swift-iso-9899

Foundation-free Swift implementation of ISO/IEC 9899 (C Standard) mathematical functions.

Overview

This package provides Swift access to mathematical functions defined in ISO/IEC 9899:2018 Section 7.12 (Mathematics) without requiring Foundation. It wraps the platform's standard C math library with a clean, type-safe Swift API.

Why ISO 9899?

• IEEE 754-2019 only recommends mathematical functions (Clause 9), doesn't require them
• ISO/IEC 9899 (C Standard) defines the complete math library in Section 7.12
• ISO 9899 specifies function prototypes, behavior, and semantics
• This is the authoritative standard for mathematical function interfaces

Complete ISO/IEC 9899:2018 Section 7.12 Coverage

This package provides complete coverage of all mathematical functions defined in ISO/IEC 9899:2018 Section 7.12.

Classification Functions (Section 7.12.3)

• fpclassify(_:) - Classify floating-point value (normal, zero, subnormal, infinite, NaN)
• isfinite(_:) - Test for finite value
• isinf(_:) - Test for infinity
• isnan(_:) - Test for NaN
• isnormal(_:) - Test for normal value
• signbit(_:) - Test sign bit

Trigonometric Functions (Section 7.12.4)

• sin(_:), cos(_:), tan(_:) - Basic trigonometric functions
• asin(_:), acos(_:), atan(_:) - Inverse trigonometric functions
• atan2(_:_:) - Arc tangent of y/x with quadrant information

Hyperbolic Functions (Section 7.12.5)

• sinh(_:), cosh(_:), tanh(_:) - Hyperbolic functions
• asinh(_:), acosh(_:), atanh(_:) - Inverse hyperbolic functions

Exponential and Logarithmic Functions (Section 7.12.6)

• exp(_:), exp2(_:) - Exponential functions (e^x, 2^x)
• log(_:), log2(_:), log10(_:) - Logarithmic functions
• expm1(_:), log1p(_:) - High-precision variants for values near zero

Power and Absolute-Value Functions (Section 7.12.7)

• pow(_:_:) - Compute x raised to the power y
• sqrt(_:), cbrt(_:) - Square root and cube root
• fabs(_:) - Absolute value
• hypot(_:_:) - Euclidean distance (sqrt(x² + y²))

Error and Gamma Functions (Section 7.12.8)

• erf(_:), erfc(_:) - Error function and complementary error function
• tgamma(_:), lgamma(_:) - Gamma function and log gamma

Rounding Functions (Section 7.12.9)

• ceil(_:), floor(_:), trunc(_:) - Directional rounding
• round(_:) - Round to nearest (ties away from zero)
• rint(_:), nearbyint(_:) - Round using current rounding mode
• lrint(_:), llrint(_:) - Round and convert to integer
• lround(_:), llround(_:) - Round (ties away) and convert to integer

Remainder Functions (Section 7.12.10)

• fmod(_:_:) - Floating-point remainder
• remainder(_:_:) - IEEE remainder
• remquo(_:_:_:) - Remainder with quotient

Manipulation Functions (Section 7.12.11)

• copysign(_:_:) - Copy sign between values
• nan(_:), nanf(_:) - Create NaN with payload
• nextafter(_:_:), nexttoward(_:_:) - Next representable value

Maximum, Minimum, and Difference (Section 7.12.12)

• fmax(_:_:), fmin(_:_:) - Maximum and minimum (NaN-aware)
• fdim(_:_:) - Positive difference

Floating Multiply-Add (Section 7.12.13)

• fma(_:_:_:) - Fused multiply-add with single rounding

Comparison Macros (Section 7.12.14)

• isgreater(_:_:) - Quiet > comparison (no exception on NaN)
• isgreaterequal(_:_:) - Quiet >= comparison
• isless(_:_:) - Quiet < comparison
• islessequal(_:_:) - Quiet <= comparison
• islessgreater(_:_:) - Quiet != comparison
• isunordered(_:_:) - Test for unordered (NaN) arguments

Mathematical Constants

• Fundamental: π, e, τ
• Square roots: √2, √3, √5, 1/√2
• Logarithms: ln(2), ln(10), log₂(e), log₁₀(e), log₂(10)
• Golden ratio: φ
• Angular conversions: degrees ↔ radians
• Common π fractions: π/2, π/3, π/4, π/6, 2π
• Euler-Mascheroni: γ

All functions implement IEEE 754 semantics per Annex F.

