// p12 if i_0=1, N mod 4 = 1,3};;{ .mfi        nop.m 999       fms.s1        FR_s = FR_s, f1, FR_r        nop.i 999}{ .mfi        nop.m 999////     S = S - r//     U_2 = U_2 + w//     load S_1//       fma.s1        FR_rsq = FR_r, FR_r, f0        nop.i 999 ;;}{ .mfi        nop.m 999       fma.s1        FR_U_2 = FR_U_2, f1, FR_w        nop.i 999}{ .mfi        nop.m 999       fmerge.se FR_tmp_result = FR_r, FR_r        nop.i 999 ;;}{ .mfi        nop.m 999(p10)  fma.s1 FR_tmp_result = f0, f1, f1        nop.i 999 ;;}{ .mfi        nop.m 999////     FR_rsq = r * r//     Save r as the result.//       fms.s1        FR_c = FR_s, f1, FR_U_1        nop.i 999 ;;}{ .mfi        nop.m 999////     if ( i_1 ==0) poly = c + S_1*r*r*r//     else Result = 1//(p12)  fnma.s1 FR_tmp_result = FR_tmp_result, f1, f0        nop.i 999}{ .mfi        nop.m 999       fma.s1        FR_r = FR_S_1, FR_r, f0        nop.i 999 ;;}{ .mfi        nop.m 999       fma.s0        FR_S_1 = FR_S_1, FR_S_1, f0        nop.i 999 ;;}{ .mfi        nop.m 999////     If i_1 != 0, poly = 2**(-67)//       fms.s1 FR_c = FR_c, f1, FR_U_2        nop.i 999 ;;}{ .mfi        nop.m 999////     c = c - U_2//(p9)   fma.s1 FR_poly = FR_r, FR_rsq, FR_c        nop.i 999 ;;}{ .mfi        nop.m 999////     i_0 != 0, so Result = -Result//(p11)  fma.s0 FR_Result = FR_tmp_result, f1, FR_poly        nop.i 999 ;;}{ .mfb        nop.m 999(p12)  fms.s0 FR_Result = FR_tmp_result, f1, FR_poly////     if (i_0 == 0),  Result = Result + poly//     else            Result = Result - poly//        br.ret.sptk   b0         // Exit if |s| < 2^-33, and pi/4 <= |x| < 2^24};;SINCOSL_LARGER_ARG://// Here if 2^24 <= |x| < 2^63//{ .mfi      ldfe FR_d_1 = [GR_ad_p], 16          // Load d_1 for |x| >= 2^24 path       fma.s1 FR_N_0 = FR_Input_X, FR_Inv_P_0, f0        nop.i 999};;////     N_0 = Arg * Inv_P_0////     Load values 2**(-14) and -2**(-14){ .mmi       ldfps FR_Two_to_M14, FR_Neg_Two_to_M14 = [GR_ad_m14]        nop.i 999 ;;}{ .mfi      ldfe FR_d_2 = [GR_ad_p], 16          // Load d_2 for |x| >= 2^24 path        nop.f 999        nop.i 999 ;;}{ .mfi        nop.m 999////       fcvt.fx.s1 FR_N_0_fix = FR_N_0        nop.i 999 ;;}{ .mfi        nop.m 999////     N_0_fix  = integer part of N_0//       fcvt.xf FR_N_0 = FR_N_0_fix        nop.i 999 ;;}{ .mfi        nop.m 999////     Make N_0 the integer part//       fnma.s1 FR_ArgPrime = FR_N_0, FR_P_0, FR_Input_X        nop.i 999}{ .mfi        nop.m 999       fma.s1 FR_w = FR_N_0, FR_d_1, f0        nop.i 999 ;;}{ .mfi        nop.m 999////     Arg' = -N_0 * P_0 + Arg//     w  = N_0 * d_1//       fma.s1 FR_N_float = FR_ArgPrime, FR_Inv_pi_by_2, f0        nop.i 999 ;;}{ .mfi        nop.m 999////     N = A' * 