.file "fmodf.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
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// 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
// 08/15/00 Bundle added after call to __libm_error_support to properly
// set [the previously overwritten] GR_Parameter_RESULT.
// 11/28/00 Set FR_Y to f9
// 03/11/02 Fixed flags for fmodf(qnan,zero)
// 05/20/02 Cleaned up namespace and sf0 syntax
// 02/10/03 Reordered header: .section, .global, .proc, .align
// 04/28/03 Fix: fmod(sNaN,0) no longer sets errno
//
// API
//====================================================================
// float fmodf(float,float);
//
// Overview of operation
//====================================================================
// fmod(a,b)=a-i*b,
// where i is an integer such that, if b!=0,
// |i|<|a/b| and |a/b-i|<1
// Algorithm
//====================================================================
// a). if |a|<|b|, return a
// b). get quotient and reciprocal overestimates accurate to
// 33 bits (q2,y2)
// c). if the exponent difference (exponent(a)-exponent(b))
// is less than 32, truncate quotient to integer and
// finish in one iteration
// d). if exponent(a)-exponent(b)>=32 (q2>=2^32)
// round quotient estimate to single precision (k=RN(q2)),
// calculate partial remainder (a'=a-k*b),
// get quotient estimate (a'*y2), and repeat from c).
// Special cases
//====================================================================
// b=+/-0: return NaN, call libm_error_support
// a=+/-Inf, a=NaN or b=NaN: return NaN
// Registers used
//====================================================================
// Predicate registers: p6-p11
// General registers: r2,r29,r32 (ar.pfs), r33-r39
// Floating point registers: f6-f15
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(fmodf)
// inputs in f8, f9
// result in f8
{ .mfi
alloc r32=ar.pfs,1,4,4,0
// f6=|a|
fmerge.s f6=f0,f8
mov r2 = 0x0ffdd
}
{.mfi
nop.m 0
// f7=|b|
fmerge.s f7=f0,f9
nop.i 0;;
}
{ .mfi
setf.exp f11 = r2
// (1) y0
frcpa.s1 f10,p6=f6,f7
nop.i 0
}
// eliminate special cases
// Y +-NAN, +-inf, +-0? p7
{ .mfi
nop.m 999
fclass.m.unc p7,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
}
// |x| < |y|? Return x p8
{ .mfi
nop.m 999
fcmp.lt.unc.s1 p8,p0 = f6,f7
nop.i 999 ;;
}
{ .mfi
nop.m 0
// normalize y (if |x|<|y|)
(p8) fma.s0 f9=f9,f1,f0
nop.i 0;;
}
{ .mfi
mov r2=0x1001f
// (2) q0=a*y0
(p6) fma.s1 f13=f6,f10,f0
nop.i 0
}
{ .mfi
nop.m 0
// (3) e0 = 1 - b * y0
(p6) fnma.s1 f12=f7,f10,f1
nop.i 0;;
}
{.mfi
nop.m 0
// normalize x (if |x|<|y|)
(p8) fma.s.s0 f8=f8,f1,f0
nop.i 0
}
{.bbb
(p9) br.cond.spnt FMOD_X_NAN_INF
(p7) br.cond.spnt FMOD_Y_NAN_INF_ZERO
// if |x|<|y|, return
(p8) br.ret.spnt b0;;
}
{.mfi
nop.m 0
// normalize x
fma.s0 f6=f6,f1,f0
nop.i 0
}
{.mfi
nop.m 0
// normalize y
fma.s0 f7=f7,f1,f0
nop.i 0;;
}
{.mfi
// f15=2^32
setf.exp f15=r2
// (4) q1=q0+e0*q0
(p6) fma.s1 f13=f12,f13,f13
nop.i 0
}
{ .mfi
nop.m 0
// (5) e1 = e0 * e0 + 2^-34
(p6) fma.s1 f14=f12,f12,f11
nop.i 0;;
}
{.mlx
nop.m 0
movl r2=0x33a00000;;
}
{ .mfi
nop.m 0
// (6) y1 = y0 + e0 * y0
(p6) fma.s1 f10=f12,f10,f10
nop.i 0;;
}
{.mfi
// set f12=1.25*2^{-24}
setf.s f12=r2
// (7) q2=q1+e1*q1
(p6) fma.s1 f13=f13,f14,f13
nop.i 0;;
}
{.mfi
nop.m 0
fmerge.s f9=f8,f9
nop.i 0
}
{ .mfi
nop.m 0
// (8) y2 = y1 + e1 * y1
(p6) fma.s1 f10=f14,f10,f10
// set p6=0, p10=0
cmp.ne.and p6,p10=r0,r0;;
}
.align 32
loop24:
{.mfi
nop.m 0
// compare q2, 2^32
fcmp.lt.unc.s1 p8,p7=f13,f15
nop.i 0
}
{.mfi
nop.m 0
// will truncate quotient to integer, if exponent<32 (in advance)
fcvt.fx.trunc.s1 f11=f13
nop.i 0;;
}
{.mfi
nop.m 0
// if exponent>32, round quotient to single precision (perform in advance)
fma.s.s1 f13=f13,f1,f0
nop.i 0;;
}
{.mfi
nop.m 0
// set f12=sgn(a)
(p8) fmerge.s f12=f8,f1
nop.i 0
}
{.mfi
nop.m 0
// normalize truncated quotient
(p8) fcvt.xf f13=f11
nop.i 0;;
}
{ .mfi
nop.m 0
// calculate remainder (assuming f13=RZ(Q))
(p7) fnma.s1 f14=f13,f7,f6
nop.i 0
}
{.mfi
nop.m 0
// also if exponent>32, round quotient to single precision
// and subtract 1 ulp: q=q-q*(1.25*2^{-24})
(p7) fnma.s.s1 f11=f13,f12,f13
nop.i 0;;
}
{.mfi
nop.m 0
// (p8) calculate remainder (82-bit format)
(p8) fnma.s1 f11=f13,f7,f6
nop.i 0
}
{.mfi
nop.m 0
// (p7) calculate remainder (assuming f11=RZ(Q))
(p7) fnma.s1 f6=f11,f7,f6
nop.i 0;;
}
{.mfi
nop.m 0
// Final iteration (p8): is f6 the correct remainder (quotient was not overestimated) ?
