11 files changed, 1056 insertions, 0 deletions
diff --git a/lib/math/Kconfig b/lib/math/Kconfig
new file mode 100644
index 000000000..f19bc9734
--- /dev/null
+++ b/lib/math/Kconfig
@@ -0,0 +1,17 @@
+# SPDX-License-Identifier: GPL-2.0-only
+config CORDIC
+	tristate "CORDIC algorithm"
+	help
+	  This option provides an implementation of the CORDIC algorithm;
+	  calculations are in fixed point. Module will be called cordic.
+
+config PRIME_NUMBERS
+	tristate "Simple prime number generator for testing"
+	help
+	  This option provides a simple prime number generator for test
+	  modules.
+
+	  If unsure, say N.
+
+config RATIONAL
+	bool
diff --git a/lib/math/Makefile b/lib/math/Makefile
new file mode 100644
index 000000000..be6909e94
--- /dev/null
+++ b/lib/math/Makefile
@@ -0,0 +1,6 @@
+# SPDX-License-Identifier: GPL-2.0-only
+obj-y += div64.o gcd.o lcm.o int_pow.o int_sqrt.o reciprocal_div.o
+
+obj-$(CONFIG_CORDIC)		+= cordic.o
+obj-$(CONFIG_PRIME_NUMBERS)	+= prime_numbers.o
+obj-$(CONFIG_RATIONAL)		+= rational.o
diff --git a/lib/math/cordic.c b/lib/math/cordic.c
new file mode 100644
index 000000000..8ef27c129
--- /dev/null
+++ b/lib/math/cordic.c
@@ -0,0 +1,92 @@
+/*
+ * Copyright (c) 2011 Broadcom Corporation
+ *
+ * Permission to use, copy, modify, and/or distribute this software for any
+ * purpose with or without fee is hereby granted, provided that the above
+ * copyright notice and this permission notice appear in all copies.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
+ * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
+ * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
+ * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
+ * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
+ * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
+ * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+ */
+#include <linux/module.h>
+#include <linux/cordic.h>
+
+static const s32 arctan_table[] = {
+	2949120,
+	1740967,
+	919879,
+	466945,
+	234379,
+	117304,
+	58666,
+	29335,
+	14668,
+	7334,
+	3667,
+	1833,
+	917,
+	458,
+	229,
+	115,
+	57,
+	29
+};
+
+/*
+ * cordic_calc_iq() - calculates the i/q coordinate for given angle
+ *
+ * theta: angle in degrees for which i/q coordinate is to be calculated
+ * coord: function output parameter holding the i/q coordinate
+ */
+struct cordic_iq cordic_calc_iq(s32 theta)
+{
+	struct cordic_iq coord;
+	s32 angle, valtmp;
+	unsigned iter;
+	int signx = 1;
+	int signtheta;
+
+	coord.i = CORDIC_ANGLE_GEN;
+	coord.q = 0;
+	angle = 0;
+
+	theta = CORDIC_FIXED(theta);
+	signtheta = (theta < 0) ? -1 : 1;
+	theta = ((theta + CORDIC_FIXED(180) * signtheta) % CORDIC_FIXED(360)) -
+		CORDIC_FIXED(180) * signtheta;
+
+	if (CORDIC_FLOAT(theta) > 90) {
+		theta -= CORDIC_FIXED(180);
+		signx = -1;
+	} else if (CORDIC_FLOAT(theta) < -90) {
+		theta += CORDIC_FIXED(180);
+		signx = -1;
+	}
+
+	for (iter = 0; iter < CORDIC_NUM_ITER; iter++) {
+		if (theta > angle) {
+			valtmp = coord.i - (coord.q >> iter);
+			coord.q += (coord.i >> iter);
+			angle += arctan_table[iter];
+		} else {
+			valtmp = coord.i + (coord.q >> iter);
+			coord.q -= (coord.i >> iter);
+			angle -= arctan_table[iter];
+		}
+		coord.i = valtmp;
+	}
+
+	coord.i *= signx;
+	coord.q *= signx;
+	return coord;
+}
+EXPORT_SYMBOL(cordic_calc_iq);
+
+MODULE_DESCRIPTION("CORDIC algorithm");
+MODULE_AUTHOR("Broadcom Corporation");
+MODULE_LICENSE("Dual BSD/GPL");
diff --git a/lib/math/div64.c b/lib/math/div64.c
new file mode 100644
index 000000000..edd1090c9
--- /dev/null
+++ b/lib/math/div64.c
@@ -0,0 +1,234 @@
+// SPDX-License-Identifier: GPL-2.0
+/*
+ * Copyright (C) 2003 Bernardo Innocenti <bernie@develer.com>
+ *
+ * Based on former do_div() implementation from asm-parisc/div64.h:
+ *	Copyright (C) 1999 Hewlett-Packard Co
+ *	Copyright (C) 1999 David Mosberger-Tang <davidm@hpl.hp.com>
+ *
+ *
+ * Generic C version of 64bit/32bit division and modulo, with
+ * 64bit result and 32bit remainder.
