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We stopped adding "Contributed by" or similar lines in sources in 2012 in favour of git logs and keeping the Contributors section of the glibc manual up to date. Removing these lines makes the license header a bit more consistent across files and also removes the possibility of error in attribution when license blocks or files are copied across since the contributed-by lines don't actually reflect reality in those cases. Move all "Contributed by" and similar lines (Written by, Test by, etc.) into a new file CONTRIBUTED-BY to retain record of these contributions. These contributors are also mentioned in manual/contrib.texi, so we just maintain this additional record as a courtesy to the earlier developers. The following scripts were used to filter a list of files to edit in place and to clean up the CONTRIBUTED-BY file respectively. These were not added to the glibc sources because they're not expected to be of any use in future given that this is a one time task: https://gist.github.com/siddhesh/b5ecac94eabfd72ed2916d6d8157e7dc https://gist.github.com/siddhesh/15ea1f5e435ace9774f485030695ee02 Reviewed-by: Carlos O'Donell <carlos@redhat.com>
1138 lines
37 KiB
ArmAsm
1138 lines
37 KiB
ArmAsm
.file "asinh.s"
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// Copyright (c) 2000 - 2005, Intel Corporation
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// All rights reserved.
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//
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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// ==============================================================
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// History
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// ==============================================================
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// 04/02/01 Initial version
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// 04/19/01 Improved speed of the paths #1,2,3,4,5
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// 10/18/01 Improved accuracy
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 02/06/03 Reordered header: .section, .global, .proc, .align
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// 05/21/03 Improved performance, fixed to handle unorms
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// 03/31/05 Reformatted delimiters between data tables
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//
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// API
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// ==============================================================
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// double asinh(double)
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//
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// Overview of operation
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// ==============================================================
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//
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// There are 7 paths:
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// 1. x = 0.0
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// Return asinh(x) = 0.0
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//
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// 2. 0.0 <|x| < 2^(-3)
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// Return asinh(x) = POL13(x),
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// where POL13(x) = (x^2*C13 + ...)*x^2 + C5)*x^2 + C3)*x^3 + x
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//
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// 3. 2^(-3) <= |x| < 2^63
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// Return asinh(x) = sign(x)*(log(|x| + sqrt(x^2 + 1.0)))
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// To compute x + sqrt(x^2 + 1.0) modified Newton Raphson method is used
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// (3 iterations)
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// Algorithm description for log function see below.
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//
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// 4. 2^63 <= |x| < +INF
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// Return asinh(x) = sign(x)*log(2*|x|)
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// Algorithm description for log function see below.
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//
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// 5. x = INF
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// Return asinh(x) = INF
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//
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// 6. x = [S,Q]NaN
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// Return asinh(x) = QNaN
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//
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// 7. x = denormal
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// Return asinh(x) = x correctly rounded
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//
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//==============================================================
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// Algorithm Description for log(x) function
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// Below we are using the fact that inequality x - 1.0 > 2^(-6) is always
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// true for this asinh implementation
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//
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// Consider x = 2^N 1.f1 f2 f3 f4...f63
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// Log(x) = log(frcpa(x) x/frcpa(x))
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// = log(1/frcpa(x)) + log(frcpa(x) x)
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// = -log(frcpa(x)) + log(frcpa(x) x)
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//
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// frcpa(x) = 2^-N frcpa((1.f1 f2 ... f63)
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//
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// -log(frcpa(x)) = -log(C)
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// = -log(2^-N) - log(frcpa(1.f1 f2 ... f63))
