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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>
1202 lines
30 KiB
ArmAsm
1202 lines
30 KiB
ArmAsm
.file "logl.s"
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// Copyright (c) 2000 - 2003, 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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// 05/21/01 Extracted logl and log10l from log1pl.s file, and optimized
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// all paths.
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// 06/20/01 Fixed error tag for x=-inf.
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 02/10/03 Reordered header: .section, .global, .proc, .align;
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// used data8 for long double table values
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//
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//*********************************************************************
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//
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//*********************************************************************
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//
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// Function: Combined logl(x) and log10l(x) where
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// logl(x) = ln(x), for double-extended precision x values
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// log10l(x) = log (x), for double-extended precision x values
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// 10
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//
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//*********************************************************************
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//
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// Resources Used:
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//
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// Floating-Point Registers: f8 (Input and Return Value)
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// f34-f76
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//
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// General Purpose Registers:
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// r32-r56
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// r53-r56 (Used to pass arguments to error handling routine)
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//
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// Predicate Registers: p6-p14
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//
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//*********************************************************************
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//
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// IEEE Special Conditions:
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//
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// Denormal fault raised on denormal inputs
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// Overflow exceptions cannot occur
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// Underflow exceptions raised when appropriate for log1p
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// (Error Handling Routine called for underflow)
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// Inexact raised when appropriate by algorithm
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//
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// logl(inf) = inf
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// logl(-inf) = QNaN
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// logl(+/-0) = -inf
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// logl(SNaN) = QNaN
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// logl(QNaN) = QNaN
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// logl(EM_special Values) = QNaN
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// log10l(inf) = inf
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// log10l(-inf) = QNaN
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// log10l(+/-0) = -inf
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// log10l(SNaN) = QNaN
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// log10l(QNaN) = QNaN
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// log10l(EM_special Values) = QNaN
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//
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//*********************************************************************
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//
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// Overview
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//
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// The method consists of two cases.
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//
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// If |X-1| < 2^(-7) use case log_near1;
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// else use case log_regular;
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//
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// Case log_near1:
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//
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// logl( 1 + X ) can be approximated by a simple polynomial
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// in W = X-1. This polynomial resembles the truncated Taylor
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// series W - W^/2 + W^3/3 - ...
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//
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// Case log_regular:
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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), we
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// 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)
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// = logl(1/G) + logl(1 + (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 ). Obtain N, S_hi such that
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//
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// X = 2^N * S_hi exactly
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//
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// where S_hi in [1,2)
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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)
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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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//
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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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//
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// Finally, logl( X ) is given by
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//
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// logl( X ) = logl( 2^N * S_hi )
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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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// **** Algorithm ****
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//
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// Case log_near1:
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//
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// Here we compute a simple polynomial. To exploit parallelism, we split
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// the polynomial into two portions.
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//
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// W := X - 1
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// Wsq := W * W
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// W4 := Wsq*Wsq
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// W6 := W4*Wsq
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// Y_hi := W + Wsq*(P_1 + W*(P_2 + W*(P_3 + W*P_4))
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// Y_lo := W6*(P_5 + W*(P_6 + W*(P_7 + W*P_8)))
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//
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// Case log_regular:
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//
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// We present the algorithm in four steps.
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//
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// Step 0. Initialization
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// ----------------------
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//
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// Z := X
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// N := unbaised exponent of Z
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// S_hi := 2^(-N) * Z
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//
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// Step 1. Argument Reduction
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// --------------------------
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//
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// Let
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//
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// Z = 2^N * S_hi = 2^N * 1.d_1 d_2 d_3 ... d_63
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//
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// We obtain G_1, G_2, G_3 by the following steps.
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//
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//
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// Define X_0 := 1.d_1 d_2 ... d_14. This is extracted
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// from S_hi.
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//
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// Define A_1 := 1.d_1 d_2 d_3 d_4. This is X_0 truncated
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// to lsb = 2^(-4).
