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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>
816 lines
22 KiB
ArmAsm
816 lines
22 KiB
ArmAsm
.file "log2l.s"
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// Copyright (c) 2000 - 2003, Intel Corporation
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// All rights reserved.
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//
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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// History
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//==============================================================
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// 09/25/00 Initial version
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// 11/22/00 Fixed accuracy bug (for mantissas near 1, 2)
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// 12/07/00 Fixed C_1l constant, eliminated rounding errors in
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// reduced argument (x*frcpa(x)-1)
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// 05/20/02 Cleaned up namespace and sf0 syntax
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// 02/10/03 Reordered header: .section, .global, .proc, .align
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//
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// API
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//==============================================================
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// long double log2l(long double)
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//
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// Overview of operation
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//==============================================================
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// Background
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//
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// Implementation
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//
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// Let x = 2^l * m, where m=1.b1 b2 ... b8 b9 ... b52
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// y=frcpa(m), r=m*y-1, f=b1 b2 .. b8
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// T_hi is a table that stores the 24 most significant bits of log2(1/y)
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// (in entries 1..255) in single precision format
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// T_low is a table that stores (log2(1/y)-T_high), rounded to double
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// precision
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//
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// f is used as an index; T_high[255]=T_low[255]=0
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//
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// If f=0 and b9=0, r is set to 2^{-8}* 0.b9 b10 ... b52 = m-1 (fractional part of m),
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// and 0 is used instead of T_high[0], T_low[0]
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// (polynomial evaluation only, for m=1+r, 0<=r<2^{-9})
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// If f=255, r is set to (m-2)/2 (T[255]=0, and only polynomial evaluation is used
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// for m=2(1-r'), 0<=r'<2^{-9})
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//
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// If 2^{-9}<=m<2-2^{-8} or (input not near 1), let C1r=(2^{16}+C1*r)-2^{16}
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// and let E=((RN(m*y)-1)-r)+(m*y-RN(m*y))
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// Else let C1r=C1*r (rounded to 64 significant bits) and let E=0
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//
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// Let D=C1*r-C1r
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//
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//
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// log2l(x) is approximated as
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// (l+T_high[f]+C1r) + (D+r*(c1+c2*r+c3*r^2...+c8*r^7)+(T_low[f]+C_1*E))
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//
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// Special values
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//==============================================================
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// log2l(0)=-inf, raises Divide by Zero
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// log2l(+inf)=inf
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// log2l(x)=NaN, raises Invalid if x<0
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//