Usage

Direct Namespace Access

import ISO_9899

// Power functions
let power = ISO_9899.Math.pow(2.0, 3.0)  // 8.0
let gamma = ISO_9899.Math.pow(c, 1.0/2.4)  // Gamma correction
let root = ISO_9899.Math.sqrt(16.0)  // 4.0

// Trigonometric functions
let sine = ISO_9899.Math.sin(.pi / 2)  // 1.0
let cosine = ISO_9899.Math.cos(0)  // 1.0
let angle = ISO_9899.Math.atan2(1.0, 1.0)  // π/4

// Exponential and logarithmic functions
let e = ISO_9899.Math.exp(1.0)  // 2.71828...
let power2 = ISO_9899.Math.exp2(10.0)  // 1024.0
let ln = ISO_9899.Math.log(2.71828)  // 1.0
let log2 = ISO_9899.Math.log2(1024.0)  // 10.0

// Absolute value and additional power functions
let abs = ISO_9899.Math.fabs(-3.14)   // 3.14
let dist = ISO_9899.Math.hypot(3.0, 4.0)   // 5.0
let cubeRoot = ISO_9899.Math.cbrt(27.0)    // 3.0
let max = ISO_9899.Math.fmax(3.0, 5.0)     // 5.0
let min = ISO_9899.Math.fmin(3.0, 5.0)     // 3.0

// Rounding functions
let rounded = ISO_9899.Math.ceil(2.3)   // 3.0
let floored = ISO_9899.Math.floor(2.7)  // 2.0
let nearest = ISO_9899.Math.round(2.5)  // 3.0 (ties away from zero)
let truncated = ISO_9899.Math.trunc(-2.7)  // -2.0

// Classification functions
let classification = ISO_9899.Math.fpclassify(1.0)    // .normal
let isFinite = ISO_9899.Math.isfinite(.infinity)      // false
let isNaN = ISO_9899.Math.isnan(.nan)                 // true
let signBit = ISO_9899.Math.signbit(-0.0)             // true

// Comparison functions (quiet - no exception on NaN)
let greater = ISO_9899.Math.isgreater(5.0, 3.0)      // true
let lessOrGreater = ISO_9899.Math.islessgreater(5.0, .nan)  // false
let unordered = ISO_9899.Math.isunordered(.nan, 5.0)  // true

// Integer-returning rounding
let asInt = ISO_9899.Math.lround(2.5)                 // 3
let asInt64 = ISO_9899.Math.llround(2.5)              // 3

// Mathematical constants
let circumference = 2 * ISO_9899.Math.Constants.pi * radius
let radians = degrees * ISO_9899.Math.Constants.degreesToRadians
let sqrt2 = ISO_9899.Math.Constants.sqrt2
let goldenRatio = ISO_9899.Math.Constants.phi

// Works with Float too
let f: Float = ISO_9899.Math.sin(Float.pi / 4)

Ergonomic .c Namespace (Swifty API)

import ISO_9899

let x = 2.0

// Power functions
let squared = x.c.pow(3.0)      // 8.0
let root = x.c.sqrt             // 1.41421356...

// Trigonometric functions
let sine = x.c.sin              // 0.90929742...
let cosine = x.c.cos            // -0.41614683...
let tangent = x.c.tan           // -2.18503986...

// Exponential and logarithmic functions
let exp = x.c.exp               // 7.389056...
let log = x.c.log               // 0.693147180...
let log2 = x.c.log2             // 1.0

// Absolute value and additional power functions
let abs = (-x).c.abs            // 2.0
let dist = x.c.hypot(3.0)       // 3.60555127...
let cube = x.c.cbrt             // 1.25992104...
let maximum = x.c.max(5.0)      // 5.0
let minimum = x.c.min(5.0)      // 2.0

// Rounding functions
let ceil = (2.3).c.ceil         // 3.0
let floor = (2.7).c.floor       // 2.0
let round = (2.5).c.round       // 3.0
let trunc = (-2.7).c.trunc      // -2.0

// Classification functions
let classification = (1.0).c.classification          // .normal
let isFinite = Double.infinity.c.isFinite            // false
let isNaN = Double.nan.c.isNaN                       // true
let hasNegativeSign = (-0.0).c.hasNegativeSign       // true

// Comparison functions (quiet - no exception on NaN)
let greater = (5.0).c.isGreater(than: 3.0)           // true
let lessOrGreater = (5.0).c.isNotEqual(to: .nan)     // false
let unordered = Double.nan.c.isUnordered(with: 5.0)  // true

// Integer-returning rounding
let asInt = (2.5).c.roundToInt()                     // 3
let asInt64 = (2.5).c.roundToInt64()                 // 3

// Works with Float too
let y: Float = 1.5
let result = y.c.sqrt           // 1.22474487

Platform Support

• macOS 13+
• iOS 16+
• tvOS 16+
• watchOS 9+
• Linux (via Glibc)
• Windows (via UCRT)

Implementation

The package consists of:

1. CISO9899Math - C module providing platform-agnostic wrappers
2. ISO 9899 - Swift interface with clean API and documentation

All functions are inlined for optimal performance.

Standards Reference

• ISO/IEC 9899:2018 - Programming Languages — C
  • Section 7.12: Mathematics <math.h>
  • Section 7.12.4: Trigonometric functions
  • Section 7.12.6: Exponential and logarithmic functions
  • Section 7.12.7: Power and absolute-value functions
  • Section 7.12.9: Rounding functions
  • Annex F: IEC 60559 floating-point arithmetic (IEEE 754 compliance)

Requirements

• Swift 6.0+
• No Foundation dependency
• Platform C standard library

License

Apache 2.0