2/pi//       fcvt.fx.s1 FR_N_fix = FR_N_float        nop.i 999 ;;}{ .mfi        nop.m 999////     N_fix is the integer part//       fcvt.xf FR_N_float = FR_N_fix        nop.i 999 ;;}{ .mfi       getf.sig GR_N_Inc = FR_N_fix        nop.f 999        nop.i 999 ;;}{ .mii        nop.m 999        nop.i 999 ;;       add GR_N_Inc = GR_N_Inc, GR_Sin_or_Cos ;;}{ .mfi        nop.m 999////     N is the integer part of the reduced-reduced argument.//     Put the integer in a GP register//       fnma.s1 FR_s = FR_N_float, FR_P_1, FR_ArgPrime        nop.i 999}{ .mfi        nop.m 999       fnma.s1 FR_w = FR_N_float, FR_P_2, FR_w        nop.i 999 ;;}{ .mfi        nop.m 999////     s = -N*P_1 + Arg'//     w = -N*P_2 + w//     N_fix_gr = N_fix_gr + N_inc//       fcmp.lt.unc.s1 p9, p8 = FR_s, FR_Two_to_M14        nop.i 999 ;;}{ .mfi        nop.m 999(p9)   fcmp.gt.s1 p9, p8 = FR_s, FR_Neg_Two_to_M14  // p9 if |s| < 2^-14        nop.i 999 ;;}{ .mfi        nop.m 999////     For |s|  > 2**(-14) r = S + w (r complete)//     Else       U_hi = N_0 * d_1//(p9)   fma.s1 FR_V_hi = FR_N_float, FR_P_2, f0        nop.i 999}{ .mfi        nop.m 999(p9)   fma.s1 FR_U_hi = FR_N_0, FR_d_1, f0        nop.i 999 ;;}{ .mfi        nop.m 999////     Either S <= -2**(-14) or S >= 2**(-14)//     or -2**(-14) < s < 2**(-14)//(p8)   fma.s1 FR_r = FR_s, f1, FR_w        nop.i 999}{ .mfi        nop.m 999(p9)   fma.s1 FR_w = FR_N_float, FR_P_3, f0        nop.i 999 ;;}{ .mfi        nop.m 999////     We need abs of both U_hi and V_hi - don't//     worry about switched sign of V_hi.//(p9)   fms.s1 FR_A = FR_U_hi, f1, FR_V_hi        nop.i 999}{ .mfi        nop.m 999////     Big s: finish up c = (S - r) + w (c complete)//     Case 4: A =  U_hi + V_hi//     Note: Worry about switched sign of V_hi, so subtract instead of add.//(p9)   fnma.s1 FR_V_lo = FR_N_float, FR_P_2, FR_V_hi        nop.i 999 ;;}{ .mmf        nop.m 999        nop.m 999(p9)   fms.s1 FR_U_lo = FR_N_0, FR_d_1, FR_U_hi}{ .mfi        nop.m 999(p9)   fmerge.s FR_V_hiabs = f0, FR_V_hi        nop.i 999 ;;}//{ .mfb//(p9)   fmerge.s f8= FR_V_lo,FR_V_lo//(p9)   br.ret.sptk b0//}//;;{ .mfi        nop.m 999//     For big s: c = S - r//     For small s do more work: U_lo = N_0 * d_1 - U_hi//(p9)   fmerge.s FR_U_hiabs = f0, FR_U_hi        nop.i 999}{ .mfi        nop.m 999////     For big s: Is |r| < 2**(-3)//     For big s: if p12 set, prepare to branch to Small_R.//     For big s: If p13 set, prepare to branch to Normal_R.//(p8)   fms.s1 FR_c = FR_s, f1, FR_r        nop.i 999 ;;}{ .mfi        nop.m 999////     For small S: V_hi = N * P_2//                  w = N * P_3//     Note the product does not include the (-) as in the writeup//     so (-) missing for V_hi and w.