Mathematics

The standard mathematics family separates binary floating-point, exact native integer, and decimal-precision work. It is part of the normal Level G product; it is not guaranteed by the minimal Level B bootstrap closure. The rxint and rxdecimal modules are nevertheless authored in Level B, so installed callers can use their signatures from Level B source.

Binary float: rxfloat

Import rxfloat for scalar operations on the native .float type:

options levelb
import rxfloat

hypotenuse = rxfloat..hypot(3.0, 4.0)
angle = rxfloat..atan2(1.0, 0.0)

rxfloat is a process-reentrant native provider backed by the host C maths library. The compiler records the provider dependency in RXBIN metadata; rxvm discovers the dynamic provider automatically, and crexx -native selects the canonical static archive automatically. No Rexx wrapper or remembered plugin argument is required.

The surface contains:

• trigonometric: sin, cos, tan, asin, acos, atan, atan2;
• hyperbolic: sinh, cosh, tanh, asinh, acosh, atanh;
• exponential and logarithmic: exp, exp2, expm1, log, log2, log10, log1p, pow, pow10;
• rounding and remainder: ceil, floor, round, trunc, fmod;
• roots and special functions: sqrt, cbrt, hypot, erf, erfc, tgamma, lgamma, fabs; and
• constants: pi() and euler().

The same scalar procedures are published as direct rxmath compatibility names by the rxfloat provider. The compatibility names do not load a second library and add no Rexx call layer. New code should import rxfloat. Historical rxmath statistics, hashes, UUID generation, and inlinec are not part of this provider. rxstats is the separate packed .packedfloat bulk statistics provider; it uses the BINARY-01 storage boundary and does not retain the pre-release boxed-array surface.

Domain and range behaviour follows the platform C implementation: operations such as a negative square root return IEEE NaN, poles can return infinity, and signed zero is preserved where the corresponding C function specifies it.

The black-box float contract suite is lib/plugins/float/rxfloat_test.crexx. Its typed assertions live in the pure Level B tests/support/numeric_test_support.crexx module and are shared with the integer and decimal suites. The helper is test machinery rather than a source of expected values. The suite covers every canonical procedure, every compatibility alias, and the representative IEEE/domain boundaries promised above. The risk-weighted requirements for all three numeric families are in the RCC-5 mathematics validation strategy.

Native integer: rxint

rxint supplies checked algorithms over the signed native .int type:

options levelb
import rxint

divisor = rxint..gcd(54, 24)
root = rxint..isqrt(9223372036854775807)
residue = rxint..powmod(2, 10, 1000)

Procedure	Contract
gcd(first, second)	Non-negative greatest common divisor; gcd(0,0) is zero.
lcm(first, second)	Non-negative least common multiple with divide-before-multiply overflow control.
isqrt(value)	Floor of the square root of a non-negative integer.
powmod(base, exponent, modulus)	Normalized modular power using overflow-safe modular doubling.
factorial(value)	Exact factorial for values from 0 through 20.

Invalid domains raise INVALID_ARGUMENTS. A mathematically valid result that does not fit .int raises OVERFLOW_UNDERFLOW.

Decimal: rxdecimal

rxdecimal operates directly on .decimal; it never converts through binary .float:

options levelb
import rxdecimal

calculate: procedure = .decimal
  numeric digits 32
  return rxdecimal..sqrt(2)

The initial surface is sqrt, exp, ln, sin, cos, pi, and euler. Each public procedure inherits the caller’s numeric context and rounds once when returning to the caller. Work precision is 18 digits through caller 9, 32 through caller 18, 64 through caller 32, and 96 through caller 64. Wider callers use their requested precision plus 32 guard digits; this is selected dynamically and does not introduce another fixed ceiling. The surface is qualified through a 128-digit caller context. That qualification boundary is the tested assurance limit, not the implementation’s runtime maximum. Negative square-root arguments and non-positive logarithm arguments raise INVALID_ARGUMENTS.

An ordinary dotted source literal is converted directly from its original spelling when the surrounding typed context expects .decimal; it is not first rounded to binary64. Explicit .float(...) conversion and options floats_binary remain binary boundaries.

The exact-integer and decimal contract suites are lib/rxfnsg/tests_functional/ts_math_integer_contract.crexx and ts_math_decimal_contract.crexx. Their offline oracle commands, versions, rounding policy, and reviewed SHA-256 identities are retained in math-reference-provenance.md beside the suites.