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2758 lines
58 KiB
ArmAsm
2758 lines
58 KiB
ArmAsm
.file "libm_sincos_large.s"
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// Copyright (c) 2002 - 2003, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2002 by the Intel Numerics Group, Intel Corporation
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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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://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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// History
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//==============================================================
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// 02/15/02 Initial version
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// 05/13/02 Changed interface to __libm_pi_by_2_reduce
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// 02/10/03 Reordered header: .section, .global, .proc, .align;
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// used data8 for long double table values
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// 05/15/03 Reformatted data tables
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//
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//
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// Overview of operation
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//==============================================================
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//
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// These functions calculate the sin and cos for inputs
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// greater than 2^10
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//
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// __libm_sin_large#
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// __libm_cos_large#
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// They accept argument in f8
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// and return result in f8 without final rounding
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//
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// __libm_sincos_large#
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// It accepts argument in f8
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// and returns cos in f8 and sin in f9 without final rounding
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//
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//
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//*********************************************************************
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//
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// Accuracy: Within .7 ulps for 80-bit floating point values
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// 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 as Input Value, f8 and f9 as Return Values
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// f32-f103
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//
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// General Purpose Registers:
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// r32-r43
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// r44-r45 (Used to pass arguments to pi_by_2 reduce routine)
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//
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// Predicate Registers: p6-p13
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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 sin
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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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// sin(SNaN) = QNaN
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// sin(QNaN) = QNaN
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// sin(inf) = QNaN
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// sin(+/-0) = +/-0
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// cos(inf) = QNaN
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// cos(SNaN) = QNaN
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// cos(QNaN) = QNaN
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// cos(0) = 1
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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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//
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// The computation of FSIN and FCOS is best handled in one piece of
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// code. The main reason is that given any argument Arg, computation
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// of trigonometric functions first calculate N and an approximation
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// to alpha where
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//
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// Arg = N pi/2 + alpha, |alpha| <= pi/4.
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//
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// Since
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//
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// cos( Arg ) = sin( (N+1) pi/2 + alpha ),
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//
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// therefore, the code for computing sine will produce cosine as long
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// as 1 is added to N immediately after the argument reduction
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// process.
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//
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// Let M = N if sine
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// N+1 if cosine.
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//
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// Now, given
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//
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// Arg = M pi/2 + alpha, |alpha| <= pi/4,
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//
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// let I = M mod 4, or I be the two lsb of M when M is represented
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// as 2's complement. I = [i_0 i_1]. Then
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//
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// sin( Arg ) = (-1)^i_0 sin( alpha ) if i_1 = 0,
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// = (-1)^i_0 cos( alpha ) if i_1 = 1.
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//
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// For example:
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// if M = -1, I = 11
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// sin ((-pi/2 + alpha) = (-1) cos (alpha)
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// if M = 0, I = 00
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// sin (alpha) = sin (alpha)
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// if M = 1, I = 01
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// sin (pi/2 + alpha) = cos (alpha)
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// if M = 2, I = 10
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// sin (pi + alpha) = (-1) sin (alpha)
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// if M = 3, I = 11
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// sin ((3/2)pi + alpha) = (-1) cos (alpha)
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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, sin(r+c) and cos(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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// sin(r + c) = r + c - r^3/6 accurately
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// cos(r + c) = 1 - 2^(-67) accurately
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//
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// Case 4:
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// -------
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//
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// sin(r + c) = r + c - r^3/6 + r^5/120 accurately
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// cos(r + c) = 1 - r^2/2 + r^4/24 accurately
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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 required calculation is either
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//
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// sin(r + c) = sin(r) + correction, or
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// cos(r + c) = cos(r) + correction.
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//
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// Specifically,
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//
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// sin(r + c) = sin(r) + c sin'(r) + O(c^2)
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// = sin(r) + c cos (r) + O(c^2)
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// = sin(r) + c(1 - r^2/2) accurately.
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// Similarly,
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//
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// cos(r + c) = cos(r) - c sin(r) + O(c^2)
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// = cos(r) - c(r - r^3/6) accurately.
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//
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// We therefore concentrate on accurately calculating sin(r) and
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// cos(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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// The greatest challenge of this task is that the second terms of
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// the Taylor series
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//
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// r - r^3/3! + r^r/5! - ...
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//
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// and
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//
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// 1 - r^2/2! + r^4/4! - ...
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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^-3, however, the second terms will be small
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// enough (6 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 sin(r) and cos(r), |r| <= pi/4.
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//
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// Case small_r: |r| < 2^(-3)
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// --------------------------
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//
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// Since Arg = M pi/4 + r + c accurately, and M mod 4 is [i_0 i_1],
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// we have
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//
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// sin(Arg) = (-1)^i_0 * sin(r + c) if i_1 = 0
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// = (-1)^i_0 * cos(r + c) if i_1 = 1
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//
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// can be accurately approximated by
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//
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// sin(Arg) = (-1)^i_0 * [sin(r) + c] if i_1 = 0
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// = (-1)^i_0 * [cos(r) - c*r] if i_1 = 1
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//
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// because |r| is small and thus the second terms in the correction
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// are unneccessary.
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//
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// Finally, sin(r) and cos(r) are approximated by polynomials of
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// moderate lengths.
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//
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// sin(r) = r + S_1 r^3 + S_2 r^5 + ... + S_5 r^11
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// cos(r) = 1 + C_1 r^2 + C_2 r^4 + ... + C_5 r^10
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//
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// We can make use of predicates to selectively calculate
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// sin(r) or cos(r) based on i_1.
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//
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// Case normal_r: 2^(-3) <= |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]. Again,
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//
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// sin(Arg) = (-1)^i_0 * sin(r + c) if i_1 = 0
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// = (-1)^i_0 * cos(r + c) if i_1 = 1.
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//
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// Because |r| is now larger, we need one extra term in the
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// correction. sin(Arg) can be accurately approximated by
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//
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// sin(Arg) = (-1)^i_0 * [sin(r) + c(1-r^2/2)] if i_1 = 0
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// = (-1)^i_0 * [cos(r) - c*r*(1 - r^2/6)] i_1 = 1.
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//
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// Finally, sin(r) and cos(r) are approximated by polynomials of
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// moderate lengths.
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//
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// sin(r) = r + PP_1_hi r^3 + PP_1_lo r^3 +
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// PP_2 r^5 + ... + PP_8 r^17
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//
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// cos(r) = 1 + QQ_1 r^2 + QQ_2 r^4 + ... + QQ_8 r^16
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//
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// where PP_1_hi is only about 16 bits long and QQ_1 is -1/2.
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// The crux in accurate computation is to calculate
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//
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// r + PP_1_hi r^3 or 1 + QQ_1 r^2
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//
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// accurately as two pieces: U_hi and U_lo. The way to achieve this
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// is to obtain r_hi as a 10 sig. bit number that approximates r to
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// roughly 8 bits or so of accuracy. (One convenient way is
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//
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// r_hi := frcpa( frcpa( r ) ).)
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//
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// This way,
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//
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// r + PP_1_hi r^3 = r + PP_1_hi r_hi^3 +
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// PP_1_hi (r^3 - r_hi^3)
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// = [r + PP_1_hi r_hi^3] +
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// [PP_1_hi (r - r_hi)
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// (r^2 + r_hi r + r_hi^2) ]
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// = U_hi + U_lo
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//
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// Since r_hi is only 10 bit long and PP_1_hi is only 16 bit long,
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// PP_1_hi * r_hi^3 is only at most 46 bit long and thus computed
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// exactly. Furthermore, r and PP_1_hi r_hi^3 are of opposite sign
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// and that there is no more than 8 bit shift off between r and
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// PP_1_hi * r_hi^3. Hence the sum, U_hi, is representable and thus
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// calculated without any error. Finally, the fact that
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//
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// |U_lo| <= 2^(-8) |U_hi|
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//
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// says that U_hi + U_lo is approximating r + PP_1_hi r^3 to roughly
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// 8 extra bits of accuracy.
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//
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// Similarly,
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//
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// 1 + QQ_1 r^2 = [1 + QQ_1 r_hi^2] +
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// [QQ_1 (r - r_hi)(r + r_hi)]
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// = U_hi + U_lo.
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//
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// Summarizing, we calculate r_hi = frcpa( frcpa( r ) ).
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//
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// If i_1 = 0, then
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//
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// U_hi := r + PP_1_hi * r_hi^3
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// U_lo := PP_1_hi * (r - r_hi) * (r^2 + r*r_hi + r_hi^2)
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// poly := PP_1_lo r^3 + PP_2 r^5 + ... + PP_8 r^17
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// correction := c * ( 1 + C_1 r^2 )
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//
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// Else ...i_1 = 1
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//
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// U_hi := 1 + QQ_1 * r_hi * r_hi
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// U_lo := QQ_1 * (r - r_hi) * (r + r_hi)
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// poly := QQ_2 * r^4 + QQ_3 * r^6 + ... + QQ_8 r^16
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// correction := -c * r * (1 + S_1 * r^2)
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//
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// End
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//
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// Finally,
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//
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// V := poly + ( U_lo + correction )
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//
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// / U_hi + V if i_0 = 0
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// result := |
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// \ (-U_hi) - V if i_0 = 1
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//
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// It is important that in the last step, negation of U_hi is
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// performed prior to the subtraction which is to be performed in
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// the user-set rounding mode.
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//
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//
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// Algorithmic Description
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// =======================
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//
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// The argument reduction algorithm is tightly integrated into FSIN
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// and FCOS which share the same code. The following is complete and
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// self-contained. The argument reduction description given
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// previously is repeated below.
