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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>
981 lines
29 KiB
ArmAsm
981 lines
29 KiB
ArmAsm
.file "erfcf.s"
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// Copyright (c) 2002 - 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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// History
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//==============================================================
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// 01/17/02 Initial version
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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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// 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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// float erfcf(float)
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//
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// Overview of operation
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//==============================================================
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// 1. 0 <= x <= 10.06
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//
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// erfcf(x) = P15(x) * exp( -x^2 )
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//
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// Comment:
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//
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// Let x(0)=0, x(i) = 2^(i), i=1,...3, x(4)= 10.06
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//
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// Let x(i)<= x < x(i+1).
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// We can find i as exponent of argument x (let i = 0 for 0<= x < 2 )
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//
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// Let P15(x) - polynomial approximation of degree 15 for function
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// erfcf(x) * exp( x^2) and x(i) <= x <= x(i+1), i = 0,1,2,3
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// Polynomial coefficients we have in the table erfc_p_table.
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//
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// So we can find result for erfcf(x) as above.
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// Algorithm description for exp function see below.
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//
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// 2. -4.4 <= x < 0
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//
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// erfcf(x) = 2.0 - erfcf(-x)
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//
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// 3. x > 10.06
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//
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// erfcf(x) ~=~ 0.0
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//
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// 4. x < -4.4
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//
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// erfcf(x) ~=~ 2.0
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// Special values
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//==============================================================
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// erfcf(+0) = 1.0
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// erfcf(-0) = 1.0
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// erfcf(+qnan) = +qnan
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// erfcf(-qnan) = -qnan
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// erfcf(+snan) = +qnan
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// erfcf(-snan) = -qnan
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// erfcf(-inf) = 2.0
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// erfcf(+inf) = +0
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//==============================================================
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// Take double exp(double) from libm_64.
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//
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// Overview of operation
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//==============================================================
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// Take the input x. w is "how many log2/128 in x?"
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// w = x * 128/log2
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// n = int(w)
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// x = n log2/128 + r + delta
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// n = 128M + index_1 + 2^4 index_2
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// x = M log2 + (log2/128) index_1 + (log2/8) index_2 + r + delta
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// exp(x) = 2^M 2^(index_1/128) 2^(index_2/8) exp(r) exp(delta)
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// Construct 2^M
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// Get 2^(index_1/128) from table_1;
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// Get 2^(index_2/8) from table_2;
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// Calculate exp(r) by series
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// r = x - n (log2/128)_high
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// delta = - n (log2/128)_low
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// Calculate exp(delta) as 1 + delta
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//
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// Comment for erfcf:
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//
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// Let exp(r) = 1 + x + 0.5*x^2 + (1/6)*x^3
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// Let delta = 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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// f6,f7,f9 -> f11, f32 -> f92
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// General registers used:
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// r14 -> r22,r32 -> r50
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// Predicate registers used:
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// p6 -> p15
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// Assembly macros
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//==============================================================
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EXP_AD_TB1 = r14
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exp_GR_sig_inv_ln2 = r15
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exp_TB1_size = r16
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exp_GR_rshf_2to56 = r17
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exp_GR_exp_2tom56 = r18
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exp_GR_rshf = r33
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EXP_AD_TB2 = r34
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EXP_AD_P = r35
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exp_GR_N = r36
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exp_GR_index_1 = r37
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exp_GR_index_2_16 = r38
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exp_GR_biased_M = r39
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EXP_AD_T1 = r40
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EXP_AD_T2 = r41
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exp_TB2_size = r42
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// GR for erfcf(x)
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//==============================================================
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GR_IndxPlusBias = r19
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GR_ExpMask = r20
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GR_BIAS = r21
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GR_ShftPi_bias = r22
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GR_P_POINT_1 = r43