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//
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// Define index_1 := [ d_1 d_2 d_3 d_4 ].
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//
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// Fetch Z_1 := (1/A_1) rounded UP in fixed point with
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// fixed point lsb = 2^(-15).
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// Z_1 looks like z_0.z_1 z_2 ... z_15
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// Note that the fetching is done using index_1.
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// A_1 is actually not needed in the implementation
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// and is used here only to explain how is the value
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// Z_1 defined.
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//
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// Fetch G_1 := (1/A_1) truncated to 21 sig. bits.
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// floating pt. Again, fetching is done using index_1. A_1
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// explains how G_1 is defined.
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//
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// Calculate X_1 := X_0 * Z_1 truncated to lsb = 2^(-14)
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// = 1.0 0 0 0 d_5 ... d_14
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// This is accomplished by integer multiplication.
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// It is proved that X_1 indeed always begin
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// with 1.0000 in fixed point.
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//
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//
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// Define A_2 := 1.0 0 0 0 d_5 d_6 d_7 d_8. This is X_1
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// truncated to lsb = 2^(-8). Similar to A_1,
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// A_2 is not needed in actual implementation. It
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// helps explain how some of the values are defined.
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//
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// Define index_2 := [ d_5 d_6 d_7 d_8 ].
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//
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// Fetch Z_2 := (1/A_2) rounded UP in fixed point with
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// fixed point lsb = 2^(-15). Fetch done using index_2.
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// Z_2 looks like z_0.z_1 z_2 ... z_15
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//
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// Fetch G_2 := (1/A_2) truncated to 21 sig. bits.
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// floating pt.
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//
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// Calculate X_2 := X_1 * Z_2 truncated to lsb = 2^(-14)
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// = 1.0 0 0 0 0 0 0 0 d_9 d_10 ... d_14
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// This is accomplished by integer multiplication.
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// It is proved that X_2 indeed always begin
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// with 1.00000000 in fixed point.
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//
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//
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// Define A_3 := 1.0 0 0 0 0 0 0 0 d_9 d_10 d_11 d_12 d_13 1.
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// This is 2^(-14) + X_2 truncated to lsb = 2^(-13).
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//
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// Define index_3 := [ d_9 d_10 d_11 d_12 d_13 ].
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//
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// Fetch G_3 := (1/A_3) truncated to 21 sig. bits.
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// floating pt. Fetch is done using index_3.
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//
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// Compute G := G_1 * G_2 * G_3.
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//
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// This is done exactly since each of G_j only has 21 sig. bits.
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//
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// Compute
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//
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// r := (G*S_hi - 1)
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//
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//
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// Step 2. Approximation
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// ---------------------
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//
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// This step computes an approximation to logl( 1 + r ) where r is the
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// reduced argument just obtained. It is proved that |r| <= 1.9*2^(-13);
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// thus logl(1+r) can be approximated by a short polynomial:
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//
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// logl(1+r) ~=~ poly = r + Q1 r^2 + ... + Q4 r^5
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//
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//
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// Step 3. Reconstruction
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// ----------------------
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//
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// This step computes the desired result of logl(X):
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//
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// logl(X) = logl( 2^N * S_hi )
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// = N*logl(2) + logl( S_hi )
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// = N*logl(2) + logl(1/G) +
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// logl(1 + G*S_hi - 1 )
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//
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// logl(2), logl(1/G_j) are stored as pairs of (single,double) numbers:
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// log2_hi, log2_lo, log1byGj_hi, log1byGj_lo. The high parts are
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// single-precision numbers and the low parts are double precision
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// numbers. These have the property that
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//
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// N*log2_hi + SUM ( log1byGj_hi )
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//
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// is computable exactly in double-extended precision (64 sig. bits).