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//
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// -log(frcpa(x)) = -log(C)
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// = +Nlog2 - log(frcpa(1.f1 f2 ... f63))
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//
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// -log(frcpa(x)) = -log(C)
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// = +Nlog2 + log(frcpa(1.f1 f2 ... f63))
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//
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// Log(x) = log(1/frcpa(x)) + log(frcpa(x) x)
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//
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// Log(x) = +Nlog2 + log(1./frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
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// Log(x) = +Nlog2 - log(/frcpa(1.f1 f2 ... f63)) + log(frcpa(x) x)
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// Log(x) = +Nlog2 + T + log(frcpa(x) x)
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//
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// Log(x) = +Nlog2 + T + log(C x)
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//
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// Cx = 1 + r
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//
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// Log(x) = +Nlog2 + T + log(1+r)
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// Log(x) = +Nlog2 + T + Series( r - r^2/2 + r^3/3 - r^4/4 ....)
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//
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// 1.f1 f2 ... f8 has 256 entries.
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// They are 1 + k/2^8, k = 0 ... 255
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// These 256 values are the table entries.
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//
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// Implementation
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//==============================================================
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// C = frcpa(x)
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// r = C * x - 1
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//
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// Form rseries = r + P1*r^2 + P2*r^3 + P3*r^4 + P4*r^5 + P5*r^6
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//
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// x = f * 2*n where f is 1.f_1f_2f_3....f_63
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// Nfloat = float(n) where n is the true unbiased exponent
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// pre-index = f_1f_2....f_8
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// index = pre_index * 16
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// get the dxt table entry at index + offset = T
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//
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// result = (T + Nfloat * log(2)) + rseries
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//
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// The T table is calculated as follows
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// Form x_k = 1 + k/2^8 where k goes from 0... 255
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// y_k = frcpa(x_k)
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// log(1/y_k) in quad and round to double-extended
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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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// f9 -> f15, f32 -> f68
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// General registers used:
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// r14 -> r27
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// Predicate registers used:
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// p6 -> p14
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// p6 to filter out case when x = [Q,S]NaN or INF or zero
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// p7 to filter out case when x < 0.0
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// p8 to select path #2
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// p9 used in the frcpa from path #3
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// p11 to filter out case when x >= 0
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// p12 to filter out case when x = unorm
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// p13 to select path #4
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// Assembly macros
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//==============================================================
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log_GR_exp_17_ones = r14
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log_GR_signexp_f8 = r15
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log_table_address2 = r16
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log_GR_exp_16_ones = r17
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log_GR_exp_f8 = r18
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log_GR_true_exp_f8 = r19
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log_GR_significand_f8 = r20
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log_GR_index = r21
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log_GR_comp2 = r22
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asinh_GR_f8 = r23
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asinh_GR_comp = r24
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asinh_GR_f8 = r25
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log_table_address3 = r26
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NR_table_address = r27
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//==============================================================
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log_y = f9
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NR1 = f10
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NR2 = f11
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log_y_rs = f12
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log_y_rs_iter = f13
