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3312 lines
76 KiB
3312 lines
76 KiB
.file "libm_tan.s"
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// Copyright (c) 2000, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
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// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
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//
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// WARRANTY DISCLAIMER
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://developer.intel.com/opensource.
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//
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//*********************************************************************
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//
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// History:
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// 02/02/00 Initial Version
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// 4/04/00 Unwind support added
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//
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//*********************************************************************
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//
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// Function: tan(x) = tangent(x), for double precision x values
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//
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//*********************************************************************
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//
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// Accuracy: Very accurate for double-precision values
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//
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//*********************************************************************
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//
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// Resources Used:
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//
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// Floating-Point Registers: f8 (Input and Return Value)
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// f9-f15
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// f32-f112
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//
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// General Purpose Registers:
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// r32-r48
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// r49-r50 (Used to pass arguments to pi_by_2 reduce routine)
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//
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// Predicate Registers: p6-p15
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//
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//*********************************************************************
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//
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// IEEE Special Conditions:
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//
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// Denormal fault raised on denormal inputs
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// Overflow exceptions do not occur
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// Underflow exceptions raised when appropriate for tan
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// (No specialized error handling for this routine)
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// Inexact raised when appropriate by algorithm
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//
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// tan(SNaN) = QNaN
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// tan(QNaN) = QNaN
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// tan(inf) = QNaN
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// tan(+/-0) = +/-0
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//
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//*********************************************************************
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//
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// Mathematical Description
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//
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// We consider the computation of FPTAN of Arg. Now, given
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//
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// Arg = N pi/2 + alpha, |alpha| <= pi/4,
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//
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// basic mathematical relationship shows that
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//
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// tan( Arg ) = tan( alpha ) if N is even;
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// = -cot( alpha ) otherwise.
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//
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// The value of alpha is obtained by argument reduction and
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// represented by two working precision numbers r and c where
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//
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// alpha = r + c accurately.
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//
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// The reduction method is described in a previous write up.
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// The argument reduction scheme identifies 4 cases. For Cases 2
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// and 4, because |alpha| is small, tan(r+c) and -cot(r+c) can be
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// computed very easily by 2 or 3 terms of the Taylor series
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// expansion as follows:
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//
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// Case 2:
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// -------
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//
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// tan(r + c) = r + c + r^3/3 ...accurately
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// -cot(r + c) = -1/(r+c) + r/3 ...accurately
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//
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// Case 4:
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// -------
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//
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// tan(r + c) = r + c + r^3/3 + 2r^5/15 ...accurately
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// -cot(r + c) = -1/(r+c) + r/3 + r^3/45 ...accurately
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//
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//
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// The only cases left are Cases 1 and 3 of the argument reduction
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// procedure. These two cases will be merged since after the
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// argument is reduced in either cases, we have the reduced argument
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// represented as r + c and that the magnitude |r + c| is not small
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// enough to allow the usage of a very short approximation.
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//
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// The greatest challenge of this task is that the second terms of
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// the Taylor series for tan(r) and -cot(r)
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//
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// r + r^3/3 + 2 r^5/15 + ...
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//
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// and
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//
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// -1/r + r/3 + r^3/45 + ...
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//
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// are not very small when |r| is close to pi/4 and the rounding
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// errors will be a concern if simple polynomial accumulation is
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// used. When |r| < 2^(-2), however, the second terms will be small
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// enough (5 bits or so of right shift) that a normal Horner
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// recurrence suffices. Hence there are two cases that we consider
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// in the accurate computation of tan(r) and cot(r), |r| <= pi/4.
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//
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// Case small_r: |r| < 2^(-2)
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// --------------------------
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//
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// Since Arg = N pi/4 + r + c accurately, we have
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//
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// tan(Arg) = tan(r+c) for N even,
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// = -cot(r+c) otherwise.
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//
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// Here for this case, both tan(r) and -cot(r) can be approximated
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// by simple polynomials:
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//
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// tan(r) = r + P1_1 r^3 + P1_2 r^5 + ... + P1_9 r^19
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// -cot(r) = -1/r + Q1_1 r + Q1_2 r^3 + ... + Q1_7 r^13
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//
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// accurately. Since |r| is relatively small, tan(r+c) and
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// -cot(r+c) can be accurately approximated by replacing r with
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// r+c only in the first two terms of the corresponding polynomials.
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//
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// Note that P1_1 (and Q1_1 for that matter) approximates 1/3 to
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// almost 64 sig. bits, thus
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//
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// P1_1 (r+c)^3 = P1_1 r^3 + c * r^2 accurately.