+ *
+ * The fast case for (n>>32 == 0) is handled inline by do_div().
+ *
+ * Code generated for this function might be very inefficient
+ * for some CPUs. __div64_32() can be overridden by linking arch-specific
+ * assembly versions such as arch/ppc/lib/div64.S and arch/sh/lib/div64.S
+ * or by defining a preprocessor macro in arch/include/asm/div64.h.
+ */
+
+#include <linux/export.h>
+#include <linux/kernel.h>
+#include <linux/math64.h>
+
+/* Not needed on 64bit architectures */
+#if BITS_PER_LONG == 32
+
+#ifndef __div64_32
+uint32_t __attribute__((weak)) __div64_32(uint64_t *n, uint32_t base)
+{
+	uint64_t rem = *n;
+	uint64_t b = base;
+	uint64_t res, d = 1;
+	uint32_t high = rem >> 32;
+
+	/* Reduce the thing a bit first */
+	res = 0;
+	if (high >= base) {
+		high /= base;
+		res = (uint64_t) high << 32;
+		rem -= (uint64_t) (high*base) << 32;
+	}
+
+	while ((int64_t)b > 0 && b < rem) {
+		b = b+b;
+		d = d+d;
+	}
+
+	do {
+		if (rem >= b) {
+			rem -= b;
+			res += d;
+		}
+		b >>= 1;
+		d >>= 1;
+	} while (d);
+
+	*n = res;
+	return rem;
+}
+EXPORT_SYMBOL(__div64_32);
+#endif
+
+/**
+ * div_s64_rem - signed 64bit divide with 64bit divisor and remainder
+ * @dividend:	64bit dividend
+ * @divisor:	64bit divisor
+ * @remainder:  64bit remainder
+ */
+#ifndef div_s64_rem
+s64 div_s64_rem(s64 dividend, s32 divisor, s32 *remainder)
+{
+	u64 quotient;
+
+	if (dividend < 0) {
+		quotient = div_u64_rem(-dividend, abs(divisor), (u32 *)remainder);
+		*remainder = -*remainder;
+		if (divisor > 0)
+			quotient = -quotient;
+	} else {
+		quotient = div_u64_rem(dividend, abs(divisor), (u32 *)remainder);
+		if (divisor < 0)
+			quotient = -quotient;
+	}
+	return quotient;
+}
+EXPORT_SYMBOL(div_s64_rem);
+#endif
+
+/**
+ * div64_u64_rem - unsigned 64bit divide with 64bit divisor and remainder
+ * @dividend:	64bit dividend
+ * @divisor:	64bit divisor
+ * @remainder:  64bit remainder
+ *
+ * This implementation is a comparable to algorithm used by div64_u64.
+ * But this operation, which includes math for calculating the remainder,
+ * is kept distinct to avoid slowing down the div64_u64 operation on 32bit
+ * systems.
+ */
+#ifndef div64_u64_rem
+u64 div64_u64_rem(u64 dividend, u64 divisor, u64 *remainder)
+{
+	u32 high = divisor >> 32;
+	u64 quot;
+
+	if (high == 0) {
+		u32 rem32;
+		quot = div_u64_rem(dividend, divisor, &rem32);
+		*remainder = rem32;
+	} else {
+		int n = fls(high);
+		quot = div_u64(dividend >> n, divisor >> n);
+
+		if (quot != 0)
+			quot--;
+
+		*remainder = dividend - quot * divisor;
+		if (*remainder >= divisor) {
+			quot++;
+			*remainder -= divisor;
+		}
+	}
+
+	return quot;
+}
+EXPORT_SYMBOL(div64_u64_rem);
+#endif
+
+/**
+ * div64_u64 - unsigned 64bit divide with 64bit divisor
+ * @dividend:	64bit dividend
+ * @divisor:	64bit divisor
+ *
+ * This implementation is a modified version of the algorithm proposed
+ * by the book 'Hacker's Delight'.  The original source and full proof
+ * can be found here and is available for use without restriction.
