diff --git a/gnu/local.mk b/gnu/local.mk
index 8d817379a7..b6a5113063 100644
--- a/gnu/local.mk
+++ b/gnu/local.mk
@@ -1896,6 +1896,7 @@ dist_patch_DATA =						\
   %D%/packages/patches/python-waitress-fix-tests.patch		\
   %D%/packages/patches/python-werkzeug-tests.patch		\
   %D%/packages/patches/python-zeep-Fix-pytest_httpx-test-cases.patch	\
+  %D%/packages/patches/qd-fix-accuracy-in-angle-computation.patch	\
   %D%/packages/patches/qemu-build-info-manual.patch		\
   %D%/packages/patches/qemu-disable-some-qtests-tests.patch	\
   %D%/packages/patches/qemu-glibc-2.27.patch 			\
diff --git a/gnu/packages/multiprecision.scm b/gnu/packages/multiprecision.scm
index 11afcfe4a0..453b351a65 100644
--- a/gnu/packages/multiprecision.scm
+++ b/gnu/packages/multiprecision.scm
@@ -259,7 +259,8 @@ (define-public qd
        (uri (string-append "https://crd-legacy.lbl.gov/~dhbailey/mpdist/qd-"
                            version ".tar.gz"))
        (sha256
-        (base32 "09pfd77rmy370hy7qdqw84z21y9zpl3fcwzf93rhiv0kwhfg9smk"))))
+        (base32 "09pfd77rmy370hy7qdqw84z21y9zpl3fcwzf93rhiv0kwhfg9smk"))
+       (patches (search-patches "qd-fix-accuracy-in-angle-computation.patch"))))
     (build-system gnu-build-system)
     (native-inputs
      (list gfortran))
diff --git a/gnu/packages/patches/qd-fix-accuracy-in-angle-computation.patch b/gnu/packages/patches/qd-fix-accuracy-in-angle-computation.patch
new file mode 100644
index 0000000000..288d56919e
--- /dev/null
+++ b/gnu/packages/patches/qd-fix-accuracy-in-angle-computation.patch
@@ -0,0 +1,258 @@
+From e5ccba8fc889c38f49a247ff3060e8462388f6f9 Mon Sep 17 00:00:00 2001
+From: Sharlatan Hellseher <sharlatanus@gmail.com>
+Date: Thu, 2 Nov 2023 02:49:54 +0000
+Subject: [PATCH] Fix accuracy in angle computation (#224)
+
+Author: Mihai Cara <mcara@users.noreply.github.com>
+Source: https://github.com/spacetelescope/spherical_geometry/pull/224
+
+* Fix accuracy in angle computation
+
+* Enhance comparisons and expose QD 2*pi
+---
+ include/qd/c_dd.h    |  2 ++
+ include/qd/c_qd.h    |  4 ++-
+ include/qd/qd_real.h | 11 ++++----
+ src/c_dd.cpp         |  8 ++++++
+ src/c_qd.cpp         | 15 +++++++++--
+ src/qd_real.cpp      | 63 +++++++++++++++++++++++++++-----------------
+ 6 files changed, 71 insertions(+), 32 deletions(-)
+
+diff --git a/include/qd/c_dd.h b/include/qd/c_dd.h
+index 203a8fa..7ffcb01 100644
+--- a/include/qd/c_dd.h
++++ b/include/qd/c_dd.h
+@@ -90,6 +90,8 @@ void c_dd_comp(const double *a, const double *b, int *result);
+ void c_dd_comp_dd_d(const double *a, double b, int *result);
+ void c_dd_comp_d_dd(double a, const double *b, int *result);
+ void c_dd_pi(double *a);
++void c_dd_2pi(double *a);
++double c_dd_epsilon(void);
+ 
+ #ifdef __cplusplus
+ }
+diff --git a/include/qd/c_qd.h b/include/qd/c_qd.h
+index 9062d1d..b118f26 100644
+--- a/include/qd/c_qd.h
++++ b/include/qd/c_qd.h
+@@ -65,7 +65,7 @@ void c_qd_copy(const double *a, double *b);
+ void c_qd_copy_dd(const double *a, double *b);
+ void c_qd_copy_d(double a, double *b);
+ 
+-void c_qd_sqrt(const double *a, double *b);
++int c_qd_sqrt(const double *a, double *b);
+ void c_qd_sqr(const double *a, double *b);
+ 
+ void c_qd_abs(const double *a, double *b);
+@@ -111,6 +111,8 @@ void c_qd_comp(const double *a, const double *b, int *result);
+ void c_qd_comp_qd_d(const double *a, double b, int *result);
+ void c_qd_comp_d_qd(double a, const double *b, int *result);
+ void c_qd_pi(double *a);
++void c_qd_2pi(double *a);
++double c_qd_epsilon(void);
+ 
+ #ifdef __cplusplus
+ }
+diff --git a/include/qd/qd_real.h b/include/qd/qd_real.h
+index 32079d0..9435678 100644
+--- a/include/qd/qd_real.h
++++ b/include/qd/qd_real.h
+@@ -120,16 +120,16 @@ struct QD_API qd_real {
+   static qd_real rand(void);
+ 
+   void to_digits(char *s, int &expn, int precision = _ndigits) const;
+-  void write(char *s, int len, int precision = _ndigits, 
++  void write(char *s, int len, int precision = _ndigits,
+       bool showpos = false, bool uppercase = false) const;