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// Finally
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//
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// Y_hi := N*log2_hi + SUM ( log1byGj_hi )
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// Y_lo := poly_hi + [ poly_lo +
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// ( SUM ( log1byGj_lo ) + N*log2_lo ) ]
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//
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RODATA
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.align 64
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// ************* DO NOT CHANGE THE ORDER OF THESE TABLES *************
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// P_8, P_7, P_6, P_5, P_4, P_3, P_2, and P_1
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LOCAL_OBJECT_START(Constants_P)
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data8 0xE3936754EFD62B15,0x00003FFB
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data8 0x8003B271A5E56381,0x0000BFFC
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data8 0x9249248C73282DB0,0x00003FFC
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data8 0xAAAAAA9F47305052,0x0000BFFC
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data8 0xCCCCCCCCCCD17FC9,0x00003FFC
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data8 0x8000000000067ED5,0x0000BFFD
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data8 0xAAAAAAAAAAAAAAAA,0x00003FFD
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data8 0xFFFFFFFFFFFFFFFE,0x0000BFFD
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LOCAL_OBJECT_END(Constants_P)
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// log2_hi, log2_lo, Q_4, Q_3, Q_2, and Q_1
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LOCAL_OBJECT_START(Constants_Q)
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data8 0xB172180000000000,0x00003FFE
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data8 0x82E308654361C4C6,0x0000BFE2
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data8 0xCCCCCAF2328833CB,0x00003FFC
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data8 0x80000077A9D4BAFB,0x0000BFFD
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data8 0xAAAAAAAAAAABE3D2,0x00003FFD
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data8 0xFFFFFFFFFFFFDAB7,0x0000BFFD
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LOCAL_OBJECT_END(Constants_Q)
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// 1/ln10_hi, 1/ln10_lo
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LOCAL_OBJECT_START(Constants_1_by_LN10)