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log_y_rs_iter1 = f14
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fNormX = f15
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asinh_w_sq = f32
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log_C13 = f33
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log_C11 = f34
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log_P3 = f35
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log_P2 = f36
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log_P1 = f37
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log_P5 = f38
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log_P4 = f39
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log_C3 = f40
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log_C5 = f41
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log_C7 = f42
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log2 = f43
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asinh_f8 = f44
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log_C = f45
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log_arg = f46
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log_C9 = f47
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asinh_w_four = f48
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log_int_Nfloat = f49
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log_r = f50
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log_rsq = f51
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log_rp_p4 = f52
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log_rp_p32 = f53
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log_rcube = f54
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log_rp_p10 = f55
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log_rp_p2 = f56
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log_Nfloat = f57
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log_T = f58
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log_r2P_r = f59
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log_T_plus_Nlog2 = f60
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asinh_w_3 = f61
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asinh_w_5 = f62
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asinh_w_cube = f63
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asinh_w_7 = f64
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log_arg_early = f65
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asinh_w_9 = f66
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asinh_w_13 = f67
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asinh_w_seven = f68
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// Data tables
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//==============================================================
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RODATA
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.align 16
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LOCAL_OBJECT_START(log_table_1)
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data8 0xBFC5555DA7212371 // P5
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data8 0x3FC999A19EEF5826 // P4
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data8 0xBFCFFFFFFFFEF009 // P3
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data8 0x3FD555555554ECB2 // P2
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data8 0xBFE0000000000000 // P1 = -0.5
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data8 0x0000000000000000 // pad
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data8 0xb17217f7d1cf79ac, 0x00003ffe // log2
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LOCAL_OBJECT_END(log_table_1)
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LOCAL_OBJECT_START(log_table_2)
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data8 0x3FE0000000000000 // 0.5
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data8 0x4008000000000000 // 3.0
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//
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data8 0x8824BE4D74BC4F00, 0x00003FF9 // C13
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data8 0xB725A2CD9556CC57, 0x0000BFF9 // C11
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data8 0xF8E339127FBFF49D, 0x00003FF9 // C9
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data8 0xB6DB6D7DCE17CB78, 0x0000BFFA // C7
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data8 0x999999998802CCEF, 0x00003FFB // C5
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data8 0xAAAAAAAAAAA8DC40, 0x0000BFFC // C3
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LOCAL_OBJECT_END(log_table_2)
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LOCAL_OBJECT_START(log_table_3)
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data8 0x80200aaeac44ef38 , 0x00003ff6 // log(1/frcpa(1+ 0/2^-8))
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//
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data8 0xc09090a2c35aa070 , 0x00003ff7 // log(1/frcpa(1+ 1/2^-8))
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data8 0xa0c94fcb41977c75 , 0x00003ff8 // log(1/frcpa(1+ 2/2^-8))
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data8 0xe18b9c263af83301 , 0x00003ff8 // log(1/frcpa(1+ 3/2^-8))
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data8 0x8d35c8d6399c30ea , 0x00003ff9 // log(1/frcpa(1+ 4/2^-8))
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data8 0xadd4d2ecd601cbb8 , 0x00003ff9 // log(1/frcpa(1+ 5/2^-8))
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//
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data8 0xce95403a192f9f01 , 0x00003ff9 // log(1/frcpa(1+ 6/2^-8))
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data8 0xeb59392cbcc01096 , 0x00003ff9 // log(1/frcpa(1+ 7/2^-8))
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data8 0x862c7d0cefd54c5d , 0x00003ffa // log(1/frcpa(1+ 8/2^-8))
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data8 0x94aa63c65e70d499 , 0x00003ffa // log(1/frcpa(1+ 9/2^-8))
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data8 0xa54a696d4b62b382 , 0x00003ffa // log(1/frcpa(1+ 10/2^-8))
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//
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data8 0xb3e4a796a5dac208 , 0x00003ffa // log(1/frcpa(1+ 11/2^-8))