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// Registers used
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//==============================================================
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// f6-f15, f32-f36
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// r2-r3, r23-r23
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// p6,p7,p8,p12
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//
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GR_SAVE_B0 = r33
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GR_SAVE_PFS = r34
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GR_SAVE_GP = r35 // This reg. can safely be used
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GR_SAVE_SP = r36
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GR_Parameter_X = r37
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GR_Parameter_Y = r38
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GR_Parameter_RESULT = r39
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GR_Parameter_TAG = r40
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FR_X = f10
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FR_Y = f1
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FR_RESULT = f8
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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(poly_coeffs)
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data8 0xb8aa3b295c17f0bc, 0x00003fff // C_1
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data8 0x3fca61762a7aded9, 0xbfc71547652b82fe // C_7, C_8
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data8 0x3fd2776c50ef9bfe, 0xbfcec709dc3a03fd // C_5, C_6
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data8 0x3fdec709dc3a03fd, 0xbfd71547652b82fe // C_3, C_4
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//data8 0xd871319ff0342580, 0x0000bfbd // C_1l (low part of C1)
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data8 0x82f0025f2dc582ee, 0x0000bfbe // C_1l (low part of C1)
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data8 0xb8aa3b295c17f0bc, 0x0000bffe // C_2
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LOCAL_OBJECT_END(poly_coeffs)
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LOCAL_OBJECT_START(T_table)
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data4 0x3b38d875, 0x3c0ae7f4, 0x3c67f738, 0x3ca2b253
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data4 0x3ccbb91d, 0x3cfac91e, 0x3d1504a5, 0x3d29c4a0
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data4 0x3d419264, 0x3d567aa6, 0x3d6e76ca, 0x3d81c3f7
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data4 0x3d8c5630, 0x3d9876e9, 0x3da31e0a, 0x3dadcf09
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data4 0x3db889f9, 0x3dc34eec, 0x3dce1df5, 0x3dd8f726
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data4 0x3de3da94, 0x3deec851, 0x3df82ea4, 0x3e0197dd
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data4 0x3e071dad, 0x3e0ca8ca, 0x3e116d6e, 0x3e170281
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data4 0x3e1bcfbc, 0x3e216ee9, 0x3e2644dc, 0x3e2b1ee1
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data4 0x3e30cd12, 0x3e35affd, 0x3e3a970f, 0x3e3f824f
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data4 0x3e4544c0, 0x3e4a3926, 0x3e4f31d1, 0x3e542ec7
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data4 0x3e593012, 0x3e5e35b7, 0x3e633fbf, 0x3e677625
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data4 0x3e6c884b, 0x3e719eea, 0x3e76ba0a, 0x3e7bd9b2
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data4 0x3e80111d, 0x3e82a523, 0x3e84ccec, 0x3e876533
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data4 0x3e89ffd1, 0x3e8c2d22, 0x3e8e5c18, 0x3e90fd0a
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data4 0x3e932fa9, 0x3e95d506, 0x3e980b5a, 0x3e9a4361
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data4 0x3e9c7d1f, 0x3e9f2b16, 0x3ea168a0, 0x3ea3a7ea
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data4 0x3ea5e8f5, 0x3ea82bc4, 0x3eaa705b, 0x3eacb6bb
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data4 0x3eaefee7, 0x3eb148e3, 0x3eb394b1, 0x3eb5e255
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data4 0x3eb831d0, 0x3eba8327, 0x3ebcd65c, 0x3ebeb3e0
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data4 0x3ec10a7a, 0x3ec362f9, 0x3ec5bd63, 0x3ec7a0b3
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data4 0x3ec9fe96, 0x3ecc5e6c, 0x3ece4619, 0x3ed0a978
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data4 0x3ed293fe, 0x3ed4faf1, 0x3ed6e859, 0x3ed952eb
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data4 0x3edb433c, 0x3eddb178, 0x3edfa4bc, 0x3ee19953
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data4 0x3ee40cee, 0x3ee60484, 0x3ee7fd73, 0x3ee9f7bb
