mirror of
https://sourceware.org/git/glibc.git
synced 2024-11-23 21:40:12 +00:00
ee6189855a
equivalent, but shorter instructions. * sysdeps/unix/sysv/linux/x86_64/sysdep.h: Likewise. * sysdeps/unix/sysv/linux/x86_64/setcontext.S: Likewise. * sysdeps/unix/sysv/linux/x86_64/clone.S: Likewise. * sysdeps/unix/sysv/linux/x86_64/swapcontext.S: Likewise. * sysdeps/unix/x86_64/sysdep.S: Likewise. * sysdeps/x86_64/strchr.S: Likewise. * sysdeps/x86_64/memset.S: Likewise. * sysdeps/x86_64/strcspn.S: Likewise. * sysdeps/x86_64/strcmp.S: Likewise. * sysdeps/x86_64/elf/start.S: Likewise. * sysdeps/x86_64/strspn.S: Likewise. * sysdeps/x86_64/dl-machine.h: Likewise. * sysdeps/x86_64/bsd-_setjmp.S: Likewise. * sysdeps/x86_64/bsd-setjmp.S: Likewise. * sysdeps/x86_64/strtok.S: Likewise.
591 lines
12 KiB
ArmAsm
591 lines
12 KiB
ArmAsm
.file "remainder.s"
|
|
|
|
|
|
// Copyright (c) 2000 - 2003, Intel Corporation
|
|
// All rights reserved.
|
|
//
|
|
// Contributed 2000 by the Intel Numerics Group, Intel Corporation
|
|
//
|
|
// Redistribution and use in source and binary forms, with or without
|
|
// modification, are permitted provided that the following conditions are
|
|
// met:
|
|
//
|
|
// * Redistributions of source code must retain the above copyright
|
|
// notice, this list of conditions and the following disclaimer.
|
|
//
|
|
// * Redistributions in binary form must reproduce the above copyright
|
|
// notice, this list of conditions and the following disclaimer in the
|
|
// documentation and/or other materials provided with the distribution.
|
|
//
|
|
// * The name of Intel Corporation may not be used to endorse or promote
|
|
// products derived from this software without specific prior written
|
|
// permission.
|
|
|
|
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
|
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
|
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
|
|
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL INTEL OR ITS
|
|
// CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
|
|
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
|
|
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
|
|
// PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
|
|
// OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY OR TORT (INCLUDING
|
|
// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
|
|
// SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
|
|
//
|
|
// Intel Corporation is the author of this code, and requests that all
|
|
// problem reports or change requests be submitted to it directly at
|
|
// http://www.intel.com/software/products/opensource/libraries/num.htm.
|
|
//
|
|
// History
|
|
//====================================================================
|
|
// 02/02/00 Initial version
|
|
// 03/02/00 New Algorithm
|
|
// 04/04/00 Unwind support added
|
|
// 07/21/00 Fixed quotient=2^{24*m+23}*1.q1...q23 1 bug
|
|
// 08/15/00 Bundle added after call to __libm_error_support to properly
|
|
// set [the previously overwritten] GR_Parameter_RESULT.
|
|
// 11/29/00 Set FR_Y to f9
|
|
// 05/20/02 Cleaned up namespace and sf0 syntax
|
|
// 02/10/03 Reordered header: .section, .global, .proc, .align
|
|
//
|
|
// API
|
|
//====================================================================
|
|
// double remainder(double,double);
|
|
//
|
|
// Overview of operation
|
|
//====================================================================
|
|
// remainder(a,b)=a-i*b,
|
|
// where i is an integer such that, if b!=0 and a is finite,
|
|
// |a/b-i|<=1/2. If |a/b-i|=1/2, i is even.
|
|
//
|
|
// Algorithm
|
|
//====================================================================
|
|
// a). eliminate special cases
|
|
// b). if |a/b|<0.25 (first quotient estimate), return a
|
|
// c). use single precision divide algorithm to get quotient q
|
|
// rounded to 24 bits of precision
|
|
// d). calculate partial remainders (using both q and q-ulp);
|
|
// select one and RZ(a/b) based on the sign of |a|-|b|*q
|
|
// e). if the exponent difference (exponent(a)-exponent(b))
|
|
// is less than 24 (quotient estimate<2^{24}-2), use RZ(a/b)
|
|
// and sticky bits to round to integer; exit loop and
|
|
// calculate final remainder
|
|
// f). if exponent(a)-exponent(b)>=24, select new value of a as
|
|
// the partial remainder calculated using RZ(a/b);
|
|
// repeat from c).
