/**
 * Fixed-point arithmetic utilities for rasterization
 *
 * FreeType uses several fixed-point formats:
 * - F26Dot6: 26.6 format (64 units per pixel) for coordinates
 * - F16Dot16: 16.16 format for high-precision calculations
 * - F2Dot14: 2.14 format for normalized vectors
 */
export declare const PIXEL_BITS = 8;
export declare const ONE_PIXEL: number;
export declare const PIXEL_MASK: number;
export declare const F26DOT6_SHIFT = 6;
export declare const F26DOT6_ONE: number;
export declare const F16DOT16_SHIFT = 16;
export declare const F16DOT16_ONE: number;
/**
 * Convert float to 26.6 fixed-point
 */
export declare function floatToF26Dot6(x: number): number;
/**
 * Convert 26.6 fixed-point to float
 */
export declare function f26Dot6ToFloat(x: number): number;
/**
 * Convert float to internal raster coordinates (PIXEL_BITS precision)
 * Input is in font units, output has 256 subpixel levels per pixel
 */
export declare function floatToPixel(x: number, scale: number): number;
/**
 * Truncate to pixel (floor for positive, ceil for negative)
 */
export declare function truncPixel(x: number): number;
/**
 * Get fractional part (0 to ONE_PIXEL-1)
 */
export declare function fracPixel(x: number): number;
/**
 * Round to nearest pixel
 */
export declare function roundPixel(x: number): number;
/**
 * Floor to pixel boundary
 */
export declare function floorPixel(x: number): number;
/**
 * Ceiling to pixel boundary
 */
export declare function ceilPixel(x: number): number;
/**
 * Upscale from 26.6 to internal PIXEL_BITS format
 * PIXEL_BITS=8 means 2 extra bits of precision vs 26.6
 */
export declare function upscale(x: number): number;
/**
 * Downscale from internal format to 26.6
 */
export declare function downscale(x: number): number;
/**
 * Multiply two fixed-point numbers and divide, avoiding overflow
 * Computes (a * b) / c with 64-bit intermediate precision when needed
 */
export declare function mulDiv(a: number, b: number, c: number): number;
/**
 * Multiply two 16.16 fixed-point numbers
 */
export declare function mulFix(a: number, b: number): number;
/**
 * Divide two numbers and return 16.16 fixed-point result
 */
export declare function divFix(a: number, b: number): number;
/**
 * Fast approximation of sqrt(x*x + y*y) using "alpha max plus beta min" algorithm.
 * Uses alpha = 1, beta = 3/8 for max error < 7% vs exact value.
 * From FreeType's FT_HYPOT macro.
 */
export declare function hypot(x: number, y: number): number;
/**
 * Calculate the length of a 2D vector (integer math)
 * Uses FreeType's "alpha max plus beta min" approximation
 */
export declare function vectorLength(dx: number, dy: number): number;
/**
 * Normalize a 2D vector to unit length (16.16 fixed-point output)
 */
export declare function normalizeVector(dx: number, dy: number): {
    x: number;
    y: number;
};
/**
 * Clamp value to range
 */
export declare function clamp(x: number, min: number, max: number): number;
/**
 * Absolute value
 */
export declare function abs(x: number): number;
/**
 * Sign of value (-1, 0, or 1)
 */
export declare function sign(x: number): number;