.file "nextafter.s"

// Copyright (c) 2000 - 2004, 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

// 03/03/00 Modified to conform to C9X, and improve speed of main path

// 03/14/00 Fixed case where x is a power of 2, and x > y, improved speed

// 04/04/00 Unwind support added

// 05/12/00 Fixed erroneous denormal flag setting for exponent change cases 1,3

// 08/15/00 Bundle added after call to __libm_error_support to properly

//          set [the previously overwritten] GR_Parameter_RESULT.

// 09/09/00 Updated fcmp so that qnans do not raise invalid

// 12/15/00 Corrected behavior when both args are zero to conform to C99, and

//          fixed flag settings for several cases

// 05/20/02 Cleaned up namespace and sf0 syntax

// 02/10/03 Reordered header: .section, .global, .proc, .align

// 12/14/04 Added error handling on underflow.

//

// API

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

// double nextafter( double x, double y );

// input  floating point f8, f9

// output floating point f8

//

// Registers used

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

GR_max_pexp     = r14

GR_min_pexp     = r15

GR_exp          = r16

GR_sig          = r17

GR_lnorm_sig    = r18

GR_sign_mask    = r19

GR_exp_mask     = r20

GR_sden_sig     = r21

GR_new_sig      = r22

GR_new_exp      = r23

GR_lden_sig     = r24

GR_snorm_sig    = r25

GR_exp1         = r26

GR_x_exp        = r27

GR_min_den_rexp = r28

// r36-39 parameters for libm_error_support

GR_SAVE_B0                = r34

GR_SAVE_GP                = r35

GR_SAVE_PFS               = r32

GR_Parameter_X            = r36

GR_Parameter_Y            = r37

GR_Parameter_RESULT       = r38

GR_Parameter_TAG          = r39

FR_lnorm_sig       = f10

FR_lnorm_exp       = f11

FR_lnorm           = f12

FR_sden_sig        = f13

FR_sden_exp        = f14

FR_sden            = f15

FR_save_f8         = f33

FR_new_exp         = f34

FR_new_sig         = f35

FR_lden_sig        = f36

FR_snorm_sig       = f37

FR_exp1            = f38

FR_tmp             = f39

//

// Overview of operation

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

// nextafter determines the next representable value

// after x in the direction of y.

.section .text

GLOBAL_LIBM_ENTRY(nextafter)

// Extract signexp from x

// Is x < y ?  p10 if yes, p11 if no

// Form smallest denormal significand = ulp size

{ .mfi

      getf.exp GR_exp      = f8

      fcmp.lt.s1 p10,p11 = f8, f9

      addl GR_sden_sig = 0x800, r0

}

// Form largest normal significand 0xfffffffffffff800

// Form smallest normal exponent

{ .mfi

      addl GR_lnorm_sig = -0x800,r0

      nop.f 999

      addl GR_min_pexp = 0x0fc01, r0 ;;

}

// Extract significand from x

// Is x=y?

// Form largest normal exponent

{ .mfi

      getf.sig GR_sig      = f8

      fcmp.eq.s0 p6,p0 = f8, f9

      addl GR_max_pexp = 0x103fe, r0

}

// Move largest normal significand to fp reg for special cases

{ .mfi

      setf.sig FR_lnorm_sig = GR_lnorm_sig

      nop.f 999

      addl GR_sign_mask = 0x20000, r0 ;;

}

// Move smallest denormal significand and signexp to fp regs

// Is x=nan?

// Set p12 and p13 based on whether significand increases or decreases

// It increases (p12 set) if x<y and x>=0 or if x>y and x<0

// It decreases (p13 set) if x<y and x<0  or if x>y and x>=0

{ .mfi

      setf.sig FR_sden_sig = GR_sden_sig

      fclass.m  p8,p0 = f8, 0xc3

(p10) cmp.lt p12,p13 = GR_exp, GR_sign_mask

}

{ .mfi

      setf.exp FR_sden_exp = GR_min_pexp

(p11) cmp.ge p12,p13 = GR_exp, GR_sign_mask ;;

}

.pred.rel "mutex",p12,p13

// Form expected new significand, adding or subtracting 1 ulp increment

// If x=y set result to y

// Form smallest normal significand and largest denormal significand

{ .mfi

(p12) add GR_new_sig = GR_sig, GR_sden_sig

(p6)  fmerge.s f8=f9,f9

      dep.z GR_snorm_sig = 1,63,1 // 0x8000000000000000

}

{ .mlx

(p13) sub GR_new_sig = GR_sig, GR_sden_sig

      movl GR_lden_sig = 0x7ffffffffffff800 ;;

}

// Move expected result significand and signexp to fp regs

// Is y=nan?

