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ee6189855a
equivalent, but shorter instructions. * sysdeps/unix/sysv/linux/x86_64/sysdep.h: Likewise. * sysdeps/unix/sysv/linux/x86_64/setcontext.S: Likewise. * sysdeps/unix/sysv/linux/x86_64/clone.S: Likewise. * sysdeps/unix/sysv/linux/x86_64/swapcontext.S: Likewise. * sysdeps/unix/x86_64/sysdep.S: Likewise. * sysdeps/x86_64/strchr.S: Likewise. * sysdeps/x86_64/memset.S: Likewise. * sysdeps/x86_64/strcspn.S: Likewise. * sysdeps/x86_64/strcmp.S: Likewise. * sysdeps/x86_64/elf/start.S: Likewise. * sysdeps/x86_64/strspn.S: Likewise. * sysdeps/x86_64/dl-machine.h: Likewise. * sysdeps/x86_64/bsd-_setjmp.S: Likewise. * sysdeps/x86_64/bsd-setjmp.S: Likewise. * sysdeps/x86_64/strtok.S: Likewise.
790 lines
22 KiB
ArmAsm
790 lines
22 KiB
ArmAsm
.file "log1pf.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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// Contributed 2000 by the Intel Numerics Group, Intel Corporation
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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// History
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//==============================================================
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// 02/02/00 Initial version
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// 04/04/00 Unwind support added
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// 08/15/00 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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// 06/29/01 Improved speed of all paths
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 10/02/02 Improved performance by basing on log algorithm
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// 02/10/03 Reordered header: .section, .global, .proc, .align
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// 04/18/03 Eliminate possible WAW dependency warning
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// 12/16/03 Fixed parameter passing to/from error handling routine
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//
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// API
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//==============================================================
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// float log1pf(float)
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//
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// log1p(x) = log(x+1)
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//
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// Overview of operation
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//==============================================================
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// Background
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// ----------
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//
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// This algorithm is based on fact that
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// log1p(x) = log(1+x) and
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// log(a b) = log(a) + log(b).
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// In our case we have 1+x = 2^N f, where 1 <= f < 2.
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// So
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// log(1+x) = log(2^N f) = log(2^N) + log(f) = n*log(2) + log(f)
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//
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// To calculate log(f) we do following
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// log(f) = log(f * frcpa(f) / frcpa(f)) =
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// = log(f * frcpa(f)) + log(1/frcpa(f))
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//
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// According to definition of IA-64's frcpa instruction it's a
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// floating point that approximates 1/f using a lookup on the
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// top of 8 bits of the input number's + 1 significand with relative
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// error < 2^(-8.886). So we have following
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//
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// |(1/f - frcpa(f)) / (1/f))| = |1 - f*frcpa(f)| < 1/256
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//
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// and
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//
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// log(f) = log(f * frcpa(f)) + log(1/frcpa(f)) =
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// = log(1 + r) + T
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//
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// The first value can be computed by polynomial P(r) approximating
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// log(1 + r) on |r| < 1/256 and the second is precomputed tabular
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// value defined by top 8 bit of f.
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//
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// Finally we have that log(1+x) ~ (N*log(2) + T) + P(r)
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//
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// Note that if input argument is close to 0.0 (in our case it means
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// that |x| < 1/256) we can use just polynomial approximation
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// because 1+x = 2^0 * f = f = 1 + r and
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// log(1+x) = log(1 + r) ~ P(r)
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//
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//
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// Implementation
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// --------------
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//
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// 1. |x| >= 2^(-8), and x > -1
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// InvX = frcpa(x+1)
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// r = InvX*(x+1) - 1
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// P(r) = r*((1 - A2*4) + r^2*(A3 - A4*r)) = r*P2(r),
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// A4,A3,A2 are created with setf instruction.
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// We use Taylor series and so A4 = 1/4, A3 = 1/3,
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// A2 = 1/2 rounded to double.