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//
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//
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// Step 0. Initialization.
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//
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// If FSIN is invoked, set N_inc := 0; else if FCOS is invoked,
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// set N_inc := 1.
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//
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// Step 1. Check for exceptional and special cases.
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//
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// * If Arg is +-0, +-inf, NaN, NaT, go to Step 10 for special
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// handling.
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// * If |Arg| < 2^24, go to Step 2 for reduction of moderate
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// arguments. This is the most likely case.
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// * If |Arg| < 2^63, go to Step 8 for pre-reduction of large
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// arguments.
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// * If |Arg| >= 2^63, go to Step 10 for special handling.
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//
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// Step 2. Reduction of moderate arguments.
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//
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// If |Arg| < pi/4 ...quick branch
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// N_fix := N_inc (integer)
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// r := Arg
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// c := 0.0
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// Branch to Step 4, Case_1_complete
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// Else ...cf. argument reduction
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// N := Arg * two_by_PI (fp)
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// N_fix := fcvt.fx( N ) (int)
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// N := fcvt.xf( N_fix )
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// N_fix := N_fix + N_inc
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// s := Arg - N * P_1 (first piece of pi/2)
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// w := -N * P_2 (second piece of pi/2)
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//
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// If |s| >= 2^(-33)
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// go to Step 3, Case_1_reduce
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// Else
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// go to Step 7, Case_2_reduce
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// Endif
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// Endif
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//
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// Step 3. Case_1_reduce.
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//
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// r := s + w
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// c := (s - r) + w ...observe order
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//
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// Step 4. Case_1_complete
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//
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// ...At this point, the reduced argument alpha is
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// ...accurately represented as r + c.
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// If |r| < 2^(-3), go to Step 6, small_r.
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//
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// Step 5. Normal_r.
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//
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// Let [i_0 i_1] by the 2 lsb of N_fix.
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// FR_rsq := r * r
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// r_hi := frcpa( frcpa( r ) )
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// r_lo := r - r_hi
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//
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// If i_1 = 0, then
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// poly := r*FR_rsq*(PP_1_lo + FR_rsq*(PP_2 + ... FR_rsq*PP_8))
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// U_hi := r + PP_1_hi*r_hi*r_hi*r_hi ...any order
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// U_lo := PP_1_hi*r_lo*(r*r + r*r_hi + r_hi*r_hi)
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// correction := c + c*C_1*FR_rsq ...any order
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// Else
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// poly := FR_rsq*FR_rsq*(QQ_2 + FR_rsq*(QQ_3 + ... + FR_rsq*QQ_8))
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// U_hi := 1 + QQ_1 * r_hi * r_hi ...any order
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// U_lo := QQ_1 * r_lo * (r + r_hi)
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// correction := -c*(r + S_1*FR_rsq*r) ...any order
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// Endif
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//
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// V := poly + (U_lo + correction) ...observe order
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//
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// result := (i_0 == 0? 1.0 : -1.0)
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//
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// Last instruction in user-set rounding mode
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//
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// result := (i_0 == 0? result*U_hi + V :
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// result*U_hi - V)
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//
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// Return
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//
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// Step 6. Small_r.
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//
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// ...Use flush to zero mode without causing exception
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// Let [i_0 i_1] be the two lsb of N_fix.
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//
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// FR_rsq := r * r
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//
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// If i_1 = 0 then
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// z := FR_rsq*FR_rsq; z := FR_rsq*z *r
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// poly_lo := S_3 + FR_rsq*(S_4 + FR_rsq*S_5)
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// poly_hi := r*FR_rsq*(S_1 + FR_rsq*S_2)
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// correction := c
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// result := r
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// Else
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// z := FR_rsq*FR_rsq; z := FR_rsq*z
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// poly_lo := C_3 + FR_rsq*(C_4 + FR_rsq*C_5)
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// poly_hi := FR_rsq*(C_1 + FR_rsq*C_2)
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// correction := -c*r
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// result := 1
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// Endif
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//
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// poly := poly_hi + (z * poly_lo + correction)
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//
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// If i_0 = 1, result := -result
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//
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// Last operation. Perform in user-set rounding mode
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//
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// result := (i_0 == 0? result + poly :
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// result - poly )
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// Return
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//
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// Step 7. Case_2_reduce.
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//
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// ...Refer to the write up for argument reduction for
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// ...rationale. The reduction algorithm below is taken from
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// ...argument reduction description and integrated this.
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//
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// w := N*P_3
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// U_1 := N*P_2 + w ...FMA
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// U_2 := (N*P_2 - U_1) + w ...2 FMA
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// ...U_1 + U_2 is N*(P_2+P_3) accurately
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//
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// r := s - U_1
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// c := ( (s - r) - U_1 ) - U_2
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//
|
|
// ...The mathematical sum r + c approximates the reduced
|
|
// ...argument accurately. Note that although compared to
|
|
// ...Case 1, this case requires much more work to reduce
|
|
// ...the argument, the subsequent calculation needed for
|
|
// ...any of the trigonometric function is very little because
|
|
// ...|alpha| < 1.01*2^(-33) and thus two terms of the
|
|
// ...Taylor series expansion suffices.
|
|
//
|
|
// If i_1 = 0 then
|
|
// poly := c + S_1 * r * r * r ...any order
|
|
// result := r
|
|
// Else
|
|
// poly := -2^(-67)
|
|
// result := 1.0
|
|
// Endif
|
|
//
|
|
// If i_0 = 1, result := -result
|
|
//
|
|
// Last operation. Perform in user-set rounding mode
|
|
//
|
|
// result := (i_0 == 0? result + poly :
|
|
// result - poly )
|
|
//
|
|
// Return
|
|
//
|
|
//
|
|
// Step 8. Pre-reduction of large arguments.
|
|
//
|
|
// ...Again, the following reduction procedure was described
|
|
// ...in the separate write up for argument reduction, which
|
|
// ...is tightly integrated here.
|
|
|
|
// N_0 := Arg * Inv_P_0
|
|
// N_0_fix := fcvt.fx( N_0 )
|
|
// N_0 := fcvt.xf( N_0_fix)
|
|
|
|
// Arg' := Arg - N_0 * P_0
|
|
// w := N_0 * d_1
|
|
// N := Arg' * two_by_PI
|
|
// N_fix := fcvt.fx( N )
|
|
// N := fcvt.xf( N_fix )
|
|
// N_fix := N_fix + N_inc
|
|
//
|
|
// s := Arg' - N * P_1
|
|
// w := w - N * P_2
|
|
//
|
|
// If |s| >= 2^(-14)
|
|
// go to Step 3
|
|
// Else
|
|
// go to Step 9
|
|
// Endif
|
|
//
|
|
// Step 9. Case_4_reduce.
|
|
//
|
|
// ...first obtain N_0*d_1 and -N*P_2 accurately
|
|
// U_hi := N_0 * d_1 V_hi := -N*P_2
|
|
// U_lo := N_0 * d_1 - U_hi V_lo := -N*P_2 - U_hi ...FMAs
|
|
//
|
|
// ...compute the contribution from N_0*d_1 and -N*P_3
|
|
// w := -N*P_3
|
|
// w := w + N_0*d_2
|
|
// t := U_lo + V_lo + w ...any order
|
|
//
|
|
// ...at this point, the mathematical value
|
|
// ...s + U_hi + V_hi + t approximates the true reduced argument
|
|
// ...accurately. Just need to compute this accurately.
|
|
//
|
|
// ...Calculate U_hi + V_hi accurately:
|
|
// A := U_hi + V_hi
|
|
// if |U_hi| >= |V_hi| then
|
|
// a := (U_hi - A) + V_hi
|
|
// else
|
|
// a := (V_hi - A) + U_hi
|
|
// endif
|
|
// ...order in computing "a" must be observed. This branch is
|
|
// ...best implemented by predicates.
|
|
// ...A + a is U_hi + V_hi accurately. Moreover, "a" is
|
|
// ...much smaller than A: |a| <= (1/2)ulp(A).
|
|
//
|
|
// ...Just need to calculate s + A + a + t
|
|
// C_hi := s + A t := t + a
|
|
// C_lo := (s - C_hi) + A
|
|
// C_lo := C_lo + t
|
|
//
|
|
// ...Final steps for reduction
|
|
// r := C_hi + C_lo
|
|
// c := (C_hi - r) + C_lo
|
|
//
|
|
// ...At this point, we have r and c
|
|
// ...And all we need is a couple of terms of the corresponding
|
|
// ...Taylor series.
|
|
//
|
|
// If i_1 = 0
|
|
// poly := c + r*FR_rsq*(S_1 + FR_rsq*S_2)
|
|
// result := r
|
|
// Else
|
|
// poly := FR_rsq*(C_1 + FR_rsq*C_2)
|
|
// result := 1
|
|
// Endif
|
|
//
|
|
// If i_0 = 1, result := -result
|
|
//
|
|
// Last operation. Perform in user-set rounding mode
|
|
//
|
|
// result := (i_0 == 0? result + poly :
|
|
// result - poly )
|
|
// Return
|
|
//
|
|
// Large Arguments: For arguments above 2**63, a Payne-Hanek
|
|
// style argument reduction is used and pi_by_2 reduce is called.