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//
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// Hence,
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//
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// tan(r+c) = r + P1_1 r^3 + P1_2 r^5 + ... + P1_9 r^19
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// + c*(1 + r^2)
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//
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// -cot(r+c) = -1/(r+c) + Q1_1 r + Q1_2 r^3 + ... + Q1_7 r^13
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// + Q1_1*c
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//
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//
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// Case normal_r: 2^(-2) <= |r| <= pi/4
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// ------------------------------------
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//
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// This case is more likely than the previous one if one considers
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// r to be uniformly distributed in [-pi/4 pi/4].
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//
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// The required calculation is either
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//
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// tan(r + c) = tan(r) + correction, or
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// -cot(r + c) = -cot(r) + correction.
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//
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// Specifically,
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//
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// tan(r + c) = tan(r) + c tan'(r) + O(c^2)
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// = tan(r) + c sec^2(r) + O(c^2)
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// = tan(r) + c SEC_sq ...accurately
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// as long as SEC_sq approximates sec^2(r)
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// to, say, 5 bits or so.
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//
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// Similarly,
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//
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// -cot(r + c) = -cot(r) - c cot'(r) + O(c^2)
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// = -cot(r) + c csc^2(r) + O(c^2)
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// = -cot(r) + c CSC_sq ...accurately
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// as long as CSC_sq approximates csc^2(r)
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// to, say, 5 bits or so.
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//
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// We therefore concentrate on accurately calculating tan(r) and
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// cot(r) for a working-precision number r, |r| <= pi/4 to within
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// 0.1% or so.
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//
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// We will employ a table-driven approach. Let
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//
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// r = sgn_r * 2^k * 1.b_1 b_2 ... b_5 ... b_63
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// = sgn_r * ( B + x )
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//
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// where
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//
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// B = 2^k * 1.b_1 b_2 ... b_5 1
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// x = |r| - B
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//
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// Now,
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// tan(B) + tan(x)
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// tan( B + x ) = ------------------------
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// 1 - tan(B)*tan(x)
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//
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// / \
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// | tan(B) + tan(x) |
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// = tan(B) + | ------------------------ - tan(B) |
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// | 1 - tan(B)*tan(x) |
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// \ /
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//
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// sec^2(B) * tan(x)
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// = tan(B) + ------------------------
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// 1 - tan(B)*tan(x)
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//
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// (1/[sin(B)*cos(B)]) * tan(x)
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// = tan(B) + --------------------------------
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// cot(B) - tan(x)
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//
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//
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// Clearly, the values of tan(B), cot(B) and 1/(sin(B)*cos(B)) are
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// calculated beforehand and stored in a table. Since
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//
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// |x| <= 2^k * 2^(-6) <= 2^(-7) (because k = -1, -2)
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//
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// a very short polynomial will be sufficient to approximate tan(x)
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// accurately. The details involved in computing the last expression
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// will be given in the next section on algorithm description.
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//
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//
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// Now, we turn to the case where cot( B + x ) is needed.
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//
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//
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// 1 - tan(B)*tan(x)
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// cot( B + x ) = ------------------------
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// tan(B) + tan(x)
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//
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// / \
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// | 1 - tan(B)*tan(x) |
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// = cot(B) + | ----------------------- - cot(B) |
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// | tan(B) + tan(x) |
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// \ /
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//
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// [tan(B) + cot(B)] * tan(x)
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// = cot(B) - ----------------------------
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// tan(B) + tan(x)
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//
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// (1/[sin(B)*cos(B)]) * tan(x)
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// = cot(B) - --------------------------------
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// tan(B) + tan(x)
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//
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//
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// Note that the values of tan(B), cot(B) and 1/(sin(B)*cos(B)) that
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// are needed are the same set of values needed in the previous
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// case.
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//
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// Finally, we can put all the ingredients together as follows:
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//
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// Arg = N * pi/2 + r + c ...accurately
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//
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// tan(Arg) = tan(r) + correction if N is even;
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// = -cot(r) + correction otherwise.