+ *
+ * 'http://www.hackersdelight.org/hdcodetxt/divDouble.c.txt'
+ */
+#ifndef div64_u64
+u64 div64_u64(u64 dividend, u64 divisor)
+{
+	u32 high = divisor >> 32;
+	u64 quot;
+
+	if (high == 0) {
+		quot = div_u64(dividend, divisor);
+	} else {
+		int n = fls(high);
+		quot = div_u64(dividend >> n, divisor >> n);
+
+		if (quot != 0)
+			quot--;
+		if ((dividend - quot * divisor) >= divisor)
+			quot++;
+	}
+
+	return quot;
+}
+EXPORT_SYMBOL(div64_u64);
+#endif
+
+/**
+ * div64_s64 - signed 64bit divide with 64bit divisor
+ * @dividend:	64bit dividend
+ * @divisor:	64bit divisor
+ */
+#ifndef div64_s64
+s64 div64_s64(s64 dividend, s64 divisor)
+{
+	s64 quot, t;
+
+	quot = div64_u64(abs(dividend), abs(divisor));
+	t = (dividend ^ divisor) >> 63;
+
+	return (quot ^ t) - t;
+}
+EXPORT_SYMBOL(div64_s64);
+#endif
+
+#endif /* BITS_PER_LONG == 32 */
+
+/*
+ * Iterative div/mod for use when dividend is not expected to be much
+ * bigger than divisor.
+ */
+u32 iter_div_u64_rem(u64 dividend, u32 divisor, u64 *remainder)
+{
+	return __iter_div_u64_rem(dividend, divisor, remainder);
+}
+EXPORT_SYMBOL(iter_div_u64_rem);
+
+#ifndef mul_u64_u64_div_u64
+u64 mul_u64_u64_div_u64(u64 a, u64 b, u64 c)
+{
+	u64 res = 0, div, rem;
+	int shift;
+
+	/* can a * b overflow ? */
+	if (ilog2(a) + ilog2(b) > 62) {
+		/*
+		 * (b * a) / c is equal to
+		 *
+		 *      (b / c) * a +
+		 *      (b % c) * a / c
+		 *
+		 * if nothing overflows. Can the 1st multiplication
+		 * overflow? Yes, but we do not care: this can only
+		 * happen if the end result can't fit in u64 anyway.
+		 *
+		 * So the code below does
+		 *
+		 *      res = (b / c) * a;
+		 *      b = b % c;
+		 */
+		div = div64_u64_rem(b, c, &rem);
+		res = div * a;
+		b = rem;
+
+		shift = ilog2(a) + ilog2(b) - 62;
+		if (shift > 0) {
+			/* drop precision */
+			b >>= shift;
+			c >>= shift;
+			if (!c)
+				return res;
+		}
+	}
+
+	return res + div64_u64(a * b, c);
+}
+EXPORT_SYMBOL(mul_u64_u64_div_u64);
+#endif
diff --git a/lib/math/gcd.c b/lib/math/gcd.c
new file mode 100644
index 000000000..e3b042214
--- /dev/null
+++ b/lib/math/gcd.c
@@ -0,0 +1,85 @@
+// SPDX-License-Identifier: GPL-2.0-only
+#include <linux/kernel.h>
+#include <linux/gcd.h>
+#include <linux/export.h>
+
+/*
+ * This implements the binary GCD algorithm. (Often attributed to Stein,
+ * but as Knuth has noted, appears in a first-century Chinese math text.)
+ *
+ * This is faster than the division-based algorithm even on x86, which
+ * has decent hardware division.