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data4 0x3eec7280, 0x3eee6fda, 0x3ef06e94, 0x3ef26eb1
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data4 0x3ef47031, 0x3ef67317, 0x3ef8f8b2, 0x3efafec5
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data4 0x3efd0644, 0x3eff0f32, 0x3f008cc8, 0x3f0192b0
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data4 0x3f029952, 0x3f03a0b0, 0x3f0466b2, 0x3f056f5a
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data4 0x3f0678c0, 0x3f0782e6, 0x3f088dcc, 0x3f099973
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data4 0x3f0aa5dd, 0x3f0b6fac, 0x3f0c7d6d, 0x3f0d8bf4
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data4 0x3f0e575b, 0x3f0f673e, 0x3f1077e9, 0x3f1144ef
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data4 0x3f1256fc, 0x3f1369d6, 0x3f143880, 0x3f154cc1
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data4 0x3f161c7a, 0x3f173227, 0x3f1802f2, 0x3f191a0f
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data4 0x3f19ebee, 0x3f1b047e, 0x3f1bd775, 0x3f1cf17b
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data4 0x3f1dc58e, 0x3f1ee10f, 0x3f1fb63f, 0x3f208bea
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data4 0x3f21a98f, 0x3f22805c, 0x3f2357a7, 0x3f247778
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data4 0x3f254fe9, 0x3f2628d9, 0x3f270249, 0x3f2824fb
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data4 0x3f28ff97, 0x3f29dab4, 0x3f2ab654, 0x3f2b9277
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data4 0x3f2cb8c8, 0x3f2d961e, 0x3f2e73fa, 0x3f2f525b
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data4 0x3f303143, 0x3f3110b1, 0x3f31f0a7, 0x3f32d125
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data4 0x3f33b22b, 0x3f3493bc, 0x3f3575d6, 0x3f36587b
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data4 0x3f373bab, 0x3f381f68, 0x3f3903b1, 0x3f39e888
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data4 0x3f3acdec, 0x3f3bb3e0, 0x3f3c9a63, 0x3f3d8177
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data4 0x3f3e1bd4, 0x3f3f03d9, 0x3f3fec71, 0x3f40d59b
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data4 0x3f41bf59, 0x3f42a9ab, 0x3f434635, 0x3f443180
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data4 0x3f451d61, 0x3f4609d9, 0x3f46a7d3, 0x3f479549
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data4 0x3f488357, 0x3f492261, 0x3f4a1171, 0x3f4b011c
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data4 0x3f4ba139, 0x3f4c91e8, 0x3f4d8334, 0x3f4e246a
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data4 0x3f4f16be, 0x3f5009b1, 0x3f50ac02, 0x3f51a001
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data4 0x3f524305, 0x3f533812, 0x3f53dbca, 0x3f54d1e7
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data4 0x3f55c8a8, 0x3f566d85, 0x3f57655b, 0x3f580af0
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data4 0x3f58b0d0, 0x3f59aa2c, 0x3f5a50c7, 0x3f5b4b3c
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data4 0x3f5bf294, 0x3f5cee26, 0x3f5d963c, 0x3f5e92ed
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data4 0x3f5f3bc3, 0x3f5fe4e7, 0x3f60e32d, 0x3f618d13
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data4 0x3f623748, 0x3f63372a, 0x3f63e223, 0x3f648d6b
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data4 0x3f658eee, 0x3f663afe, 0x3f66e75e, 0x3f67ea86
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data4 0x3f6897b0, 0x3f69452c, 0x3f69f2f9, 0x3f6af847
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data4 0x3f6ba6e2, 0x3f6c55d0, 0x3f6d0510, 0x3f6e0c8d
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data4 0x3f6ebc9f, 0x3f6f6d04, 0x3f701dbe, 0x3f70cecd
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data4 0x3f718030, 0x3f728ae6, 0x3f733d20, 0x3f73efaf
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data4 0x3f74a296, 0x3f7555d3, 0x3f760967, 0x3f76bd53
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data4 0x3f777197, 0x3f7880a1, 0x3f7935c2, 0x3f79eb3c
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data4 0x3f7aa10f, 0x3f7b573b, 0x3f7c0dc2, 0x3f7cc4a3
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data4 0x3f7d7bdf, 0x3f7e3376, 0x3f7eeb68, 0x00000000
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LOCAL_OBJECT_END(T_table)
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LOCAL_OBJECT_START(T_low)
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data8 0x3dc0b97f689876ef, 0x3dfd5d906028ac01
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data8 0x3df8b9cbb8d7240b, 0x3de0c941a2f220cd
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data8 0x3e09c6aecba15936, 0x3dfa6d528241827c
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data8 0x3dd0bad25714903c, 0x3e2776b01dc036a2
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data8 0x3e2b914bc77f158b, 0x3e1c0fafd29dc74a
