Allow construct RIF element from question-style string

src/sage/libs/mpfi/__init__.pxd

@@ -26,7 +26,7 @@ cdef extern from "mpfi.h":
     int mpfi_set_z(mpfi_ptr, mpz_t)
     int mpfi_set_q(mpfi_ptr, mpq_t)
     int mpfi_set_fr(mpfi_ptr, mpfr_srcptr)
-    int mpfi_set_str(mpfi_ptr, char *, int)
+    int mpfi_set_str(mpfi_ptr, const char *, int)
 
     # combined initialization and assignment functions
     int mpfi_init_set(mpfi_ptr, mpfi_srcptr)
@@ -36,7 +36,7 @@ cdef extern from "mpfi.h":
     int mpfi_init_set_z(mpfi_ptr, mpz_srcptr)
     int mpfi_init_set_q(mpfi_ptr, mpq_srcptr)
     int mpfi_init_set_fr(mpfi_ptr, mpfr_srcptr)
-    int mpfi_init_set_str(mpfi_ptr, char *, int)
+    int mpfi_init_set_str(mpfi_ptr, const char *, int)
 
     # swapping two intervals
     void mpfi_swap(mpfi_ptr, mpfi_ptr)

src/sage/libs/mpfr/__init__.pxd

@@ -27,7 +27,7 @@ cdef extern from "mpfr.h":
     # int mpfr_set_f(mpfr_t rop, mpf_t op, mpfr_rnd_t rnd)
     int mpfr_set_ui_2exp(mpfr_t rop, unsigned long int op, mp_exp_t e, mpfr_rnd_t rnd)
     int mpfr_set_si_2exp(mpfr_t rop, long int op, mp_exp_t e, mpfr_rnd_t rnd)
-    int mpfr_set_str(mpfr_t rop,  char *s, int base, mpfr_rnd_t rnd)
+    int mpfr_set_str(mpfr_t rop,  const char *s, int base, mpfr_rnd_t rnd)
     int mpfr_strtofr(mpfr_t rop, char *nptr, char **endptr, int base, mpfr_rnd_t rnd)
     void mpfr_set_inf(mpfr_t x, int sign)
     void mpfr_set_nan(mpfr_t x)
@@ -43,7 +43,7 @@ cdef extern from "mpfr.h":
     int mpfr_init_set_z(mpfr_t rop, mpz_t op, mpfr_rnd_t rnd)
     int mpfr_init_set_q(mpfr_t rop, mpq_t op, mpfr_rnd_t rnd)
     # int mpfr_init_set_f(mpfr_t rop, mpf_t op, mpfr_rnd_t rnd)
-    int mpfr_init_set_str(mpfr_t x, char *s, int base, mpfr_rnd_t rnd)
+    int mpfr_init_set_str(mpfr_t x, const char *s, int base, mpfr_rnd_t rnd)
 
     # Conversion Functions
     double mpfr_get_d(mpfr_t op, mpfr_rnd_t rnd)

src/sage/rings/convert/mpfi.pyx

@@ -11,11 +11,16 @@ Convert Sage/Python objects to real/complex intervals
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
 
+import re
+
 from cpython.float cimport PyFloat_AS_DOUBLE
 from cpython.complex cimport PyComplex_RealAsDouble, PyComplex_ImagAsDouble
 
+from libc.stdio cimport printf
+
 from sage.libs.mpfr cimport *
 from sage.libs.mpfi cimport *
+from sage.libs.gmp.mpz cimport *
 from sage.libs.gsl.complex cimport *
 
 from sage.arith.long cimport integer_check_long
@@ -45,6 +50,243 @@ cdef inline int return_real(mpfi_ptr im) noexcept:
     return 0
 
