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We stopped adding "Contributed by" or similar lines in sources in 2012 in favour of git logs and keeping the Contributors section of the glibc manual up to date. Removing these lines makes the license header a bit more consistent across files and also removes the possibility of error in attribution when license blocks or files are copied across since the contributed-by lines don't actually reflect reality in those cases. Move all "Contributed by" and similar lines (Written by, Test by, etc.) into a new file CONTRIBUTED-BY to retain record of these contributions. These contributors are also mentioned in manual/contrib.texi, so we just maintain this additional record as a courtesy to the earlier developers. The following scripts were used to filter a list of files to edit in place and to clean up the CONTRIBUTED-BY file respectively. These were not added to the glibc sources because they're not expected to be of any use in future given that this is a one time task: https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02 Reviewed-by: Carlos O'Donell <carlos@redhat.com>
1713 lines
43 KiB
ArmAsm
1713 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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//
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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 approximation 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
|
|
data8 0xBD8B4291B10238DC
|
|
data4 0x3F7FDC00,0x3A100A21
|
|
data8 0xBD89CCB83B1952CA
|
|
data4 0x3F7FD400,0x3A300F22
|
|
data8 0xBDB107071DC46826
|
|
data4 0x3F7FCC08,0x3A4FF51C
|
|
data8 0x3DB6FCB9F43307DB
|
|
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 argument 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)
|
|
libm_alias_ldouble_other (acosh, acosh)
|
|
|
|
|
|
|
|
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#
|