00004000
+data8    0x807ABF8D28E64AFD, 0x00004000
+data8    0x8031EF26863B4FD8, 0x00004000
+data8    0x800960ADAE8C11FD, 0x00004000
+data8    0x8000E1475FDBEC21, 0x00004000
+data8    0x80186650A07791FA, 0x00004000
+LOCAL_OBJECT_END(tanl_table_scim1)
+
+Arg                 = f8
+Save_Norm_Arg       = f8        // For input to reduction routine
+Result              = f8
+r                   = f8        // For output from reduction routine
+c                   = f9        // For output from reduction routine
+U_2                 = f10
+rsq                 = f11
+C_hi                = f12
+C_lo                = f13
+T_hi                = f14
+T_lo                = f15
+
+d_1                 = f33
+N_0                 = f34
+tail                = f35
+tanx                = f36
+Cx                  = f37
+Sx                  = f38
+sgn_r               = f39
+CORR                = f40
+P                   = f41
+D                   = f42
+ArgPrime            = f43
+P_0                 = f44
+
+P2_1                = f45
+P2_2                = f46
+P2_3                = f47
+
+P1_1                = f45
+P1_2                = f46
+P1_3                = f47
+
+P1_4                = f48
+P1_5                = f49
+P1_6                = f50
+P1_7                = f51
+P1_8                = f52
+P1_9                = f53
+
+x                   = f56
+xsq                 = f57
+Tx                  = f58
+Tx1                 = f59
+Set                 = f60
+poly1               = f61
+poly2               = f62
+Poly                = f63
+Poly1               = f64
+Poly2               = f65
+r_to_the_8          = f66
+B                   = f67
+SC_inv              = f68
+Pos_r               = f69
+N_0_fix             = f70
+d_2                 = f71
+PI_BY_4             = f72
+TWO_TO_NEG14        = f74
+TWO_TO_NEG33        = f75
+NEGTWO_TO_NEG14     = f76
+NEGTWO_TO_NEG33     = f77
+two_by_PI           = f78
+N                   = f79
+N_fix               = f80
+P_1                 = f81
+P_2                 = f82
+P_3                 = f83
+s_val               = f84
+w                   = f85
+B_mask1             = f86
+B_mask2             = f87
+w2                  = f88
+A                   = f89
+a                   = f90
+t                   = f91
+U_1                 = f92
+NEGTWO_TO_NEG2      = f93
+TWO_TO_NEG2         = f94
+Q1_1                = f95
+Q1_2                = f96
+Q1_3                = f97
+Q1_4                = f98
+Q1_5                = f99
+Q1_6                = f100
+Q1_7                = f101
+Q1_8                = f102
+S_hi                = f103
+S_lo                = f104
+V_hi                = f105
+V_lo                = f106
+U_hi                = f107
+U_lo                = f108
+U_hiabs             = f109
+V_hiabs             = f110
+V                   = f111
+Inv_P_0             = f112
+
+FR_inv_pi_2to63     = f113
+FR_rshf_2to64       = f114
+FR_2tom64           = f115
+FR_rshf             = f116
+Norm_Arg            = f117
+Abs_Arg             = f118
+TWO_TO_NEG65        = f119
+fp_tmp              = f120
+mOne                = f121
+
+GR_SAVE_B0     = r33
+GR_SAVE_GP     = r34
+GR_SAVE_PFS    = r35
+table_base     = r36
+table_ptr1     = r37
+table_ptr2     = r38
+table_ptr3     = r39
+lookup         = r40
+N_fix_gr       = r41
+GR_exp_2tom2   = r42
+GR_exp_2tom65  = r43
+exp_r          = r44
+sig_r          = r45
+bmask1         = r46
+table_offset   = r47
+bmask2         = r48
+gr_tmp         = r49
+cot_flag       = r50
+
+GR_sig_inv_pi  = r51
+GR_rshf_2to64  = r52
+GR_exp_2tom64  = r53
+GR_rshf        = r54
+GR_exp_2_to_63 = r55
+GR_exp_2_to_24 = r56
+GR_signexp_x   = r57
+GR_exp_x       = r58
+GR_exp_mask    = r59
+GR_exp_2tom14  = r60
+GR_exp_m2tom14 = r61
+GR_exp_2tom33  = r62
+GR_exp_m2tom33 = r63
+
+GR_SAVE_B0                  = r64
+GR_SAVE_PFS                 = r65
+GR_SAVE_GP                  = r66
+
+GR_Parameter_X              = r67
+GR_Parameter_Y              = r68
+GR_Parameter_RESULT         = r69
+GR_Parameter_Tag            = r70
+
+
+.section .text
+.global __libm_tanl#
+.global __libm_cotl#
+
+.proc __libm_cotl#
+__libm_cotl:
+.endp __libm_cotl#
+LOCAL_LIBM_ENTRY(cotl)
+
+{ .mlx
+      alloc r32 = ar.pfs, 0,35,4,0
+      movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi
+}
+{ .mlx
+      mov GR_exp_mask = 0x1ffff            // Exponent mask
+      movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64)
+}
+;;
+
+//     Check for NatVals, Infs , NaNs, and Zeros
+{ .mfi
+      getf.exp GR_signexp_x = Arg          // Get sign and exponent of x
+      fclass.m  p6,p0 = Arg, 0x1E7         // Test for natval, nan, inf, zero
+      mov cot_flag = 0x1
+}
+{ .mfb
+      addl table_base = @ltoff(TANL_BASE_CONSTANTS), gp // Pointer to table ptr
+      fnorm.s1 Norm_Arg = Arg              // Normalize x
+      br.cond.sptk COMMON_PATH
+};;
+
+LOCAL_LIBM_END(cotl)
+
+
+.proc __libm_tanl#
+__libm_tanl:
+.endp __libm_tanl#
+GLOBAL_IEEE754_ENTRY(tanl)
+
+{ .mlx
+      alloc r32 = ar.pfs, 0,35,4,0
+      movl GR_sig_inv_pi = 0xa2f9836e4e44152a // significand of 1/pi
+}
+{ .mlx
+      mov GR_exp_mask = 0x1ffff            // Exponent mask
+      movl GR_rshf_2to64 = 0x47e8000000000000 // 1.1000 2^(63+64)
+}
+;;
+
+//     Check for NatVals, Infs , NaNs, and Zeros
+{ .mfi
+      getf.exp GR_signexp_x = Arg          // Get sign and exponent of x
+      fclass.m  p6,p0 = Arg, 0x1E7         // Test for natval, nan, inf, zero
+      mov cot_flag = 0x0
+}
+{ .mfi
+      addl table_base = @ltoff(TANL_BASE_CONSTANTS), gp // Pointer to table ptr
+      fnorm.s1 Norm_Arg = Arg              // Normalize x
+      nop.i 0
+};;
+
+// Common path for both tanl and cotl
+COMMON_PATH:
+{ .mfi
+      setf.sig FR_inv_pi_2to63 = GR_sig_inv_pi // Form 1/pi * 2^63
+      fclass.m p9, p0 = Arg, 0x0b          // Test x denormal
+      mov GR_exp_2tom64 = 0xffff - 64      // Scaling constant to compute N
+}
+{ .mlx
+      setf.d FR_rshf_2to64 = GR_rshf_2to64 // Form const 1.1000 * 2^(63+64)
+      movl GR_rshf = 0x43e8000000000000    // Form const 1.1000 * 2^63
+}
+;;
+
+// Check for everything - if false, then must be pseudo-zero or pseudo-nan.
+// Branch out to deal with special values.
