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-.file "libm_tan.s"
-
-// Copyright (C) 2000, 2001, Intel Corporation
-// All rights reserved.
-//
-// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
-// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
-//
-// 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://developer.intel.com/opensource.
-//
-// *********************************************************************
-//
-// History:
-// 02/02/00 Initial Version
-// 4/04/00 Unwind support added
-// 12/28/00 Fixed false invalid flags
-//
-// *********************************************************************
-//
-// Function: tan(x) = tangent(x), for double precision x values
-//
-// *********************************************************************
-//
-// Accuracy: Very accurate for double-precision values
-//
-// *********************************************************************
-//
-// Resources Used:
-//
-// Floating-Point Registers: f8 (Input and Return Value)
-// f9-f15
-// f32-f112
-//
-// General Purpose Registers:
-// r32-r48
-// r49-r50 (Used to pass arguments to pi_by_2 reduce routine)
-//
-// Predicate Registers: p6-p15
-//
-// *********************************************************************
-//
-// IEEE Special Conditions:
-//
-// 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
-//
-// tan(SNaN) = QNaN
-// tan(QNaN) = QNaN
-// tan(inf) = QNaN
-// tan(+/-0) = +/-0
-//
-// *********************************************************************
-//
-// Mathematical Description
-//
-// We consider the computation of FPTAN 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
-// Result := c + r * rsq * P1_1
-// Result := r + Result ...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
-// Result := c + r * rsq * (P1_1 + rsq * P1_2)
-// Result := r + Result ...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
-// Result := r*Poly + CORR
-// Result := r + Result ...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))
-//
-// Result := r*P + S_lo
-// Result := S_hi + Result ...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.
-//
-//
-
-#include "libm_support.h"
-
-#ifdef _LIBC
-.rodata
-#else
-.data
-#endif
-
-.align 128
-
-TAN_BASE_CONSTANTS:
-ASM_TYPE_DIRECTIVE(TAN_BASE_CONSTANTS,@object)
-data4 0x4B800000, 0xCB800000, 0x38800000, 0xB8800000 // two**24, -two**24
- // two**-14, -two**-14
-data4 0x4E44152A, 0xA2F9836E, 0x00003FFE, 0x00000000 // two_by_pi
-data4 0xCE81B9F1, 0xC84D32B0, 0x00004016, 0x00000000 // P_0
-data4 0x2168C235, 0xC90FDAA2, 0x00003FFF, 0x00000000 // P_1
-data4 0xFC8F8CBB, 0xECE675D1, 0x0000BFBD, 0x00000000 // P_2
-data4 0xACC19C60, 0xB7ED8FBB, 0x0000BF7C, 0x00000000 // P_3
-data4 0x5F000000, 0xDF000000, 0x00000000, 0x00000000 // two_to_63, -two_to_63
-data4 0x6EC6B45A, 0xA397E504, 0x00003FE7, 0x00000000 // Inv_P_0
-data4 0xDBD171A1, 0x8D848E89, 0x0000BFBF, 0x00000000 // d_1
-data4 0x18A66F8E, 0xD5394C36, 0x0000BF7C, 0x00000000 // d_2
-data4 0x2168C234, 0xC90FDAA2, 0x00003FFE, 0x00000000 // PI_BY_4
-data4 0x2168C234, 0xC90FDAA2, 0x0000BFFE, 0x00000000 // MPI_BY_4
-data4 0x3E800000, 0xBE800000, 0x00000000, 0x00000000 // two**-2, -two**-2
-data4 0x2F000000, 0xAF000000, 0x00000000, 0x00000000 // two**-33, -two**-33
-data4 0xAAAAAABD, 0xAAAAAAAA, 0x00003FFD, 0x00000000 // P1_1
-data4 0x88882E6A, 0x88888888, 0x00003FFC, 0x00000000 // P1_2
-data4 0x0F0177B6, 0xDD0DD0DD, 0x00003FFA, 0x00000000 // P1_3
-data4 0x646B8C6D, 0xB327A440, 0x00003FF9, 0x00000000 // P1_4
-data4 0x1D5F7D20, 0x91371B25, 0x00003FF8, 0x00000000 // P1_5
-data4 0x61C67914, 0xEB69A5F1, 0x00003FF6, 0x00000000 // P1_6
-data4 0x019318D2, 0xBEDD37BE, 0x00003FF5, 0x00000000 // P1_7
-data4 0x3C794015, 0x9979B146, 0x00003FF4, 0x00000000 // P1_8
-data4 0x8C6EB58A, 0x8EBD21A3, 0x00003FF3, 0x00000000 // P1_9
-data4 0xAAAAAAB4, 0xAAAAAAAA, 0x00003FFD, 0x00000000 // Q1_1
-data4 0x0B5FC93E, 0xB60B60B6, 0x00003FF9, 0x00000000 // Q1_2
-data4 0x0C9BBFBF, 0x8AB355E0, 0x00003FF6, 0x00000000 // Q1_3
-data4 0xCBEE3D4C, 0xDDEBBC89, 0x00003FF2, 0x00000000 // Q1_4
-data4 0x5F80BBB6, 0xB3548A68, 0x00003FEF, 0x00000000 // Q1_5
-data4 0x4CED5BF1, 0x91362560, 0x00003FEC, 0x00000000 // Q1_6
-data4 0x8EE92A83, 0xF189D95A, 0x00003FE8, 0x00000000 // Q1_7
-data4 0xAAAB362F, 0xAAAAAAAA, 0x00003FFD, 0x00000000 // P2_1
-data4 0xE97A6097, 0x88888886, 0x00003FFC, 0x00000000 // P2_2
-data4 0x25E716A1, 0xDD108EE0, 0x00003FFA, 0x00000000 // P2_3
-//
-// 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)
-//
-data4 0x62400794, 0x3FD09BC3, 0x23A05C32, 0x00000000
-data4 0xDFFBC074, 0x3FD124A9, 0x240078B2, 0x00000000
-data4 0x5BD4920F, 0x3FD1AE23, 0x23826B8E, 0x00000000
-data4 0x15E2701D, 0x3FD23835, 0x22D31154, 0x00000000
-data4 0x63739C2D, 0x3FD2C2E4, 0x2265C9E2, 0x00000000
-data4 0xAFEEA48B, 0x3FD34E36, 0x245C05EB, 0x00000000
-data4 0x7DBB35D1, 0x3FD3DA31, 0x24749F2D, 0x00000000
-data4 0x67321619, 0x3FD466DA, 0x2462CECE, 0x00000000
-data4 0x1F94A4D5, 0x3FD4F437, 0x246D0DF1, 0x00000000
