//      Exact, regardless ...of rounding direction//      A_lo := x*p_3 - A_hi ...fma, exact//    Endif{ .mfi      nop.m 999      fmpy.s3 FR_Tmp_C = FR_X,FR_p_1      nop.i 999};;{ .mfi      mov GR_TEMP3 = 0x0FF3F      fmpy.s1 FR_p_2 = FR_p_2,FR_ScaleP2      nop.i 999};;{ .mmf      setf.exp FR_ScaleP4 = GR_TEMP3      mov GR_TEMP4 = 0x10045      fmpy.s1 FR_p_3 = FR_p_3,FR_ScaleP3};;{ .mfi      nop.m 999      fadd.s3 FR_C_hi = FR_sigma_C,FR_Tmp_C   // For Tmp_C < sigma_C case      nop.i 999};;{ .mmf      setf.exp FR_Tmp2_C = GR_TEMP4      nop.m 999      fmpy.s3 FR_Tmp_B = FR_X,FR_p_2};;{ .mfi      addl           GR_BASE   = @ltoff(Constants_Bits_of_pi_by_2#), gp      fcmp.ge.s1 p12,  p9 = FR_Tmp_C,FR_sigma_C      nop.i 999}{ .mfi      nop.m 999      fmpy.s3 FR_Tmp_A = FR_X,FR_p_3      nop.i 99};;{ .mfi      ld8 GR_BASE = [GR_BASE](p12) mov FR_C_hi = FR_Tmp_C      nop.i 999}{ .mfi      nop.m 999(p9)  fsub.s1 FR_C_hi = FR_C_hi,FR_sigma_C      nop.i 999};;//   End If//   Step 3. Get reduced argument//   If sgn_x == 0 (that is original x is positive)//      D_hi := Pi_by_2_hi//      D_lo := Pi_by_2_lo//      Load from table//   Else//      D_hi := neg_Pi_by_2_hi//      D_lo := neg_Pi_by_2_lo//      Load from table//   End If{ .mfi      nop.m 999      fmpy.s1 FR_p_4 = FR_p_4,FR_ScaleP4      nop.i 999}{ .mfi      nop.m 999      fadd.s3 FR_B_hi = FR_sigma_B,FR_Tmp_B     // For Tmp_B < sigma_B case      nop.i 999};;{ .mfi      nop.m 999      fadd.s3 FR_A_hi = FR_sigma_A,FR_Tmp_A     // For Tmp_A < sigma_A case      nop.i 999};;{ .mfi      nop.m 999      fcmp.ge.s1 p13, p10 = FR_Tmp_B,FR_sigma_B      nop.i 999}{ .mfi      nop.m 999      fms.s1 FR_C_lo = FR_X,FR_p_1,FR_C_hi      nop.i 999};;{ .mfi      ldfe FR_D_hi = [GR_BASE],16      fcmp.ge.s1 p14, p11 = FR_Tmp_A,FR_sigma_A      nop.i 999};;{ .mfi      ldfe FR_D_lo = [GR_BASE](p13) mov FR_B_hi = FR_Tmp_B      nop.i 999}{ .mfi      nop.m 999(p10) fsub.s1 FR_B_hi = FR_B_hi,FR_sigma_B      nop.i 999};;{ .mfi      nop.m 999(p14) mov FR_A_hi = FR_Tmp_A      nop.i 999}{ .mfi      nop.m 999(p11) fsub.s1 FR_A_hi = FR_A_hi,FR_sigma_A      nop.i 999};;//    Note that C_hi is of integer value. We need only the//    last few bits. Thus we can ensure C_hi is never a big//    integer, freeing us from overflow worry.//    Tmp_C := fadd.fpsr3( C_hi, 2^(70) ) - 2^(70);//    Tmp_C is the upper portion of C_hi{ .mfi      nop.m 999      fadd.s3 FR_Tmp_C = FR_C_hi,FR_Tmp2_C      tbit.z p12,p9 = GR_Exp_x, 17};;{ .mfi      nop.m 999      fms.s1 FR_B_lo = FR_X,FR_p_2,FR_B_hi      nop.i 999}{ .mfi      nop.m 999      fadd.s3 FR_A = FR_B_hi,FR_C_lo      nop.i 999};;{ .mfi      nop.m 999      fms.s1 FR_A_lo = FR_X,FR_p_3,FR_A_hi      nop.i 999};;{ .mfi      nop.m 999      fsub.s1 FR_Tmp_C = FR_Tmp_C,FR_Tmp2_C      nop.i 999};;//    *******************//    Step 2. Get N and f//    *******************//    We have all the components to obtain//    S_0, S_1, S_2, S_3 and thus N and f. We start by adding//    C_lo and B_hi. This sum together with C_hi estimates//    N and f well.