+{ .mfi
+      addl gr_tmp = -1,r0
+      fclass.nm  p7,p0 = Arg, 0x1FF        // Test x unsupported
+      mov GR_exp_2_to_63 = 0xffff + 63     // Exponent of 2^63
+}
+{ .mfb
+      ld8 table_base = [table_base]        // Get pointer to constant table
+      fms.s1 mOne = f0, f0, f1
+(p6)  br.cond.spnt TANL_SPECIAL            // Branch if x natval, nan, inf, zero
+}
+;;
+
+{ .mmb
+      setf.sig fp_tmp = gr_tmp   // Make a constant so fmpy produces inexact
+      mov GR_exp_2_to_24 = 0xffff + 24     // Exponent of 2^24
+(p9)  br.cond.spnt TANL_DENORMAL           // Branch if x denormal
+}
+;;
+
+TANL_COMMON:
+// Return to here if x denormal
+//
+// Do fcmp to generate Denormal exception
+//  - can't do FNORM (will generate Underflow when U is unmasked!)
+// Branch out to deal with unsupporteds values.
+{ .mfi
+      setf.exp FR_2tom64 = GR_exp_2tom64 // Form 2^-64 for scaling N_float
+      fcmp.eq.s0 p0, p6 = Arg, f1        // Dummy to flag denormals
+      add table_ptr1 = 0, table_base     // Point to tanl_table_1
+}
+{ .mib
+      setf.d FR_rshf = GR_rshf           // Form right shift const 1.1000 * 2^63
+      add table_ptr2 = 80, table_base    // Point to tanl_table_2
+(p7)  br.cond.spnt TANL_UNSUPPORTED      // Branch if x unsupported type
+}
+;;
+
+{ .mfi
+      and GR_exp_x = GR_exp_mask, GR_signexp_x // Get exponent of x
+      fmpy.s1 Save_Norm_Arg = Norm_Arg, f1     // Save x if large arg reduction
+      dep.z bmask1 = 0x7c, 56, 8               // Form mask to get 5 msb of r
+                                               // bmask1 = 0x7c00000000000000
+}
+;;
+
+//
+//     Decide about the paths to take:
+//     Set PR_6 if |Arg| >= 2**63
+//     Set PR_9 if |Arg| < 2**24 - CASE 1 OR 2
+//     OTHERWISE Set PR_8 - CASE 3 OR 4
+//
+//     Branch out if the magnitude of the input argument is >= 2^63
+//     - do this branch before the next.
+{ .mfi
+      ldfe two_by_PI = [table_ptr1],16        // Load 2/pi
+      nop.f 999
+      dep.z bmask2 = 0x41, 57, 7              // Form mask to OR to produce B
+                                              // bmask2 = 0x8200000000000000
+}
+{ .mib
+      ldfe PI_BY_4 = [table_ptr2],16          // Load pi/4
+      cmp.ge p6,p0 = GR_exp_x, GR_exp_2_to_63 // Is |x| >= 2^63
+(p6)  br.cond.spnt TANL_ARG_TOO_LARGE         // Branch if |x| >= 2^63
+}
+;;
+
+{ .mmi
+      ldfe P_0 = [table_ptr1],16              // Load P_0
+      ldfe Inv_P_0 = [table_ptr2],16          // Load Inv_P_0
+      nop.i 999
+}
+;;
+
+{ .mfi
+      ldfe P_1 = [table_ptr1],16              // Load P_1
+      fmerge.s Abs_Arg = f0, Norm_Arg         // Get |x|
+      mov GR_exp_m2tom33 = 0x2ffff - 33       // Form signexp of -2^-33
+}
+{ .mfi
+      ldfe d_1 = [table_ptr2],16              // Load d_1 for 2^24 <= |x| < 2^63
+      nop.f 999
+      mov GR_exp_2tom33 = 0xffff - 33         // Form signexp of 2^-33
+}
+;;
+
+{ .mmi
+      ldfe P_2 = [table_ptr1],16              // Load P_2
+      ldfe d_2 = [table_ptr2],16              // Load d_2 for 2^24 <= |x| < 2^63
+      cmp.ge p8,p0 = GR_exp_x, GR_exp_2_to_24 // Is |x| >= 2^24
+}
+;;
+
+// Use special scaling to right shift so N=Arg * 2/pi is in rightmost bits
+// Branch to Cases 3 or 4 if Arg <= -2**24 or Arg >= 2**24
+{ .mfb
+      ldfe   P_3 = [table_ptr1],16            // Load P_3
+      fma.s1      N_fix = Norm_Arg, FR_inv_pi_2to63, FR_rshf_2to64
+(p8)  br.cond.spnt TANL_LARGER_ARG            // Branch if 2^24 <= |x| < 2^63
+}
+;;
+
+// Here if 0 < |x| < 2^24
+//     ARGUMENT REDUCTION CODE - CASE 1 and 2
+//
+{ .mmf
+      setf.exp TWO_TO_NEG33 = GR_exp_2tom33      // Form 2^-33
+      setf.exp NEGTWO_TO_NEG33 = GR_exp_m2tom33  // Form -2^-33
+      fmerge.s r = Norm_Arg,Norm_Arg          // Assume r=x, ok if |x| < pi/4
+}
+;;
+
+//
+// If |Arg| < pi/4,  set PR_8, else  pi/4 <=|Arg| < 2^24 - set PR_9.
+//
+//     Case 2: Convert integer N_fix back to normalized floating-point value.
+{ .mfi
+      getf.sig sig_r = Norm_Arg               // Get sig_r if 1/4 <= |x| < pi/4
+      fcmp.lt.s1 p8,p9= Abs_Arg,PI_BY_4       // Test |x| < pi/4
+      mov GR_exp_2tom2 = 0xffff - 2           // Form signexp of 2^-2
+}
+{ .mfi
+      ldfps TWO_TO_NEG2, NEGTWO_TO_NEG2 = [table_ptr2] // Load 2^-2, -2^-2
+      fms.s1 N = N_fix, FR_2tom64, FR_rshf    // Use scaling to get N floated
+      mov N_fix_gr = r0                       // Assume N=0, ok if |x| < pi/4
+}
+;;
+
+//
+//     Case 1: Is |r| < 2**(-2).
+//     Arg is the same as r in this case.
+//     r = Arg
+//     c = 0
+//
+//     Case 2: Place integer part of N in GP register.
+{ .mfi
+(p9)  getf.sig N_fix_gr = N_fix
+      fmerge.s c = f0, f0                     // Assume c=0, ok if |x| < pi/4
+      cmp.lt p10, p0 = GR_exp_x, GR_exp_2tom2 // Test if |x| < 1/4
+}
+;;
+
+{ .mfi
+      setf.sig B_mask1 = bmask1               // Form mask to get 5 msb of r
+      nop.f 999
+      mov exp_r = GR_exp_x                    // Get exp_r if 1/4 <= |x| < pi/4
+}
+{ .mbb
+      setf.sig B_mask2 = bmask2               // Form mask to form B from r
+(p10) br.cond.spnt TANL_SMALL_R               // Branch if 0 < |x| < 1/4
+(p8)  br.cond.spnt TANL_NORMAL_R              // Branch if 1/4 <= |x| < pi/4
+}
+;;
+
+// Here if pi/4 <= |x| < 2^24
+//
+//     Case 1: PR_3 is only affected  when PR_1 is set.