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GR_P_POINT_2 = r44
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GR_P_POINT_3 = r45
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GR_P_POINT_4 = r46
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GR_ShftPi = r47
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GR_EpsNorm = r48
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GR_05 = r49
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GR_1_by_6 = r50
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// GR for __libm_support call
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//==============================================================
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GR_SAVE_B0 = r43
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GR_SAVE_PFS = r44
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GR_SAVE_GP = r45
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GR_SAVE_SP = r46
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GR_Parameter_X = r47
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GR_Parameter_Y = r48
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GR_Parameter_RESULT = r49
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GR_Parameter_TAG = r50
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// FR for exp(-x^2)
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//==============================================================
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FR_X = f10
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FR_Y = f1
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FR_RESULT = f8
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EXP_2TOM56 = f6
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EXP_INV_LN2_2TO63 = f7
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EXP_W_2TO56_RSH = f9
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exp_ln2_by_128_hi = f11
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EXP_RSHF_2TO56 = f32
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exp_ln2_by_128_lo = f33
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EXP_RSHF = f34
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EXP_Nfloat = f35
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exp_r = f36
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exp_rsq = f37
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EXP_2M = f38
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exp_S1 = f39
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exp_T1 = f40
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exp_P = f41
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exp_S = f42
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EXP_NORM_f8 = f43
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exp_S2 = f44
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exp_T2 = f45
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// FR for erfcf(x)
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//==============================================================
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FR_AbsArg = f46
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FR_Tmp = f47
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FR_Tmp1 = f48
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FR_Tmpf = f49
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FR_NormX = f50
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FR_A15 = f51
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FR_A14 = f52
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FR_A13 = f53
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FR_A12 = f54
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FR_A11 = f55
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FR_A10 = f56
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FR_A9 = f57
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FR_A8 = f58
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FR_A7 = f59
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FR_A6 = f60
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FR_A5 = f61
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FR_A4 = f62
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FR_A3 = f63
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FR_A2 = f64
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FR_A1 = f65
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FR_A0 = f66
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FR_P15_0_1 = f67
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FR_P15_1_1 = f68
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FR_P15_1_2 = f69
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FR_P15_2_1 = f70
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FR_P15_2_2 = f71
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FR_P15_3_1 = f72
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FR_P15_3_2 = f73
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FR_P15_4_1 = f74
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FR_P15_4_2 = f75
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FR_P15_7_1 = f76
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FR_P15_7_2 = f77
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FR_P15_8_1 = f78
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FR_P15_9_1 = f79
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FR_P15_9_2 = f80
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FR_P15_13_1 = f81
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FR_P15_14_1 = f82
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FR_P15_14_2 = f83
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FR_2 = f84
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FR_05 = f85
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FR_1_by_6 = f86
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FR_Pol = f87
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FR_Exp = f88
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FR_POS_ARG_ASYMP = f89
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FR_NEG_ARG_ASYMP = f90
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FR_UnfBound = f91
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FR_EpsNorm = f92
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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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// ************* DO NOT CHANGE ORDER OF THESE TABLES ********************
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// double-extended 1/ln(2)
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// 3fff b8aa 3b29 5c17 f0bb be87fed0691d3e88
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// 3fff b8aa 3b29 5c17 f0bc
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// For speed the significand will be loaded directly with a movl and setf.sig
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// and the exponent will be bias+63 instead of bias+0. Thus subsequent
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// computations need to scale appropriately.
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// The constant 128/ln(2) is needed for the computation of w. This is also
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// obtained by scaling the computations.
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//
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// Two shifting constants are loaded directly with movl and setf.d.
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// 1. EXP_RSHF_2TO56 = 1.1000..00 * 2^(63-7)
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// This constant is added to x*1/ln2 to shift the integer part of
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// x*128/ln2 into the rightmost bits of the significand.
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// The result of this fma is EXP_W_2TO56_RSH.
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// 2. EXP_RSHF = 1.1000..00 * 2^(63)
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// This constant is subtracted from EXP_W_2TO56_RSH * 2^(-56) to give
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// the integer part of w, n, as a floating-point number.
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// The result of this fms is EXP_Nfloat.