-data4 0x740C3E6D, 0x3FD5824D, 0x240A85B5, 0x00000000
-data4 0x4CB1E73D, 0x3FD61123, 0x23F96E33, 0x00000000
-data4 0xAD9EA64B, 0x3FD6A0BE, 0x247C5393, 0x00000000
-data4 0xB804FD01, 0x3FD73125, 0x241F3B29, 0x00000000
-data4 0xAB53EE83, 0x3FD7C25E, 0x2479989B, 0x00000000
-data4 0xE6640EED, 0x3FD8546F, 0x23B343BC, 0x00000000
-data4 0xE8AF1892, 0x3FD8E75F, 0x241454D1, 0x00000000
-data4 0x53928BDA, 0x3FD97B35, 0x238613D9, 0x00000000
-data4 0xEB9DE4DE, 0x3FDA0FF6, 0x22859FA7, 0x00000000
-data4 0x99ECF92D, 0x3FDAA5AB, 0x237A6D06, 0x00000000
-data4 0x6D8F1796, 0x3FDB3C5A, 0x23952F6C, 0x00000000
-data4 0x9CFB8BE4, 0x3FDBD40A, 0x2280FC95, 0x00000000
-data4 0x87943100, 0x3FDC6CC3, 0x245D2EC0, 0x00000000
-data4 0xB736C500, 0x3FDD068C, 0x23C4AD7D, 0x00000000
-data4 0xE1DDBC31, 0x3FDDA16D, 0x23D076E6, 0x00000000
-data4 0xEB515A93, 0x3FDE3D6E, 0x244809A6, 0x00000000
-data4 0xE6E9E5F1, 0x3FDEDA97, 0x220856C8, 0x00000000
-data4 0x1963CE69, 0x3FDF78F1, 0x244BE993, 0x00000000
-data4 0x7D635BCE, 0x3FE00C41, 0x23D21799, 0x00000000
-data4 0x1C302CD3, 0x3FE05CAB, 0x248A1B1D, 0x00000000
-data4 0xDB6A1FA0, 0x3FE0ADB9, 0x23D53E33, 0x00000000
-data4 0x4A20BA81, 0x3FE0FF72, 0x24DB9ED5, 0x00000000
-data4 0x153FA6F5, 0x3FE151D9, 0x24E9E451, 0x00000000
-//
-// 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)
-//
-data4 0xBA1BE39E, 0x3FE1CEC4, 0x24B60F9E, 0x00000000
-data4 0x5ABD9B2D, 0x3FE277E4, 0x248C2474, 0x00000000
-data4 0x0272B110, 0x3FE32418, 0x247B8311, 0x00000000
-data4 0x890E2DF0, 0x3FE3D38B, 0x24C55751, 0x00000000
-data4 0x46236871, 0x3FE4866D, 0x24E5BC34, 0x00000000
-data4 0x45E044B0, 0x3FE53CEE, 0x24001BA4, 0x00000000
-data4 0x82EC06E4, 0x3FE5F742, 0x24B973DC, 0x00000000
-data4 0x25DF43F9, 0x3FE6B5A1, 0x24895440, 0x00000000
-data4 0xCAFD348C, 0x3FE77844, 0x240021CA, 0x00000000
-data4 0xCEED6B92, 0x3FE83F6B, 0x24C45372, 0x00000000
-data4 0xA34F3665, 0x3FE90B58, 0x240DAD33, 0x00000000
-data4 0x2C1E56B4, 0x3FE9DC52, 0x24F846CE, 0x00000000
-data4 0x27041578, 0x3FEAB2A4, 0x2323FB6E, 0x00000000
-data4 0x9DD8C373, 0x3FEB8E9F, 0x24B3090B, 0x00000000
-data4 0x65C9AA7B, 0x3FEC709B, 0x2449F611, 0x00000000
-data4 0xACCF8435, 0x3FED58F4, 0x23616A7E, 0x00000000
-data4 0x97635082, 0x3FEE480F, 0x24C2FEAE, 0x00000000
-data4 0xF0ACC544, 0x3FEF3E57, 0x242CE964, 0x00000000
-data4 0xF7E06E4B, 0x3FF01E20, 0x2480D3EE, 0x00000000
-data4 0x8A798A69, 0x3FF0A125, 0x24DB8967, 0x00000000
-//
-// 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)
-//
-data4 0xE63EFBD0, 0x400ED3E2, 0x259D94D4, 0x00000000
-data4 0xC515DAB5, 0x400DDDB4, 0x245F0537, 0x00000000
-data4 0xBE19A79F, 0x400CF57A, 0x25D4EA9F, 0x00000000
-data4 0xD15298ED, 0x400C1A06, 0x24AE40A0, 0x00000000
-data4 0x164B2708, 0x400B4A4C, 0x25A5AAB6, 0x00000000
-data4 0x5285B068, 0x400A855A, 0x25524F18, 0x00000000
-data4 0x3FFA549F, 0x4009CA5A, 0x24C999C0, 0x00000000
-data4 0x646AF623, 0x4009188A, 0x254FD801, 0x00000000
-data4 0x6084D0E7, 0x40086F3C, 0x2560F5FD, 0x00000000
-data4 0xA29A76EE, 0x4007CDD2, 0x255B9D19, 0x00000000
-data4 0x6C8ECA95, 0x400733BE, 0x25CB021B, 0x00000000
-data4 0x1F8DDC52, 0x4006A07E, 0x24AB4722, 0x00000000
-data4 0xC298AD58, 0x4006139B, 0x252764E2, 0x00000000
-data4 0xBAD7164B, 0x40058CAB, 0x24DAF5DB, 0x00000000
-data4 0xAE31A5D3, 0x40050B4B, 0x25EA20F4, 0x00000000
-data4 0x89F85A8A, 0x40048F21, 0x2583A3E8, 0x00000000
-data4 0xA862380D, 0x400417DA, 0x25DCC4CC, 0x00000000
-data4 0x1088FCFE, 0x4003A52B, 0x2430A492, 0x00000000
-data4 0xCD3527D5, 0x400336CC, 0x255F77CF, 0x00000000
-data4 0x5760766D, 0x4002CC7F, 0x25DA0BDA, 0x00000000
-data4 0x11CE02E3, 0x40026607, 0x256FF4A2, 0x00000000
-data4 0xD37BBE04, 0x4002032C, 0x25208AED, 0x00000000
-data4 0x7F050775, 0x4001A3BD, 0x24B72DD6, 0x00000000
-data4 0xA554848A, 0x40014789, 0x24AB4DAA, 0x00000000
-data4 0x323E81B7, 0x4000EE65, 0x2584C440, 0x00000000
-data4 0x21CF1293, 0x40009827, 0x25C9428D, 0x00000000
-data4 0x3D415EEB, 0x400044A9, 0x25DC8482, 0x00000000
-data4 0xBD72C577, 0x3FFFE78F, 0x257F5070, 0x00000000
-data4 0x75EFD28E, 0x3FFF4AC3, 0x23EBBF7A, 0x00000000
-data4 0x60B52DDE, 0x3FFEB2AF, 0x22EECA07, 0x00000000
-data4 0x35204180, 0x3FFE1F19, 0x24191079, 0x00000000
-data4 0x54F7E60A, 0x3FFD8FCA, 0x248D3058, 0x00000000
-//
-// 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)
-//
-data4 0x79F6FADE, 0x3FFCC06A, 0x239C7886, 0x00000000
-data4 0x891662A6, 0x3FFBB91F, 0x250BD191, 0x00000000
-data4 0x529F155D, 0x3FFABFB6, 0x256CC3E6, 0x00000000
-data4 0x2E964AE9, 0x3FF9D300, 0x250843E3, 0x00000000
-data4 0x89DCB383, 0x3FF8F1EF, 0x2277C87E, 0x00000000
-data4 0x7C87DBD6, 0x3FF81B93, 0x256DA6CF, 0x00000000
-data4 0x1042EDE4, 0x3FF74F14, 0x2573D28A, 0x00000000
-data4 0x1784B360, 0x3FF68BAF, 0x242E489A, 0x00000000
-data4 0x7C923C4C, 0x3FF5D0B5, 0x2532D940, 0x00000000
-data4 0xF418EF20, 0x3FF51D88, 0x253C7DD6, 0x00000000
-data4 0x02F88DAE, 0x3FF4719A, 0x23DB59BF, 0x00000000
-data4 0x49DA0788, 0x3FF3CC66, 0x252B4756, 0x00000000
-data4 0x0B980DB8, 0x3FF32D77, 0x23FE585F, 0x00000000
