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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>
716 lines
20 KiB
ArmAsm
716 lines
20 KiB
ArmAsm
.file "log2.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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// 09/11/00 Initial version
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// 03/19/01 Added one polynomial coefficient, to improve accuracy
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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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// 04/18/03 Reformatted T[255]
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//
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// API
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//=================================================================
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// double log2(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 (table index)
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// j=0 if f<128; j=1 if f>=128
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// T is a table that stores log2(1/y) (in entries 1..255) rounded to
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// double extended precision; f is used as an index; T[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[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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// log2(x) is approximated as
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// (l-j) + T[f] + (c1*r+c2*r^2+...+c7*r^7), if f>0
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//
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// Special values
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//=================================================================
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// log2(0)=-inf, raises Divide by Zero
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// log2(+inf)=inf
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// log2(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-f33
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// r2-r3, r23-r30
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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 0xbfd0000000000000, 0x3fc999999999999a //C_4, C_5
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data8 0xbfc5555555555555, 0x3fc2492492492492 //C_6, C_7
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data8 0xb8aa3b295c17f0bc, 0x00003fff // C_1
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data8 0xaaaaaaaaaaaaaaab, 0x00003ffd // C_3=1/3
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LOCAL_OBJECT_END(poly_coeffs)
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LOCAL_OBJECT_START(T_table)
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data8 0x9d3cbe69aecac4c2, 0x0000bffc
|
|
data8 0x99574f13c570d0fb, 0x0000bffc
|
|
data8 0x96bce349bf7ee6c7, 0x0000bffc
|
|
data8 0x92d30c9b86cee18e, 0x0000bffc
|
|
data8 0x9035adef17c5bd5c, 0x0000bffc
|
|
data8 0x8c4765e8e8b5f251, 0x0000bffc
|
|
data8 0x89a70da448316ffa, 0x0000bffc
|
|
data8 0x85b44a24474af78a, 0x0000bffc
|
|
data8 0x8310f17aab5adf70, 0x0000bffc
|
|
data8 0x806c6388d0965f29, 0x0000bffc
|
|
data8 0xf8e69092bf0c5ead, 0x0000bffb
|
|
data8 0xf397608bfd2d90e6, 0x0000bffb
|
|
data8 0xee45be24d0eedbc4, 0x0000bffb
|
|
data8 0xe646af233db881e9, 0x0000bffb
|
|
data8 0xe0eee4e1ce3d06fb, 0x0000bffb
|
|
data8 0xdb94a049e6e87a4f, 0x0000bffb
|
|
