lib/builtins/fp_div_impl.inc

3 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
18 // respectively. Due to number of significant bits being roughly doubled
26 // Half the bit-size of rep_t
28 // rep_t-sized bitmask with lower half of bits set to ones
84     // One or both of a or b is denormal.  The other (if applicable) is a
85     // normal number.  Renormalize one or both of a and b, and set scale to
103   // Align the significand of b as a UQ1.(n-1) fixed-point number in the range
116   // obtained from IEEE754 representation of function argument (with the
121   // bits of divisor significand (with the implicit bit set). Corresponds to
123   // version of b_UQ1.
159   // An e_0 error is comprised of errors due to
160   // * x0 being an inherently imprecise first approximation of 1/b_hw
163   // reciprocal of b_hw (that is, **truncated** version of b).
179   // For half-width iterations, b_hw is used instead of b.
182     // of corr_UQ1_hw.
193     // From the above analysis of f(x), if corr_UQ1_hw would be represented
194     // without any intermediate loss of precision (that is, in twice_rep_t)
199     // The fact corr_UQ1_hw was virtually round up (due to result of
201     // error estimations) can increase x_UQ0_hw by up to 2*Ulp of x_UQ0_hw.
205     // any number of iterations, so just subtract 2 from the reciprocal
226   // truncation), the result of x_UQ0_hw * corr_UQ1_hw should be either maximum
229   // once after the final iteration. On the other hand, an effective value of
257   // the total number of iterations should be at least 3 even for float32.
262   // of particular structure of operands.
280           - REP_C(2); // 1 to account for the highest bit of corr_UQ1 can be 1
282   // Just like the case of half-width iterations but with possibility
283   // of overflowing by one extra Ulp of x_UQ0.
303   // W0 is the precision of C
331 #error Invalid number of iterations
365   // Different cases (<---> is of 2^-SB length, * = a/b that is shown as a midpoint):