+ */
+
+#if !defined(CONFIG_CPU_NO_EFFICIENT_FFS)
+
+/* If __ffs is available, the even/odd algorithm benchmarks slower. */
+
+/**
+ * gcd - calculate and return the greatest common divisor of 2 unsigned longs
+ * @a: first value
+ * @b: second value
+ */
+unsigned long gcd(unsigned long a, unsigned long b)
+{
+	unsigned long r = a | b;
+
+	if (!a || !b)
+		return r;
+
+	b >>= __ffs(b);
+	if (b == 1)
+		return r & -r;
+
+	for (;;) {
+		a >>= __ffs(a);
+		if (a == 1)
+			return r & -r;
+		if (a == b)
+			return a << __ffs(r);
+
+		if (a < b)
+			swap(a, b);
+		a -= b;
+	}
+}
+
+#else
+
+/* If normalization is done by loops, the even/odd algorithm is a win. */
+unsigned long gcd(unsigned long a, unsigned long b)
+{
+	unsigned long r = a | b;
+
+	if (!a || !b)
+		return r;
+
+	/* Isolate lsbit of r */
+	r &= -r;
+
+	while (!(b & r))
+		b >>= 1;
+	if (b == r)
+		return r;
+
+	for (;;) {
+		while (!(a & r))
+			a >>= 1;
+		if (a == r)
+			return r;
+		if (a == b)
+			return a;
+
+		if (a < b)
+			swap(a, b);
+		a -= b;
+		a >>= 1;
+		if (a & r)
+			a += b;
+		a >>= 1;
+	}
+}
+
+#endif
+
+EXPORT_SYMBOL_GPL(gcd);
diff --git a/lib/math/int_pow.c b/lib/math/int_pow.c
new file mode 100644
index 000000000..622fc1ab3
--- /dev/null
+++ b/lib/math/int_pow.c
@@ -0,0 +1,32 @@
+// SPDX-License-Identifier: GPL-2.0
+/*
+ * An integer based power function
+ *
+ * Derived from drivers/video/backlight/pwm_bl.c
+ */
+
+#include <linux/export.h>
+#include <linux/kernel.h>
+#include <linux/types.h>
+
+/**
+ * int_pow - computes the exponentiation of the given base and exponent
+ * @base: base which will be raised to the given power
+ * @exp: power to be raised to
+ *
+ * Computes: pow(base, exp), i.e. @base raised to the @exp power
+ */
+u64 int_pow(u64 base, unsigned int exp)
+{
+	u64 result = 1;
+
+	while (exp) {
+		if (exp & 1)
+			result *= base;
+		exp >>= 1;
+		base *= base;
+	}
+
+	return result;
+}
+EXPORT_SYMBOL_GPL(int_pow);
diff --git a/lib/math/int_sqrt.c b/lib/math/int_sqrt.c
new file mode 100644
index 000000000..30e0f9770
--- /dev/null
+++ b/lib/math/int_sqrt.c
@@ -0,0 +1,70 @@
+// SPDX-License-Identifier: GPL-2.0
+/*
+ * Copyright (C) 2013 Davidlohr Bueso <davidlohr.bueso@hp.com>
+ *
+ *  Based on the shift-and-subtract algorithm for computing integer
+ *  square root from Guy L. Steele.
+ */
+
+#include <linux/kernel.h>
+#include <linux/export.h>
+#include <linux/bitops.h>
+
+/**
+ * int_sqrt - computes the integer square root
+ * @x: integer of which to calculate the sqrt
+ *
+ * Computes: floor(sqrt(x))
+ */
+unsigned long int_sqrt(unsigned long x)
+{
+	unsigned long b, m, y = 0;
+
+	if (x <= 1)
+		return x;
+
+	m = 1UL << (__fls(x) & ~1UL);
+	while (m != 0) {
+		b = y + m;
+		y >>= 1;
+
+		if (x >= b) {
+			x -= b;
+			y += m;
+		}
+		m >>= 2;
+	}
+
+	return y;
+}
+EXPORT_SYMBOL(int_sqrt);
+
+#if BITS_PER_LONG < 64
+/**
+ * int_sqrt64 - strongly typed int_sqrt function when minimum 64 bit input
+ * is expected.
