mirror of
git://sourceware.org/git/glibc.git
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0347518d63
Many ia64 files have trailing whitespace which gets in the way and
annoys me. So strip it away:
find `find sysdeps/ -name ia64` -type f -exec sed -i 's:[[:space:]]*$::' {} +
Signed-off-by: Mike Frysinger <vapier@gentoo.org>
1717 lines
43 KiB
ArmAsm
1717 lines
43 KiB
ArmAsm
.file "acoshl.s"
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// Copyright (c) 2000 - 2005, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2000 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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//*********************************************************************
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//
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// History:
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// 10/01/01 Initial version
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// 10/10/01 Performance inproved
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// 12/11/01 Changed huges_logp to not be global
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// 01/02/02 Corrected .restore syntax
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 08/14/02 Changed mli templates to mlx
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// 02/06/03 Reorganized data tables
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// 03/31/05 Reformatted delimiters between data tables
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//
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//*********************************************************************
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//
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// API
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//==============================================================
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// long double acoshl(long double);
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//
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// Overview of operation
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//==============================================================
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//
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// There are 6 paths:
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// 1. x = 1
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// Return acoshl(x) = 0;
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//
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// 2. x < 1
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// Return acoshl(x) = Nan (Domain error, error handler call with tag 135);
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//
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// 3. x = [S,Q]Nan or +INF
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// Return acoshl(x) = x + x;
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//
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// 4. 'Near 1': 1 < x < 1+1/8
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// Return acoshl(x) = sqrtl(2*y)*(1-P(y)/Q(y)),
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// where y = 1, P(y)/Q(y) - rational approximation
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//
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// 5. 'Huges': x > 0.5*2^64
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// Return acoshl(x) = (logl(2*x-1));
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//
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// 6. 'Main path': 1+1/8 < x < 0.5*2^64
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// b_hi + b_lo = x + sqrt(x^2 - 1);
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// acoshl(x) = logl_special(b_hi, b_lo);
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//
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// Algorithm description
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//==============================================================
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//
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// I. Near 1 path algorithm
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// **************************************************************
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// The formula is acoshl(x) = sqrtl(2*y)*(1-P(y)/Q(y)),
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// where y = 1, P(y)/Q(y) - rational approximation
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//
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// 1) y = x - 1, y2 = 2 * y
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//
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// 2) Compute in parallel sqrtl(2*y) and P(y)/Q(y)
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// a) sqrtl computation method described below (main path algorithm, item 2))
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// As result we obtain (gg+gl) - multiprecision result
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// as pair of double extended values
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// b) P(y) and Q(y) calculated without any extra precision manipulations
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// c) P/Q division:
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// y = frcpa(Q) initial approximation of 1/Q
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// z = P*y initial approximation of P/Q
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//
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// e = 1 - b*y
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// e2 = e + e^2
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// e1 = e^2
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// y1 = y + y*e2 = y + y*(e+e^2)
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//
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// e3 = e + e1^2
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// y2 = y + y1*e3 = y + y*(e+e^2+..+e^6)
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//
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// r = P - Q*z
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// e = 1 - Q*y2
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// xx = z + r*y2 high part of a/b
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//
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// y3 = y2 + y2*e4
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// r1 = P - Q*xx
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// xl = r1*y3 low part of a/b
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//
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// 3) res = sqrt(2*y) - sqrt(2*y)*(P(y)/Q(y)) =
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// = (gg+gl) - (gg + gl)*(xx+xl);
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//
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// a) hh = gg*xx; hl = gg*xl; lh = gl*xx; ll = gl*xl;
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// b) res = ((((gl + ll) + lh) + hl) + hh) + gg;
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// (exactly in this order)
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//
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// II. Main path algorithm
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// ( thanks to Peter Markstein for the idea of sqrt(x^2+1) computation! )
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// **********************************************************************
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//
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// There are 3 parts of x+sqrt(x^2-1) computation:
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//
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// 1) m2 = (m2_hi+m2_lo) = x^2-1 obtaining
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// ------------------------------------
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// m2_hi = x2_hi - 1, where x2_hi = x * x;
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// m2_lo = x2_lo + p1_lo, where
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// x2_lo = FMS(x*x-x2_hi),
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// p1_lo = (1 + m2_hi) - x2_hi;
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//
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// 2) g = (g_hi+g_lo) = sqrt(m2) = sqrt(m2_hi+m2_lo)
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// ----------------------------------------------
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// r = invsqrt(m2_hi) (8-bit reciprocal square root approximation);
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// g = m2_hi * r (first 8 bit-approximation of sqrt);
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//
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// h = 0.5 * r;
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// e = 0.5 - g * h;
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// g = g * e + g (second 16 bit-approximation of sqrt);
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//
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// h = h * e + h;
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// e = 0.5 - g * h;
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// g = g * e + g (third 32 bit-approximation of sqrt);
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//
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// h = h * e + h;
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// e = 0.5 - g * h;
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// g_hi = g * e + g (fourth 64 bit-approximation of sqrt);
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//
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// Remainder computation:
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// h = h * e + h;
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// d = (m2_hi - g_hi * g_hi) + m2_lo;
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// g_lo = d * h;
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//
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// 3) b = (b_hi + b_lo) = x + g, where g = (g_hi + g_lo) = sqrt(x^2-1)
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// -------------------------------------------------------------------
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// b_hi = (g_hi + x) + gl;
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// b_lo = (x - b_hi) + g_hi + gl;
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//
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// Now we pass b presented as sum b_hi + b_lo to special version
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// of logl function which accept a pair of arguments as
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// mutiprecision value.
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//
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// Special log algorithm overview
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// ================================
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// Here we use a table lookup method. The basic idea is that in
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// order to compute logl(Arg) for an argument Arg in [1,2),
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// we construct a value G such that G*Arg is close to 1 and that
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// logl(1/G) is obtainable easily from a table of values calculated
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// beforehand. Thus
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//
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// logl(Arg) = logl(1/G) + logl((G*Arg - 1))
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//
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// Because |G*Arg - 1| is small, the second term on the right hand
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// side can be approximated by a short polynomial. We elaborate
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// this method in four steps.