-data4 0xE56C987A, 0x3FF2945F, 0x25378A63, 0x00000000
-data4 0xB16523F6, 0x3FF200BD, 0x247BB2E0, 0x00000000
-data4 0x8CE27778, 0x3FF17235, 0x24446538, 0x00000000
-data4 0xFDEFE692, 0x3FF0E873, 0x2514638F, 0x00000000
-data4 0x33154062, 0x3FF0632C, 0x24A7FC27, 0x00000000
-data4 0xB3EF115F, 0x3FEFC42E, 0x248FD0FE, 0x00000000
-data4 0x135D26F6, 0x3FEEC9E8, 0x2385C719, 0x00000000
-//
-// Entries SC_inv in Swapped IEEE format (extended)
-// Index = 0,1,...,31 B = 2^(-2)*(1+Index/32+1/64)
-//
-data4 0x1BF30C9E, 0x839D6D4A, 0x00004001, 0x00000000
-data4 0x554B0EB0, 0x80092804, 0x00004001, 0x00000000
-data4 0xA1CF0DE9, 0xF959F94C, 0x00004000, 0x00000000
-data4 0x77378677, 0xF3086BA0, 0x00004000, 0x00000000
-data4 0xCCD4723C, 0xED154515, 0x00004000, 0x00000000
-data4 0x1C27CF25, 0xE7790944, 0x00004000, 0x00000000
-data4 0x8DDACB88, 0xE22D037D, 0x00004000, 0x00000000
-data4 0x89C73522, 0xDD2B2D8A, 0x00004000, 0x00000000
-data4 0xBB2C1171, 0xD86E1A23, 0x00004000, 0x00000000
-data4 0xDFF5E0F9, 0xD3F0E288, 0x00004000, 0x00000000
-data4 0x283BEBD5, 0xCFAF16B1, 0x00004000, 0x00000000
-data4 0x0D88DD53, 0xCBA4AFAA, 0x00004000, 0x00000000
-data4 0xCA67C43D, 0xC7CE03CC, 0x00004000, 0x00000000
-data4 0x0CA0DDB0, 0xC427BC82, 0x00004000, 0x00000000
-data4 0xF13D8CAB, 0xC0AECD57, 0x00004000, 0x00000000
-data4 0x71ECE6B1, 0xBD606C38, 0x00004000, 0x00000000
-data4 0xA44C4929, 0xBA3A0A96, 0x00004000, 0x00000000
-data4 0xE5CCCEC1, 0xB7394F6F, 0x00004000, 0x00000000
-data4 0x9637D8BC, 0xB45C1203, 0x00004000, 0x00000000
-data4 0x92CB051B, 0xB1A05528, 0x00004000, 0x00000000
-data4 0x6BA2FFD0, 0xAF04432B, 0x00004000, 0x00000000
-data4 0x7221235F, 0xAC862A23, 0x00004000, 0x00000000
-data4 0x5F00A9D1, 0xAA2478AF, 0x00004000, 0x00000000
-data4 0x81E082BF, 0xA7DDBB0C, 0x00004000, 0x00000000
-data4 0x45684FEE, 0xA5B0987D, 0x00004000, 0x00000000
-data4 0x627A8F53, 0xA39BD0F5, 0x00004000, 0x00000000
-data4 0x6EC5C8B0, 0xA19E3B03, 0x00004000, 0x00000000
-data4 0x91CD7C66, 0x9FB6C1F0, 0x00004000, 0x00000000
-data4 0x1FA3DF8A, 0x9DE46410, 0x00004000, 0x00000000
-data4 0xA8F6B888, 0x9C263139, 0x00004000, 0x00000000
-data4 0xC27B0450, 0x9A7B4968, 0x00004000, 0x00000000
-data4 0x5EE614EE, 0x98E2DB7E, 0x00004000, 0x00000000
-//
-// Entries SC_inv in Swapped IEEE format (extended)
-// Index = 0,1,...,19 B = 2^(-1)*(1+Index/32+1/64)
-//
-data4 0x13B2B5BA, 0x969F335C, 0x00004000, 0x00000000
-data4 0xD4C0F548, 0x93D446D9, 0x00004000, 0x00000000
-data4 0x61B798AF, 0x9147094F, 0x00004000, 0x00000000
-data4 0x758787AC, 0x8EF317CC, 0x00004000, 0x00000000
-data4 0xB99EEFDB, 0x8CD498B3, 0x00004000, 0x00000000
-data4 0xDFF8BC37, 0x8AE82A7D, 0x00004000, 0x00000000
-data4 0xE3C55D42, 0x892AD546, 0x00004000, 0x00000000
-data4 0xD15573C1, 0x8799FEA9, 0x00004000, 0x00000000
-data4 0x435A4B4C, 0x86335F88, 0x00004000, 0x00000000
-data4 0x3E93A87B, 0x84F4FB6E, 0x00004000, 0x00000000
-data4 0x80A382FB, 0x83DD1952, 0x00004000, 0x00000000
-data4 0xA4CB8C9E, 0x82EA3D7F, 0x00004000, 0x00000000
-data4 0x6861D0A8, 0x821B247C, 0x00004000, 0x00000000
-data4 0x63E8D244, 0x816EBED1, 0x00004000, 0x00000000
-data4 0x27E4CFC6, 0x80E42D91, 0x00004000, 0x00000000
-data4 0x28E64AFD, 0x807ABF8D, 0x00004000, 0x00000000
-data4 0x863B4FD8, 0x8031EF26, 0x00004000, 0x00000000
-data4 0xAE8C11FD, 0x800960AD, 0x00004000, 0x00000000
-data4 0x5FDBEC21, 0x8000E147, 0x00004000, 0x00000000
-data4 0xA07791FA, 0x80186650, 0x00004000, 0x00000000
-
-Arg = f8
-Result = f8
-fp_tmp = f9
-U_2 = f10
-rsq = f11
-C_hi = f12
-C_lo = f13
-T_hi = f14
-T_lo = f15
-
-N_0 = f32
-d_1 = f33
-MPI_BY_4 = 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
-
-TWO_TO_63 = f54
-NEGTWO_TO_63 = f55
-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
-PI_BY_4 = f71
-NEGTWO_TO_NEG2 = f72
-TWO_TO_24 = f73
-TWO_TO_NEG14 = f74
-TWO_TO_NEG33 = f75
-NEGTWO_TO_24 = f76
-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
-c = f86
-r = f87
-Z = f88
-A = f89
-a = f90
-t = f91
-U_1 = f92
-d_2 = 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
-
-GR_SAVE_B0 = r33
-GR_SAVE_GP = r34
-GR_SAVE_PFS = r35
-
-delta1 = r36
-table_ptr1 = r37
-table_ptr2 = r38
-i_0 = r39
-i_1 = r40
-N_fix_gr = r41
-N_inc = r42
-exp_Arg = r43
-exp_r = r44
-sig_r = r45
-lookup = r46
-table_offset = r47
-Create_B = r48
-gr_tmp = r49
-
-GR_Parameter_X = r49
-GR_Parameter_r = r50
-
-
-
-.global __libm_tan
-.section .text
-.proc __libm_tan
-
-
-__libm_tan:
-
-{ .mfi
-alloc r32 = ar.pfs, 0,17,2,0
-(p0) fclass.m.unc p6,p0 = Arg, 0x1E7
- addl gr_tmp = -1,r0
-}
-;;
-
-{ .mfi
- nop.m 999
-(p0) fclass.nm.unc p7,p0 = Arg, 0x1FF
- nop.i 999
-}
-;;
-
-{ .mfi
-(p0) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp
- nop.f 999
- nop.i 999
-}
-;;
-
-{ .mmi
- ld8 table_ptr1 = [table_ptr1]
- setf.sig fp_tmp = gr_tmp // Make a constant so fmpy produces inexact
- nop.i 999
-}
-;;
-
-//
-// Check for NatVals, Infs , NaNs, and Zeros
-// Check for everything - if false, then must be pseudo-zero
-// or pseudo-nan.
