1604 lines
36 KiB
ArmAsm
1604 lines
36 KiB
ArmAsm
.file "exp_m1l.s"
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// Copyright (c) 2000, 2001, Intel Corporation
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// All rights reserved.
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//
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// Contributed 2/2/2000 by John Harrison, Ted Kubaska, Bob Norin, Shane Story,
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// and Ping Tak Peter Tang of the Computational Software Lab, Intel Corporation.
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//
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// WARRANTY DISCLAIMER
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//
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://developer.intel.com/opensource.
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//
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// History
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//==============================================================
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// 4/04/00 Unwind support added
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// 8/15/00 Bundle added after call to __libm_error_support to properly
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// set [the previously overwritten] GR_Parameter_RESULT.
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//
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// *********************************************************************
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//
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// Function: Combined expl(x) and expm1l(x), where
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// x
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// expl(x) = e , for double-extended precision x values
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// x
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// expm1l(x) = e - 1 for double-extended precision x values
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//
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// *********************************************************************
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//
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// Resources Used:
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//
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// Floating-Point Registers: f8 (Input and Return Value)
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// f9,f32-f61, f99-f102
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//
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// General Purpose Registers:
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// r32-r61
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// r62-r65 (Used to pass arguments to error handling routine)
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//
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// Predicate Registers: p6-p15
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//
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// *********************************************************************
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//
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// IEEE Special Conditions:
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//
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// Denormal fault raised on denormal inputs
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// Overflow exceptions raised when appropriate for exp and expm1
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// Underflow exceptions raised when appropriate for exp and expm1
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// (Error Handling Routine called for overflow and Underflow)
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// Inexact raised when appropriate by algorithm
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//
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// expl(inf) = inf
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// expl(-inf) = +0
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// expl(SNaN) = QNaN
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// expl(QNaN) = QNaN
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// expl(0) = 1
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// expl(EM_special Values) = QNaN
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// expl(inf) = inf
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// expm1l(-inf) = -1
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// expm1l(SNaN) = QNaN
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// expm1l(QNaN) = QNaN
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// expm1l(0) = 0
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// expm1l(EM_special Values) = QNaN
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//
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// *********************************************************************
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//
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// Implementation and Algorithm Notes:
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//
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// ker_exp_64( in_FR : X,
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// in_GR : Flag,
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// in_GR : Expo_Range
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// out_FR : Y_hi,
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// out_FR : Y_lo,
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// out_FR : scale,
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// out_PR : Safe )
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//
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// On input, X is in register format and
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// Flag = 0 for exp,
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// Flag = 1 for expm1,
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//
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// On output, provided X and X_cor are real numbers, then
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//
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// scale*(Y_hi + Y_lo) approximates expl(X) if Flag is 0
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// scale*(Y_hi + Y_lo) approximates expl(X)-1 if Flag is 1
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//
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// The accuracy is sufficient for a highly accurate 64 sig.
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// bit implementation. Safe is set if there is no danger of
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// overflow/underflow when the result is composed from scale,
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// Y_hi and Y_lo. Thus, we can have a fast return if Safe is set.
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// Otherwise, one must prepare to handle the possible exception
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// appropriately. Note that SAFE not set (false) does not mean
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// that overflow/underflow will occur; only the setting of SAFE
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// guarantees the opposite.
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//
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// **** High Level Overview ****
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//
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// The method consists of three cases.
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//
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// If |X| < Tiny use case exp_tiny;
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// else if |X| < 2^(-6) use case exp_small;
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// else use case exp_regular;
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//
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// Case exp_tiny:
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//
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// 1 + X can be used to approximate expl(X) or expl(X+X_cor);
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// X + X^2/2 can be used to approximate expl(X) - 1
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//
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// Case exp_small:
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//
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// Here, expl(X), expl(X+X_cor), and expl(X) - 1 can all be
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// appproximated by a relatively simple polynomial.
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//
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// This polynomial resembles the truncated Taylor series
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//
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// expl(w) = 1 + w + w^2/2! + w^3/3! + ... + w^n/n!
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//
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// Case exp_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 expl(X), we accurately decompose X into
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//
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// X = N * log(2)/(2^12) + r, |r| <= log(2)/2^13.
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//
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// Hence
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//
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// expl(X) = 2^( N / 2^12 ) * expl(r).
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//
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// The value 2^( N / 2^12 ) is obtained by simple combinations
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// of values calculated beforehand and stored in table; expl(r)
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// is approximated by a short polynomial because |r| is small.
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//
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// We elaborate this method in 4 steps.
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//
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// Step 1: Reduction
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//
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// The value 2^12/log(2) is stored as a double-extended number
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// L_Inv.
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//
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// N := round_to_nearest_integer( X * L_Inv )
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//
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// The value log(2)/2^12 is stored as two numbers L_hi and L_lo so
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// that r can be computed accurately via
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//
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// r := (X - N*L_hi) - N*L_lo
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//
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// We pick L_hi such that N*L_hi is representable in 64 sig. bits
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// and thus the FMA X - N*L_hi is error free. So r is the
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// 1 rounding error from an exact reduction with respect to
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//
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// L_hi + L_lo.
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//
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// In particular, L_hi has 30 significant bit and can be stored
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// as a double-precision number; L_lo has 64 significant bits and
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// stored as a double-extended number.
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//
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// In the case Flag = 2, we further modify r by
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//
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// r := r + X_cor.
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//
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// Step 2: Approximation
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//
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// expl(r) - 1 is approximated by a short polynomial of the form
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//
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// r + A_1 r^2 + A_2 r^3 + A_3 r^4 .
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//
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// Step 3: Composition from Table Values
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//
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// The value 2^( N / 2^12 ) can be composed from a couple of tables
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// of precalculated values. First, express N as three integers
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// K, M_1, and M_2 as
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//
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// N = K * 2^12 + M_1 * 2^6 + M_2
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//
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// Where 0 <= M_1, M_2 < 2^6; and K can be positive or negative.
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// When N is represented in 2's complement, M_2 is simply the 6
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// lsb's, M_1 is the next 6, and K is simply N shifted right
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// arithmetically (sign extended) by 12 bits.
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//
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// Now, 2^( N / 2^12 ) is simply
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//
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// 2^K * 2^( M_1 / 2^6 ) * 2^( M_2 / 2^12 )
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//
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// Clearly, 2^K needs no tabulation. The other two values are less
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// trivial because if we store each accurately to more than working
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// precision, than its product is too expensive to calculate. We
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// use the following method.
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//
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// Define two mathematical values, delta_1 and delta_2, implicitly
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// such that
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//
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// T_1 = expl( [M_1 log(2)/2^6] - delta_1 )
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// T_2 = expl( [M_2 log(2)/2^12] - delta_2 )
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//
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// are representable as 24 significant bits. To illustrate the idea,
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// we show how we define delta_1:
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//
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// T_1 := round_to_24_bits( expl( M_1 log(2)/2^6 ) )
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// delta_1 = (M_1 log(2)/2^6) - log( T_1 )
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//
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// The last equality means mathematical equality. We then tabulate
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//
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// W_1 := expl(delta_1) - 1
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// W_2 := expl(delta_2) - 1
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//
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// Both in double precision.