// Form new exponent in case result exponent needs incrementing or decrementing

{ .mfi

      setf.exp FR_new_exp = GR_exp

      fclass.m  p9,p0 = f9, 0xc3

(p12) add GR_exp1 = 1, GR_exp

}

{ .mib

      setf.sig FR_new_sig = GR_new_sig

(p13) add GR_exp1 = -1, GR_exp

(p6)  br.ret.spnt    b0 ;;             // Exit if x=y

}

// Move largest normal signexp to fp reg for special cases

// Is x=zero?

{ .mfi

      setf.exp FR_lnorm_exp = GR_max_pexp

      fclass.m  p7,p0 = f8, 0x7

      nop.i 999

}

{ .mfb

      nop.m 999

(p8)  fma.s0 f8 = f8,f1,f9

(p8)  br.ret.spnt    b0 ;;             // Exit if x=nan

}

// Move exp+-1 and smallest normal significand to fp regs for special cases

// Is x=inf?

{ .mfi

      setf.exp FR_exp1 = GR_exp1

      fclass.m  p6,p0 = f8, 0x23

      addl GR_exp_mask = 0x1ffff, r0

}

{ .mfb

      setf.sig FR_snorm_sig = GR_snorm_sig

(p9)  fma.s0 f8 = f8,f1,f9

(p9)  br.ret.spnt    b0 ;;             // Exit if y=nan

}

// Move largest denormal significand to fp regs for special cases

// Save x

{ .mfb

      setf.sig FR_lden_sig = GR_lden_sig

      mov FR_save_f8 = f8

(p7)  br.cond.spnt NEXT_ZERO ;;   // Exit if x=0

}

// Mask off the sign to get x_exp

{ .mfb

      and GR_x_exp = GR_exp_mask, GR_exp

      nop.f 999

(p6)  br.cond.spnt NEXT_INF ;;   // Exit if x=inf

}

// Check 6 special cases when significand rolls over:

//  1 sig size incr, x_sig=max_sig, x_exp < max_exp

//     Set p6, result is sig=min_sig, exp++

//  2 sig size incr, x_sig=max_sig, x_exp >= max_exp

//     Set p7, result is inf, signal overflow

//  3 sig size decr, x_sig=min_sig, x_exp > min_exp

//     Set p8, result is sig=max_sig, exp--

//  4 sig size decr, x_sig=min_sig, x_exp = min_exp

//     Set p9, result is sig=max_den_sig, exp same, signal underflow and inexact

//  5 sig size decr, x_sig=min_den_sig, x_exp = min_exp

//     Set p10, result is zero, sign of x, signal underflow and inexact

//  6 sig size decr, x_sig=min_sig, x_exp < min_exp

//     Set p14, result is zero, sign of x, signal underflow and inexact

//

// Form exponent of smallest double denormal (if normalized register format)

{ .mmi

      adds GR_min_den_rexp = -52, GR_min_pexp

(p12) cmp.eq.unc p6,p0 = GR_new_sig, r0

(p13) cmp.eq.unc p8,p10 = GR_new_sig, GR_lden_sig ;;

}

{ .mmi

(p6)  cmp.lt.unc p6,p7 = GR_x_exp, GR_max_pexp

(p8)  cmp.gt.unc p8,p9 = GR_x_exp, GR_min_pexp

(p10) cmp.eq.unc p10,p0 = GR_new_sig, r0 ;;

}

// Create small normal in case need to generate underflow flag

{ .mfi

(p10) cmp.le.unc p10,p0 = GR_x_exp, GR_min_pexp

      fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig

(p9)  cmp.gt.unc p9,p14 = GR_x_exp, GR_min_den_rexp

}

// Branch if cases 1, 2, 3

{ .bbb

(p6)  br.cond.spnt NEXT_EXPUP

(p7)  br.cond.spnt NEXT_OVERFLOW

(p8)  br.cond.spnt NEXT_EXPDOWN ;;

}

// Branch if cases 4, 5, 6

{ .bbb

(p9)  br.cond.spnt NEXT_NORM_TO_DENORM

(p10) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO

(p14) br.cond.spnt NEXT_UNDERFLOW_TO_ZERO ;;

}

// Here if no special cases

// Set p6 if result will be a denormal, so can force underflow flag

//    Case 1:  x_exp=min_exp, x_sig=unnormalized

//    Case 2:  x_exp

{ .mfi

      cmp.lt p6,p7 = GR_x_exp, GR_min_pexp

      fmerge.se f8 = FR_new_exp, FR_new_sig

      nop.i 999 ;;

}

{ .mfi

      nop.m 999

      nop.f 999

(p7)  tbit.z p6,p0 = GR_new_sig, 63 ;;

}

NEXT_COMMON_FINISH:

// Force underflow and inexact if denormal result

{ .mfi

      nop.m 999

(p6)  fma.d.s0 FR_tmp = FR_tmp,FR_tmp,f0

      nop.i 999

}

{ .mfb

      nop.m 999

      fnorm.d.s0 f8 = f8 // Final normalization to result precision

(p6)  br.cond.spnt NEXT_UNDERFLOW ;;

}

{ .mfb

      nop.m 999

      nop.f 999

      br.ret.sptk b0;;

}

//Special cases

NEXT_EXPUP:

{ .mfb

      cmp.lt p6,p7 = GR_x_exp, GR_min_pexp

      fmerge.se f8 = FR_exp1, FR_snorm_sig

      br.cond.sptk NEXT_COMMON_FINISH ;;

}

NEXT_EXPDOWN:

{ .mfb

      cmp.lt p6,p7 = GR_x_exp, GR_min_pexp

      fmerge.se f8 = FR_exp1, FR_lnorm_sig

      br.cond.sptk NEXT_COMMON_FINISH ;;

}

NEXT_NORM_TO_DENORM:

{ .mfi

      nop.m 999

      fmerge.se f8 = FR_new_exp, FR_lden_sig

      nop.i 999

}

// Force underflow and inexact if denormal result

{ .mfb

      nop.m 999

      fma.d.s0 FR_tmp = FR_tmp,FR_tmp,f0

      br.cond.sptk NEXT_UNDERFLOW ;;

}

NEXT_UNDERFLOW_TO_ZERO:

{ .mfb

      cmp.eq p6,p0 = r0,r0

      fmerge.s f8 = FR_save_f8,f0

      br.cond.sptk NEXT_COMMON_FINISH ;;

}

NEXT_INF:

// Here if f8 is +- infinity

// INF

// if f8 is +inf, no matter what y is return  largest double

// if f8 is -inf, no matter what y is return -largest double

{ .mfi

      nop.m 999

      fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig

      nop.i 999 ;;

}

{ .mfb

      nop.m 999

      fmerge.s f8 = f8,FR_lnorm

      br.ret.sptk    b0 ;;

}

NEXT_ZERO:

// Here if f8 is +- zero

// ZERO

// if f8 is zero and y is +, return + smallest double denormal

// if f8 is zero and y is -, return - smallest double denormal

{ .mfi

      nop.m 999

      fmerge.se FR_sden = FR_sden_exp,FR_sden_sig

      nop.i 999 ;;

}

// Create small normal to generate underflow flag

{ .mfi

      nop.m 999

      fmerge.se FR_tmp = FR_sden_exp, FR_lnorm_sig

      nop.i 999 ;;

}

// Add correct sign from direction arg

{ .mfi

      nop.m 999

      fmerge.s f8 = f9,FR_sden

      nop.i 999 ;;

}

// Force underflow and inexact flags

{ .mfb

      nop.m 999

      fma.d.s0 FR_tmp = FR_tmp,FR_tmp,f0

      br.cond.sptk NEXT_UNDERFLOW ;;

}

NEXT_UNDERFLOW:

// Here if result is a denorm, or input is finite and result is zero

// Call error support to report possible range error

{ .mib

      alloc          r32=ar.pfs,2,2,4,0

      mov           GR_Parameter_TAG = 268      // Error code

      br.cond.sptk  __libm_error_region    // Branch to error call

}

;;

NEXT_OVERFLOW:

// Here if input is finite, but result will be infinite

// Use frcpa to generate infinity of correct sign

// Call error support to report possible range error

{ .mfi

      alloc          r32=ar.pfs,2,2,4,0

      frcpa.s1 f8,p6 = FR_save_f8, f0

      nop.i 999 ;;

}

// Create largest double

{ .mfi

      nop.m 999

      fmerge.se FR_lnorm = FR_lnorm_exp,FR_lnorm_sig

      nop.i 999 ;;

}

// Force overflow and inexact flags to be set

{ .mfb

      mov           GR_Parameter_TAG = 154      // Error code

      fma.d.s0 FR_tmp = FR_lnorm,FR_lnorm,f0

      br.cond.sptk  __libm_error_region    // Branch to error call

}

;;

GLOBAL_LIBM_END(nextafter)

libm_alias_double_other (nextafter, nextafter)

LOCAL_LIBM_ENTRY(__libm_error_region)

.prologue

// (1)

{ .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

};;

// (2)

{ .mmi

        stfd [GR_Parameter_Y] = f9,16         // STORE 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

// (3)

{ .mib

        stfd [GR_Parameter_X] = FR_save_f8              // STORE Parameter 1 on stack

        add   GR_Parameter_RESULT = 0,GR_Parameter_Y           // Parameter 3 address

        nop.b 0

}

{ .mib

        stfd [GR_Parameter_Y] = f8              // 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

};;

// (4)

{ .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#