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data8 0xDE5BD8A937287195,0x00003FFD
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data8 0xD56EAABEACCF70C8,0x00003FBB
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LOCAL_OBJECT_END(Constants_1_by_LN10)
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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
|
|
data4 0x3F73A0D0,0x3D4AE46F
|
|
data8 0x3E1D9202F8FBA6CF
|
|
data4 0x3F72B9D0,0x3D5A1756
|
|
data8 0xBE1DCCC4BA796223
|
|
data4 0x3F71D488,0x3D693B9D
|
|
data8 0xBE049391B6B7C239
|
|
LOCAL_OBJECT_END(Constants_G_H_h2)
|
|
|
|
// G3 and H3 - IEEE single and h3 - IEEE double
|
|
|
|
LOCAL_OBJECT_START(Constants_G_H_h3)
|
|
data4 0x3F7FFC00,0x38800100
|
|
data8 0x3D355595562224CD
|
|
data4 0x3F7FF400,0x39400480
|
|
data8 0x3D8200A206136FF6
|
|
data4 0x3F7FEC00,0x39A00640
|
|
data8 0x3DA4D68DE8DE9AF0
|
|
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)
|
|
|
|
|
|
// Floating Point Registers
|
|
|
|
FR_Input_X = f8
|
|
|
|
FR_Y_hi = f34
|
|
FR_Y_lo = f35
|
|
|
|
FR_Scale = f36
|
|
FR_X_Prime = f37
|
|
FR_S_hi = f38
|
|
FR_W = f39
|
|
FR_G = f40
|
|
|
|
FR_H = f41
|
|
FR_wsq = f42
|
|
FR_w4 = f43
|
|
FR_h = f44
|
|
FR_w6 = f45
|
|
|
|
FR_G2 = f46
|
|
FR_H2 = f47
|
|
FR_poly_lo = f48
|
|
FR_P8 = f49
|
|
FR_poly_hi = f50
|
|
|
|
FR_P7 = f51
|
|
FR_h2 = f52
|
|
FR_rsq = f53
|
|
FR_P6 = f54
|
|
FR_r = f55
|
|
|
|
FR_log2_hi = f56
|
|
FR_log2_lo = f57
|
|
FR_p87 = f58
|
|
FR_p876 = f58
|
|
FR_p8765 = f58
|
|
FR_float_N = f59
|
|
FR_Q4 = f60
|
|
|
|
FR_p43 = f61
|
|
FR_p432 = f61
|
|
FR_p4321 = f61
|
|
FR_P4 = f62
|
|
FR_G3 = f63
|
|
FR_H3 = f64
|
|
FR_h3 = f65
|
|
|
|
FR_Q3 = f66
|
|
FR_P3 = f67
|
|
FR_Q2 = f68
|
|
FR_P2 = f69
|
|
FR_1LN10_hi = f70
|
|
|
|
FR_Q1 = f71
|
|
FR_P1 = f72
|
|
FR_1LN10_lo = f73
|
|
FR_P5 = f74
|
|
FR_rcub = f75
|
|
|
|
FR_Output_X_tmp = f76
|
|
|
|
FR_X = f8
|
|
FR_Y = f0
|
|
FR_RESULT = f76
|
|
|
|
|
|
// General Purpose Registers
|
|
|
|
GR_ad_p = r33
|
|
GR_Index1 = r34
|
|
GR_Index2 = r35
|
|
GR_signif = r36
|
|
GR_X_0 = r37
|
|
GR_X_1 = r38
|
|
GR_X_2 = r39
|
|
GR_Z_1 = r40
|
|
GR_Z_2 = r41
|
|
GR_N = r42
|
|
GR_Bias = r43
|
|
GR_M = r44
|
|
GR_Index3 = r45
|
|
GR_ad_p2 = r46
|
|
GR_exp_mask = r47
|
|
GR_exp_2tom7 = r48
|
|
GR_ad_ln10 = r49
|
|
GR_ad_tbl_1 = r50
|
|
GR_ad_tbl_2 = r51
|
|
GR_ad_tbl_3 = r52
|
|
GR_ad_q = r53
|
|
GR_ad_z_1 = r54
|
|
GR_ad_z_2 = r55
|
|
GR_ad_z_3 = r56
|
|
|
|
//
|
|
// Added for unwind support
|
|
//
|
|
|
|
GR_SAVE_PFS = r50
|
|
GR_SAVE_B0 = r51
|
|
GR_SAVE_GP = r52
|
|
GR_Parameter_X = r53
|
|
GR_Parameter_Y = r54
|
|
GR_Parameter_RESULT = r55
|
|
