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Version: 0.1.13

X07 external math package — v1 (normative)

This document pins the v1 contract for x07-ext-math.

Single canonical way (agent-facing)​

Agents should only use:

  • std.math (facade)
  • std.math.f64 (binary64 floats as F64LE bytes)
  • std.math.i32 (small integer helpers)

Anything under std.math._internal.* is forbidden for production agents.

Float representation: F64LE​

A float value is represented as 8 bytes little-endian containing IEEE-754 binary64 bits.

  • Bytes [0..4) are the low u32 word (lo).
  • Bytes [4..8) are the high u32 word (hi).
  • In hi:
    • sign bit = bit 31
    • exponent = bits 20..30 (11 bits)
    • mantissa_hi = bits 0..19
  • lo contains mantissa low 32 bits.

The package provides constructors and helpers so agents never build bit patterns manually.

Determinism policy​

  • Pure bit-level operations (is_nan_v1, total_cmp_v1, constants) are implemented in x07AST and deterministic everywhere.
  • Arithmetic/libm/text conversion functions are implemented by a pinned native backend (see vendor guidance).

Error codes (SPEC_ERR_MATH_*, numeric)​

This package uses a dedicated error space that must not overlap OS/NET/DB errors:

  • SPEC_ERR_MATH_BASE = 40000
  • SPEC_ERR_F64_BAD_LEN = 40010
  • SPEC_ERR_F64_PARSE_INVALID = 40001
  • SPEC_ERR_F64_PARSE_OVERFLOW = 40002
  • SPEC_ERR_F64_PARSE_UNDERFLOW = 40003
  • SPEC_ERR_F64_TO_I32_NAN_INF = 40020
  • SPEC_ERR_F64_TO_I32_RANGE = 40021

parse_v1 returns result_bytes:

  • OK payload: F64LE (8 bytes)
  • ERR payload: error code (u32)

Public API surface (v1)​

std.math (facade)​

  • Re-exports std.math.f64 and std.math.i32.

std.math.f64 (F64LE floats)​

Constructors:

  • zero_v1() -> bytes
  • one_v1() -> bytes
  • two_v1() -> bytes
  • four_v1() -> bytes
  • neg_zero_v1() -> bytes
  • nan_v1() -> bytes (canonical quiet NaN)
  • inf_v1() -> bytes
  • neg_inf_v1() -> bytes

Classification (pure, deterministic):

  • is_nan_v1(x: bytes_view) -> i32
  • is_inf_v1(x: bytes_view) -> i32
  • is_finite_v1(x: bytes_view) -> i32
  • is_neg_zero_v1(x: bytes_view) -> i32

Ordering (pure, deterministic):

  • total_cmp_v1(a: bytes_view, b: bytes_view) -> i32 (-1/0/1) with NaNs ordered after all numbers
  • cmp_u8_v1(a: bytes_view, b: bytes_view) -> i32 (0/1/2) agent-friendly comparator

Arithmetic/libm (native backend, deterministic if pinned):

  • add_v1/sub_v1/mul_v1/div_v1
  • abs_v1, neg_v1, min_v1, max_v1
  • sqrt_v1, sin_v1, cos_v1, tan_v1, exp_v1, log_v1, pow_v1, atan2_v1, floor_v1, ceil_v1

Text I/O (native backend, deterministic if pinned; see vendor guidance):

  • fmt_shortest_v1(x: bytes_view) -> bytes
  • parse_v1(s: bytes_view) -> result_bytes (accepts optional sign, trims ASCII whitespace, accepts nan / inf / -inf)

Examples:

  • fmt_shortest_v1(from_i32_v1(42)) -> "42"
  • fmt_shortest_v1(neg_zero_v1()) -> "-0"

Conversions:

  • from_i32_v1(x: i32) -> bytes
  • to_i32_trunc_v1(x: bytes_view) -> result_i32
  • to_bits_u64le_v1(x: bytes_view) -> bytes
  • from_bits_u64le_v1(bits_u64le: bytes_view) -> result_bytes

std.math.i32 (minimal helpers)​

  • abs_v1, min_v1, max_v1, clamp_v1