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//
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// From the tabulated values T_1, T_2, W_1, W_2, we compose the values
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// T and W via
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//
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// T := T_1 * T_2 ...exactly
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// W := W_1 + (1 + W_1)*W_2
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//
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// W approximates expl( delta ) - 1 where delta = delta_1 + delta_2.
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// The mathematical product of T and (W+1) is an accurate representation
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// of 2^(M_1/2^6) * 2^(M_2/2^12).
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//
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// Step 4. Reconstruction
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//
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// Finally, we can reconstruct expl(X), expl(X) - 1.
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// Because
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//
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// X = K * log(2) + (M_1*log(2)/2^6 - delta_1)
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// + (M_2*log(2)/2^12 - delta_2)
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// + delta_1 + delta_2 + r ...accurately
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// We have
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//
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// expl(X) ~=~ 2^K * ( T + T*[expl(delta_1+delta_2+r) - 1] )
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// ~=~ 2^K * ( T + T*[expl(delta + r) - 1] )
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// ~=~ 2^K * ( T + T*[(expl(delta)-1)
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// + expl(delta)*(expl(r)-1)] )
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// ~=~ 2^K * ( T + T*( W + (1+W)*poly(r) ) )
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// ~=~ 2^K * ( Y_hi + Y_lo )
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//
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// where Y_hi = T and Y_lo = T*(W + (1+W)*poly(r))
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//
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// For expl(X)-1, we have
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//
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// expl(X)-1 ~=~ 2^K * ( Y_hi + Y_lo ) - 1
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// ~=~ 2^K * ( Y_hi + Y_lo - 2^(-K) )
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//
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// and we combine Y_hi + Y_lo - 2^(-N) into the form of two
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// numbers Y_hi + Y_lo carefully.
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//
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// **** Algorithm Details ****
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//
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// A careful algorithm must be used to realize the mathematical ideas
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// accurately. We describe each of the three cases. We assume SAFE
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// is preset to be TRUE.
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//
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// Case exp_tiny:
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//
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// The important points are to ensure an accurate result under
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// different rounding directions and a correct setting of the SAFE
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// flag.
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//
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// If Flag is 1, then
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// SAFE := False ...possibility of underflow
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// Scale := 1.0
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// Y_hi := X
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// Y_lo := 2^(-17000)
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// Else
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// Scale := 1.0
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// Y_hi := 1.0
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// Y_lo := X ...for different rounding modes
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// Endif
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//
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// Case exp_small:
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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 several portions.
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//
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// Let r = X
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//
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// If Flag is not 1 ...i.e. expl( argument )
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//
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// rsq := r * r;
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// r4 := rsq*rsq
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// poly_lo := P_3 + r*(P_4 + r*(P_5 + r*P_6))
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// poly_hi := r + rsq*(P_1 + r*P_2)
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// Y_lo := poly_hi + r4 * poly_lo
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// set lsb(Y_lo) to 1
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// Y_hi := 1.0
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// Scale := 1.0
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//
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// Else ...i.e. expl( argument ) - 1
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//
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// rsq := r * r
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// r4 := rsq * rsq
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// r6 := rsq * r4
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// poly_lo := r6*(Q_5 + r*(Q_6 + r*Q_7))
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// poly_hi := Q_1 + r*(Q_2 + r*(Q_3 + r*Q_4))
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// Y_lo := rsq*poly_hi + poly_lo
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// set lsb(Y_lo) to 1
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// Y_hi := X
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// Scale := 1.0
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//
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// Endif
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//
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// Case exp_regular:
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//
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// The previous description contain enough information except the
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// computation of poly and the final Y_hi and Y_lo in the case for