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data8 0x3e28dadc119cd3de, 0x3e3bca869da085be
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data8 0x3e19d1e700f2200a, 0x3e3e13530cc37504
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data8 0x3e3936464d9c41ee, 0x3e3c3fa21c9499d0
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data8 0x3e3259e079b6c6e8, 0x3e2a364069c4f7f3
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data8 0x3e1274c84f6c6364, 0x3e3796170159f454
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data8 0x3e26e1e389f4364e, 0x3e28cedda8c7f658
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data8 0x3e376c2028433268, 0x3e4aee6d650c82e1
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data8 0x3e33e65094fbeeb4, 0x3e4c7d125aa92c5d
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data8 0x3e1559a4b69691d8, 0x3e18efabeb7d7221
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data8 0x3e4c2b255abaa8de, 0x3e37436952a4538b
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data8 0x3e4e6807f4ba00b8, 0x3e33ff5964190e42
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data8 0x3e4f5d798cead43c, 0x3e4f3676443bf453
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data8 0x3e4660f8d5bc1bf5, 0x3e2d4f9f3ab04f36
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data8 0x3e357f7a64ccd537, 0x3e394caf7c9b05af
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data8 0x3e225c7d17ab29b0, 0x3e4eb202f6d55a12
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data8 0x3e32faa68b19bcd2, 0x3e45ee1c9b566a8b
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data8 0x3e4770a67de054ff, 0x3e42234fb9de6d6b
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data8 0x3e4ad139825c6e19, 0x3e47f3d334814a93
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data8 0x3e2af1ec402867b6, 0x3e2bfbda0c956e3d
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data8 0x3e4287b831e77ff2, 0x3e54bf0eb77f7b89
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data8 0x3e5b9259a1029607, 0x3e4a764b015e699d
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data8 0x3e4d0b68ea883ab5, 0x3e33e829ecdadf46
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data8 0x3e52f27efef3031b, 0x3e3073979e4af89e
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data8 0x3e3b980f2cd6c253, 0x3e2a5f0f5f7f66a9
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data8 0x3e37788738117b02, 0x3e58aa29a784d52f
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data8 0x3e4f5504c4ff2466, 0x3e002d40340fa647
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data8 0x3e5f53b64592f4c3, 0x3e543f222c526802
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data8 0x3e5680e547a872fa, 0x3e5e234bd1154450
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data8 0x3e3000edc18b6d21, 0x3e1c3c1f000942a8
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data8 0x3e51eeae0e442d6e, 0x3e4fb265376623f2
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data8 0x3e57b5941782d830, 0x3e3a4b83f24ae52c
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data8 0x3e5a5fb4f23978de, 0x3e51ed071563fb02
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data8 0x3e49e2071f51a7a8, 0x3e5e43ae5b924234
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data8 0x3dfa2be9aedf374a, 0x3e56dea3dbba67d5
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data8 0x3e3375fe732b3c3e, 0x3e5a0c6f91f2e77e
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data8 0x3e55e1bf1c969e41, 0x3e30a5a5166b8eee
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data8 0x3e53e6e9a539d46c, 0x3e542981b3d7b0e6
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data8 0x3e595fd8ff36ad64, 0x3e5edeb9e65cbbb4
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data8 0x3e46aeab4d3434c1, 0x3e4ea3ff0564b010
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data8 0x3e59b00be2e3c25a, 0x3e5b887cd7b0821f
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data8 0x3e5f666668547b4d, 0x3e4d0733a805273f
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data8 0x3e26a2ff21c4aec5, 0x3e4c336f7a3a78f3
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data8 0x3e11ad12b628e2d0, 0x3e56d43ff3f0ea64
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data8 0x3e238809433cccd2, 0x3e40d9734147d40f
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data8 0x3e54245fe3e24e06, 0x3e251441fce4d48c
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data8 0x3e517114efc5d1f9, 0x3e5e9a99154b0d82
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data8 0x3e442a71337970f8, 0x3e420c7c69211fdf
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data8 0x3e537e7d5d43c6a7, 0x3e4376c66ad9ad8b
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data8 0x3e49054d678a4f1c, 0x3e5d23cb3bc19f18
