Summary

The existing mantissa parsing code uses a floating point variable to accumulate digits.

Using an mp_float_uint_t variable instead, and casting to mp_float_t at the very end is more efficient and reduces code size. In some cases, it also improves the rounding behaviour as extra digits are taken into account by the int-to-float conversion code.

Testing

The new code was unit-tested using a small program generating 100'000 random mantissa and exponents, parsing the resulting number as a float and comparing the result to the value obtained via bigint arithmetic.

• when using MICROPY_FLOAT_IMPL_DOUBLE, with exponents between -200 and 200
  • the max relative error of the old code is around 5.7e-16
  • the max relative error of the new code is around 4.3e-16
  • CPython max relative error is around 3.6e-16
• when using MICROPY_FLOAT_IMPL_FLOAT, with exponents between -20 and 50
  • the max relative error of the old code is around 4.3e-7
  • the max relative error of the new code is around 2.4e-7

The code size reduction was observed on binaries built using gcc-arm-none-eabi-9-2019-q4-major

Trade-offs and Alternatives

A further improvement in precision for positive exponents could be obtained by leveraging bigint arithmetic up to the computation of the final value:

        #if MICROPY_FLOAT_IMPL == MICROPY_FLOAT_IMPL_FLOAT
        mp_obj_t mant_obj = mp_obj_new_int_from_uint(mantissa);
        #else
        mp_obj_t mant_obj = mp_obj_new_int_from_ulonglong(mantissa);
        #endif
        mp_binary_op_t combine_op = MP_BINARY_OP_MULTIPLY;
        if (exp_val < 0) {
            combine_op = MP_BINARY_OP_TRUE_DIVIDE;
            exp_val = -exp_val;
        }
        mp_obj_t exp_obj = MP_OBJ_NEW_SMALL_INT(exp_val);
        mp_obj_t pow_obj = mp_binary_op(MP_BINARY_OP_POWER, MP_OBJ_NEW_SMALL_INT(10), exp_obj);
        mp_obj_t res_obj = mp_binary_op(combine_op, mant_obj, pow_obj);
        dec_val = mp_obj_get_float(res_obj);

This would however increase the code size, and cause dynamic object allocation in case the mantissa is larger then 9 digits or the absolute value of the exponent is bigger than 9, so this idea was dropped.