s_tanl.s

glibc 2.9,最新版的C语言库函数

      nop.i 999
}
;;

//     Case 2_reduce: U_1 = N * P_2 + w
{ .mfi
      nop.m 999
      fma.s1  U_1 = N, P_2, w2              // U_1 = N * P_2 + w for |s| < 2^-33
      nop.i 999
}
;;

//
//     Decide between case_1 and case_2 reduce:
//     Case 1_reduce:  |s| >= 2**(-33)
//     Case 2_reduce:  |s| < 2**(-33)
//
{ .mfi
      nop.m 999
      fcmp.lt.s1 p9, p8 = s_val, TWO_TO_NEG33
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p9)  fcmp.gt.s1 p9, p8 = s_val, NEGTWO_TO_NEG33
      nop.i 999
}
;;

//     Case 1_reduce: c = s - r
{ .mfi
      nop.m 999
      fsub.s1 c = s_val, r                     // c = s_val - r for |s| >= 2^-33
      nop.i 999
}
;;

//     Case 2_reduce: r is complete here - continue to calculate c .
//     r = s - U_1
{ .mfi
      nop.m 999
(p9)  fsub.s1 r = s_val, U_1
      nop.i 999
}
{ .mfi
      nop.m 999
(p9)  fms.s1 U_2 = N, P_2, U_1
      nop.i 999
}
;;

//
//     Case 1_reduce: Is |r| < 2**(-2), if so set PR_10
//     else set PR_13.
//

{ .mfi
      nop.m 999
      fand B = B_mask1, r
      nop.i 999
}
{ .mfi
      nop.m 999
(p8)  fcmp.lt.unc.s1 p10, p13 = r, TWO_TO_NEG2
      nop.i 999
}
;;

{ .mfi
(p8)  getf.sig sig_r = r               // Get signif of r if |s| >= 2^-33
      nop.f 999
      nop.i 999
}
;;

{ .mfi
(p8)  getf.exp exp_r = r               // Extract signexp of r if |s| >= 2^-33
(p10) fcmp.gt.s1 p10, p13 = r, NEGTWO_TO_NEG2
      nop.i 999
}
;;

//     Case 1_reduce: c is complete here.
//     Case 1: Branch to SMALL_R or NORMAL_R.
//     c = c + w (w has not been negated.)
{ .mfi
      nop.m 999
(p8)  fsub.s1 c = c, w                         // c = c - w for |s| >= 2^-33
      nop.i 999
}
{ .mbb
      nop.m 999
(p10) br.cond.spnt TANL_SMALL_R     // Branch if pi/4 < |x| < 2^24 and |r|<1/4
(p13) br.cond.sptk TANL_NORMAL_R_A  // Branch if pi/4 < |x| < 2^24 and |r|>=1/4
}
;;


// Here if pi/4 < |x| < 2^24 and |s| < 2^-33
//
//     Is i_1 = lsb of N_fix_gr even or odd?
//     if i_1 == 0, set p11, else set p12.
//
{ .mfi
      nop.m 999
      fsub.s1 s_val = s_val, r
      add N_fix_gr = N_fix_gr, cot_flag // N = N + 1 (for cotl)
}
{ .mfi
      nop.m 999
//
//     Case 2_reduce:
//     U_2 = N * P_2 - U_1
//     Not needed until later.
//
      fadd.s1 U_2 = U_2, w2
//
//     Case 2_reduce:
//     s = s - r
//     U_2 = U_2 + w
//
      nop.i 999
}
;;

//
//     Case 2_reduce:
//     c = c - U_2
//     c is complete here
//     Argument reduction ends here.
//
{ .mfi
      nop.m 999
      fmpy.s1 rsq = r, r
      tbit.z p11, p12 = N_fix_gr, 0 ;;    // Set p11 if N even, p12 if odd
}

{ .mfi
      nop.m 999
(p12) frcpa.s1 S_hi,p0 = f1, r
      nop.i 999
}
{ .mfi
      nop.m 999
      fsub.s1 c = s_val, U_1
      nop.i 999
}
;;

