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glibc/sysdeps/ia64/fpu/e_remainderl.S
Jakub Jelinek 0ecb606cb6 2.5-18.1
2007-07-12 18:26:36 +00:00

618 lines
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ArmAsm
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.file "remainderl.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
//====================================================================
// long double remainderl(long double,long 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(remainderl)
// 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
getf.sig r29=f9
// f14=|b|
fmerge.s f14=f0,f9
nop.i 0;;
}
{.mlx
mov r28=0x2ffdd
// r2=2^{23}
movl r3=0x4b000000;;
}
{.mmi
setf.exp f32=r28
nop.m 0
// y pseudo-zero ?
cmp.eq p11,p10=r29,r0;;
}
// Y +-NAN, +-inf, +-0? p11
{ .mfi
nop.m 999
(p10) fclass.m p11,p10 = 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,p8 = 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;;
}
// Y +-NAN, +-inf, +-0? p11
{ .mfi
nop.m 999
// pseudo-NaN ?
(p10) fclass.nm p11,p0 = f9, 0xff
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
(p8) fclass.nm p9,p0 = f8, 0xff
nop.i 999;;
}
{.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 f15
(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.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.s1 f12=f9,f11,f8
nop.i 0
}
{.mfi
nop.m 0
// get remainder
fnma.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) fnma.s0 f9=f9,f1,f9
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.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.s0 f8=f8,f1,f0
(p7) br.ret.spnt b0 ;;
}
// Y NAN?
{ .mfi
nop.m 999
fclass.m.unc p9,p10 = f9, 0xc3
nop.i 999 ;;
}
{ .mfi
nop.m 999
(p10) fclass.nm p9,p0 = f9, 0xff
nop.i 999 ;;
}
{ .mfb
nop.m 999
(p9) fma.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.s0 f8=f11,f1,f0
nop.i 999;;
}
EXP_ERROR_RETURN:
{ .mib
mov GR_Parameter_TAG = 123
nop.i 999
br.sptk __libm_error_region;;
}
GLOBAL_IEEE754_END(remainderl)
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
stfe [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
stfe [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
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#
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