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//
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// N = float(n) where n is true unbiased exponent of x
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//
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// T is tabular value of log(1/frcpa(x)) calculated in quad precision
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// and rounded to double. To load T we get bits from 55 to 62 of register
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// format significand as index and calculate address
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// ad_T = table_base_addr + 8 * index
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//
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// L1 (log(2)) is calculated in quad precision and rounded to double;
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// it's created with setf
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//
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// And final result = P2(r)*r + (T + N*L1)
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//
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//
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// 2. 2^(-40) <= |x| < 2^(-8)
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// r = x
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// P(r) = r*((1 - A2*4) + r^2*(A3 - A4*r)) = r*P2(r),
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// A4,A3,A2 are the same as in case |x| >= 1/256
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//
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// And final result = P2(r)*r
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//
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// 3. 0 < |x| < 2^(-40)
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// Although log1p(x) is basically x, we would like to preserve the inexactness
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// nature as well as consistent behavior under different rounding modes.
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// We can do this by computing the result as
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//
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// log1p(x) = x - x*x
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//
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//
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// Note: NaT, any NaNs, +/-INF, +/-0, negatives and unnormalized numbers are
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// filtered and processed on special branches.
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//
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//
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// Special values
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//==============================================================
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//
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// log1p(-1) = -inf // Call error support
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//
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// log1p(+qnan) = +qnan
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// log1p(-qnan) = -qnan
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// log1p(+snan) = +qnan
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// log1p(-snan) = -qnan
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//
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// log1p(x),x<-1= QNAN Indefinite // Call error support
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// log1p(-inf) = QNAN Indefinite
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// log1p(+inf) = +inf
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// log1p(+/-0) = +/-0
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//
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//
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// Registers used
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//==============================================================
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// Floating Point registers used:
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// f8, input
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// f7 -> f15, f32 -> f36
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//
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// General registers used:
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// r8 -> r11
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// r14 -> r22
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//
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// Predicate registers used:
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// p6 -> p12
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// Assembly macros
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//==============================================================
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GR_TAG = r8
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GR_ad_T = r9
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GR_Exp = r10
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GR_N = r11
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GR_signexp_x = r14
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GR_exp_mask = r15
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GR_exp_bias = r16
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GR_05 = r17
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GR_A3 = r18
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GR_Sig = r19
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GR_Ind = r19
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GR_exp_x = r20
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GR_Ln2 = r21
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GR_025 = r22
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GR_SAVE_B0 = r33
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GR_SAVE_PFS = r34
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GR_SAVE_GP = r35
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GR_SAVE_SP = r36
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GR_Parameter_X = r37
