e_exp.s

glibc 2.9,最新版的C语言库函数

;;

// Nfloat = round_int(W)
// The signficand of fW_2TO56_RSH contains the rounded integer part of W,
// as a twos complement number in the lower bits (that is, it may be negative).
// That twos complement number (called N) is put into rN.

// Since fW_2TO56_RSH is scaled by 2^56, it must be multiplied by 2^-56
// before the shift constant 1.10000 * 2^63 is subtracted to yield fNfloat.
// Thus, fNfloat contains the floating point version of N

{ .mfb
      ldfpd           fP3, fP2  = [rAD_P]
      fms.s1          fNfloat = fW_2TO56_RSH, f2TOM56, fRSHF
(p11) br.cond.spnt    EXP_CERTAIN_UNDERFLOW
}
;;

{ .mfi
      getf.sig        rN        = fW_2TO56_RSH
      nop.f           0
      nop.i           0
}
;;

// rIndex_1 has index_1
// rIndex_2_16 has index_2 * 16
// rBiased_M has M
// rIndex_1_16 has index_1 * 16

// rM has true M
// r = x - Nfloat * ln2_by_128_hi
// f = 1 - Nfloat * ln2_by_128_lo
{ .mfi
      and             rIndex_1 = 0x0f, rN
      fnma.s1         fR   = fNfloat, fLn2_by_128_hi, fNormX
      shr             rM = rN,  0x7
}
{ .mfi
      and             rIndex_2_16 = 0x70, rN
      fnma.s1         fF   = fNfloat, fLn2_by_128_lo, f1
      nop.i           0
}
;;

// rAD_T1 has address of T1
// rAD_T2 has address if T2

{ .mmi
      add             rBiased_M = rExp_bias, rM
      add             rAD_T2 = rAD_TB2, rIndex_2_16
      shladd          rAD_T1 = rIndex_1, 4, rAD_TB1
}
;;

// Create Scale = 2^M
{ .mmi
      setf.exp        f2M = rBiased_M
      ldfe            fT2  = [rAD_T2]
      nop.i           0
}
;;

// Load T1 and T2
{ .mfi
      ldfe            fT1  = [rAD_T1]
      fmpy.s0         fTmp = fLn2_by_128_lo, fLn2_by_128_lo // Force inexact
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fma.s1          fRsq = fR, fR, f0
      nop.i           0
}
{ .mfi
      nop.m           0
      fma.s1          fP54 = fR, fP5, fP4
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fcmp.lt.s1      p13,p0 = fNormX,fMIN_DBL_NORM_ARG
      nop.i           0
}
{ .mfi
      nop.m           0
      fma.s1          fP32 = fR, fP3, fP2
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fma.s1          fP5432  = fRsq, fP54, fP32
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fma.s1          fS1  = f2M,fT1,f0
      nop.i           0
}
{ .mfi
      nop.m           0
      fma.s1          fS2  = fF,fT2,f0
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fma.s1          fP     = fRsq, fP5432, fR
      nop.i           0
}
{ .mfi
      nop.m           0
      fma.s1          fS   = fS1,fS2,f0
      nop.i           0
}
;;

{ .mbb
      nop.m           0
(p13) br.cond.spnt    EXP_POSSIBLE_UNDERFLOW
(p14) br.cond.spnt    EXP_POSSIBLE_OVERFLOW
}
;;

{ .mfb
      nop.m           0
      fma.d.s0        f8 = fS, fP, fS
      br.ret.sptk     b0                  // Normal path exit
}
;;


EXP_POSSIBLE_OVERFLOW:

// Here if fMAX_DBL_NORM_ARG < x < fMIN_DBL_OFLOW_ARG
// This cannot happen if input is a double, only if input higher precision.
// Overflow is a possibility, not a certainty.

// Recompute result using status field 2 with user's rounding mode,
// and wre set.  If result is larger than largest double, then we have
// overflow

{ .mfi
      mov             rGt_ln  = 0x103ff // Exponent for largest dbl + 1 ulp
      fsetc.s2        0x7F,0x42         // Get user's round mode, set wre
      nop.i           0
}
;;

{ .mfi
      setf.exp        fGt_pln = rGt_ln  // Create largest double + 1 ulp
      fma.d.s2        fWre_urm_f8 = fS, fP, fS    // Result with wre set
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fsetc.s2        0x7F,0x40                   // Turn off wre in sf2
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fcmp.ge.s1      p6, p0 =  fWre_urm_f8, fGt_pln // Test for overflow
      nop.i           0
}
;;

{ .mfb
      nop.m           0
      nop.f           0
(p6)  br.cond.spnt    EXP_CERTAIN_OVERFLOW // Branch if overflow
}
;;