-// Local table pointer
-//
-
-{ .mbb
-(p0) add table_ptr2 = 96, table_ptr1
-(p6) br.cond.spnt __libm_TAN_SPECIAL
-(p7) br.cond.spnt __libm_TAN_SPECIAL ;;
-}
-//
-// Point to Inv_P_0
-// Branch out to deal with unsupporteds and special values.
-//
-
-{ .mmf
-(p0) ldfs TWO_TO_24 = [table_ptr1],4
-(p0) ldfs TWO_TO_63 = [table_ptr2],4
-//
-// Load -2**24, load -2**63.
-//
-(p0) fcmp.eq.s0 p0, p6 = Arg, f1 ;;
-}
-
-{ .mfi
-(p0) ldfs NEGTWO_TO_63 = [table_ptr2],12
-(p0) fnorm.s1 Arg = Arg
- nop.i 999
-}
-//
-// Load 2**24, Load 2**63.
-//
-
-{ .mmi
-(p0) ldfs NEGTWO_TO_24 = [table_ptr1],12 ;;
-//
-// Do fcmp to generate Denormal exception
-// - can't do FNORM (will generate Underflow when U is unmasked!)
-// Normalize input argument.
-//
-(p0) ldfe two_by_PI = [table_ptr1],16
- nop.i 999
-}
-
-{ .mmi
-(p0) ldfe Inv_P_0 = [table_ptr2],16 ;;
-(p0) ldfe d_1 = [table_ptr2],16
- nop.i 999
-}
-//
-// Decide about the paths to take:
-// PR_1 and PR_3 set if -2**24 < Arg < 2**24 - CASE 1 OR 2
-// OTHERWISE - CASE 3 OR 4
-// Load inverse of P_0 .
-// Set PR_6 if Arg <= -2**63
-// Are there any Infs, NaNs, or zeros?
-//
-
-{ .mmi
-(p0) ldfe P_0 = [table_ptr1],16 ;;
-(p0) ldfe d_2 = [table_ptr2],16
- nop.i 999
-}
-//
-// Set PR_8 if Arg <= -2**24
-// Set PR_6 if Arg >= 2**63
-//
-
-{ .mmi
-(p0) ldfe P_1 = [table_ptr1],16 ;;
-(p0) ldfe PI_BY_4 = [table_ptr2],16
- nop.i 999
-}
-//
-// Set PR_8 if Arg >= 2**24
-//
-
-{ .mmi
-(p0) ldfe P_2 = [table_ptr1],16 ;;
-(p0) ldfe MPI_BY_4 = [table_ptr2],16
- nop.i 999
-}
-//
-// Load P_2 and PI_BY_4
-//
-
-{ .mfi
-(p0) ldfe P_3 = [table_ptr1],16
- nop.f 999
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p0) fcmp.le.unc.s1 p6,p7 = Arg,NEGTWO_TO_63
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p0) fcmp.le.unc.s1 p8,p9 = Arg,NEGTWO_TO_24
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p7) fcmp.ge.s1 p6,p0 = Arg,TWO_TO_63
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p9) fcmp.ge.s1 p8,p0 = Arg,TWO_TO_24
- nop.i 999 ;;
-}
-
-{ .mib
- nop.m 999
- nop.i 999
-//
-// Load P_3 and -PI_BY_4
-//
-(p6) br.cond.spnt TAN_ARG_TOO_LARGE ;;
-}
-
-{ .mib
- nop.m 999
- nop.i 999
-//
-// Load 2**(-2).
-// Load -2**(-2).
-// Branch out if we have a special argument.
-// Branch out if the magnitude of the input argument is too large
-// - do this branch before the next.
-//
-(p8) br.cond.spnt TAN_LARGER_ARG ;;
-}
-//
-// Branch to Cases 3 or 4 if Arg <= -2**24 or Arg >= 2**24
-//
-
-{ .mfi
-(p0) ldfs TWO_TO_NEG2 = [table_ptr2],4
-// ARGUMENT REDUCTION CODE - CASE 1 and 2
-// Load 2**(-2).
-// Load -2**(-2).
-(p0) fmpy.s1 N = Arg,two_by_PI
- nop.i 999 ;;
-}
-
-{ .mfi
-(p0) ldfs NEGTWO_TO_NEG2 = [table_ptr2],12
-//
-// N = Arg * 2/pi
-//
-(p0) fcmp.lt.unc.s1 p8,p9= Arg,PI_BY_4
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// if Arg < pi/4, set PR_8.
-//
-(p8) fcmp.gt.s1 p8,p9= Arg,MPI_BY_4
- nop.i 999 ;;
-}
-//
-// Case 1: Is |r| < 2**(-2).
-// Arg is the same as r in this case.
-// r = Arg
-// c = 0
-//
-
-{ .mfi
-(p8) mov N_fix_gr = r0
-//
-// if Arg > -pi/4, reset PR_8.
-// Select the case when |Arg| < pi/4 - set PR[8] = true.
-// Else Select the case when |Arg| >= pi/4 - set PR[9] = true.
-//
-(p0) fcvt.fx.s1 N_fix = N
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Grab the integer part of N .
-//
-(p8) mov r = Arg
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p8) mov c = f0
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p8) fcmp.lt.unc.s1 p10, p11 = Arg, TWO_TO_NEG2
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p10) fcmp.gt.s1 p10,p0 = Arg, NEGTWO_TO_NEG2
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 2: Place integer part of N in GP register.
-//
-(p9) fcvt.xf N = N_fix
- nop.i 999 ;;
-}
-
-{ .mib
-(p9) getf.sig N_fix_gr = N_fix
- nop.i 999
-//
-// Case 2: Convert integer N_fix back to normalized floating-point value.
-//
-(p10) br.cond.spnt TAN_SMALL_R ;;
-}
-
-{ .mib
- nop.m 999
- nop.i 999
-(p8) br.cond.sptk TAN_NORMAL_R ;;
-}
-//
-// Case 1: PR_3 is only affected when PR_1 is set.
-//
-
-{ .mmi
-(p9) ldfs TWO_TO_NEG33 = [table_ptr2], 4 ;;
-//
-// Case 2: Load 2**(-33).
