Stage 0 Draft / May 28, 2026

Fused Multiply Add

1 FMAMultiply ( x, y )

The abstract operation FMAMultiply takes arguments x (a Number) and y (a Number) and returns either a non-zero mathematical value, not-a-number, positive-infinity, negative-infinity, positive-zero, or negative-zero. It computes the exact mathematical product of x and y.

The behaviour matches that of Number::multiply except that no rounding takes place and the result is either an exact non-zero mathematical value or an enum indicating a signed zero, a signed infinity, or NaN.

It performs the following steps when called:

  1. If x is NaN or y is NaN, return not-a-number.
  2. Let sign be 1.
  3. If x is -0๐”ฝ or x < -0๐”ฝ, then
    1. Set x to Number::unaryMinus(x).
    2. Set sign to -sign.
  4. If y is -0๐”ฝ or y < -0๐”ฝ, then
    1. Set y to Number::unaryMinus(y).
    2. Set sign to -sign.
  5. Assert: x and y both have positive signs.
  6. If x is +โˆž๐”ฝ or y is +โˆž๐”ฝ, then
    1. If x is +0๐”ฝ or y is +0๐”ฝ, return not-a-number.
    2. If sign is -1, return negative-infinity.
    3. Return positive-infinity.
  7. If x is +0๐”ฝ or y is +0๐”ฝ, then
    1. If sign is -1, return negative-zero.
    2. Return positive-zero.
  8. Assert: x and y are both non-zero and finite.
  9. Return sign ร— โ„(x) ร— โ„(y).

2 Math.fma ( x, y, z )

This function performs fused multiply-add according to the rules of IEEE 754-2019 binary double-precision arithmetic, computing (x ร— y) + z as a single operation with no intermediate rounding of the product.

It performs the following steps when called:

  1. Let nx be ?ย ToNumber(x).
  2. Let ny be ?ย ToNumber(y).
  3. Let nz be ?ย ToNumber(z).
  4. Let product be FMAMultiply(nx, ny).
  5. If product is not-a-number or nz is NaN, return NaN.
  6. If product is positive-infinity, then
    1. If nz is -โˆž๐”ฝ, return NaN.
    2. Return +โˆž๐”ฝ.
  7. If product is negative-infinity, then
    1. If nz is +โˆž๐”ฝ, return NaN.
    2. Return -โˆž๐”ฝ.
  8. If nz is either +โˆž๐”ฝ or -โˆž๐”ฝ, return nz.
  9. If product is negative-zero, return nz.
  10. If product is positive-zero, set product to 0.
  11. Assert: product and nz are both finite.
  12. Return ๐”ฝ(product + โ„(nz)).
 Note

The single call to ๐”ฝ in the final step performs exactly one rounding of the infinite-precision product and sum.

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