|
|
//
|
|
|
|
|
|
RODATA
|
|
.align 16
|
|
|
|
LOCAL_OBJECT_START(FSINCOS_CONSTANTS)
|
|
|
|
data4 0x4B800000 // two**24
|
|
data4 0xCB800000 // -two**24
|
|
data4 0x00000000 // pad
|
|
data4 0x00000000 // pad
|
|
data8 0xA2F9836E4E44152A, 0x00003FFE // Inv_pi_by_2
|
|
data8 0xC84D32B0CE81B9F1, 0x00004016 // P_0
|
|
data8 0xC90FDAA22168C235, 0x00003FFF // P_1
|
|
data8 0xECE675D1FC8F8CBB, 0x0000BFBD // P_2
|
|
data8 0xB7ED8FBBACC19C60, 0x0000BF7C // P_3
|
|
data4 0x5F000000 // two**63
|
|
data4 0xDF000000 // -two**63
|
|
data4 0x00000000 // pad
|
|
data4 0x00000000 // pad
|
|
data8 0xA397E5046EC6B45A, 0x00003FE7 // Inv_P_0
|
|
data8 0x8D848E89DBD171A1, 0x0000BFBF // d_1
|
|
data8 0xD5394C3618A66F8E, 0x0000BF7C // d_2
|
|
data8 0xC90FDAA22168C234, 0x00003FFE // pi_by_4
|
|
data8 0xC90FDAA22168C234, 0x0000BFFE // neg_pi_by_4
|
|
data4 0x3E000000 // two**-3
|
|
data4 0xBE000000 // -two**-3
|
|
data4 0x00000000 // pad
|
|
data4 0x00000000 // pad
|
|
data4 0x2F000000 // two**-33
|
|
data4 0xAF000000 // -two**-33
|
|
data4 0x9E000000 // -two**-67
|
|
data4 0x00000000 // pad
|
|
data8 0xCC8ABEBCA21C0BC9, 0x00003FCE // PP_8
|
|
data8 0xD7468A05720221DA, 0x0000BFD6 // PP_7
|
|
data8 0xB092382F640AD517, 0x00003FDE // PP_6
|
|
data8 0xD7322B47D1EB75A4, 0x0000BFE5 // PP_5
|
|
data8 0xFFFFFFFFFFFFFFFE, 0x0000BFFD // C_1
|
|
data8 0xAAAA000000000000, 0x0000BFFC // PP_1_hi
|
|
data8 0xB8EF1D2ABAF69EEA, 0x00003FEC // PP_4
|
|
data8 0xD00D00D00D03BB69, 0x0000BFF2 // PP_3
|
|
data8 0x8888888888888962, 0x00003FF8 // PP_2
|
|
data8 0xAAAAAAAAAAAB0000, 0x0000BFEC // PP_1_lo
|
|
data8 0xD56232EFC2B0FE52, 0x00003FD2 // QQ_8
|
|
data8 0xC9C99ABA2B48DCA6, 0x0000BFDA // QQ_7
|
|
data8 0x8F76C6509C716658, 0x00003FE2 // QQ_6
|
|
data8 0x93F27DBAFDA8D0FC, 0x0000BFE9 // QQ_5
|
|
data8 0xAAAAAAAAAAAAAAAA, 0x0000BFFC // S_1
|
|
data8 0x8000000000000000, 0x0000BFFE // QQ_1
|
|
data8 0xD00D00D00C6E5041, 0x00003FEF // QQ_4
|
|
data8 0xB60B60B60B607F60, 0x0000BFF5 // QQ_3
|
|
data8 0xAAAAAAAAAAAAAA9B, 0x00003FFA // QQ_2
|
|
data8 0xFFFFFFFFFFFFFFFE, 0x0000BFFD // C_1
|
|
data8 0xAAAAAAAAAAAA719F, 0x00003FFA // C_2
|
|
data8 0xB60B60B60356F994, 0x0000BFF5 // C_3
|
|
data8 0xD00CFFD5B2385EA9, 0x00003FEF // C_4
|
|
data8 0x93E4BD18292A14CD, 0x0000BFE9 // C_5
|
|
data8 0xAAAAAAAAAAAAAAAA, 0x0000BFFC // S_1
|
|
data8 0x88888888888868DB, 0x00003FF8 // S_2
|
|
data8 0xD00D00D0055EFD4B, 0x0000BFF2 // S_3
|
|
data8 0xB8EF1C5D839730B9, 0x00003FEC // S_4
|
|
data8 0xD71EA3A4E5B3F492, 0x0000BFE5 // S_5
|
|
data4 0x38800000 // two**-14
|
|
data4 0xB8800000 // -two**-14
|
|
LOCAL_OBJECT_END(FSINCOS_CONSTANTS)
|
|
|
|
// sin and cos registers
|
|
|
|
// FR
|
|
FR_Input_X = f8
|
|
|
|
FR_r = f8
|
|
FR_c = f9
|
|
|
|
FR_Two_to_63 = f32
|
|
FR_Two_to_24 = f33
|
|
FR_Pi_by_4 = f33
|
|
FR_Two_to_M14 = f34
|
|
FR_Two_to_M33 = f35
|
|
FR_Neg_Two_to_24 = f36
|
|
FR_Neg_Pi_by_4 = f36
|
|
FR_Neg_Two_to_M14 = f37
|
|
FR_Neg_Two_to_M33 = f38
|
|
FR_Neg_Two_to_M67 = f39
|
|
FR_Inv_pi_by_2 = f40
|
|
FR_N_float = f41
|
|
FR_N_fix = f42
|
|
FR_P_1 = f43
|
|
FR_P_2 = f44
|
|
FR_P_3 = f45
|
|
FR_s = f46
|
|
FR_w = f47
|
|
FR_d_2 = f48
|
|
FR_prelim = f49
|
|
FR_Z = f50
|
|
FR_A = f51
|
|
FR_a = f52
|
|
FR_t = f53
|
|
FR_U_1 = f54
|
|
FR_U_2 = f55
|
|
FR_C_1 = f56
|
|
FR_C_2 = f57
|
|
FR_C_3 = f58
|
|
FR_C_4 = f59
|
|
FR_C_5 = f60
|
|
FR_S_1 = f61
|
|
FR_S_2 = f62
|
|
FR_S_3 = f63
|
|
FR_S_4 = f64
|
|
FR_S_5 = f65
|
|
FR_poly_hi = f66
|
|
FR_poly_lo = f67
|
|
FR_r_hi = f68
|
|
FR_r_lo = f69
|
|
FR_rsq = f70
|
|
FR_r_cubed = f71
|
|
FR_C_hi = f72
|
|
FR_N_0 = f73
|
|
FR_d_1 = f74
|
|
FR_V = f75
|
|
FR_V_hi = f75
|
|
FR_V_lo = f76
|
|
FR_U_hi = f77
|
|
FR_U_lo = f78
|
|
FR_U_hiabs = f79
|
|
FR_V_hiabs = f80
|
|
FR_PP_8 = f81
|
|
FR_QQ_8 = f81
|
|
FR_PP_7 = f82
|
|
FR_QQ_7 = f82
|
|
FR_PP_6 = f83
|
|
FR_QQ_6 = f83
|
|
FR_PP_5 = f84
|
|
FR_QQ_5 = f84
|
|
FR_PP_4 = f85
|
|
FR_QQ_4 = f85
|
|
FR_PP_3 = f86
|
|
FR_QQ_3 = f86
|
|
FR_PP_2 = f87
|
|
FR_QQ_2 = f87
|
|
FR_QQ_1 = f88
|
|
FR_N_0_fix = f89
|
|
FR_Inv_P_0 = f90
|
|
FR_corr = f91
|
|
FR_poly = f92
|
|
FR_Neg_Two_to_M3 = f93
|
|
FR_Two_to_M3 = f94
|
|
FR_Neg_Two_to_63 = f94
|
|
FR_P_0 = f95
|
|
FR_C_lo = f96
|
|
FR_PP_1 = f97
|
|
FR_PP_1_lo = f98
|
|
FR_ArgPrime = f99
|
|
|
|
// GR
|
|
GR_Table_Base = r32
|
|
GR_Table_Base1 = r33
|
|
GR_i_0 = r34
|
|
GR_i_1 = r35
|
|
GR_N_Inc = r36
|
|
GR_Sin_or_Cos = r37
|
|
|
|
GR_SAVE_B0 = r39
|
|
GR_SAVE_GP = r40
|
|
GR_SAVE_PFS = r41
|
|
|
|
// sincos combined routine registers
|
|
|
|
// GR
|
|
GR_SINCOS_SAVE_PFS = r32
|
|
GR_SINCOS_SAVE_B0 = r33
|
|
GR_SINCOS_SAVE_GP = r34
|
|
|
|
// FR
|
|
FR_SINCOS_ARG = f100
|
|
FR_SINCOS_RES_SIN = f101
|
|
|
|
|
|
.section .text
|
|
|
|
|
|
GLOBAL_LIBM_ENTRY(__libm_sincos_large)
|
|
|
|
{ .mfi
|
|
alloc GR_SINCOS_SAVE_PFS = ar.pfs,0,3,0,0
|
|
fma.s1 FR_SINCOS_ARG = f8, f1, f0 // Save argument for sin and cos
|
|
mov GR_SINCOS_SAVE_B0 = b0
|
|
};;
|
|
|
|
{ .mfb
|
|
mov GR_SINCOS_SAVE_GP = gp
|
|
nop.f 0
|
|
br.call.sptk b0 = __libm_sin_large // Call sin
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_SINCOS_RES_SIN = f8, f1, f0 // Save sin result
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.s1 f8 = FR_SINCOS_ARG, f1, f0 // Arg for cos
|
|
br.call.sptk b0 = __libm_cos_large // Call cos
|
|
};;
|
|
|
|
{ .mfi
|
|
mov gp = GR_SINCOS_SAVE_GP
|
|
fma.s1 f9 = FR_SINCOS_RES_SIN, f1, f0 // Out sin result
|
|
mov b0 = GR_SINCOS_SAVE_B0
|
|
};;
|
|
|
|
{ .mib
|
|
nop.m 0
|
|
mov ar.pfs = GR_SINCOS_SAVE_PFS
|
|
br.ret.sptk b0 // sincos_large exit
|
|
};;
|
|
|
|
GLOBAL_LIBM_END(__libm_sincos_large)
|
|
|
|
|
|
|
|
|
|
GLOBAL_LIBM_ENTRY(__libm_sin_large)
|
|
|
|
{ .mlx
|
|
alloc GR_Table_Base = ar.pfs,0,12,2,0
|
|
movl GR_Sin_or_Cos = 0x0 ;;
|
|
}
|
|
|
|
{ .mmi
|
|
nop.m 999
|
|
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
ld8 GR_Table_Base = [GR_Table_Base]
|
|
nop.m 999
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
br.cond.sptk SINCOS_CONTINUE ;;
|
|
}
|
|
|
|
GLOBAL_LIBM_END(__libm_sin_large)
|
|
|
|
GLOBAL_LIBM_ENTRY(__libm_cos_large)
|
|
|
|
{ .mlx
|
|
alloc GR_Table_Base= ar.pfs,0,12,2,0
|
|
movl GR_Sin_or_Cos = 0x1 ;;
|
|
}
|
|
|
|
{ .mmi
|
|
nop.m 999
|
|
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
ld8 GR_Table_Base = [GR_Table_Base]
|
|
nop.m 999
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
//
|
|
// Load Table Address
|
|
//
|
|
SINCOS_CONTINUE:
|
|
|
|
{ .mmi
|
|
add GR_Table_Base1 = 96, GR_Table_Base
|
|
ldfs FR_Two_to_24 = [GR_Table_Base], 4
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
nop.m 999
|
|
//
|
|
// Load 2**24, load 2**63.