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// expl(X)-1.
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//
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// The computation of poly for Step 2:
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//
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// rsq := r*r
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// poly := r + rsq*(A_1 + r*(A_2 + r*A_3))
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//
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// For the case expl(X) - 1, we need to incorporate 2^(-K) into
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// Y_hi and Y_lo at the end of Step 4.
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//
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// If K > 10 then
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// Y_lo := Y_lo - 2^(-K)
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// Else
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// If K < -10 then
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// Y_lo := Y_hi + Y_lo
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// Y_hi := -2^(-K)
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// Else
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// Y_hi := Y_hi - 2^(-K)
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// End If
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// End If
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//
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#include "libm_support.h"
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#ifdef _LIBC
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.rodata
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#else
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.data
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#endif
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.align 64
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Constants_exp_64_Arg:
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ASM_TYPE_DIRECTIVE(Constants_exp_64_Arg,@object)
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data4 0x5C17F0BC,0xB8AA3B29,0x0000400B,0x00000000
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data4 0x00000000,0xB17217F4,0x00003FF2,0x00000000
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data4 0xF278ECE6,0xF473DE6A,0x00003FD4,0x00000000
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// /* Inv_L, L_hi, L_lo */
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ASM_SIZE_DIRECTIVE(Constants_exp_64_Arg)
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.align 64
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Constants_exp_64_Exponents:
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ASM_TYPE_DIRECTIVE(Constants_exp_64_Exponents,@object)
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data4 0x0000007E,0x00000000,0xFFFFFF83,0xFFFFFFFF
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data4 0x000003FE,0x00000000,0xFFFFFC03,0xFFFFFFFF
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data4 0x00003FFE,0x00000000,0xFFFFC003,0xFFFFFFFF
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data4 0x00003FFE,0x00000000,0xFFFFC003,0xFFFFFFFF
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data4 0xFFFFFFE2,0xFFFFFFFF,0xFFFFFFC4,0xFFFFFFFF
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data4 0xFFFFFFBA,0xFFFFFFFF,0xFFFFFFBA,0xFFFFFFFF
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ASM_SIZE_DIRECTIVE(Constants_exp_64_Exponents)
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.align 64
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Constants_exp_64_A:
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ASM_TYPE_DIRECTIVE(Constants_exp_64_A,@object)
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data4 0xB1B736A0,0xAAAAAAAB,0x00003FFA,0x00000000
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data4 0x90CD6327,0xAAAAAAAB,0x00003FFC,0x00000000
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data4 0xFFFFFFFF,0xFFFFFFFF,0x00003FFD,0x00000000
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// /* Reversed */
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ASM_SIZE_DIRECTIVE(Constants_exp_64_A)
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.align 64
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Constants_exp_64_P:
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ASM_TYPE_DIRECTIVE(Constants_exp_64_P,@object)
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data4 0x43914A8A,0xD00D6C81,0x00003FF2,0x00000000
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data4 0x30304B30,0xB60BC4AC,0x00003FF5,0x00000000
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data4 0x7474C518,0x88888888,0x00003FF8,0x00000000
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data4 0x8DAE729D,0xAAAAAAAA,0x00003FFA,0x00000000
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data4 0xAAAAAF61,0xAAAAAAAA,0x00003FFC,0x00000000
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data4 0x000004C7,0x80000000,0x00003FFE,0x00000000
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// /* Reversed */
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ASM_SIZE_DIRECTIVE(Constants_exp_64_P)
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.align 64
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Constants_exp_64_Q:
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ASM_TYPE_DIRECTIVE(Constants_exp_64_Q,@object)
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data4 0xA49EF6CA,0xD00D56F7,0x00003FEF,0x00000000
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data4 0x1C63493D,0xD00D59AB,0x00003FF2,0x00000000
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data4 0xFB50CDD2,0xB60B60B5,0x00003FF5,0x00000000
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data4 0x7BA68DC8,0x88888888,0x00003FF8,0x00000000
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data4 0xAAAAAC8D,0xAAAAAAAA,0x00003FFA,0x00000000
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data4 0xAAAAACCA,0xAAAAAAAA,0x00003FFC,0x00000000
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data4 0x00000000,0x80000000,0x00003FFE,0x00000000
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// /* Reversed */
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ASM_SIZE_DIRECTIVE(Constants_exp_64_Q)
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.align 64
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Constants_exp_64_T1:
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ASM_TYPE_DIRECTIVE(Constants_exp_64_T1,@object)
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data4 0x3F800000,0x3F8164D2,0x3F82CD87,0x3F843A29
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data4 0x3F85AAC3,0x3F871F62,0x3F88980F,0x3F8A14D5
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data4 0x3F8B95C2,0x3F8D1ADF,0x3F8EA43A,0x3F9031DC
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data4 0x3F91C3D3,0x3F935A2B,0x3F94F4F0,0x3F96942D
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data4 0x3F9837F0,0x3F99E046,0x3F9B8D3A,0x3F9D3EDA
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data4 0x3F9EF532,0x3FA0B051,0x3FA27043,0x3FA43516
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data4 0x3FA5FED7,0x3FA7CD94,0x3FA9A15B,0x3FAB7A3A
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data4 0x3FAD583F,0x3FAF3B79,0x3FB123F6,0x3FB311C4