//(p8)   fcmp.lt.unc.s1 p12, p13 = FR_r, FR_Two_to_M3        nop.i 999 ;;}{ .mfi        nop.m 999(p12)  fcmp.gt.s1 p12, p13 = FR_r, FR_Neg_Two_to_M3        nop.i 999 ;;}{ .mfi        nop.m 999(p8)   fma.s1 FR_c = FR_c, f1, FR_w        nop.i 999}{ .mfb        nop.m 999(p9)   fms.s1 FR_w = FR_N_0, FR_d_2, FR_w(p12)  br.cond.spnt SINCOSL_SMALL_R      // Branch if |r| < 2^-3                                         // and 2^24 <= |x| < 2^63};;{ .mib        nop.m 999        nop.i 999(p13)  br.cond.sptk SINCOSL_NORMAL_R     // Branch if |r| >= 2^-3                                         // and 2^24 <= |x| < 2^63};;SINCOSL_LARGER_S_TINY://// Here if |s| < 2^-14, and 2^24 <= |x| < 2^63//{ .mfi        nop.m 999////     Big s: Vector off when |r| < 2**(-3).  Recall that p8 will be true.//     The remaining stuff is for Case 4.//     Small s: V_lo = N * P_2 + U_hi (U_hi is in place of V_hi in writeup)//     Note: the (-) is still missing for V_lo.//     Small s: w = w + N_0 * d_2//     Note: the (-) is now incorporated in w.//       fcmp.ge.unc.s1 p7, p8 = FR_U_hiabs, FR_V_hiabs}{ .mfi        nop.m 999////     C_hi = S + A//       fma.s1 FR_t = FR_U_lo, f1, FR_V_lo};;{ .mfi        nop.m 999////     t = U_lo + V_lo////(p7)  fms.s1 FR_a = FR_U_hi, f1, FR_A        nop.i 999 ;;}{ .mfi        nop.m 999(p8)  fma.s1 FR_a = FR_V_hi, f1, FR_A        nop.i 999};;{ .mfi////     Is U_hiabs >= V_hiabs?//        nop.m 999       fma.s1 FR_C_hi = FR_s, f1, FR_A        nop.i 999 ;;}{ .mmi       ldfe FR_C_1 = [GR_ad_c], 16 ;;       ldfe FR_C_2 = [GR_ad_c], 64        nop.i 999 ;;}////     c = c + C_lo  finished.//     Load  C_2//{ .mfi       ldfe        FR_S_1 = [GR_ad_s], 16////     C_lo = S - C_hi//       fma.s1 FR_t = FR_t, f1, FR_w        nop.i 999 ;;}////     r and c have been computed.//     Make sure ftz mode is set - should be automatic when using wre//     |r| < 2**(-3)//     Get [i_0,i_1] - two lsb of N_fix.//     Load S_1//{ .mfi       ldfe FR_S_2 = [GR_ad_s], 64////     t = t + w//(p7)  fms.s1 FR_a = FR_a, f1, FR_V_hi      tbit.z p9,p10 = GR_N_Inc, 0      // p9  if i_1=0, N mod 4 = 0,1                                       // p10 if i_1=1, N mod 4 = 2,3};;{ .mfi        nop.m 999////     For larger u than v: a = U_hi - A//     Else a = V_hi - A (do an add to account for missing (-) on V_hi//       fms.s1 FR_C_lo = FR_s, f1, FR_C_hi        nop.i 999 ;;}{ .mfi        nop.m 999(p8)  fms.s1 FR_a = FR_U_hi, f1, FR_a      tbit.z p11,p12 = GR_N_Inc, 1     // p11 if i_0=0, N mod 4 = 0,2                                       // p12 if i_0=1, N mod 4 = 1,3};;{ .mfi        nop.m 999////     If u > v: a = (U_hi - A)  + V_hi//     Else      a = (V_hi - A)  + U_hi//     In each case account for negative missing from V_hi.