GR_Parameter_TAG = r56
|
|
|
|
.section .text
|
|
|
|
GLOBAL_IEEE754_ENTRY(logl)
|
|
{ .mfi
|
|
alloc r32 = ar.pfs,0,21,4,0
|
|
fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test for natval, nan, inf
|
|
cmp.eq p7, p14 = r0, r0 // Set p7 if logl
|
|
}
|
|
{ .mfb
|
|
addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp
|
|
fnorm.s1 FR_X_Prime = FR_Input_X // Normalize x
|
|
br.cond.sptk LOGL_BEGIN
|
|
}
|
|
;;
|
|
|
|
GLOBAL_IEEE754_END(logl)
|
|
libm_alias_ldouble_other (__log, log)
|
|
|
|
|
|
GLOBAL_IEEE754_ENTRY(log10l)
|
|
{ .mfi
|
|
alloc r32 = ar.pfs,0,21,4,0
|
|
fclass.m p6, p0 = FR_Input_X, 0x1E3 // Test for natval, nan, inf
|
|
cmp.ne p7, p14 = r0, r0 // Set p14 if log10l
|
|
}
|
|
{ .mfb
|
|
addl GR_ad_z_1 = @ltoff(Constants_Z_1#),gp
|
|
fnorm.s1 FR_X_Prime = FR_Input_X // Normalize x
|
|
nop.b 999
|
|
}
|
|
;;
|
|
|
|
|
|
// Common code for logl and log10
|
|
LOGL_BEGIN:
|
|
{ .mfi
|
|
ld8 GR_ad_z_1 = [GR_ad_z_1] // Get pointer to Constants_Z_1
|
|
fclass.m p10, p0 = FR_Input_X, 0x0b // Test for denormal
|
|
mov GR_exp_2tom7 = 0x0fff8 // Exponent of 2^-7
|
|
}
|
|
;;
|
|
|
|
{ .mfb
|
|
getf.sig GR_signif = FR_Input_X // Get significand of x
|
|
fcmp.eq.s1 p9, p0 = FR_Input_X, f1 // Test for x=1.0
|
|
(p6) br.cond.spnt LOGL_64_special // Branch for nan, inf, natval
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
add GR_ad_tbl_1 = 0x040, GR_ad_z_1 // Point to Constants_G_H_h1
|
|
fcmp.lt.s1 p13, p0 = FR_Input_X, f0 // Test for x<0
|
|
add GR_ad_p = -0x100, GR_ad_z_1 // Point to Constants_P
|
|
}
|
|
{ .mib
|
|
add GR_ad_z_2 = 0x140, GR_ad_z_1 // Point to Constants_Z_2
|
|
add GR_ad_tbl_2 = 0x180, GR_ad_z_1 // Point to Constants_G_H_h2
|
|
(p10) br.cond.spnt LOGL_64_denormal // Branch for denormal
|
|
}
|
|
;;
|
|
|
|
LOGL_64_COMMON:
|
|
{ .mfi
|
|
add GR_ad_q = 0x080, GR_ad_p // Point to Constants_Q
|
|
fcmp.eq.s1 p8, p0 = FR_Input_X, f0 // Test for x=0
|
|
extr.u GR_Index1 = GR_signif, 59, 4 // Get high 4 bits of signif
|
|
}
|
|
{ .mfb
|
|
add GR_ad_tbl_3 = 0x280, GR_ad_z_1 // Point to Constants_G_H_h3
|
|
(p9) fma.s0 f8 = FR_Input_X, f0, f0 // If x=1, return +0.0
|
|
(p9) br.ret.spnt b0 // Exit if x=1
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
shladd GR_ad_z_1 = GR_Index1, 2, GR_ad_z_1 // Point to Z_1
|
|
fclass.nm p10, p0 = FR_Input_X, 0x1FF // Test for unsupported
|
|
extr.u GR_X_0 = GR_signif, 49, 15 // Get high 15 bits of significand
|
|
}
|
|
{ .mfi
|
|
ldfe FR_P8 = [GR_ad_p],16 // Load P_8 for near1 path
|
|
fsub.s1 FR_W = FR_X_Prime, f1 // W = x - 1
|
|
add GR_ad_ln10 = 0x060, GR_ad_q // Point to Constants_1_by_LN10
