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authorUlrich Drepper <drepper@gmail.com>2012-01-07 11:19:05 -0500
committerUlrich Drepper <drepper@gmail.com>2012-01-07 11:19:05 -0500
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Remove IA-64 support
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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#