 
+NUMBER = re.compile(rb'([+-]?(0[XxBb])?[0-9A-Za-z]+)\.([0-9A-Za-z]*)\?([0-9]*)(?:([EePp@])([+-]?[0-9]+))?')
+# example: -0xABC.DEF?12@5
+# match groups: (-0xABC) (0x) (DEF) (12) (@) (5)
+
+cdef int _from_str_question_style(mpfi_ptr x, bytes s, int base) except -1:
+    """
+    Convert a string in question style to an MPFI interval.
+
+    INPUT:
+
+    - ``x`` -- a pre-initialized MPFI interval
+
+    - ``s`` -- the string to convert
+
+    - ``base`` -- base to use for string conversion
+
+    OUTPUT:
+
+    - if conversion is possible: set ``x`` and return 0.
+
+    - in all other cases: return some nonzero value, or raise an exception.
+
+    TESTS:
+
+    Double check that ``ZZ``, ``RR`` and ``RIF`` follows the string
+    conversion rule for base different from `10` (except ``ZZ``
+    which only allows base up to `36`)::
+
+        sage: ZZ("0x123", base=0)
+        291
+        sage: RR("0x123.e1", base=0)  # rel tol 1e-12
+        291.878906250000
+        sage: RR("0x123.@1", base=0)  # rel tol 1e-12
+        4656.00000000000
+        sage: RIF("0x123.4@1", base=0)
+        4660
+        sage: ZZ("1Xx", base=36)  # case insensitive
+        2517
+        sage: ZZ("1Xx", base=62)
+        Traceback (most recent call last):
+        ...
+        ValueError: base (=62) must be 0 or between 2 and 36
+        sage: RR("1Xx", base=36)  # rel tol 1e-12
+        2517.00000000000
+        sage: RR("0x123", base=36)  # rel tol 1e-12
+        1.54101900000000e6
+        sage: RR("-1Xx@-1", base=62)  # rel tol 1e-12
+        -95.9516129032258
+        sage: RIF("1Xx@-1", base=62)  # rel tol 1e-12
+        95.95161290322580?
+        sage: RIF("1aE1", base=11)
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '1aE1' to real interval
+        sage: RIF("1aE1", base=11)
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '1aE1' to real interval
+
+    General checks::
+
+        sage: RIF("123456.?2").endpoints()  # rel tol 1e-12
+        (123454.0, 123458.0)
+        sage: RIF("1234.56?2").endpoints()  # rel tol 1e-12
+        (1234.54, 1234.58)
+        sage: RIF("1234.56?2e2").endpoints()  # rel tol 1e-12
+        (123454.0, 123458.0)
+        sage: x = RIF("-1234.56?2e2"); x.endpoints()  # rel tol 1e-12
+        (-123458.0, -123454.0)
+        sage: x
+        -1.2346?e5
+        sage: x.str(style="question", error_digits=1)
+        '-123456.?2'
+        sage: RIF("1.?100").endpoints()  # rel tol 1e-12
+        (-99.0, 101.0)
+        sage: RIF("1.?100").str(style="question", error_digits=3)
+        '1.?100'
+
+    Large exponent (ensure precision is not lost)::
+
+        sage: x = RIF("1.123456?2e100000000"); x
+        1.12346?e100000000
+        sage: x.str(style="question", error_digits=3)
+        '1.12345600?201e100000000'
+
+    Large precision::
+
+        sage: F = RealIntervalField(1000)
+        sage: x = F(sqrt(2)); x.endpoints()  # rel tol 1e-290
+        (1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140798,
+         1.41421356237309504880168872420969807856967187537694807317667973799073247846210703885038753432764157273501384623091229702492483605585073721264412149709993583141322266592750559275579995050115278206057147010955997160597027453459686201472851741864088919860955232923048430871432145083976260362799525140799)
+        sage: x in F(x.str(style="question", error_digits=3))
+        True
+        sage: x in F(x.str(style="question", error_digits=0))
+        True
+        sage: F("1.123456789123456789123456789123456789123456789123456789123456789123456789?987654321987654321987654321e500").endpoints()  # rel tol 1e-290
+        (1.123456789123456789123456789123456789123456788135802467135802467135802468e500,
+         1.12345678912345678912345678912345678912345679011111111111111111111111111e500)
+
+    Stress test::
+
+        sage: for F in [RealIntervalField(15), RIF, RealIntervalField(100), RealIntervalField(1000)]:
+        ....:     for i in range(1000):
+        ....:         a, b = randint(-10^9, 10^9), randint(0, 50)
+        ....:         c, d = randint(-2^b, 2^b), randint(2, 5)
+        ....:         x = a * F(d)^c
+        ....:         assert x in F(x.str(style="question", error_digits=3)), (x, a, c, d)
+        ....:         assert x in F(x.str(style="question", error_digits=0)), (x, a, c, d)
+
+    Base different from `10` (note that the error and exponent are specified in decimal)::
+
+        sage: RIF("10000.?0", base=2).endpoints()  # rel tol 1e-12
+        (16.0, 16.0)
+        sage: RIF("10000.?0e10", base=2).endpoints()  # rel tol 1e-12
+        (16384.0, 16384.0)
+        sage: x = RIF("10000.?10", base=2); x.endpoints()  # rel tol 1e-12
+        (6.0, 26.0)
+        sage: x.str(base=2, style="question", error_digits=2)
+        '10000.000?80'
+        sage: x = RIF("10000.000?80", base=2); x.endpoints()  # rel tol 1e-12
+        (6.0, 26.0)
+        sage: x = RIF("12a.?", base=16); x.endpoints()  # rel tol 1e-12
+        (297.0, 299.0)
+        sage: x = RIF("12a.BcDeF?", base=16); x.endpoints()  # rel tol 1e-12
+        (298.737775802611, 298.737777709962)
+        sage: x = RIF("12a.BcDeF?@10", base=16); x.endpoints()  # rel tol 1e-12
+        (3.28465658150911e14, 3.28465660248065e14)
+        sage: x = RIF("12a.BcDeF?p10", base=16); x.endpoints()  # rel tol 1e-12
+        (305907.482421875, 305907.484375000)
+        sage: x = RIF("0x12a.BcDeF?p10", base=0); x.endpoints()  # rel tol 1e-12
+        (305907.482421875, 305907.484375000)
+
+    Space is allowed::
+
+        sage: RIF("-1234.56?2").endpoints()  # rel tol 1e-12
+        (-1234.58, -1234.54)
+        sage: RIF("- 1234.56 ?2").endpoints()  # rel tol 1e-12
+        (-1234.58, -1234.54)
+
+    Erroneous input::
+
+        sage: RIF("1234.56?2e2.3")
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '1234.56?2e2.3' to real interval
+        sage: RIF("1234?2")  # decimal point required
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '1234?2' to real interval
+        sage: RIF("1234.?2e")
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '1234.?2e' to real interval
+        sage: RIF("1.?e999999999999999999999999")
+        [-infinity .. +infinity]
+        sage: RIF("0X1.?", base=33)  # X is not valid digit in base 33
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '0X1.?' to real interval
+        sage: RIF("1.a?1e10", base=12)
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '1.a?1e10' to real interval
+        sage: RIF("1.1?a@10", base=12)
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '1.1?a@10' to real interval
+        sage: RIF("0x1?2e1", base=0)  # e is not allowed in base > 10, use @ instead
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '0x1?2e1' to real interval
+        sage: RIF("0x1?2p1", base=36)
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '0x1?2p1' to real interval
+    """
+    cdef mpz_t error_part
+    cdef mpfi_t error
+    cdef mpfr_t radius, neg_radius
+    cdef bytes int_part_string, base_prefix, frac_part_string, error_string, e, sci_expo_string, optional_expo, tmp
+
+    match = NUMBER.fullmatch(s)
+    if match is None:
+        return 1
+    int_part_string, base_prefix, frac_part_string, error_string, e, sci_expo_string = match.groups()
+
+    if (base > 10 or (base == 0 and base_prefix in (b'0X', b'0X'))) and e in (b'e', b'E'):
+        return 1
+    if base > 16 and e in (b'p', b'P'):
+        return 1
+    if base > 16 or not base_prefix:
+        base_prefix = b''
+
+    if error_string:
+        if mpz_init_set_str(error_part, error_string, 10):
+            mpz_clear(error_part)
+            return 1
+    else:
+        mpz_init_set_ui(error_part, 1)
+
+    optional_expo = e + sci_expo_string if e else b''
+    if mpfi_set_str(x, int_part_string + b'.' + frac_part_string + optional_expo, base):
+        mpz_clear(error_part)
+        return 1
+
+    mpfr_init2(radius, mpfi_get_prec(x))
+    tmp = base_prefix + (
+            b'0.' + b'0'*(len(frac_part_string)-1) + b'1' + optional_expo
+            if frac_part_string else
+            b'1.' + optional_expo)
+    # if base = 0:
+    #     when s = '-0x123.456@7', tmp = '0x0.001@7'
+    #     when s = '-0x123.@7', tmp = '0x1.@7'
+    # if base = 36:
+    #     when s = '-0x123.456@7', tmp = '0.001@7'
+    if mpfr_set_str(radius, tmp, base, MPFR_RNDU):
+        mpfr_clear(radius)
+        mpz_clear(error_part)
+        return 1
+
+    mpfr_mul_z(radius, radius, error_part, MPFR_RNDU)
+    mpz_clear(error_part)
+
+    mpfr_init2(neg_radius, mpfi_get_prec(x))
+    mpfr_neg(neg_radius, radius, MPFR_RNDD)
+
+    mpfi_init2(error, mpfi_get_prec(x))
+    mpfi_interv_fr(error, neg_radius, radius)
+    mpfr_clear(radius)
+    mpfr_clear(neg_radius)
+
+    mpfi_add(x, x, error)
+    mpfi_clear(error)
+
+    return 0
+
+
 cdef int mpfi_set_sage(mpfi_ptr re, mpfi_ptr im, x, field, int base) except -1:
     """
     Convert any object ``x`` to an MPFI interval or a pair of
@@ -72,13 +314,42 @@ cdef int mpfi_set_sage(mpfi_ptr re, mpfi_ptr im, x, field, int base) except -1:
       imaginary component is 0.
 