|
|
//
|
|
// Special cases
|
|
//====================================================================
|
|
// a=+/- Inf, or b=+/-0: return NaN, call libm_error_support
|
|
// a=NaN or b=NaN: return NaN
|
|
|
|
// Registers used
|
|
//====================================================================
|
|
// Predicate registers: p6-p14
|
|
// General registers: r2,r3,r28,r29,r32 (ar.pfs), r33-r39
|
|
// Floating point registers: f6-f15,f32
|
|
|
|
GR_SAVE_B0 = r33
|
|
GR_SAVE_PFS = r34
|
|
GR_SAVE_GP = r35
|
|
GR_SAVE_SP = r36
|
|
|
|
GR_Parameter_X = r37
|
|
GR_Parameter_Y = r38
|
|
GR_Parameter_RESULT = r39
|
|
GR_Parameter_TAG = r40
|
|
|
|
FR_X = f10
|
|
FR_Y = f9
|
|
FR_RESULT = f8
|
|
|
|
|
|
.section .text
|
|
GLOBAL_IEEE754_ENTRY(remainder)
|
|
|
|
// inputs in f8, f9
|
|
// result in f8
|
|
|
|
{ .mfi
|
|
alloc r32=ar.pfs,1,4,4,0
|
|
// f13=|a|
|
|
fmerge.s f13=f0,f8
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// f14=|b|
|
|
fmerge.s f14=f0,f9
|
|
nop.i 0;;
|
|
}
|
|
{.mlx
|
|
mov r28=0x2ffdd
|
|
// r2=2^{23}
|
|
movl r3=0x4b000000;;
|
|
}
|
|
|
|
// Y +-NAN, +-inf, +-0? p11
|
|
{ .mfi
|
|
setf.exp f32=r28
|
|
fclass.m.unc p11,p0 = f9, 0xe7
|
|
nop.i 999
|
|
}
|
|
// qnan snan inf norm unorm 0 -+
|
|
// 1 1 1 0 0 0 11
|
|
// e 3
|
|
// X +-NAN, +-inf, ? p9
|
|
{ .mfi
|
|
nop.m 999
|
|
fclass.m.unc p9,p0 = f8, 0xe3
|
|
nop.i 999;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
mov f12=f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
// set p7=1
|
|
cmp.eq.unc p7,p0=r0,r0
|
|
// Step (1)
|
|
// y0 = 1 / b in f10
|
|
frcpa.s1 f10,p6=f13,f14
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.bbb
|
|
(p9) br.cond.spnt FREM_X_NAN_INF
|
|
(p11) br.cond.spnt FREM_Y_NAN_INF_ZERO
|
|
nop.b 0
|
|
} {.mfi
|
|
nop.m 0
|
|
// set D flag if a (f8) is denormal
|
|
fnma.s0 f6=f8,f1,f8
|
|
nop.i 0;;
|
|
}
|
|
|
|
|
|
remloop24:
|
|
{ .mfi
|
|
nop.m 0
|
|
// Step (2)
|
|
// q0 = a * y0 in f12
|
|
(p6) fma.s1 f12=f13,f10,f0
|
|
nop.i 0
|
|
} { .mfi
|
|
nop.m 0
|
|
// Step (3)
|
|
// e0 = 1 - b * y0 in f7
|
|
(p6) fnma.s1 f7=f14,f10,f1
|
|
nop.i 0;;
|
|
} {.mlx
|
|
nop.m 0
|
|
// r2=1.25*2^{-24}
|
|
movl r2=0x33a00000;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 0
|
|
// q1=q0*(1+e0)
|
|
(p6) fma.s1 f15=f12,f7,f12
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 0
|
|
// Step (4)
|
|
// e1 = e0 * e0 + E in f7
|
|
(p6) fma.s1 f7=f7,f7,f32
|
|
nop.i 0;;
|
|
}
|
|
{.mii
|
|
(p7) getf.exp r29=f12
|
|
(p7) mov r28=0xfffd
|
|
nop.i 0;;
|
|
}
|
|
{ .mfi
|
|
// f12=2^{23}
|
|
setf.s f12=r3
|
|
// Step (5)
|
|
// q2 = q1 + e1 * q1 in f11
|
|
(p6) fma.s.s1 f11=f7,f15,f15
|
|
nop.i 0
|
|
} { .mfi
|
|
nop.m 0
|
|
// Step (6)
|
|
// q2 = q1 + e1 * q1 in f6
|
|
(p6) fma.s1 f6=f7,f15,f15
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mmi
