mirror of
git://sourceware.org/git/glibc.git
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0347518d63
Many ia64 files have trailing whitespace which gets in the way and
annoys me. So strip it away:
find `find sysdeps/ -name ia64` -type f -exec sed -i 's:[[:space:]]*$::' {} +
Signed-off-by: Mike Frysinger <vapier@gentoo.org>
712 lines
20 KiB
ArmAsm
712 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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// Contributed 2000 by the Intel Numerics Group, Intel Corporation
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//
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// Redistribution and use in source and binary forms, with or without
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// modification, are permitted provided that the following conditions are
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// met:
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//
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// * Redistributions of source code must retain the above copyright
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// notice, this list of conditions and the following disclaimer.
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//
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// * Redistributions in binary form must reproduce the above copyright
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// notice, this list of conditions and the following disclaimer in the
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// documentation and/or other materials provided with the distribution.
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//
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// * The name of Intel Corporation may not be used to endorse or promote
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// products derived from this software without specific prior written
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// permission.
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// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
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// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
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// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
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// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
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// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
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// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
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// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
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// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
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// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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//
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// Intel Corporation is the author of this code, and requests that all
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// problem reports or change requests be submitted to it directly at
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// http://www.intel.com/software/products/opensource/libraries/num.htm.
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//
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// History
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//=================================================================
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// 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 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
|
|
GLOBAL_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;;
|
|
}
|
|
|
|
GLOBAL_LIBM_END(log2)
|
|
|
|
|
|
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#
|
|
|
|
|