.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#