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ld4 GR_Z_1 = [GR_ad_z_1] // Load Z_1
|
|
nop.f 999
|
|
mov GR_exp_mask = 0x1FFFF // Create exponent mask
|
|
}
|
|
{ .mib
|
|
shladd GR_ad_tbl_1 = GR_Index1, 4, GR_ad_tbl_1 // Point to G_1
|
|
mov GR_Bias = 0x0FFFF // Create exponent bias
|
|
(p13) br.cond.spnt LOGL_64_negative // Branch if x<0
|
|
}
|
|
;;
|
|
|
|
{ .mfb
|
|
ldfps FR_G, FR_H = [GR_ad_tbl_1],8 // Load G_1, H_1
|
|
fmerge.se FR_S_hi = f1,FR_X_Prime // Form |x|
|
|
(p8) br.cond.spnt LOGL_64_zero // Branch if x=0
|
|
}
|
|
;;
|
|
|
|
{ .mmb
|
|
getf.exp GR_N = FR_X_Prime // Get N = exponent of x
|
|
ldfd FR_h = [GR_ad_tbl_1] // Load h_1
|
|
(p10) br.cond.spnt LOGL_64_unsupported // Branch for unsupported type
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfe FR_log2_hi = [GR_ad_q],16 // Load log2_hi
|
|
fcmp.eq.s0 p8, p0 = FR_Input_X, f0 // Dummy op to flag denormals
|
|
pmpyshr2.u GR_X_1 = GR_X_0,GR_Z_1,15 // Get bits 30-15 of X_0 * Z_1
|
|
}
|
|
;;
|
|
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mmi
|
|
ldfe FR_log2_lo = [GR_ad_q],16 // Load log2_lo
|
|
(p14) ldfe FR_1LN10_hi = [GR_ad_ln10],16 // If log10l, load 1/ln10_hi
|
|
sub GR_N = GR_N, GR_Bias
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
ldfe FR_Q4 = [GR_ad_q],16 // Load Q4
|
|
(p14) ldfe FR_1LN10_lo = [GR_ad_ln10] // If log10l, load 1/ln10_lo
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
ldfe FR_Q3 = [GR_ad_q],16 // Load Q3
|
|
setf.sig FR_float_N = GR_N // Put integer N into rightmost significand
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
getf.exp GR_M = FR_W // Get signexp of w = x - 1
|
|
ldfe FR_Q2 = [GR_ad_q],16 // Load Q2
|
|
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
|
|
add GR_ad_p2 = 0x30,GR_ad_p // Point to P_4
|
|
}
|
|
;;
|
|
|
|
{ .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
|
|
and GR_M = GR_exp_mask, GR_M // Get exponent of w = x - 1
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
ldfps FR_G2, FR_H2 = [GR_ad_tbl_2],8 // Load G_2, H_2
|
|
cmp.lt p8, p9 = GR_M, GR_exp_2tom7 // Test |x-1| < 2^-7
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
// Paths are merged.
|
|
// p8 is for the near1 path: |x-1| < 2^-7
|
|
// p9 is for regular path: |x-1| >= 2^-7
|
|
|
|
{ .mmi
|
|
ldfd FR_h2 = [GR_ad_tbl_2] // Load h_2
|
|
nop.m 999
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
(p8) ldfe FR_P7 = [GR_ad_p],16 // Load P_7 for near1 path
|
|
(p8) ldfe FR_P4 = [GR_ad_p2],16 // Load P_4 for near1 path
|
|
(p9) pmpyshr2.u GR_X_2 = GR_X_1,GR_Z_2,15 // Get bits 30-15 of X_1 * Z_2
|
|
}
|
|
;;
|
|
|
|
//
|
|
// For performance, don't use result of pmpyshr2.u for 4 cycles.