-//
-(p9) ldfs NEGTWO_TO_NEG33 = [table_ptr2], 4
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 2: Load -2**(-33).
-//
-(p9) fnma.s1 s_val = N, P_1, Arg
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p9) fmpy.s1 w = N, P_2
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 2: w = N * P_2
-// Case 2: s_val = -N * P_1 + Arg
-//
-(p0) fcmp.lt.unc.s1 p9,p8 = s_val, TWO_TO_NEG33
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Decide between case_1 and case_2 reduce:
-//
-(p9) fcmp.gt.s1 p9, p8 = s_val, NEGTWO_TO_NEG33
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 1_reduce: s <= -2**(-33) or s >= 2**(-33)
-// Case 2_reduce: -2**(-33) < s < 2**(-33)
-//
-(p8) fsub.s1 r = s_val, w
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p9) fmpy.s1 w = N, P_3
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p9) fma.s1 U_1 = N, P_2, w
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 1_reduce: Is |r| < 2**(-2), if so set PR_10
-// else set PR_11.
-//
-(p8) fsub.s1 c = s_val, r
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 1_reduce: r = s + w (change sign)
-// Case 2_reduce: w = N * P_3 (change sign)
-//
-(p8) fcmp.lt.unc.s1 p10, p11 = r, TWO_TO_NEG2
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p10) fcmp.gt.s1 p10, p11 = r, NEGTWO_TO_NEG2
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p9) fsub.s1 r = s_val, U_1
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 1_reduce: c is complete here.
-// c = c + w (w has not been negated.)
-// Case 2_reduce: r is complete here - continue to calculate c .
-// r = s - U_1
-//
-(p9) fms.s1 U_2 = N, P_2, U_1
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 1_reduce: c = s - r
-// Case 2_reduce: U_1 = N * P_2 + w
-//
-(p8) fsub.s1 c = c, w
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p9) fsub.s1 s_val = s_val, r
- nop.i 999
-}
-
-{ .mfb
- nop.m 999
-//
-// Case 2_reduce:
-// U_2 = N * P_2 - U_1
-// Not needed until later.
-//
-(p9) fadd.s1 U_2 = U_2, w
-//
-// Case 2_reduce:
-// s = s - r
-// U_2 = U_2 + w
-//
-(p10) br.cond.spnt TAN_SMALL_R ;;
-}
-
-{ .mib
- nop.m 999
- nop.i 999
-(p11) br.cond.sptk TAN_NORMAL_R ;;
-}
-
-{ .mii
- nop.m 999
-//
-// Case 2_reduce:
-// c = c - U_2
-// c is complete here
-// Argument reduction ends here.
-//
-(p9) extr.u i_1 = N_fix_gr, 0, 1 ;;
-(p9) cmp.eq.unc p11, p12 = 0x0000,i_1 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Is i_1 even or odd?
-// if i_1 == 0, set p11, else set p12.
-//
-(p11) fmpy.s1 rsq = r, Z
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p12) frcpa.s1 S_hi,p0 = f1, r
- nop.i 999
-}
-
-//
-// Case 1: Branch to SMALL_R or NORMAL_R.
-// Case 1 is done now.
-//
-
-{ .mfi
-(p9) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp
-(p9) fsub.s1 c = s_val, U_1
- nop.i 999 ;;
-}
-;;
-
-{ .mmi
-(p9) ld8 table_ptr1 = [table_ptr1]
- nop.m 999
- nop.i 999
-}
-;;
-
-{ .mmi
-(p9) add table_ptr1 = 224, table_ptr1 ;;
-(p9) ldfe P1_1 = [table_ptr1],144
- nop.i 999 ;;
-}
-//
-// Get [i_1] - lsb of N_fix_gr .
-// Load P1_1 and point to Q1_1 .
-//
-
-{ .mfi
-(p9) ldfe Q1_1 = [table_ptr1] , 0
-//
-// 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 Result = r, rsq, c
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// N even: Result = 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
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// N even: Result = Result + r
-// N odd: poly1 = 1.0 + S_hi * r 32 bits partial
-//
-(p11) fadd.s0 Result = r, Result
- 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
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-//
-// N odd: Result = S_hi + S_lo
-//
-(p0) fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-//
-// N odd: S_lo = S_lo + Q1_1 * r
-//
-(p12) fadd.s0 Result = S_hi, S_lo
-(p0) br.ret.sptk b0 ;;
-}
-
-
-TAN_LARGER_ARG:
-
-{ .mmf
-(p0) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp
- nop.m 999
-(p0) fmpy.s1 N_0 = Arg, Inv_P_0
-}
-;;
-
-//
-// ARGUMENT REDUCTION CODE - CASE 3 and 4
-//
-//
-// Adjust table_ptr1 to beginning of table.
-// N_0 = Arg * Inv_P_0
-//
-
-
-{ .mmi
-(p0) ld8 table_ptr1 = [table_ptr1]
- nop.m 999
- nop.i 999
-}
-;;
-
-
-{ .mmi
-(p0) add table_ptr1 = 8, table_ptr1 ;;
-//
-// Point to 2*-14
-//
-(p0) ldfs TWO_TO_NEG14 = [table_ptr1], 4
- nop.i 999 ;;
-}
-//
-// Load 2**(-14).
-//
-
-{ .mmi
-(p0) ldfs NEGTWO_TO_NEG14 = [table_ptr1], 180 ;;
-//
-// N_0_fix = integer part of N_0 .
-// Adjust table_ptr1 to beginning of table.
-//
-(p0) ldfs TWO_TO_NEG2 = [table_ptr1], 4
- nop.i 999 ;;
-}
-//
-// Make N_0 the integer part.
-//
-
-{ .mfi
-(p0) ldfs NEGTWO_TO_NEG2 = [table_ptr1]
-//
-// Load -2**(-14).
-//
-(p0) fcvt.fx.s1 N_0_fix = N_0
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p0) fcvt.xf N_0 = N_0_fix
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p0) fnma.s1 ArgPrime = N_0, P_0, Arg
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p0) fmpy.s1 w = N_0, d_1
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// ArgPrime = -N_0 * P_0 + Arg
-// w = N_0 * d_1
-//
-(p0) fmpy.s1 N = ArgPrime, two_by_PI
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// N = ArgPrime * 2/pi
-//
-(p0) fcvt.fx.s1 N_fix = N
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// N_fix is the integer part.
-//
-(p0) fcvt.xf N = N_fix
- nop.i 999 ;;
-}
-
-{ .mfi
-(p0) getf.sig N_fix_gr = N_fix
- nop.f 999
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// N is the integer part of the reduced-reduced argument.
-// Put the integer in a GP register.
-//
-(p0) fnma.s1 s_val = N, P_1, ArgPrime
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p0) fnma.s1 w = N, P_2, w
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// s_val = -N*P_1 + ArgPrime
-// w = -N*P_2 + w
-//
-(p0) fcmp.lt.unc.s1 p11, p10 = s_val, TWO_TO_NEG14
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p11) fcmp.gt.s1 p11, p10 = s_val, NEGTWO_TO_NEG14
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 3: r = s_val + w (Z complete)
-// Case 4: U_hi = N_0 * d_1
-//
-(p10) fmpy.s1 V_hi = N, P_2
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p11) fmpy.s1 U_hi = N_0, d_1
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 3: r = s_val + w (Z complete)
-// Case 4: U_hi = N_0 * d_1
-//
-(p11) fmpy.s1 V_hi = N, P_2
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p11) fmpy.s1 U_hi = N_0, d_1
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Decide between case 3 and 4:
-// Case 3: s <= -2**(-14) or s >= 2**(-14)
-// Case 4: -2**(-14) < s < 2**(-14)
-//
-(p10) fadd.s1 r = s_val, w
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p11) fmpy.s1 w = N, P_3
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 4: We need abs of both U_hi and V_hi - dont
-// worry about switched sign of V_hi .