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GR_Parameter_Y = r38
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GR_Parameter_RESULT = r39
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GR_Parameter_TAG = r40
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FR_NormX = f7
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FR_RcpX = f9
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FR_r = f10
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FR_r2 = f11
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FR_r4 = f12
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FR_N = f13
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FR_Ln2 = f14
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FR_Xp1 = f15
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FR_A4 = f33
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FR_A3 = f34
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FR_A2 = f35
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FR_T = f36
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FR_NxLn2pT = f36
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FR_Y = f1
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FR_X = f10
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FR_RESULT = f8
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// Data
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//==============================================================
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RODATA
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.align 16
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LOCAL_OBJECT_START(log_data)
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// ln(1/frcpa(1+i/256)), i=0...255
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data8 0x3F60040155D5889E // 0
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data8 0x3F78121214586B54 // 1
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data8 0x3F841929F96832F0 // 2
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data8 0x3F8C317384C75F06 // 3
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data8 0x3F91A6B91AC73386 // 4
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data8 0x3F95BA9A5D9AC039 // 5
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data8 0x3F99D2A8074325F4 // 6
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data8 0x3F9D6B2725979802 // 7
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data8 0x3FA0C58FA19DFAAA // 8
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data8 0x3FA2954C78CBCE1B // 9
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data8 0x3FA4A94D2DA96C56 // 10
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data8 0x3FA67C94F2D4BB58 // 11
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data8 0x3FA85188B630F068 // 12
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data8 0x3FAA6B8ABE73AF4C // 13
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data8 0x3FAC441E06F72A9E // 14
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data8 0x3FAE1E6713606D07 // 15
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data8 0x3FAFFA6911AB9301 // 16
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data8 0x3FB0EC139C5DA601 // 17
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data8 0x3FB1DBD2643D190B // 18
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data8 0x3FB2CC7284FE5F1C // 19
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data8 0x3FB3BDF5A7D1EE64 // 20
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data8 0x3FB4B05D7AA012E0 // 21
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data8 0x3FB580DB7CEB5702 // 22
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data8 0x3FB674F089365A7A // 23
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data8 0x3FB769EF2C6B568D // 24
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data8 0x3FB85FD927506A48 // 25
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data8 0x3FB9335E5D594989 // 26
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data8 0x3FBA2B0220C8E5F5 // 27
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data8 0x3FBB0004AC1A86AC // 28
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data8 0x3FBBF968769FCA11 // 29
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data8 0x3FBCCFEDBFEE13A8 // 30
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data8 0x3FBDA727638446A2 // 31
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data8 0x3FBEA3257FE10F7A // 32
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data8 0x3FBF7BE9FEDBFDE6 // 33
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data8 0x3FC02AB352FF25F4 // 34
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data8 0x3FC097CE579D204D // 35
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data8 0x3FC1178E8227E47C // 36
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data8 0x3FC185747DBECF34 // 37
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data8 0x3FC1F3B925F25D41 // 38
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data8 0x3FC2625D1E6DDF57 // 39
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data8 0x3FC2D1610C86813A // 40
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data8 0x3FC3B08B6757F2A9 // 42
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data8 0x3FC4EF51F6466DE4 // 45
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data8 0x3FD7D81B037EB6A6 // 115
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data8 0x3FD8069E33827231 // 116
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data8 0x3FD82996D3EF8BCB // 117
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data8 0x3FD92C59E79C0E56 // 123
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data8 0x3FDA0325ED14FDA4 // 128
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data8 0x3FDA57725E80C383 // 130
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data8 0x3FDA87D0165DD199 // 131
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data8 0x3FDAAC2E6C03F896 // 132
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data8 0x3FDADCCC6FDF6A81 // 133
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data8 0x3FDB015B3EB1E790 // 134
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data8 0x3FDB323A3A635948 // 135
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data8 0x3FDB56FA04462909 // 136