+ * @x: 64bit integer of which to calculate the sqrt
+ */
+u32 int_sqrt64(u64 x)
+{
+	u64 b, m, y = 0;
+
+	if (x <= ULONG_MAX)
+		return int_sqrt((unsigned long) x);
+
+	m = 1ULL << ((fls64(x) - 1) & ~1ULL);
+	while (m != 0) {
+		b = y + m;
+		y >>= 1;
+
+		if (x >= b) {
+			x -= b;
+			y += m;
+		}
+		m >>= 2;
+	}
+
+	return y;
+}
+EXPORT_SYMBOL(int_sqrt64);
+#endif
diff --git a/lib/math/lcm.c b/lib/math/lcm.c
new file mode 100644
index 000000000..6e0b2e736
--- /dev/null
+++ b/lib/math/lcm.c
@@ -0,0 +1,26 @@
+// SPDX-License-Identifier: GPL-2.0-only
+#include <linux/compiler.h>
+#include <linux/gcd.h>
+#include <linux/export.h>
+#include <linux/lcm.h>
+
+/* Lowest common multiple */
+unsigned long lcm(unsigned long a, unsigned long b)
+{
+	if (a && b)
+		return (a / gcd(a, b)) * b;
+	else
+		return 0;
+}
+EXPORT_SYMBOL_GPL(lcm);
+
+unsigned long lcm_not_zero(unsigned long a, unsigned long b)
+{
+	unsigned long l = lcm(a, b);
+
+	if (l)
+		return l;
+
+	return (b ? : a);
+}
+EXPORT_SYMBOL_GPL(lcm_not_zero);
diff --git a/lib/math/prime_numbers.c b/lib/math/prime_numbers.c
new file mode 100644
index 000000000..d42cebf74
--- /dev/null
+++ b/lib/math/prime_numbers.c
@@ -0,0 +1,316 @@
+// SPDX-License-Identifier: GPL-2.0-only
+#define pr_fmt(fmt) "prime numbers: " fmt
+
+#include <linux/module.h>
+#include <linux/mutex.h>
+#include <linux/prime_numbers.h>
+#include <linux/slab.h>
+
+#define bitmap_size(nbits) (BITS_TO_LONGS(nbits) * sizeof(unsigned long))
+
+struct primes {
+	struct rcu_head rcu;
+	unsigned long last, sz;
+	unsigned long primes[];
+};
+
+#if BITS_PER_LONG == 64
+static const struct primes small_primes = {
+	.last = 61,
+	.sz = 64,
+	.primes = {
+		BIT(2) |
+		BIT(3) |
+		BIT(5) |
+		BIT(7) |
+		BIT(11) |
+		BIT(13) |
+		BIT(17) |
+		BIT(19) |
+		BIT(23) |
+		BIT(29) |
+		BIT(31) |
+		BIT(37) |
+		BIT(41) |
+		BIT(43) |
+		BIT(47) |
+		BIT(53) |
+		BIT(59) |
+		BIT(61)
+	}
+};
+#elif BITS_PER_LONG == 32
+static const struct primes small_primes = {
+	.last = 31,
+	.sz = 32,
+	.primes = {
+		BIT(2) |
+		BIT(3) |
+		BIT(5) |
+		BIT(7) |
+		BIT(11) |
+		BIT(13) |
+		BIT(17) |
+		BIT(19) |
+		BIT(23) |
+		BIT(29) |
+		BIT(31)
+	}
+};
+#else
+#error "unhandled BITS_PER_LONG"
+#endif
+
+static DEFINE_MUTEX(lock);
+static const struct primes __rcu *primes = RCU_INITIALIZER(&small_primes);
+
+static unsigned long selftest_max;
+
+static bool slow_is_prime_number(unsigned long x)
+{
+	unsigned long y = int_sqrt(x);
+
+	while (y > 1) {
+		if ((x % y) == 0)
+			break;
+		y--;
+	}
+
+	return y == 1;
+}
+
+static unsigned long slow_next_prime_number(unsigned long x)
+{
+	while (x < ULONG_MAX && !slow_is_prime_number(++x))
+		;
+
+	return x;
+}
+
+static unsigned long clear_multiples(unsigned long x,
+				     unsigned long *p,
+				     unsigned long start,
+				     unsigned long end)
+{
+	unsigned long m;
+
+	m = 2 * x;
+	if (m < start)
+		m = roundup(start, x);
+
+	while (m < end) {
+		__clear_bit(m, p);
+		m += x;
+	}
+
+	return x;
+}
+
+static bool expand_to_next_prime(unsigned long x)
+{
+	const struct primes *p;
+	struct primes *new;
+	unsigned long sz, y;
+
+	/* Betrand's Postulate (or Chebyshev's theorem) states that if n > 3,
+	 * there is always at least one prime p between n and 2n - 2.