|
|
//
|
|
{ .mmi
|
|
(p8) ldfe FR_P6 = [GR_ad_p],16 // Load P_6 for near1 path
|
|
(p8) ldfe FR_P3 = [GR_ad_p2],16 // Load P_3 for near1 path
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmf
|
|
(p8) ldfe FR_P5 = [GR_ad_p],16 // Load P_5 for near1 path
|
|
(p8) ldfe FR_P2 = [GR_ad_p2],16 // Load P_2 for near1 path
|
|
(p8) fmpy.s1 FR_wsq = FR_W, FR_W // wsq = w * w for near1 path
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
(p8) ldfe FR_P1 = [GR_ad_p2],16 ;; // Load P_1 for near1 path
|
|
nop.m 999
|
|
(p9) extr.u GR_Index3 = GR_X_2, 1, 5 // Extract bits 1-5 of X_2
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
(p9) shladd GR_ad_tbl_3 = GR_Index3, 4, GR_ad_tbl_3 // Point to G_3
|
|
(p9) fcvt.xf FR_float_N = FR_float_N
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
(p9) ldfps FR_G3, FR_H3 = [GR_ad_tbl_3],8 // Load G_3, H_3
|
|
nop.f 999
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
(p9) ldfd FR_h3 = [GR_ad_tbl_3] // Load h_3
|
|
(p9) fmpy.s1 FR_G = FR_G, FR_G2 // G = G_1 * G_2
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fadd.s1 FR_H = FR_H, FR_H2 // H = H_1 + H_2
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmf
|
|
nop.m 999
|
|
nop.m 999
|
|
(p9) fadd.s1 FR_h = FR_h, FR_h2 // h = h_1 + h_2
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fmpy.s1 FR_w4 = FR_wsq, FR_wsq // w4 = w^4 for near1 path
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 FR_p87 = FR_W, FR_P8, FR_P7 // p87 = w * P8 + P7
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 FR_p43 = FR_W, FR_P4, FR_P3 // p43 = w * P4 + P3
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fmpy.s1 FR_G = FR_G, FR_G3 // G = (G_1 * G_2) * G_3
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fadd.s1 FR_H = FR_H, FR_H3 // H = (H_1 + H_2) + H_3
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fadd.s1 FR_h = FR_h, FR_h3 // h = (h_1 + h_2) + h_3
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fmpy.s1 FR_w6 = FR_w4, FR_wsq // w6 = w^6 for near1 path
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 FR_p432 = FR_W, FR_p43, FR_P2 // p432 = w * p43 + P2
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 FR_p876 = FR_W, FR_p87, FR_P6 // p876 = w * p87 + P6
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fms.s1 FR_r = FR_G, FR_S_hi, f1 // r = G * S_hi - 1
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_Y_hi = FR_float_N, FR_log2_hi, FR_H // Y_hi = N * log2_hi + H
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_h = FR_float_N, FR_log2_lo, FR_h // h = N * log2_lo + h
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 FR_p4321 = FR_W, FR_p432, FR_P1 // p4321 = w * p432 + P1
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 FR_p8765 = FR_W, FR_p876, FR_P5 // p8765 = w * p876 + P5
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_poly_lo = FR_r, FR_Q4, FR_Q3 // poly_lo = r * Q4 + Q3
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fmpy.s1 FR_rsq = FR_r, FR_r // rsq = r * r
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 FR_Y_lo = FR_wsq, FR_p4321, f0 // Y_lo = wsq * p4321
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 FR_Y_hi = FR_W, f1, f0 // Y_hi = w for near1 path
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_r, FR_Q2 // poly_lo = poly_lo * r + Q2
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_rcub = FR_rsq, FR_r, f0 // rcub = r^3
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.s1 FR_Y_lo = FR_w6, FR_p8765,FR_Y_lo // Y_lo = w6 * p8765 + w2 * p4321
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_poly_hi = FR_Q1, FR_rsq, FR_r // poly_hi = Q1 * rsq + r
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fma.s1 FR_poly_lo = FR_poly_lo, FR_rcub, FR_h // poly_lo = poly_lo*r^3 + h
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p9) fadd.s1 FR_Y_lo = FR_poly_hi, FR_poly_lo // Y_lo = poly_hi + poly_lo
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
// Remainder of code is common for near1 and regular paths
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fadd.s0 f8 = FR_Y_lo,FR_Y_hi // If logl, result=Y_lo+Y_hi
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p14) fmpy.s1 FR_Output_X_tmp = FR_Y_lo,FR_1LN10_hi
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p14) fma.s1 FR_Output_X_tmp = FR_Y_hi,FR_1LN10_lo,FR_Output_X_tmp
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
(p14) fma.s0 f8 = FR_Y_hi,FR_1LN10_hi,FR_Output_X_tmp
|
|
br.ret.sptk b0 // Common exit for 0 < x < inf
|
|
}
|
|
;;
|
|
|
|
|
|
// Here if x=+-0
|
|
LOGL_64_zero:
|
|
//
|
|
// If x=+-0 raise divide by zero and return -inf
|
|
//
|
|
{ .mfi
|
|
(p7) mov GR_Parameter_TAG = 0
|
|
fsub.s1 FR_Output_X_tmp = f0, f1
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfb
|
|
(p14) mov GR_Parameter_TAG = 6
|
|
frcpa.s0 FR_Output_X_tmp, p8 = FR_Output_X_tmp, f0
|
|
br.cond.sptk __libm_error_region
|
|
}
|
|
;;
|
|
|
|
LOGL_64_special:
|
|
{ .mfi
|
|
nop.m 999
|
|
fclass.m.unc p8, p0 = FR_Input_X, 0x1E1 // Test for natval, nan, +inf
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
//
|
|
// For SNaN raise invalid and return QNaN.