-//
-(p11) fsub.s1 A = U_hi, V_hi
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 4: A = U_hi + V_hi
-// Note: Worry about switched sign of V_hi, so subtract instead of add.
-//
-(p11) fnma.s1 V_lo = N, P_2, V_hi
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p11) fms.s1 U_lo = N_0, d_1, U_hi
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p11) fabs V_hiabs = V_hi
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 4: V_hi = N * P_2
-// w = N * P_3
-// Note the product does not include the (-) as in the writeup
-// so (-) missing for V_hi and w .
-(p10) fadd.s1 r = s_val, w
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 3: c = s_val - r
-// Case 4: U_lo = N_0 * d_1 - U_hi
-//
-(p11) fabs U_hiabs = U_hi
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p11) fmpy.s1 w = N, P_3
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 4: Set P_12 if U_hiabs >= V_hiabs
-//
-(p11) fadd.s1 C_hi = s_val, A
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 4: C_hi = s_val + A
-//
-(p11) fadd.s1 t = U_lo, V_lo
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 3: Is |r| < 2**(-2), if so set PR_7
-// else set PR_8.
-// Case 3: If PR_7 is set, prepare to branch to Small_R.
-// Case 3: If PR_8 is set, prepare to branch to Normal_R.
-//
-(p10) fsub.s1 c = s_val, r
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 3: c = (s - r) + w (c complete)
-//
-(p11) fcmp.ge.unc.s1 p12, p13 = U_hiabs, V_hiabs
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p11) fms.s1 w = N_0, d_2, w
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 4: V_hi = N * P_2
-// w = N * P_3
-// Note the product does not include the (-) as in the writeup
-// so (-) missing for V_hi and w .
-//
-(p10) fcmp.lt.unc.s1 p14, p15 = r, TWO_TO_NEG2
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p14) fcmp.gt.s1 p14, p15 = r, NEGTWO_TO_NEG2
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-//
-// 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 .
-// Case 4: w = w + N_0 * d_2
-// Note: the (-) is now incorporated in w .
-//
-(p10) fadd.s1 c = c, w
-//
-// Case 4: t = U_lo + V_lo
-// Note: remember V_lo should be (-), subtract instead of add. NO
-//
-(p14) br.cond.spnt TAN_SMALL_R ;;
-}
-
-{ .mib
- nop.m 999
- nop.i 999
-(p15) br.cond.spnt TAN_NORMAL_R ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 3: Vector off when |r| < 2**(-2). Recall that PR_3 will be true.
-// The remaining stuff is for Case 4.
-//
-(p12) fsub.s1 a = U_hi, A
-(p11) extr.u i_1 = N_fix_gr, 0, 1 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 4: C_lo = s_val - C_hi
-//
-(p11) fadd.s1 t = t, w
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p13) fadd.s1 a = V_hi, A
- nop.i 999 ;;
-}
-
-//
-// Case 4: a = U_hi - A
-// a = V_hi - A (do an add to account for missing (-) on V_hi
-//
-
-{ .mfi
-(p11) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp
-(p11) fsub.s1 C_lo = s_val, C_hi
- nop.i 999
-}
-;;
-
-{ .mmi
-(p11) ld8 table_ptr1 = [table_ptr1]
- nop.m 999
- 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 .
-//
-//
-// Case 4: C_lo = (s_val - C_hi) + A
-//
-
-{ .mmi
-(p11) add table_ptr1 = 224, table_ptr1 ;;
-(p11) ldfe P1_1 = [table_ptr1], 16
- nop.i 999 ;;
-}
-
-{ .mfi
-(p11) ldfe P1_2 = [table_ptr1], 128
-//
-// Case 4: w = U_lo + V_lo + w
-//
-(p12) fsub.s1 a = a, V_hi
- nop.i 999 ;;
-}
-//
-// Case 4: r = C_hi + C_lo
-//
-
-{ .mfi
-(p11) ldfe Q1_1 = [table_ptr1], 16
-(p11) fadd.s1 C_lo = C_lo, A
- nop.i 999 ;;
-}
-//
-// Case 4: c = C_hi - r
-// Get [i_1] - lsb of N_fix_gr.
-//
-
-{ .mfi
-(p11) ldfe Q1_2 = [table_ptr1], 16
- nop.f 999
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p13) fsub.s1 a = U_hi, a
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p11) fadd.s1 t = t, a
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 4: t = t + a
-//
-(p11) fadd.s1 C_lo = C_lo, t
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 4: C_lo = C_lo + t
-//
-(p11) fadd.s1 r = C_hi, C_lo
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p11) fsub.s1 c = C_hi, r
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-//
-// Case 4: c = c + C_lo finished.
-// Is i_1 even or odd?
-// if i_1 == 0, set PR_4, else set PR_5.
-//
-// r and c have been computed.
-// We known whether this is the sine or cosine routine.
-// Make sure ftz mode is set - should be automatic when using wre
-(p0) fmpy.s1 rsq = r, r
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p11) fadd.s1 c = c , C_lo
-(p11) cmp.eq.unc p11, p12 = 0x0000, i_1 ;;
-}
-
-{ .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 Result = 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)
-//
-(p0) 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 Result = rsq, Result
- 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 = Result * rsq
-// N odd: S_hi = S_hi + S_hi*poly1 16 bits account for necessary
-//
-(p11) fma.s1 Result = r, Result, 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
-//
-(p11) fadd.s0 Result= r, Result
- 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 = Result * 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: Result1 = Result + 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
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-//
-// N odd: S_lo = S_lo + r * P
-//
-(p12) fadd.s0 Result = S_hi, S_lo
-(p0) br.ret.sptk b0 ;;
-}
-
-
-TAN_SMALL_R:
-
-{ .mii
- nop.m 999
-(p0) extr.u i_1 = N_fix_gr, 0, 1 ;;
-(p0) cmp.eq.unc p11, p12 = 0x0000, i_1
-}
-
-{ .mfi
- nop.m 999
-(p0) fmpy.s1 rsq = r, r
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p12) frcpa.s1 S_hi, p0 = f1, r
- nop.i 999
-}
-
-{ .mfi
-(p0) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp
- nop.f 999
- nop.i 999
-}
-;;
-
-{ .mmi
-(p0) ld8 table_ptr1 = [table_ptr1]
- nop.m 999
- nop.i 999
-}
-;;
-
-// *****************************************************************
-// *****************************************************************
-// *****************************************************************
-
-{ .mmi
-(p0) add table_ptr1 = 224, table_ptr1 ;;
-(p0) ldfe P1_1 = [table_ptr1], 16
- nop.i 999 ;;
-}
-// r and c have been computed.
-// We known whether this is the sine or cosine routine.