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data8 0xc28c45b1878340a9 , 0x00003ffa // log(1/frcpa(1+ 12/2^-8))
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data8 0xd35c55f39d7a6235 , 0x00003ffa // log(1/frcpa(1+ 13/2^-8))
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data8 0xe220f037b954f1f5 , 0x00003ffa // log(1/frcpa(1+ 14/2^-8))
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data8 0xf0f3389b036834f3 , 0x00003ffa // log(1/frcpa(1+ 15/2^-8))
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//
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data8 0xffd3488d5c980465 , 0x00003ffa // log(1/frcpa(1+ 16/2^-8))
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data8 0x87609ce2ed300490 , 0x00003ffb // log(1/frcpa(1+ 17/2^-8))
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data8 0x8ede9321e8c85927 , 0x00003ffb // log(1/frcpa(1+ 18/2^-8))
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data8 0x96639427f2f8e2f4 , 0x00003ffb // log(1/frcpa(1+ 19/2^-8))
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data8 0x9defad3e8f73217b , 0x00003ffb // log(1/frcpa(1+ 20/2^-8))
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//
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data8 0xa582ebd50097029c , 0x00003ffb // log(1/frcpa(1+ 21/2^-8))
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data8 0xac06dbe75ab80fee , 0x00003ffb // log(1/frcpa(1+ 22/2^-8))
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data8 0xb3a78449b2d3ccca , 0x00003ffb // log(1/frcpa(1+ 23/2^-8))
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data8 0xbb4f79635ab46bb2 , 0x00003ffb // log(1/frcpa(1+ 24/2^-8))
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data8 0xc2fec93a83523f3f , 0x00003ffb // log(1/frcpa(1+ 25/2^-8))
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//
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data8 0xc99af2eaca4c4571 , 0x00003ffb // log(1/frcpa(1+ 26/2^-8))
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data8 0xd1581106472fa653 , 0x00003ffb // log(1/frcpa(1+ 27/2^-8))
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data8 0xd8002560d4355f2e , 0x00003ffb // log(1/frcpa(1+ 28/2^-8))
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data8 0xdfcb43b4fe508632 , 0x00003ffb // log(1/frcpa(1+ 29/2^-8))
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data8 0xe67f6dff709d4119 , 0x00003ffb // log(1/frcpa(1+ 30/2^-8))
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//
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data8 0xed393b1c22351280 , 0x00003ffb // log(1/frcpa(1+ 31/2^-8))
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data8 0xf5192bff087bcc35 , 0x00003ffb // log(1/frcpa(1+ 32/2^-8))
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data8 0xfbdf4ff6dfef2fa3 , 0x00003ffb // log(1/frcpa(1+ 33/2^-8))
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data8 0x81559a97f92f9cc7 , 0x00003ffc // log(1/frcpa(1+ 34/2^-8))
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data8 0x84be72bce90266e8 , 0x00003ffc // log(1/frcpa(1+ 35/2^-8))
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//
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data8 0x88bc74113f23def2 , 0x00003ffc // log(1/frcpa(1+ 36/2^-8))
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data8 0x8c2ba3edf6799d11 , 0x00003ffc // log(1/frcpa(1+ 37/2^-8))
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data8 0x8f9dc92f92ea08b1 , 0x00003ffc // log(1/frcpa(1+ 38/2^-8))
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data8 0x9312e8f36efab5a7 , 0x00003ffc // log(1/frcpa(1+ 39/2^-8))
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data8 0x968b08643409ceb6 , 0x00003ffc // log(1/frcpa(1+ 40/2^-8))
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//
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data8 0x9a062cba08a1708c , 0x00003ffc // log(1/frcpa(1+ 41/2^-8))
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data8 0x9d845b3abf95485c , 0x00003ffc // log(1/frcpa(1+ 42/2^-8))
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data8 0xa06fd841bc001bb4 , 0x00003ffc // log(1/frcpa(1+ 43/2^-8))
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data8 0xa3f3a74652fbe0db , 0x00003ffc // log(1/frcpa(1+ 44/2^-8))
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data8 0xa77a8fb2336f20f5 , 0x00003ffc // log(1/frcpa(1+ 45/2^-8))
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//
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data8 0xab0497015d28b0a0 , 0x00003ffc // log(1/frcpa(1+ 46/2^-8))
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data8 0xae91c2be6ba6a615 , 0x00003ffc // log(1/frcpa(1+ 47/2^-8))
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data8 0xb189d1b99aebb20b , 0x00003ffc // log(1/frcpa(1+ 48/2^-8))
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data8 0xb51cced5de9c1b2c , 0x00003ffc // log(1/frcpa(1+ 49/2^-8))
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data8 0xb819bee9e720d42f , 0x00003ffc // log(1/frcpa(1+ 50/2^-8))
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//
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data8 0xbbb2a0947b093a5d , 0x00003ffc // log(1/frcpa(1+ 51/2^-8))
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data8 0xbf4ec1505811684a , 0x00003ffc // log(1/frcpa(1+ 52/2^-8))
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data8 0xc2535bacfa8975ff , 0x00003ffc // log(1/frcpa(1+ 53/2^-8))
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data8 0xc55a3eafad187eb8 , 0x00003ffc // log(1/frcpa(1+ 54/2^-8))
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data8 0xc8ff2484b2c0da74 , 0x00003ffc // log(1/frcpa(1+ 55/2^-8))
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//
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data8 0xcc0b1a008d53ab76 , 0x00003ffc // log(1/frcpa(1+ 56/2^-8))
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data8 0xcfb6203844b3209b , 0x00003ffc // log(1/frcpa(1+ 57/2^-8))
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data8 0xd2c73949a47a19f5 , 0x00003ffc // log(1/frcpa(1+ 58/2^-8))
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data8 0xd5daae18b49d6695 , 0x00003ffc // log(1/frcpa(1+ 59/2^-8))
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data8 0xd8f08248cf7e8019 , 0x00003ffc // log(1/frcpa(1+ 60/2^-8))
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//