|
|
// For QNaN raise invalid and return QNaN.
|
|
// For +Inf return +Inf.
|
|
//
|
|
{ .mfb
|
|
nop.m 999
|
|
(p8) fmpy.s0 f8 = FR_Input_X, f1
|
|
(p8) br.ret.sptk b0 // Return for natval, nan, +inf
|
|
}
|
|
;;
|
|
|
|
//
|
|
// For -Inf raise invalid and return QNaN.
|
|
//
|
|
{ .mmi
|
|
(p7) mov GR_Parameter_TAG = 1
|
|
nop.m 999
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mfb
|
|
(p14) mov GR_Parameter_TAG = 7
|
|
fmpy.s0 FR_Output_X_tmp = FR_Input_X, f0
|
|
br.cond.sptk __libm_error_region
|
|
}
|
|
;;
|
|
|
|
// Here if x denormal or unnormal
|
|
LOGL_64_denormal:
|
|
{ .mmi
|
|
getf.sig GR_signif = FR_X_Prime // Get significand of normalized input
|
|
nop.m 999
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mmb
|
|
getf.exp GR_N = FR_X_Prime // Get exponent of normalized input
|
|
nop.m 999
|
|
br.cond.sptk LOGL_64_COMMON // Branch back to common code
|
|
}
|
|
;;
|
|
|
|
LOGL_64_unsupported:
|
|
//
|
|
// Return generated NaN or other value.
|
|
//
|
|
{ .mfb
|
|
nop.m 999
|
|
fmpy.s0 f8 = FR_Input_X, f0
|
|
br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
// Here if -inf < x < 0
|
|
LOGL_64_negative:
|
|
//
|
|
// Deal with x < 0 in a special way - raise
|
|
// invalid and produce QNaN indefinite.
|
|
//
|
|
{ .mfi
|
|
(p7) mov GR_Parameter_TAG = 1
|
|
frcpa.s0 FR_Output_X_tmp, p8 = f0, f0
|
|
nop.i 999
|
|
}
|
|
;;
|
|
|
|
{ .mib
|
|
(p14) mov GR_Parameter_TAG = 7
|
|
nop.i 999
|
|
br.cond.sptk __libm_error_region
|
|
}
|
|
;;
|
|
|
|
|
|
GLOBAL_IEEE754_END(log10l)
|
|
libm_alias_ldouble_other (__log10, log10)
|
|
|
|
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_Y,16 // Save Parameter 2 on 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_X // Store Parameter 1 on stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y
|
|
nop.b 0 // Parameter 3 address
|
|
}
|
|
{ .mib
|
|
stfe [GR_Parameter_Y] = FR_RESULT // Store Parameter 3 on stack
|
|
add GR_Parameter_Y = -16,GR_Parameter_Y
|
|
br.call.sptk b0=__libm_error_support# // Call error handling function
|
|
};;
|
|
{ .mmi
|
|
nop.m 999
|
|
nop.m 999
|
|
add GR_Parameter_RESULT = 48,sp
|
|
};;
|
|
{ .mmi
|
|
ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
|
|
.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#
|