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//
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// Step 0: Initialization
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//
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// We need to calculate logl( X+1 ). Obtain N, S_hi such that
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//
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// X = 2^N * ( S_hi + S_lo ) exactly
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//
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// where S_hi in [1,2) and S_lo is a correction to S_hi in the sense
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// that |S_lo| <= ulp(S_hi).
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//
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// For the special version of logl: S_lo = b_lo
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// !-----------------------------------------------!
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//
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// Step 1: Argument Reduction
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//
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// Based on S_hi, obtain G_1, G_2, G_3 from a table and calculate
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//
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// G := G_1 * G_2 * G_3
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// r := (G * S_hi - 1) + G * S_lo
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//
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// These G_j's have the property that the product is exactly
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// representable and that |r| < 2^(-12) as a result.
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//
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// Step 2: Approximation
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//
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// logl(1 + r) is approximated by a short polynomial poly(r).
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//
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// Step 3: Reconstruction
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//
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// Finally, logl( X ) = logl( X+1 ) is given by
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//
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// logl( X ) = logl( 2^N * (S_hi + S_lo) )
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// ~=~ N*logl(2) + logl(1/G) + logl(1 + r)
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// ~=~ N*logl(2) + logl(1/G) + poly(r).
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//
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// For detailed description see logl or log1pl function, regular path.
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//
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// Registers used
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//==============================================================
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// Floating Point registers used:
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// f8, input
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// f32 -> f95 (64 registers)
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// General registers used:
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// r32 -> r67 (36 registers)
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// Predicate registers used:
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// p7 -> p11
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// p7 for 'NaNs, Inf' path
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// p8 for 'near 1' path
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// p9 for 'huges' path
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// p10 for x = 1
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// p11 for x < 1
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//
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//*********************************************************************
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// IEEE Special Conditions:
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//
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// acoshl(+inf) = +inf
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// acoshl(-inf) = QNaN
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// acoshl(1) = 0
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// acoshl(x<1) = QNaN
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// acoshl(SNaN) = QNaN
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// acoshl(QNaN) = QNaN
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//
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// Data tables
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//==============================================================
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RODATA
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.align 64
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// Near 1 path rational aproximation coefficients
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LOCAL_OBJECT_START(Poly_P)
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data8 0xB0978143F695D40F, 0x3FF1 // .84205539791447100108478906277453574946e-4
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data8 0xB9800D841A8CAD29, 0x3FF6 // .28305085180397409672905983082168721069e-2
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data8 0xC889F455758C1725, 0x3FF9 // .24479844297887530847660233111267222945e-1
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data8 0x9BE1DFF006F45F12, 0x3FFB // .76114415657565879842941751209926938306e-1
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data8 0x9E34AF4D372861E0, 0x3FFB // .77248925727776366270605984806795850504e-1
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data8 0xF3DC502AEE14C4AE, 0x3FA6 // .3077953476682583606615438814166025592e-26
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LOCAL_OBJECT_END(Poly_P)
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//
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LOCAL_OBJECT_START(Poly_Q)
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data8 0xF76E3FD3C7680357, 0x3FF1 // .11798413344703621030038719253730708525e-3