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data8 0xdca7749f1b3e540e , 0x00003ffc // log(1/frcpa(1+ 61/2^-8))
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data8 0xdfc28e033aaaf7c7 , 0x00003ffc // log(1/frcpa(1+ 62/2^-8))
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data8 0xe2e012a5f91d2f55 , 0x00003ffc // log(1/frcpa(1+ 63/2^-8))
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data8 0xe600064ed9e292a8 , 0x00003ffc // log(1/frcpa(1+ 64/2^-8))
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data8 0xe9226cce42b39f60 , 0x00003ffc // log(1/frcpa(1+ 65/2^-8))
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//
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data8 0xec4749fd97a28360 , 0x00003ffc // log(1/frcpa(1+ 66/2^-8))
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data8 0xef6ea1bf57780495 , 0x00003ffc // log(1/frcpa(1+ 67/2^-8))
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data8 0xf29877ff38809091 , 0x00003ffc // log(1/frcpa(1+ 68/2^-8))
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data8 0xf5c4d0b245cb89be , 0x00003ffc // log(1/frcpa(1+ 69/2^-8))
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data8 0xf8f3afd6fcdef3aa , 0x00003ffc // log(1/frcpa(1+ 70/2^-8))
|
|
//
|
|
data8 0xfc2519756be1abc7 , 0x00003ffc // log(1/frcpa(1+ 71/2^-8))
|
|
data8 0xff59119f503e6832 , 0x00003ffc // log(1/frcpa(1+ 72/2^-8))
|
|
data8 0x8147ce381ae0e146 , 0x00003ffd // log(1/frcpa(1+ 73/2^-8))
|
|
data8 0x82e45f06cb1ad0f2 , 0x00003ffd // log(1/frcpa(1+ 74/2^-8))
|
|
data8 0x842f5c7c573cbaa2 , 0x00003ffd // log(1/frcpa(1+ 75/2^-8))
|
|
//
|
|
data8 0x85ce471968c8893a , 0x00003ffd // log(1/frcpa(1+ 76/2^-8))
|
|
data8 0x876e8305bc04066d , 0x00003ffd // log(1/frcpa(1+ 77/2^-8))
|
|
data8 0x891012678031fbb3 , 0x00003ffd // log(1/frcpa(1+ 78/2^-8))
|
|
data8 0x8a5f1493d766a05f , 0x00003ffd // log(1/frcpa(1+ 79/2^-8))
|
|
data8 0x8c030c778c56fa00 , 0x00003ffd // log(1/frcpa(1+ 80/2^-8))
|
|
//
|
|
data8 0x8da85df17e31d9ae , 0x00003ffd // log(1/frcpa(1+ 81/2^-8))
|
|
data8 0x8efa663e7921687e , 0x00003ffd // log(1/frcpa(1+ 82/2^-8))
|
|
data8 0x90a22b6875c6a1f8 , 0x00003ffd // log(1/frcpa(1+ 83/2^-8))
|
|
data8 0x91f62cc8f5d24837 , 0x00003ffd // log(1/frcpa(1+ 84/2^-8))
|
|
data8 0x93a06cfc3857d980 , 0x00003ffd // log(1/frcpa(1+ 85/2^-8))
|
|
//
|
|
data8 0x94f66d5e6fd01ced , 0x00003ffd // log(1/frcpa(1+ 86/2^-8))
|
|
data8 0x96a330156e6772f2 , 0x00003ffd // log(1/frcpa(1+ 87/2^-8))
|
|
data8 0x97fb3582754ea25b , 0x00003ffd // log(1/frcpa(1+ 88/2^-8))
|
|
data8 0x99aa8259aad1bbf2 , 0x00003ffd // log(1/frcpa(1+ 89/2^-8))
|
|
data8 0x9b0492f6227ae4a8 , 0x00003ffd // log(1/frcpa(1+ 90/2^-8))
|
|
//
|
|
data8 0x9c5f8e199bf3a7a5 , 0x00003ffd // log(1/frcpa(1+ 91/2^-8))
|
|
data8 0x9e1293b9998c1daa , 0x00003ffd // log(1/frcpa(1+ 92/2^-8))
|
|
data8 0x9f6fa31e0b41f308 , 0x00003ffd // log(1/frcpa(1+ 93/2^-8))
|
|
data8 0xa0cda11eaf46390e , 0x00003ffd // log(1/frcpa(1+ 94/2^-8))
|
|
data8 0xa22c8f029cfa45aa , 0x00003ffd // log(1/frcpa(1+ 95/2^-8))
|
|
//
|
|
data8 0xa3e48badb7856b34 , 0x00003ffd // log(1/frcpa(1+ 96/2^-8))
|
|
data8 0xa5459a0aa95849f9 , 0x00003ffd // log(1/frcpa(1+ 97/2^-8))
|
|
data8 0xa6a79c84480cfebd , 0x00003ffd // log(1/frcpa(1+ 98/2^-8))
|
|
data8 0xa80a946d0fcb3eb2 , 0x00003ffd // log(1/frcpa(1+ 99/2^-8))
|
|
data8 0xa96e831a3ea7b314 , 0x00003ffd // log(1/frcpa(1+100/2^-8))
|
|
//
|
|
data8 0xaad369e3dc544e3b , 0x00003ffd // log(1/frcpa(1+101/2^-8))
|
|
data8 0xac92e9588952c815 , 0x00003ffd // log(1/frcpa(1+102/2^-8))
|
|
data8 0xadfa035aa1ed8fdc , 0x00003ffd // log(1/frcpa(1+103/2^-8))
|
|
data8 0xaf6219eae1ad6e34 , 0x00003ffd // log(1/frcpa(1+104/2^-8))
|
|
data8 0xb0cb2e6d8160f753 , 0x00003ffd // log(1/frcpa(1+105/2^-8))
|
|
//
|
|
data8 0xb2354249ad950f72 , 0x00003ffd // log(1/frcpa(1+106/2^-8))
|
|
data8 0xb3a056e98ef4a3b4 , 0x00003ffd // log(1/frcpa(1+107/2^-8))
|
|
data8 0xb50c6dba52c6292a , 0x00003ffd // log(1/frcpa(1+108/2^-8))
|
|
data8 0xb679882c33876165 , 0x00003ffd // log(1/frcpa(1+109/2^-8))
|
|
data8 0xb78c07429785cedc , 0x00003ffd // log(1/frcpa(1+110/2^-8))
|
|
//
|
|
data8 0xb8faeb8dc4a77d24 , 0x00003ffd // log(1/frcpa(1+111/2^-8))
|
|
data8 0xba6ad77eb36ae0d6 , 0x00003ffd // log(1/frcpa(1+112/2^-8))
|
|
data8 0xbbdbcc915e9bee50 , 0x00003ffd // log(1/frcpa(1+113/2^-8))
|
|
data8 0xbd4dcc44f8cf12ef , 0x00003ffd // log(1/frcpa(1+114/2^-8))
|
|
data8 0xbec0d81bf5b531fa , 0x00003ffd // log(1/frcpa(1+115/2^-8))
|
|
//
|
|
data8 0xc034f19c139186f4 , 0x00003ffd // log(1/frcpa(1+116/2^-8))
|
|
data8 0xc14cb69f7c5e55ab , 0x00003ffd // log(1/frcpa(1+117/2^-8))
|
|
data8 0xc2c2abbb6e5fd56f , 0x00003ffd // log(1/frcpa(1+118/2^-8))
|
|
data8 0xc439b2c193e6771e , 0x00003ffd // log(1/frcpa(1+119/2^-8))
|
|
data8 0xc553acb9d5c67733 , 0x00003ffd // log(1/frcpa(1+120/2^-8))
|
|
//
|
|
data8 0xc6cc96e441272441 , 0x00003ffd // log(1/frcpa(1+121/2^-8))
|
|
data8 0xc8469753eca88c30 , 0x00003ffd // log(1/frcpa(1+122/2^-8))
|
|
data8 0xc962cf3ce072b05c , 0x00003ffd // log(1/frcpa(1+123/2^-8))
|
|
data8 0xcadeba8771f694aa , 0x00003ffd // log(1/frcpa(1+124/2^-8))
|
|
data8 0xcc5bc08d1f72da94 , 0x00003ffd // log(1/frcpa(1+125/2^-8))
|
|
//
|
|
data8 0xcd7a3f99ea035c29 , 0x00003ffd // log(1/frcpa(1+126/2^-8))
|
|
data8 0xcef93860c8a53c35 , 0x00003ffd // log(1/frcpa(1+127/2^-8))
|
|
data8 0xd0192f68a7ed23df , 0x00003ffd // log(1/frcpa(1+128/2^-8))
|
|
data8 0xd19a201127d3c645 , 0x00003ffd // log(1/frcpa(1+129/2^-8))
|
|
data8 0xd2bb92f4061c172c , 0x00003ffd // log(1/frcpa(1+130/2^-8))
|
|
//
|
|
data8 0xd43e80b2ee8cc8fc , 0x00003ffd // log(1/frcpa(1+131/2^-8))
|
|
data8 0xd56173601fc4ade4 , 0x00003ffd // log(1/frcpa(1+132/2^-8))
|
|
data8 0xd6e6637efb54086f , 0x00003ffd // log(1/frcpa(1+133/2^-8))
|
|
data8 0xd80ad9f58f3c8193 , 0x00003ffd // log(1/frcpa(1+134/2^-8))
|
|
data8 0xd991d1d31aca41f8 , 0x00003ffd // log(1/frcpa(1+135/2^-8))
|
|
//
|
|
data8 0xdab7d02231484a93 , 0x00003ffd // log(1/frcpa(1+136/2^-8))
|
|
data8 0xdc40d532cde49a54 , 0x00003ffd // log(1/frcpa(1+137/2^-8))
|
|
data8 0xdd685f79ed8b265e , 0x00003ffd // log(1/frcpa(1+138/2^-8))
|
|
data8 0xde9094bbc0e17b1d , 0x00003ffd // log(1/frcpa(1+139/2^-8))
|
|
data8 0xe01c91b78440c425 , 0x00003ffd // log(1/frcpa(1+140/2^-8))
|
|
//
|
|
data8 0xe14658f26997e729 , 0x00003ffd // log(1/frcpa(1+141/2^-8))
|
|
data8 0xe270cdc2391e0d23 , 0x00003ffd // log(1/frcpa(1+142/2^-8))
|
|