|
|
//
|
|
ldfs FR_Neg_Two_to_24 = [GR_Table_Base], 12
|
|
mov r41 = ar.pfs ;;
|
|
}
|
|
|
|
{ .mfi
|
|
ldfs FR_Two_to_63 = [GR_Table_Base1], 4
|
|
//
|
|
// Check for unnormals - unsupported operands. We do not want
|
|
// to generate denormal exception
|
|
// Check for NatVals, QNaNs, SNaNs, +/-Infs
|
|
// Check for EM unsupporteds
|
|
// Check for Zero
|
|
//
|
|
fclass.m.unc p6, p8 = FR_Input_X, 0x1E3
|
|
mov r40 = gp ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fclass.nm.unc p8, p0 = FR_Input_X, 0x1FF
|
|
// GR_Sin_or_Cos denotes
|
|
mov r39 = b0
|
|
}
|
|
|
|
{ .mfb
|
|
ldfs FR_Neg_Two_to_63 = [GR_Table_Base1], 12
|
|
fclass.m.unc p10, p0 = FR_Input_X, 0x007
|
|
(p6) br.cond.spnt SINCOS_SPECIAL ;;
|
|
}
|
|
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
(p8) br.cond.spnt SINCOS_SPECIAL ;;
|
|
}
|
|
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
//
|
|
// Branch if +/- NaN, Inf.
|
|
// Load -2**24, load -2**63.
|
|
//
|
|
(p10) br.cond.spnt SINCOS_ZERO ;;
|
|
}
|
|
|
|
{ .mmb
|
|
ldfe FR_Inv_pi_by_2 = [GR_Table_Base], 16
|
|
ldfe FR_Inv_P_0 = [GR_Table_Base1], 16
|
|
nop.b 999 ;;
|
|
}
|
|
|
|
{ .mmb
|
|
nop.m 999
|
|
ldfe FR_d_1 = [GR_Table_Base1], 16
|
|
nop.b 999 ;;
|
|
}
|
|
//
|
|
// Raise possible denormal operand flag with useful fcmp
|
|
// Is x <= -2**63
|
|
// Load Inv_P_0 for pre-reduction
|
|
// Load Inv_pi_by_2
|
|
//
|
|
|
|
{ .mmb
|
|
ldfe FR_P_0 = [GR_Table_Base], 16
|
|
ldfe FR_d_2 = [GR_Table_Base1], 16
|
|
nop.b 999 ;;
|
|
}
|
|
//
|
|
// Load P_0
|
|
// Load d_1
|
|
// Is x >= 2**63
|
|
// Is x <= -2**24?
|
|
//
|
|
|
|
{ .mmi
|
|
ldfe FR_P_1 = [GR_Table_Base], 16 ;;
|
|
//
|
|
// Load P_1
|
|
// Load d_2
|
|
// Is x >= 2**24?
|
|
//
|
|
ldfe FR_P_2 = [GR_Table_Base], 16
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mmf
|
|
nop.m 999
|
|
ldfe FR_P_3 = [GR_Table_Base], 16
|
|
fcmp.le.unc.s1 p7, p8 = FR_Input_X, FR_Neg_Two_to_24
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Branch if +/- zero.
|
|
// Decide about the paths to take:
|
|
// If -2**24 < FR_Input_X < 2**24 - CASE 1 OR 2
|
|
// OTHERWISE - CASE 3 OR 4
|
|
//
|
|
fcmp.le.unc.s1 p10, p11 = FR_Input_X, FR_Neg_Two_to_63
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fcmp.ge.s1 p7, p0 = FR_Input_X, FR_Two_to_24
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
ldfe FR_Pi_by_4 = [GR_Table_Base1], 16
|
|
(p11) fcmp.ge.s1 p10, p0 = FR_Input_X, FR_Two_to_63
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mmi
|
|
ldfe FR_Neg_Pi_by_4 = [GR_Table_Base1], 16 ;;
|
|
ldfs FR_Two_to_M3 = [GR_Table_Base1], 4
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mib
|
|
ldfs FR_Neg_Two_to_M3 = [GR_Table_Base1], 12
|
|
nop.i 999
|
|
//
|
|
// Load P_2
|
|
// Load P_3
|
|
// Load pi_by_4
|
|
// Load neg_pi_by_4
|
|
// Load 2**(-3)
|
|
// Load -2**(-3).
|
|
//
|
|
(p10) br.cond.spnt SINCOS_ARG_TOO_LARGE ;;
|
|
}
|
|
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
//
|
|
// Branch out if x >= 2**63. Use Payne-Hanek Reduction
|
|
//
|
|
(p7) br.cond.spnt SINCOS_LARGER_ARG ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Branch if Arg <= -2**24 or Arg >= 2**24 and use pre-reduction.
|
|
//
|
|
fma.s1 FR_N_float = FR_Input_X, FR_Inv_pi_by_2, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fcmp.lt.unc.s1 p6, p7 = FR_Input_X, FR_Pi_by_4
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Select the case when |Arg| < pi/4
|
|
// Else Select the case when |Arg| >= pi/4
|
|
//
|
|
fcvt.fx.s1 FR_N_fix = FR_N_float
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// N = Arg * 2/pi
|
|
// Check if Arg < pi/4
|
|
//
|
|
(p6) fcmp.gt.s1 p6, p7 = FR_Input_X, FR_Neg_Pi_by_4
|
|
nop.i 999 ;;
|
|
}
|
|
//
|
|
// Case 2: Convert integer N_fix back to normalized floating-point value.
|
|
// Case 1: p8 is only affected when p6 is set
|
|
//
|
|
|
|
{ .mfi
|
|
(p7) ldfs FR_Two_to_M33 = [GR_Table_Base1], 4
|
|
//
|
|
// Grab the integer part of N and call it N_fix
|
|
//
|
|
(p6) fmerge.se FR_r = FR_Input_X, FR_Input_X
|
|
// If |x| < pi/4, r = x and c = 0
|
|
// lf |x| < pi/4, is x < 2**(-3).
|
|
// r = Arg
|
|
// c = 0
|
|
(p6) mov GR_N_Inc = GR_Sin_or_Cos ;;
|
|
}
|
|
|
|
{ .mmf
|
|
nop.m 999
|
|
(p7) ldfs FR_Neg_Two_to_M33 = [GR_Table_Base1], 4
|
|
(p6) fmerge.se FR_c = f0, f0
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p6) fcmp.lt.unc.s1 p8, p9 = FR_Input_X, FR_Two_to_M3
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// lf |x| < pi/4, is -2**(-3)< x < 2**(-3) - set p8.
|
|
// If |x| >= pi/4,
|
|
// Create the right N for |x| < pi/4 and otherwise
|
|
// Case 2: Place integer part of N in GP register
|
|
//
|
|
(p7) fcvt.xf FR_N_float = FR_N_fix
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mmf
|
|
nop.m 999
|
|
(p7) getf.sig GR_N_Inc = FR_N_fix
|
|
(p8) fcmp.gt.s1 p8, p0 = FR_Input_X, FR_Neg_Two_to_M3 ;;
|
|
}
|
|
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
//
|
|
// Load 2**(-33), -2**(-33)
|
|
//
|
|
(p8) br.cond.spnt SINCOS_SMALL_R ;;
|
|
}
|
|
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
(p6) br.cond.sptk SINCOS_NORMAL_R ;;
|
|
}
|
|
//
|
|
// if |x| < pi/4, branch based on |x| < 2**(-3) or otherwise.
|
|
//
|
|
//
|
|
// In this branch, |x| >= pi/4.