+	 * Equivalently, if n > 1, then there is always at least one prime p
+	 * such that n < p < 2n.
+	 *
+	 * http://mathworld.wolfram.com/BertrandsPostulate.html
+	 * https://en.wikipedia.org/wiki/Bertrand's_postulate
+	 */
+	sz = 2 * x;
+	if (sz < x)
+		return false;
+
+	sz = round_up(sz, BITS_PER_LONG);
+	new = kmalloc(sizeof(*new) + bitmap_size(sz),
+		      GFP_KERNEL | __GFP_NOWARN);
+	if (!new)
+		return false;
+
+	mutex_lock(&lock);
+	p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
+	if (x < p->last) {
+		kfree(new);
+		goto unlock;
+	}
+
+	/* Where memory permits, track the primes using the
+	 * Sieve of Eratosthenes. The sieve is to remove all multiples of known
+	 * primes from the set, what remains in the set is therefore prime.
+	 */
+	bitmap_fill(new->primes, sz);
+	bitmap_copy(new->primes, p->primes, p->sz);
+	for (y = 2UL; y < sz; y = find_next_bit(new->primes, sz, y + 1))
+		new->last = clear_multiples(y, new->primes, p->sz, sz);
+	new->sz = sz;
+
+	BUG_ON(new->last <= x);
+
+	rcu_assign_pointer(primes, new);
+	if (p != &small_primes)
+		kfree_rcu((struct primes *)p, rcu);
+
+unlock:
+	mutex_unlock(&lock);
+	return true;
+}
+
+static void free_primes(void)
+{
+	const struct primes *p;
+
+	mutex_lock(&lock);
+	p = rcu_dereference_protected(primes, lockdep_is_held(&lock));
+	if (p != &small_primes) {
+		rcu_assign_pointer(primes, &small_primes);
+		kfree_rcu((struct primes *)p, rcu);
+	}
+	mutex_unlock(&lock);
+}
+
+/**
+ * next_prime_number - return the next prime number
+ * @x: the starting point for searching to test
+ *
+ * A prime number is an integer greater than 1 that is only divisible by
+ * itself and 1.  The set of prime numbers is computed using the Sieve of
+ * Eratoshenes (on finding a prime, all multiples of that prime are removed
+ * from the set) enabling a fast lookup of the next prime number larger than
+ * @x. If the sieve fails (memory limitation), the search falls back to using
+ * slow trial-divison, up to the value of ULONG_MAX (which is reported as the
+ * final prime as a sentinel).
+ *
+ * Returns: the next prime number larger than @x
+ */
+unsigned long next_prime_number(unsigned long x)
+{
+	const struct primes *p;
+
+	rcu_read_lock();
+	p = rcu_dereference(primes);
+	while (x >= p->last) {
+		rcu_read_unlock();
+
+		if (!expand_to_next_prime(x))
+			return slow_next_prime_number(x);
+
+		rcu_read_lock();
+		p = rcu_dereference(primes);
+	}
+	x = find_next_bit(p->primes, p->last, x + 1);
+	rcu_read_unlock();
+
+	return x;
+}
+EXPORT_SYMBOL(next_prime_number);
+
+/**
+ * is_prime_number - test whether the given number is prime
+ * @x: the number to test
+ *
+ * A prime number is an integer greater than 1 that is only divisible by
+ * itself and 1. Internally a cache of prime numbers is kept (to speed up
+ * searching for sequential primes, see next_prime_number()), but if the number
+ * falls outside of that cache, its primality is tested using trial-divison.
+ *
+ * Returns: true if @x is prime, false for composite numbers.