//       fma.s1 FR_C_lo = FR_C_lo, f1, FR_A        nop.i 999 ;;}{ .mfi        nop.m 999////     C_lo = (S - C_hi) + A//       fma.s1 FR_t = FR_t, f1, FR_a        nop.i 999 ;;}{ .mfi        nop.m 999////     t = t + a//       fma.s1 FR_C_lo = FR_C_lo, f1, FR_t        nop.i 999 ;;}{ .mfi        nop.m 999////     C_lo = C_lo + t//       fma.s1 FR_r = FR_C_hi, f1, FR_C_lo        nop.i 999 ;;}{ .mfi        nop.m 999////     Load S_2//       fma.s1 FR_rsq = FR_r, FR_r, f0        nop.i 999}{ .mfi        nop.m 999////     r = C_hi + C_lo//       fms.s1 FR_c = FR_C_hi, f1, FR_r        nop.i 999 ;;}{ .mfi        nop.m 999////     if i_1 ==0: poly = S_2 * FR_rsq + S_1//     else        poly = C_2 * FR_rsq + C_1//(p9)  fma.s1 FR_tmp_result = f0, f1, FR_r        nop.i 999 ;;}{ .mfi        nop.m 999(p10)  fma.s1 FR_tmp_result = f0, f1, f1        nop.i 999 ;;}{ .mfi        nop.m 999////     Compute r_cube = FR_rsq * r//(p9)  fma.s1 FR_poly = FR_rsq, FR_S_2, FR_S_1        nop.i 999 ;;}{ .mfi        nop.m 999(p10)  fma.s1 FR_poly = FR_rsq, FR_C_2, FR_C_1        nop.i 999}{ .mfi        nop.m 999////     Compute FR_rsq = r * r//     Is i_1 == 0 ?//       fma.s1 FR_r_cubed = FR_rsq, FR_r, f0        nop.i 999 ;;}{ .mfi        nop.m 999////     c = C_hi - r//     Load  C_1//       fma.s1 FR_c = FR_c, f1, FR_C_lo        nop.i 999}{ .mfi        nop.m 999////     if i_1 ==0: poly = r_cube * poly + c//     else        poly = FR_rsq * poly//(p12)  fms.s1 FR_tmp_result = f0, f1, FR_tmp_result        nop.i 999 ;;}{ .mfi        nop.m 999////     if i_1 ==0: Result = r//     else        Result = 1.0//(p9)  fma.s1 FR_poly = FR_r_cubed, FR_poly, FR_c        nop.i 999 ;;}{ .mfi        nop.m 999(p10)  fma.s1 FR_poly = FR_rsq, FR_poly, f0        nop.i 999 ;;}{ .mfi        nop.m 999////     if i_0 !=0: Result = -Result//(p11)   fma.s0 FR_Result = FR_tmp_result, f1, FR_poly        nop.i 999 ;;}{ .mfb        nop.m 999(p12)  fms.s0 FR_Result = FR_tmp_result, f1, FR_poly////     if i_0 == 0: Result = Result + poly//     else         Result = Result - poly//      br.ret.sptk   b0         // Exit for |s| < 2^-14, and 2^24 <= |x| < 2^63};;SINCOSL_SMALL_R://// Here if |r| < 2^-3//// Enter with r, c, and N_Inc computed////      Compare both i_1 and i_0 with 0.//      if i_1 == 0, set p9.//      if i_0 == 0, set p11.//{ .mfi      nop.m 999      fma.s1 FR_rsq = FR_r, FR_r, f0   // rsq = r * r      tbit.z p9,p10 = GR_N_Inc, 0      // p9  if i_1=0, N mod 4 = 0,1                                       // p10 if i_1=1, N mod 4 = 2,3};;{ .mmi(p9)  ldfe FR_S_5 = [GR_ad_se], -16    // Load S_5 if i_1=0(p10) ldfe FR_C_5 = [GR_ad_ce], -16    // Load C_5 if i_1=1      nop.i 999