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//
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// For Cases 2 and 4,
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//
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// Case 2:
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// tan(Arg) = tan(r + c) = r + c + r^3/3 N even
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// = -cot(r + c) = -1/(r+c) + r/3 N odd
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// Case 4:
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// tan(Arg) = tan(r + c) = r + c + r^3/3 + 2r^5/15 N even
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// = -cot(r + c) = -1/(r+c) + r/3 + r^3/45 N odd
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//
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//
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// For Cases 1 and 3,
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//
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// Case small_r: |r| < 2^(-2)
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//
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// tan(Arg) = r + P1_1 r^3 + P1_2 r^5 + ... + P1_9 r^19
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// + c*(1 + r^2) N even
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//
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// = -1/(r+c) + Q1_1 r + Q1_2 r^3 + ... + Q1_7 r^13
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// + Q1_1*c N odd
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//
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// Case normal_r: 2^(-2) <= |r| <= pi/4
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//
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// tan(Arg) = tan(r) + c * sec^2(r) N even
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// = -cot(r) + c * csc^2(r) otherwise
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//
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// For N even,
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//
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// tan(Arg) = tan(r) + c*sec^2(r)
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// = tan( sgn_r * (B+x) ) + c * sec^2(|r|)
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// = sgn_r * ( tan(B+x) + sgn_r*c*sec^2(|r|) )
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// = sgn_r * ( tan(B+x) + sgn_r*c*sec^2(B) )
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//
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// since B approximates |r| to 2^(-6) in relative accuracy.
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//
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// / (1/[sin(B)*cos(B)]) * tan(x)
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// tan(Arg) = sgn_r * | tan(B) + --------------------------------
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// \ cot(B) - tan(x)
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// \
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// + CORR |
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// /
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// where
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//
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// CORR = sgn_r*c*tan(B)*SC_inv(B); SC_inv(B) = 1/(sin(B)*cos(B)).
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//
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// For N odd,
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//
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// tan(Arg) = -cot(r) + c*csc^2(r)
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// = -cot( sgn_r * (B+x) ) + c * csc^2(|r|)
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// = sgn_r * ( -cot(B+x) + sgn_r*c*csc^2(|r|) )
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// = sgn_r * ( -cot(B+x) + sgn_r*c*csc^2(B) )
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//
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// since B approximates |r| to 2^(-6) in relative accuracy.
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//
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// / (1/[sin(B)*cos(B)]) * tan(x)
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// tan(Arg) = sgn_r * | -cot(B) + --------------------------------
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// \ tan(B) + tan(x)
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// \
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// + CORR |
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// /
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// where
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//
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// CORR = sgn_r*c*cot(B)*SC_inv(B); SC_inv(B) = 1/(sin(B)*cos(B)).
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//
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//
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// The actual algorithm prescribes how all the mathematical formulas
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// are calculated.
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//
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//
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// 2. Algorithmic Description
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// ==========================
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//
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// 2.1 Computation for Cases 2 and 4.
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// ----------------------------------
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//
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// For Case 2, we use two-term polynomials.
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//
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// For N even,
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//
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// rsq := r * r
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// Result := c + r * rsq * P1_1
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// Result := r + Result ...in user-defined rounding
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//
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// For N odd,
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// S_hi := -frcpa(r) ...8 bits
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// S_hi := S_hi + S_hi*(1 + S_hi*r) ...16 bits
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// S_hi := S_hi + S_hi*(1 + S_hi*r) ...32 bits
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// S_hi := S_hi + S_hi*(1 + S_hi*r) ...64 bits
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// S_lo := S_hi*( (1 + S_hi*r) + S_hi*c )
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// ...S_hi + S_lo is -1/(r+c) to extra precision
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// S_lo := S_lo + Q1_1*r
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//
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// Result := S_hi + S_lo ...in user-defined rounding
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//
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// For Case 4, we use three-term polynomials
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//
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// For N even,
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//
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// rsq := r * r
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// Result := c + r * rsq * (P1_1 + rsq * P1_2)
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// Result := r + Result ...in user-defined rounding
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//
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// For N odd,
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// S_hi := -frcpa(r) ...8 bits
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// S_hi := S_hi + S_hi*(1 + S_hi*r) ...16 bits
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// S_hi := S_hi + S_hi*(1 + S_hi*r) ...32 bits
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// S_hi := S_hi + S_hi*(1 + S_hi*r) ...64 bits
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// S_lo := S_hi*( (1 + S_hi*r) + S_hi*c )
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// ...S_hi + S_lo is -1/(r+c) to extra precision
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// rsq := r * r
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// P := Q1_1 + rsq*Q1_2
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// S_lo := S_lo + r*P
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//
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// Result := S_hi + S_lo ...in user-defined rounding
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//
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//
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// Note that the coefficients P1_1, P1_2, Q1_1, and Q1_2 are
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// the same as those used in the small_r case of Cases 1 and 3
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// below.