//    A := fadd.fpsr3( B_hi, C_lo )//    B := max( B_hi, C_lo )//    b := min( B_hi, C_lo ){ .mfi      nop.m 999      fmax.s1 FR_B = FR_B_hi,FR_C_lo      nop.i 999};;// We use a right-shift trick to get the integer part of A into the rightmost// bits of the significand by adding 1.1000..00 * 2^63.  This operation is good// if |A| < 2^61, which it is in this case.  We are doing this to save a few// cycles over using fcvt.fx followed by fnorm.  The second step of the trick// is to subtract the same constant to float the rounded integer into a fp reg.{ .mfi      nop.m 999//    N := round_to_nearest_integer_value( A );      fma.s1 FR_N_fix = FR_A, f1, FR_RSHF      nop.i 999};;{ .mfi      nop.m 999      fmin.s1 FR_b = FR_B_hi,FR_C_lo      nop.i 999}{ .mfi      nop.m 999//    C_hi := C_hi - Tmp_C ...0 <= C_hi < 2^7      fsub.s1 FR_C_hi = FR_C_hi,FR_Tmp_C      nop.i 999};;{ .mfi      nop.m 999//    a := (B - A) + b: Exact - note that a is either 0 or 2^(-64).      fsub.s1 FR_a = FR_B,FR_A      nop.i 999};;{ .mfi      nop.m 999      fms.s1 FR_N = FR_N_fix, f1, FR_RSHF      nop.i 999};;{ .mfi      nop.m 999      fadd.s1 FR_a = FR_a,FR_b      nop.i 999};;//    f := A - N; Exact because lsb(A) >= 2^(-64) and |f| <= 1/2.//    N := convert to integer format( C_hi + N );//    M := P_0 * x_lo;//    N := N + M;{ .mfi      nop.m 999      fsub.s1 FR_f = FR_A,FR_N      nop.i 999}{ .mfi      nop.m 999      fadd.s1 FR_N = FR_N,FR_C_hi      nop.i 999};;{ .mfi      nop.m 999(p9)  fsub.s1 FR_D_hi = f0, FR_D_hi      nop.i 999}{ .mfi      nop.m 999(p9)  fsub.s1 FR_D_lo = f0, FR_D_lo      nop.i 999};;{ .mfi      nop.m 999      fadd.s1 FR_g = FR_A_hi,FR_B_lo          // For Case 1, g=A_hi+B_lo      nop.i 999}{ .mfi      nop.m 999      fadd.s3 FR_A = FR_A_hi,FR_B_lo          // For Case 2, A=A_hi+B_lo w/ sf3      nop.i 999};;{ .mfi      mov GR_Temp = 0x0FFCD                   // For Case 2, exponent of 2^-50      fmax.s1 FR_B = FR_A_hi,FR_B_lo          // For Case 2, B=max(A_hi,B_lo)      nop.i 999};;//    f = f + a      Exact because a is 0 or 2^(-64);//    the msb of the sum is <= 1/2 and lsb >= 2^(-64).{ .mfi      setf.exp FR_TWOM50 = GR_Temp            // For Case 2, form 2^-50      fcvt.fx.s1 FR_N = FR_N      nop.i 999}{ .mfi      nop.m 999      fadd.s1 FR_f = FR_f,FR_a      nop.i 999};;{ .mfi      nop.m 999      fmin.s1 FR_b = FR_A_hi,FR_B_lo          // For Case 2, b=min(A_hi,B_lo)      nop.i 999};;{ .mfi      nop.m 999      fsub.s1 FR_a = FR_B,FR_A                // For Case 2, a=B-A      nop.i 999};;{ .mfi      nop.m 999      fadd.s1 FR_s_hi = FR_f,FR_g             // For Case 1, s_hi=f+g      nop.i 999}{ .mfi      nop.m 999      fadd.s1 FR_f_hi = FR_A,FR_f             // For Case 2, f_hi=A+f      nop.i 999};;{ .mfi      nop.m 999      fabs FR_f_abs = FR_f      nop.i 999};;{ .mfi      getf.sig GR_N = FR_N      fsetc.s3 0x7F,0x40                 // Reset sf3 to user settings + td      nop.i 999};;{ .mfi      nop.m 999      fsub.s1 FR_s_lo = FR_f,FR_s_hi          // For Case 1, s_lo=f-s_hi      nop.i 999}{ .mfi      nop.m 999      fsub.s1 FR_f_lo = FR_f,FR_f_hi          // For Case 2, f_lo=f-f_hi      nop.i 999};;{ .mfi      nop.m 999      fmpy.s1 FR_r_hi = FR_s_hi,FR_D_hi       // For Case 1, r_hi=s_hi*D_hi      nop.i 999}{ .mfi      nop.m 999      fadd.s1 FR_a = FR_a,FR_b                // For Case 2, a=a+b      nop.i 999};;//    If sgn_x == 1 (that is original x was negative)//       N := 2^10 - N//       this maintains N to be non-negative, but still//       equivalent to the (negated N) mod 4.