-// Make sure ftz mode is set - should be automatic when using wre
-// |r| < 2**(-2)
-
-{ .mfi
-(p0) ldfe P1_2 = [table_ptr1], 16
-(p11) fmpy.s1 r_to_the_8 = rsq, rsq
- nop.i 999 ;;
-}
-//
-// Set table_ptr1 to beginning of constant table.
-// Get [i_1] - lsb of N_fix_gr.
-//
-
-{ .mfi
-(p0) ldfe P1_3 = [table_ptr1], 96
-//
-// N even: rsq = r * r
-// N odd: S_hi = frcpa(r)
-//
-(p12) fmerge.ns S_hi = S_hi, S_hi
- nop.i 999 ;;
-}
-//
-// Is i_1 even or odd?
-// if i_1 == 0, set PR_11.
-// if i_1 != 0, set PR_12.
-//
-
-{ .mfi
-(p11) ldfe P1_9 = [table_ptr1], -16
-//
-// N even: Poly2 = P1_7 + Poly2 * rsq
-// N odd: poly2 = Q1_5 + poly2 * rsq
-//
-(p11) fadd.s1 CORR = rsq, f1
- nop.i 999 ;;
-}
-
-{ .mmi
-(p11) ldfe P1_8 = [table_ptr1], -16 ;;
-//
-// N even: Poly1 = P1_2 + P1_3 * rsq
-// N odd: poly1 = 1.0 + S_hi * r
-// 16 bits partial account for necessary (-1)
-//
-(p11) ldfe P1_7 = [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
-//
-
-{ .mfi
-(p11) ldfe P1_6 = [table_ptr1], -16
-//
-// N even: Poly2 = P1_5 + Poly2 * rsq
-// N odd: poly2 = Q1_3 + poly2 * rsq
-//
-(p11) fmpy.s1 r_to_the_8 = r_to_the_8, r_to_the_8
- nop.i 999 ;;
-}
-//
-// N even: Poly1 = Poly1 * rsq
-// N odd: poly1 = 1.0 + S_hi * r 32 bits partial
-//
-
-{ .mfi
-(p11) ldfe P1_5 = [table_ptr1], -16
-(p12) fma.s1 poly1 = S_hi, r, f1
- nop.i 999 ;;
-}
-//
-// 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
-(p0) addl table_ptr2 = @ltoff(TAN_BASE_CONSTANTS), gp
-(p11) ldfe P1_4 = [table_ptr1], -16
-(p11) fmpy.s1 CORR = CORR, c
-}
-;;
-
-
-{ .mmi
-(p0) ld8 table_ptr2 = [table_ptr2]
- nop.m 999
- nop.i 999
-}
-;;
-
-
-{ .mii
-(p0) add table_ptr2 = 464, table_ptr2
- nop.i 999 ;;
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p11) fma.s1 Poly1 = P1_3, rsq, P1_2
- nop.i 999 ;;
-}
-
-{ .mfi
-(p0) ldfe Q1_7 = [table_ptr2], -16
-(p12) fma.s1 S_hi = S_hi, poly1, S_hi
- nop.i 999 ;;
-}
-
-{ .mfi
-(p0) ldfe Q1_6 = [table_ptr2], -16
-(p11) fma.s1 Poly2 = P1_9, rsq, P1_8
- nop.i 999 ;;
-}
-
-{ .mmi
-(p0) 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: Result = 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 Result = Poly, r, CORR
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// N even: Result = r + Result (User supplied rounding mode)
-// N odd: poly1 = S_hi * c + poly1
-//
-(p12) fmpy.s1 S_lo = S_hi, poly1
- nop.i 999
-}
-
-{ .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
-//
-(p11) fadd.s0 Result = Result, r
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// N odd: S_lo = S_hi * poly1
-//
-(p12) fma.s1 S_lo = Q1_1, c, S_lo
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-//
-// N odd: Result = Result + S_hi (user supplied rounding mode)
-//
-(p0) fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// N odd: S_lo = Q1_1 * c + S_lo
-//
-(p12) fma.s1 Result = P, r, S_lo
- nop.i 999 ;;
-}
-
-{ .mfb
- nop.m 999
-//
-// N odd: Result = S_lo + r * P
-//
-(p12) fadd.s0 Result = Result, S_hi
-(p0) br.ret.sptk b0 ;;
-}
-
-
-TAN_NORMAL_R:
-
-{ .mfi
-(p0) getf.sig sig_r = r
-// *******************************************************************
-// *******************************************************************
-// *******************************************************************
-//
-// r and c have been computed.
-// Make sure ftz mode is set - should be automatic when using wre
-//
-//
-// Get [i_1] - lsb of N_fix_gr alone.
-//
-(p0) fmerge.s Pos_r = f1, r
-(p0) extr.u i_1 = N_fix_gr, 0, 1 ;;
-}
-
-{ .mfi
- nop.m 999
-(p0) fmerge.s sgn_r = r, f1
-(p0) cmp.eq.unc p11, p12 = 0x0000, i_1 ;;
-}
-
-{ .mfi
- nop.m 999
- nop.f 999
-(p0) extr.u lookup = sig_r, 58, 5
-}
-
-{ .mlx
- nop.m 999
-(p0) movl Create_B = 0x8200000000000000 ;;
-}
-
-{ .mfi
-(p0) addl table_ptr1 = @ltoff(TAN_BASE_CONSTANTS), gp
- nop.f 999
-(p0) dep Create_B = lookup, Create_B, 58, 5
-}
-;;
-
-//
-// Get [i_1] - lsb of N_fix_gr alone.
-// Pos_r = abs (r)
-//
-
-
-{ .mmi
- ld8 table_ptr1 = [table_ptr1]
- nop.m 999
- nop.i 999
-}
-;;
-
-
-{ .mmi
- nop.m 999
-(p0) setf.sig B = Create_B
-//
-// Set table_ptr1 and table_ptr2 to base address of
-// constant table.
-//
-(p0) add table_ptr1 = 480, table_ptr1 ;;
-}
-
-{ .mmb
- nop.m 999
-//
-// Is i_1 or i_0 == 0 ?
-// Create the constant 1 00000 1000000000000000000000...
-//
-(p0) ldfe P2_1 = [table_ptr1], 16
- nop.b 999
-}
-
-{ .mmi
- nop.m 999 ;;
-(p0) getf.exp exp_r = Pos_r
- nop.i 999
-}
-//
-// Get r's exponent
-// Get r's significand
-//
-
-{ .mmi
-(p0) ldfe P2_2 = [table_ptr1], 16 ;;
-//
-// Get the 5 bits or r for the lookup. 1.xxxxx ....
-// from sig_r.
-// Grab lsb of exp of B
-//
-(p0) ldfe P2_3 = [table_ptr1], 16
- nop.i 999 ;;
-}
-
-{ .mii
- nop.m 999
-(p0) andcm table_offset = 0x0001, exp_r ;;
-(p0) shl table_offset = table_offset, 9 ;;
-}
-
-{ .mii
- nop.m 999
-//
-// Deposit 0 00000 1000000000000000000000... on
-// 1 xxxxx yyyyyyyyyyyyyyyyyyyyyy...,
-// getting rid of the ys.
-// Is B = 2** -2 or B= 2** -1? If 2**-1, then
-// we want an offset of 512 for table addressing.
-//
-(p0) shladd table_offset = lookup, 4, table_offset ;;
-//
-// B = ........ 1xxxxx 1000000000000000000...