data8 0xe3ffce3a2aa64922 , 0x00003ffd // log(1/frcpa(1+143/2^-8))
|
|
data8 0xe52bdb274ed82887 , 0x00003ffd // log(1/frcpa(1+144/2^-8))
|
|
data8 0xe6589852e75d7df6 , 0x00003ffd // log(1/frcpa(1+145/2^-8))
|
|
//
|
|
data8 0xe786068c79937a7d , 0x00003ffd // log(1/frcpa(1+146/2^-8))
|
|
data8 0xe91903adad100911 , 0x00003ffd // log(1/frcpa(1+147/2^-8))
|
|
data8 0xea481236f7d35bb0 , 0x00003ffd // log(1/frcpa(1+148/2^-8))
|
|
data8 0xeb77d48c692e6b14 , 0x00003ffd // log(1/frcpa(1+149/2^-8))
|
|
data8 0xeca84b83d7297b87 , 0x00003ffd // log(1/frcpa(1+150/2^-8))
|
|
//
|
|
data8 0xedd977f4962aa158 , 0x00003ffd // log(1/frcpa(1+151/2^-8))
|
|
data8 0xef7179a22f257754 , 0x00003ffd // log(1/frcpa(1+152/2^-8))
|
|
data8 0xf0a450d139366ca7 , 0x00003ffd // log(1/frcpa(1+153/2^-8))
|
|
data8 0xf1d7e0524ff9ffdb , 0x00003ffd // log(1/frcpa(1+154/2^-8))
|
|
data8 0xf30c29036a8b6cae , 0x00003ffd // log(1/frcpa(1+155/2^-8))
|
|
//
|
|
data8 0xf4412bc411ea8d92 , 0x00003ffd // log(1/frcpa(1+156/2^-8))
|
|
data8 0xf576e97564c8619d , 0x00003ffd // log(1/frcpa(1+157/2^-8))
|
|
data8 0xf6ad62fa1b5f172f , 0x00003ffd // log(1/frcpa(1+158/2^-8))
|
|
data8 0xf7e499368b55c542 , 0x00003ffd // log(1/frcpa(1+159/2^-8))
|
|
data8 0xf91c8d10abaffe22 , 0x00003ffd // log(1/frcpa(1+160/2^-8))
|
|
//
|
|
data8 0xfa553f7018c966f3 , 0x00003ffd // log(1/frcpa(1+161/2^-8))
|
|
data8 0xfb8eb13e185d802c , 0x00003ffd // log(1/frcpa(1+162/2^-8))
|
|
data8 0xfcc8e3659d9bcbed , 0x00003ffd // log(1/frcpa(1+163/2^-8))
|
|
data8 0xfe03d6d34d487fd2 , 0x00003ffd // log(1/frcpa(1+164/2^-8))
|
|
data8 0xff3f8c7581e9f0ae , 0x00003ffd // log(1/frcpa(1+165/2^-8))
|
|
//
|
|
data8 0x803e029e280173ae , 0x00003ffe // log(1/frcpa(1+166/2^-8))
|
|
data8 0x80dca10cc52d0757 , 0x00003ffe // log(1/frcpa(1+167/2^-8))
|
|
data8 0x817ba200632755a1 , 0x00003ffe // log(1/frcpa(1+168/2^-8))
|
|
data8 0x821b05f3b01d6774 , 0x00003ffe // log(1/frcpa(1+169/2^-8))
|
|
data8 0x82bacd623ff19d06 , 0x00003ffe // log(1/frcpa(1+170/2^-8))
|
|
//
|
|
data8 0x835af8c88e7a8f47 , 0x00003ffe // log(1/frcpa(1+171/2^-8))
|
|
data8 0x83c5f8299e2b4091 , 0x00003ffe // log(1/frcpa(1+172/2^-8))
|
|
data8 0x8466cb43f3d87300 , 0x00003ffe // log(1/frcpa(1+173/2^-8))
|
|
data8 0x850803a67c80ca4b , 0x00003ffe // log(1/frcpa(1+174/2^-8))
|
|
data8 0x85a9a1d11a23b461 , 0x00003ffe // log(1/frcpa(1+175/2^-8))
|
|
//
|
|
data8 0x864ba644a18e6e05 , 0x00003ffe // log(1/frcpa(1+176/2^-8))
|
|
data8 0x86ee1182dcc432f7 , 0x00003ffe // log(1/frcpa(1+177/2^-8))
|
|
data8 0x875a925d7e48c316 , 0x00003ffe // log(1/frcpa(1+178/2^-8))
|
|
data8 0x87fdaa109d23aef7 , 0x00003ffe // log(1/frcpa(1+179/2^-8))
|
|
data8 0x88a129ed4becfaf2 , 0x00003ffe // log(1/frcpa(1+180/2^-8))
|
|
//
|
|
data8 0x89451278ecd7f9cf , 0x00003ffe // log(1/frcpa(1+181/2^-8))
|
|
data8 0x89b29295f8432617 , 0x00003ffe // log(1/frcpa(1+182/2^-8))
|
|
data8 0x8a572ac5a5496882 , 0x00003ffe // log(1/frcpa(1+183/2^-8))
|
|
data8 0x8afc2d0ce3b2dadf , 0x00003ffe // log(1/frcpa(1+184/2^-8))
|
|
data8 0x8b6a69c608cfd3af , 0x00003ffe // log(1/frcpa(1+185/2^-8))
|
|
//
|
|
data8 0x8c101e106e899a83 , 0x00003ffe // log(1/frcpa(1+186/2^-8))
|
|
data8 0x8cb63de258f9d626 , 0x00003ffe // log(1/frcpa(1+187/2^-8))
|
|
data8 0x8d2539c5bd19e2b1 , 0x00003ffe // log(1/frcpa(1+188/2^-8))
|
|
data8 0x8dcc0e064b29e6f1 , 0x00003ffe // log(1/frcpa(1+189/2^-8))
|
|
data8 0x8e734f45d88357ae , 0x00003ffe // log(1/frcpa(1+190/2^-8))
|
|
//
|
|
data8 0x8ee30cef034a20db , 0x00003ffe // log(1/frcpa(1+191/2^-8))
|
|
data8 0x8f8b0515686d1d06 , 0x00003ffe // log(1/frcpa(1+192/2^-8))
|
|
data8 0x90336bba039bf32f , 0x00003ffe // log(1/frcpa(1+193/2^-8))
|
|
data8 0x90a3edd23d1c9d58 , 0x00003ffe // log(1/frcpa(1+194/2^-8))
|
|
data8 0x914d0de2f5d61b32 , 0x00003ffe // log(1/frcpa(1+195/2^-8))
|
|
//
|
|
data8 0x91be0c20d28173b5 , 0x00003ffe // log(1/frcpa(1+196/2^-8))
|
|
data8 0x9267e737c06cd34a , 0x00003ffe // log(1/frcpa(1+197/2^-8))
|
|
data8 0x92d962ae6abb1237 , 0x00003ffe // log(1/frcpa(1+198/2^-8))
|
|
data8 0x9383fa6afbe2074c , 0x00003ffe // log(1/frcpa(1+199/2^-8))
|
|
data8 0x942f0421651c1c4e , 0x00003ffe // log(1/frcpa(1+200/2^-8))
|
|
//
|
|
data8 0x94a14a3845bb985e , 0x00003ffe // log(1/frcpa(1+201/2^-8))
|
|
data8 0x954d133857f861e7 , 0x00003ffe // log(1/frcpa(1+202/2^-8))
|
|
data8 0x95bfd96468e604c4 , 0x00003ffe // log(1/frcpa(1+203/2^-8))
|
|
data8 0x9632d31cafafa858 , 0x00003ffe // log(1/frcpa(1+204/2^-8))
|
|
data8 0x96dfaabd86fa1647 , 0x00003ffe // log(1/frcpa(1+205/2^-8))
|
|
//
|
|
data8 0x9753261fcbb2a594 , 0x00003ffe // log(1/frcpa(1+206/2^-8))
|
|
data8 0x9800c11b426b996d , 0x00003ffe // log(1/frcpa(1+207/2^-8))
|
|
data8 0x9874bf4d45ae663c , 0x00003ffe // log(1/frcpa(1+208/2^-8))
|
|
data8 0x99231f5ee9a74f79 , 0x00003ffe // log(1/frcpa(1+209/2^-8))
|
|
data8 0x9997a18a56bcad28 , 0x00003ffe // log(1/frcpa(1+210/2^-8))
|
|
//
|
|
data8 0x9a46c873a3267e79 , 0x00003ffe // log(1/frcpa(1+211/2^-8))
|
|
data8 0x9abbcfc621eb6cb6 , 0x00003ffe // log(1/frcpa(1+212/2^-8))
|
|
data8 0x9b310cb0d354c990 , 0x00003ffe // log(1/frcpa(1+213/2^-8))
|
|
data8 0x9be14cf9e1b3515c , 0x00003ffe // log(1/frcpa(1+214/2^-8))
|
|
data8 0x9c5710b8cbb73a43 , 0x00003ffe // log(1/frcpa(1+215/2^-8))
|
|
//
|
|
data8 0x9ccd0abd301f399c , 0x00003ffe // log(1/frcpa(1+216/2^-8))
|
|
data8 0x9d7e67f3bdce8888 , 0x00003ffe // log(1/frcpa(1+217/2^-8))
|
|
data8 0x9df4ea81a99daa01 , 0x00003ffe // log(1/frcpa(1+218/2^-8))
|
|
data8 0x9e6ba405a54514ba , 0x00003ffe // log(1/frcpa(1+219/2^-8))
|
|
data8 0x9f1e21c8c7bb62b3 , 0x00003ffe // log(1/frcpa(1+220/2^-8))
|
|
//
|
|
data8 0x9f956593f6b6355c , 0x00003ffe // log(1/frcpa(1+221/2^-8))
|
|
data8 0xa00ce1092e5498c3 , 0x00003ffe // log(1/frcpa(1+222/2^-8))
|
|
data8 0xa0c08309c4b912c1 , 0x00003ffe // log(1/frcpa(1+223/2^-8))
|
|
data8 0xa1388a8c6faa2afa , 0x00003ffe // log(1/frcpa(1+224/2^-8))
|
|
data8 0xa1b0ca7095b5f985 , 0x00003ffe // log(1/frcpa(1+225/2^-8))
|
|
//
|
|
data8 0xa22942eb47534a00 , 0x00003ffe // log(1/frcpa(1+226/2^-8))
|
|
data8 0xa2de62326449d0a3 , 0x00003ffe // log(1/frcpa(1+227/2^-8))
|
|
data8 0xa357690f88bfe345 , 0x00003ffe // log(1/frcpa(1+228/2^-8))
|
|
data8 0xa3d0a93f45169a4b , 0x00003ffe // log(1/frcpa(1+229/2^-8))
|
|
data8 0xa44a22f7ffe65f30 , 0x00003ffe // log(1/frcpa(1+230/2^-8))
|
|
//
|
|
data8 0xa500c5e5b4c1aa36 , 0x00003ffe // log(1/frcpa(1+231/2^-8))
|
|
data8 0xa57ad064eb2ebbc2 , 0x00003ffe // log(1/frcpa(1+232/2^-8))
|
|