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data8 0x3FDB881AA659BC93 // 137
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data8 0x3FDBAD0BEF3DB165 // 138
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data8 0x3FDBD21297781C2F // 139
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data8 0x3FDC039236F08819 // 140
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data8 0x3FDC28CB1E4D32FD // 141
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data8 0x3FDC4E19B84723C2 // 142
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data8 0x3FDC7FF9C74554C9 // 143
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data8 0x3FDCA57B64E9DB05 // 144
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data8 0x3FDCCB130A5CEBB0 // 145
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data8 0x3FDCF0C0D18F326F // 146
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data8 0x3FDD232075B5A201 // 147
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data8 0x3FDD490246DEFA6B // 148
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data8 0x3FDD6EFA918D25CD // 149
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data8 0x3FDD9509707AE52F // 150
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data8 0x3FDDBB2EFE92C554 // 151
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data8 0x3FDDEE2F3445E4AF // 152
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data8 0x3FDE148A1A2726CE // 153
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data8 0x3FDE3AFC0A49FF40 // 154
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data8 0x3FDE6185206D516E // 155
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data8 0x3FDE882578823D52 // 156
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data8 0x3FDEAEDD2EAC990C // 157
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data8 0x3FDED5AC5F436BE3 // 158
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data8 0x3FDEFC9326D16AB9 // 159
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data8 0x3FDF2391A2157600 // 160
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data8 0x3FDF4AA7EE03192D // 161
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data8 0x3FDF71D627C30BB0 // 162
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data8 0x3FDF991C6CB3B379 // 163
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data8 0x3FDFC07ADA69A910 // 164
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data8 0x3FDFE7F18EB03D3E // 165
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data8 0x3FE007C053C5002E // 166
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data8 0x3FE01B942198A5A1 // 167
|
|
data8 0x3FE02F74400C64EB // 168
|
|
data8 0x3FE04360BE7603AD // 169
|
|
data8 0x3FE05759AC47FE34 // 170
|
|
data8 0x3FE06B5F1911CF52 // 171
|
|
data8 0x3FE078BF0533C568 // 172
|
|
data8 0x3FE08CD9687E7B0E // 173
|
|
data8 0x3FE0A10074CF9019 // 174
|
|
data8 0x3FE0B5343A234477 // 175
|
|
data8 0x3FE0C974C89431CE // 176
|
|
data8 0x3FE0DDC2305B9886 // 177
|
|
data8 0x3FE0EB524BAFC918 // 178
|
|
data8 0x3FE0FFB54213A476 // 179
|
|
data8 0x3FE114253DA97D9F // 180
|
|
data8 0x3FE128A24F1D9AFF // 181
|
|
data8 0x3FE1365252BF0865 // 182
|
|
data8 0x3FE14AE558B4A92D // 183
|
|
data8 0x3FE15F85A19C765B // 184
|
|
data8 0x3FE16D4D38C119FA // 185
|
|
data8 0x3FE18203C20DD133 // 186
|
|
data8 0x3FE196C7BC4B1F3B // 187
|
|
data8 0x3FE1A4A738B7A33C // 188
|
|
data8 0x3FE1B981C0C9653D // 189
|
|
data8 0x3FE1CE69E8BB106B // 190
|
|
data8 0x3FE1DC619DE06944 // 191
|
|
data8 0x3FE1F160A2AD0DA4 // 192
|
|
data8 0x3FE2066D7740737E // 193
|
|
data8 0x3FE2147DBA47A394 // 194
|
|
data8 0x3FE229A1BC5EBAC3 // 195
|
|
data8 0x3FE237C1841A502E // 196
|
|
data8 0x3FE24CFCE6F80D9A // 197
|
|
data8 0x3FE25B2C55CD5762 // 198
|
|
data8 0x3FE2707F4D5F7C41 // 199
|
|
data8 0x3FE285E0842CA384 // 200
|
|
data8 0x3FE294294708B773 // 201
|
|
data8 0x3FE2A9A2670AFF0C // 202
|
|
data8 0x3FE2B7FB2C8D1CC1 // 203
|
|
data8 0x3FE2C65A6395F5F5 // 204
|
|
data8 0x3FE2DBF557B0DF43 // 205
|
|
data8 0x3FE2EA64C3F97655 // 206
|
|
data8 0x3FE3001823684D73 // 207
|
|
data8 0x3FE30E97E9A8B5CD // 208
|
|
data8 0x3FE32463EBDD34EA // 209
|
|
data8 0x3FE332F4314AD796 // 210
|
|
data8 0x3FE348D90E7464D0 // 211
|
|
data8 0x3FE35779F8C43D6E // 212
|
|
data8 0x3FE36621961A6A99 // 213
|
|
data8 0x3FE37C299F3C366A // 214
|
|
data8 0x3FE38AE2171976E7 // 215
|
|
data8 0x3FE399A157A603E7 // 216
|
|
data8 0x3FE3AFCCFE77B9D1 // 217
|
|
data8 0x3FE3BE9D503533B5 // 218
|
|
data8 0x3FE3CD7480B4A8A3 // 219
|
|
data8 0x3FE3E3C43918F76C // 220
|
|
data8 0x3FE3F2ACB27ED6C7 // 221
|
|
data8 0x3FE4019C2125CA93 // 222
|
|
data8 0x3FE4181061389722 // 223
|
|
data8 0x3FE42711518DF545 // 224
|
|
data8 0x3FE436194E12B6BF // 225
|
|
data8 0x3FE445285D68EA69 // 226
|
|
data8 0x3FE45BCC464C893A // 227
|
|
data8 0x3FE46AED21F117FC // 228
|
|
data8 0x3FE47A1527E8A2D3 // 229
|
|
data8 0x3FE489445EFFFCCC // 230
|
|
data8 0x3FE4A018BCB69835 // 231
|
|
data8 0x3FE4AF5A0C9D65D7 // 232
|
|
data8 0x3FE4BEA2A5BDBE87 // 233
|
|
data8 0x3FE4CDF28F10AC46 // 234
|
|
data8 0x3FE4DD49CF994058 // 235
|
|
data8 0x3FE4ECA86E64A684 // 236
|
|
data8 0x3FE503C43CD8EB68 // 237
|
|
data8 0x3FE513356667FC57 // 238
|
|
data8 0x3FE522AE0738A3D8 // 239
|
|
data8 0x3FE5322E26867857 // 240
|
|
data8 0x3FE541B5CB979809 // 241
|
|
data8 0x3FE55144FDBCBD62 // 242
|
|
data8 0x3FE560DBC45153C7 // 243
|
|
data8 0x3FE5707A26BB8C66 // 244
|
|
data8 0x3FE587F60ED5B900 // 245
|
|
data8 0x3FE597A7977C8F31 // 246
|
|
data8 0x3FE5A760D634BB8B // 247
|
|
data8 0x3FE5B721D295F10F // 248
|
|
data8 0x3FE5C6EA94431EF9 // 249
|
|
data8 0x3FE5D6BB22EA86F6 // 250
|
|
data8 0x3FE5E6938645D390 // 251
|
|
data8 0x3FE5F673C61A2ED2 // 252
|
|
data8 0x3FE6065BEA385926 // 253
|
|
data8 0x3FE6164BFA7CC06B // 254
|
|
data8 0x3FE62643FECF9743 // 255
|
|
LOCAL_OBJECT_END(log_data)
|
|
|
|
|
|
// Code
|
|
//==============================================================
|
|
|
|
.section .text
|
|
GLOBAL_IEEE754_ENTRY(log1pf)
|
|
{ .mfi
|
|
getf.exp GR_signexp_x = f8 // if x is unorm then must recompute
|
|
fadd.s1 FR_Xp1 = f8, f1 // Form 1+x
|
|
mov GR_05 = 0xfffe
|
|
}
|
|
{ .mlx
|
|
addl GR_ad_T = @ltoff(log_data),gp
|
|
movl GR_A3 = 0x3fd5555555555555 // double precision memory
|
|
// representation of A3
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ld8 GR_ad_T = [GR_ad_T]
|
|
fclass.m p8,p0 = f8,0xb // Is x unorm?