|
|
//
|
|
|
|
{ .mfi
|
|
ldfs FR_Neg_Two_to_M67 = [GR_Table_Base1], 8
|
|
//
|
|
// Load -2**(-67)
|
|
//
|
|
fnma.s1 FR_s = FR_N_float, FR_P_1, FR_Input_X
|
|
//
|
|
// w = N * P_2
|
|
// s = -N * P_1 + Arg
|
|
//
|
|
add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 FR_w = FR_N_float, FR_P_2, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Adjust N_fix by N_inc to determine whether sine or
|
|
// cosine is being calculated
|
|
//
|
|
fcmp.lt.unc.s1 p7, p6 = FR_s, FR_Two_to_M33
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fcmp.gt.s1 p7, p6 = FR_s, FR_Neg_Two_to_M33
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
// Remember x >= pi/4.
|
|
// Is s <= -2**(-33) or s >= 2**(-33) (p6)
|
|
// or -2**(-33) < s < 2**(-33) (p7)
|
|
(p6) fms.s1 FR_r = FR_s, f1, FR_w
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fma.s1 FR_w = FR_N_float, FR_P_3, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fma.s1 FR_U_1 = FR_N_float, FR_P_2, FR_w
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p6) fms.s1 FR_c = FR_s, f1, FR_r
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// For big s: r = s - w: No futher reduction is necessary
|
|
// For small s: w = N * P_3 (change sign) More reduction
|
|
//
|
|
(p6) fcmp.lt.unc.s1 p8, p9 = FR_r, FR_Two_to_M3
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fcmp.gt.s1 p8, p9 = FR_r, FR_Neg_Two_to_M3
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fms.s1 FR_r = FR_s, f1, FR_U_1
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
//
|
|
// For big s: Is |r| < 2**(-3)?
|
|
// For big s: c = S - r
|
|
// For small s: U_1 = N * P_2 + w
|
|
//
|
|
// If p8 is set, prepare to branch to Small_R.
|
|
// If p9 is set, prepare to branch to Normal_R.
|
|
// For big s, r is complete here.
|
|
//
|
|
(p6) fms.s1 FR_c = FR_c, f1, FR_w
|
|
//
|
|
// For big s: c = c + w (w has not been negated.)
|
|
// For small s: r = S - U_1
|
|
//
|
|
(p8) br.cond.spnt SINCOS_SMALL_R ;;
|
|
}
|
|
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
(p9) br.cond.sptk SINCOS_NORMAL_R ;;
|
|
}
|
|
|
|
{ .mfi
|
|
(p7) add GR_Table_Base1 = 224, GR_Table_Base1
|
|
//
|
|
// Branch to SINCOS_SMALL_R or SINCOS_NORMAL_R
|
|
//
|
|
(p7) fms.s1 FR_U_2 = FR_N_float, FR_P_2, FR_U_1
|
|
//
|
|
// c = S - U_1
|
|
// r = S_1 * r
|
|
//
|
|
//
|
|
(p7) extr.u GR_i_1 = GR_N_Inc, 0, 1
|
|
}
|
|
|
|
{ .mmi
|
|
nop.m 999 ;;
|
|
//
|
|
// Get [i_0,i_1] - two lsb of N_fix_gr.
|
|
// Do dummy fmpy so inexact is always set.
|
|
//
|
|
(p7) cmp.eq.unc p9, p10 = 0x0, GR_i_1
|
|
(p7) extr.u GR_i_0 = GR_N_Inc, 1, 1 ;;
|
|
}
|
|
//
|
|
// For small s: U_2 = N * P_2 - U_1
|
|
// S_1 stored constant - grab the one stored with the
|
|
// coefficients.
|
|
//
|
|
|
|
{ .mfi
|
|
(p7) ldfe FR_S_1 = [GR_Table_Base1], 16
|
|
//
|
|
// Check if i_1 and i_0 != 0
|
|
//
|
|
(p10) fma.s1 FR_poly = f0, f1, FR_Neg_Two_to_M67
|
|
(p7) cmp.eq.unc p11, p12 = 0x0, GR_i_0 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fms.s1 FR_s = FR_s, f1, FR_r
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// S = S - r
|
|
// U_2 = U_2 + w
|
|
// load S_1
|
|
//
|
|
(p7) fma.s1 FR_rsq = FR_r, FR_r, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fma.s1 FR_U_2 = FR_U_2, f1, FR_w
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//(p7) fmerge.se FR_Input_X = FR_r, FR_r
|
|
(p7) fmerge.se FR_prelim = FR_r, FR_r
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//(p10) fma.s1 FR_Input_X = f0, f1, f1
|
|
(p10) fma.s1 FR_prelim = f0, f1, f1
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// FR_rsq = r * r
|
|
// Save r as the result.
|
|
//
|
|
(p7) fms.s1 FR_c = FR_s, f1, FR_U_1
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if ( i_1 ==0) poly = c + S_1*r*r*r
|
|
// else Result = 1
|
|
//
|
|
//(p12) fnma.s1 FR_Input_X = FR_Input_X, f1, f0
|
|
(p12) fnma.s1 FR_prelim = FR_prelim, f1, f0
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fma.s1 FR_r = FR_S_1, FR_r, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fma.d.s1 FR_S_1 = FR_S_1, FR_S_1, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// If i_1 != 0, poly = 2**(-67)
|
|
//
|
|
(p7) fms.s1 FR_c = FR_c, f1, FR_U_2
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// c = c - U_2
|
|
//
|
|
(p9) fma.s1 FR_poly = FR_r, FR_rsq, FR_c
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// i_0 != 0, so Result = -Result
|
|
//
|
|
(p11) fma.s1 FR_Input_X = FR_prelim, f1, FR_poly
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
(p12) fms.s1 FR_Input_X = FR_prelim, f1, FR_poly
|
|
//
|
|
// if (i_0 == 0), Result = Result + poly
|
|
// else Result = Result - poly
|
|
//
|
|
br.ret.sptk b0 ;;
|
|
}
|
|
SINCOS_LARGER_ARG:
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 FR_N_0 = FR_Input_X, FR_Inv_P_0, f0
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
// This path for argument > 2*24
|
|
// Adjust table_ptr1 to beginning of table.
|
|
//
|
|
|
|
{ .mmi
|
|
nop.m 999
|
|
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
ld8 GR_Table_Base = [GR_Table_Base]
|
|
nop.m 999
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
|
|
//
|
|
// Point to 2*-14
|
|
// N_0 = Arg * Inv_P_0
|
|
//
|
|
|
|
{ .mmi
|
|
add GR_Table_Base = 688, GR_Table_Base ;;
|
|
ldfs FR_Two_to_M14 = [GR_Table_Base], 4
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
ldfs FR_Neg_Two_to_M14 = [GR_Table_Base], 0
|
|
nop.f 999
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Load values 2**(-14) and -2**(-14)
|
|
//
|
|
fcvt.fx.s1 FR_N_0_fix = FR_N_0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// N_0_fix = integer part of N_0
|
|
//
|
|
fcvt.xf FR_N_0 = FR_N_0_fix
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Make N_0 the integer part
|
|
//
|
|
fnma.s1 FR_ArgPrime = FR_N_0, FR_P_0, FR_Input_X
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 FR_w = FR_N_0, FR_d_1, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Arg' = -N_0 * P_0 + Arg
|
|
// w = N_0 * d_1
|
|
//
|
|
fma.s1 FR_N_float = FR_ArgPrime, FR_Inv_pi_by_2, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// N = A' * 2/pi
|
|
//
|
|
fcvt.fx.s1 FR_N_fix = FR_N_float
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// N_fix is the integer part
|
|
//
|
|
fcvt.xf FR_N_float = FR_N_fix
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
getf.sig GR_N_Inc = FR_N_fix
|
|
nop.f 999
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mii
|
|
nop.m 999
|
|
nop.i 999 ;;
|
|
add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// N is the integer part of the reduced-reduced argument.
|
|
// Put the integer in a GP register
|
|
//
|
|
fnma.s1 FR_s = FR_N_float, FR_P_1, FR_ArgPrime
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fnma.s1 FR_w = FR_N_float, FR_P_2, FR_w
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// s = -N*P_1 + Arg'
|
|
// w = -N*P_2 + w
|
|
// N_fix_gr = N_fix_gr + N_inc
|
|
//
|
|
fcmp.lt.unc.s1 p9, p8 = FR_s, FR_Two_to_M14
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fcmp.gt.s1 p9, p8 = FR_s, FR_Neg_Two_to_M14
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// For |s| > 2**(-14) r = S + w (r complete)
|
|
// Else U_hi = N_0 * d_1
|
|
//
|
|
(p9) fma.s1 FR_V_hi = FR_N_float, FR_P_2, f0
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_U_hi = FR_N_0, FR_d_1, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Either S <= -2**(-14) or S >= 2**(-14)
|
|
// or -2**(-14) < s < 2**(-14)
|
|
//
|
|
(p8) fma.s1 FR_r = FR_s, f1, FR_w
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_w = FR_N_float, FR_P_3, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// We need abs of both U_hi and V_hi - don't
|
|
// worry about switched sign of V_hi.
|
|
//
|
|
(p9) fms.s1 FR_A = FR_U_hi, f1, FR_V_hi
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Big s: finish up c = (S - r) + w (c complete)
|
|
// Case 4: A = U_hi + V_hi
|
|
// Note: Worry about switched sign of V_hi, so subtract instead of add.