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data8 0x3e6ebcd449dcab2b, 0x3e67f5fc2849c88a
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data8 0x3e63f388395d3e84, 0x3e65c1103b0ad7e9
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data8 0x3e6d5d1dd031f353, 0x3e5a159dae75c4d0
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data8 0x3e4d5e22aa75f71d, 0x3e5e379ee62e1e35
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data8 0x3e4df082213cb2dc, 0x3e6bfa06c156f521
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data8 0x3e66e2d3c19b517b, 0x3e426b7098590071
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data8 0x3e541bd027e9854e, 0x3e5061dd924b0ac0
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data8 0x3e6dae01df373a03, 0x3e3baec80b207b0b
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data8 0x3e6b6a6fe06bebac, 0x3e61aebcfc3ab5d1
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data8 0x3e584ee3e7c79d83, 0x3e6b3c1b2840cb40
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data8 0x3e6c842085d6befd, 0x3e6ac04fd7b141e0
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data8 0x3e6c48250474141d, 0x3e2d889b86125f69
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data8 0x3e6e74740225dad0, 0x3e45940d31d50a7c
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data8 0x3e695476a6c39ddc, 0x3e6d9a6d857a060a
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data8 0x3e4a3e9bb4b69337, 0x3e484f3ce4707ed6
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data8 0x3e39dd125d25fc27, 0x3e563fb400de8732
|
|
data8 0x3e5fdd6d0ee28b48, 0x3e669d15b869bb07
|
|
data8 0x3e40687cfad7964d, 0x3e69317990d43957
|
|
data8 0x3e633d57e24ae1bd, 0x3e618bf03710eabb
|
|
data8 0x3e4b4df6fccd1160, 0x3e3fb26ddaa1ec45
|
|
data8 0x3e3810a5e1817fd4, 0x3e6857373642fa5c
|
|
data8 0x3e673db6193add31, 0x3e63200c8acbc9c3
|
|
data8 0x3e3d2dee448ebb62, 0x3e6a19723a80db6a
|
|
data8 0x3e5e7cdab8fd3e6a, 0x3e671855cd660672
|
|
data8 0x3e473c3c78a85ecd, 0x3e5f5e23056a7cf2
|
|
data8 0x3e52538519527367, 0x3e4b573bcf2580e9
|
|
data8 0x3e6d6f856fe90c60, 0x3e2d932a8487642e
|
|
data8 0x3e5236fc78b6174c, 0x3e50cb91d406db50
|
|
data8 0x3e650e8bd562aa57, 0x3e424ee3d9a82f2e
|
|
data8 0x3e59363960e1e3d9, 0x3e379604c1150a3e
|
|
data8 0x3e6d914f6c2ac258, 0x3e62967a451a7b48
|
|
data8 0x3e684b5f01139cb2, 0x3e448bbfbf6d292c
|
|
data8 0x3e6227e7fb487e73, 0x3e6d39d50290f458
|
|
data8 0x3e58368342b4b668, 0x3e65dc0c25bd1763
|
|
data8 0x3e61b7dc362e22b5, 0x3e671691f094bb80
|
|
data8 0x3e5011642d5123f2, 0x3e4c4eb7f11e41be
|
|
data8 0x3e5dcee36ca242cf, 0x3e6791cefff688f1
|
|
data8 0x3e60e23c8dda4ecd, 0x3e48e6a22fe78cfe
|
|
data8 0x3e6d703f244adc86, 0x3e6a281a85a5049d
|
|
data8 0x3e570f20e6403d9e, 0x3e2211518a12956f
|
|
data8 0x3e6737d1e54d71df, 0x3e66b1881476f5e9
|
|
data8 0x3e6e1bbeef085376, 0x3e47cad4944a32be
|
|
data8 0x3e527f2c738e7ee9, 0x3e699883a4b9fb29
|
|
data8 0x3e5c17d1108740d9, 0x3e5d4a9c79a43389
|
|
data8 0x3e49fdc24462ba3b, 0x3e24dbb3a60cceb2
|
|
data8 0x3e5c5bf618780748, 0x3e5c38005b0c778c
|
|
data8 0x3e6be168dd6dd3fe, 0x3e633ab9370693b0
|
|
data8 0x3dd290556b0ae339, 0x3e607c317927096a
|
|
data8 0x3e59651353b3d90e, 0x3e4d8751e5e0ae0d
|
|
data8 0x3e46c81023272a85, 0x3e6b23c988f391b2
|
|
data8 0x3e608741d215209c, 0x3e60b8ba506d758f
|
|
data8 0x3e62ddbe74803297, 0x3e5dbb8b5087587d
|
|
data8 0x3e642aa529048131, 0x3e3dcbda6835dcf4
|
|
data8 0x3e6db503ce854d2a, 0x3e6dd00b49bc6849
|
|
data8 0x3e4db2f11243bc84, 0x3e3b9848efc2ea97
|
|
data8 0x3e58f18e17c82609, 0x3e6ed8645e16c312
|
|
data8 0x3e4065bdb60a5dd4, 0x3e490453c6e6c30a
|
|
data8 0x3e62373994aa31ba, 0x3e56305f0e6b2a95
|
|
data8 0x3e68c1601a6614ee, 0x3e614e204f19d93f
|
|
data8 0x3e6e5037ca773299, 0x3e693f98892561a6
|
|
data8 0x3e639de4f4bf700d, 0x3e416c071e93fd97
|
|
data8 0x3e65466991b415ef, 0x3e6896a324afac9d
|
|
data8 0x3e44f64802e2f11c, 0x3e64d7d747e2191a
|
|
data8 0x3e6174b7581de84c, 0x3e44c7b946e1d43c
|
|
data8 0x3e6a3bcbe30512ec, 0x3e5d3ed411c95ce4
|
|
data8 0x3e3e5b5735cfaf8e, 0x3e6e538ab34efb51
|
|
data8 0x3e514e204f19d93f, 0x3e5a88e6550c89a4
|
|
data8 0x3e66b97a5d9dfd8b, 0x3e5f46b1e14ebaf3
|
|
data8 0x3e357665f6893f5d, 0x3e6bbf633078d1d5
|
|
data8 0x3e5e7337a212c417, 0x3e3570fde15fc8cc
|
|
data8 0x3e21119402da92b4, 0x3e6566e830d1ff3b
|
|
data8 0x3e558883e480e220, 0x3e589ca3a68da411
|
|
data8 0x3e44eb66df73d648, 0x3e1a0a629b1b7e68
|
|
data8 0x3e54cc207b8c1116, 0x0000000000000000
|
|
LOCAL_OBJECT_END(T_low)
|
|
|
|
|
|
.section .text
|
|
GLOBAL_IEEE754_ENTRY(log2l)
|
|
|
|
{ .mfi
|
|
alloc r32=ar.pfs,1,4,4,0
|
|
// normalize x
|
|
// y=frcpa(x)
|
|
frcpa.s1 f41,p0=f1,f8
|
|
// r26=bias-1
|
|
mov r26=0xfffe
|
|
}
|
|
{.mfi
|
|
// r23=bias+16
|
|
mov r23=0xffff+16
|
|
fma.s1 f7=f8,f1,f0
|
|
// r2 = pointer to C_1...C_6 followed by T_table
|
|
addl r2 = @ltoff(poly_coeffs), gp;;
|
|
}
|
|
{.mfi
|
|
// get significand
|
|
getf.sig r25=f8
|
|
// f8 denormal ?
