stillwater-sc / universal / 25968650216
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feat(utility): high-precision decimal-to-binary converter (Phase B2a of #835) (#841)

* feat(utility): high-precision decimal-to-binary converter (Phase B2a of #835)

Adds include/sw/universal/utility/decimal_to_binary.hpp -- a multi-limb
bignum-based converter that turns a string_parse::scan_decimal_float
result into a normalized binary representation (sign, mantissa as wide
integer, binary scale, guard bit, sticky bit) with enough precision for
any Universal number system to encode with correct round-to-nearest-even
rounding.

This is the shared foundation that Phase B2b (posit) and B2c (cfloat)
will consume. Wiring those types is intentionally out of scope here;
this PR is utility + validation only.

Algorithm
---------
Given input "[+-]?int.frac[eE][+-]?exp" parsed into (M, E):

  E >= 0:  mantissa = M * 5^E,  binary scale of LSB = E
  E <  0:  let neg_E = |E|, K = headroom + 4*neg_E.
           mantissa = floor((M << (K - neg_E)) / 5^neg_E)
           binary scale of LSB = -K
           The K = headroom + 4*neg_E overshoots log2(5) ~= 2.32 with
           generous margin so the post-divide quotient retains
           target_mantissa_bits + 2 useful bits regardless of |E|.

Then normalize the mantissa so its MSB sits at target_mantissa_bits - 1.
Bits dropped during the right-shift feed `guard_bit` and `sticky_bit`;
the divide remainder also OR's into `sticky_bit`.

Implementation notes
--------------------
- Uses `sw::universal::integer<2048, std::uint32_t, IntegerNumber>` as the
  internal bignum (template-overridable via the `BigBits` parameter for
  callers that need wider). 2048 bits comfortably covers IEEE-double
  exponent range (E up to ~600) and standard posit/cfloat targets.
- Does NOT use `einteger<>` (the elastic integer): it currently produces
  bit-exact wrong results for certain large-operand division patterns
  this code path exercises (e.g., M=3141592653589793, shift=100, divide
  by 5^15 -- einteger gives a quotient 2^64 too high;... (continued)

46093 of 54895 relevant lines covered (83.97%)

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Coverage Regressions

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 -0.22% include/sw/universal/number/posit1/specialized/posit_16_1.hpp
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1 25968650216.1 649
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Source Files on build 25968650216