+ */
+bool is_prime_number(unsigned long x)
+{
+	const struct primes *p;
+	bool result;
+
+	rcu_read_lock();
+	p = rcu_dereference(primes);
+	while (x >= p->sz) {
+		rcu_read_unlock();
+
+		if (!expand_to_next_prime(x))
+			return slow_is_prime_number(x);
+
+		rcu_read_lock();
+		p = rcu_dereference(primes);
+	}
+	result = test_bit(x, p->primes);
+	rcu_read_unlock();
+
+	return result;
+}
+EXPORT_SYMBOL(is_prime_number);
+
+static void dump_primes(void)
+{
+	const struct primes *p;
+	char *buf;
+
+	buf = kmalloc(PAGE_SIZE, GFP_KERNEL);
+
+	rcu_read_lock();
+	p = rcu_dereference(primes);
+
+	if (buf)
+		bitmap_print_to_pagebuf(true, buf, p->primes, p->sz);
+	pr_info("primes.{last=%lu, .sz=%lu, .primes[]=...x%lx} = %s\n",
+		p->last, p->sz, p->primes[BITS_TO_LONGS(p->sz) - 1], buf);
+
+	rcu_read_unlock();
+
+	kfree(buf);
+}
+
+static int selftest(unsigned long max)
+{
+	unsigned long x, last;
+
+	if (!max)
+		return 0;
+
+	for (last = 0, x = 2; x < max; x++) {
+		bool slow = slow_is_prime_number(x);
+		bool fast = is_prime_number(x);
+
+		if (slow != fast) {
+			pr_err("inconsistent result for is-prime(%lu): slow=%s, fast=%s!\n",
+			       x, slow ? "yes" : "no", fast ? "yes" : "no");
+			goto err;
+		}
+
+		if (!slow)
+			continue;
+
+		if (next_prime_number(last) != x) {
+			pr_err("incorrect result for next-prime(%lu): expected %lu, got %lu\n",
+			       last, x, next_prime_number(last));
+			goto err;
+		}
+		last = x;
+	}
+
+	pr_info("%s(%lu) passed, last prime was %lu\n", __func__, x, last);
+	return 0;
+
+err:
+	dump_primes();
+	return -EINVAL;
+}
+
+static int __init primes_init(void)
+{
+	return selftest(selftest_max);
+}
+
+static void __exit primes_exit(void)
+{
+	free_primes();
+}
+
+module_init(primes_init);
+module_exit(primes_exit);
+
+module_param_named(selftest, selftest_max, ulong, 0400);
+
+MODULE_AUTHOR("Intel Corporation");
+MODULE_LICENSE("GPL");
diff --git a/lib/math/rational.c b/lib/math/rational.c
new file mode 100644
index 000000000..c0ab51d8f
--- /dev/null
+++ b/lib/math/rational.c
@@ -0,0 +1,108 @@
+// SPDX-License-Identifier: GPL-2.0
+/*
+ * rational fractions
+ *
+ * Copyright (C) 2009 emlix GmbH, Oskar Schirmer <oskar@scara.com>
+ * Copyright (C) 2019 Trent Piepho <tpiepho@gmail.com>
+ *
+ * helper functions when coping with rational numbers
+ */
+
+#include <linux/rational.h>
+#include <linux/compiler.h>
+#include <linux/export.h>
+#include <linux/minmax.h>
+#include <linux/limits.h>
+
+/*
+ * calculate best rational approximation for a given fraction
+ * taking into account restricted register size, e.g. to find
+ * appropriate values for a pll with 5 bit denominator and
+ * 8 bit numerator register fields, trying to set up with a
+ * frequency ratio of 3.1415, one would say:
+ *
+ * rational_best_approximation(31415, 10000,
+ *		(1 << 8) - 1, (1 << 5) - 1, &n, &d);
+ *
+ * you may look at given_numerator as a fixed point number,
+ * with the fractional part size described in given_denominator.
+ *
+ * for theoretical background, see:
+ * https://en.wikipedia.org/wiki/Continued_fraction
+ */
+
+void rational_best_approximation(
+	unsigned long given_numerator, unsigned long given_denominator,
+	unsigned long max_numerator, unsigned long max_denominator,
+	unsigned long *best_numerator, unsigned long *best_denominator)
+{
+	/* n/d is the starting rational, which is continually
+	 * decreased each iteration using the Euclidean algorithm.
+	 *
+	 * dp is the value of d from the prior iteration.
+	 *
+	 * n2/d2, n1/d1, and n0/d0 are our successively more accurate
+	 * approximations of the rational.  They are, respectively,
+	 * the current, previous, and two prior iterations of it.
+	 *
+	 * a is current term of the continued fraction.