+//
+//
+//     Case 2: w = N * P_2
+//     Case 2: s_val = -N * P_1  + Arg
+//
+
+{ .mfi
+      nop.m 999
+      fnma.s1 s_val = N, P_1, Norm_Arg
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fmpy.s1 w = N, P_2                     // w = N * P_2 for |s| >= 2^-33
+      nop.i 999
+}
+;;
+
+//     Case 2_reduce: w = N * P_3 (change sign)
+{ .mfi
+      nop.m 999
+      fmpy.s1 w2 = N, P_3                    // w = N * P_3 for |s| < 2^-33
+      nop.i 999
+}
+;;
+
+//     Case 1_reduce: r = s + w (change sign)
+{ .mfi
+      nop.m 999
+      fsub.s1 r = s_val, w                   // r = s_val - w for |s| >= 2^-33
+      nop.i 999
+}
+;;
+
+//     Case 2_reduce: U_1 = N * P_2 + w
+{ .mfi
+      nop.m 999
+      fma.s1  U_1 = N, P_2, w2              // U_1 = N * P_2 + w for |s| < 2^-33
+      nop.i 999
+}
+;;
+
+//
+//     Decide between case_1 and case_2 reduce:
+//     Case 1_reduce:  |s| >= 2**(-33)
+//     Case 2_reduce:  |s| < 2**(-33)
+//
+{ .mfi
+      nop.m 999
+      fcmp.lt.s1 p9, p8 = s_val, TWO_TO_NEG33
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p9)  fcmp.gt.s1 p9, p8 = s_val, NEGTWO_TO_NEG33
+      nop.i 999
+}
+;;
+
+//     Case 1_reduce: c = s - r
+{ .mfi
+      nop.m 999
+      fsub.s1 c = s_val, r                     // c = s_val - r for |s| >= 2^-33
+      nop.i 999
+}
+;;
+
+//     Case 2_reduce: r is complete here - continue to calculate c .
+//     r = s - U_1
+{ .mfi
+      nop.m 999
+(p9)  fsub.s1 r = s_val, U_1
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p9)  fms.s1 U_2 = N, P_2, U_1
+      nop.i 999
+}
+;;
+
+//
+//     Case 1_reduce: Is |r| < 2**(-2), if so set PR_10
+//     else set PR_13.
+//
+
+{ .mfi
+      nop.m 999
+      fand B = B_mask1, r
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p8)  fcmp.lt.unc.s1 p10, p13 = r, TWO_TO_NEG2
+      nop.i 999
+}
+;;
+
+{ .mfi
+(p8)  getf.sig sig_r = r               // Get signif of r if |s| >= 2^-33
+      nop.f 999
+      nop.i 999
+}
+;;
+
+{ .mfi
+(p8)  getf.exp exp_r = r               // Extract signexp of r if |s| >= 2^-33
+(p10) fcmp.gt.s1 p10, p13 = r, NEGTWO_TO_NEG2
+      nop.i 999
+}
+;;
+
+//     Case 1_reduce: c is complete here.
+//     Case 1: Branch to SMALL_R or NORMAL_R.
+//     c = c + w (w has not been negated.)
+{ .mfi
+      nop.m 999
+(p8)  fsub.s1 c = c, w                         // c = c - w for |s| >= 2^-33
+      nop.i 999
+}
+{ .mbb
+      nop.m 999
+(p10) br.cond.spnt TANL_SMALL_R     // Branch if pi/4 < |x| < 2^24 and |r|<1/4
+(p13) br.cond.sptk TANL_NORMAL_R_A  // Branch if pi/4 < |x| < 2^24 and |r|>=1/4
+}
+;;
+
+
+// Here if pi/4 < |x| < 2^24 and |s| < 2^-33
+//
+//     Is i_1 = lsb of N_fix_gr even or odd?
+//     if i_1 == 0, set p11, else set p12.
+//
+{ .mfi
+      nop.m 999
+      fsub.s1 s_val = s_val, r
+      add N_fix_gr = N_fix_gr, cot_flag // N = N + 1 (for cotl)
+}
+{ .mfi
+      nop.m 999
+//
+//     Case 2_reduce:
+//     U_2 = N * P_2 - U_1
+//     Not needed until later.
+//
+      fadd.s1 U_2 = U_2, w2
+//
+//     Case 2_reduce:
+//     s = s - r
+//     U_2 = U_2 + w
+//
+      nop.i 999
+}
+;;
+
+//
+//     Case 2_reduce:
+//     c = c - U_2
+//     c is complete here
+//     Argument reduction ends here.
+//
+{ .mfi
+      nop.m 999
+      fmpy.s1 rsq = r, r
+      tbit.z p11, p12 = N_fix_gr, 0 ;;    // Set p11 if N even, p12 if odd
+}
+
+{ .mfi
+      nop.m 999
+(p12) frcpa.s1 S_hi,p0 = f1, r
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fsub.s1 c = s_val, U_1
+      nop.i 999
+}
+;;
+
+{ .mmi
+      add table_ptr1 = 160, table_base ;;  // Point to tanl_table_p1
+      ldfe P1_1 = [table_ptr1],144
+      nop.i 999 ;;
+}
+//
+//     Load P1_1 and point to Q1_1 .
+//
+{ .mfi
+      ldfe Q1_1 = [table_ptr1]
+//
+//     N even: rsq = r * Z
+//     N odd:  S_hi = frcpa(r)
+//
+(p12) fmerge.ns S_hi = S_hi, S_hi
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+//
+//     Case 2_reduce:
+//     c = s - U_1
+//
+(p9)  fsub.s1 c = c, U_2
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1  poly1 = S_hi, r, f1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//     N odd:  Change sign of S_hi
+//
+(p11) fmpy.s1 rsq = rsq, P1_1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 S_hi = S_hi, poly1, S_hi
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//     N even: rsq = rsq * P1_1
+//     N odd:  poly1 =  1.0 +  S_hi * r    16 bits partial  account for necessary
+//
+(p11) fma.s1 Poly = r, rsq, c
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//     N even: Poly = c  + r * rsq
+//     N odd:  S_hi  = S_hi + S_hi*poly1  16 bits account for necessary
+//
+(p12) fma.s1 poly1 = S_hi, r, f1
+(p11) tbit.z.unc p14, p15 = cot_flag, 0 ;; // p14=1 for tanl; p15=1 for cotl
+}
+{ .mfi
+      nop.m 999
+//
+//     N even: Result = Poly + r
+//     N odd:  poly1  = 1.0 + S_hi * r        32 bits partial
+//
+(p14) fadd.s0 Result = r, Poly             // for tanl
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p15) fms.s0 Result = r, mOne, Poly        // for cotl
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p12) fma.s1  S_hi = S_hi, poly1, S_hi
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//     N even: Result1 = Result + r
+//     N odd:   S_hi  = S_hi * poly1 + S_hi   32 bits
+//
+(p12) fma.s1 poly1 = S_hi, r, f1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//     N odd:  poly1  =  S_hi * r + 1.0       64 bits partial
+//
+(p12) fma.s1 S_hi = S_hi, poly1, S_hi
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//     N odd:  poly1  =  S_hi * poly + 1.0    64 bits
+//
+(p12) fma.s1 poly1 = S_hi, r, f1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//     N odd:  poly1  =  S_hi * r + 1.0
+//
+(p12) fma.s1 poly1 = S_hi, c, poly1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//     N odd:  poly1  =  S_hi * c + poly1
+//
+(p12) fmpy.s1 S_lo = S_hi, poly1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//     N odd:  S_lo  =  S_hi *  poly1
+//
+(p12) fma.s1 S_lo = Q1_1, r, S_lo
+(p12) tbit.z.unc p14, p15 = cot_flag, 0 // p14=1 for tanl; p15=1 for cotl
+}
+{ .mfi
+      nop.m 999
+//
+//     N odd:  Result =  S_hi + S_lo
+//
+      fmpy.s0 fp_tmp = fp_tmp, fp_tmp  // Dummy mult to set inexact
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//     N odd:  S_lo  =  S_lo + Q1_1 * r
+//
+(p14) fadd.s0 Result = S_hi, S_lo          // for tanl
+      nop.i 999
+}
+{ .mfb
+      nop.m 999
+(p15) fms.s0 Result = S_hi, mOne, S_lo     // for cotl
+      br.ret.sptk b0 ;;          // Exit for pi/4 <= |x| < 2^24 and |s| < 2^-33
+}
+
+
+TANL_LARGER_ARG:
+// Here if 2^24 <= |x| < 2^63
+//
+// ARGUMENT REDUCTION CODE - CASE 3 and 4
+//
+
+{ .mmf
+      mov GR_exp_2tom14 = 0xffff - 14          // Form signexp of 2^-14
+      mov GR_exp_m2tom14 = 0x2ffff - 14        // Form signexp of -2^-14
+      fmpy.s1 N_0 = Norm_Arg, Inv_P_0
+}
+;;
+
+{ .mmi
+      setf.exp TWO_TO_NEG14 = GR_exp_2tom14    // Form 2^-14
+      setf.exp NEGTWO_TO_NEG14 = GR_exp_m2tom14// Form -2^-14
+      nop.i 999
+}
+;;
+
+
+//
+//    Adjust table_ptr1 to beginning of table.