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LOCAL_OBJECT_START(exp_table_1)
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data4 0x4120f5c3, 0x408ccccd //POS_ARG_ASYMP = 10.06, NEG_ARG_ASYMP = 4.4
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data4 0x41131Cdf, 0x00800000 //UnfBound ~=~ 9.1, EpsNorm ~=~ 1.1754944e-38
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//
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data8 0xb17217f7d1cf79ab , 0x00003ff7 // ln2/128 hi
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data8 0xc9e3b39803f2f6af , 0x00003fb7 // ln2/128 lo
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//
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// Table 1 is 2^(index_1/128) where
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// index_1 goes from 0 to 15
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//
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data8 0x8000000000000000 , 0x00003FFF
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data8 0x80B1ED4FD999AB6C , 0x00003FFF
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data8 0x8164D1F3BC030773 , 0x00003FFF
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data8 0x8218AF4373FC25EC , 0x00003FFF
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data8 0x82CD8698AC2BA1D7 , 0x00003FFF
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data8 0x8383594EEFB6EE37 , 0x00003FFF
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data8 0x843A28C3ACDE4046 , 0x00003FFF
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data8 0x84F1F656379C1A29 , 0x00003FFF
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data8 0x85AAC367CC487B15 , 0x00003FFF
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data8 0x8664915B923FBA04 , 0x00003FFF
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data8 0x871F61969E8D1010 , 0x00003FFF
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data8 0x87DB357FF698D792 , 0x00003FFF
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data8 0x88980E8092DA8527 , 0x00003FFF
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data8 0x8955EE03618E5FDD , 0x00003FFF
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data8 0x8A14D575496EFD9A , 0x00003FFF
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data8 0x8AD4C6452C728924 , 0x00003FFF
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LOCAL_OBJECT_END(exp_table_1)
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// Table 2 is 2^(index_1/8) where
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// index_2 goes from 0 to 7
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LOCAL_OBJECT_START(exp_table_2)
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data8 0x8000000000000000 , 0x00003FFF
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data8 0x8B95C1E3EA8BD6E7 , 0x00003FFF
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data8 0x9837F0518DB8A96F , 0x00003FFF
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data8 0xA5FED6A9B15138EA , 0x00003FFF
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data8 0xB504F333F9DE6484 , 0x00003FFF
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data8 0xC5672A115506DADD , 0x00003FFF
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data8 0xD744FCCAD69D6AF4 , 0x00003FFF
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data8 0xEAC0C6E7DD24392F , 0x00003FFF
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LOCAL_OBJECT_END(exp_table_2)
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LOCAL_OBJECT_START(erfc_p_table)
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// Pol_0
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data8 0xBEA3260C63CB0446 //A15 = -5.70673541831883454676e-07
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data8 0x3EE63D6178077654 //A14 = +1.06047480138940182343e-05
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data8 0xBF18646BC5FC70A7 //A13 = -9.30491237309283694347e-05
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data8 0x3F40F92F909117FE //A12 = +5.17986512144075019133e-04