data8 0xd3888ef9a4249f5a, 0x0000bffb
|
|
data8 0xce280e6fbac39194, 0x0000bffb
|
|
data8 0xc8c50b72319ad574, 0x0000bffb
|
|
data8 0xc0abcd39f41e329b, 0x0000bffb
|
|
data8 0xbb4279cfa7f9667b, 0x0000bffb
|
|
data8 0xb5d69bac77ec398a, 0x0000bffb
|
|
data8 0xb068306bf20d6233, 0x0000bffb
|
|
data8 0xa83dc1b019ddb6a8, 0x0000bffb
|
|
data8 0xa2c8eb1886c2d024, 0x0000bffb
|
|
data8 0x9d517ee93f8e16c0, 0x0000bffb
|
|
data8 0x97d77aae659b92fb, 0x0000bffb
|
|
data8 0x8f9b91da5736d415, 0x0000bffb
|
|
data8 0x8a1b06b09b7fd1d1, 0x0000bffb
|
|
data8 0x8497daca0a2e077a, 0x0000bffb
|
|
data8 0xfe241745a453f10c, 0x0000bffa
|
|
data8 0xf3132d6708d723c5, 0x0000bffa
|
|
data8 0xe7fcf2e21a0e7d77, 0x0000bffa
|
|
data8 0xd75198b04afb8da9, 0x0000bffa
|
|
data8 0xcc2dfe1a4a8ca305, 0x0000bffa
|
|
data8 0xc10500d63aa65882, 0x0000bffa
|
|
data8 0xb5d69bac77ec398a, 0x0000bffa
|
|
data8 0xaaa2c95dc66abcde, 0x0000bffa
|
|
data8 0x9f6984a342d13101, 0x0000bffa
|
|
data8 0x942ac82e5387ac51, 0x0000bffa
|
|
data8 0x88e68ea899a0976c, 0x0000bffa
|
|
data8 0xefebc4409ccf872e, 0x0000bff9
|
|
data8 0xd947b0c6642ef69e, 0x0000bff9
|
|
data8 0xc2987d51e043d407, 0x0000bff9
|
|
data8 0xabde1eeee6bfd257, 0x0000bff9
|
|
data8 0x95188a9917cf2e01, 0x0000bff9
|
|
data8 0xfc8f6a777c1b7f1e, 0x0000bff8
|
|
data8 0xced727635c59725c, 0x0000bff8
|
|
data8 0xa108358a4c904615, 0x0000bff8
|
|
data8 0xe644fcbeb3ac9c90, 0x0000bff7
|
|
data8 0x8a4bd667bf08e7de, 0x0000bff7
|
|
data8 0x0000000000000000 // T[255] Low
|
|
data8 0x0000000000000000 // T[255] High
|
|
LOCAL_OBJECT_END(T_table)
|
|
|
|
|
|
|
|
.section .text
|
|
WEAK_LIBM_ENTRY(log2)
|
|
|
|
{ .mfi
|
|
alloc r32=ar.pfs,1,4,4,0
|
|
// y=frcpa(x)
|
|
frcpa.s1 f6,p0=f1,f8
|
|
// will form significand of 1.5 (to test whether the index is 128 or above)
|
|
mov r24=0xc
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// normalize x
|
|
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
|
|
// will form significand of 1.5 (to test whether the index is 128 or above)
|
|
shl r24=r24,60
|
|
}
|
|
{.mfi
|
|
mov r26=0x804
|
|
nop.f 0
|
|
// r23=bias-1
|
|
mov r23=0xfffe;;
|
|
}
|
|
|
|
{.mmf
|
|
getf.exp r29=f8
|
|
// load start address for C_1...C_6 followed by T_table
|
|
ld8 r2=[r2]
|
|
// will continue only for positive normal/denormal numbers
|
|
fclass.nm.unc p12,p7 = 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=0.5
|
|
setf.exp f32=r23
|
|
nop.f 0
|
|
// r27=bias
|
|
mov r27=0xffff;;
|
|
}
|
|
|
|
{.mmi
|
|
// denormal input, repeat get exponent (after normalization)
|
|
(p8) getf.exp r29=f7
|
|
mov r23=0xff
|
|
// r26=0x80400...0 (threshold for using polynomial approximation)
|
|
shl r26=r26,64-12;;
|
|
}
|
|
|
|
{.mfb
|
|
add r3=48,r2
|
|
// r=1-x*y
|
|
fms.s1 f6=f6,f8,f1
|
|
(p12) br.cond.spnt SPECIAL_LOG2
|
|
}
|
|
{.mfi
|
|
// load C_4, C_5
|
|
ldfpd f10,f11=[r2],16
|
|
nop.f 0
|
|
cmp.geu p12,p0=r25,r24;;
|
|
}
|
|
|
|
{.mmi
|
|
// load C_6, C_7
|
|
ldfpd f12,f13=[r2],16
|
|
// r27=bias-1 (if index >=128, will add exponent+1)
|
|
(p12) mov r27=0xfffe
|
|
(p8) shr.u r28=r25,63-8;;
|
|
}
|
|
|
|
|
|
{.mfi
|
|
// load C_1
|
|
ldfe f14=[r2],32
|
|
fmerge.se f7=f1,f7
|
|
// if first 9 bits after leading 1 are all zero, then p8=1
|
|
cmp.ltu p8,p12=r25,r26
|
|
}
|
|
{.mfi
|
|
// load C_3
|
|
ldfe f15=[r3]
|
|
nop.f 0
|
|
// get T_index
|
|
and r28=r28,r23;;
|
|
}
|
|
{.mfi
|
|
// r29=exponent-bias
|
|
sub r29=r29,r27
|
|
// x=1, return 0
|
|
(p6) fma.d.s0 f8=f0,f0,f0
|
|
// get T address
|
|
shladd r2=r28,4,r2
|
|
}
|
|
{.mfb
|
|
// first 8 bits after leading 1 are all ones ?