|
|
mov GR_exp_mask = 0x1ffff
|
|
}
|
|
{ .mfi
|
|
mov GR_025 = 0xfffd // Exponent of 0.25
|
|
fnorm.s1 FR_NormX = f8 // Normalize x
|
|
mov GR_exp_bias = 0xffff
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
setf.exp FR_A2 = GR_05 // create A2 = 0.5
|
|
fclass.m p9,p0 = f8,0x1E1 // is x NaN, NaT or +Inf?
|
|
nop.i 0
|
|
}
|
|
{ .mib
|
|
setf.d FR_A3 = GR_A3 // create A3
|
|
nop.i 0
|
|
(p8) br.cond.spnt log1p_unorm // Branch if x=unorm
|
|
}
|
|
;;
|
|
|
|
log1p_common:
|
|
{ .mfi
|
|
setf.exp FR_A4 = GR_025 // create A4 = 0.25
|
|
frcpa.s1 FR_RcpX,p0 = f1,FR_Xp1
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p9) fma.s.s0 f8 = f8,f1,f0 // set V-flag
|
|
(p9) br.ret.spnt b0 // exit for NaN, NaT and +Inf
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
getf.exp GR_Exp = FR_Xp1 // signexp of x+1
|
|
fclass.m p10,p0 = FR_Xp1,0x3A // is 1+x < 0?
|
|
and GR_exp_x = GR_exp_mask, GR_signexp_x // biased exponent of x
|
|
}
|
|
{ .mlx
|
|
nop.m 0
|
|
movl GR_Ln2 = 0x3FE62E42FEFA39EF // double precision memory
|
|
// representation of log(2)
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
getf.sig GR_Sig = FR_Xp1 // get significand to calculate index
|
|
// for T if |x| >= 2^-8
|
|
fcmp.eq.s1 p12,p0 = f8,f0 // is x equal to 0?
|
|
sub GR_exp_x = GR_exp_x, GR_exp_bias // true exponent of x
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
sub GR_N = GR_Exp,GR_exp_bias // true exponent of x+1
|
|
fcmp.eq.s1 p11,p0 = FR_Xp1,f0 // is x = -1?