|
|
//
|
|
(p9) fnma.s1 FR_V_lo = FR_N_float, FR_P_2, FR_V_hi
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fms.s1 FR_U_lo = FR_N_0, FR_d_1, FR_U_hi
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fmerge.s FR_V_hiabs = f0, FR_V_hi
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
// For big s: c = S - r
|
|
// For small s do more work: U_lo = N_0 * d_1 - U_hi
|
|
//
|
|
(p9) fmerge.s FR_U_hiabs = f0, FR_U_hi
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// For big s: Is |r| < 2**(-3)
|
|
// For big s: if p12 set, prepare to branch to Small_R.
|
|
// For big s: If p13 set, prepare to branch to Normal_R.
|
|
//
|
|
(p8) fms.s1 FR_c = FR_s, f1, FR_r
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// For small S: V_hi = N * P_2
|
|
// w = N * P_3
|
|
// Note the product does not include the (-) as in the writeup
|
|
// so (-) missing for V_hi and w.
|
|
//
|
|
(p8) fcmp.lt.unc.s1 p12, p13 = FR_r, FR_Two_to_M3
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) fcmp.gt.s1 p12, p13 = FR_r, FR_Neg_Two_to_M3
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 FR_c = FR_c, f1, FR_w
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
(p9) fms.s1 FR_w = FR_N_0, FR_d_2, FR_w
|
|
(p12) br.cond.spnt SINCOS_SMALL_R ;;
|
|
}
|
|
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
(p13) br.cond.sptk SINCOS_NORMAL_R ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Big s: Vector off when |r| < 2**(-3). Recall that p8 will be true.
|
|
// The remaining stuff is for Case 4.
|
|
// Small s: V_lo = N * P_2 + U_hi (U_hi is in place of V_hi in writeup)
|
|
// Note: the (-) is still missing for V_lo.
|
|
// Small s: w = w + N_0 * d_2
|
|
// Note: the (-) is now incorporated in w.
|
|
//
|
|
(p9) fcmp.ge.unc.s1 p10, p11 = FR_U_hiabs, FR_V_hiabs
|
|
extr.u GR_i_1 = GR_N_Inc, 0, 1 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// C_hi = S + A
|
|
//
|
|
(p9) fma.s1 FR_t = FR_U_lo, f1, FR_V_lo
|
|
extr.u GR_i_0 = GR_N_Inc, 1, 1 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// t = U_lo + V_lo
|
|
//
|
|
//
|
|
(p10) fms.s1 FR_a = FR_U_hi, f1, FR_A
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p11) fma.s1 FR_a = FR_V_hi, f1, FR_A
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
nop.m 999
|
|
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
ld8 GR_Table_Base = [GR_Table_Base]
|
|
nop.m 999
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
|
|
{ .mfi
|
|
add GR_Table_Base = 528, GR_Table_Base
|
|
//
|
|
// Is U_hiabs >= V_hiabs?
|
|
//
|
|
(p9) fma.s1 FR_C_hi = FR_s, f1, FR_A
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mmi
|
|
ldfe FR_C_1 = [GR_Table_Base], 16 ;;
|
|
ldfe FR_C_2 = [GR_Table_Base], 64
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mmf
|
|
nop.m 999
|
|
//
|
|
// c = c + C_lo finished.
|
|
// Load C_2
|
|
//
|
|
ldfe FR_S_1 = [GR_Table_Base], 16
|
|
//
|
|
// C_lo = S - C_hi
|
|
//
|
|
fma.s1 FR_t = FR_t, f1, FR_w ;;
|
|
}
|
|
//
|
|
// r and c have been computed.
|
|
// Make sure ftz mode is set - should be automatic when using wre
|
|
// |r| < 2**(-3)
|
|
// Get [i_0,i_1] - two lsb of N_fix.
|
|
// Load S_1
|
|
//
|
|
|
|
{ .mfi
|
|
ldfe FR_S_2 = [GR_Table_Base], 64
|
|
//
|
|
// t = t + w
|
|
//
|
|
(p10) fms.s1 FR_a = FR_a, f1, FR_V_hi
|
|
cmp.eq.unc p9, p10 = 0x0, GR_i_0
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// For larger u than v: a = U_hi - A
|
|
// Else a = V_hi - A (do an add to account for missing (-) on V_hi
|
|
//
|
|
fms.s1 FR_C_lo = FR_s, f1, FR_C_hi
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p11) fms.s1 FR_a = FR_U_hi, f1, FR_a
|
|
cmp.eq.unc p11, p12 = 0x0, GR_i_1
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// If u > v: a = (U_hi - A) + V_hi
|
|
// Else a = (V_hi - A) + U_hi
|
|
// In each case account for negative missing from V_hi.
|
|
//
|
|
fma.s1 FR_C_lo = FR_C_lo, f1, FR_A
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// C_lo = (S - C_hi) + A
|
|
//
|
|
fma.s1 FR_t = FR_t, f1, FR_a
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// t = t + a
|
|
//
|
|
fma.s1 FR_C_lo = FR_C_lo, f1, FR_t
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// C_lo = C_lo + t
|
|
// Adjust Table_Base to beginning of table
|
|
//
|
|
fma.s1 FR_r = FR_C_hi, f1, FR_C_lo
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Load S_2
|
|
//
|
|
fma.s1 FR_rsq = FR_r, FR_r, f0
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Table_Base points to C_1
|
|
// r = C_hi + C_lo
|
|
//
|
|
fms.s1 FR_c = FR_C_hi, f1, FR_r
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if i_1 ==0: poly = S_2 * FR_rsq + S_1
|
|
// else poly = C_2 * FR_rsq + C_1
|
|
//
|
|
//(p11) fma.s1 FR_Input_X = f0, f1, FR_r
|
|
(p11) fma.s1 FR_prelim = f0, f1, FR_r
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//(p12) fma.s1 FR_Input_X = f0, f1, f1
|
|
(p12) fma.s1 FR_prelim = f0, f1, f1
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Compute r_cube = FR_rsq * r
|
|
//
|
|
(p11) fma.s1 FR_poly = FR_rsq, FR_S_2, FR_S_1
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) fma.s1 FR_poly = FR_rsq, FR_C_2, FR_C_1
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Compute FR_rsq = r * r
|
|
// Is i_1 == 0 ?
|
|
//
|
|
fma.s1 FR_r_cubed = FR_rsq, FR_r, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// c = C_hi - r
|
|
// Load C_1
|
|
//
|
|
fma.s1 FR_c = FR_c, f1, FR_C_lo
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if i_1 ==0: poly = r_cube * poly + c
|
|
// else poly = FR_rsq * poly
|
|
//
|
|
//(p10) fms.s1 FR_Input_X = f0, f1, FR_Input_X
|
|
(p10) fms.s1 FR_prelim = f0, f1, FR_prelim
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if i_1 ==0: Result = r
|
|
// else Result = 1.0
|
|
//
|
|
(p11) fma.s1 FR_poly = FR_r_cubed, FR_poly, FR_c
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) fma.s1 FR_poly = FR_rsq, FR_poly, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if i_0 !=0: Result = -Result
|
|
//
|
|
(p9) fma.s1 FR_Input_X = FR_prelim, f1, FR_poly
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
(p10) fms.s1 FR_Input_X = FR_prelim, f1, FR_poly
|
|
//
|
|
// if i_0 == 0: Result = Result + poly
|
|
// else Result = Result - poly
|
|
//
|
|
br.ret.sptk b0 ;;
|
|
}
|
|
SINCOS_SMALL_R:
|
|
|
|
{ .mii
|
|
nop.m 999
|
|
extr.u GR_i_1 = GR_N_Inc, 0, 1 ;;
|
|
//
|
|
//
|
|
// Compare both i_1 and i_0 with 0.
|
|
// if i_1 == 0, set p9.
|
|
// if i_0 == 0, set p11.
|
|
//
|
|
cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 FR_rsq = FR_r, FR_r, f0
|
|
extr.u GR_i_0 = GR_N_Inc, 1, 1 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Z = Z * FR_rsq
|
|
//
|
|
(p10) fnma.s1 FR_c = FR_c, FR_r, f0
|
|
cmp.eq.unc p11, p12 = 0x0, GR_i_0
|
|
}
|
|
;;
|
|
|
|
// ******************************************************************
|
|
// ******************************************************************
|
|
// ******************************************************************
|
|
// r and c have been computed.
|
|
// We know whether this is the sine or cosine routine.
|
|
// Make sure ftz mode is set - should be automatic when using wre
|
|
// |r| < 2**(-3)
|
|
//
|
|
// Set table_ptr1 to beginning of constant table.
|
|
// Get [i_0,i_1] - two lsb of N_fix_gr.
|
|
//
|
|
|
|
{ .mmi
|
|
nop.m 999
|
|
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
ld8 GR_Table_Base = [GR_Table_Base]
|
|
nop.m 999
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
|
|
//
|
|
// Set table_ptr1 to point to S_5.
|
|
// Set table_ptr1 to point to C_5.
|
|
// Compute FR_rsq = r * r
|
|
//
|
|
|
|
{ .mfi
|
|
(p9) add GR_Table_Base = 672, GR_Table_Base
|
|
(p10) fmerge.s FR_r = f1, f1
|
|
(p10) add GR_Table_Base = 592, GR_Table_Base ;;
|
|
}
|
|
//
|
|
// Set table_ptr1 to point to S_5.
|
|
// Set table_ptr1 to point to C_5.
