1 files changed, 170 insertions, 0 deletions
diff --git a/src/math/fma.go b/src/math/fma.go
new file mode 100644
index 0000000..db78dfa
--- /dev/null
+++ b/src/math/fma.go
@@ -0,0 +1,170 @@
+// Copyright 2019 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package math
+
+import "math/bits"
+
+func zero(x uint64) uint64 {
+	if x == 0 {
+		return 1
+	}
+	return 0
+	// branchless:
+	// return ((x>>1 | x&1) - 1) >> 63
+}
+
+func nonzero(x uint64) uint64 {
+	if x != 0 {
+		return 1
+	}
+	return 0
+	// branchless:
+	// return 1 - ((x>>1|x&1)-1)>>63
+}
+
+func shl(u1, u2 uint64, n uint) (r1, r2 uint64) {
+	r1 = u1<<n | u2>>(64-n) | u2<<(n-64)
+	r2 = u2 << n
+	return
+}
+
+func shr(u1, u2 uint64, n uint) (r1, r2 uint64) {
+	r2 = u2>>n | u1<<(64-n) | u1>>(n-64)
+	r1 = u1 >> n
+	return
+}
+
+// shrcompress compresses the bottom n+1 bits of the two-word
+// value into a single bit. the result is equal to the value
+// shifted to the right by n, except the result's 0th bit is
+// set to the bitwise OR of the bottom n+1 bits.
+func shrcompress(u1, u2 uint64, n uint) (r1, r2 uint64) {
+	// TODO: Performance here is really sensitive to the
+	// order/placement of these branches. n == 0 is common
+	// enough to be in the fast path. Perhaps more measurement
+	// needs to be done to find the optimal order/placement?
+	switch {
+	case n == 0:
+		return u1, u2
+	case n == 64:
+		return 0, u1 | nonzero(u2)
+	case n >= 128:
+		return 0, nonzero(u1 | u2)
+	case n < 64:
+		r1, r2 = shr(u1, u2, n)
+		r2 |= nonzero(u2 & (1<<n - 1))
+	case n < 128:
+		r1, r2 = shr(u1, u2, n)
+		r2 |= nonzero(u1&(1<<(n-64)-1) | u2)
+	}
+	return
+}
+
+func lz(u1, u2 uint64) (l int32) {
+	l = int32(bits.LeadingZeros64(u1))
+	if l == 64 {
+		l += int32(bits.LeadingZeros64(u2))
+	}
+	return l
+}
+
+// split splits b into sign, biased exponent, and mantissa.
+// It adds the implicit 1 bit to the mantissa for normal values,
+// and normalizes subnormal values.
+func split(b uint64) (sign uint32, exp int32, mantissa uint64) {
+	sign = uint32(b >> 63)
+	exp = int32(b>>52) & mask
+	mantissa = b & fracMask
+
+	if exp == 0 {
+		// Normalize value if subnormal.
+		shift := uint(bits.LeadingZeros64(mantissa) - 11)
+		mantissa <<= shift
+		exp = 1 - int32(shift)
+	} else {
+		// Add implicit 1 bit
+		mantissa |= 1 << 52
+	}
+	return
+}
+
+// FMA returns x * y + z, computed with only one rounding.
+// (That is, FMA returns the fused multiply-add of x, y, and z.)
+func FMA(x, y, z float64) float64 {
+	bx, by, bz := Float64bits(x), Float64bits(y), Float64bits(z)
+
+	// Inf or NaN or zero involved. At most one rounding will occur.
+	if x == 0.0 || y == 0.0 || z == 0.0 || bx&uvinf == uvinf || by&uvinf == uvinf {
+		return x*y + z
+	}
+	// Handle non-finite z separately. Evaluating x*y+z where
+	// x and y are finite, but z is infinite, should always result in z.
+	if bz&uvinf == uvinf {
+		return z
+	}
+
+	// Inputs are (sub)normal.
+	// Split x, y, z into sign, exponent, mantissa.
+	xs, xe, xm := split(bx)
+	ys, ye, ym := split(by)
+	zs, ze, zm := split(bz)
+
+	// Compute product p = x*y as sign, exponent, two-word mantissa.
+	// Start with exponent. "is normal" bit isn't subtracted yet.
+	pe := xe + ye - bias + 1
+
+	// pm1:pm2 is the double-word mantissa for the product p.
+	// Shift left to leave top bit in product. Effectively
+	// shifts the 106-bit product to the left by 21.
+	pm1, pm2 := bits.Mul64(xm<<10, ym<<11)
+	zm1, zm2 := zm<<10, uint64(0)
+	ps := xs ^ ys // product sign
+
+	// normalize to 62nd bit
+	is62zero := uint((^pm1 >> 62) & 1)
+	pm1, pm2 = shl(pm1, pm2, is62zero)
+	pe -= int32(is62zero)
+
+	// Swap addition operands so |p| >= |z|
+	if pe < ze || (pe == ze && (pm1 < zm1 || (pm1 == zm1 && pm2 < zm2))) {
+		ps, pe, pm1, pm2, zs, ze, zm1, zm2 = zs, ze, zm1, zm2, ps, pe, pm1, pm2
+	}
+
+	// Align significands
+	zm1, zm2 = shrcompress(zm1, zm2, uint(pe-ze))
+
+	// Compute resulting significands, normalizing if necessary.
+	var m, c uint64
+	if ps == zs {
+		// Adding (pm1:pm2) + (zm1:zm2)
+		pm2, c = bits.Add64(pm2, zm2, 0)
+		pm1, _ = bits.Add64(pm1, zm1, c)
+		pe -= int32(^pm1 >> 63)
+		pm1, m = shrcompress(pm1, pm2, uint(64+pm1>>63))
+	} else {
+		// Subtracting (pm1:pm2) - (zm1:zm2)
+		// TODO: should we special-case cancellation?
+		pm2, c = bits.Sub64(pm2, zm2, 0)
+		pm1, _ = bits.Sub64(pm1, zm1, c)
+		nz := lz(pm1, pm2)
+		pe -= nz
+		m, pm2 = shl(pm1, pm2, uint(nz-1))
+		m |= nonzero(pm2)
+	}
+
+	// Round and break ties to even
+	if pe > 1022+bias || pe == 1022+bias && (m+1<<9)>>63 == 1 {
+		// rounded value overflows exponent range
+		return Float64frombits(uint64(ps)<<63 | uvinf)
+	}
+	if pe < 0 {
+		n := uint(-pe)
+		m = m>>n | nonzero(m&(1<<n-1))
+		pe = 0
+	}
+	m = ((m + 1<<9) >> 10) & ^zero((m&(1<<10-1))^1<<9)
+	pe &= -int32(nonzero(m))
+	return Float64frombits(uint64(ps)<<63 + uint64(pe)<<52 + m)
+}