e_atanhl.s

glibc 库, 不仅可以学习使用库函数,还可以学习函数的具体实现,是提高功力的好资料

      fmax.s1       FR_AA = FR_X,f1 // for S_lo,form AA = max(X,1.0)
      nop.i         0
}
{ .mfi
      shladd        GR_ad_tbl_1 = GR_Index1,4,GR_ad_tbl_1 // point to G_1
      nop.f         0
      mov           GR_Bias = 0x0FFFF // exponent bias
};;
{ .mfi
      ldfps         FR_G,FR_H = [GR_ad_tbl_1],8  // load G_1,H_1
      fmerge.se     FR_S_hi =  f1,FR_Z // form |x+1|
      nop.i         0
};;
{ .mfi
      getf.exp      GR_N =  FR_Z // get N = exponent of x+1
      nop.f         0
      nop.i         0
}
{ .mfi
      ldfd          FR_h = [GR_ad_tbl_1] // load h_1
      fnma.s1       FR_R1 = FR_B_lo,FR_X,FR_R1 // r1 = r1-b_lo*x
      nop.i         0
};;
{ .mfi
      ldfe          FR_log2_hi = [GR_ad_q],16 // load log2_hi
      nop.f         0
      pmpyshr2.u    GR_X_1 = GR_X_0,GR_Z_1,15 // get bits 30-15 of X_0 * Z_1
};;
//
//    For performance,don't use result of pmpyshr2.u for 4 cycles.
//
{ .mfi
      ldfe          FR_log2_lo = [GR_ad_q],16 // load log2_lo
      nop.f         0
      sub           GR_N = GR_N,GR_Bias 
};;
{ .mfi
      ldfe          FR_Q4 = [GR_ad_q],16  // load Q4
      fms.s1        FR_S_lo = FR_AA,f1,FR_Z // form S_lo = AA - Z 
      sub           GR_minus_N = GR_Bias,GR_N // form exponent of 2^(-N)
};;
{ .mmf
      ldfe          FR_Q3 = [GR_ad_q],16 // load Q3
      // put integer N into rightmost significand
      setf.sig      FR_float_N = GR_N
      fmin.s1       FR_BB = FR_X,f1 // for S_lo,form BB = min(X,1.0)
};;
{ .mfi
      ldfe          FR_Q2 = [GR_ad_q],16 // load Q2
      nop.f         0
      extr.u        GR_Index2 = GR_X_1,6,4 // extract bits 6-9 of X_1 
};;
{ .mmi
      ldfe          FR_Q1 = [GR_ad_q] // load Q1
      shladd        GR_ad_z_2 = GR_Index2,2,GR_ad_z_2 // point to Z_2
      nop.i         0
};;
{ .mmi
      ld4           GR_Z_2 = [GR_ad_z_2] // load Z_2
      shladd        GR_ad_tbl_2 = GR_Index2,4,GR_ad_tbl_2 // point to G_2
      nop.i         0
};;
{ .mfi
      ldfps         FR_G2,FR_H2 = [GR_ad_tbl_2],8 // load G_2,H_2
      nop.f         0
      nop.i         0
};;
{ .mfi
      ldfd          FR_h2 = [GR_ad_tbl_2] // load h_2
      fma.s1        FR_S_lo = FR_S_lo,f1,FR_BB // S_lo = S_lo + BB
      nop.i         0
}
{ .mfi
      setf.exp      FR_2_to_minus_N = GR_minus_N // form 2^(-N)
      fma.s1        FR_X_lo = FR_R1,FR_Y3,f0 // x_lo = r1*y3
      nop.i         0
};;
{ .mfi
      nop.m         0
      nop.f         0
      pmpyshr2.u    GR_X_2 = GR_X_1,GR_Z_2,15 // get bits 30-15 of X_1 * Z_2
};;
//
//    For performance,don't use result of pmpyshr2.u for 4 cycles
//
{ .mfi
      add           GR_ad2_tbl_3 = 8,GR_ad_tbl_3
      nop.f         0
      nop.i         0
}
{ .mfi
      nop.m         0
      nop.f         0 
      nop.i         0
};;
{ .mfi
      nop.m         0
      nop.f         0 
      nop.i         0
};;
{ .mfi
      nop.m         0
      nop.f         0 
      nop.i         0
};;