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data4 0x3FB504F3,0x3FB6FD92,0x3FB8FBAF,0x3FBAFF5B
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data4 0x3FBD08A4,0x3FBF179A,0x3FC12C4D,0x3FC346CD
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data4 0x3FC5672A,0x3FC78D75,0x3FC9B9BE,0x3FCBEC15
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data4 0x3FCE248C,0x3FD06334,0x3FD2A81E,0x3FD4F35B
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data4 0x3FD744FD,0x3FD99D16,0x3FDBFBB8,0x3FDE60F5
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data4 0x3FE0CCDF,0x3FE33F89,0x3FE5B907,0x3FE8396A
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data4 0x3FEAC0C7,0x3FED4F30,0x3FEFE4BA,0x3FF28177
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data4 0x3FF5257D,0x3FF7D0DF,0x3FFA83B3,0x3FFD3E0C
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ASM_SIZE_DIRECTIVE(Constants_exp_64_T1)
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.align 64
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Constants_exp_64_T2:
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ASM_TYPE_DIRECTIVE(Constants_exp_64_T2,@object)
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data4 0x3F800000,0x3F80058C,0x3F800B18,0x3F8010A4
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data4 0x3F801630,0x3F801BBD,0x3F80214A,0x3F8026D7
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data4 0x3F802C64,0x3F8031F2,0x3F803780,0x3F803D0E
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data4 0x3F80429C,0x3F80482B,0x3F804DB9,0x3F805349
|
|
data4 0x3F8058D8,0x3F805E67,0x3F8063F7,0x3F806987
|
|
data4 0x3F806F17,0x3F8074A8,0x3F807A39,0x3F807FCA
|
|
data4 0x3F80855B,0x3F808AEC,0x3F80907E,0x3F809610
|
|
data4 0x3F809BA2,0x3F80A135,0x3F80A6C7,0x3F80AC5A
|
|
data4 0x3F80B1ED,0x3F80B781,0x3F80BD14,0x3F80C2A8
|
|
data4 0x3F80C83C,0x3F80CDD1,0x3F80D365,0x3F80D8FA
|
|
data4 0x3F80DE8F,0x3F80E425,0x3F80E9BA,0x3F80EF50
|
|
data4 0x3F80F4E6,0x3F80FA7C,0x3F810013,0x3F8105AA
|
|
data4 0x3F810B41,0x3F8110D8,0x3F81166F,0x3F811C07
|
|
data4 0x3F81219F,0x3F812737,0x3F812CD0,0x3F813269
|
|
data4 0x3F813802,0x3F813D9B,0x3F814334,0x3F8148CE
|
|
data4 0x3F814E68,0x3F815402,0x3F81599C,0x3F815F37
|
|
ASM_SIZE_DIRECTIVE(Constants_exp_64_T2)
|
|
|
|
.align 64
|
|
Constants_exp_64_W1:
|
|
ASM_TYPE_DIRECTIVE(Constants_exp_64_W1,@object)
|
|
data4 0x00000000,0x00000000,0x171EC4B4,0xBE384454
|
|
data4 0x4AA72766,0xBE694741,0xD42518F8,0xBE5D32B6
|
|
data4 0x3A319149,0x3E68D96D,0x62415F36,0xBE68F4DA
|
|
data4 0xC9C86A3B,0xBE6DDA2F,0xF49228FE,0x3E6B2E50
|
|
data4 0x1188B886,0xBE49C0C2,0x1A4C2F1F,0x3E64BFC2
|
|
data4 0x2CB98B54,0xBE6A2FBB,0x9A55D329,0x3E5DC5DE
|
|
data4 0x39A7AACE,0x3E696490,0x5C66DBA5,0x3E54728B
|
|
data4 0xBA1C7D7D,0xBE62B0DB,0x09F1AF5F,0x3E576E04
|
|
data4 0x1A0DD6A1,0x3E612500,0x795FBDEF,0xBE66A419
|
|
data4 0xE1BD41FC,0xBE5CDE8C,0xEA54964F,0xBE621376
|
|
data4 0x476E76EE,0x3E6370BE,0x3427EB92,0x3E390D1A
|
|
data4 0x2BF82BF8,0x3E1336DE,0xD0F7BD9E,0xBE5FF1CB
|
|
data4 0x0CEB09DD,0xBE60A355,0x0980F30D,0xBE5CA37E
|
|
data4 0x4C082D25,0xBE5C541B,0x3B467D29,0xBE5BBECA
|
|
data4 0xB9D946C5,0xBE400D8A,0x07ED374A,0xBE5E2A08
|
|
data4 0x365C8B0A,0xBE66CB28,0xD3403BCA,0x3E3AAD5B
|
|
data4 0xC7EA21E0,0x3E526055,0xE72880D6,0xBE442C75
|
|
data4 0x85222A43,0x3E58B2BB,0x522C42BF,0xBE5AAB79
|
|
data4 0x469DC2BC,0xBE605CB4,0xA48C40DC,0xBE589FA7
|
|
data4 0x1AA42614,0xBE51C214,0xC37293F4,0xBE48D087
|
|
data4 0xA2D673E0,0x3E367A1C,0x114F7A38,0xBE51BEBB
|
|
data4 0x661A4B48,0xBE6348E5,0x1D3B9962,0xBDF52643
|
|
data4 0x35A78A53,0x3E3A3B5E,0x1CECD788,0xBE46C46C
|
|
data4 0x7857D689,0xBE60B7EC,0xD14F1AD7,0xBE594D3D
|
|
data4 0x4C9A8F60,0xBE4F9C30,0x02DFF9D2,0xBE521873
|
|
data4 0x55E6D68F,0xBE5E4C88,0x667F3DC4,0xBE62140F
|
|
data4 0x3BF88747,0xBE36961B,0xC96EC6AA,0x3E602861
|
|
data4 0xD57FD718,0xBE3B5151,0xFC4A627B,0x3E561CD0
|
|
data4 0xCA913FEA,0xBE3A5217,0x9A5D193A,0x3E40A3CC
|
|
data4 0x10A9C312,0xBE5AB713,0xC5F57719,0x3E4FDADB
|
|
data4 0xDBDF59D5,0x3E361428,0x61B4180D,0x3E5DB5DB
|
|
data4 0x7408D856,0xBE42AD5F,0x31B2B707,0x3E2A3148
|
|
ASM_SIZE_DIRECTIVE(Constants_exp_64_W1)
|
|
|
|
.align 64
|
|
Constants_exp_64_W2:
|
|
ASM_TYPE_DIRECTIVE(Constants_exp_64_W2,@object)
|
|
data4 0x00000000,0x00000000,0x37A3D7A2,0xBE641F25
|
|
data4 0xAD028C40,0xBE68DD57,0xF212B1B6,0xBE5C77D8
|
|
data4 0x1BA5B070,0x3E57878F,0x2ECAE6FE,0xBE55A36A
|
|
data4 0x569DFA3B,0xBE620608,0xA6D300A3,0xBE53B50E
|
|
data4 0x223F8F2C,0x3E5B5EF2,0xD6DE0DF4,0xBE56A0D9
|
|
data4 0xEAE28F51,0xBE64EEF3,0x367EA80B,0xBE5E5AE2
|
|
data4 0x5FCBC02D,0x3E47CB1A,0x9BDAFEB7,0xBE656BA0
|
|
data4 0x805AFEE7,0x3E6E70C6,0xA3415EBA,0xBE6E0509
|
|
data4 0x49BFF529,0xBE56856B,0x00508651,0x3E66DD33
|
|
data4 0xC114BC13,0x3E51165F,0xC453290F,0x3E53333D
|
|
data4 0x05539FDA,0x3E6A072B,0x7C0A7696,0xBE47CD87
|
|
data4 0xEB05C6D9,0xBE668BF4,0x6AE86C93,0xBE67C3E3
|
|
data4 0xD0B3E84B,0xBE533904,0x556B53CE,0x3E63E8D9
|
|
data4 0x63A98DC8,0x3E212C89,0x032A7A22,0xBE33138F
|
|
data4 0xBC584008,0x3E530FA9,0xCCB93C97,0xBE6ADF82
|
|
data4 0x8370EA39,0x3E5F9113,0xFB6A05D8,0x3E5443A4
|
|
data4 0x181FEE7A,0x3E63DACD,0xF0F67DEC,0xBE62B29D
|
|
data4 0x3DDE6307,0x3E65C483,0xD40A24C1,0x3E5BF030
|
|
data4 0x14E437BE,0x3E658B8F,0xED98B6C7,0xBE631C29
|
|
data4 0x04CF7C71,0x3E6335D2,0xE954A79D,0x3E529EED
|
|
data4 0xF64A2FB8,0x3E5D9257,0x854ED06C,0xBE6BED1B
|
|
data4 0xD71405CB,0x3E5096F6,0xACB9FDF5,0xBE3D4893
|
|
data4 0x01B68349,0xBDFEB158,0xC6A463B9,0x3E628D35
|
|
data4 0xADE45917,0xBE559725,0x042FC476,0xBE68C29C
|
|
data4 0x01E511FA,0xBE67593B,0x398801ED,0xBE4A4313
|
|
data4 0xDA7C3300,0x3E699571,0x08062A9E,0x3E5349BE
|
|
data4 0x755BB28E,0x3E5229C4,0x77A1F80D,0x3E67E426
|
|
data4 0x6B69C352,0xBE52B33F,0x084DA57F,0xBE6B3550
|
|
data4 0xD1D09A20,0xBE6DB03F,0x2161B2C1,0xBE60CBC4
|
|
data4 0x78A2B771,0x3E56ED9C,0x9D0FA795,0xBE508E31
|
|
data4 0xFD1A54E9,0xBE59482A,0xB07FD23E,0xBE2A17CE
|
|
data4 0x17365712,0x3E68BF5C,0xB3785569,0x3E3956F9
|
|
ASM_SIZE_DIRECTIVE(Constants_exp_64_W2)
|
|
|
|
GR_SAVE_PFS = r59
|
|
GR_SAVE_B0 = r60
|
|
GR_SAVE_GP = r61
|
|
GR_Parameter_X = r62
|
|
GR_Parameter_Y = r63
|
|
GR_Parameter_RESULT = r64
|
|
GR_Parameter_TAG = r65
|
|
|
|
FR_X = f9
|
|
FR_Y = f9
|
|
FR_RESULT = f99
|
|
|
|
.section .text
|
|
.proc expm1l#
|
|
.global expm1l#
|
|
.align 64
|
|
expm1l:
|
|
#ifdef _LIBC
|
|
.global __expm1l#
|
|
__expm1l:
|
|
#endif
|
|
{ .mii
|
|
alloc r32 = ar.pfs,0,30,4,0
|
|
(p0) add r33 = 1, r0
|
|
(p0) cmp.eq.unc p7, p0 = r0, r0
|
|
}
|
|
{ .mbb
|
|
nop.m 999
|
|
(p0) br.cond.sptk exp_continue
|
|
nop.b 999 ;;
|
|
}
|
|
|
|
//
|
|
// Set p7 true for expm1
|
|
// Set Flag = r33 = 1 for expm1
|
|
//
|
|
|
|
.endp expm1l
|
|
ASM_SIZE_DIRECTIVE(expm1l)
|
|
|
|
.section .text
|
|
.proc expl#
|
|
.global expl#
|
|
.align 64
|
|
expl:
|
|
#ifdef _LIBC
|
|
.global __ieee754_expl#
|
|
__ieee754_expl:
|
|
#endif
|
|
{ .mii
|
|
alloc r32 = ar.pfs,0,30,4,0
|
|
(p0) add r33 = r0, r0
|
|
(p0) cmp.eq.unc p0, p7 = r0, r0 ;;
|
|
}
|
|
exp_continue:
|
|
{ .mfi
|
|
(p0) add r32 = 2,r0
|
|
(p0) fnorm.s1 f9 = f8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
(p0) nop.m 0
|
|
//
|
|
// Set p7 false for exp
|
|
// Set Flag = r33 = 0 for exp
|
|
//
|
|
(p0) fclass.m.unc p6, p8 = f8, 0x1E7
|
|
nop.i 0;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fclass.nm.unc p9, p0 = f8, 0x1FF
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) mov f36 = f1
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
//
|
|
// Identify NatVals, NaNs, Infs, and Zeros.