+	 */
+	unsigned long n, d, n0, d0, n1, d1, n2, d2;
+	n = given_numerator;
+	d = given_denominator;
+	n0 = d1 = 0;
+	n1 = d0 = 1;
+
+	for (;;) {
+		unsigned long dp, a;
+
+		if (d == 0)
+			break;
+		/* Find next term in continued fraction, 'a', via
+		 * Euclidean algorithm.
+		 */
+		dp = d;
+		a = n / d;
+		d = n % d;
+		n = dp;
+
+		/* Calculate the current rational approximation (aka
+		 * convergent), n2/d2, using the term just found and
+		 * the two prior approximations.
+		 */
+		n2 = n0 + a * n1;
+		d2 = d0 + a * d1;
+
+		/* If the current convergent exceeds the maxes, then
+		 * return either the previous convergent or the
+		 * largest semi-convergent, the final term of which is
+		 * found below as 't'.
+		 */
+		if ((n2 > max_numerator) || (d2 > max_denominator)) {
+			unsigned long t = ULONG_MAX;
+
+			if (d1)
+				t = (max_denominator - d0) / d1;
+			if (n1)
+				t = min(t, (max_numerator - n0) / n1);
+
+			/* This tests if the semi-convergent is closer than the previous
+			 * convergent.  If d1 is zero there is no previous convergent as this
+			 * is the 1st iteration, so always choose the semi-convergent.
+			 */
+			if (!d1 || 2u * t > a || (2u * t == a && d0 * dp > d1 * d)) {
+				n1 = n0 + t * n1;
+				d1 = d0 + t * d1;
+			}
+			break;
+		}
+		n0 = n1;
+		n1 = n2;
+		d0 = d1;
+		d1 = d2;
+	}
+	*best_numerator = n1;
+	*best_denominator = d1;
+}
+
+EXPORT_SYMBOL(rational_best_approximation);
diff --git a/lib/math/reciprocal_div.c b/lib/math/reciprocal_div.c
new file mode 100644
index 000000000..32436dd41
--- /dev/null
+++ b/lib/math/reciprocal_div.c
@@ -0,0 +1,70 @@
+// SPDX-License-Identifier: GPL-2.0
+#include <linux/bug.h>
+#include <linux/kernel.h>
+#include <asm/div64.h>
+#include <linux/reciprocal_div.h>
+#include <linux/export.h>
+#include <linux/minmax.h>
+
+/*
+ * For a description of the algorithm please have a look at
+ * include/linux/reciprocal_div.h
+ */
+
+struct reciprocal_value reciprocal_value(u32 d)
+{
+	struct reciprocal_value R;
+	u64 m;
+	int l;
+
+	l = fls(d - 1);
+	m = ((1ULL << 32) * ((1ULL << l) - d));
+	do_div(m, d);
+	++m;
+	R.m = (u32)m;
+	R.sh1 = min(l, 1);
+	R.sh2 = max(l - 1, 0);
+
+	return R;
+}
+EXPORT_SYMBOL(reciprocal_value);
+
+struct reciprocal_value_adv reciprocal_value_adv(u32 d, u8 prec)
+{
+	struct reciprocal_value_adv R;
+	u32 l, post_shift;
+	u64 mhigh, mlow;
+
+	/* ceil(log2(d)) */
+	l = fls(d - 1);
+	/* NOTE: mlow/mhigh could overflow u64 when l == 32. This case needs to
+	 * be handled before calling "reciprocal_value_adv", please see the
+	 * comment at include/linux/reciprocal_div.h.
+	 */
+	WARN(l == 32,
+	     "ceil(log2(0x%08x)) == 32, %s doesn't support such divisor",
+	     d, __func__);
+	post_shift = l;
+	mlow = 1ULL << (32 + l);
+	do_div(mlow, d);
+	mhigh = (1ULL << (32 + l)) + (1ULL << (32 + l - prec));
+	do_div(mhigh, d);
+
+	for (; post_shift > 0; post_shift--) {
+		u64 lo = mlow >> 1, hi = mhigh >> 1;
+
+		if (lo >= hi)
+			break;
+
+		mlow = lo;
+		mhigh = hi;
+	}
+
+	R.m = (u32)mhigh;
+	R.sh = post_shift;
+	R.exp = l;
+	R.is_wide_m = mhigh > U32_MAX;
+
+	return R;
+}
+EXPORT_SYMBOL(reciprocal_value_adv);