From f6819755779a084bf2f82cb90175a4d9a018de73 Mon Sep 17 00:00:00 2001
From: Rich Felker <dalias@aerifal.cx>
Date: Mon, 30 Apr 2012 03:26:53 -0400
Subject: [PATCH] first try at writing an efficient and "correct" exp10

this is a nonstandard function so it's not clear what conditions it
should satisfy. my intent is that it be fast and exact for positive
integral exponents when the result fits in the destination type, and
fast and correctly rounded for small negative integral exponents.
otherwise we aim for at most 1ulp error; it seems to differ from pow
by at most 1ulp and it's often 2-5 times faster than pow.
---
 include/math.h    |  4 ++++
 src/math/exp10.c  | 19 +++++++++++++++++++
 src/math/exp10f.c | 17 +++++++++++++++++
 src/math/exp10l.c | 19 +++++++++++++++++++
 4 files changed, 59 insertions(+)
 create mode 100644 src/math/exp10.c
 create mode 100644 src/math/exp10f.c
 create mode 100644 src/math/exp10l.c

diff --git a/include/math.h b/include/math.h
index bc0159e6..65b1e915 100644
--- a/include/math.h
+++ b/include/math.h
@@ -387,6 +387,10 @@ float       y1f(float);
 long double y1l(long double);
 float       ynf(int, float);
 long double ynl(int, long double);
+
+double      exp10(double);
+float       exp10f(float);
+long double exp10l(long double);
 #endif
 
 #ifdef __cplusplus
diff --git a/src/math/exp10.c b/src/math/exp10.c
new file mode 100644
index 00000000..7fd86fba
--- /dev/null
+++ b/src/math/exp10.c
@@ -0,0 +1,19 @@
+#define _GNU_SOURCE
+#include <math.h>
+
+double exp10(double x)
+{
+	static const double p10[] = {
+		1e-15, 1e-14, 1e-13, 1e-12, 1e-11, 1e-10,
+		1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1,
+		1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
+		1e10, 1e11, 1e12, 1e13, 1e14, 1e15
+	};
+	double n, y = modf(x, &n);
+	if (fabs(n) < 16) {
+		if (!y) return p10[(int)n+15];
+		y = exp2(3.32192809488736234787031942948939 * y);
+		return y * p10[(int)n+15];
+	}
+	return pow(10.0, x);
+}
diff --git a/src/math/exp10f.c b/src/math/exp10f.c
new file mode 100644
index 00000000..c9521411
--- /dev/null
+++ b/src/math/exp10f.c
@@ -0,0 +1,17 @@
+#define _GNU_SOURCE
+#include <math.h>
+
+float exp10f(float x)
+{
+	static const float p10[] = {
+		1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1,
+		1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7
+	};
+	float n, y = modff(x, &n);
+	if (fabsf(n) < 8) {
+		if (!y) return p10[(int)n+7];
+		y = exp2f(3.32192809488736234787031942948939f * y);
+		return y * p10[(int)n+7];
+	}
+	return exp2(3.32192809488736234787031942948939 * x);
+}
diff --git a/src/math/exp10l.c b/src/math/exp10l.c
new file mode 100644
index 00000000..4d0c5a01
--- /dev/null
+++ b/src/math/exp10l.c
@@ -0,0 +1,19 @@
+#define _GNU_SOURCE
+#include <math.h>
+
+long double exp10l(long double x)
+{
+	static const long double p10[] = {
+		1e-15, 1e-14, 1e-13, 1e-12, 1e-11, 1e-10,
+		1e-9, 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1,
+		1, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9,
+		1e10, 1e11, 1e12, 1e13, 1e14, 1e15
+	};
+	long double n, y = modfl(x, &n);
+	if (fabsl(n) < 16) {
+		if (!y) return p10[(int)n+15];
+		y = exp2l(3.32192809488736234787031942948939L * y);
+		return y * p10[(int)n+15];
+	}
+	return powl(10.0, x);
+}
-- 
2.25.1