data8 0xa5f5152dedf4384e , 0x00003ffe // log(1/frcpa(1+233/2^-8))
|
|
data8 0xa66f9478856233ec , 0x00003ffe // log(1/frcpa(1+234/2^-8))
|
|
data8 0xa6ea4e7cca02c32e , 0x00003ffe // log(1/frcpa(1+235/2^-8))
|
|
//
|
|
data8 0xa765437325341ccf , 0x00003ffe // log(1/frcpa(1+236/2^-8))
|
|
data8 0xa81e21e6c75b4020 , 0x00003ffe // log(1/frcpa(1+237/2^-8))
|
|
data8 0xa899ab333fe2b9ca , 0x00003ffe // log(1/frcpa(1+238/2^-8))
|
|
data8 0xa9157039c51ebe71 , 0x00003ffe // log(1/frcpa(1+239/2^-8))
|
|
data8 0xa991713433c2b999 , 0x00003ffe // log(1/frcpa(1+240/2^-8))
|
|
//
|
|
data8 0xaa0dae5cbcc048b3 , 0x00003ffe // log(1/frcpa(1+241/2^-8))
|
|
data8 0xaa8a27ede5eb13ad , 0x00003ffe // log(1/frcpa(1+242/2^-8))
|
|
data8 0xab06de228a9e3499 , 0x00003ffe // log(1/frcpa(1+243/2^-8))
|
|
data8 0xab83d135dc633301 , 0x00003ffe // log(1/frcpa(1+244/2^-8))
|
|
data8 0xac3fb076adc7fe7a , 0x00003ffe // log(1/frcpa(1+245/2^-8))
|
|
//
|
|
data8 0xacbd3cbbe47988f1 , 0x00003ffe // log(1/frcpa(1+246/2^-8))
|
|
data8 0xad3b06b1a5dc57c3 , 0x00003ffe // log(1/frcpa(1+247/2^-8))
|
|
data8 0xadb90e94af887717 , 0x00003ffe // log(1/frcpa(1+248/2^-8))
|
|
data8 0xae3754a218f7c816 , 0x00003ffe // log(1/frcpa(1+249/2^-8))
|
|
data8 0xaeb5d9175437afa2 , 0x00003ffe // log(1/frcpa(1+250/2^-8))
|
|
//
|
|
data8 0xaf349c322e9c7cee , 0x00003ffe // log(1/frcpa(1+251/2^-8))
|
|
data8 0xafb39e30d1768d1c , 0x00003ffe // log(1/frcpa(1+252/2^-8))
|
|
data8 0xb032df51c2c93116 , 0x00003ffe // log(1/frcpa(1+253/2^-8))
|
|
data8 0xb0b25fd3e6035ad9 , 0x00003ffe // log(1/frcpa(1+254/2^-8))
|
|
data8 0xb1321ff67cba178c , 0x00003ffe // log(1/frcpa(1+255/2^-8))
|
|
LOCAL_OBJECT_END(log_table_3)
|
|
|
|
|
|
.section .text
|
|
GLOBAL_LIBM_ENTRY(asinh)
|
|
|
|
{ .mfi
|
|
getf.exp asinh_GR_f8 = f8 // Must recompute later if x unorm
|
|
fclass.m p12,p0 = f8, 0x0b // Test x unorm
|
|
mov log_GR_exp_17_ones = 0x1ffff
|
|
}
|
|
{ .mfi
|
|
addl NR_table_address = @ltoff(log_table_1), gp
|
|
fma.s1 log_y = f8, f8, f1 // y = x^2 + 1
|
|
mov asinh_GR_comp = 0xfffc
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
mov log_GR_exp_16_ones = 0xffff //BIAS
|
|
fclass.m p6,p0 = f8, 0xe7 // Test for x = NaN and inf and zero
|
|
mov log_GR_comp2 = 0x1003e
|
|
}
|
|
{ .mfi
|
|
ld8 NR_table_address = [NR_table_address]
|
|
fma.s1 asinh_w_sq = f8,f8,f0 // x^2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fcmp.lt.s1 p7,p11 = f8,f0 // if x<0
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
fnorm.s1 fNormX = f8 // Normalize x
|
|
(p12) br.cond.spnt ASINH_UNORM // Branch if x=unorm
|
|
}
|
|
;;
|
|
|
|
ASINH_COMMON:
|
|
// Return here if x=unorm and not denorm
|
|
{ .mfi
|
|
//to get second table address
|
|
adds log_table_address2 = 0x40, NR_table_address
|
|
fma.s1 log_arg = f8,f1,f8
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p6) fma.d.s0 f8 = f8,f1,f8 // quietize nan result if x=nan
|
|
(p6) br.ret.spnt b0 // Exit for x=nan and inf and zero
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfpd NR1,NR2 = [log_table_address2],16
|
|
frsqrta.s1 log_y_rs,p0 = log_y // z=1/sqrt(y)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfe log_C13 = [log_table_address2],16
|
|
nop.f 0
|
|
and asinh_GR_f8 = asinh_GR_f8,log_GR_exp_17_ones
|
|
}
|
|
;;
|
|
|
|
{ .mib
|
|
ldfe log_C11 = [log_table_address2],16
|
|
cmp.le p13,p0 = log_GR_comp2,asinh_GR_f8
|
|
(p13) br.cond.spnt LOG_COMMON1 // Branch if path 4, |x| >= 2^63
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_y_rs_iter = log_y_rs,log_y,f0 // y*z
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
.pred.rel "mutex",p7,p11
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) mov asinh_f8 = fNormX
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
cmp.gt p8,p0 = asinh_GR_comp,asinh_GR_f8
|
|
(p7) fnma.s1 asinh_f8 = fNormX,f1,f0
|
|
(p8) br.cond.spnt ASINH_NEAR_ZERO // Branch if path 2, 0 < |x| < 2^-3
|
|
}
|
|
;;
|
|
|
|
// Here if main path, 2^-3 <= |x| < 2^63
|
|
///////////////////////////////// The first iteration /////////////////////////
|
|
{ .mfi
|
|
ldfpd log_P5,log_P4 = [NR_table_address],16
|
|
fnma.s1 log_y_rs_iter = log_y_rs_iter,log_y_rs,NR2 // 3-(y*z)*z
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_y_rs_iter1 = log_y_rs,NR1,f0 // 0.5*z
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfpd log_P3,log_P2 = [NR_table_address],16
|
|
// (0.5*z)*(3-(y*z)*z)
|
|
fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs_iter,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
/////////////////////////// The second iteration /////////////////////////////
|
|
{ .mfi
|
|
ldfd log_P1 = [NR_table_address],16
|
|
fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfe log2 = [NR_table_address],16
|
|
// (0.5*z)*(3-(y*z)*z)
|
|
fma.s1 log_y_rs_iter = log_y_rs_iter1,log_y_rs,f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// (0.5*z)*(3-(y*z)*z)
|
|
fma.s1 log_arg_early = log_y_rs_iter1,log_y_rs,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
////////////////////////////////// The third iteration ////////////////////////
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_y_rs = log_y_rs_iter,log_y,f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_y_rs_iter1 = log_y_rs_iter,NR1,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_arg_early = log_arg_early,log_y,asinh_f8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fnma.s1 log_y_rs = log_y_rs,log_y_rs_iter,NR2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_y_rs_iter1 = log_y_rs_iter1,log_y,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
frcpa.s1 log_C,p0 = f1,log_arg_early
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
getf.exp log_GR_signexp_f8 = log_arg_early
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
getf.sig log_GR_significand_f8 = log_arg_early
|
|
// (0.5*z)*(3-(y*z)*z)*y + |x|
|
|
fma.s1 log_arg = log_y_rs_iter1,log_y_rs,asinh_f8
|
|
//to get third table address
|
|
adds log_table_address3 = 0x70, NR_table_address
|
|
}
|
|
;;
|
|
|
|
///////////////////////////////// The end NR iterations /////////////////////
|
|
{ .mfi
|
|
nop.m 0
|
|
nop.f 0
|
|
//significant bit destruction
|
|
and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
//BIAS subtraction
|
|
sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
|
|
(p7) fnma.s1 log2 = log2,f1,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
setf.sig log_int_Nfloat = log_GR_true_exp_f8
|
|