{ .mmi
      add table_ptr1 = 160, table_base ;;  // Point to tanl_table_p1
      ldfe P1_1 = [table_ptr1],144
      nop.i 999 ;;
}
//
//     Load P1_1 and point to Q1_1 .
//
{ .mfi
      ldfe Q1_1 = [table_ptr1]
//
//     N even: rsq = r * Z
//     N odd:  S_hi = frcpa(r)
//
(p12) fmerge.ns S_hi = S_hi, S_hi
      nop.i 999
}
{ .mfi
      nop.m 999
//
//     Case 2_reduce:
//     c = s - U_1
//
(p9)  fsub.s1 c = c, U_2
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
(p12) fma.s1  poly1 = S_hi, r, f1
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
//
//     N odd:  Change sign of S_hi
//
(p11) fmpy.s1 rsq = rsq, P1_1
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
(p12) fma.s1 S_hi = S_hi, poly1, S_hi
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
//
//     N even: rsq = rsq * P1_1
//     N odd:  poly1 =  1.0 +  S_hi * r    16 bits partial  account for necessary
//
(p11) fma.s1 Poly = r, rsq, c
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
//
//     N even: Poly = c  + r * rsq
//     N odd:  S_hi  = S_hi + S_hi*poly1  16 bits account for necessary
//
(p12) fma.s1 poly1 = S_hi, r, f1
(p11) tbit.z.unc p14, p15 = cot_flag, 0 ;; // p14=1 for tanl; p15=1 for cotl
}
{ .mfi
      nop.m 999
//
//     N even: Result = Poly + r
//     N odd:  poly1  = 1.0 + S_hi * r        32 bits partial
//
(p14) fadd.s0 Result = r, Poly             // for tanl
      nop.i 999
}
{ .mfi
      nop.m 999
(p15) fms.s0 Result = r, mOne, Poly        // for cotl
      nop.i 999
}
;;

{ .mfi
      nop.m 999
(p12) fma.s1  S_hi = S_hi, poly1, S_hi
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
//
//     N even: Result1 = Result + r
//     N odd:   S_hi  = S_hi * poly1 + S_hi   32 bits
//
(p12) fma.s1 poly1 = S_hi, r, f1
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
//
//     N odd:  poly1  =  S_hi * r + 1.0       64 bits partial
//
(p12) fma.s1 S_hi = S_hi, poly1, S_hi
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
//
//     N odd:  poly1  =  S_hi * poly + 1.0    64 bits
//
(p12) fma.s1 poly1 = S_hi, r, f1
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
//
//     N odd:  poly1  =  S_hi * r + 1.0
//
(p12) fma.s1 poly1 = S_hi, c, poly1
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
//
//     N odd:  poly1  =  S_hi * c + poly1
//
(p12) fmpy.s1 S_lo = S_hi, poly1
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
//
//     N odd:  S_lo  =  S_hi *  poly1
//
(p12) fma.s1 S_lo = Q1_1, r, S_lo
(p12) tbit.z.unc p14, p15 = cot_flag, 0 // p14=1 for tanl; p15=1 for cotl
}
{ .mfi
      nop.m 999
//
//     N odd:  Result =  S_hi + S_lo
//
      fmpy.s0 fp_tmp = fp_tmp, fp_tmp  // Dummy mult to set inexact
      nop.i 999 ;;
}
{ .mfi
      nop.m 999
//
//     N odd:  S_lo  =  S_lo + Q1_1 * r
//
(p14) fadd.s0 Result = S_hi, S_lo          // for tanl
      nop.i 999
}
{ .mfb
      nop.m 999
(p15) fms.s0 Result = S_hi, mOne, S_lo     // for cotl
      br.ret.sptk b0 ;;          // Exit for pi/4 <= |x| < 2^24 and |s| < 2^-33
}


TANL_LARGER_ARG:
// Here if 2^24 <= |x| < 2^63
//
// ARGUMENT REDUCTION CODE - CASE 3 and 4
//

{ .mmf
      mov GR_exp_2tom14 = 0xffff - 14          // Form signexp of 2^-14
      mov GR_exp_m2tom14 = 0x2ffff - 14        // Form signexp of -2^-14
      fmpy.s1 N_0 = Norm_Arg, Inv_P_0
}
;;

{ .mmi
      setf.exp TWO_TO_NEG14 = GR_exp_2tom14    // Form 2^-14
      setf.exp NEGTWO_TO_NEG14 = GR_exp_m2tom14// Form -2^-14
      nop.i 999
}
;;


//
//    Adjust table_ptr1 to beginning of table.
//    N_0 = Arg * Inv_P_0
//
{ .mmi
      add table_ptr2 = 144, table_base ;;     // Point to 2^-2
      ldfps TWO_TO_NEG2, NEGTWO_TO_NEG2 = [table_ptr2]
      nop.i 999
}
;;

