×

Glyph cross product: width-3 vectors × multiply into the perpendicular vector.

Syntax: <expression> × <expression>

Category#

arithmetic

Related#

• vector

Examples#

radix/corpus/vector/glyph-cross.fab (canonical · operator-group)#

Glyph cross product: width-3 vectors × multiply into the perpendicular vector.

# =============================================================================
# × — glyph cross product (width-3 vectors).
# =============================================================================
#
# What this teaches:
#   • Cross product — `a × b` on two width-3 vectors yields the perpendicular vector
#   • Width pin — the glyph rejects non-3 widths at compile time (physics 3-vector convention)
#
# Common mistakes:
#   • cross on width ≠ 3 vectors — width 4 (or non-vector operands) fail closed with a rank diagnostic
#   • confusing `×` with elementwise multiply — Hadamard is `⊙`; `×` is the cross product glyph
#
# See also: vector
# =============================================================================



# vector × vector → perpendicular vector (width 3 only)
#
# WHY: `×` is pinned to the width-3 cross product in Phase 1. `emit_vector_transversum`
# enforces width 3 in codegen; the typecheck rejects any other width with a
# structured issue. Result lanes are the standard cross-product formulas.
#
# a = [1.0, 2.0, 3.0]  b = [4.0, 5.0, 6.0]
# a × b = [2*6 - 3*5, 3*4 - 1*6, 1*5 - 2*4] = [-3.0, 6.0, -3.0]
#
# EXPECTED stdout:
#   [-3.0, 6.0, -3.0]

main {
    const vf32[3] a ← [1.0, 2.0, 3.0] ↦ vf32[3]
    const vf32[3] b ← [4.0, 5.0, 6.0] ↦ vf32[3]
    const vf32[3] c ← a × b
    print c
}

Expected output:

[-3.0, 6.0, -3.0]