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data8 0xD107D2E7273263AE, 0x3FF7 // .63791065024872525660782716786703188820e-2
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data8 0xB609BE5CDE206AEF, 0x3FFB // .88885771950814004376363335821980079985e-1
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data8 0xF7DEACAC28067C8A, 0x3FFD // .48412074662702495416825113623936037072302
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data8 0x8F9BE5890CEC7E38, 0x3FFF // 1.1219450873557867470217771071068369729526
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data8 0xED4F06F3D2BC92D1, 0x3FFE // .92698710873331639524734537734804056798748
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LOCAL_OBJECT_END(Poly_Q)
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// Q coeffs
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LOCAL_OBJECT_START(Constants_Q)
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data4 0x00000000,0xB1721800,0x00003FFE,0x00000000
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data4 0x4361C4C6,0x82E30865,0x0000BFE2,0x00000000
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data4 0x328833CB,0xCCCCCAF2,0x00003FFC,0x00000000
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data4 0xA9D4BAFB,0x80000077,0x0000BFFD,0x00000000
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data4 0xAAABE3D2,0xAAAAAAAA,0x00003FFD,0x00000000
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data4 0xFFFFDAB7,0xFFFFFFFF,0x0000BFFD,0x00000000
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LOCAL_OBJECT_END(Constants_Q)
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// Z1 - 16 bit fixed
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LOCAL_OBJECT_START(Constants_Z_1)
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data4 0x00008000
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data4 0x00007879
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data4 0x000071C8
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data4 0x00006BCB
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data4 0x00006667
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data4 0x00006187
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data4 0x00005D18
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data4 0x0000590C
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data4 0x00005556
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data4 0x000051EC
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data4 0x00004EC5
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data4 0x00004BDB
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data4 0x00004925
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data4 0x0000469F
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data4 0x00004445
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data4 0x00004211
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LOCAL_OBJECT_END(Constants_Z_1)
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// G1 and H1 - IEEE single and h1 - IEEE double
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LOCAL_OBJECT_START(Constants_G_H_h1)
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data4 0x3F800000,0x00000000
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data8 0x0000000000000000
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data4 0x3F70F0F0,0x3D785196
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data8 0x3DA163A6617D741C
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data4 0x3F638E38,0x3DF13843
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data8 0x3E2C55E6CBD3D5BB
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data4 0x3F579430,0x3E2FF9A0
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data8 0xBE3EB0BFD86EA5E7
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data4 0x3F4CCCC8,0x3E647FD6
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data8 0x3E2E6A8C86B12760
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data4 0x3F430C30,0x3E8B3AE7
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data8 0x3E47574C5C0739BA
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data4 0x3F3A2E88,0x3EA30C68
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data8 0x3E20E30F13E8AF2F
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data4 0x3F321640,0x3EB9CEC8
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data8 0xBE42885BF2C630BD
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data4 0x3F2AAAA8,0x3ECF9927
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data8 0x3E497F3497E577C6
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data4 0x3F23D708,0x3EE47FC5
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data8 0x3E3E6A6EA6B0A5AB
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data4 0x3F1D89D8,0x3EF8947D
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data8 0xBDF43E3CD328D9BE
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data4 0x3F17B420,0x3F05F3A1
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data8 0x3E4094C30ADB090A
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data4 0x3F124920,0x3F0F4303
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data8 0xBE28FBB2FC1FE510
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data4 0x3F0D3DC8,0x3F183EBF
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data8 0x3E3A789510FDE3FA
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data4 0x3F088888,0x3F20EC80
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data8 0x3E508CE57CC8C98F
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data4 0x3F042108,0x3F29516A
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data8 0xBE534874A223106C
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LOCAL_OBJECT_END(Constants_G_H_h1)
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// Z2 - 16 bit fixed
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LOCAL_OBJECT_START(Constants_Z_2)
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data4 0x00008000
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data4 0x00007F81
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data4 0x00007F02
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data4 0x00007E85
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data4 0x00007E08
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data4 0x00007D8D
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data4 0x00007D12
