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5691 #--TERM IN SGL. NOTE THAT PI IS 64-BIT LONG, THUS N*PI/2 IS AT
6737 # form. Thus taking the branch to Step 2 guarantees #
6776 # cancellation. Thus, R is practically X+N(L1+L2) to full #
6787 # Now |X| <= 16446 log2, thus #
6833 # approximately M. Thus 6.2 will never cause #
6875 # with an inexact result. Thus, 9.5 always raises the #
7605 # overflow. Thus, we calculate sinh(X) as follows: #
7719 # Thus, we calculate sinh(X) as follows: #
7842 # 6. (|X| >= 50 log2) Tanh(X) = +-1 (round to nearest). Thus, we #
8018 # Note 1. There are 64 different possible values for F, thus 64 #
8248 #--X = 2^(K) * Y, 1 <= Y < 2. THUS, Y = 1.XXXXXXXX....XX IN BINARY.
8252 #--NOTE THAT U = (Y-F)/F IS VERY SMALL AND THUS APPROXIMATING
8874 # Thus Fact1 + Fact2 = 2**(M) * 2**(j/64). #
9403 # Step 9. At this point, R = 2^(-j)*X - Q Y = Y. Thus, #
9546 #..expo(X) < expo(Y). Thus X = mod(X,Y)
9726 #..R = 2^(-j)X - Q Y = Y, thus R = 0 and quotient = 2^j (Q+1)
Indexes created Wed Oct 29 07:09:46 GMT 2025