|
|
cmp.gt p6,p7 = -8, GR_exp_x // Is |x| < 2^-8
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
nop.f 0
|
|
(p10) br.cond.spnt log1p_lt_minus_1 // jump if x < -1
|
|
}
|
|
;;
|
|
|
|
// p6 is true if |x| < 1/256
|
|
// p7 is true if |x| >= 1/256
|
|
.pred.rel "mutex",p6,p7
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fms.s1 FR_r = f8,f1,f0 // range reduction for |x|<1/256
|
|
(p6) cmp.gt.unc p10,p0 = -40, GR_exp_x // Is |x| < 2^-40
|
|
}
|
|
{ .mfb
|
|
(p7) setf.sig FR_N = GR_N // copy unbiased exponent of x to the
|
|
// significand field of FR_N
|
|
(p7) fms.s1 FR_r = FR_RcpX,FR_Xp1,f1 // range reduction for |x|>=1/256
|
|
(p12) br.ret.spnt b0 // exit for x=0, return x
|
|
}
|
|
;;
|
|
|
|
{ .mib
|
|
setf.d FR_Ln2 = GR_Ln2 // create log(2)
|
|
(p7) extr.u GR_Ind = GR_Sig,55,8 // get bits from 55 to 62 as index
|
|
(p11) br.cond.spnt log1p_eq_minus_1 // jump if x = -1
|
|
}
|
|
;;
|
|
|
|
{ .mmf
|
|
(p7) shladd GR_ad_T = GR_Ind,3,GR_ad_T // address of T
|
|
nop.m 0
|
|
(p10) fnma.s.s0 f8 = f8,f8,f8 // If |x| very small, result=x-x*x
|
|
}
|
|
;;
|
|
|
|
{ .mmb
|
|
(p7) ldfd FR_T = [GR_ad_T]
|
|
nop.m 0
|
|
(p10) br.ret.spnt b0 // Exit if |x| < 2^-40
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_r2 = FR_r,FR_r,f0 // r^2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_A2 = FR_A2,FR_r,f1 // 1.0 - A2*r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 FR_A3 = FR_A4,FR_r,FR_A3 // A3 - A4*r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fcvt.xf FR_N = FR_N
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// (A3*r+A2)*r^2+r
|
|
fma.s1 FR_A2 = FR_A3,FR_r2,FR_A2 // (A4*r+A3)*r^2+(A2*r+1)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// N*Ln2hi+T
|
|
(p7) fma.s1 FR_NxLn2pT = FR_N,FR_Ln2,FR_T
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
.pred.rel "mutex",p6,p7
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fma.s.s0 f8 = FR_A2,FR_r,f0 // result if 2^(-40) <= |x| < 1/256
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p7) fma.s.s0 f8 = FR_A2,FR_r,FR_NxLn2pT // result if |x| >= 1/256
|
|
br.ret.sptk b0 // Exit if |x| >= 2^(-40)
|
|
}
|
|
;;
|
|
|
|
.align 32
|
|
log1p_unorm:
|
|
// Here if x=unorm
|
|
{ .mfb
|
|
getf.exp GR_signexp_x = FR_NormX // recompute biased exponent
|
|
nop.f 0
|
|
br.cond.sptk log1p_common
|
|
}
|
|
;;
|
|
|
|
.align 32
|
|
log1p_eq_minus_1:
|
|
// Here if x=-1
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.s FR_X = f8,f8 // keep input argument for subsequent
|
|
// call of __libm_error_support#
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
mov GR_TAG = 142 // set libm error in case of log1p(-1).
|
|
frcpa.s0 f8,p0 = f8,f0 // log1p(-1) should be equal to -INF.
|
|
// We can get it using frcpa because it
|
|
// sets result to the IEEE-754 mandated
|
|
// quotient of f8/f0.
|
|
nop.i 0
|
|
}
|
|
{ .mib
|
|
nop.m 0
|
|
nop.i 0
|
|
br.cond.sptk log_libm_err
|
|
}
|
|
;;
|
|
|
|
.align 32
|
|
log1p_lt_minus_1:
|
|
// Here if x < -1
|
|
{ .mfi
|
|
nop.m 0
|
|
fmerge.s FR_X = f8,f8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
mov GR_TAG = 143 // set libm error in case of x < -1.
|
|
frcpa.s0 f8,p0 = f0,f0 // log1p(x) x < -1 should be equal to NaN.
|
|
// We can get it using frcpa because it
|
|
// sets result to the IEEE-754 mandated
|
|
// quotient of f0/f0 i.e. NaN.
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
.align 32
|
|
log_libm_err:
|
|
{ .mmi
|
|
alloc r32 = ar.pfs,1,4,4,0
|
|
mov GR_Parameter_TAG = GR_TAG
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
GLOBAL_IEEE754_END(log1pf)
|
|
|
|
|
|
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
|
|
stfs [GR_Parameter_Y] = FR_Y,16 // STORE 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
|
|
stfs [GR_Parameter_X] = FR_X // STORE Parameter 1 on stack
|
|
add GR_Parameter_RESULT = 0,GR_Parameter_Y // Parameter 3 address
|
|
nop.b 0
|
|
}
|
|
{ .mib
|
|
stfs [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
|
|
add GR_Parameter_RESULT = 48,sp
|
|
nop.m 0
|
|
nop.i 0
|
|
};;
|
|
{ .mmi
|
|
ldfs 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#
|
|
|