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data4 0x00007C98
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data4 0x00007C20
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data4 0x00007BA8
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data4 0x00007B31
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data4 0x00007ABB
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data4 0x00007A45
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data4 0x000079D1
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data4 0x0000795D
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data4 0x000078EB
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LOCAL_OBJECT_END(Constants_Z_2)
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// G2 and H2 - IEEE single and h2 - IEEE double
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LOCAL_OBJECT_START(Constants_G_H_h2)
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data4 0x3F800000,0x00000000
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data8 0x0000000000000000
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data4 0x3F7F00F8,0x3B7F875D
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data8 0x3DB5A11622C42273
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data4 0x3F7E03F8,0x3BFF015B
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data8 0x3DE620CF21F86ED3
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data4 0x3F7D08E0,0x3C3EE393
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data8 0xBDAFA07E484F34ED
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data4 0x3F7C0FC0,0x3C7E0586
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data8 0xBDFE07F03860BCF6
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data4 0x3F7B1880,0x3C9E75D2
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data8 0x3DEA370FA78093D6
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data4 0x3F7A2328,0x3CBDC97A
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data8 0x3DFF579172A753D0
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data4 0x3F792FB0,0x3CDCFE47
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|
data8 0x3DFEBE6CA7EF896B
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data4 0x3F783E08,0x3CFC15D0
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data8 0x3E0CF156409ECB43
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|
data4 0x3F774E38,0x3D0D874D
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|
data8 0xBE0B6F97FFEF71DF
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|
data4 0x3F766038,0x3D1CF49B
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|
data8 0xBE0804835D59EEE8
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|
data4 0x3F757400,0x3D2C531D
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data8 0x3E1F91E9A9192A74
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data4 0x3F748988,0x3D3BA322
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data8 0xBE139A06BF72A8CD
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data4 0x3F73A0D0,0x3D4AE46F
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data8 0x3E1D9202F8FBA6CF
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data4 0x3F72B9D0,0x3D5A1756
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data8 0xBE1DCCC4BA796223
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data4 0x3F71D488,0x3D693B9D
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data8 0xBE049391B6B7C239
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LOCAL_OBJECT_END(Constants_G_H_h2)
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// G3 and H3 - IEEE single and h3 - IEEE double
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LOCAL_OBJECT_START(Constants_G_H_h3)
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data4 0x3F7FFC00,0x38800100
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data8 0x3D355595562224CD
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data4 0x3F7FF400,0x39400480
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data8 0x3D8200A206136FF6
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data4 0x3F7FEC00,0x39A00640
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data8 0x3DA4D68DE8DE9AF0
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data4 0x3F7FE400,0x39E00C41
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data8 0xBD8B4291B10238DC
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data4 0x3F7FDC00,0x3A100A21
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data8 0xBD89CCB83B1952CA
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data4 0x3F7FD400,0x3A300F22
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|
data8 0xBDB107071DC46826
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data4 0x3F7FCC08,0x3A4FF51C
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data8 0x3DB6FCB9F43307DB
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data4 0x3F7FC408,0x3A6FFC1D
|
|
data8 0xBD9B7C4762DC7872
|
|
data4 0x3F7FBC10,0x3A87F20B
|
|
data8 0xBDC3725E3F89154A
|
|
data4 0x3F7FB410,0x3A97F68B
|
|
data8 0xBD93519D62B9D392
|
|
data4 0x3F7FAC18,0x3AA7EB86
|
|
data8 0x3DC184410F21BD9D
|
|
data4 0x3F7FA420,0x3AB7E101
|
|
data8 0xBDA64B952245E0A6
|
|
data4 0x3F7F9C20,0x3AC7E701
|
|
data8 0x3DB4B0ECAABB34B8
|
|
data4 0x3F7F9428,0x3AD7DD7B
|
|
data8 0x3D9923376DC40A7E
|
|
data4 0x3F7F8C30,0x3AE7D474
|
|
data8 0x3DC6E17B4F2083D3
|
|
data4 0x3F7F8438,0x3AF7CBED
|
|
data8 0x3DAE314B811D4394
|
|
data4 0x3F7F7C40,0x3B03E1F3
|
|
data8 0xBDD46F21B08F2DB1
|
|
data4 0x3F7F7448,0x3B0BDE2F
|
|
data8 0xBDDC30A46D34522B
|
|
data4 0x3F7F6C50,0x3B13DAAA
|
|
data8 0x3DCB0070B1F473DB
|
|
data4 0x3F7F6458,0x3B1BD766
|
|
data8 0xBDD65DDC6AD282FD
|
|
data4 0x3F7F5C68,0x3B23CC5C
|
|
data8 0xBDCDAB83F153761A
|
|
data4 0x3F7F5470,0x3B2BC997
|
|
data8 0xBDDADA40341D0F8F
|
|
data4 0x3F7F4C78,0x3B33C711
|
|
data8 0x3DCD1BD7EBC394E8
|
|
data4 0x3F7F4488,0x3B3BBCC6
|
|
data8 0xBDC3532B52E3E695
|
|
data4 0x3F7F3C90,0x3B43BAC0
|
|
data8 0xBDA3961EE846B3DE
|
|
data4 0x3F7F34A0,0x3B4BB0F4
|
|
data8 0xBDDADF06785778D4
|
|
data4 0x3F7F2CA8,0x3B53AF6D
|
|
data8 0x3DCC3ED1E55CE212
|
|
data4 0x3F7F24B8,0x3B5BA620
|
|
data8 0xBDBA31039E382C15
|
|
data4 0x3F7F1CC8,0x3B639D12
|
|
data8 0x3D635A0B5C5AF197
|
|
data4 0x3F7F14D8,0x3B6B9444
|
|
data8 0xBDDCCB1971D34EFC
|
|
data4 0x3F7F0CE0,0x3B7393BC
|
|
data8 0x3DC7450252CD7ADA
|
|
data4 0x3F7F04F0,0x3B7B8B6D
|
|
data8 0xBDB68F177D7F2A42
|
|
LOCAL_OBJECT_END(Constants_G_H_h3)