//
//    Now GR_X_2 can be used
//
{ .mfi
      nop.m         0
      nop.f         0
      extr.u        GR_Index3 = GR_X_2,1,5 // extract bits 1-5 of X_2
}
{ .mfi
      nop.m         0
      fma.s1        FR_S_lo = FR_S_lo,f1,FR_X_lo // S_lo = S_lo + Arg_lo
      nop.i         0
};;

{ .mfi
      shladd        GR_ad_tbl_3 = GR_Index3,4,GR_ad_tbl_3 // point to G_3
      fcvt.xf       FR_float_N = FR_float_N
      nop.i         0
}
{ .mfi
      shladd        GR_ad2_tbl_3 = GR_Index3,4,GR_ad2_tbl_3 // point to h_3
      fma.s1        FR_Q1 = FR_Q1,FR_Half,f0 // sign(arg)*Q1/2
      nop.i         0
};;
{ .mmi
      ldfps         FR_G3,FR_H3 = [GR_ad_tbl_3],8 // load G_3,H_3
      ldfd          FR_h3 = [GR_ad2_tbl_3] // load h_3
      nop.i         0
};;
{ .mfi
      nop.m         0
      fmpy.s1       FR_G = FR_G,FR_G2 // G = G_1 * G_2
      nop.i         0
}
{ .mfi
      nop.m         0
      fadd.s1       FR_H = FR_H,FR_H2 // H = H_1 + H_2
      nop.i         0
};;
{ .mfi
      nop.m         0
      fadd.s1       FR_h = FR_h,FR_h2 // h = h_1 + h_2
      nop.i         0
};;
{ .mfi
      nop.m         0
      // S_lo = S_lo * 2^(-N)
      fma.s1        FR_S_lo = FR_S_lo,FR_2_to_minus_N,f0
      nop.i         0
};;
{ .mfi
      nop.m         0
      fmpy.s1       FR_G = FR_G,FR_G3 // G = (G_1 * G_2) * G_3
      nop.i         0
}
{ .mfi
      nop.m         0
      fadd.s1       FR_H = FR_H,FR_H3 // H = (H_1 + H_2) + H_3
      nop.i         0
};;
{ .mfi
      nop.m         0
      fadd.s1       FR_h = FR_h,FR_h3 // h = (h_1 + h_2) + h_3
      nop.i         0
};;
{ .mfi
      nop.m         0
      fms.s1        FR_r = FR_G,FR_S_hi,f1 // r = G * S_hi - 1
      nop.i         0
}
{ .mfi
      nop.m         0
      // Y_hi = N * log2_hi + H
      fma.s1        FR_Y_hi = FR_float_N,FR_log2_hi,FR_H
      nop.i         0
};;
{ .mfi
      nop.m         0
      fma.s1        FR_h = FR_float_N,FR_log2_lo,FR_h // h = N * log2_lo + h
      nop.i         0
};;
{ .mfi
      nop.m         0
      fma.s1        FR_r = FR_G,FR_S_lo,FR_r // r = G * S_lo + (G * S_hi - 1)
      nop.i         0
};;
{ .mfi
      nop.m         0
      fma.s1        FR_poly_lo = FR_r,FR_Q4,FR_Q3 // poly_lo = r * Q4 + Q3
      nop.i         0
}
{ .mfi
      nop.m         0
      fmpy.s1       FR_rsq = FR_r,FR_r // rsq = r * r
      nop.i         0
};;
{ .mfi
      nop.m         0
      fma.s1        FR_05r = FR_r,FR_Half,f0 // sign(arg)*r/2
      nop.i         0
};;
{ .mfi
      nop.m         0
      // poly_lo = poly_lo * r + Q2
      fma.s1        FR_poly_lo = FR_poly_lo,FR_r,FR_Q2
      nop.i         0
}
{ .mfi
      nop.m         0
      fma.s1        FR_rcub = FR_rsq,FR_r,f0 // rcub = r^3
      nop.i         0
};;
{ .mfi
      nop.m         0
      // poly_hi = sing(arg)*(Q1*r^2 + r)/2
      fma.s1        FR_poly_hi = FR_Q1,FR_rsq,FR_05r
      nop.i         0
};;
{ .mfi
      nop.m         0
      // poly_lo = poly_lo*r^3 + h
      fma.s1        FR_poly_lo = FR_poly_lo,FR_rcub,FR_h
      nop.i         0
};;
{ .mfi
      nop.m         0
      // Y_lo = poly_hi + poly_lo/2
      fma.s0        FR_Y_lo = FR_poly_lo,FR_Half,FR_poly_hi
      nop.i         0
};;
{ .mfb
      nop.m         0
     // Result = arctanh(x) = Y_hi/2 + Y_lo
      fma.s0        f8 = FR_Y_hi,FR_Half,FR_Y_lo
      br.ret.sptk   b0
};;