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data8 0xBF611344289DE1E6 //A11 = -2.08438217390159994419e-03
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data8 0x3F7AF9FE6AD16DC0 //A10 = +6.58606893292862351928e-03
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data8 0xBF91D219E196CBA7 //A9 = -1.74030345858217321001e-02
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data8 0x3FA4AFDDA355854C //A8 = +4.04042493708041968315e-02
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data8 0xBFB5D465BB7025AE //A7 = -8.52721769916999425445e-02
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data8 0x3FC54C15A95B717D //A6 = +1.66384418195672549029e-01
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data8 0xBFD340A75B4B1AB5 //A5 = -3.00821150926292166899e-01
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data8 0x3FDFFFC0BFCD247F //A4 = +4.99984919839853542841e-01
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data8 0xBFE81270C361852B //A3 = -7.52251035312075583309e-01
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data8 0x3FEFFFFFC67295FC //A2 = +9.99999892800303301771e-01
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data8 0xBFF20DD74F8CD2BF //A1 = -1.12837916445020868099e+00
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data8 0x3FEFFFFFFFFE7C1D //A0 = +9.99999999988975570714e-01
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// Pol_1
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data8 0xBDE8EC4BDD953B56 //A15 = -1.81338928934942767144e-10
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data8 0x3E43607F269E2A1C //A14 = +9.02309090272196442358e-09
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data8 0xBE8C4D9E69C10E02 //A13 = -2.10875261143659275328e-07
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data8 0x3EC9CF2F84566725 //A12 = +3.07671055805877356583e-06
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data8 0xBF007980B1B46A4D //A11 = -3.14228438702169818945e-05
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data8 0x3F2F4C3AD6DEF24A //A10 = +2.38783056770846320260e-04
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data8 0xBF56F5129F8D30FA //A9 = -1.40120333363130546426e-03
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data8 0x3F7AA6C7ABFC38EE //A8 = +6.50671002200751820429e-03
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data8 0xBF98E7522CB84BEF //A7 = -2.43199195666185511109e-02
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data8 0x3FB2F68EB1C3D073 //A6 = +7.40746673580490638637e-02
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data8 0xBFC7C16055AC6385 //A5 = -1.85588876564704611769e-01
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data8 0x3FD8A707AEF5A440 //A4 = +3.85194702967570635211e-01
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data8 0xBFE547BFE39AE2EA //A3 = -6.65008492032112467310e-01
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data8 0x3FEE7C91BDF13578 //A2 = +9.52706213932898128515e-01
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data8 0xBFF1CB5B61F8C589 //A1 = -1.11214769621105541214e+00
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data8 0x3FEFEA56BC81FD37 //A0 = +9.97355812243688815239e-01
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// Pol_2
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data8 0xBD302724A12F46E0 //A15 = -5.73866382814058809406e-14
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data8 0x3D98889B75D3102E //A14 = +5.57829983681360947356e-12
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data8 0xBDF16EA15074A1E9 //A13 = -2.53671153922423457844e-10
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data8 0x3E3EC6E688CFEE5F //A12 = +7.16581828336436419561e-09
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data8 0xBE82E5ED44C52609 //A11 = -1.40802202239825487803e-07
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data8 0x3EC120BE5CE42353 //A10 = +2.04180535157522081699e-06