|
|
// f15=1.25*2^{-24}
|
|
setf.s f15=r2
|
|
// q<1/4 ? (i.e. expon< -2)
|
|
(p7) cmp.gt p7,p0=r28,r29
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfb
|
|
// r29= -32+bias
|
|
mov r29=0xffdf
|
|
// if |a/b|<1/4, set D flag before returning
|
|
(p7) fma.d.s0 f9=f9,f0,f8
|
|
nop.b 0;;
|
|
}
|
|
{.mfb
|
|
nop.m 0
|
|
// can be combined with bundle above if sign of 0 or
|
|
// FTZ enabled are not important
|
|
(p7) fmerge.s f8=f8,f9
|
|
// return if |a|<4*|b| (estimated quotient < 1/4)
|
|
(p7) br.ret.spnt b0;;
|
|
}
|
|
{.mfi
|
|
// f7=2^{-32}
|
|
setf.exp f7=r29
|
|
// set f8 to current a value | sign
|
|
fmerge.s f8=f8,f13
|
|
nop.i 0;;
|
|
}
|
|
|
|
|
|
{.mfi
|
|
getf.exp r28=f6
|
|
// last step ? (q<2^{23})
|
|
fcmp.lt.unc.s1 p0,p12=f6,f12
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// r=a-b*q
|
|
fnma.s1 f6=f14,f11,f13
|
|
nop.i 0
|
|
} {.mfi
|
|
// r2=23+bias
|
|
mov r2=0xffff+23
|
|
// q'=q-q*(1.25*2^{-24}) (q'=q-ulp)
|
|
fnma.s.s1 f15=f11,f15,f11
|
|
nop.i 0;;
|
|
}
|
|
{.mmi
|
|
nop.m 0
|
|
cmp.eq p11,p14=r2,r28
|
|
nop.i 0;;
|
|
}
|
|
|
|
.pred.rel "mutex",p11,p14
|
|
{.mfi
|
|
nop.m 0
|
|
// if exp_q=2^23, then r=a-b*2^{23}
|
|
(p11) fnma.s1 f13=f12,f14,f13
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// r2=a-b*q'
|
|
(p14) fnma.s1 f13=f14,f15,f13
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// r>0 iff q=RZ(a/b) and inexact
|
|
fcmp.gt.unc.s1 p8,p0=f6,f0
|
|
nop.i 0
|
|
} {.mfi
|
|
nop.m 0
|
|
// r<0 iff q'=RZ(a/b) and inexact
|
|
(p14) fcmp.lt.unc.s1 p9,p10=f6,f0
|
|
nop.i 0;;
|
|
}
|
|
|
|
.pred.rel "mutex",p8,p9
|
|
{.mfi
|
|
nop.m 0
|
|
// (p8) Q=q+(last iteration ? sticky bits:0)
|
|
// i.e. Q=q+q*x (x=2^{-32} or 0)
|
|
(p8) fma.s1 f11=f11,f7,f11
|
|
nop.i 0
|
|
} {.mfi
|
|
nop.m 0
|
|
// (p9) Q=q'+(last iteration ? sticky bits:0)
|
|
// i.e. Q=q'+q'*x (x=2^{-32} or 0)
|
|
(p9) fma.s1 f11=f15,f7,f15
|
|
nop.i 0;;
|
|
}
|
|
|
|
{.mfb
|
|
nop.m 0
|
|
// (p9) set r=r2 (new a, if not last iteration)
|
|
// (p10) new a =r
|
|
(p10) mov f13=f6
|
|
(p12) br.cond.sptk remloop24;;
|
|
}
|
|
|
|
// last iteration
|
|
{.mfi
|
|
nop.m 0
|
|
// set f9=|b|*sgn(a)
|
|
fmerge.s f9=f8,f9
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// round to integer
|
|
fcvt.fx.s1 f11=f11
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// save sign of a
|
|
fmerge.s f7=f8,f8
|
|
nop.i 0
|
|
} {.mfi
|
|
nop.m 0
|
|
// normalize
|
|
fcvt.xf f11=f11
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// This can be removed if sign of 0 is not important
|
|
// get remainder using sf1
|
|
fnma.d.s1 f12=f9,f11,f8
|
|
nop.i 0
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// get remainder
|
|
fnma.d.s0 f8=f9,f11,f8
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
// f12=0?
