Initial import

libc/math/fma.c

@@ -0,0 +1,186 @@
+#include "libc/math/math.h"
+/* #include "libc/math/atomic.h" */
+static inline int a_clz_64(uint64_t x)
+{
+	__asm__( "bsr %1,%0 ; xor $63,%0" : "=r"(x) : "r"(x) );
+	return x;
+}
+
+#define ASUINT64(x) ((union {double f; uint64_t i;}){x}).i
+#define ZEROINFNAN (0x7ff-0x3ff-52-1)
+
+struct num { uint64_t m; int e; int sign; };
+
+static struct num normalize(double x)
+{
+	uint64_t ix = ASUINT64(x);
+	int e = ix>>52;
+	int sign = e & 0x800;
+	e &= 0x7ff;
+	if (!e) {
+		ix = ASUINT64(x*0x1p63);
+		e = ix>>52 & 0x7ff;
+		e = e ? e-63 : 0x800;
+	}
+	ix &= (1ull<<52)-1;
+	ix |= 1ull<<52;
+	ix <<= 1;
+	e -= 0x3ff + 52 + 1;
+	return (struct num){ix,e,sign};
+}
+
+static void mul(uint64_t *hi, uint64_t *lo, uint64_t x, uint64_t y)
+{
+	uint64_t t1,t2,t3;
+	uint64_t xlo = (uint32_t)x, xhi = x>>32;
+	uint64_t ylo = (uint32_t)y, yhi = y>>32;
+
+	t1 = xlo*ylo;
+	t2 = xlo*yhi + xhi*ylo;
+	t3 = xhi*yhi;
+	*lo = t1 + (t2<<32);
+	*hi = t3 + (t2>>32) + (t1 > *lo);
+}
+
+double fma(double x, double y, double z)
+{
+	#pragma STDC FENV_ACCESS ON
+
+	/* normalize so top 10bits and last bit are 0 */
+	struct num nx, ny, nz;
+	nx = normalize(x);
+	ny = normalize(y);
+	nz = normalize(z);
+
+	if (nx.e >= ZEROINFNAN || ny.e >= ZEROINFNAN)
+		return x*y + z;
+	if (nz.e >= ZEROINFNAN) {
+		if (nz.e > ZEROINFNAN) /* z==0 */
+			return x*y + z;
+		return z;
+	}
+
+	/* mul: r = x*y */
+	uint64_t rhi, rlo, zhi, zlo;
+	mul(&rhi, &rlo, nx.m, ny.m);
+	/* either top 20 or 21 bits of rhi and last 2 bits of rlo are 0 */
+
+	/* align exponents */
+	int e = nx.e + ny.e;
+	int d = nz.e - e;
+	/* shift bits z<<=kz, r>>=kr, so kz+kr == d, set e = e+kr (== ez-kz) */
+	if (d > 0) {
+		if (d < 64) {
+			zlo = nz.m<<d;
+			zhi = nz.m>>64-d;
+		} else {
+			zlo = 0;
+			zhi = nz.m;
+			e = nz.e - 64;
+			d -= 64;
+			if (d == 0) {
+			} else if (d < 64) {
+				rlo = rhi<<64-d | rlo>>d | !!(rlo<<64-d);
+				rhi = rhi>>d;
+			} else {
+				rlo = 1;
+				rhi = 0;
+			}
+		}
+	} else {
+		zhi = 0;
+		d = -d;
+		if (d == 0) {
+			zlo = nz.m;
+		} else if (d < 64) {
+			zlo = nz.m>>d | !!(nz.m<<64-d);
+		} else {
+			zlo = 1;
+		}
+	}
+
+	/* add */
+	int sign = nx.sign^ny.sign;
+	int samesign = !(sign^nz.sign);
+	int nonzero = 1;
+	if (samesign) {
+		/* r += z */
+		rlo += zlo;
+		rhi += zhi + (rlo < zlo);
+	} else {
+		/* r -= z */
+		uint64_t t = rlo;
+		rlo -= zlo;
+		rhi = rhi - zhi - (t < rlo);
+		if (rhi>>63) {
+			rlo = -rlo;
+			rhi = -rhi-!!rlo;
+			sign = !sign;
+		}
+		nonzero = !!rhi;
+	}
+
+	/* set rhi to top 63bit of the result (last bit is sticky) */
+	if (nonzero) {
+		e += 64;
+		d = a_clz_64(rhi)-1;
+		/* note: d > 0 */
+		rhi = rhi<<d | rlo>>64-d | !!(rlo<<d);
+	} else if (rlo) {
+		d = a_clz_64(rlo)-1;
+		if (d < 0)
+			rhi = rlo>>1 | (rlo&1);
+		else
+			rhi = rlo<<d;
+	} else {
+		/* exact +-0 */
+		return x*y + z;
+	}
+	e -= d;
+
+	/* convert to double */
+	int64_t i = rhi; /* i is in [1<<62,(1<<63)-1] */
+	if (sign)
+		i = -i;
+	double r = i; /* |r| is in [0x1p62,0x1p63] */
+
+	if (e < -1022-62) {
+		/* result is subnormal before rounding */
+		if (e == -1022-63) {
+			double c = 0x1p63;
+			if (sign)
+				c = -c;
+			if (r == c) {
+				/* min normal after rounding, underflow depends
+				   on arch behaviour which can be imitated by
+				   a double to float conversion */
+				float fltmin = 0x0.ffffff8p-63*FLT_MIN * r;
+				return DBL_MIN/FLT_MIN * fltmin;
+			}
+			/* one bit is lost when scaled, add another top bit to
+			   only round once at conversion if it is inexact */
+			if (rhi << 53) {
+				i = rhi>>1 | (rhi&1) | 1ull<<62;
+				if (sign)
+					i = -i;
+				r = i;
+				r = 2*r - c; /* remove top bit */
+
+				/* raise underflow portably, such that it
+				   cannot be optimized away */
+				{
+					double_t tiny = DBL_MIN/FLT_MIN * r;
+					r += (double)(tiny*tiny) * (r-r);
+				}
+			}
+		} else {
+			/* only round once when scaled */
+			d = 10;
+			i = ( rhi>>d | !!(rhi<<64-d) ) << d;
+			if (sign)
+				i = -i;
+			r = i;
+		}
+	}
+	return scalbn(r, e);
+}