|
|
//
|
|
|
|
{ .mmi
|
|
(p9) ldfe FR_S_5 = [GR_Table_Base], -16 ;;
|
|
//
|
|
// if (i_1 == 0) load S_5
|
|
// if (i_1 != 0) load C_5
|
|
//
|
|
(p9) ldfe FR_S_4 = [GR_Table_Base], -16
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mmf
|
|
(p10) ldfe FR_C_5 = [GR_Table_Base], -16
|
|
//
|
|
// Z = FR_rsq * FR_rsq
|
|
//
|
|
(p9) ldfe FR_S_3 = [GR_Table_Base], -16
|
|
//
|
|
// Compute FR_rsq = r * r
|
|
// if (i_1 == 0) load S_4
|
|
// if (i_1 != 0) load C_4
|
|
//
|
|
fma.s1 FR_Z = FR_rsq, FR_rsq, f0 ;;
|
|
}
|
|
//
|
|
// if (i_1 == 0) load S_3
|
|
// if (i_1 != 0) load C_3
|
|
//
|
|
|
|
{ .mmi
|
|
(p9) ldfe FR_S_2 = [GR_Table_Base], -16 ;;
|
|
//
|
|
// if (i_1 == 0) load S_2
|
|
// if (i_1 != 0) load C_2
|
|
//
|
|
(p9) ldfe FR_S_1 = [GR_Table_Base], -16
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mmi
|
|
(p10) ldfe FR_C_4 = [GR_Table_Base], -16 ;;
|
|
(p10) ldfe FR_C_3 = [GR_Table_Base], -16
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mmi
|
|
(p10) ldfe FR_C_2 = [GR_Table_Base], -16 ;;
|
|
(p10) ldfe FR_C_1 = [GR_Table_Base], -16
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1 != 0):
|
|
// poly_lo = FR_rsq * C_5 + C_4
|
|
// poly_hi = FR_rsq * C_2 + C_1
|
|
//
|
|
(p9) fma.s1 FR_Z = FR_Z, FR_r, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1 == 0) load S_1
|
|
// if (i_1 != 0) load C_1
|
|
//
|
|
(p9) fma.s1 FR_poly_lo = FR_rsq, FR_S_5, FR_S_4
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// c = -c * r
|
|
// dummy fmpy's to flag inexact.
|
|
//
|
|
(p9) fma.d.s1 FR_S_4 = FR_S_4, FR_S_4, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// poly_lo = FR_rsq * poly_lo + C_3
|
|
// poly_hi = FR_rsq * poly_hi
|
|
//
|
|
fma.s1 FR_Z = FR_Z, FR_rsq, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_poly_hi = FR_rsq, FR_S_2, FR_S_1
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1 == 0):
|
|
// poly_lo = FR_rsq * S_5 + S_4
|
|
// poly_hi = FR_rsq * S_2 + S_1
|
|
//
|
|
(p10) fma.s1 FR_poly_lo = FR_rsq, FR_C_5, FR_C_4
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1 == 0):
|
|
// Z = Z * r for only one of the small r cases - not there
|
|
// in original implementation notes.
|
|
//
|
|
(p9) fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_S_3
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_poly_hi = FR_rsq, FR_C_2, FR_C_1
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.d.s1 FR_C_1 = FR_C_1, FR_C_1, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// poly_lo = FR_rsq * poly_lo + S_3
|
|
// poly_hi = FR_rsq * poly_hi
|
|
//
|
|
(p10) fma.s1 FR_poly_lo = FR_rsq, FR_poly_lo, FR_C_3
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_poly_hi = FR_poly_hi, FR_rsq, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1 == 0): dummy fmpy's to flag inexact
|
|
// r = 1
|
|
//
|
|
(p9) fma.s1 FR_poly_hi = FR_r, FR_poly_hi, f0
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// poly_hi = r * poly_hi
|
|
//
|
|
fma.s1 FR_poly = FR_Z, FR_poly_lo, FR_c
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) fms.s1 FR_r = f0, f1, FR_r
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// poly_hi = Z * poly_lo + c
|
|
// if i_0 == 1: r = -r
|
|
//
|
|
fma.s1 FR_poly = FR_poly, f1, FR_poly_hi
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) fms.s1 FR_Input_X = FR_r, f1, FR_poly
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
//
|
|
// poly = poly + poly_hi
|
|
//
|
|
(p11) fma.s1 FR_Input_X = FR_r, f1, FR_poly
|
|
//
|
|
// if (i_0 == 0) Result = r + poly
|
|
// if (i_0 != 0) Result = r - poly
|
|
//
|
|
br.ret.sptk b0 ;;
|
|
}
|
|
SINCOS_NORMAL_R:
|
|
|
|
{ .mii
|
|
nop.m 999
|
|
extr.u GR_i_1 = GR_N_Inc, 0, 1 ;;
|
|
//
|
|
// Set table_ptr1 and table_ptr2 to base address of
|
|
// constant table.
|
|
cmp.eq.unc p9, p10 = 0x0, GR_i_1 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.s1 FR_rsq = FR_r, FR_r, f0
|
|
extr.u GR_i_0 = GR_N_Inc, 1, 1 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
frcpa.s1 FR_r_hi, p6 = f1, FR_r
|
|
cmp.eq.unc p11, p12 = 0x0, GR_i_0
|
|
}
|
|
;;
|
|
|
|
// ******************************************************************
|
|
// ******************************************************************
|
|
// ******************************************************************
|
|
//
|
|
// r and c have been computed.
|
|
// We known whether this is the sine or cosine routine.
|
|
// Make sure ftz mode is set - should be automatic when using wre
|
|
// Get [i_0,i_1] - two lsb of N_fix_gr alone.
|
|
//
|
|
|
|
{ .mmi
|
|
nop.m 999
|
|
addl GR_Table_Base = @ltoff(FSINCOS_CONSTANTS#), gp
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
ld8 GR_Table_Base = [GR_Table_Base]
|
|
nop.m 999
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
|
|
{ .mfi
|
|
(p10) add GR_Table_Base = 384, GR_Table_Base
|
|
//(p12) fms.s1 FR_Input_X = f0, f1, f1
|
|
(p12) fms.s1 FR_prelim = f0, f1, f1
|
|
(p9) add GR_Table_Base = 224, GR_Table_Base ;;
|
|
}
|
|
|
|
{ .mmf
|
|
nop.m 999
|
|
(p10) ldfe FR_QQ_8 = [GR_Table_Base], 16
|
|
//
|
|
// if (i_1==0) poly = poly * FR_rsq + PP_1_lo
|
|
// else poly = FR_rsq * poly
|
|
//
|
|
//(p11) fma.s1 FR_Input_X = f0, f1, f1 ;;
|
|
(p11) fma.s1 FR_prelim = f0, f1, f1 ;;
|
|
}
|
|
|
|
{ .mmf
|
|
(p10) ldfe FR_QQ_7 = [GR_Table_Base], 16
|
|
//
|
|
// Adjust table pointers based on i_0
|
|
// Compute rsq = r * r
|
|
//
|
|
(p9) ldfe FR_PP_8 = [GR_Table_Base], 16
|
|
fma.s1 FR_r_cubed = FR_r, FR_rsq, f0 ;;
|
|
}
|
|
|
|
{ .mmf
|
|
(p9) ldfe FR_PP_7 = [GR_Table_Base], 16
|
|
(p10) ldfe FR_QQ_6 = [GR_Table_Base], 16
|
|
//
|
|
// Load PP_8 and QQ_8; PP_7 and QQ_7
|
|
//
|
|
frcpa.s1 FR_r_hi, p6 = f1, FR_r_hi ;;
|
|
}
|
|
//
|
|
// if (i_1==0) poly = PP_7 + FR_rsq * PP_8.
|
|
// else poly = QQ_7 + FR_rsq * QQ_8.
|
|
//
|
|
|
|
{ .mmb
|
|
(p9) ldfe FR_PP_6 = [GR_Table_Base], 16
|
|
(p10) ldfe FR_QQ_5 = [GR_Table_Base], 16
|
|
nop.b 999 ;;
|
|
}
|
|
|
|
{ .mmb
|
|
(p9) ldfe FR_PP_5 = [GR_Table_Base], 16
|
|
(p10) ldfe FR_S_1 = [GR_Table_Base], 16
|
|
nop.b 999 ;;
|
|
}
|
|
|
|
{ .mmb
|
|
(p10) ldfe FR_QQ_1 = [GR_Table_Base], 16
|
|
(p9) ldfe FR_C_1 = [GR_Table_Base], 16
|
|
nop.b 999 ;;
|
|
}
|
|
|
|
{ .mmi
|
|
(p10) ldfe FR_QQ_4 = [GR_Table_Base], 16 ;;
|
|
(p9) ldfe FR_PP_1 = [GR_Table_Base], 16
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mmf
|
|
(p10) ldfe FR_QQ_3 = [GR_Table_Base], 16
|
|
//
|
|
// if (i_1=0) corr = corr + c*c
|
|
// else corr = corr * c
|
|
//
|
|
(p9) ldfe FR_PP_4 = [GR_Table_Base], 16
|
|
(p10) fma.s1 FR_poly = FR_rsq, FR_QQ_8, FR_QQ_7 ;;
|
|
}
|
|
//
|
|
// if (i_1=0) poly = rsq * poly + PP_5
|
|
// else poly = rsq * poly + QQ_5
|
|
// Load PP_4 or QQ_4
|
|
//
|
|
|
|
{ .mmf
|
|
(p9) ldfe FR_PP_3 = [GR_Table_Base], 16
|
|
(p10) ldfe FR_QQ_2 = [GR_Table_Base], 16
|
|
//
|
|
// r_hi = frcpa(frcpa(r)).
|
|
// r_cube = r * FR_rsq.