|
|
cmp.eq p10,p0=r23,r28
|
|
// if first 8 bits after leading bit are 0, use polynomial approx. only
|
|
(p8) fms.s1 f6=f7,f1,f1
|
|
// x=1, return
|
|
(p6) br.ret.spnt b0;;
|
|
}
|
|
{.mfi
|
|
// r26=1
|
|
mov r26=1
|
|
// if first 8 bits after leading 1 are all ones, use polynomial approx. only
|
|
(p10) fms.s1 f6=f7,f32,f1
|
|
nop.i 0;;
|
|
}
|
|
|
|
.pred.rel "mutex",p8,p12
|
|
{.mmf
|
|
// load T (unless first 9 bits after leading 1 are 0)
|
|
(p12) ldfe f33=[r2]
|
|
// f8=expon - bias
|
|
setf.sig f8=r29
|
|
// set T=0 (if first 9 bits after leading 1 are 0)
|
|
(p8) fma.s1 f33=f0,f0,f0;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// P12=1-0.5*r
|
|
fnma.s1 f32=f32,f6,f1
|
|
// r26=2^{63}
|
|
shl r26=r26,63
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// r2=r*r
|
|
fma.s1 f7=f6,f6,f0
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
// significand(x)=1 ?
|
|
cmp.eq p0,p6=r26,r25
|
|
// P67=C_6+C_7*r
|
|
fma.s1 f13=f13,f6,f12
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// P45=C_4+C_5*r
|
|
fma.s1 f10=f11,f6,f10
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// C_1*r
|
|
(p6) fma.s1 f14=f14,f6,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
|
|
// P13=1-0.5*r+C_3*r^2
|
|
(p6) fma.s1 f15=f15,f7,f32
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// P47=P45+r2*P67
|
|
(p6) fma.s1 f13=f13,f7,f10
|
|
// if significand(x)=1, return exponent (l)
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// r3=r^3
|
|
(p6) fma.s1 f7=f7,f6,f0
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// add T+l
|
|
(p6) fma.s1 f8=f8,f1,f33
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// P17=P13+r3*P47
|
|
(p6) fma.s1 f13=f13,f7,f15
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfb
|
|
nop.m 0
|
|
// result=T+l+(C_1*r)*P16
|
|
(p6) fma.d.s0 f8=f13,f14,f8
|
|
// return
|
|
br.ret.sptk b0;;
|
|
}
|
|
|
|
|
|
SPECIAL_LOG2:
|
|
{.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=f8,0x7
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// x=-Infinity, -normal, -denormal ?
|
|
fclass.m p6,p0=f8,0x3a
|
|
nop.i 0;;
|
|
}
|
|
{.mfb
|
|
nop.m 0
|
|
// log2(+Infinity)=+Infinity
|
|
nop.f 0
|
|
(p7) br.ret.spnt b0;;
|
|
}
|
|
{.mfi
|
|
(p8) mov GR_Parameter_TAG = 170
|
|
// log2(+/-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 = 171
|
|
// 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.d.s0 f8=f8,f1,f0
|
|
br.ret.sptk b0;;
|
|
}
|
|
|
|
WEAK_LIBM_END(log2)
|
|
libm_alias_double_other (__log2, log2)
|
|
#ifdef SHARED
|
|
.symver log2,log2@@GLIBC_2.29
|
|
.weak __log2_compat
|
|
.set __log2_compat,__log2
|
|
.symver __log2_compat,log2@GLIBC_2.2
|
|
#endif
|
|
|
|
|
|
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
|
|
stfd [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
|
|
stfd [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
|
|
stfd [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
|
|
ldfd 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#
|