(p8) fcmp.lt.unc.s1 p6,p10=f11,f0
nop.i 0;;
}
{.mfi
nop.m 0
// get new quotient estimation: a'*y2
(p7) fma.s1 f13=f14,f10,f0
nop.i 0
}
{.mfb
nop.m 0
// was f14=RZ(Q) ? (then new remainder f14>=0)
(p7) fcmp.lt.unc.s1 p7,p9=f14,f0
nop.b 0;;
}
.pred.rel "mutex",p6,p10
{.mfb
nop.m 0
// add b to estimated remainder (to cover the case when the quotient was overestimated)
// also set correct sign by using f9=|b|*sgn(a), f12=sgn(a)
(p6) fma.s.s0 f8=f11,f12,f9
nop.b 0
}
{.mfb
nop.m 0
// calculate remainder (single precision)
// set correct sign of result before returning
(p10) fma.s.s0 f8=f11,f12,f0
(p8) br.ret.sptk b0;;
}
{.mfi
nop.m 0
// if f13!=RZ(Q), get alternative quotient estimation: a''*y2
(p7) fma.s1 f13=f6,f10,f0
nop.i 0
}
{.mfb
nop.m 0
// if f14 was RZ(Q), set remainder to f14
(p9) mov f6=f14
br.cond.sptk loop24;;
}
{ .mmb
nop.m 0
nop.m 0
br.ret.sptk b0;;
}
FMOD_X_NAN_INF:
// Y zero ?
{.mfi
nop.m 0
fclass.m p10,p0=f8,0xc3 // Test x=nan
nop.i 0
}
{.mfi
nop.m 0
fma.s1 f10=f9,f1,f0
nop.i 0;;
}
{.mfi
nop.m 0
fma.s0 f8=f8,f1,f0
nop.i 0
}
{.mfi
nop.m 0
(p10) fclass.m p10,p0=f9,0x07 // Test x=nan, and y=zero
nop.i 0;;
}
{.mfb
nop.m 0
fcmp.eq.unc.s1 p11,p0=f10,f0
(p10) br.ret.spnt b0;; // Exit with result=x if x=nan and y=zero
}
{.mib
nop.m 0
nop.i 0
// if Y zero
(p11) br.cond.spnt FMOD_Y_ZERO;;
}
// X infinity? Return QNAN indefinite
{ .mfi
nop.m 999
fclass.m.unc p8,p9 = f8, 0x23
nop.i 999;;
}
// Y NaN ?
{.mfi
nop.m 999
(p8) fclass.m p9,p8=f9,0xc3
nop.i 0;;
}
{.mfi
nop.m 999
(p8) frcpa.s0 f8,p0 = f8,f8
nop.i 0
}
{ .mfi
nop.m 999
// also set Denormal flag if necessary
(p8) fma.s0 f9=f9,f1,f0
nop.i 999 ;;
}
{ .mfb
nop.m 999
(p8) fma.s.s0 f8=f8,f1,f0
nop.b 999 ;;
}
{ .mfb
nop.m 999
(p9) frcpa.s0 f8,p7=f8,f9
br.ret.sptk b0 ;;
}
FMOD_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.s.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.s.s0 f8=f9,f1,f0
(p9) br.ret.spnt b0 ;;
}
FMOD_Y_ZERO:
// Y zero? Must be zero at this point
// because it is the only choice left.
// Return QNAN indefinite
{.mfi
nop.m 0
// set Invalid
frcpa.s0 f12,p0=f0,f0
nop.i 999
}
// 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.s.s0 f8=f11,f1,f0
nop.i 999;;
}
EXP_ERROR_RETURN:
{ .mib
nop.m 0
mov GR_Parameter_TAG=122
br.sptk __libm_error_region;;
}
GLOBAL_IEEE754_END(fmodf)
libm_alias_float_other (__fmod, fmod)
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
stfs [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
stfs [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
stfs [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
ldfs 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#