|
|
fclass.m p8,p10=f8,0x9
|
|
// r24=bias-8
|
|
mov r24=0xffff-8;;
|
|
}
|
|
{.mfi
|
|
setf.exp f36=r26
|
|
nop.f 0
|
|
// r27=bias
|
|
mov r27=0xffff;;
|
|
}
|
|
|
|
{.mmf
|
|
getf.exp r29=f8
|
|
// load start address for C_1...C_7 followed by T_table
|
|
ld8 r2=[r2]
|
|
// will continue only for positive normal/unnormal numbers
|
|
fclass.m.unc p0,p12 = f8, 0x19;;
|
|
}
|
|
|
|
|
|
.pred.rel "mutex",p8,p10
|
|
{.mfi
|
|
// denormal input, repeat get significand (after normalization)
|
|
(p8) getf.sig r25=f7
|
|
// x=1 ?
|
|
fcmp.eq.s0 p6,p0=f8,f1
|
|
// get T_index
|
|
(p10) shr.u r28=r25,63-8
|
|
}
|
|
{.mfi
|
|
// f32=2^16
|
|
setf.exp f32=r23
|
|
nop.f 0
|
|
mov r26=0x804;;
|
|
}
|
|
|
|
{.mfi
|
|
// denormal input, repeat get exponent (after normalization)
|
|
(p8) getf.exp r29=f7
|
|
// f33=0
|
|
mov f33=f0
|
|
// r26=0x80400...0 (threshold for using polynomial approximation)
|
|
shl r26=r26,64-12;;
|
|
}
|
|
|
|
{.mfb
|
|
add r3=16,r2
|
|
// r=x*y-1
|
|
fms.s1 f6=f41,f8,f1
|
|
(p12) br.cond.spnt SPECIAL_log2l
|
|
}
|
|
{.mfi
|
|
// load C_1
|
|
ldfe f14=[r2],48
|
|
// RN(x*y)
|
|
fma.s1 f43=f41,f8,f0
|
|
mov r23=0xff;;
|
|
}
|
|
|
|
{.mmi
|
|
// load C_7, C_8
|
|
ldfpd f10,f11=[r3],16
|
|
// load C_3,C_4
|
|
ldfpd f15,f42=[r2],16
|
|
(p8) shr.u r28=r25,63-8;;
|
|
}
|
|
|
|
|
|
{.mfi
|
|
// load C_5, C_6
|
|
ldfpd f12,f13=[r3]
|
|
// pseudo-zero ?
|
|
fcmp.eq.s0 p7,p0=f7,f0
|
|
// if first 9 bits after leading 1 are all zero, then p8=1
|
|
cmp.ltu p8,p12=r25,r26
|
|
}
|
|
{.mfi
|
|
// load C1l
|
|
ldfe f34=[r2],16
|
|
fmerge.se f7=f1,f7
|
|
// get T_index
|
|
and r28=r28,r23;;
|
|
}
|
|
{.mfi
|
|
// r29=exponent-bias
|
|
sub r29=r29,r27
|
|
// if first 8 bits after leading bit are 0, use polynomial approx. only
|
|
(p8) fms.s1 f6=f7,f1,f1
|
|
// start address of T_low
|
|
add r3=1024+16,r2
|
|
}
|
|
{.mfi
|
|
// load C_2
|
|
ldfe f35=[r2],16
|
|
// x=1, return 0
|
|
(p6) fma.s0 f8=f0,f0,f0
|
|
// first 8 bits after leading 1 are all ones ?