|
|
// Identify EM unsupporteds.
|
|
// Save special input registers
|
|
(p0) mov f32 = f0
|
|
//
|
|
// Create FR_X_cor = 0.0
|
|
// GR_Flag = 0
|
|
// GR_Expo_Range = 2 (r32) for double-extended precision
|
|
// FR_Scale = 1.0
|
|
//
|
|
(p6) br.cond.spnt EXPL_64_SPECIAL ;;
|
|
}
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
(p9) br.cond.spnt EXPL_64_UNSUPPORTED ;;
|
|
}
|
|
{ .mfi
|
|
(p0) cmp.ne.unc p12, p13 = 0x01, r33
|
|
//
|
|
// Branch out for special input values
|
|
//
|
|
(p0) fcmp.lt.unc.s0 p9,p0 = f8, f0
|
|
(p0) cmp.eq.unc p15, p0 = r0, r0
|
|
}
|
|
{ .mmi
|
|
nop.m 999
|
|
//
|
|
// Raise possible denormal operand exception
|
|
// Normalize x
|
|
//
|
|
// This function computes expl( x + x_cor)
|
|
// Input FR 1: FR_X
|
|
// Input FR 2: FR_X_cor
|
|
// Input GR 1: GR_Flag
|
|
// Input GR 2: GR_Expo_Range
|
|
// Output FR 3: FR_Y_hi
|
|
// Output FR 4: FR_Y_lo
|
|
// Output FR 5: FR_Scale
|
|
// Output PR 1: PR_Safe
|
|
(p0) addl r34 = @ltoff(Constants_exp_64_Arg#),gp
|
|
(p0) addl r40 = @ltoff(Constants_exp_64_W1#),gp
|
|
};;
|
|
//
|
|
// Prepare to load constants
|
|
// Set Safe = True
|
|
//
|
|
|
|
{ .mmi
|
|
ld8 r34 = [r34]
|
|
ld8 r40 = [r40]
|
|
(p0) addl r41 = @ltoff(Constants_exp_64_W2#),gp
|
|
};;
|
|
|
|
{ .mmi
|
|
(p0) ldfe f37 = [r34],16
|
|
(p0) ld8 r41 = [r41] ;;
|
|
}
|
|
|
|
//
|
|
// N = fcvt.fx(float_N)
|
|
// Set p14 if -6 > expo_X
|
|
//
|
|
//
|
|
// Bias = 0x0FFFF
|
|
// expo_X = expo_X and Mask
|
|
//
|
|
|
|
{ .mmi
|
|
(p0) ldfe f40 = [r34],16
|
|
nop.m 999
|
|
//
|
|
// Load L_lo
|
|
// Set p10 if 14 < expo_X
|
|
//
|
|
(p0) addl r50 = @ltoff(Constants_exp_64_T1#),gp
|
|
}
|
|
{ .mmi
|
|
nop.m 999
|
|
nop.m 999
|
|
(p0) addl r51 = @ltoff(Constants_exp_64_T2#),gp ;;
|
|
}
|
|
//
|
|
// Load W2_ptr
|
|
// Branch to SMALL is expo_X < -6
|
|
//
|
|
|
|
{.mmi
|
|
(p0) ld8 r50 = [r50]
|
|
(p0) ld8 r51 = [r51]
|
|
};;
|
|
|
|
{ .mlx
|
|
(p0) ldfe f41 = [r34],16
|
|
//
|
|
// float_N = X * L_Inv
|
|
// expo_X = exponent of X
|
|
// Mask = 0x1FFFF
|
|
//
|
|
(p0) movl r58 = 0x0FFFF
|
|
}
|
|
{ .mlx
|
|
nop.m 999
|
|
(p0) movl r39 = 0x1FFFF ;;
|
|
}
|
|
{ .mmi
|
|
(p0) getf.exp r37 = f9
|
|
nop.m 999
|
|
(p0) addl r34 = @ltoff(Constants_exp_64_Exponents#),gp ;;
|
|
}
|
|
{ .mii
|
|
(p0) ld8 r34 = [r34]
|
|
nop.i 999
|
|
(p0) and r37 = r37, r39 ;;
|
|
}
|
|
{ .mmi
|
|
(p0) sub r37 = r37, r58 ;;
|
|
(p0) cmp.gt.unc p14, p0 = -6, r37
|
|
(p0) cmp.lt.unc p10, p0 = 14, r37 ;;
|
|
}
|
|
{ .mfi
|
|
(p0) nop.m 0
|
|
//
|
|
// Load L_inv
|
|
// Set p12 true for Flag = 0 (exp)
|
|
// Set p13 true for Flag = 1 (expm1)
|
|
//
|
|
(p0) fmpy.s1 f38 = f9, f37
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
//
|
|
// Load L_hi
|
|
// expo_X = expo_X - Bias
|
|
// get W1_ptr
|
|
//
|
|
(p0) fcvt.fx.s1 f39 = f38
|
|
(p14) br.cond.spnt EXPL_SMALL ;;
|
|
}
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
(p10) br.cond.spnt EXPL_HUGE ;;
|
|
}
|
|
{ .mmi
|
|
(p0) shladd r34 = r32,4,r34
|
|
nop.m 999
|
|
(p0) addl r35 = @ltoff(Constants_exp_64_A#),gp ;;
|
|
}
|
|
//
|
|
// Load T_1,T_2
|
|
//
|
|
{ .mmi
|
|
nop.m 999
|
|
ld8 r35 =[r35]
|
|
nop.i 99
|
|
};;
|
|
{ .mmb
|
|
(p0) ldfe f51 = [r35],16
|
|
(p0) ld8 r45 = [r34],8
|
|
nop.b 999 ;;
|
|
}
|
|
//
|
|
// Set Safe = True if k >= big_expo_neg
|
|
// Set Safe = False if k < big_expo_neg
|
|
//
|
|
{ .mmb
|
|
(p0) ldfe f49 = [r35],16
|
|
(p0) ld8 r48 = [r34],0
|
|
nop.b 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Branch to HUGE is expo_X > 14
|
|
//
|
|
(p0) fcvt.xf f38 = f39
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
(p0) getf.sig r52 = f39
|
|
nop.f 999
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mii
|
|
nop.m 999
|
|
(p0) extr.u r43 = r52, 6, 6 ;;
|
|
//
|
|
// r = r - float_N * L_lo
|
|
// K = extr(N_fix,12,52)
|
|
//
|
|
(p0) shladd r40 = r43,3,r40 ;;
|
|
}
|
|
{ .mfi
|
|
(p0) shladd r50 = r43,2,r50
|
|
(p0) fnma.s1 f42 = f40, f38, f9
|
|
//
|
|
// float_N = float(N)
|
|
// N_fix = signficand N
|
|
//
|
|
(p0) extr.u r42 = r52, 0, 6
|
|
}
|
|
{ .mmi
|
|
(p0) ldfd f43 = [r40],0 ;;
|
|
(p0) shladd r41 = r42,3,r41
|
|
(p0) shladd r51 = r42,2,r51
|
|
}
|
|
//
|
|
// W_1_p1 = 1 + W_1
|
|
//
|
|
{ .mmi
|
|
(p0) ldfs f44 = [r50],0 ;;
|
|
(p0) ldfd f45 = [r41],0