|
|
|
|
// Assembly macros
|
|
//==============================================================
|
|
|
|
// Floating Point Registers
|
|
|
|
FR_Arg = f8
|
|
FR_Res = f8
|
|
|
|
|
|
FR_PP0 = f32
|
|
FR_PP1 = f33
|
|
FR_PP2 = f34
|
|
FR_PP3 = f35
|
|
FR_PP4 = f36
|
|
FR_PP5 = f37
|
|
FR_QQ0 = f38
|
|
FR_QQ1 = f39
|
|
FR_QQ2 = f40
|
|
FR_QQ3 = f41
|
|
FR_QQ4 = f42
|
|
FR_QQ5 = f43
|
|
|
|
FR_Q1 = f44
|
|
FR_Q2 = f45
|
|
FR_Q3 = f46
|
|
FR_Q4 = f47
|
|
|
|
FR_Half = f48
|
|
FR_Two = f49
|
|
|
|
FR_log2_hi = f50
|
|
FR_log2_lo = f51
|
|
|
|
|
|
FR_X2 = f52
|
|
FR_M2 = f53
|
|
FR_M2L = f54
|
|
FR_Rcp = f55
|
|
FR_GG = f56
|
|
FR_HH = f57
|
|
FR_EE = f58
|
|
FR_DD = f59
|
|
FR_GL = f60
|
|
FR_Tmp = f61
|
|
|
|
|
|
FR_XM1 = f62
|
|
FR_2XM1 = f63
|
|
FR_XM12 = f64
|
|
|
|
|
|
|
|
// Special logl registers
|
|
FR_XLog_Hi = f65
|
|
FR_XLog_Lo = f66
|
|
|
|
FR_Y_hi = f67
|
|
FR_Y_lo = f68
|
|
|
|
FR_S_hi = f69
|
|
FR_S_lo = f70
|
|
|
|
FR_poly_lo = f71
|
|
FR_poly_hi = f72
|
|
|
|
FR_G = f73
|
|
FR_H = f74
|
|
FR_h = f75
|
|
|
|
FR_G2 = f76
|
|
FR_H2 = f77
|
|
FR_h2 = f78
|
|
|
|
FR_r = f79
|
|
FR_rsq = f80
|
|
FR_rcub = f81
|
|
|
|
FR_float_N = f82
|
|
|
|
FR_G3 = f83
|
|
FR_H3 = f84
|
|
FR_h3 = f85
|
|
|
|
FR_2_to_minus_N = f86
|
|
|
|
|
|
// Near 1 registers
|
|
FR_PP = f65
|
|
FR_QQ = f66
|
|
|
|
|
|
FR_PV6 = f69
|
|
FR_PV4 = f70
|
|
FR_PV3 = f71
|
|
FR_PV2 = f72
|
|
|
|
FR_QV6 = f73
|
|
FR_QV4 = f74
|
|
FR_QV3 = f75
|
|
FR_QV2 = f76
|
|
|
|
FR_Y0 = f77
|
|
FR_Q0 = f78
|
|
FR_E0 = f79
|
|
FR_E2 = f80
|
|
FR_E1 = f81
|
|
FR_Y1 = f82
|
|
FR_E3 = f83
|
|
FR_Y2 = f84
|
|
FR_R0 = f85
|
|
FR_E4 = f86
|
|
FR_Y3 = f87
|
|
FR_R1 = f88
|
|
FR_X_Hi = f89
|
|
FR_X_lo = f90
|
|
|
|
FR_HH = f91
|
|
FR_LL = f92
|
|
FR_HL = f93
|
|
FR_LH = f94
|
|
|
|
|
|
|
|
// Error handler registers
|
|
FR_Arg_X = f95
|
|
FR_Arg_Y = f0
|
|
|
|
|
|
// General Purpose Registers
|
|
|
|
// General prolog registers
|
|
GR_PFS = r32
|
|
GR_OneP125 = r33
|
|
GR_TwoP63 = r34
|
|
GR_Arg = r35
|
|
GR_Half = r36
|
|
|
|
// Near 1 path registers
|
|
GR_Poly_P = r37
|
|
GR_Poly_Q = r38
|
|
|
|
// Special logl registers
|
|
GR_Index1 = r39
|
|
GR_Index2 = r40
|
|
GR_signif = r41
|
|
GR_X_0 = r42
|
|
GR_X_1 = r43
|
|
GR_X_2 = r44
|
|
GR_minus_N = r45
|
|
GR_Z_1 = r46
|
|
GR_Z_2 = r47
|
|
GR_N = r48
|
|
GR_Bias = r49
|
|
GR_M = r50
|
|
GR_Index3 = r51
|
|
GR_exp_2tom80 = r52
|
|
GR_exp_mask = r53
|
|
GR_exp_2tom7 = r54
|
|
GR_ad_ln10 = r55
|
|
GR_ad_tbl_1 = r56
|
|
GR_ad_tbl_2 = r57
|
|
GR_ad_tbl_3 = r58
|
|
GR_ad_q = r59
|
|
GR_ad_z_1 = r60
|
|
GR_ad_z_2 = r61
|
|
GR_ad_z_3 = r62
|
|
|
|
//
|
|
// Added for unwind support
|
|
//
|
|
GR_SAVE_PFS = r32
|
|
GR_SAVE_B0 = r33
|
|
GR_SAVE_GP = r34
|
|
|
|
GR_Parameter_X = r64
|
|
GR_Parameter_Y = r65
|
|
GR_Parameter_RESULT = r66
|
|
GR_Parameter_TAG = r67
|
|
|
|
|
|
|
|
.section .text
|
|
GLOBAL_LIBM_ENTRY(acoshl)
|
|
|
|
{ .mfi
|
|
alloc GR_PFS = ar.pfs,0,32,4,0 // Local frame allocation
|
|
fcmp.lt.s1 p11, p0 = FR_Arg, f1 // if arg is less than 1
|
|
mov GR_Half = 0xfffe // 0.5's exp
|
|
}
|
|
{ .mfi
|
|
addl GR_Poly_Q = @ltoff(Poly_Q), gp // Address of Q-coeff table
|
|
fma.s1 FR_X2 = FR_Arg, FR_Arg, f0 // Obtain x^2
|
|
addl GR_Poly_P = @ltoff(Poly_P), gp // Address of P-coeff table
|
|
};;
|
|
|
|
{ .mfi
|
|
getf.d GR_Arg = FR_Arg // get arument as double (int64)
|
|
fma.s0 FR_Two = f1, f1, f1 // construct 2.0
|
|
addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp // logl tables
|
|
}
|
|
{ .mlx
|
|
nop.m 0
|
|
movl GR_TwoP63 = 0x43E8000000000000 // 0.5*2^63 (huge arguments)
|
|
};;
|
|
|
|
{ .mfi
|
|
ld8 GR_Poly_P = [GR_Poly_P] // get actual P-coeff table address
|
|
fcmp.eq.s1 p10, p0 = FR_Arg, f1 // if arg == 1 (return 0)
|
|
nop.i 0
|
|
}
|
|
{ .mlx
|
|
ld8 GR_Poly_Q = [GR_Poly_Q] // get actual Q-coeff table address
|
|
movl GR_OneP125 = 0x3FF2000000000000 // 1.125 (near 1 path bound)
|
|
};;
|
|
|
|
{ .mfi
|
|
ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1
|
|
fclass.m p7,p0 = FR_Arg, 0xe3 // if arg NaN inf
|
|
cmp.le p9, p0 = GR_TwoP63, GR_Arg // if arg > 0.5*2^63 ('huges')
|
|
}
|
|
{ .mfb
|
|
cmp.ge p8, p0 = GR_OneP125, GR_Arg // if arg<1.125 -near 1 path
|
|
fms.s1 FR_XM1 = FR_Arg, f1, f1 // X0 = X-1 (for near 1 path)
|
|
(p11) br.cond.spnt acoshl_lt_pone // error branch (less than 1)
|
|
};;
|
|
|
|
{ .mmi
|
|
setf.exp FR_Half = GR_Half // construct 0.5
|
|
(p9) setf.s FR_XLog_Lo = r0 // Low of logl arg=0 (Huges path)
|
|
mov GR_exp_mask = 0x1FFFF // Create exponent mask
|
|
};;
|
|
|
|
{ .mmf
|
|
(p8) ldfe FR_PP5 = [GR_Poly_P],16 // Load P5
|
|
(p8) ldfe FR_QQ5 = [GR_Poly_Q],16 // Load Q5
|
|
fms.s1 FR_M2 = FR_X2, f1, f1 // m2 = x^2 - 1
|
|
};;
|
|
|
|
{ .mfi
|
|
(p8) ldfe FR_QQ4 = [GR_Poly_Q],16 // Load Q4
|
|
fms.s1 FR_M2L = FR_Arg, FR_Arg, FR_X2 // low part of
|
|
// m2 = fma(X*X - m2)
|
|
add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1
|
|
}
|
|
{ .mfb
|
|
(p8) ldfe FR_PP4 = [GR_Poly_P],16 // Load P4
|
|
(p7) fma.s0 FR_Res = FR_Arg,f1,FR_Arg // r = a + a (Nan, Inf)
|
|
(p7) br.ret.spnt b0 // return (Nan, Inf)
|
|
};;
|
|
|
|
{ .mfi
|
|
(p8) ldfe FR_PP3 = [GR_Poly_P],16 // Load P3
|
|
nop.f 0
|
|
add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_P
|
|
}
|
|
{ .mfb
|
|
(p8) ldfe FR_QQ3 = [GR_Poly_Q],16 // Load Q3
|
|
(p9) fms.s1 FR_XLog_Hi = FR_Two, FR_Arg, f1 // Hi of log arg = 2*X-1
|
|
(p9) br.cond.spnt huges_logl // special version of log
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
(p8) ldfe FR_PP2 = [GR_Poly_P],16 // Load P2
|
|
(p8) fma.s1 FR_2XM1 = FR_Two, FR_XM1, f0 // 2X0 = 2 * X0
|
|
add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2
|
|
}
|
|
{ .mfb
|
|
(p8) ldfe FR_QQ2 = [GR_Poly_Q],16 // Load Q2
|
|
(p10) fma.s0 FR_Res = f0,f1,f0 // r = 0 (arg = 1)
|
|
(p10) br.ret.spnt b0 // return (arg = 1)
|
|
};;
|
|
|
|
{ .mmi
|
|
(p8) ldfe FR_PP1 = [GR_Poly_P],16 // Load P1
|
|
(p8) ldfe FR_QQ1 = [GR_Poly_Q],16 // Load Q1
|
|
add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
(p8) ldfe FR_PP0 = [GR_Poly_P] // Load P0
|
|
fma.s1 FR_Tmp = f1, f1, FR_M2 // Tmp = 1 + m2
|
|
add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3
|
|
}
|
|
{ .mfb
|
|
(p8) ldfe FR_QQ0 = [GR_Poly_Q]
|
|
nop.f 0
|
|
(p8) br.cond.spnt near_1 // near 1 path
|
|
};;
|
|
{ .mfi
|
|
ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi
|
|
nop.f 0
|
|
mov GR_Bias = 0x0FFFF // Create exponent bias
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
frsqrta.s1 FR_Rcp, p0 = FR_M2 // Rcp = 1/m2 reciprocal appr.