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//
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//
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// 2.2 Computation for Cases 1 and 3.
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// ----------------------------------
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// This is further divided into the case of small_r,
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// where |r| < 2^(-2), and the case of normal_r, where |r| lies between
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// 2^(-2) and pi/4.
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//
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// Algorithm for the case of small_r
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// ---------------------------------
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//
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// For N even,
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// rsq := r * r
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// Poly1 := rsq*(P1_1 + rsq*(P1_2 + rsq*P1_3))
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// r_to_the_8 := rsq * rsq
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// r_to_the_8 := r_to_the_8 * r_to_the_8
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// Poly2 := P1_4 + rsq*(P1_5 + rsq*(P1_6 + ... rsq*P1_9))
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// CORR := c * ( 1 + rsq )
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// Poly := Poly1 + r_to_the_8*Poly2
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// Result := r*Poly + CORR
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// Result := r + Result ...in user-defined rounding
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// ...note that Poly1 and r_to_the_8 can be computed in parallel
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// ...with Poly2 (Poly1 is intentionally set to be much
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// ...shorter than Poly2 so that r_to_the_8 and CORR can be hidden)
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//
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// For N odd,
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// S_hi := -frcpa(r) ...8 bits
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// S_hi := S_hi + S_hi*(1 + S_hi*r) ...16 bits
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// S_hi := S_hi + S_hi*(1 + S_hi*r) ...32 bits
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// S_hi := S_hi + S_hi*(1 + S_hi*r) ...64 bits
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// S_lo := S_hi*( (1 + S_hi*r) + S_hi*c )
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// ...S_hi + S_lo is -1/(r+c) to extra precision
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// S_lo := S_lo + Q1_1*c
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//
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// ...S_hi and S_lo are computed in parallel with
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// ...the following
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// rsq := r*r
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// P := Q1_1 + rsq*(Q1_2 + rsq*(Q1_3 + ... + rsq*Q1_7))
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//
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// Result := r*P + S_lo
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// Result := S_hi + Result ...in user-defined rounding
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//
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//
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// Algorithm for the case of normal_r
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// ----------------------------------
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//
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|
// Here, we first consider the computation of tan( r + c ). As
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// presented in the previous section,
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|
//
|
|
// tan( r + c ) = tan(r) + c * sec^2(r)
|
|
// = sgn_r * [ tan(B+x) + CORR ]
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// CORR = sgn_r * c * tan(B) * 1/[sin(B)*cos(B)]
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//
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|
// because sec^2(r) = sec^(|r|), and B approximate |r| to 6.5 bits.
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|
//
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|
// tan( r + c ) =
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// / (1/[sin(B)*cos(B)]) * tan(x)
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|
// sgn_r * | tan(B) + -------------------------------- +
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// \ cot(B) - tan(x)
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// \
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// CORR |
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|
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// /
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//
|
|
// 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.
|
|
//
|
|
//
|
|
|
|
.data
|
|
|
|
.align 128
|
|
|
|
TAN_BASE_CONSTANTS:
|
|
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
|
|
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 = f98
|
|
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_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
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .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]
|
|
nop.m 999
|
|
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 Q1_1 = Q1_1, Q1_1
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
//
|
|
// N odd: S_lo = S_lo + Q1_1 * r
|
|
//
|
|
(p12) fadd.s0 Result = S_hi, S_lo
|
|
//
|
|
// Do a dummy multiply to raise inexact.
|
|
//
|
|
(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 Q1_1 = Q1_1, Q1_1
|
|
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
|
|
//
|
|
// Do dummy multiply to raise inexact.
|
|
//
|
|
(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 Q1_1 = Q1_1, Q1_1
|
|
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
|
|
//
|
|
// Do multiply to raise inexact.
|
|
//
|
|
(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 P2_1 = P2_1, P2_1
|
|
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
|
|
//
|
|
// Do a multiply to raise inexact.
|
|
//
|
|
(p0) br.ret.sptk b0 ;;
|
|
}
|
|
|
|
.endp __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
|
|
add sp = 64,sp // Restore stack pointer
|
|
(p6) br.cond.spnt TAN_SMALL_R
|
|
(p0) br.cond.sptk TAN_NORMAL_R
|
|
}
|
|
;;
|
|
.endp __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
|
|
|
|
|
|
.type __libm_pi_by_2_reduce#,@function
|
|
.global __libm_pi_by_2_reduce#
|