|
|
//
|
|
// M_2 = extr(N_fix,0,6)
|
|
// M_1 = extr(N_fix,6,6)
|
|
// r = X - float_N * L_hi
|
|
//
|
|
(p0) extr r44 = r52, 12, 52
|
|
}
|
|
{ .mmi
|
|
(p0) ldfs f46 = [r51],0 ;;
|
|
(p0) sub r46 = r58, r44
|
|
(p0) cmp.gt.unc p8, p15 = r44, r45
|
|
}
|
|
//
|
|
// W = W_1 + W_1_p1*W_2
|
|
// Load A_2
|
|
// Bias_m_K = Bias - K
|
|
//
|
|
{ .mii
|
|
(p0) ldfe f40 = [r35],16
|
|
//
|
|
// load A_1
|
|
// poly = A_2 + r*A_3
|
|
// rsq = r * r
|
|
// neg_2_mK = exponent of Bias_m_k
|
|
//
|
|
(p0) add r47 = r58, r44 ;;
|
|
//
|
|
// Set Safe = True if k <= big_expo_pos
|
|
// Set Safe = False if k > big_expo_pos
|
|
// Load A_3
|
|
//
|
|
(p15) cmp.lt p8,p15 = r44,r48 ;;
|
|
}
|
|
{ .mmf
|
|
(p0) setf.exp f61 = r46
|
|
//
|
|
// Bias_p + K = Bias + K
|
|
// T = T_1 * T_2
|
|
//
|
|
(p0) setf.exp f36 = r47
|
|
(p0) fnma.s1 f42 = f41, f38, f42 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Load W_1,W_2
|
|
// Load big_exp_pos, load big_exp_neg
|
|
//
|
|
(p0) fadd.s1 f47 = f43, f1
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fma.s1 f52 = f42, f51, f49
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fmpy.s1 f48 = f42, f42
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fmpy.s1 f53 = f44, f46
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fma.s1 f54 = f45, f47, f43
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fneg f61 = f61
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fma.s1 f52 = f42, f52, f40
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fadd.s1 f55 = f54, f1
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// W + Wp1 * poly
|
|
//
|
|
(p0) mov f34 = f53
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// A_1 + r * poly
|
|
// Scale = setf_expl(Bias_p_k)
|
|
//
|
|
(p0) fma.s1 f52 = f48, f52, f42
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// poly = r + rsq(A_1 + r*poly)
|
|
// Wp1 = 1 + W
|
|
// neg_2_mK = -neg_2_mK
|
|
//
|
|
(p0) fma.s1 f35 = f55, f52, f54
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
(p0) fmpy.s1 f35 = f35, f53
|
|
//
|
|
// Y_hi = T
|
|
// Y_lo = T * (W + Wp1*poly)
|
|
//
|
|
(p12) br.cond.sptk EXPL_MAIN ;;
|
|
}
|
|
//
|
|
// Branch if expl(x)
|
|
// Continue for expl(x-1)
|
|
//
|
|
{ .mii
|
|
(p0) cmp.lt.unc p12, p13 = 10, r44
|
|
nop.i 999 ;;
|
|
//
|
|
// Set p12 if 10 < K, Else p13
|
|
//
|
|
(p13) cmp.gt.unc p13, p14 = -10, r44 ;;
|
|
}
|
|
//
|
|
// K > 10: Y_lo = Y_lo + neg_2_mK
|
|
// K <=10: Set p13 if -10 > K, Else set p14
|
|
//
|
|
{ .mfi
|
|
(p13) cmp.eq p15, p0 = r0, r0
|
|
(p14) fadd.s1 f34 = f61, f34
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) fadd.s1 f35 = f35, f61
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p13) fadd.s1 f35 = f35, f34
|
|
nop.i 999
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
//
|
|
// K <= 10 and K < -10, Set Safe = True
|
|
// K <= 10 and K < 10, Y_lo = Y_hi + Y_lo
|
|
// K <= 10 and K > =-10, Y_hi = Y_hi + neg_2_mk
|
|
//
|
|
(p13) mov f34 = f61
|
|
(p0) br.cond.sptk EXPL_MAIN ;;
|
|
}
|
|
EXPL_SMALL:
|
|
{ .mmi
|
|
nop.m 999
|
|
(p0) addl r34 = @ltoff(Constants_exp_64_Exponents#),gp
|
|
(p12) addl r35 = @ltoff(Constants_exp_64_P#),gp ;;
|
|
}
|
|
.pred.rel "mutex",p12,p13
|
|
{ .mmi
|
|
(p12) ld8 r35=[r35]
|
|
nop.m 999
|
|
(p13) addl r35 = @ltoff(Constants_exp_64_Q#),gp
|
|
};;
|
|
{ .mmi
|
|
(p13) ld8 r35=[r35]
|
|
(p0) ld8 r34=[r34]
|
|
nop.i 999
|
|
};;
|
|
{ .mfi
|
|
(p0) add r34 = 0x48,r34
|
|
//
|
|
// Return
|
|
// K <= 10 and K < 10, Y_hi = neg_2_mk
|
|
//
|
|
// /*******************************************************/
|
|
// /*********** Branch EXPL_SMALL ************************/
|
|
// /*******************************************************/
|
|
(p0) mov f42 = f9
|
|
nop.i 999 ;;
|
|
}
|
|
//
|
|
// Flag = 0
|
|
// r4 = rsq * rsq
|
|
//
|
|
{ .mfi
|
|
(p0) ld8 r49 =[r34],0
|
|
nop.f 999
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mii
|
|
nop.m 999
|
|
nop.i 999 ;;
|
|
//
|
|
// Flag = 1
|
|
//
|
|
(p0) cmp.lt.unc p14, p0 = r37, r49 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// r = X
|
|
//
|
|
(p0) fmpy.s1 f48 = f42, f42
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
//
|
|
// rsq = r * r
|
|
//
|
|
(p0) fmpy.s1 f50 = f48, f48
|
|
//
|
|
// Is input very small?