+//    N_0 = Arg * Inv_P_0
+//
+{ .mmi
+      add table_ptr2 = 144, table_base ;;     // Point to 2^-2
+      ldfps TWO_TO_NEG2, NEGTWO_TO_NEG2 = [table_ptr2]
+      nop.i 999
+}
+;;
+
+//
+//    N_0_fix  = integer part of N_0 .
+//
+//
+//    Make N_0 the integer part.
+//
+{ .mfi
+      nop.m 999
+      fcvt.fx.s1 N_0_fix = N_0
+      nop.i 999 ;;
+}
+{ .mfi
+      setf.sig B_mask1 = bmask1               // Form mask to get 5 msb of r
+      fcvt.xf N_0 = N_0_fix
+      nop.i 999 ;;
+}
+{ .mfi
+      setf.sig B_mask2 = bmask2               // Form mask to form B from r
+      fnma.s1 ArgPrime = N_0, P_0, Norm_Arg
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fmpy.s1 w = N_0, d_1
+      nop.i 999 ;;
+}
+//
+//    ArgPrime = -N_0 * P_0 + Arg
+//    w  = N_0 * d_1
+//
+//
+//    N = ArgPrime * 2/pi
+//
+//      fcvt.fx.s1 N_fix = N
+// Use special scaling to right shift so N=Arg * 2/pi is in rightmost bits
+// Branch to Cases 3 or 4 if Arg <= -2**24 or Arg >= 2**24
+{ .mfi
+      nop.m 999
+      fma.s1      N_fix = ArgPrime, FR_inv_pi_2to63, FR_rshf_2to64
+
+      nop.i 999 ;;
+}
+//     Convert integer N_fix back to normalized floating-point value.
+{ .mfi
+      nop.m 999
+      fms.s1 N = N_fix, FR_2tom64, FR_rshf    // Use scaling to get N floated
+      nop.i 999
+}
+;;
+
+//
+//    N is the integer part of the reduced-reduced argument.
+//    Put the integer in a GP register.
+//
+{ .mfi
+      getf.sig N_fix_gr = N_fix
+      nop.f 999
+      nop.i 999
+}
+;;
+
+//
+//    s_val = -N*P_1 + ArgPrime
+//    w = -N*P_2 + w
+//
+{ .mfi
+      nop.m 999
+      fnma.s1 s_val = N, P_1, ArgPrime
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fnma.s1 w = N, P_2, w
+      nop.i 999
+}
+;;
+
+//    Case 4: V_hi = N * P_2
+//    Case 4: U_hi = N_0 * d_1
+{ .mfi
+      nop.m 999
+      fmpy.s1 V_hi = N, P_2               // V_hi = N * P_2 for |s| < 2^-14
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fmpy.s1 U_hi = N_0, d_1             // U_hi = N_0 * d_1 for |s| < 2^-14
+      nop.i 999
+}
+;;
+
+//    Case 3: r = s_val + w (Z complete)
+//    Case 4: w = N * P_3
+{ .mfi
+      nop.m 999
+      fadd.s1 r = s_val, w                // r = s_val + w for |s| >= 2^-14
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fmpy.s1 w2 = N, P_3                 // w = N * P_3 for |s| < 2^-14
+      nop.i 999
+}
+;;
+
+//    Case 4: A =  U_hi + V_hi
+//    Note: Worry about switched sign of V_hi, so subtract instead of add.
+//    Case 4: V_lo = -N * P_2 - V_hi (U_hi is in place of V_hi in writeup)
+//    Note: the (-) is still missing for V_hi.
+{ .mfi
+      nop.m 999
+      fsub.s1 A = U_hi, V_hi           // A = U_hi - V_hi for |s| < 2^-14
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fnma.s1 V_lo = N, P_2, V_hi      // V_lo = V_hi - N * P_2 for |s| < 2^-14
+      nop.i 999
+}
+;;
+
+//    Decide between case 3 and 4:
+//    Case 3:  |s| >= 2**(-14)     Set p10
+//    Case 4:  |s| <  2**(-14)     Set p11
+//
+//    Case 4: U_lo = N_0 * d_1 - U_hi
+{ .mfi
+      nop.m 999
+      fms.s1 U_lo = N_0, d_1, U_hi     // U_lo = N_0*d_1 - U_hi for |s| < 2^-14
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fcmp.lt.s1 p11, p10 = s_val, TWO_TO_NEG14
+      nop.i 999
+}
+;;
+
+//    Case 4: We need abs of both U_hi and V_hi - dont
+//    worry about switched sign of V_hi.
+{ .mfi
+      nop.m 999
+      fabs V_hiabs = V_hi              // |V_hi| for |s| < 2^-14
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p11) fcmp.gt.s1 p11, p10 = s_val, NEGTWO_TO_NEG14
+      nop.i 999
+}
+;;
+
+//    Case 3: c = s_val - r
+{ .mfi
+      nop.m 999
+      fabs U_hiabs = U_hi              // |U_hi| for |s| < 2^-14
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fsub.s1 c = s_val, r             // c = s_val - r    for |s| >= 2^-14
+      nop.i 999
+}
+;;
+
+// For Case 3, |s| >= 2^-14, determine if |r| < 1/4
+//
+//    Case 4: C_hi = s_val + A
+//
+{ .mfi
+      nop.m 999
+(p11) fadd.s1 C_hi = s_val, A              // C_hi = s_val + A for |s| < 2^-14
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p10) fcmp.lt.unc.s1 p14, p15 = r, TWO_TO_NEG2
+      nop.i 999
+}
+;;
+
+{ .mfi
+      getf.sig sig_r = r               // Get signif of r if |s| >= 2^-33
+      fand B = B_mask1, r
+      nop.i 999
+}
+;;
+
+//    Case 4: t = U_lo + V_lo
+{ .mfi
+      getf.exp exp_r = r               // Extract signexp of r if |s| >= 2^-33
+(p11) fadd.s1 t = U_lo, V_lo               // t = U_lo + V_lo for |s| < 2^-14
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p14) fcmp.gt.s1 p14, p15 = r, NEGTWO_TO_NEG2
+      nop.i 999
+}
+;;
+
+//    Case 3: c = (s - r) + w (c complete)
+{ .mfi
+      nop.m 999
+(p10) fadd.s1 c = c, w              // c = c + w for |s| >= 2^-14
+      nop.i 999
+}
+{ .mbb
+      nop.m 999
+(p14) br.cond.spnt TANL_SMALL_R     // Branch if 2^24 <= |x| < 2^63 and |r|< 1/4
+(p15) br.cond.sptk TANL_NORMAL_R_A  // Branch if 2^24 <= |x| < 2^63 and |r|>=1/4
+}
+;;
+
+
+// Here if 2^24 <= |x| < 2^63 and |s| < 2^-14  >>>>>>>  Case 4.