|
|
cmp.eq p10,p0=r23,r28;;
|
|
}
|
|
|
|
{.mfb
|
|
// if first 8 bits after leading 1 are all ones, use polynomial approx. only
|
|
// add 1 to the exponent additive term, and estimate log2(1-r)
|
|
(p10) add r29=1,r29
|
|
nop.f 0
|
|
(p7) br.cond.spnt LOG2_PSEUDO_ZERO
|
|
}
|
|
{.mfi
|
|
// get T_low address
|
|
shladd r3=r28,3,r3
|
|
// if first 8 bits after leading 1 are all ones, use polynomial approx. only
|
|
(p10) fms.s1 f6=f7,f36,f1
|
|
// p10 --> p8=1, p12=0
|
|
(p10) cmp.eq p8,p12=r0,r0;;
|
|
}
|
|
|
|
{.mfi
|
|
// get T_high address
|
|
shladd r2=r28,2,r2
|
|
// L(x*y)=x*y-RN(x*y)
|
|
fms.s1 f41=f41,f8,f43
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
// p13=p12
|
|
(p12) cmp.eq.unc p13,p0=r0,r0
|
|
// RtH=RN(x*y)-1 (will eliminate rounding errors in r)
|
|
fms.s1 f43=f43,f1,f1
|
|
nop.i 0;;
|
|
}
|
|
|
|
.pred.rel "mutex",p8,p12
|
|
{.mfb
|
|
// load T_high (unless first 9 bits after leading 1 are 0)
|
|
(p12) ldfs f7=[r2]
|
|
// set T_high=0 (if first 9 bits after leading 1 are 0)
|
|
(p8) fma.s1 f7=f0,f0,f0
|
|
// x=1, return
|
|
(p6) br.ret.spnt b0
|
|
}
|
|
.pred.rel "mutex",p8,p12
|
|
{.mfi
|
|
// p12: load T_low
|
|
(p12) ldfd f36=[r3]
|
|
// p8: set T_low=0
|
|
(p8) fma.s1 f36=f0,f0,f0
|
|
(p8) cmp.eq p8,p12=r29,r0;; //nop.i 0;;
|
|
}
|
|
|
|
.pred.rel "mutex",p8,p12
|
|
{.mfi
|
|
// f8=expon - bias
|
|
setf.sig f8=r29
|
|
// general case: 2^{16}+C1*r
|
|
(p12) fma.s1 f33=f6,f14,f32
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
// r26=1
|
|
mov r26=1
|
|
// p8 (mantissa is close to 1, or close to 2): 2^{-8}+C1*r
|
|
(p8) fma.s1 f32=f6,f14,f33
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// P78=C_7+C_8*r
|
|
fma.s1 f10=f11,f6,f10
|
|
// r26=2^{63}
|
|
shl r26=r26,63
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// P34=C_3+r*C_4
|
|
fma.s1 f15=f42,f6,f15
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// r2=r*r
|
|
fma.s1 f11=f6,f6,f0
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// P56=C_5+C_6*r
|
|
fma.s1 f13=f13,f6,f12
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// Rth-r
|
|
(p13) fms.s1 f43=f43,f1,f6
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
// significand(x)=1 ?
|
|
cmp.eq p0,p6=r25,r26
|
|
// P12=C1l+C_2*r
|
|
fma.s1 f34=f35,f6,f34
|
|
nop.i 0;;
|
|
}
|
|
|
|
.pred.rel "mutex",p8,p12
|
|
{.mfi
|
|
nop.m 0
|
|
// p12: C1r=(2^{16}+C1*r)-2^{16}
|
|
(p12) fms.s1 f32=f33,f1,f32
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// p8: C1r=C1*r (double extended)
|
|
(p8) fms.s1 f32=f32,f1,f33
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// L(x*y)*C_1+T_low
|
|
(p13) fma.s1 f36=f41,f14,f36
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// P58=P56+r2*P78
|
|
fma.s1 f13=f11,f10,f13
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// P14=P12+r2*P34
|
|
fma.s1 f15=f15,f11,f34
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// r4=r2*r2
|
|
fma.s1 f11=f11,f11,f0
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// normalize additive term (l=exponent of x)
|
|
fcvt.xf f8=f8
|
|
nop.i 0;;
|
|
}
|
|
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// D=C1*r-C1r
|
|
(p6) fms.s1 f12=f14,f6,f32
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// T_low'=(Rth-r)*C1+(L(x*y)*C1+T_low)
|
|
(p13) fma.s1 f36=f43,f14,f36
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// P18=P14+r4*P58
|
|
(p6) fma.s1 f13=f11,f13,f15
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// add T_high+l
|
|
(p6) fma.s1 f8=f8,f1,f7
|
|
nop.i 0;;
|
|
}
|
|
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// D+T_low
|
|
(p6) fma.s1 f12=f12,f1,f36
|
|
nop.i 0;;
|
|
}
|
|
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// (T_high+l)+C1r
|
|
(p6) fma.s1 f8=f8,f1,f32
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// (D+T_low)+r*P18
|
|
(p6) fma.s1 f13=f13,f6,f12
|
|
nop.i 0;;
|
|
}
|
|
|
|
//{.mfb
|
|
//nop.m 0
|
|
//mov f8=f36
|
|
//fma.s0 f8=f13,f6,f0
|
|
//br.ret.sptk b0;;
|
|
//}
|
|
|
|
|
|
{.mfb
|
|
nop.m 0
|
|
// result=((T_high+l)+C1r)+((D+T_low)+r*P18)
|
|
(p6) fma.s0 f8=f13,f1,f8
|
|
// return
|
|
br.ret.sptk b0;;
|
|
}
|
|
|
|
|
|
SPECIAL_log2l:
|
|
{.mfi
|
|
nop.m 0
|
|
mov FR_X=f8
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// x=+Infinity ?