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo
|
|
fms.s1 FR_Tmp = FR_X2, f1, FR_Tmp // Tmp = x^2 - Tmp
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_Q4 = [GR_ad_q],16 // Load Q4
|
|
fma.s1 FR_GG = FR_Rcp, FR_M2, f0 // g = Rcp * m2
|
|
// 8 bit Newton Raphson iteration
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_Half, FR_Rcp, f0 // h = 0.5 * Rcp
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
ldfe FR_Q3 = [GR_ad_q],16 // Load Q3
|
|
fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_M2L = FR_Tmp, f1, FR_M2L // low part of m2 = Tmp+m2l
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_Q2 = [GR_ad_q],16 // Load Q2
|
|
fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g
|
|
// 16 bit Newton Raphson iteration
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_Q1 = [GR_ad_q] // Load Q1
|
|
fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g
|
|
// 32 bit Newton Raphson iteration
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g
|
|
// 64 bit Newton Raphson iteration
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_DD = FR_GG, FR_GG, FR_M2 // Remainder d = g * g - p2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_XLog_Hi = FR_Arg, f1, FR_GG // bh = z + gh
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_DD = FR_DD, f1, FR_M2L // add p2l: d = d + p2l
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
getf.sig GR_signif = FR_XLog_Hi // Get significand of x+1
|
|
nop.f 0
|
|
mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_GL = FR_DD, FR_HH, f0 // gl = d * h
|
|
extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_XLog_Hi = FR_DD, FR_HH, FR_XLog_Hi // bh = bh + gl
|
|
nop.i 0
|
|
};;
|
|
|
|
|
|
|
|
{ .mmi
|
|
shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1
|
|
shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1
|
|
extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of signif.
|
|
};;
|
|
|
|
{ .mmi
|
|
ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_XLog_Lo = FR_Arg, f1, FR_XLog_Hi // bl = x - bh
|
|
pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1
|
|
};;
|
|
|
|
// WE CANNOT USE GR_X_1 IN NEXT 3 CYCLES BECAUSE OF POSSIBLE 10 CLOCKS STALL!
|
|
// "DEAD" ZONE!
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.se FR_S_hi = f1,FR_XLog_Hi // Form |x+1|
|
|
nop.i 0
|
|
};;
|
|
|
|
|
|
{ .mmi
|
|
getf.exp GR_N = FR_XLog_Hi // Get N = exponent of x+1
|
|
ldfd FR_h = [GR_ad_tbl_1] // Load h_1
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1
|
|
};;
|
|
|
|
{ .mfi
|
|
shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2
|
|
fma.s1 FR_XLog_Lo = FR_XLog_Lo, f1, FR_GG // bl = bl + gg
|
|
mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80
|
|
}
|
|
{ .mfi
|
|
shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2
|
|
nop.f 0
|
|
sub GR_N = GR_N, GR_Bias // sub bias from exp
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2
|
|
ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2
|
|
sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N)
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
setf.sig FR_float_N = GR_N // Put integer N into rightmost sign
|
|
setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N)
|
|
pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2
|
|
};;
|
|
|
|
// WE CANNOT USE GR_X_2 IN NEXT 3 CYCLES ("DEAD" ZONE!)
|
|
// BECAUSE OF POSSIBLE 10 CLOCKS STALL!
|
|
// (Just nops added - nothing to do here)
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_XLog_Lo = FR_XLog_Lo, f1, FR_GL // bl = bl + gl
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
|
|
};;
|
|
|
|
{ .mfi
|
|
shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3
|
|
fcvt.xf FR_float_N = FR_float_N
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_S_lo = FR_XLog_Lo, FR_2_to_minus_N, f0 //S_lo=S_lo*2^(-N)
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi=N*log2_hi+H
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h=N*log2_lo+h
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_r = FR_G, FR_S_lo, FR_r // r=G*S_lo+(G*S_hi-1)
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo=poly_lo*r+Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s0 FR_Y_lo = FR_poly_hi, FR_poly_lo
|
|
// Y_lo=poly_hi+poly_lo
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
fadd.s0 FR_Res = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi
|
|
br.ret.sptk b0 // Common exit for 2^-7 < x < inf
|
|
};;
|
|
|
|
|
|
huges_logl:
|
|
{ .mmi
|
|
getf.sig GR_signif = FR_XLog_Hi // Get significand of x+1
|
|
mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1
|
|
nop.f 0
|
|
add GR_ad_q = -0x60, GR_ad_z_1 // Point to Constants_P
|
|
}
|
|
{ .mfi
|
|
add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2
|
|
nop.f 0
|
|
add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2
|
|
};;
|
|
|
|
{ .mfi
|
|
add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3
|
|
nop.f 0
|
|
extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif
|
|
};;
|
|
|
|
{ .mfi
|
|
shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1
|
|
nop.f 0
|
|
extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of signif.