+//
+//    Case 4: Set P_12 if U_hiabs >= V_hiabs
+//    Case 4: w = w + N_0 * d_2
+//    Note: the (-) is now incorporated in w .
+{ .mfi
+      add table_ptr1 = 160, table_base           // Point to tanl_table_p1
+      fcmp.ge.unc.s1 p12, p13 = U_hiabs, V_hiabs
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fms.s1 w2 = N_0, d_2, w2
+      nop.i 999
+}
+;;
+
+//    Case 4: C_lo = s_val - C_hi
+{ .mfi
+      ldfe P1_1 = [table_ptr1], 16               // Load P1_1
+      fsub.s1 C_lo = s_val, C_hi
+      nop.i 999
+}
+;;
+
+//
+//    Case 4: a = U_hi - A
+//            a = V_hi - A (do an add to account for missing (-) on V_hi
+//
+{ .mfi
+      ldfe P1_2 = [table_ptr1], 128              // Load P1_2
+(p12) fsub.s1 a = U_hi, A
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p13) fadd.s1 a = V_hi, A
+      nop.i 999
+}
+;;
+
+//    Case 4: t = U_lo + V_lo  + w
+{ .mfi
+      ldfe Q1_1 = [table_ptr1], 16               // Load Q1_1
+      fadd.s1 t = t, w2
+      nop.i 999
+}
+;;
+
+//    Case 4: a = (U_hi - A)  + V_hi
+//            a = (V_hi - A)  + U_hi
+//    In each case account for negative missing form V_hi .
+//
+{ .mfi
+      ldfe Q1_2 = [table_ptr1], 16               // Load Q1_2
+(p12) fsub.s1 a = a, V_hi
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p13) fsub.s1 a = U_hi, a
+      nop.i 999
+}
+;;
+
+//
+//    Case 4: C_lo = (s_val - C_hi) + A
+//
+{ .mfi
+      nop.m 999
+      fadd.s1 C_lo = C_lo, A
+      nop.i 999 ;;
+}
+//
+//    Case 4: t = t + a
+//
+{ .mfi
+      nop.m 999
+      fadd.s1 t = t, a
+      nop.i 999
+}
+;;
+
+//    Case 4: C_lo = C_lo + t
+//    Case 4: r = C_hi + C_lo
+{ .mfi
+      nop.m 999
+      fadd.s1 C_lo = C_lo, t
+      nop.i 999
+}
+;;
+
+{ .mfi
+      nop.m 999
+      fadd.s1 r = C_hi, C_lo
+      nop.i 999
+}
+;;
+
+//
+//    Case 4: c = C_hi - r
+//
+{ .mfi
+      nop.m 999
+      fsub.s1 c = C_hi, r
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fmpy.s1 rsq = r, r
+      add N_fix_gr = N_fix_gr, cot_flag // N = N + 1 (for cotl)
+}
+;;
+
+//    Case 4: c = c + C_lo  finished.
+//
+//    Is i_1 = lsb of N_fix_gr even or odd?
+//    if i_1 == 0, set PR_11, else set PR_12.
+//
+{ .mfi
+      nop.m 999
+      fadd.s1 c = c , C_lo
+      tbit.z p11, p12 =  N_fix_gr, 0
+}
+;;
+
+// r and c have been computed.
+{ .mfi
+      nop.m 999
+(p12) frcpa.s1 S_hi, p0 = f1, r
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+//
+//    N odd: Change sign of S_hi
+//
+(p11) fma.s1 Poly = rsq, P1_2, P1_1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 P = rsq, Q1_2, Q1_1
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+//
+//    N odd:  Result  =  S_hi + S_lo      (User supplied rounding mode for C1)
+//
+       fmpy.s0 fp_tmp = fp_tmp, fp_tmp  // Dummy mult to set inexact
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: rsq = r * r
+//    N odd:  S_hi = frcpa(r)
+//
+(p12) fmerge.ns S_hi = S_hi, S_hi
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: rsq = rsq * P1_2 + P1_1
+//    N odd:  poly1 =  1.0 +  S_hi * r    16 bits partial  account for necessary
+//
+(p11) fmpy.s1 Poly = rsq, Poly
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 poly1 = S_hi, r,f1
+(p11) tbit.z.unc p14, p15 = cot_flag, 0 // p14=1 for tanl; p15=1 for cotl
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: Poly =  Poly * rsq
+//    N odd:  S_hi  = S_hi + S_hi*poly1  16 bits account for necessary
+//
+(p11) fma.s1 Poly = r, Poly, c
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 S_hi = S_hi, poly1, S_hi
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+//
+//    N odd:   S_hi  = S_hi * poly1 + S_hi   32 bits
+//
+(p14) fadd.s0 Result = r, Poly          // for tanl
+      nop.i 999 ;;
+}
+
+.pred.rel "mutex",p15,p12
+{ .mfi
+      nop.m 999
+(p15) fms.s0 Result = r, mOne, Poly     // for cotl
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 poly1 =  S_hi, r, f1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: Poly = Poly * r + c
+//    N odd:  poly1  = 1.0 + S_hi * r        32 bits partial
+//
+(p12) fma.s1 S_hi = S_hi, poly1, S_hi
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 poly1 = S_hi, r, f1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: Result = Poly + r  (Rounding mode S0)
+//    N odd:  poly1  =  S_hi * r + 1.0       64 bits partial
+//
+(p12) fma.s1 S_hi = S_hi, poly1, S_hi
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N odd:  poly1  =  S_hi * poly + S_hi    64 bits
+//
+(p12) fma.s1 poly1 = S_hi, r, f1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N odd:  poly1  =  S_hi * r + 1.0
+//
+(p12) fma.s1 poly1 = S_hi, c, poly1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N odd:  poly1  =  S_hi * c + poly1
+//
+(p12) fmpy.s1 S_lo = S_hi, poly1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N odd:  S_lo  =  S_hi *  poly1
+//
+(p12) fma.s1 S_lo = P, r, S_lo
+(p12) tbit.z.unc p14, p15 = cot_flag, 0 ;; // p14=1 for tanl; p15=1 for cotl
+}
+
+{ .mfi
+      nop.m 999
+(p14) fadd.s0 Result = S_hi, S_lo           // for tanl
+      nop.i 999
+}
+{ .mfb
+      nop.m 999
+//
+//    N odd:  S_lo  =  S_lo + r * P
+//
+(p15) fms.s0 Result = S_hi, mOne, S_lo      // for cotl
+      br.ret.sptk b0 ;;      // Exit for 2^24 <= |x| < 2^63 and |s| < 2^-14
+}
+
+
+TANL_SMALL_R:
+// Here if |r| < 1/4
+// r and c have been computed.
+// *****************************************************************
+// *****************************************************************
+// *****************************************************************
+//    N odd:  S_hi = frcpa(r)
+//    Get [i_1] - lsb of N_fix_gr.  Set p11 if N even, p12 if N odd.
