Solidean's Minimalist Approach to Fixed-Width Arithmetic Could Disrupt Exact Computing

Solidean has open-sourced a surprisingly effective approach to fixed-width integer arithmetic that challenges conventional wisdom in numerical computing. Their uint128 implementation - using just two uint64 values and compiler intrinsics - achieves performance identical to built-in types while enabling exact calculations in geometric algorithms.

The Precision Problem in Modern Computing

Many computational geometry and CAD systems struggle with floating-point inaccuracies during operations like mesh boolean operations. Traditional solutions either accept error-prone results or pay heavy performance penalties with arbitrary-precision libraries. Solidean's approach offers a third path: exactly representing numbers within known bounds using fixed-width integers.

"For most geometric operations, we don't need infinite precision - we need enough precision to be exact for our problem domain," explains Solidean's technical lead. "A 128-bit integer handles most cases, and when it doesn't, we scale to 256 or 512 bits with minimal overhead."

Hardware-Aligned Arithmetic

The key innovation lies in Solidean's barebones implementation:

• Represents 128-bit numbers as two 64-bit "limbs"
• Uses processor-specific intrinsics (_addcarry_u64, _mulx_u64)
• Generates assembly identical to compiler-built __uint128_t

This Godbolt example shows how their addition and multiplication operators compile to optimal x64 instructions. The approach scales linearly - each additional 64-bit limb adds just one more instruction for basic operations.

Market Implications

While the technology appears niche, fixed-width exact arithmetic has broad applications:

• CAD/CAM systems: Eliminate geometric artifacts in manufacturing designs
• Blockchain: More efficient cryptographic operations
• GIS mapping: Prevent coordinate system drift
• Financial systems: Exact decimal calculations without BigDecimal overhead

Solidean has already implemented this approach in their exact mesh boolean operations, achieving significant performance gains over floating-point alternatives. The company's focus on predictable performance rather than maximum abstraction mirrors trends in game engine development and high-frequency trading systems.

Looking Ahead

This uint128 implementation represents just the first step in Solidean's exact arithmetic roadmap. The same principles extend naturally to 256-bit and 512-bit integers, with their production systems already using 564-bit numbers for edge cases. As computing demands more precision without sacrificing speed, Solidean's hardware-aligned approach positions them uniquely in the emerging exact computation market.