//
//    N_0_fix  = integer part of N_0 .
//
//
//    Make N_0 the integer part.
//
{ .mfi
      nop.m 999
      fcvt.fx.s1 N_0_fix = N_0
      nop.i 999 ;;
}
{ .mfi
      setf.sig B_mask1 = bmask1               // Form mask to get 5 msb of r
      fcvt.xf N_0 = N_0_fix
      nop.i 999 ;;
}
{ .mfi
      setf.sig B_mask2 = bmask2               // Form mask to form B from r
      fnma.s1 ArgPrime = N_0, P_0, Norm_Arg
      nop.i 999
}
{ .mfi
      nop.m 999
      fmpy.s1 w = N_0, d_1
      nop.i 999 ;;
}
//
//    ArgPrime = -N_0 * P_0 + Arg
//    w  = N_0 * d_1
//
//
//    N = ArgPrime * 2/pi
//
//      fcvt.fx.s1 N_fix = N
// Use special scaling to right shift so N=Arg * 2/pi is in rightmost bits
// Branch to Cases 3 or 4 if Arg <= -2**24 or Arg >= 2**24
{ .mfi
      nop.m 999
      fma.s1      N_fix = ArgPrime, FR_inv_pi_2to63, FR_rshf_2to64

      nop.i 999 ;;
}
//     Convert integer N_fix back to normalized floating-point value.
{ .mfi
      nop.m 999
      fms.s1 N = N_fix, FR_2tom64, FR_rshf    // Use scaling to get N floated
      nop.i 999
}
;;

//
//    N is the integer part of the reduced-reduced argument.
//    Put the integer in a GP register.
//
{ .mfi
      getf.sig N_fix_gr = N_fix
      nop.f 999
      nop.i 999
}
;;

//
//    s_val = -N*P_1 + ArgPrime
//    w = -N*P_2 + w
//
{ .mfi
      nop.m 999
      fnma.s1 s_val = N, P_1, ArgPrime
      nop.i 999
}
{ .mfi
      nop.m 999
      fnma.s1 w = N, P_2, w
      nop.i 999
}
;;

//    Case 4: V_hi = N * P_2
//    Case 4: U_hi = N_0 * d_1
{ .mfi
      nop.m 999
      fmpy.s1 V_hi = N, P_2               // V_hi = N * P_2 for |s| < 2^-14
      nop.i 999
}
{ .mfi
      nop.m 999
      fmpy.s1 U_hi = N_0, d_1             // U_hi = N_0 * d_1 for |s| < 2^-14
      nop.i 999
}
;;

//    Case 3: r = s_val + w (Z complete)
//    Case 4: w = N * P_3
{ .mfi
      nop.m 999
      fadd.s1 r = s_val, w                // r = s_val + w for |s| >= 2^-14
      nop.i 999
}
{ .mfi
      nop.m 999
      fmpy.s1 w2 = N, P_3                 // w = N * P_3 for |s| < 2^-14
      nop.i 999
}
;;

//    Case 4: A =  U_hi + V_hi
//    Note: Worry about switched sign of V_hi, so subtract instead of add.
//    Case 4: V_lo = -N * P_2 - V_hi (U_hi is in place of V_hi in writeup)
//    Note: the (-) is still missing for V_hi.
{ .mfi
      nop.m 999
      fsub.s1 A = U_hi, V_hi           // A = U_hi - V_hi for |s| < 2^-14
      nop.i 999
}
{ .mfi
      nop.m 999
      fnma.s1 V_lo = N, P_2, V_hi      // V_lo = V_hi - N * P_2 for |s| < 2^-14
      nop.i 999
}
;;

//    Decide between case 3 and 4:
//    Case 3:  |s| >= 2**(-14)     Set p10
//    Case 4:  |s| <  2**(-14)     Set p11
//
//    Case 4: U_lo = N_0 * d_1 - U_hi
{ .mfi
      nop.m 999
      fms.s1 U_lo = N_0, d_1, U_hi     // U_lo = N_0*d_1 - U_hi for |s| < 2^-14
      nop.i 999
}
{ .mfi
      nop.m 999
      fcmp.lt.s1 p11, p10 = s_val, TWO_TO_NEG14
      nop.i 999
}
;;

//    Case 4: We need abs of both U_hi and V_hi - dont
//    worry about switched sign of V_hi.
{ .mfi
      nop.m 999
      fabs V_hiabs = V_hi              // |V_hi| for |s| < 2^-14
      nop.i 999
}
{ .mfi
      nop.m 999
(p11) fcmp.gt.s1 p11, p10 = s_val, NEGTWO_TO_NEG14
      nop.i 999
}
;;

//    Case 3: c = s_val - r
{ .mfi
      nop.m 999