|
|
fclass.m p7,p0=f8,0x21
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// x=+/-Zero ?
|
|
fclass.m p8,p0=f7,0x7
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// x=-Infinity, -normal, -denormal ?
|
|
fclass.m p6,p0=f8,0x3a
|
|
nop.i 0;;
|
|
}
|
|
{.mfb
|
|
nop.m 0
|
|
// log2l(+Infinity)=+Infinity
|
|
nop.f 0
|
|
(p7) br.ret.spnt b0;;
|
|
}
|
|
{.mfi
|
|
(p8) mov GR_Parameter_TAG = 168
|
|
// log2l(+/-0)=-infinity, raises Divide by Zero
|
|
// set f8=-0
|
|
(p8) fmerge.ns f8=f0,f8
|
|
nop.i 0;;
|
|
}
|
|
{.mfb
|
|
nop.m 0
|
|
(p8) frcpa.s0 f8,p0=f1,f8
|
|
(p8) br.cond.sptk __libm_error_region;;
|
|
}
|
|
{.mfb
|
|
(p6) mov GR_Parameter_TAG = 169
|
|
// x<0: return NaN, raise Invalid
|
|
(p6) frcpa.s0 f8,p0=f0,f0
|
|
(p6) br.cond.sptk __libm_error_region;;
|
|
}
|
|
|
|
|
|
{.mfb
|
|
nop.m 0
|
|
// Remaining cases: NaNs
|
|
fma.s0 f8=f8,f1,f0
|
|
br.ret.sptk b0;;
|
|
}
|
|
|
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LOG2_PSEUDO_ZERO:
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|
|
|
{.mfi
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nop.m 0
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|
mov FR_X=f8
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nop.i 0
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}
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|
{.mfi
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|
mov GR_Parameter_TAG = 168
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// log2l(+/-0)=-infinity, raises Divide by Zero
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|
// set f8=-0
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|
fmerge.ns f8=f0,f8
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|
nop.i 0;;
|
|
}
|
|
{.mfb
|
|
nop.m 0
|
|
frcpa.s0 f8,p0=f1,f8
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|
br.cond.sptk __libm_error_region;;
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|
}
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|
|
|
|
|
GLOBAL_IEEE754_END(log2l)
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libm_alias_ldouble_other (__log2, log2)
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|
|
|
|
|
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
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|
mov GR_SAVE_PFS=ar.pfs // Save ar.pfs
|
|
}
|
|
{ .mfi
|
|
.fframe 64
|
|
add sp=-64,sp // Create new stack
|
|
nop.f 0
|
|
mov GR_SAVE_GP=gp // Save gp
|
|
};;
|
|
{ .mmi
|
|
stfe [GR_Parameter_Y] = FR_Y,16 // 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
|
|
stfe [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
|
|
stfe [GR_Parameter_Y] = FR_RESULT // STORE Parameter 3 on stack
|
|
add GR_Parameter_Y = -16,GR_Parameter_Y
|
|
br.call.sptk b0=__libm_error_support# // Call error handling function
|
|
};;
|
|
{ .mmi
|
|
nop.m 0
|
|
nop.m 0
|
|
add GR_Parameter_RESULT = 48,sp
|
|
};;
|
|
{ .mmi
|
|
ldfe f8 = [GR_Parameter_RESULT] // Get return result off stack
|
|
.restore sp
|
|
add sp = 64,sp // Restore stack pointer
|
|
mov b0 = GR_SAVE_B0 // Restore return address
|
|
};;
|
|
{ .mib
|
|
mov gp = GR_SAVE_GP // Restore gp
|
|
mov ar.pfs = GR_SAVE_PFS // Restore ar.pfs
|
|
br.ret.sptk b0 // Return
|
|
};;
|
|
|
|
LOCAL_LIBM_END(__libm_error_region)
|
|
.type __libm_error_support#,@function
|
|
.global __libm_error_support#
|