fms.s1 log_r = log_C,log_arg,f1 // C = frcpa(x); r = C * x - 1
|
|
extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
//pre-index*16 + index
|
|
shladd log_table_address3 = log_GR_index,4,log_table_address3
|
|
;;
|
|
ldfe log_T = [log_table_address3]
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_rsq = log_r, log_r, f0 //r^2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_rp_p4 = log_P5, log_r, log_P4 //P5*r + P4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
//convert N to the floating-point format
|
|
fcvt.xf log_Nfloat = log_int_Nfloat
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_rcube = log_rsq, log_r, f0 //r^3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_rp_p10 = log_rsq, log_P1, log_r //P1*r^2 + r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
//(P5*r + P4)*r^2 + P3*r + P2
|
|
fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
.pred.rel "mutex",p7,p11
|
|
{ .mfi
|
|
nop.m 0
|
|
(p11) fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T if x>0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fms.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 - T if x<0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
//((P5*r + P4)*r^2 + P3*r + P2)*w^3 + P1*r^2 + r
|
|
fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
// N*log2 + T + ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
|
|
(p11) fadd.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
// -N*log2 - T - ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
|
|
(p7) fsub.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
|
|
br.ret.sptk b0 // Exit main path, path 3: 2^-3 <= |x| < 2^63
|
|
}
|
|
;;
|
|
|
|
// Here if path 4, |x| >= 2^63
|
|
LOG_COMMON1:
|
|
{ .mfi
|
|
ldfpd log_P5,log_P4 = [NR_table_address],16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfpd log_P3,log_P2 = [NR_table_address],16
|
|
frcpa.s1 log_C,p0 = f1,log_arg
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
getf.exp log_GR_signexp_f8 = log_arg
|
|
ldfd log_P1 = [NR_table_address],16
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
getf.sig log_GR_significand_f8 = log_arg
|
|
ldfe log2 = [NR_table_address],16
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
adds log_table_address3 = 0x70, NR_table_address
|
|
nop.f 0
|
|
//significant bit destruction
|
|
and log_GR_exp_f8 = log_GR_signexp_f8, log_GR_exp_17_ones
|
|
}
|
|
;;
|
|
|
|
{ .mmf
|
|
nop.m 0
|
|
//BIAS subtraction
|
|
sub log_GR_true_exp_f8 = log_GR_exp_f8, log_GR_exp_16_ones
|
|
fms.s1 log_r = log_C,log_arg,f1 //C = frcpa(x); r = C * x - 1
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
setf.sig log_int_Nfloat = log_GR_true_exp_f8
|
|
nop.f 0
|
|
extr.u log_GR_index = log_GR_significand_f8,55,8 //Extract 8 bits
|
|
}
|
|
;;
|
|
|
|
{ .mmi
|
|
//pre-index*16 + index
|
|
shladd log_table_address3 = log_GR_index,4,log_table_address3
|
|
;;
|
|
ldfe log_T = [log_table_address3]
|
|
nop.i 0
|
|
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_rsq = log_r, log_r, f0 //r^2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_rp_p4 = log_P5, log_r, log_P4 //P5*r + P4
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_rp_p32 = log_P3, log_r, log_P2 //P3*r + P2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fnma.s1 log2 = log2,f1,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_rcube = log_rsq, log_r, f0 //r^3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_rp_p10 = log_rsq, log_P1, log_r //P1*r^2 + r
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
//convert N to the floating-point format
|
|
fcvt.xf log_Nfloat = log_int_Nfloat
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
//(P5*r + P4)*r^2 + P3*r + P2
|
|
fma.s1 log_rp_p2 = log_rp_p4, log_rsq, log_rp_p32
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fnma.s1 log_T = log_T,f1,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 log_T_plus_Nlog2 = log_Nfloat,log2,log_T //N*log2 + T
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
//((P5*r + P4)*r^2 + P3*r + P2)*w^3 + P1*r^2 + r
|
|
fma.s1 log_r2P_r = log_rp_p2, log_rcube, log_rp_p10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
.pred.rel "mutex",p7,p11
|
|
{ .mfi
|
|
nop.m 0
|
|
// N*log2 + T + ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
|
|
(p11) fadd.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
// -N*log2 - T - ((P5*r + P4)*r^2 + P3*r + P2)*r^3 + P1*r^2 + r
|
|
(p7) fsub.d.s0 f8 = log_T_plus_Nlog2,log_r2P_r
|
|
br.ret.sptk b0 // Exit path 4, |x| >= 2^63
|
|
}
|
|
;;
|
|
|
|
// Here is path 2, 0 < |x| < 2^-3
|
|
ASINH_NEAR_ZERO:
|
|
{ .mfi
|
|
ldfe log_C9 = [log_table_address2],16
|
|
fma.s1 asinh_w_cube = asinh_w_sq,fNormX,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfe log_C7 = [log_table_address2],16
|
|
fma.s1 asinh_w_four = asinh_w_sq,asinh_w_sq,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfe log_C5 = [log_table_address2],16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfe log_C3 = [log_table_address2],16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 asinh_w_13 = log_C13,asinh_w_sq,log_C11
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 asinh_w_9 = log_C9,asinh_w_sq,log_C7
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 asinh_w_3 = log_C5,asinh_w_sq,log_C3
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 asinh_w_seven = asinh_w_four,asinh_w_cube,f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 asinh_w_7 = asinh_w_13,asinh_w_four,asinh_w_9
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 asinh_w_5 = asinh_w_3,asinh_w_cube,fNormX
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
fma.d.s0 f8 = asinh_w_7,asinh_w_seven,asinh_w_5
|
|
br.ret.sptk b0 // Exit path 2 (0.0 <|x| < 2^(-3))
|
|
}
|
|
;;
|
|
|
|
ASINH_UNORM:
|
|
// Here if x=unorm
|
|
{ .mfi
|
|
getf.exp asinh_GR_f8 = fNormX // Recompute if x unorm
|
|
fclass.m p0,p13 = fNormX, 0x0b // Test x denorm
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
fcmp.eq.s0 p14,p0 = f8, f0 // Dummy to set denormal flag
|
|
(p13) br.cond.sptk ASINH_COMMON // Continue if x unorm and not denorm
|
|
}
|
|
;;
|
|
|
|
.pred.rel "mutex",p7,p11
|
|
{ .mfi
|
|
nop.m 0
|
|
(p7) fma.d.s0 f8 = f8,f8,f8 // Result x+x^2 if x=-denorm
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p11) fnma.d.s0 f8 = f8,f8,f8 // Result x-x^2 if x=+denorm
|
|
br.ret.spnt b0 // Exit if denorm
|
|
}
|
|
;;
|
|
|
|
GLOBAL_LIBM_END(asinh)
|
|
libm_alias_double_other (asinh, asinh)
|