|
|
//
|
|
(p14) br.cond.spnt EXPL_VERY_SMALL ;;
|
|
}
|
|
//
|
|
// Flag_not1: Y_hi = 1.0
|
|
// Flag is 1: r6 = rsq * r4
|
|
//
|
|
{ .mfi
|
|
(p12) ldfe f52 = [r35],16
|
|
(p12) mov f34 = f1
|
|
(p0) add r53 = 0x1,r0 ;;
|
|
}
|
|
{ .mfi
|
|
(p13) ldfe f51 = [r35],16
|
|
//
|
|
// Flag_not_1: Y_lo = poly_hi + r4 * poly_lo
|
|
//
|
|
(p13) mov f34 = f9
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mmf
|
|
(p12) ldfe f53 = [r35],16
|
|
//
|
|
// For Flag_not_1, Y_hi = X
|
|
// Scale = 1
|
|
// Create 0x000...01
|
|
//
|
|
(p0) setf.sig f37 = r53
|
|
(p0) mov f36 = f1 ;;
|
|
}
|
|
{ .mmi
|
|
(p13) ldfe f52 = [r35],16 ;;
|
|
(p12) ldfe f54 = [r35],16
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
(p13) ldfe f53 = [r35],16
|
|
(p13) fmpy.s1 f58 = f48, f50
|
|
nop.i 999 ;;
|
|
}
|
|
//
|
|
// Flag_not1: poly_lo = P_5 + r*P_6
|
|
// Flag_1: poly_lo = Q_6 + r*Q_7
|
|
//
|
|
{ .mmi
|
|
(p13) ldfe f54 = [r35],16 ;;
|
|
(p12) ldfe f55 = [r35],16
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mmi
|
|
(p12) ldfe f56 = [r35],16 ;;
|
|
(p13) ldfe f55 = [r35],16
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mmi
|
|
(p12) ldfe f57 = [r35],0 ;;
|
|
(p13) ldfe f56 = [r35],16
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
(p13) ldfe f57 = [r35],0
|
|
nop.f 999
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// For Flag_not_1, load p5,p6,p1,p2
|
|
// Else load p5,p6,p1,p2
|
|
//
|
|
(p12) fma.s1 f60 = f52, f42, f53
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p13) fma.s1 f60 = f51, f42, f52
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) fma.s1 f60 = f60, f42, f54
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) fma.s1 f59 = f56, f42, f57
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p13) fma.s1 f60 = f42, f60, f53
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) fma.s1 f59 = f59, f48, f42
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Flag_1: poly_lo = Q_5 + r*(Q_6 + r*Q_7)
|
|
// Flag_not1: poly_lo = P_4 + r*(P_5 + r*P_6)
|
|
// Flag_not1: poly_hi = (P_1 + r*P_2)
|
|
//
|
|
(p13) fmpy.s1 f60 = f60, f58
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) fma.s1 f60 = f60, f42, f55
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Flag_1: poly_lo = r6 *(Q_5 + ....)
|
|
// Flag_not1: poly_hi = r + rsq *(P_1 + r*P_2)
|
|
//
|
|
(p12) fma.s1 f35 = f60, f50, f59
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p13) fma.s1 f59 = f54, f42, f55
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Flag_not1: Y_lo = rsq* poly_hi + poly_lo
|
|
// Flag_1: poly_lo = rsq* poly_hi + poly_lo
|
|
//
|
|
(p13) fma.s1 f59 = f59, f42, f56
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Flag_not_1: (P_1 + r*P_2)
|
|
//
|
|
(p13) fma.s1 f59 = f59, f42, f57
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Flag_not_1: poly_hi = r + rsq * (P_1 + r*P_2)
|
|
//
|
|
(p13) fma.s1 f35 = f59, f48, f60
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Create 0.000...01
|
|
//
|
|
(p0) for f37 = f35, f37
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
//
|
|
// Set lsb of Y_lo to 1
|
|
//
|
|
(p0) fmerge.se f35 = f35,f37
|
|
(p0) br.cond.sptk EXPL_MAIN ;;
|
|
}
|
|
EXPL_VERY_SMALL:
|
|
{ .mmi
|
|
nop.m 999
|
|
nop.m 999
|
|
(p13) addl r34 = @ltoff(Constants_exp_64_Exponents#),gp
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) mov f35 = f9
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfb
|
|
(p13) ld8 r34 = [r34]
|
|
(p12) mov f34 = f1
|
|
(p12) br.cond.sptk EXPL_MAIN ;;
|
|
}
|
|
{ .mlx
|
|
(p13) add r34 = 8,r34
|
|
(p13) movl r39 = 0x0FFFE ;;
|
|
}
|
|
//
|
|
// Load big_exp_neg
|
|
// Create 1/2's exponent
|
|
//
|
|
{ .mii
|
|
(p13) setf.exp f56 = r39
|
|
(p13) shladd r34 = r32,4,r34 ;;
|
|
nop.i 999
|
|
}
|
|
//
|
|
// Negative exponents are stored after positive
|
|
//
|
|
{ .mfi
|
|
(p13) ld8 r45 = [r34],0
|
|
//
|
|
// Y_hi = x
|
|
// Scale = 1
|
|
//
|
|
(p13) fmpy.s1 f35 = f9, f9
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Reset Safe if necessary
|
|
// Create 1/2
|
|
//
|
|
(p13) mov f34 = f9
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
(p13) cmp.lt.unc p0, p15 = r37, r45
|
|
(p13) mov f36 = f1
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
//
|
|
// Y_lo = x * x
|
|
//
|
|
(p13) fmpy.s1 f35 = f35, f56
|
|
//
|
|
// Y_lo = x*x/2
|
|
//
|
|
(p13) br.cond.sptk EXPL_MAIN ;;
|
|
}
|
|
EXPL_HUGE:
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fcmp.gt.unc.s1 p14, p0 = f9, f0
|
|
nop.i 999
|
|
}
|
|
{ .mlx
|
|
nop.m 999
|
|
(p0) movl r39 = 0x15DC0 ;;
|
|
}
|
|
{ .mfi
|
|
(p14) setf.exp f34 = r39
|
|
(p14) mov f35 = f1
|
|
(p14) cmp.eq p0, p15 = r0, r0 ;;
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
(p14) mov f36 = f34
|
|
//
|
|
// If x > 0, Set Safe = False
|
|
// If x > 0, Y_hi = 2**(24,000)
|
|
// If x > 0, Y_lo = 1.0
|
|
// If x > 0, Scale = 2**(24,000)
|
|
//
|
|
(p14) br.cond.sptk EXPL_MAIN ;;
|
|
}
|
|
{ .mlx
|
|
nop.m 999
|
|
(p12) movl r39 = 0xA240
|
|
}
|
|
{ .mlx
|
|
nop.m 999
|
|
(p12) movl r38 = 0xA1DC ;;
|
|
}
|
|
{ .mmb
|
|
(p13) cmp.eq p15, p14 = r0, r0
|
|
(p12) setf.exp f34 = r39
|
|
nop.b 999 ;;
|
|
}
|
|
{ .mlx
|
|
(p12) setf.exp f35 = r38
|
|
(p13) movl r39 = 0xFF9C
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p13) fsub.s1 f34 = f0, f1
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p12) mov f36 = f34
|
|
(p12) cmp.eq p0, p15 = r0, r0 ;;
|
|
}
|
|
{ .mfi
|
|
(p13) setf.exp f35 = r39
|
|
(p13) mov f36 = f1
|
|
nop.i 999 ;;
|
|
}
|
|
EXPL_MAIN:
|
|
{ .mfi
|
|
(p0) cmp.ne.unc p12, p0 = 0x01, r33
|
|
(p0) fmpy.s1 f101 = f36, f35
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
(p0) fma.s0 f99 = f34, f36, f101
|
|
(p15) br.cond.sptk EXPL_64_RETURN ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fsetc.s3 0x7F,0x01
|
|
nop.i 999
|
|
}
|
|
{ .mlx
|
|
nop.m 999
|
|
(p0) movl r50 = 0x00000000013FFF ;;
|
|
}
|
|
//
|
|
// S0 user supplied status
|
|
// S2 user supplied status + WRE + TD (Overflows)
|
|
// S3 user supplied status + RZ + TD (Underflows)
|
|
//
|
|
//
|
|
// If (Safe) is true, then
|
|
// Compute result using user supplied status field.