     - in all other cases: raise an exception.
+
+    TESTS::
+
+        sage: RIF('0xabc')
+        Traceback (most recent call last):
+        ...
+        TypeError: unable to convert '0xabc' to real interval
+        sage: RIF("0x123.e1", base=0)  # rel tol 1e-12
+        291.87890625000000?
+        sage: RIF("0x123.@1", base=0)  # rel tol 1e-12
+        4656
+        sage: RIF("1Xx", base=36)  # rel tol 1e-12
+        2517
+        sage: RIF("-1Xx@-10", base=62)  # rel tol 1e-12
+        -7.088054920481391?e-15
+        sage: RIF("1", base=1)
+        Traceback (most recent call last):
+        ...
+        ValueError: base (=1) must be 0 or between 2 and 62
+        sage: RIF("1", base=-1)
+        Traceback (most recent call last):
+        ...
+        ValueError: base (=-1) must be 0 or between 2 and 62
+        sage: RIF("1", base=63)
+        Traceback (most recent call last):
+        ...
+        ValueError: base (=63) must be 0 or between 2 and 62
     """
     cdef RealIntervalFieldElement ri
     cdef ComplexIntervalFieldElement zi
     cdef ComplexNumber zn
     cdef ComplexDoubleElement zd
     cdef bytes s
 