|
|
//
|
|
(p9) fma.s1 FR_poly = FR_rsq, FR_PP_8, FR_PP_7 ;;
|
|
}
|
|
//
|
|
// Do dummy multiplies so inexact is always set.
|
|
//
|
|
|
|
{ .mfi
|
|
(p9) ldfe FR_PP_2 = [GR_Table_Base], 16
|
|
//
|
|
// r_lo = r - r_hi
|
|
//
|
|
(p9) fma.s1 FR_U_lo = FR_r_hi, FR_r_hi, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mmf
|
|
nop.m 999
|
|
(p9) ldfe FR_PP_1_lo = [GR_Table_Base], 16
|
|
(p10) fma.s1 FR_corr = FR_S_1, FR_r_cubed, FR_r
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_6
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1=0) U_lo = r_hi * r_hi
|
|
// else U_lo = r_hi + r
|
|
//
|
|
(p9) fma.s1 FR_corr = FR_C_1, FR_rsq, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1=0) corr = C_1 * rsq
|
|
// else corr = S_1 * r_cubed + r
|
|
//
|
|
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_6
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_U_lo = FR_r_hi, f1, FR_r
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1=0) U_hi = r_hi + U_hi
|
|
// else U_hi = QQ_1 * U_hi + 1
|
|
//
|
|
(p9) fma.s1 FR_U_lo = FR_r, FR_r_hi, FR_U_lo
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// U_hi = r_hi * r_hi
|
|
//
|
|
fms.s1 FR_r_lo = FR_r, f1, FR_r_hi
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Load PP_1, PP_6, PP_5, and C_1
|
|
// Load QQ_1, QQ_6, QQ_5, and S_1
|
|
//
|
|
fma.s1 FR_U_hi = FR_r_hi, FR_r_hi, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_5
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fnma.s1 FR_corr = FR_corr, FR_c, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1=0) U_lo = r * r_hi + U_lo
|
|
// else U_lo = r_lo * U_lo
|
|
//
|
|
(p9) fma.s1 FR_corr = FR_corr, FR_c, FR_c
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_5
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1 =0) U_hi = r + U_hi
|
|
// if (i_1 =0) U_lo = r_lo * U_lo
|
|
//
|
|
//
|
|
(p9) fma.d.s1 FR_PP_5 = FR_PP_5, FR_PP_4, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_U_lo = FR_r, FR_r, FR_U_lo
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1=0) poly = poly * rsq + PP_6
|
|
// else poly = poly * rsq + QQ_6
|
|
//
|
|
(p9) fma.s1 FR_U_hi = FR_r_hi, FR_U_hi, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_4
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_U_hi = FR_QQ_1, FR_U_hi, f1
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.d.s1 FR_QQ_5 = FR_QQ_5, FR_QQ_5, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1!=0) U_hi = PP_1 * U_hi
|
|
// if (i_1!=0) U_lo = r * r + U_lo
|
|
// Load PP_3 or QQ_3
|
|
//
|
|
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_4
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_U_lo = FR_r_lo, FR_U_lo, f0
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_U_lo = FR_QQ_1,FR_U_lo, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_U_hi = FR_PP_1, FR_U_hi, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_3
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Load PP_2, QQ_2
|
|
//
|
|
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_3
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1==0) poly = FR_rsq * poly + PP_3
|
|
// else poly = FR_rsq * poly + QQ_3
|
|
// Load PP_1_lo
|
|
//
|
|
(p9) fma.s1 FR_U_lo = FR_PP_1, FR_U_lo, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1 =0) poly = poly * rsq + pp_r4
|
|
// else poly = poly * rsq + qq_r4
|
|
//
|
|
(p9) fma.s1 FR_U_hi = FR_r, f1, FR_U_hi
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, FR_QQ_2
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1==0) U_lo = PP_1_hi * U_lo
|
|
// else U_lo = QQ_1 * U_lo
|
|
//
|
|
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_2
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_0==0) Result = 1
|
|
// else Result = -1
|
|
//
|
|
fma.s1 FR_V = FR_U_lo, f1, FR_corr
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1==0) poly = FR_rsq * poly + PP_2
|
|
// else poly = FR_rsq * poly + QQ_2
|
|
//
|
|
(p9) fma.s1 FR_poly = FR_rsq, FR_poly, FR_PP_1_lo
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fma.s1 FR_poly = FR_rsq, FR_poly, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// V = U_lo + corr
|
|
//
|
|
(p9) fma.s1 FR_poly = FR_r_cubed, FR_poly, f0
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// if (i_1==0) poly = r_cube * poly
|
|
// else poly = FR_rsq * poly
|
|
//
|
|
fma.s1 FR_V = FR_poly, f1, FR_V
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
//(p12) fms.s1 FR_Input_X = FR_Input_X, FR_U_hi, FR_V
|
|
(p12) fms.s1 FR_Input_X = FR_prelim, FR_U_hi, FR_V
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
//
|
|
// V = V + poly
|
|
//
|
|
//(p11) fma.s1 FR_Input_X = FR_Input_X, FR_U_hi, FR_V
|
|
(p11) fma.s1 FR_Input_X = FR_prelim, FR_U_hi, FR_V
|
|
//
|
|
// if (i_0==0) Result = Result * U_hi + V
|
|
// else Result = Result * U_hi - V
|
|
//
|
|
br.ret.sptk b0 ;;
|
|
}
|
|
|
|
//
|
|
// If cosine, FR_Input_X = 1
|
|
// If sine, FR_Input_X = +/-Zero (Input FR_Input_X)
|
|
// Results are exact, no exceptions
|
|
//
|
|
SINCOS_ZERO:
|
|
|
|
{ .mmb
|
|
cmp.eq.unc p6, p7 = 0x1, GR_Sin_or_Cos
|
|
nop.m 999
|
|
nop.b 999 ;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fmerge.s FR_Input_X = FR_Input_X, FR_Input_X
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
(p6) fmerge.s FR_Input_X = f1, f1
|
|
br.ret.sptk b0 ;;
|
|
}
|
|
|
|
SINCOS_SPECIAL:
|
|
|
|
//
|
|
// Path for Arg = +/- QNaN, SNaN, Inf
|
|
// Invalid can be raised. SNaNs
|
|
// become QNaNs
|
|
//
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
fmpy.s1 FR_Input_X = FR_Input_X, f0
|
|
br.ret.sptk b0 ;;
|
|
}
|
|
GLOBAL_LIBM_END(__libm_cos_large)
|
|
|
|
|
|
// *******************************************************************
|
|
// *******************************************************************
|
|
// *******************************************************************
|
|
//
|
|
// Special Code to handle very large argument case.
|
|
// Call int __libm_pi_by_2_reduce(x,r,c) for |arguments| >= 2**63
|
|
// The interface is custom:
|
|
// On input:
|
|
// (Arg or x) is in f8
|
|
// On output:
|
|
// r is in f8
|
|
// c is in f9
|
|
// N is in r8
|
|
// Be sure to allocate at least 2 GP registers as output registers for
|
|
// __libm_pi_by_2_reduce. This routine uses r49-50. These are used as
|
|
// scratch registers within the __libm_pi_by_2_reduce routine (for speed).
|
|
//
|
|
// We know also that __libm_pi_by_2_reduce preserves f10-15, f71-127. We
|
|
// use this to eliminate save/restore of key fp registers in this calling
|
|
// function.
|
|
//
|
|
// *******************************************************************
|
|
// *******************************************************************
|
|
// *******************************************************************
|
|
|
|
LOCAL_LIBM_ENTRY(__libm_callout_2)
|
|
SINCOS_ARG_TOO_LARGE:
|
|
|
|
.prologue
|
|
// Readjust Table ptr
|
|
{ .mfi
|
|
adds GR_Table_Base1 = -16, GR_Table_Base1
|
|
nop.f 999
|
|
.save ar.pfs,GR_SAVE_PFS
|
|
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfs FR_Two_to_M3 = [GR_Table_Base1],4
|
|
mov GR_SAVE_GP=gp // Save gp
|
|
.save b0, GR_SAVE_B0
|
|
mov GR_SAVE_B0=b0 // Save b0
|
|
};;
|
|
|
|
.body
|
|
//
|
|
// Call argument reduction with x in f8
|
|
// Returns with N in r8, r in f8, c in f9
|
|
// Assumes f71-127 are preserved across the call
|
|
//
|
|
{ .mib
|
|
ldfs FR_Neg_Two_to_M3 = [GR_Table_Base1],0
|
|
nop.i 0
|
|
br.call.sptk b0=__libm_pi_by_2_reduce#
|
|
};;
|
|
|
|
{ .mfi
|
|
add GR_N_Inc = GR_Sin_or_Cos,r8
|
|
fcmp.lt.unc.s1 p6, p0 = FR_r, FR_Two_to_M3
|
|
mov b0 = GR_SAVE_B0 // Restore return address
|
|
};;
|
|
|
|
{ .mfi
|
|
mov gp = GR_SAVE_GP // Restore gp
|
|
(p6) fcmp.gt.unc.s1 p6, p0 = FR_r, FR_Neg_Two_to_M3
|
|
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
|
|
};;
|
|
|
|
{ .mbb
|
|
nop.m 999
|
|
(p6) br.cond.spnt SINCOS_SMALL_R // Branch if |r| < 1/4
|
|
br.cond.sptk SINCOS_NORMAL_R ;; // Branch if 1/4 <= |r| < pi/4
|
|
}
|
|
|
|
LOCAL_LIBM_END(__libm_callout_2)
|
|
|
|
.type __libm_pi_by_2_reduce#,@function
|
|
.global __libm_pi_by_2_reduce#
|
|
|