-//
-(p0) add table_ptr1 = table_ptr1, table_offset ;;
-}
-
-{ .mmb
- nop.m 999
-//
-// B = ........ 1xxxxx 1000000000000000000...
-// Convert B so it has the same exponent as Pos_r
-//
-(p0) ldfd T_hi = [table_ptr1], 8
- nop.b 999 ;;
-}
-
-//
-// x = |r| - B
-// Load T_hi.
-// Load C_hi.
-//
-
-{ .mmf
-(p0) addl table_ptr2 = @ltoff(TAN_BASE_CONSTANTS), gp
-(p0) ldfs T_lo = [table_ptr1]
-(p0) fmerge.se B = Pos_r, B
-}
-;;
-
-{ .mmi
- ld8 table_ptr2 = [table_ptr2]
- nop.m 999
- nop.i 999
-}
-;;
-
-{ .mii
-(p0) add table_ptr2 = 1360, table_ptr2
- nop.i 999 ;;
-(p0) add table_ptr2 = table_ptr2, table_offset ;;
-}
-
-{ .mfi
-(p0) ldfd C_hi = [table_ptr2], 8
-(p0) fsub.s1 x = Pos_r, B
- nop.i 999 ;;
-}
-
-{ .mii
-(p0) ldfs C_lo = [table_ptr2],255
- nop.i 999 ;;
-//
-// xsq = x * x
-// N even: Tx = T_hi * x
-// Load T_lo.
-// Load C_lo - increment pointer to get SC_inv
-// - cant get all the way, do an add later.
-//
-(p0) add table_ptr2 = 569, table_ptr2 ;;
-}
-//
-// N even: Tx1 = Tx + 1
-// N odd: Cx1 = 1 - Cx
-//
-
-{ .mfi
-(p0) ldfe SC_inv = [table_ptr2], 0
- nop.f 999
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p0) fmpy.s1 xsq = x, x
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p11) fmpy.s1 Tx = T_hi, x
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p12) fmpy.s1 Cx = C_hi, x
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// N odd: Cx = C_hi * x
-//
-(p0) fma.s1 P = P2_3, xsq, P2_2
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-//
-// N even and odd: P = P2_3 + P2_2 * xsq
-//
-(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
-(p0) 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
-(p0) 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)
-//
-(p0) fmpy.s0 fp_tmp = fp_tmp, fp_tmp // Dummy mult to set inexact
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-(p0) 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
-//
-(p0) 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
-(p0) 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
-//
-(p0) 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
-//
-(p0) 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
-//
-(p0) 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
- nop.i 999
-}
-
-{ .mfi
- nop.m 999
-(p12) fnma.s1 V_lo = tanx, V_hi, V_lo
- 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
-//
-(p0) 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
-//
-(p0) fadd.s1 tail = V_hi, V_lo
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// N even and odd: tail = V_hi + V_lo
-//
-(p0) 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
-//
-(p0) fma.s1 tail = tail, Sx, CORR
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// N even and odd: tail = Sx * tail + CORR
-//
-(p0) 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
-(p0) br.ret.sptk b0 ;;
-}
-
-.endp __libm_tan
-ASM_SIZE_DIRECTIVE(__libm_tan)
-
-
-
-// *******************************************************************
-// *******************************************************************
-// *******************************************************************
-//
-// Special Code to handle very large argument case.
-// Call int pi_by_2_reduce(&x,&r)
-// for |arguments| >= 2**63
-// (Arg or x) is in f8
-// Address to save r and c as double
-
-// (1) (2) (3) (call) (4)
-// sp -> + psp -> + psp -> + sp -> +
-// | | | |
-// | r50 ->| <- r50 f0 ->| r50 -> | -> c
-// | | | |
-// sp-32 -> | <- r50 f0 ->| f0 ->| <- r50 r49 -> | -> r
-// | | | |
-// | r49 ->| <- r49 Arg ->| <- r49 | -> x
-// | | | |
-// sp -64 ->| sp -64 ->| sp -64 ->| |
-//
-// save pfs save b0 restore gp
-// save gp restore b0
-// restore pfs
-
-
-
-.proc __libm_callout
-__libm_callout:
-TAN_ARG_TOO_LARGE:
-.prologue
-// (1)
-{ .mfi
- add GR_Parameter_r =-32,sp // Parameter: r address
- nop.f 0
-.save ar.pfs,GR_SAVE_PFS
- mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
-}
-{ .mfi
-.fframe 64
- add sp=-64,sp // Create new stack
- nop.f 0
- mov GR_SAVE_GP=gp // Save gp
-};;
-
-// (2)
-{ .mmi
- stfe [GR_Parameter_r ] = f0,16 // Clear Parameter r on stack
- add GR_Parameter_X = 16,sp // Parameter x address
-.save b0, GR_SAVE_B0
- mov GR_SAVE_B0=b0 // Save b0
-};;
-
-// (3)
-.body
-{ .mib
- stfe [GR_Parameter_r ] = f0,-16 // Clear Parameter c on stack
- nop.i 0
- nop.b 0
-}
-{ .mib
- stfe [GR_Parameter_X] = Arg // Store Parameter x on stack
- nop.i 0
-(p0) br.call.sptk b0=__libm_pi_by_2_reduce#
-}
-;;
-
-
-// (4)
-{ .mmi
- mov gp = GR_SAVE_GP // Restore gp
-(p0) mov N_fix_gr = r8
- nop.i 999
-}
-;;
-
-{ .mmi
-(p0) ldfe Arg =[GR_Parameter_X],16
-(p0) ldfs TWO_TO_NEG2 = [table_ptr2],4
- nop.i 999
-}
-;;
-
-
-{ .mmb
-(p0) ldfe r =[GR_Parameter_r ],16
-(p0) ldfs NEGTWO_TO_NEG2 = [table_ptr2],4
- nop.b 999 ;;
-}
-
-{ .mfi
-(p0) ldfe c =[GR_Parameter_r ]
- nop.f 999
- nop.i 999 ;;
-}
-
-{ .mfi
- nop.m 999
-//
-// Is |r| < 2**(-2)
-//
-(p0) fcmp.lt.unc.s1 p6, p0 = r, TWO_TO_NEG2
- mov b0 = GR_SAVE_B0 // Restore return address
-}
-;;
-
-{ .mfi
- nop.m 999
-(p6) fcmp.gt.unc.s1 p6, p0 = r, NEGTWO_TO_NEG2
- mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
-}
-;;
-
-{ .mbb
-.restore sp
- add sp = 64,sp // Restore stack pointer
-(p6) br.cond.spnt TAN_SMALL_R
-(p0) br.cond.sptk TAN_NORMAL_R
-}
-;;
-.endp __libm_callout
-ASM_SIZE_DIRECTIVE(__libm_callout)
-
-
-.proc __libm_TAN_SPECIAL
-__libm_TAN_SPECIAL:
-
-//
-// Code for NaNs, Unsupporteds, Infs, or +/- zero ?
-// Invalid raised for Infs and SNaNs.
-//
-
-{ .mfb
- nop.m 999
-(p0) fmpy.s0 Arg = Arg, f0
-(p0) br.ret.sptk b0
-}
-.endp __libm_TAN_SPECIAL
-ASM_SIZE_DIRECTIVE(__libm_TAN_SPECIAL)
-
-
-.type __libm_pi_by_2_reduce#,@function
-.global __libm_pi_by_2_reduce#