+//    N even: rsq = r * r
+{ .mfi
+      add table_ptr1 = 160, table_base    // Point to tanl_table_p1
+      frcpa.s1 S_hi, p0 = f1, r           // S_hi for N odd
+      add N_fix_gr = N_fix_gr, cot_flag   // N = N + 1 (for cotl)
+}
+{ .mfi
+      add table_ptr2 = 400, table_base    // Point to Q1_7
+      fmpy.s1 rsq = r, r
+      nop.i 999
+}
+;;
+
+{ .mmi
+      ldfe P1_1 = [table_ptr1], 16
+;;
+      ldfe P1_2 = [table_ptr1], 16
+      tbit.z p11, p12 = N_fix_gr, 0
+}
+;;
+
+
+{ .mfi
+      ldfe P1_3 = [table_ptr1], 96
+      nop.f 999
+      nop.i 999
+}
+;;
+
+{ .mfi
+(p11) ldfe P1_9 = [table_ptr1], -16
+(p12) fmerge.ns S_hi = S_hi, S_hi
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p11) fmpy.s1 r_to_the_8 = rsq, rsq
+      nop.i 999
+}
+;;
+
+//
+//    N even: Poly2 = P1_7 + Poly2 * rsq
+//    N odd:  poly2 = Q1_5 + poly2 * rsq
+//
+{ .mfi
+(p11) ldfe P1_8 = [table_ptr1], -16
+(p11) fadd.s1 CORR = rsq, f1
+      nop.i 999
+}
+;;
+
+//
+//    N even: Poly1 = P1_2 + P1_3 * rsq
+//    N odd:  poly1 =  1.0 +  S_hi * r
+//    16 bits partial  account for necessary (-1)
+//
+{ .mmi
+(p11) ldfe P1_7 = [table_ptr1], -16
+;;
+(p11) ldfe P1_6 = [table_ptr1], -16
+      nop.i 999
+}
+;;
+
+//
+//    N even: Poly1 = P1_1 + Poly1 * rsq
+//    N odd:  S_hi  =  S_hi + S_hi * poly1)     16 bits account for necessary
+//
+//
+//    N even: Poly2 = P1_5 + Poly2 * rsq
+//    N odd:  poly2 = Q1_3 + poly2 * rsq
+//
+{ .mfi
+(p11) ldfe P1_5 = [table_ptr1], -16
+(p11) fmpy.s1 r_to_the_8 = r_to_the_8, r_to_the_8
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 poly1 =  S_hi, r, f1
+      nop.i 999
+}
+;;
+
+//
+//    N even: Poly1 =  Poly1 * rsq
+//    N odd:  poly1  = 1.0 + S_hi * r         32 bits partial
+//
+
+//
+//    N even: CORR =  CORR * c
+//    N odd:  S_hi  =  S_hi * poly1 + S_hi    32 bits
+//
+
+//
+//    N even: Poly2 = P1_6 + Poly2 * rsq
+//    N odd:  poly2 = Q1_4 + poly2 * rsq
+//
+
+{ .mmf
+(p11) ldfe P1_4 = [table_ptr1], -16
+      nop.m 999
+(p11) fmpy.s1 CORR =  CORR, c
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p11) fma.s1 Poly1 = P1_3, rsq, P1_2
+      nop.i 999 ;;
+}
+{ .mfi
+(p12) ldfe Q1_7 = [table_ptr2], -16
+(p12) fma.s1 S_hi = S_hi, poly1, S_hi
+      nop.i 999 ;;
+}
+{ .mfi
+(p12) ldfe Q1_6 = [table_ptr2], -16
+(p11) fma.s1 Poly2 = P1_9, rsq, P1_8
+      nop.i 999 ;;
+}
+{ .mmi
+(p12) ldfe Q1_5 = [table_ptr2], -16 ;;
+(p12) ldfe Q1_4 = [table_ptr2], -16
+      nop.i 999 ;;
+}
+{ .mfi
+(p12) ldfe Q1_3 = [table_ptr2], -16
+//
+//    N even: Poly2 = P1_8 + P1_9 * rsq
+//    N odd:  poly2 = Q1_6 + Q1_7 * rsq
+//
+(p11) fma.s1 Poly1 = Poly1, rsq, P1_1
+      nop.i 999 ;;
+}
+{ .mfi
+(p12) ldfe Q1_2 = [table_ptr2], -16
+(p12) fma.s1 poly1 = S_hi, r, f1
+      nop.i 999 ;;
+}
+{ .mfi
+(p12) ldfe Q1_1 = [table_ptr2], -16
+(p11) fma.s1 Poly2 = Poly2, rsq, P1_7
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: CORR =  rsq + 1
+//    N even: r_to_the_8 =  rsq * rsq
+//
+(p11) fmpy.s1 Poly1 = Poly1, rsq
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 S_hi = S_hi, poly1, S_hi
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 poly2 = Q1_7, rsq, Q1_6
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p11) fma.s1 Poly2 = Poly2, rsq, P1_6
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 poly1 = S_hi, r, f1
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 poly2 = poly2, rsq, Q1_5
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p11) fma.s1 Poly2= Poly2, rsq, P1_5
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 S_hi =  S_hi, poly1, S_hi
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 poly2 = poly2, rsq, Q1_4
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: r_to_the_8 = r_to_the_8 * r_to_the_8
+//    N odd:  poly1  =  S_hi * r + 1.0       64 bits partial
+//
+(p11) fma.s1 Poly2 = Poly2, rsq, P1_4
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: Poly = CORR + Poly * r
+//    N odd:  P = Q1_1 + poly2 * rsq
+//
+(p12) fma.s1 poly1 = S_hi, r, f1
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 poly2 = poly2, rsq, Q1_3
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: Poly2 = P1_4 + Poly2 * rsq
+//    N odd:  poly2 = Q1_2 + poly2 * rsq
+//
+(p11) fma.s1 Poly = Poly2, r_to_the_8, Poly1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 poly1 = S_hi, c, poly1
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 poly2 = poly2, rsq, Q1_2
+      nop.i 999 ;;
+}
+
+{ .mfi
+      nop.m 999
+//
+//    N even: Poly = Poly1 + Poly2 * r_to_the_8
+//    N odd:  S_hi =  S_hi * poly1 + S_hi    64 bits
+//
+(p11) fma.s1 Poly = Poly, r, CORR
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: Result =  r + Poly  (User supplied rounding mode)
+//    N odd:  poly1  =  S_hi * c + poly1
+//
+(p12) fmpy.s1 S_lo = S_hi, poly1
+(p11) tbit.z.unc p14, p15 = cot_flag, 0 // p14=1 for tanl; p15=1 for cotl
+}
+{ .mfi
+      nop.m 999
+(p12) fma.s1 P = poly2, rsq, Q1_1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N odd:  poly1  =  S_hi * r + 1.0
+//
+//
+//    N odd:  S_lo  =  S_hi *  poly1
+//
+(p14) fadd.s0 Result = Poly, r          // for tanl
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p15) fms.s0 Result = Poly, mOne, r     // for cotl
+      nop.i 999 ;;
+}
+
+{ .mfi
+      nop.m 999
+//
+//    N odd:  S_lo  =  Q1_1 * c + S_lo
+//
+(p12) fma.s1 S_lo = Q1_1, c, S_lo
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fmpy.s0 fp_tmp = fp_tmp, fp_tmp  // Dummy mult to set inexact
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N odd:  Result =  S_lo + r * P
+//
+(p12) fma.s1 Result = P, r, S_lo
+(p12) tbit.z.unc p14, p15 = cot_flag, 0 ;; // p14=1 for tanl; p15=1 for cotl
+}
+
+//
+//    N odd:  Result = Result + S_hi  (user supplied rounding mode)
+//
+{ .mfi
+      nop.m 999
+(p14) fadd.s0 Result = Result, S_hi         // for tanl
+      nop.i 999
+}
+{ .mfb
+      nop.m 999
+(p15) fms.s0 Result = Result, mOne, S_hi    // for cotl
+      br.ret.sptk b0 ;;              // Exit |r| < 1/4 path
+}
+
+
+TANL_NORMAL_R:
+// Here if 1/4 <= |x| < pi/4  or  if |x| >= 2^63 and |r| >= 1/4
+// *******************************************************************
+// *******************************************************************
+// *******************************************************************
+//
+//    r and c have been computed.