|
|
};;
|
|
|
|
{ .mfi
|
|
ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1
|
|
nop.f 0
|
|
mov GR_exp_mask = 0x1FFFF // Create exponent mask
|
|
}
|
|
{ .mfi
|
|
shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1
|
|
nop.f 0
|
|
mov GR_Bias = 0x0FFFF // Create exponent bias
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1
|
|
fmerge.se FR_S_hi = f1,FR_XLog_Hi // Form |x|
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
getf.exp GR_N = FR_XLog_Hi // Get N = exponent of x+1
|
|
ldfd FR_h = [GR_ad_tbl_1] // Load h_1
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi
|
|
nop.f 0
|
|
pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo
|
|
sub GR_N = GR_N, GR_Bias
|
|
mov GR_exp_2tom80 = 0x0ffaf // Exponent of 2^-80
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfe FR_Q4 = [GR_ad_q],16 // Load Q4
|
|
nop.f 0
|
|
sub GR_minus_N = GR_Bias, GR_N // Form exponent of 2^(-N)
|
|
};;
|
|
|
|
{ .mmf
|
|
ldfe FR_Q3 = [GR_ad_q],16 // Load Q3
|
|
setf.sig FR_float_N = GR_N // Put integer N into rightmost sign
|
|
nop.f 0
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfe FR_Q2 = [GR_ad_q],16 // Load Q2
|
|
nop.m 0
|
|
extr.u GR_Index2 = GR_X_1, 6, 4 // Extract bits 6-9 of X_1
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfe FR_Q1 = [GR_ad_q] // Load Q1
|
|
shladd GR_ad_z_2 = GR_Index2, 2, GR_ad_z_2 // Point to Z_2
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
ld4 GR_Z_2 = [GR_ad_z_2] // Load Z_2
|
|
shladd GR_ad_tbl_2 = GR_Index2, 4, GR_ad_tbl_2 // Point to G_2
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmf
|
|
ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2
|
|
setf.exp FR_2_to_minus_N = GR_minus_N // Form 2^(-N)
|
|
nop.f 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1*Z_2
|
|
};;
|
|
|
|
// WE CANNOT USE GR_X_2 IN NEXT 3 CYCLES ("DEAD" ZONE!)
|
|
// BECAUSE OF POSSIBLE 10 CLOCKS STALL!
|
|
// (Just nops added - nothing to do here)
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
|
|
};;
|
|
|
|
{ .mfi
|
|
shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3
|
|
fcvt.xf FR_float_N = FR_float_N
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3
|
|
nop.f 0
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3
|
|
fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mmf
|
|
nop.m 0
|
|
nop.m 0
|
|
fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2)*G_3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2)+H_3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi=N*log2_hi+H
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h = N*log2_lo+h
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo=poly_lo*r+Q2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1*rsq + r
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h//poly_lo=poly_lo*r^3+h
|
|
nop.i 0
|
|
};;
|
|
{ .mfi
|
|
nop.m 0
|
|
fadd.s0 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo=poly_hi+poly_lo
|
|
nop.i 0
|
|
};;
|
|
{ .mfb
|
|
nop.m 0
|
|
fadd.s0 FR_Res = FR_Y_lo,FR_Y_hi // Result=Y_lo+Y_hi
|
|
br.ret.sptk b0 // Common exit
|
|
};;
|
|
|
|
|
|
// NEAR ONE INTERVAL
|
|
near_1:
|
|
{ .mfi
|
|
nop.m 0
|
|
frsqrta.s1 FR_Rcp, p0 = FR_2XM1 // Rcp = 1/x reciprocal appr. &SQRT&
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_PV6 = FR_PP5, FR_XM1, FR_PP4 // pv6 = P5*xm1+P4 $POLY$
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_QV6 = FR_QQ5, FR_XM1, FR_QQ4 // qv6 = Q5*xm1+Q4 $POLY$
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_PV4 = FR_PP3, FR_XM1, FR_PP2 // pv4 = P3*xm1+P2 $POLY$
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_QV4 = FR_QQ3, FR_XM1, FR_QQ2 // qv4 = Q3*xm1+Q2 $POLY$
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_XM12 = FR_XM1, FR_XM1, f0 // xm1^2 = xm1 * xm1 $POLY$
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_PV2 = FR_PP1, FR_XM1, FR_PP0 // pv2 = P1*xm1+P0 $POLY$
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_QV2 = FR_QQ1, FR_XM1, FR_QQ0 // qv2 = Q1*xm1+Q0 $POLY$
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_GG = FR_Rcp, FR_2XM1, f0 // g = Rcp * x &SQRT&
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_Half, FR_Rcp, f0 // h = 0.5 * Rcp &SQRT&
|
|
nop.i 0
|
|
};;
|
|
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_PV3 = FR_XM12, FR_PV6, FR_PV4//pv3=pv6*xm1^2+pv4 $POLY$
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_QV3 = FR_XM12, FR_QV6, FR_QV4//qv3=qv6*xm1^2+qv4 $POLY$
|
|
nop.i 0
|
|
};;
|
|
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h &SQRT&
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_PP = FR_XM12, FR_PV3, FR_PV2 //pp=pv3*xm1^2+pv2 $POLY$
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_QQ = FR_XM12, FR_QV3, FR_QV2 //qq=qv3*xm1^2+qv2 $POLY$
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g &SQRT&
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h &SQRT&
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