{ .mfb
      nop.m           0
      fma.d.s0        f8 = fS, fP, fS
      br.ret.sptk     b0                     // Exit if really no overflow
}
;;

EXP_CERTAIN_OVERFLOW:
{ .mmi
      sub             rTmp = rExp_mask, r0, 1
;;
      setf.exp        fTmp = rTmp
      nop.i           0
}
;;

{ .mfi
      alloc           r32=ar.pfs,1,4,4,0
      fmerge.s        FR_X = f8,f8
      nop.i           0
}
{ .mfb
      mov             GR_Parameter_TAG = 14
      fma.d.s0        FR_RESULT = fTmp, fTmp, fTmp    // Set I,O and +INF result
      br.cond.sptk    __libm_error_region
}
;;

EXP_POSSIBLE_UNDERFLOW:

// Here if fMAX_DBL_ZERO_ARG < x < fMIN_DBL_NORM_ARG
// Underflow is a possibility, not a certainty

// We define an underflow when the answer with
//    ftz set
// is zero (tiny numbers become zero)

// Notice (from below) that if we have an unlimited exponent range,
// then there is an extra machine number E between the largest denormal and
// the smallest normal.

// So if with unbounded exponent we round to E or below, then we are
// tiny and underflow has occurred.

// But notice that you can be in a situation where we are tiny, namely
// rounded to E, but when the exponent is bounded we round to smallest
// normal. So the answer can be the smallest normal with underflow.

//                           E
// -----+--------------------+--------------------+-----
//      |                    |                    |
//   1.1...10 2^-3fff    1.1...11 2^-3fff    1.0...00 2^-3ffe
//   0.1...11 2^-3ffe                                   (biased, 1)
//    largest dn                               smallest normal

{ .mfi
      nop.m           0
      fsetc.s2        0x7F,0x41                // Get user's round mode, set ftz
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fma.d.s2        fFtz_urm_f8 = fS, fP, fS // Result with ftz set
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fsetc.s2        0x7F,0x40                // Turn off ftz in sf2
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fcmp.eq.s1      p6, p7 = fFtz_urm_f8, f0 // Test for underflow
      nop.i           0
}
{ .mfi
      nop.m           0
      fma.d.s0        f8 = fS, fP, fS          // Compute result, set I, maybe U
      nop.i           0
}
;;

{ .mbb
      nop.m           0
(p6)  br.cond.spnt    EXP_UNDERFLOW_COMMON     // Branch if really underflow
(p7)  br.ret.sptk     b0                       // Exit if really no underflow
}
;;

EXP_CERTAIN_UNDERFLOW:
// Here if  x < fMAX_DBL_ZERO_ARG
// Result will be zero (or smallest denorm if round to +inf) with I, U set
{ .mmi
      mov             rTmp = 1
;;
      setf.exp        fTmp = rTmp               // Form small normal
      nop.i           0
}
;;

{ .mfi
      nop.m           0
      fmerge.se       fTmp = fTmp, fLn2_by_128_lo // Small with signif lsb 1
      nop.i           0
}
;;
      
{ .mfb
      nop.m           0
      fma.d.s0        f8 = fTmp, fTmp, f0 // Set I,U, tiny (+0.0) result
      br.cond.sptk    EXP_UNDERFLOW_COMMON
}
;;

EXP_UNDERFLOW_COMMON:
// Determine if underflow result is zero or nonzero
{ .mfi
      alloc           r32=ar.pfs,1,4,4,0
      fcmp.eq.s1      p6, p0 =  f8, f0
      nop.i           0
}
;;

{ .mfb
      nop.m           0
      fmerge.s        FR_X = fNormX,fNormX
(p6)  br.cond.spnt    EXP_UNDERFLOW_ZERO
}
;;

EXP_UNDERFLOW_NONZERO:
// Here if  x < fMIN_DBL_NORM_ARG and result nonzero;
// I, U are set
{ .mfb
      mov             GR_Parameter_TAG = 15
      nop.f           0                         // FR_RESULT already set
      br.cond.sptk    __libm_error_region
}
;;

EXP_UNDERFLOW_ZERO:
// Here if x < fMIN_DBL_NORM_ARG and result zero;
// I, U are set
{ .mfb
      mov             GR_Parameter_TAG = 15
      nop.f           0                         // FR_RESULT already set
      br.cond.sptk    __libm_error_region
}
;;

GLOBAL_IEEE754_END(exp)


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
        stfd [GR_Parameter_Y] = FR_Y,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
{ .mib
        stfd [GR_Parameter_X] = FR_X            // STORE Parameter 1 on stack
        add   GR_Parameter_RESULT = 0,GR_Parameter_Y  // Parameter 3 address
	nop.b 0
}
{ .mib
        stfd [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
        add   GR_Parameter_RESULT = 48,sp
        nop.m 0
        nop.i 0
};;
{ .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#