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data8 0xBEF7B8B0311A1911 //A9 = -2.26225266204633600888e-05
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data8 0x3F29A281F43FC238 //A8 = +1.95577968156184077632e-04
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data8 0xBF55E19858B3B7A4 //A7 = -1.33552434527526534043e-03
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data8 0x3F7DAC8C3D12E5FD //A6 = +7.24463253680473816303e-03
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data8 0xBF9FF9C04613FB47 //A5 = -3.12261622211693854028e-02
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data8 0x3FBB3D5DBF9D9366 //A4 = +1.06405123978743883370e-01
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data8 0xBFD224DE9F62C258 //A3 = -2.83500342989133623476e-01
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data8 0x3FE28A95CB8C6D3E //A2 = +5.79417131000276437708e-01
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data8 0xBFEC21205D358672 //A1 = -8.79043752717008257224e-01
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data8 0x3FEDAE44D5EDFE5B //A0 = +9.27523057776805771830e-01
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// Pol_3
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data8 0xBCA3BCA734AC82F1 //A15 = -1.36952437983096410260e-16
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data8 0x3D16740DC3990612 //A14 = +1.99425676175410093285e-14
|
|
data8 0xBD77F4353812C46A //A13 = -1.36162367755616790260e-12
|
|
data8 0x3DCFD0BE13C73DB4 //A12 = +5.78718761040355136007e-11
|
|
data8 0xBE1D728DF71189B4 //A11 = -1.71406885583934105120e-09
|
|
data8 0x3E64252C8CB710B5 //A10 = +3.75233795940731111303e-08
|
|
data8 0xBEA514B93180F33D //A9 = -6.28261292774310809962e-07
|
|
data8 0x3EE1381118CC7151 //A8 = +8.21066421390821904504e-06
|
|
data8 0xBF1634404FB0FA72 //A7 = -8.47019436358372148764e-05
|
|
data8 0x3F46B2CBBCF0EB32 //A6 = +6.92700845213200923490e-04
|
|
data8 0xBF725C2B445E6D81 //A5 = -4.48243046949004063741e-03
|
|
data8 0x3F974E7CFA4D89D9 //A4 = +2.27603462002522228717e-02
|
|
data8 0xBFB6D7BAC2E342D1 //A3 = -8.92292714882032736443e-02
|
|
data8 0x3FD0D156AD9CE2A6 //A2 = +2.62777013343603696631e-01
|
|
data8 0xBFE1C228572AADB0 //A1 = -5.54950876471982857725e-01
|
|
data8 0x3FE8A739F48B9A3B //A0 = +7.70413377406675619766e-01
|
|
LOCAL_OBJECT_END(erfc_p_table)
|
|
|
|
|
|
.section .text
|
|
GLOBAL_LIBM_ENTRY(erfcf)
|
|
|
|
// Form index i for table erfc_p_table as exponent of x
|
|
// We use i + bias in real calculations
|
|
{ .mlx
|
|
getf.exp GR_IndxPlusBias = f8 // (sign + exp + bias) of x
|
|
movl exp_GR_sig_inv_ln2 = 0xb8aa3b295c17f0bc //signif.of 1/ln2
|
|
}
|
|
{ .mlx
|
|
addl EXP_AD_TB1 = @ltoff(exp_table_1), gp
|
|
movl exp_GR_rshf_2to56 = 0x4768000000000000 // 1.100 2^(63+56)
|
|
}
|
|
;;
|
|
|
|
// Form argument EXP_NORM_f8 for exp(-x^2)
|
|
{ .mfi
|
|
ld8 EXP_AD_TB1 = [EXP_AD_TB1]
|
|
fcmp.ge.s1 p6,p7 = f8, f0 // p6: x >= 0 ,p7: x<0
|
|
mov GR_BIAS = 0x0FFFF
|
|
}
|
|
{ .mfi
|
|
mov exp_GR_exp_2tom56 = 0xffff-56
|
|
fnma.s1 EXP_NORM_f8 = f8, f8, f0 // -x^2
|
|
mov GR_ExpMask = 0x1ffff
|
|
}
|
|
;;
|
|
|
|
// Form two constants we need
|
|
// 1/ln2 * 2^63 to compute w = x * 1/ln2 * 128
|
|
// 1.1000..000 * 2^(63+63-7) to right shift int(w) into the significand
|
|
|
|
// p9: x = 0,+inf,-inf,nan,unnorm.
|
|
// p10: x!= 0,+inf,-inf,nan,unnorm.
|
|
{ .mfi
|
|
setf.sig EXP_INV_LN2_2TO63 = exp_GR_sig_inv_ln2 // Form 1/ln2*2^63
|
|
fclass.m p9,p10 = f8,0xef
|
|
shl GR_ShftPi_bias = GR_BIAS, 7
|
|
}
|
|
{ .mfi
|
|
setf.d EXP_RSHF_2TO56 = exp_GR_rshf_2to56 //Const 1.10*2^(63+56)
|
|
nop.f 0
|
|
and GR_IndxPlusBias = GR_IndxPlusBias, GR_ExpMask // i + bias
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
alloc r32 = ar.pfs, 0, 15, 4, 0
|
|
(p6) fma.s1 FR_AbsArg = f1, f0, f8 // |x| if x >= 0
|
|
cmp.lt p15,p0 = GR_IndxPlusBias, GR_BIAS//p15: i < 0 (for |x|<1)
|
|
}
|
|
{ .mlx
|
|
setf.exp EXP_2TOM56 = exp_GR_exp_2tom56 //2^-56 for scaling Nfloat
|
|
movl exp_GR_rshf = 0x43e8000000000000 //1.10 2^63,right shift.