frcpa.s1 FR_Y0,p0 = f1,FR_QQ // y = frcpa(b) #DIV#
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g*h &SQRT&
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Q0 = FR_PP,FR_Y0,f0 // q = a*y #DIV#
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_E0 = FR_Y0,FR_QQ,f1 // e = 1 - b*y #DIV#
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_GG = FR_GG, FR_EE, FR_GG // g = g * e + g &SQRT&
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h &SQRT&
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_E2 = FR_E0,FR_E0,FR_E0 // e2 = e+e^2 #DIV#
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_E1 = FR_E0,FR_E0,f0 // e1 = e^2 #DIV#
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_EE = FR_GG, FR_HH, FR_Half // e = 0.5 - g * h &SQRT&
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_DD = FR_GG, FR_GG, FR_2XM1 // d = x - g * g &SQRT&
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Y1 = FR_Y0,FR_E2,FR_Y0 // y1 = y+y*e2 #DIV#
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_E3 = FR_E1,FR_E1,FR_E0 // e3 = e+e1^2 #DIV#
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_GG = FR_DD, FR_HH, FR_GG // g = d * h + g &SQRT&
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_HH, FR_EE, FR_HH // h = h * e + h &SQRT&
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Y2 = FR_Y1,FR_E3,FR_Y0 // y2 = y+y1*e3 #DIV#
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_R0 = FR_QQ,FR_Q0,FR_PP // r = a-b*q #DIV#
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_DD = FR_GG, FR_GG, FR_2XM1 // d = x - g * g &SQRT&
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_E4 = FR_QQ,FR_Y2,f1 // e4 = 1-b*y2 #DIV#
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_X_Hi = FR_R0,FR_Y2,FR_Q0 // x = q+r*y2 #DIV#
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_GL = FR_DD, FR_HH, f0 // gl = d * h &SQRT&
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Y3 = FR_Y2,FR_E4,FR_Y2 // y3 = y2+y2*e4 #DIV#
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_R1 = FR_QQ,FR_X_Hi,FR_PP // r1 = a-b*x #DIV#
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HH = FR_GG, FR_X_Hi, f0 // hh = gg * x_hi
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_LH = FR_GL, FR_X_Hi, f0 // lh = gl * x_hi
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_X_lo = FR_R1,FR_Y3,f0 // x_lo = r1*y3 #DIV#
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_LL = FR_GL, FR_X_lo, f0 // ll = gl*x_lo
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_HL = FR_GG, FR_X_lo, f0 // hl = gg * x_lo
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_Res = FR_GL, f1, FR_LL // res = gl + ll
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_Res = FR_Res, f1, FR_LH // res = res + lh
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_Res = FR_Res, f1, FR_HL // res = res + hl
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 FR_Res = FR_Res, f1, FR_HH // res = res + hh
|
|
nop.i 0
|
|
};;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.s0 FR_Res = FR_Res, f1, FR_GG // result = res + gg
|
|
br.ret.sptk b0 // Exit for near 1 path
|
|
};;
|
|
// NEAR ONE INTERVAL END
|
|
|
|
|
|
|
|
|
|
acoshl_lt_pone:
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.s FR_Arg_X = FR_Arg, FR_Arg
|
|
nop.i 0
|
|
};;
|
|
{ .mfb
|
|
mov GR_Parameter_TAG = 135
|
|
frcpa.s0 FR_Res,p0 = f0,f0 // get QNaN,and raise invalid
|
|
br.cond.sptk __libm_error_region // exit if x < 1.0
|
|
};;
|
|
|
|
GLOBAL_LIBM_END(acoshl)
|
|
|
|
|
|
|
|
LOCAL_LIBM_ENTRY(__libm_error_region)
|
|
.prologue
|
|
{ .mfi
|
|
add GR_Parameter_Y = -32,sp // Parameter 2 value
|
|
nop.f 0
|
|
.save ar.pfs,GR_SAVE_PFS
|
|
mov GR_SAVE_PFS = ar.pfs // Save ar.pfs
|
|
}
|
|
{ .mfi
|
|
.fframe 64
|
|
add sp = -64,sp // Create new stack
|
|
nop.f 0
|
|
mov GR_SAVE_GP = gp // Save gp
|
|
};;
|
|
|
|
{ .mmi
|
|
stfe [GR_Parameter_Y] = FR_Arg_Y,16 // Parameter 2 to stack
|
|
add GR_Parameter_X = 16,sp // Parameter 1 address
|
|
.save b0,GR_SAVE_B0
|
|
mov GR_SAVE_B0 = b0 // Save b0
|
|
};;
|
|
|
|
.body
|
|
{ .mib
|
|
stfe [GR_Parameter_X] = FR_Arg_X // Parameter 1 to stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
|
|
nop.b 0
|
|
}
|
|
{ .mib
|
|
stfe [GR_Parameter_Y] = FR_Res // Parameter 3 to stack
|
|
add GR_Parameter_Y = -16,GR_Parameter_Y
|
|
br.call.sptk b0 = __libm_error_support# // Error handling function
|
|
};;
|
|
|
|
{ .mmi
|
|
nop.m 0
|
|
nop.m 0
|
|
add GR_Parameter_RESULT = 48,sp
|
|
};;
|
|
|
|
{ .mmi
|
|
ldfe f8 = [GR_Parameter_RESULT] // Get return res
|
|
.restore sp
|
|
add sp = 64,sp // Restore stack pointer
|
|
mov b0 = GR_SAVE_B0 // Restore return address
|
|
};;
|
|
|
|
{ .mib
|
|
mov gp = GR_SAVE_GP // Restore gp
|
|
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
|
|
br.ret.sptk b0 // Return
|
|
};;
|
|
|
|
LOCAL_LIBM_END(__libm_error_region#)
|
|
|
|
.type __libm_error_support#,@function
|
|
.global __libm_error_support#
|
|
|
|
|
|
|
|
|