.file "remainderf.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} 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

//====================================================================

// float remainderf(float,float);

//

// 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-p12

// General registers:   r2,r3,r28,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(remainderf)

// 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

  nop.m 0

  // r2=2^{24}-2

  movl r3=0x4b7ffffe;;

}

// Y +-NAN, +-inf, +-0?     p11

{ .mfi

      nop.m 999

      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 f15=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;;

}

.align 32

remloop24:

  { .mfi

  // f12=2^{24}-2

  setf.s f12=r3

  // Step (2)

  // q0 = a * y0 in f15

  (p6) fma.s1 f15=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

  // Step (4)

  // q1 = q0 + e0 * q0 in f6

  (p6) fma.s1 f6=f7,f15,f15

  nop.i 0

}

{ .mfi

  nop.m 0

  // Step (5)

  // e1 = e0 * e0 in f7

  (p6) fma.s1 f7=f7,f7,f0

  nop.i 0;;

}

 {.mii

  (p7) getf.exp r29=f15

  (p7) mov r28=0xfffd

  nop.i 0;;

}

 { .mfi

  // f15=1.25*2^{-24}

  setf.s f15=r2

  // Step (6)

  // q2 = q1 + e1 * q1 in f6

  (p6) fma.s1 f6=f7,f6,f6

  nop.i 0

}

{ .mfi

  mov r2=0x3e7

  // Step (7)

  // e2 = e1 * e1 in f7

  (p6) fma.s1 f7=f7,f7,f0

  nop.i 0;;

}

 {.mmi

  // q<1/4 ? (i.e. expon< -2)

  (p7) cmp.gt.unc p7,p0=r28,r29

  nop.m 0

  // r2=0x3e7000000

  shl r2=r2,24;;

}

{.mfb

  // r2=0x3e7000001

  add r2=1,r2

 // if |a/b|<1/4, set D flag before returning

 (p7) fma.s.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

  nop.m 0

  // set f8 to current a value | sign

  fmerge.s f8=f8,f13

  // r2=2^{-24}+2^{-48} (double prec.)

  shl r2=r2,28;;

}

{ .mfi

  // r29= -32+bias

  mov r29=0xffdf

  // Step (8)

  // q3 = q2 + e2 * q2 in f6

  (p6) fma.d.s1 f6=f7,f6,f6

  nop.i 0;;

}

{ .mfi

  nop.m 0

  // Step (9)

  // q = q3 in f11

  (p6) fma.s.s1 f11=f6,f1,f0

  nop.i 0;;

}

  {.mfi

  // f7=2^{-24}

  setf.d f7=r2

  // last step ? (q3<2^{24}-2 --> q<2^{24})

  fcmp.lt.unc.s1 p0,p12=f6,f12

  nop.i 0

} {.mfi

  // f12=2^{-32}

   setf.exp f12=r29

   nop.f 0

   nop.i 0;;

}

  {.mfi

  nop.m 0

  // r=a-b*q

  fnma.s1 f6=f14,f11,f13

  nop.i 0

}

{.mfi

  nop.m 0

  // q'=q-q*(1.25*2^{-24})   (q'=q-ulp)

  fnma.s.s1 f15=f11,f15,f11

  nop.i 0;;

}

  {.mfi

  nop.m 0

  // r2=a-b*q'

  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

  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,f12,f11

  nop.i 0

}

{.mfi

  nop.m 0

  // (p9) Q=q'+(last iteration ? sticky bits:0)

  // i.e. Q=q'+q'*x  (x=2^{-24} or 0: if expon. difference=23, want to round back to q)

  (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.s.s1 f12=f9,f11,f8

  nop.i 0

}

  {.mfi

  nop.m 0

  // get remainder

  fnma.s.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.s.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.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 ;;

}

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.s.s0 f8=f11,f1,f0

      nop.i 999

}

EXP_ERROR_RETURN:

{ .mib

      mov   GR_Parameter_TAG = 125

	  nop.i 999

      br.sptk __libm_error_region;;

}

GLOBAL_IEEE754_END(remainderf)

libm_alias_float_other (__remainder, remainder)

weak_alias (__remainderf, dremf)

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#