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfps FR_POS_ARG_ASYMP, FR_NEG_ARG_ASYMP = [EXP_AD_TB1],8
|
|
nop.f 0
|
|
(p15) mov GR_IndxPlusBias = GR_BIAS //Let i = 0 if i < 0
|
|
}
|
|
{ .mlx
|
|
mov GR_P_POINT_3 = 0x1A0
|
|
movl GR_05 = 0x3fe0000000000000
|
|
}
|
|
;;
|
|
|
|
// Form shift GR_ShftPi from the beginning of erfc_p_table
|
|
// to the polynomial with number i
|
|
{ .mfi
|
|
ldfps FR_UnfBound, FR_EpsNorm = [EXP_AD_TB1],8
|
|
nop.f 0
|
|
shl GR_ShftPi = GR_IndxPlusBias, 7
|
|
}
|
|
{ .mfi
|
|
setf.d EXP_RSHF = exp_GR_rshf // Form right shift 1.100 * 2^63
|
|
(p7) fms.s1 FR_AbsArg = f1, f0, f8 // |x| if x < 0
|
|
mov exp_TB1_size = 0x100
|
|
}
|
|
;;
|
|
|
|
// Form pointer GR_P_POINT_3 to the beginning of erfc_p_table
|
|
{ .mfi
|
|
setf.d FR_05 = GR_05
|
|
nop.f 0
|
|
sub GR_ShftPi = GR_ShftPi,GR_ShftPi_bias
|
|
}
|
|
{ .mfb
|
|
add GR_P_POINT_3 = GR_P_POINT_3, EXP_AD_TB1
|
|
nop.f 0
|
|
(p9) br.cond.spnt SPECIAL // For x = 0,+inf,-inf,nan,unnorm
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
add GR_P_POINT_1 = GR_P_POINT_3, GR_ShftPi
|
|
nop.f 0
|
|
add GR_P_POINT_2 = GR_P_POINT_3, GR_ShftPi
|
|
}
|
|
{ .mfi
|
|
ldfe exp_ln2_by_128_hi = [EXP_AD_TB1],16
|
|
fma.s1 FR_NormX = f8,f1,f0
|
|
add GR_P_POINT_3 = GR_P_POINT_3, GR_ShftPi
|
|
}
|
|
;;
|
|
|
|
// Load coefficients for polynomial P15(x)
|
|
{ .mfi
|
|
ldfpd FR_A15, FR_A14 = [GR_P_POINT_1], 16
|
|
nop.f 0
|
|
add GR_P_POINT_3 = 0x30, GR_P_POINT_3
|
|
}
|
|
{ .mfi
|
|
ldfe exp_ln2_by_128_lo = [EXP_AD_TB1], 16
|
|
nop.f 0
|
|
add GR_P_POINT_2 = 0x20, GR_P_POINT_2
|
|
}
|
|
;;
|
|
|
|
// Now EXP_AD_TB1 points to the beginning of table 1
|
|
{ .mlx
|
|
ldfpd FR_A13, FR_A12 = [GR_P_POINT_1]
|
|
movl GR_1_by_6 = 0x3FC5555555555555
|
|
}
|
|
{ .mfi
|
|
add GR_P_POINT_4 = 0x30, GR_P_POINT_2
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfpd FR_A11, FR_A10 = [GR_P_POINT_2]
|
|
fma.s1 FR_2 = f1, f1, f1
|
|
mov exp_TB2_size = 0x80
|
|
}
|
|
{ .mfi
|
|
ldfpd FR_A9, FR_A8 = [GR_P_POINT_3],16
|
|
nop.f 0
|
|
add GR_P_POINT_1 = 0x60 ,GR_P_POINT_1
|
|
}
|
|
;;
|
|
|
|
// W = X * Inv_log2_by_128
|
|
// By adding 1.10...0*2^63 we shift and get round_int(W) in significand.
|
|
// We actually add 1.10...0*2^56 to X * Inv_log2 to do the same thing.
|
|
{ .mfi
|
|
ldfpd FR_A7, FR_A6 = [GR_P_POINT_3]
|
|
fma.s1 EXP_W_2TO56_RSH = EXP_NORM_f8,EXP_INV_LN2_2TO63,EXP_RSHF_2TO56
|
|
add EXP_AD_TB2 = exp_TB1_size, EXP_AD_TB1
|
|
|
|
}
|
|
{ .mfi
|
|
ldfpd FR_A5, FR_A4 = [GR_P_POINT_4], 16
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
ldfpd FR_A3, FR_A2 = [GR_P_POINT_4]
|
|
fmerge.s FR_X = f8,f8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfpd FR_A1, FR_A0 = [GR_P_POINT_1]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
//p14: x < - NEG_ARG_ASYMP = -4.4 -> erfcf(x) ~=~ 2.0
|
|
{ .mfi
|
|
setf.d FR_1_by_6 = GR_1_by_6
|
|
(p7) fcmp.gt.unc.s1 p14,p0 = FR_AbsArg, FR_NEG_ARG_ASYMP //p7: x < 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
//p15: x > POS_ARG_ASYMP = 10.06 -> erfcf(x) ~=~ 0.0
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fcmp.gt.unc.s1 p15,p0 = FR_AbsArg, FR_POS_ARG_ASYMP //p6: x > 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fcmp.le.s1 p8,p0 = FR_NormX, FR_UnfBound // p8: x <= UnfBound
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p14) fnma.s.s0 FR_RESULT = FR_EpsNorm, FR_EpsNorm, FR_2//y = 2 if x <-4.4
|
|
(p14) br.ret.spnt b0
|
|
}
|
|
;;
|
|
|
|
// Nfloat = round_int(W)
|
|
// The signficand of EXP_W_2TO56_RSH contains the rounded integer part of W,
|
|
// as a twos complement number in the lower bits (that is, it may be negative).