// Taylor's series
atanhl_near_zero:
{ .mfi
      nop.m         0
      fma.s1        FR_x3 = FR_x2,f8,f0
      nop.i         0
}
{ .mfi
      nop.m         0
      fma.s1        FR_x4 = FR_x2,FR_x2,f0
      nop.i         0
};;
{ .mfi
      nop.m         0
      fma.s1        FR_C17 = FR_C17,FR_x2,FR_C15
      nop.i         0
}
{ .mfi
      nop.m         0
      fma.s1        FR_C13 = FR_C13,FR_x2,FR_C11
      nop.i         0
};;
{ .mfi
      nop.m         0
      fma.s1        FR_C9 = FR_C9,FR_x2,FR_C7
      nop.i         0
}
{ .mfi
      nop.m         0
      fma.s1        FR_C5 = FR_C5,FR_x2,FR_C3
      nop.i         0
};;
{ .mfi
      nop.m         0
      fma.s1        FR_x8 = FR_x4,FR_x4,f0
      nop.i         0
};;
{ .mfi
      nop.m         0
      fma.s1        FR_C17 = FR_C17,FR_x4,FR_C13
      nop.i         0
};;
{ .mfi
      nop.m         0
      fma.s1        FR_C9 = FR_C9,FR_x4,FR_C5
      nop.i         0
};;
{ .mfi
      nop.m         0
      fma.s1        FR_C17 = FR_C17,FR_x8,FR_C9
      nop.i         0
};;
{ .mfb
      nop.m         0
      fma.s0        f8 = FR_C17,FR_x3,f8
      br.ret.sptk   b0 
};;

atanhl_eq_one:
{ .mfi
      nop.m         0
      frcpa.s0      FR_Rcp,p0 = f1,f0 // get inf,and raise Z flag
      nop.i         0
}
{ .mfi
      nop.m         0
      fmerge.s      FR_Arg_X = f8, f8
      nop.i         0
};;
{ .mfb
      mov           GR_Parameter_TAG = 130
      fmerge.s      FR_RESULT = f8,FR_Rcp // result is +-inf
      br.cond.sptk  __libm_error_region // exit if |x| = 1.0
};;

atanhl_gt_one:
{ .mfi
      nop.m         0
      fmerge.s      FR_Arg_X = f8, f8
      nop.i         0
};;
{ .mfb
      mov           GR_Parameter_TAG = 129
      frcpa.s0      FR_RESULT,p0 = f0,f0 // get QNaN,and raise invalid
      br.cond.sptk  __libm_error_region // exit if |x| > 1.0
};;

GLOBAL_LIBM_END(atanhl)

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
        stfe [GR_Parameter_Y] = FR_Arg_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
        stfe [GR_Parameter_X] = FR_Arg_X        // Store Parameter 1 on stack
        add   GR_Parameter_RESULT = 0,GR_Parameter_Y
        nop.b 0                                 // Parameter 3 address
}
{ .mib
        stfe [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
        ldfe  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#