+//
+{ .mfi
+      nop.m 999
+      fand B = B_mask1, r
+      nop.i 999
+}
+;;
+
+TANL_NORMAL_R_A:
+// Enter here if pi/4 <= |x| < 2^63 and |r| >= 1/4
+//    Get the 5 bits or r for the lookup.   1.xxxxx ....
+{ .mmi
+      add table_ptr1 = 416, table_base     // Point to tanl_table_p2
+      mov GR_exp_2tom65 = 0xffff - 65      // Scaling constant for B
+      extr.u lookup = sig_r, 58, 5
+}
+;;
+
+{ .mmi
+      ldfe P2_1 = [table_ptr1], 16
+      setf.exp TWO_TO_NEG65 = GR_exp_2tom65  // 2^-65 for scaling B if exp_r=-2
+      add N_fix_gr = N_fix_gr, cot_flag      // N = N + 1 (for cotl)
+}
+;;
+
+.pred.rel "mutex",p11,p12
+//    B =  2^63 * 1.xxxxx 100...0
+{ .mfi
+      ldfe P2_2 = [table_ptr1], 16
+      for B = B_mask2, B
+      mov table_offset = 512               // Assume table offset is 512
+}
+;;
+
+{ .mfi
+      ldfe P2_3 = [table_ptr1], 16
+      fmerge.s  Pos_r = f1, r
+      tbit.nz p8,p9 = exp_r, 0
+}
+;;
+
+//    Is  B = 2** -2 or  B= 2** -1? If 2**-1, then
+//    we want an offset of 512 for table addressing.
+{ .mii
+      add table_ptr2 = 1296, table_base     // Point to tanl_table_cm2
+(p9)  shladd table_offset = lookup, 4, table_offset
+(p8)  shladd table_offset = lookup, 4, r0
+}
+;;
+
+{ .mmi
+      add table_ptr1 = table_ptr1, table_offset  // Point to T_hi
+      add table_ptr2 = table_ptr2, table_offset  // Point to C_hi
+      add table_ptr3 = 2128, table_base     // Point to tanl_table_scim2
+}
+;;
+
+{ .mmi
+      ldfd T_hi = [table_ptr1], 8                // Load T_hi
+;;
+      ldfd C_hi = [table_ptr2], 8                // Load C_hi
+      add table_ptr3 = table_ptr3, table_offset  // Point to SC_inv
+}
+;;
+
+//
+//    x = |r| - B
+//
+//   Convert B so it has the same exponent as Pos_r before subtracting
+{ .mfi
+      ldfs T_lo = [table_ptr1]                   // Load T_lo
+(p9)  fnma.s1 x = B, FR_2tom64, Pos_r
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p8)  fnma.s1 x = B, TWO_TO_NEG65, Pos_r
+      nop.i 999
+}
+;;
+
+{ .mfi
+      ldfs C_lo = [table_ptr2]                   // Load C_lo
+      nop.f 999
+      nop.i 999
+}
+;;
+
+{ .mfi
+      ldfe SC_inv = [table_ptr3]                 // Load SC_inv
+      fmerge.s  sgn_r = r, f1
+      tbit.z p11, p12 = N_fix_gr, 0              // p11 if N even, p12 if odd
+
+}
+;;
+
+//
+//    xsq = x * x
+//    N even: Tx = T_hi * x
+//
+//    N even: Tx1 = Tx + 1
+//    N odd:  Cx1 = 1 - Cx
+//
+
+{ .mfi
+      nop.m 999
+      fmpy.s1 xsq = x, x
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p11) fmpy.s1 Tx = T_hi, x
+      nop.i 999
+}
+;;
+
+//
+//    N odd: Cx = C_hi * x
+//
+{ .mfi
+      nop.m 999
+(p12) fmpy.s1 Cx = C_hi, x
+      nop.i 999
+}
+;;
+//
+//    N even and odd: P = P2_3 + P2_2 * xsq
+//
+{ .mfi
+      nop.m 999
+      fma.s1 P = P2_3, xsq, P2_2
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p11) fadd.s1 Tx1 = Tx, f1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: D = C_hi - tanx
+//    N odd: D = T_hi + tanx
+//
+(p11) fmpy.s1 CORR = SC_inv, T_hi
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+      fmpy.s1 Sx = SC_inv, x
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fmpy.s1 CORR = SC_inv, C_hi
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fsub.s1 V_hi = f1, Cx
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+      fma.s1 P = P, xsq, P2_1
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+//
+//    N even and odd: P = P2_1 + P * xsq
+//
+(p11) fma.s1 V_hi = Tx, Tx1, f1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: Result  = sgn_r * tail + T_hi (user rounding mode for C1)
+//    N odd:  Result  = sgn_r * tail + C_hi (user rounding mode for C1)
+//
+      fmpy.s0 fp_tmp = fp_tmp, fp_tmp  // Dummy mult to set inexact
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+      fmpy.s1 CORR = CORR, c
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fnma.s1 V_hi = Cx,V_hi,f1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: V_hi = Tx * Tx1 + 1
+//    N odd: Cx1 = 1 - Cx * Cx1
+//
+      fmpy.s1 P = P, xsq
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+//
+//    N even and odd: P = P * xsq
+//
+(p11) fmpy.s1 V_hi = V_hi, T_hi
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even and odd: tail = P * tail + V_lo
+//
+(p11) fmpy.s1 T_hi = sgn_r, T_hi
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+      fmpy.s1 CORR = CORR, sgn_r
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+(p12) fmpy.s1 V_hi = V_hi,C_hi
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: V_hi = T_hi * V_hi
+//    N odd: V_hi  = C_hi * V_hi
+//
+      fma.s1 tanx = P, x, x
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fnmpy.s1 C_hi = sgn_r, C_hi
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: V_lo = 1 - V_hi + C_hi
+//    N odd: V_lo = 1 - V_hi + T_hi
+//
+(p11) fadd.s1 CORR = CORR, T_lo
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fsub.s1 CORR = CORR, C_lo
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even and odd: tanx = x + x * P
+//    N even and odd: Sx = SC_inv * x
+//
+(p11) fsub.s1 D = C_hi, tanx
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fadd.s1 D = T_hi, tanx
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N odd: CORR = SC_inv * C_hi
+//    N even: CORR = SC_inv * T_hi
+//
+      fnma.s1 D = V_hi, D, f1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even and odd: D = 1 - V_hi * D
+//    N even and odd: CORR = CORR * c
+//
+      fma.s1 V_hi = V_hi, D, V_hi
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even and odd: V_hi = V_hi + V_hi * D
+//    N even and odd: CORR = sgn_r * CORR
+//
+(p11) fnma.s1 V_lo = V_hi, C_hi, f1
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fnma.s1 V_lo = V_hi, T_hi, f1
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: CORR = COOR + T_lo
+//    N odd: CORR = CORR - C_lo
+//
+(p11) fma.s1 V_lo = tanx, V_hi, V_lo
+      tbit.nz p15, p0 = cot_flag, 0       // p15=1 if we compute cotl
+}
+{ .mfi
+      nop.m 999
+(p12) fnma.s1 V_lo = tanx, V_hi, V_lo
+      nop.i 999 ;;
+}
+
+{ .mfi
+      nop.m 999
+(p15) fms.s1 T_hi = f0, f0, T_hi        // to correct result's sign for cotl
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p15) fms.s1 C_hi = f0, f0, C_hi        // to correct result's sign for cotl
+      nop.i 999
+};;
+
+{ .mfi
+      nop.m 999
+(p15) fms.s1 sgn_r = f0, f0, sgn_r      // to correct result's sign for cotl
+      nop.i 999
+};;
+
+{ .mfi
+      nop.m 999
+//
+//    N even: V_lo = V_lo + V_hi * tanx
+//    N odd: V_lo = V_lo - V_hi * tanx
+//
+(p11) fnma.s1 V_lo = C_lo, V_hi, V_lo
+      nop.i 999
+}
+{ .mfi
+      nop.m 999
+(p12) fnma.s1 V_lo = T_lo, V_hi, V_lo
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N  even: V_lo = V_lo - V_hi * C_lo
+//    N  odd: V_lo = V_lo - V_hi * T_lo
+//
+      fmpy.s1 V_lo = V_hi, V_lo
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even and odd: V_lo = V_lo * V_hi
+//
+      fadd.s1 tail = V_hi, V_lo
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even and odd: tail = V_hi + V_lo
+//
+      fma.s1 tail = tail, P, V_lo
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even: T_hi = sgn_r * T_hi
+//    N odd : C_hi = -sgn_r * C_hi
+//
+      fma.s1 tail = tail, Sx, CORR
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even and odd: tail = Sx * tail + CORR
+//
+      fma.s1 tail = V_hi, Sx, tail
+      nop.i 999 ;;
+}
+{ .mfi
+      nop.m 999
+//
+//    N even an odd: tail = Sx * V_hi + tail
+//
+(p11) fma.s0 Result = sgn_r, tail, T_hi
+      nop.i 999
+}
+{ .mfb
+      nop.m 999
+(p12) fma.s0 Result = sgn_r, tail, C_hi
+      br.ret.sptk b0 ;;                 // Exit for 1/4 <= |r| < pi/4
+}
+
+TANL_DENORMAL:
+// Here if x denormal
+{ .mfb
+      getf.exp GR_signexp_x = Norm_Arg          // Get sign and exponent of x
+      nop.f 999
+      br.cond.sptk TANL_COMMON                  // Return to common code
+}
+;;
+
+
+TANL_SPECIAL:
+TANL_UNSUPPORTED:
+//
+//     Code for NaNs, Unsupporteds, Infs, or +/- zero ?
