Lines Matching refs:R
104 | 3.1 R := X + N*L1, where L1 := single-precision(-log2/64).
105 | 3.2 R := R + N*L2, L2 := extended-precision(-log2/64 - L1).
111 | Thus, R is practically X+N(L1+L2) to full 64 bits.
112 | d) It is important to estimate how large can |R| be after
127 | Step 4. Approximate exp(R)-1 by a polynomial
128 | p = R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5))))
133 | |p - (exp(R)-1)| < 2^(-68.8) for all |R| <= 0.0062.
137 | p = [ R + R*S*(A2 + S*A4) ] +
139 | where S = R*R.
141 | Step 5. Compute 2^(J/64)*exp(R) = 2^(J/64)*(1+p) by
153 | exp(X) = 2^M * 2^(J/64) * exp(R).
158 | Notes: If AdjFlag = 0, we have X = Mlog2 + Jlog2/64 + R,
162 | X = (M1+M)log2 + Jlog2/64 + R, |M1+M| >= 16380.
508 faddx %fp2,%fp0 | ...fp0 is R, reduced arg.
512 |--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL
513 |-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*A5))))
514 |--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R
515 |--[R+R*S*(A2+S*A4)] + [S*(A1+S*(A3+S*A5))]
518 fmulx %fp1,%fp1 | ...fp1 IS S = R*R
539 fmulx %fp0,%fp3 | ...fp3 IS R*S*(A2+S*A4)
542 faddx %fp3,%fp0 | ...fp0 IS R+R*S*(A2+S*A4),
546 faddx %fp2,%fp0 | ...fp0 is EXP(R) - 1
551 |--EXP(X) = 2^M * ( 2^(J/64) + 2^(J/64)*(EXP(R)-1) )
553 fmulx %fp1,%fp0 | ...2^(J/64)*(Exp(R)-1)
674 faddx %fp2,%fp0 | ...fp0 is R, reduced arg.
679 |--WE NOW COMPUTE EXP(R)-1 BY A POLYNOMIAL
680 |-- R + R*R*(A1 + R*(A2 + R*(A3 + R*(A4 + R*(A5 + R*A6)))))
681 |--TO FULLY UTILIZE THE PIPELINE, WE COMPUTE S = R*R
682 |--[R*S*(A2+S*(A4+S*A6))] + [R+S*(A1+S*(A3+S*A5))]
685 fmulx %fp1,%fp1 | ...fp1 IS S = R*R
718 fmulx %fp0,%fp2 | ...fp2 IS R*S*(A2+S*(A4+S*A6))
719 faddx %fp1,%fp0 | ...fp0 IS R+S*(A1+S*(A3+S*A5))
722 faddx %fp2,%fp0 | ...fp0 IS EXP(R)-1
729 fmulx (%a1),%fp0 | ...2^(J/64)*(Exp(R)-1)