//    End If{ .mfi      add GR_N = GR_N,GR_M      fcmp.ge.s1 p13, p10 = FR_f_abs,FR_TWOM33      mov GR_Temp = 0x00400};;{ .mfi(p9)  sub GR_N = GR_Temp,GR_N      fadd.s1 FR_s_lo = FR_s_lo,FR_g           // For Case 1, s_lo=s_lo+g      nop.i 999}{ .mfi      nop.m 999      fadd.s1 FR_f_lo = FR_f_lo,FR_A           // For Case 2, f_lo=f_lo+A      nop.i 999};;//       a := (B - A) + b      Exact.//       Note that a is either 0 or 2^(-128).//       f_hi := A + f;//       f_lo := (f - f_hi) + A//       f_lo=f-f_hi is exact because either |f| >= |A|, in which//       case f-f_hi is clearly exact; or otherwise, 0<|f|<|A|//       means msb(f) <= msb(A) = 2^(-64) => |f| = 2^(-64).//       If f = 2^(-64), f-f_hi involves cancellation and is//       exact. If f = -2^(-64), then A + f is exact. Hence//       f-f_hi is -A exactly, giving f_lo = 0.//       f_lo := f_lo + a;//    If |f| >= 2^(-33)//       Case 1//       CASE := 1//       g := A_hi + B_lo;//       s_hi := f + g;//       s_lo := (f - s_hi) + g;//   Else//       Case 2//       CASE := 2//       A := fadd.fpsr3( A_hi, B_lo )//       B := max( A_hi, B_lo )//       b := min( A_hi, B_lo ){ .mfi      nop.m 999(p10) fcmp.ge.unc.s1 p14, p11 = FR_f_abs,FR_TWOM50      nop.i 999}{ .mfi      nop.m 999(p13) fms.s1 FR_r_lo = FR_s_hi,FR_D_hi,FR_r_hi //For Case 1, r_lo=s_hi*D_hi+r_hi      nop.i 999};;//       If |f| >= 2^(-50) then//          s_hi := f_hi;//          s_lo := f_lo;//       Else//          f_lo := (f_lo + A_lo) + x*p_4//          s_hi := f_hi + f_lo//          s_lo := (f_hi - s_hi) + f_lo//       End If{ .mfi      nop.m 999(p14) mov FR_s_hi = FR_f_hi      nop.i 999}{ .mfi      nop.m 999(p10) fadd.s1 FR_f_lo = FR_f_lo,FR_a      nop.i 999};;{ .mfi      nop.m 999(p14) mov FR_s_lo = FR_f_lo      nop.i 999}{ .mfi      nop.m 999(p11) fadd.s1 FR_f_lo = FR_f_lo,FR_A_lo      nop.i 999};;{ .mfi      nop.m 999(p11) fma.s1 FR_f_lo = FR_X,FR_p_4,FR_f_lo      nop.i 999};;{ .mfi      nop.m 999(p13) fma.s1 FR_r_lo = FR_s_hi,FR_D_lo,FR_r_lo //For Case 1, r_lo=s_hi*D_lo+r_lo      nop.i 999}{ .mfi      nop.m 999(p11) fadd.s1 FR_s_hi = FR_f_hi,FR_f_lo      nop.i 999};;//   r_hi :=  s_hi*D_hi//   r_lo :=  s_hi*D_hi - r_hi  with fma//   r_lo := (s_hi*D_lo + r_lo) + s_lo*D_hi{ .mfi      nop.m 999(p10) fmpy.s1 FR_r_hi = FR_s_hi,FR_D_hi      nop.i 999}{ .mfi      nop.m 999(p11) fsub.s1 FR_s_lo = FR_f_hi,FR_s_hi      nop.i 999};;{ .mfi      nop.m 999(p10) fms.s1 FR_r_lo = FR_s_hi,FR_D_hi,FR_r_hi      nop.i 999}{ .mfi      nop.m 999(p11) fadd.s1 FR_s_lo = FR_s_lo,FR_f_lo      nop.i 999};;{ .mfi      nop.m 999(p10) fma.s1 FR_r_lo = FR_s_hi,FR_D_lo,FR_r_lo      nop.i 999};;//   Return  N, r_hi, r_lo//   We do not return CASE{ .mfb      nop.m 999      fma.s1 FR_r_lo = FR_s_lo,FR_D_hi,FR_r_lo      br.ret.sptk   b0};;.endp __libm_pi_by_2_reduce#