+//     Invalid raised for Infs and SNaNs.
+//
+
+{ .mfi
+      nop.m 999
+      fmerge.s  f10 = f8, f8            // Save input for error call
+      tbit.nz p6, p7 = cot_flag, 0      // p6=1 if we compute cotl
+}
+;;
+
+{ .mfi
+      nop.m 999
+(p6)  fclass.m p6, p7 = f8, 0x7         // Test for zero (cotl only)
+      nop.i 999
+}
+;;
+
+.pred.rel "mutex", p6, p7
+{ .mfi
+(p6)  mov GR_Parameter_Tag = 225        // (cotl)
+(p6)  frcpa.s0  f8, p0 = f1, f8         // cotl(+-0) = +-Inf
+      nop.i 999
+}
+{ .mfb
+      nop.m 999
+(p7)  fmpy.s0 f8 = f8, f0
+(p7)  br.ret.sptk b0
+}
+;;
+
+GLOBAL_IEEE754_END(tanl)
+
+
+LOCAL_LIBM_ENTRY(__libm_error_region)
+.prologue
+
+// (1)
+{ .mfi
+      add           GR_Parameter_Y=-32,sp        // Parameter 2 value
+      nop.f         0
+.save   ar.pfs,GR_SAVE_PFS
+      mov           GR_SAVE_PFS=ar.pfs           // Save ar.pfs
+}
+{ .mfi
+.fframe 64
+      add sp=-64,sp                              // Create new stack
+      nop.f 0
+      mov GR_SAVE_GP=gp                          // Save gp
+};;
+
+// (2)
+{ .mmi
+      stfe [GR_Parameter_Y] = f1,16              // STORE Parameter 2 on stack
+      add GR_Parameter_X = 16,sp                 // Parameter 1 address
+.save   b0, GR_SAVE_B0
+      mov GR_SAVE_B0=b0                          // Save b0
+};;
+
+.body
+// (3)
+{ .mib
+      stfe [GR_Parameter_X] = f10                // STORE Parameter 1 on stack
+      add   GR_Parameter_RESULT = 0,GR_Parameter_Y  // Parameter 3 address
+      nop.b 0
+}
+{ .mib
+      stfe [GR_Parameter_Y] = f8                 // STORE Parameter 3 on stack
+      add   GR_Parameter_Y = -16,GR_Parameter_Y
+      br.call.sptk b0=__libm_error_support#      // Call error handling function
+};;
+{ .mmi
+      nop.m 0
+      nop.m 0
+      add   GR_Parameter_RESULT = 48,sp
+};;
+
+// (4)
+{ .mmi
+      ldfe  f8 = [GR_Parameter_RESULT]           // Get return result off stack
+.restore sp
+      add   sp = 64,sp                           // Restore stack pointer
+      mov   b0 = GR_SAVE_B0                      // Restore return address
+};;
+{ .mib
+      mov   gp = GR_SAVE_GP                      // Restore gp
+      mov   ar.pfs = GR_SAVE_PFS                 // Restore ar.pfs
+      br.ret.sptk     b0                         // Return
+};;
+
+LOCAL_LIBM_END(__libm_error_region)
+
+.type   __libm_error_support#,@function
+.global __libm_error_support#
+
+
+// *******************************************************************
+// *******************************************************************
+// *******************************************************************
+//
+//     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
+//     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)
+TANL_ARG_TOO_LARGE:
+.prologue
+{ .mfi
+      add table_ptr2 = 144, table_base        // Point to 2^-2
+      nop.f 999
+.save   ar.pfs,GR_SAVE_PFS
+      mov  GR_SAVE_PFS=ar.pfs                 // Save ar.pfs
+}
+;;
+
+//     Load 2^-2, -2^-2
+{ .mmi
+      ldfps  TWO_TO_NEG2, NEGTWO_TO_NEG2 = [table_ptr2]
+      setf.sig B_mask1 = bmask1               // Form mask to get 5 msb of r
+.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
+      setf.sig B_mask2 = bmask2               // Form mask to form B from r
+      mov GR_SAVE_GP=gp                       // Save gp
+      br.call.sptk b0=__libm_pi_by_2_reduce#
+}
+;;
+
+//
+//     Is |r| < 2**(-2)
+//
+{ .mfi
+      getf.sig sig_r = r                     // Extract significand of r
+      fcmp.lt.s1  p6, p0 = r, TWO_TO_NEG2
+      mov   gp = GR_SAVE_GP                  // Restore gp
+}
+;;
+
+{ .mfi
+      getf.exp exp_r = r                     // Extract signexp of r
+      nop.f 999
+      mov    b0 = GR_SAVE_B0                 // Restore return address
+}
+;;
+
+//
+//     Get N_fix_gr
+//
+{ .mfi
+      mov   N_fix_gr = r8
+(p6)  fcmp.gt.unc.s1  p6, p0 = r, NEGTWO_TO_NEG2
+      mov   ar.pfs = GR_SAVE_PFS             // Restore pfs
+}
+;;
+
+{ .mbb
+      nop.m 999
+(p6)  br.cond.spnt TANL_SMALL_R              // Branch if |r| < 1/4
+      br.cond.sptk TANL_NORMAL_R             // Branch if 1/4 <= |r| < pi/4
+}
+;;
+
+LOCAL_LIBM_END(__libm_callout)
+
+.type __libm_pi_by_2_reduce#,@function
+.global __libm_pi_by_2_reduce#