|
|
// That twos complement number (called N) is put into exp_GR_N.
|
|
|
|
// Since EXP_W_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56
|
|
// before the shift constant 1.10000 * 2^63 is subtracted to yield EXP_Nfloat.
|
|
// Thus, EXP_Nfloat contains the floating point version of N
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fms.s1 EXP_Nfloat = EXP_W_2TO56_RSH, EXP_2TOM56, EXP_RSHF
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
(p15) mov GR_Parameter_TAG = 209
|
|
(p15) fma.s.s0 FR_RESULT = FR_EpsNorm,FR_EpsNorm,f0 //Result.for x>10.06
|
|
(p15) br.cond.spnt __libm_error_region
|
|
}
|
|
;;
|
|
|
|
// Now we can calculate polynomial P15(x)
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_1_1 = FR_AbsArg, FR_AbsArg, f0 // x ^2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_0_1 = FR_A15, FR_AbsArg, FR_A14
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_1_2 = FR_A13, FR_AbsArg, FR_A12
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
getf.sig exp_GR_N = EXP_W_2TO56_RSH
|
|
fma.s1 FR_P15_2_1 = FR_A9, FR_AbsArg, FR_A8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_2_2 = FR_A11, FR_AbsArg, FR_A10
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_3_1 = FR_A5, FR_AbsArg, FR_A4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_3_2 = FR_A7, FR_AbsArg, FR_A6
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// exp_GR_index_1 has index_1
|
|
// exp_GR_index_2_16 has index_2 * 16
|
|
// exp_GR_biased_M has M
|
|
// exp_GR_index_1_16 has index_1 * 16
|
|
|
|
// r2 has true M
|
|
{ .mfi
|
|
and exp_GR_index_1 = 0x0f, exp_GR_N
|
|
fma.s1 FR_P15_4_1 = FR_A1, FR_AbsArg, FR_A0
|
|
shr r2 = exp_GR_N, 0x7
|
|
|
|
}
|
|
{ .mfi
|
|
and exp_GR_index_2_16 = 0x70, exp_GR_N
|
|
fma.s1 FR_P15_4_2 = FR_A3, FR_AbsArg, FR_A2
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// EXP_AD_T1 has address of T1
|
|
// EXP_AD_T2 has address if T2
|
|
|
|
{ .mfi
|
|
add EXP_AD_T2 = EXP_AD_TB2, exp_GR_index_2_16
|
|
nop.f 0
|
|
shladd EXP_AD_T1 = exp_GR_index_1, 4, EXP_AD_TB1
|
|
}
|
|
{ .mfi
|
|
addl exp_GR_biased_M = 0xffff, r2
|
|
fnma.s1 exp_r = EXP_Nfloat, exp_ln2_by_128_hi, EXP_NORM_f8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// Create Scale = 2^M
|
|
// r = x - Nfloat * ln2_by_128_hi
|
|
|
|
{ .mfi
|
|
setf.exp EXP_2M = exp_GR_biased_M
|
|
fma.s1 FR_P15_7_1 = FR_P15_0_1, FR_P15_1_1, FR_P15_1_2
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
ldfe exp_T2 = [EXP_AD_T2]
|
|
nop.f 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
// Load T1 and T2
|
|
|
|
{ .mfi
|
|
ldfe exp_T1 = [EXP_AD_T1]
|
|
fma.s1 FR_P15_7_2 = FR_P15_1_1, FR_P15_1_1, f0 // x^4
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_8_1 = FR_P15_1_1, FR_P15_2_2, FR_P15_2_1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_9_1 = FR_P15_1_1, FR_P15_4_2, FR_P15_4_1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_9_2 = FR_P15_1_1, FR_P15_3_2, FR_P15_3_1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 exp_P = FR_1_by_6, exp_r, FR_05
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 exp_rsq = exp_r, exp_r, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_13_1 = FR_P15_7_2, FR_P15_7_1, FR_P15_8_1