|
|
// No overflow or underflow here, but perhaps inexact.
|
|
// Return
|
|
// Else
|
|
// Determine if overflow or underflow was raised.
|
|
// Fetch +/- overflow threshold for IEEE single, double,
|
|
// double extended
|
|
//
|
|
{ .mfi
|
|
(p0) setf.exp f60 = r50
|
|
(p0) fma.s3 f102 = f34, f36, f101
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fsetc.s3 0x7F,0x40
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// For Safe, no need to check for over/under.
|
|
// For expm1, handle errors like exp.
|
|
//
|
|
(p0) fsetc.s2 0x7F,0x42
|
|
nop.i 999;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fma.s2 f100 = f34, f36, f101
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fsetc.s2 0x7F,0x40
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fclass.m.unc p12, p0 = f102, 0x00F
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fclass.m.unc p11, p0 = f102, 0x00F
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fcmp.ge.unc.s1 p10, p0 = f100, f60
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Create largest double exponent + 1.
|
|
// Create smallest double exponent - 1.
|
|
//
|
|
(p0) fcmp.ge.unc.s1 p8, p0 = f100, f60
|
|
nop.i 999 ;;
|
|
}
|
|
//
|
|
// fcmp: resultS2 >= + overflow threshold -> set (a) if true
|
|
// fcmp: resultS2 <= - overflow threshold -> set (b) if true
|
|
// fclass: resultS3 is denorm/unorm/0 -> set (d) if true
|
|
//
|
|
{ .mib
|
|
(p10) mov GR_Parameter_TAG = 39
|
|
nop.i 999
|
|
(p10) br.cond.sptk __libm_error_region ;;
|
|
}
|
|
{ .mib
|
|
(p8) mov GR_Parameter_TAG = 12
|
|
nop.i 999
|
|
(p8) br.cond.sptk __libm_error_region ;;
|
|
}
|
|
//
|
|
// Report that exp overflowed
|
|
//
|
|
{ .mib
|
|
(p12) mov GR_Parameter_TAG = 40
|
|
nop.i 999
|
|
(p12) br.cond.sptk __libm_error_region ;;
|
|
}
|
|
{ .mib
|
|
(p11) mov GR_Parameter_TAG = 13
|
|
nop.i 999
|
|
(p11) br.cond.sptk __libm_error_region ;;
|
|
}
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
//
|
|
// Report that exp underflowed
|
|
//
|
|
(p0) br.cond.sptk EXPL_64_RETURN ;;
|
|
}
|
|
EXPL_64_SPECIAL:
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fclass.m.unc p6, p0 = f8, 0x0c3
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fclass.m.unc p13, p8 = f8, 0x007
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fclass.m.unc p14, p0 = f8, 0x007
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fclass.m.unc p12, p9 = f8, 0x021
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p0) fclass.m.unc p11, p0 = f8, 0x022
|
|
nop.i 999
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p7) fclass.m.unc p10, p0 = f8, 0x022
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
//
|
|
// Identify +/- 0, Inf, or -Inf
|
|
// Generate the right kind of NaN.
|
|
//
|
|
(p13) fadd.s0 f99 = f0, f1
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p14) mov f99 = f8
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
(p6) fadd.s0 f99 = f8, f1
|
|
//
|
|
// expl(+/-0) = 1
|
|
// expm1l(+/-0) = +/-0
|
|
// No exceptions raised
|
|
//
|
|
(p6) br.cond.sptk EXPL_64_RETURN ;;
|
|
}
|
|
{ .mib
|
|
nop.m 999
|
|
nop.i 999
|
|
(p14) br.cond.sptk EXPL_64_RETURN ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p11) mov f99 = f0
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
(p10) fsub.s1 f99 = f0, f1
|
|
//
|
|
// expl(-Inf) = 0
|
|
// expm1l(-Inf) = -1
|
|
// No exceptions raised.
|
|
//
|
|
(p10) br.cond.sptk EXPL_64_RETURN ;;
|
|
}
|
|
{ .mfb
|
|
nop.m 999
|
|
(p12) fmpy.s1 f99 = f8, f1
|
|
//
|
|
// expl(+Inf) = Inf
|
|
// No exceptions raised.
|
|
//
|
|
(p0) br.cond.sptk EXPL_64_RETURN ;;
|
|
}
|
|
EXPL_64_UNSUPPORTED:
|
|
{ .mfb
|
|
nop.m 999
|
|
(p0) fmpy.s0 f99 = f8, f0
|
|
(p0) br.cond.sptk EXPL_64_RETURN ;;
|
|
}
|
|
EXPL_64_RETURN:
|
|
{ .mfb
|
|
nop.m 999
|
|
(p0) mov f8 = f99
|
|
(p0) br.ret.sptk b0
|
|
}
|
|
.endp
|
|
ASM_SIZE_DIRECTIVE(expl)
|
|
|
|
.proc __libm_error_region
|
|
__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 0
|
|
nop.m 0
|
|
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
|
|
};;
|
|
.endp __libm_error_region
|
|
ASM_SIZE_DIRECTIVE(__libm_error_region)
|
|
|
|
.type __libm_error_support#,@function
|
|
.global __libm_error_support#
|