Initial import

libc/math/expf.c

@@ -0,0 +1,79 @@
+/*
+ * Single-precision e^x function.
+ *
+ * Copyright (c) 2017-2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include "libc/math/math.h"
+#include "libc/math/libm.h"
+#include "libc/math/exp2f_data.h"
+
+/*
+EXP2F_TABLE_BITS = 5
+EXP2F_POLY_ORDER = 3
+
+ULP error: 0.502 (nearest rounding.)
+Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
+Wrong count: 170635 (all nearest rounding wrong results with fma.)
+Non-nearest ULP error: 1 (rounded ULP error)
+*/
+
+#define N (1 << EXP2F_TABLE_BITS)
+#define InvLn2N __exp2f_data.invln2_scaled
+#define T __exp2f_data.tab
+#define C __exp2f_data.poly_scaled
+
+static inline uint32_t top12(float x)
+{
+	return asuint(x) >> 20;
+}
+
+float expf(float x)
+{
+	uint32_t abstop;
+	uint64_t ki, t;
+	double_t kd, xd, z, r, r2, y, s;
+
+	xd = (double_t)x;
+	abstop = top12(x) & 0x7ff;
+	if (predict_false(abstop >= top12(88.0f))) {
+		/* |x| >= 88 or x is nan.  */
+		if (asuint(x) == asuint(-INFINITY))
+			return 0.0f;
+		if (abstop >= top12(INFINITY))
+			return x + x;
+		if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
+			return __math_oflowf(0);
+		if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
+			return __math_uflowf(0);
+	}
+
+	/* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k.  */
+	z = InvLn2N * xd;
+
+	/* Round and convert z to int, the result is in [-150*N, 128*N] and
+	   ideally ties-to-even rule is used, otherwise the magnitude of r
+	   can be bigger which gives larger approximation error.  */
+#if TOINT_INTRINSICS
+	kd = roundtoint(z);
+	ki = converttoint(z);
+#else
+# define SHIFT __exp2f_data.shift
+	kd = eval_as_double(z + SHIFT);
+	ki = asuint64(kd);
+	kd -= SHIFT;
+#endif
+	r = z - kd;
+
+	/* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+	t = T[ki % N];
+	t += ki << (52 - EXP2F_TABLE_BITS);
+	s = asdouble(t);
+	z = C[0] * r + C[1];
+	r2 = r * r;
+	y = C[2] * r + 1;
+	y = z * r2 + y;
+	y = y * s;
+	return eval_as_float(y);
+}