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_14_1 = FR_P15_7_2, FR_P15_9_2, FR_P15_9_1
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_P15_14_2 = FR_P15_7_2, FR_P15_7_2, f0 // x^8
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 exp_P = exp_P, exp_rsq, exp_r
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 exp_S1 = EXP_2M, exp_T2, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Pol = FR_P15_14_2, FR_P15_13_1, FR_P15_14_1 // P15(x)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 exp_S = exp_S1, exp_T1, f0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s1 FR_Exp = exp_S, exp_P, exp_S // exp(-x^2)
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fma.s.s0 FR_Tmpf = f8, f1, f0 // Flag d
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
//p6: result for 0 < x < = POS_ARG_ASYMP
|
|
//p7: result for - NEG_ARG_ASYMP <= x < 0
|
|
//p8: exit for - NEG_ARG_ASYMP <= x <= UnfBound, x!=0
|
|
.pred.rel "mutex",p6,p7
|
|
{ .mfi
|
|
nop.m 0
|
|
(p6) fma.s.s0 f8 = FR_Exp, FR_Pol, f0
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
mov GR_Parameter_TAG = 209
|
|
(p7) fnma.s.s0 f8 = FR_Exp, FR_Pol, FR_2
|
|
(p8) br.ret.sptk b0
|
|
}
|
|
;;
|
|
|
|
//p10: branch for UnfBound < x < = POS_ARG_ASYMP
|
|
{ .mfb
|
|
nop.m 0
|
|
nop.f 0
|
|
(p10) br.cond.spnt __libm_error_region
|
|
}
|
|
;;
|
|
|
|
//Only via (p9) br.cond.spnt SPECIAL for x = 0,+inf,-inf,nan,unnorm
|
|
SPECIAL:
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fclass.m.unc p10,p0 = f8,0x07 // p10: x = 0
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fclass.m.unc p11,p0 = f8,0x21 // p11: x = +inf
|
|
nop.i 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fclass.m.unc p12,p0 = f8,0x22 // p12 x = -inf
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p10) fma.s.s0 f8 = f1, f1, f0
|
|
(p10) br.ret.sptk b0 // Quick exit for x = 0
|
|
}
|
|
;;
|
|
|
|
{ .mfi
|
|
nop.m 0
|
|
fclass.m.unc p13,p0 = f8,0xc3 // p13: x = nan
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p11) fma.s.s0 f8 = f0, f1, f0
|
|
(p11) br.ret.spnt b0 // Quick exit for x = +inf
|
|
}
|
|
;;
|
|
{ .mfi
|
|
nop.m 0
|
|
fclass.m.unc p14,p0 = f8,0x0b // P14: x = unnormalized
|
|
nop.i 0
|
|
}
|
|
{ .mfb
|
|
nop.m 0
|
|
(p12) fma.s.s0 f8 = f1, f1, f1
|
|
(p12) br.ret.spnt b0 // Quick exit for x = -inf
|
|
}
|
|
;;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
(p13) fma.s.s0 f8 = f8, f1, f0
|
|
(p13) br.ret.sptk b0 // Quick exit for x = nan
|
|
}
|
|
;;
|
|
|
|
{ .mfb
|
|
nop.m 0
|
|
(p14) fnma.s.s0 f8 = f8, f1, f1
|
|
(p14) br.ret.sptk b0 // Quick exit for x = unnormalized
|
|
}
|
|
;;
|
|
|
|
GLOBAL_LIBM_END(erfcf)
|
|
libm_alias_float_other (erfc, erfc)
|
|
|
|
|
|
// Call via (p10) br.cond.spnt __libm_error_region
|
|
// for UnfBound < x < = POS_ARG_ASYMP
|
|
// and
|
|
//
|
|
// call via (p15) br.cond.spnt __libm_error_region
|
|
// for x > POS_ARG_ASYMP
|
|
|
|
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
|
|
nop.m 0
|
|
nop.m 0
|
|
add GR_Parameter_RESULT = 48,sp
|
|
};;
|
|
{ .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#
|