+    if base != 0 and (base < 2 or base > 62):
+        raise ValueError(f"base (={base}) must be 0 or between 2 and 62")
     if im is not NULL and isinstance(x, tuple):
         # For complex numbers, interpret tuples as real/imag parts
         if len(x) != 2:
@@ -157,6 +428,11 @@ cdef int mpfi_set_sage(mpfi_ptr re, mpfi_ptr im, x, field, int base) except -1:
         if isinstance(x, unicode):
             x = x.encode("ascii")
         if isinstance(x, bytes):
+            if b"?" in x:
+                if _from_str_question_style(re, (<bytes>x).replace(b' ', b''), base):
+                    x = bytes_to_str(x)
+                    raise TypeError(f"unable to convert {x!r} to real interval")
+                return return_real(im)
             s = (<bytes>x).replace(b'..', b',').replace(b' ', b'').replace(b'+infinity', b'@inf@').replace(b'-infinity', b'-@inf@')
             if mpfi_set_str(re, s, base):
                 x = bytes_to_str(x)

src/sage/rings/real_mpfr.pyx

@@ -1437,6 +1437,33 @@ cdef class RealNumber(sage.structure.element.RingElement):
 
             sage: RealNumber('1_3.1e-32_45')
             1.31000000000000e-3244
+
+        Test conversion from base different from `10`::
+
+            sage: RR('0xabc')
+            Traceback (most recent call last):
+            ...
+            TypeError: unable to convert '0xabc' to a real number
+            sage: RR("0x123.e1", base=0)  # rel tol 1e-12
+            291.878906250000
+            sage: RR("0x123.@1", base=0)  # rel tol 1e-12
+            4656.00000000000
+            sage: RR("1Xx", base=36)  # rel tol 1e-12
+            2517.00000000000
+            sage: RR("-1Xx@-10", base=62)  # rel tol 1e-12
+            -7.08805492048139e-15
+            sage: RR("1", base=1)
+            Traceback (most recent call last):
+            ...
+            ValueError: base (=1) must be 0 or between 2 and 62
+            sage: RR("1", base=-1)
+            Traceback (most recent call last):
+            ...
+            ValueError: base (=-1) must be 0 or between 2 and 62
+            sage: RR("1", base=63)
+            Traceback (most recent call last):
+            ...
+            ValueError: base (=63) must be 0 or between 2 and 62
         """
         if x is not None:
             self._set(x, base)
@@ -1485,6 +1512,8 @@ cdef class RealNumber(sage.structure.element.RingElement):
         # Real Numbers are supposed to be immutable.
         cdef RealField_class parent
         parent = self._parent
+        if base != 0 and (base < 2 or base > 62):
+            raise ValueError(f"base (={base}) must be 0 or between 2 and 62")
         if isinstance(x, RealNumber):
             if isinstance(x, RealLiteral):
                 s = (<RealLiteral>x).literal