|
|
// This can be removed if sign of 0 is not important
|
|
fcmp.eq.unc.s1 p8,p0=f12,f0
|
|
nop.i 0;;
|
|
}
|
|
{.mfb
|
|
nop.m 0
|
|
// if f8=0, set sign correctly
|
|
// This can be removed if sign of 0 is not important
|
|
(p8) fmerge.s f8=f7,f8
|
|
// return
|
|
br.ret.sptk b0;;
|
|
}
|
|
|
|
|
|
FREM_X_NAN_INF:
|
|
|
|
// Y zero ?
|
|
{.mfi
|
|
nop.m 0
|
|
fma.s1 f10=f9,f1,f0
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 0
|
|
fcmp.eq.unc.s1 p11,p0=f10,f0
|
|
nop.i 0;;
|
|
}
|
|
{.mib
|
|
nop.m 0
|
|
nop.i 0
|
|
// if Y zero
|
|
(p11) br.cond.spnt FREM_Y_ZERO;;
|
|
}
|
|
|
|
// X infinity? Return QNAN indefinite
|
|
{ .mfi
|
|
nop.m 999
|
|
fclass.m.unc p8,p0 = f8, 0x23
|
|
nop.i 999
|
|
}
|
|
// X infinity? Return QNAN indefinite
|
|
{ .mfi
|
|
nop.m 999
|
|
fclass.m.unc p11,p0 = f8, 0x23
|
|
nop.i 999;;
|
|
}
|
|
// Y NaN ?
|
|
{.mfi
|
|
nop.m 999
|
|
(p8) fclass.m.unc p0,p8=f9,0xc3
|
|
nop.i 0;;
|
|
}
|
|
{.mfi
|
|
nop.m 999
|
|
// also set Denormal flag if necessary
|
|
(p8) fma.s0 f9=f9,f1,f0
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) frcpa.s0 f8,p7 = f8,f8
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 999
|
|
(p11) mov f10=f8
|
|
nop.i 0
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p8) fma.d.s0 f8=f8,f1,f0
|
|
nop.i 0 ;;
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
frcpa.s0 f8,p7=f8,f9
|
|
(p11) br.cond.spnt EXP_ERROR_RETURN;;
|
|
}
|
|
{ .mib
|
|
nop.m 0
|
|
nop.i 0
|
|
br.ret.spnt b0 ;;
|
|
}
|
|
|
|
|
|
FREM_Y_NAN_INF_ZERO:
|
|
|
|
// Y INF
|
|
{ .mfi
|
|
nop.m 999
|
|
fclass.m.unc p7,p0 = f9, 0x23
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
(p7) fma.d.s0 f8=f8,f1,f0
|
|
(p7) br.ret.spnt b0 ;;
|
|
}
|
|
|
|
// Y NAN?
|
|
{ .mfi
|
|
nop.m 999
|
|
fclass.m.unc p9,p0 = f9, 0xc3
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{ .mfb
|
|
nop.m 999
|
|
(p9) fma.d.s0 f8=f9,f1,f0
|
|
(p9) br.ret.spnt b0 ;;
|
|
}
|
|
|
|
FREM_Y_ZERO:
|
|
// Y zero? Must be zero at this point
|
|
// because it is the only choice left.
|
|
// Return QNAN indefinite
|
|
|
|
// X NAN?
|
|
{ .mfi
|
|
nop.m 999
|
|
fclass.m.unc p9,p10 = f8, 0xc3
|
|
nop.i 999 ;;
|
|
}
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) fclass.nm p9,p10 = f8, 0xff
|
|
nop.i 999 ;;
|
|
}
|
|
|
|
{.mfi
|
|
nop.m 999
|
|
(p9) frcpa.s0 f11,p7=f8,f0
|
|
nop.i 0;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
(p10) frcpa.s0 f11,p7 = f0,f0
|
|
nop.i 999;;
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fmerge.s f10 = f8, f8
|
|
nop.i 999
|
|
}
|
|
|
|
{ .mfi
|
|
nop.m 999
|
|
fma.d.s0 f8=f11,f1,f0
|
|
nop.i 999
|
|
}
|
|
|
|
|
|
EXP_ERROR_RETURN:
|
|
|
|
{ .mib
|
|
mov GR_Parameter_TAG = 124
|
|
nop.i 999
|
|
br.sptk __libm_error_region;;
|
|
}
|
|
|
|
GLOBAL_IEEE754_END(remainder)
|
|
|
|
|
|
|
|
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 // Save 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
|
|
nop.b 0 // Parameter 3 address
|
|
}
|
|
{ .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#
|
|
|
|
|