+-  std::string to_string(int precision = _ndigits, int width = 0, 
+-      std::ios_base::fmtflags fmt = static_cast<std::ios_base::fmtflags>(0), 
++  std::string to_string(int precision = _ndigits, int width = 0,
++      std::ios_base::fmtflags fmt = static_cast<std::ios_base::fmtflags>(0),
+       bool showpos = false, bool uppercase = false, char fill = ' ') const;
+   static int read(const char *s, qd_real &a);
+ 
+   /* Debugging methods */
+   void dump(const std::string &name = "", std::ostream &os = std::cerr) const;
+-  void dump_bits(const std::string &name = "", 
++  void dump_bits(const std::string &name = "",
+                  std::ostream &os = std::cerr) const;
+ 
+   static qd_real debug_rand();
+@@ -150,7 +150,7 @@ namespace std {
+ }
+ 
+ QD_API qd_real polyeval(const qd_real *c, int n, const qd_real &x);
+-QD_API qd_real polyroot(const qd_real *c, int n, 
++QD_API qd_real polyroot(const qd_real *c, int n,
+     const qd_real &x0, int max_iter = 64, double thresh = 0.0);
+ 
+ QD_API qd_real qdrand(void);
+@@ -190,6 +190,7 @@ QD_API qd_real operator/(double a, const qd_real &b);
+ 
+ QD_API qd_real sqr(const qd_real &a);
+ QD_API qd_real sqrt(const qd_real &a);
++QD_API qd_real fsqrt(const qd_real &a, int &flag);
+ QD_API qd_real pow(const qd_real &a, int n);
+ QD_API qd_real pow(const qd_real &a, const qd_real &b);
+ QD_API qd_real npwr(const qd_real &a, int n);
+diff --git a/src/c_dd.cpp b/src/c_dd.cpp
+index 1cb2989..1df03e2 100644
+--- a/src/c_dd.cpp
++++ b/src/c_dd.cpp
+@@ -311,4 +311,12 @@ void c_dd_pi(double *a) {
+   TO_DOUBLE_PTR(dd_real::_pi, a);
+ }
+ 
++void c_dd_2pi(double *a) {
++  TO_DOUBLE_PTR(dd_real::_2pi, a);
++}
++
++double c_dd_epsilon(void) {
++    return (double) std::numeric_limits<dd_real>::epsilon();
++}
++
+ }
+diff --git a/src/c_qd.cpp b/src/c_qd.cpp
+index 010cf85..95cffb3 100644
+--- a/src/c_qd.cpp
++++ b/src/c_qd.cpp
+@@ -237,11 +237,14 @@ void c_qd_copy_d(double a, double *b) {
+ }
+ 
+ 
+-void c_qd_sqrt(const double *a, double *b) {
++int c_qd_sqrt(const double *a, double *b) {
++  int flag;
+   qd_real bb;
+-  bb = sqrt(qd_real(a));
++  bb = fsqrt(qd_real(a), flag);
+   TO_DOUBLE_PTR(bb, b);
++  return flag;
+ }
++
+ void c_qd_sqr(const double *a, double *b) {
+   qd_real bb;
+   bb = sqr(qd_real(a));
+@@ -447,4 +450,12 @@ void c_qd_pi(double *a) {
+   TO_DOUBLE_PTR(qd_real::_pi, a);
+ }
+ 
++void c_qd_2pi(double *a) {
++  TO_DOUBLE_PTR(qd_real::_2pi, a);
++}
++
++double c_qd_epsilon(void) {
++    return (double) std::numeric_limits<qd_real>::epsilon();
++}
++
+ }
+diff --git a/src/qd_real.cpp b/src/qd_real.cpp
+index 70988ff..2da15c2 100644
+--- a/src/qd_real.cpp
++++ b/src/qd_real.cpp
+@@ -191,7 +191,7 @@ istream &operator>>(istream &s, qd_real &qd) {
+ ostream &operator<<(ostream &os, const qd_real &qd) {
+   bool showpos = (os.flags() & ios_base::showpos) != 0;
+   bool uppercase = (os.flags() & ios_base::uppercase) != 0;
+-  return os << qd.to_string(os.precision(), os.width(), os.flags(), 
++  return os << qd.to_string(os.precision(), os.width(), os.flags(),
+       showpos, uppercase, os.fill());
+ }
+ 
+@@ -346,9 +346,9 @@ void qd_real::to_digits(char *s, int &expn, int precision) const {
+   }
+ 
+   /* If first digit is 10, shift everything. */
+-  if (s[0] > '9') { 
+-    e++; 
+-    for (i = precision; i >= 2; i--) s[i] = s[i-1]; 
++  if (s[0] > '9') {
++    e++;
++    for (i = precision; i >= 2; i--) s[i] = s[i-1];
+     s[0] = '1';
+     s[1] = '0';
+   }
+@@ -519,7 +519,6 @@ string qd_real::to_string(int precision, int width, ios_base::fmtflags fmt,
+     	if( fabs( from_string / this->x[0] ) > 3.0 ){
+ 
+     		int point_position;
+-    		char temp;
+ 
+     		// loop on the string, find the point, move it up one
+     		// don't act on the first character
+@@ -736,37 +735,53 @@ qd_real qd_real::accurate_div(const qd_real &a, const qd_real &b) {
+   return qd_real(q0, q1, q2, q3);
+ }
+ 
+-QD_API qd_real sqrt(const qd_real &a) {
+-  /* Strategy:  
+-
+-     Perform the following Newton iteration:
++QD_API qd_real fsqrt(const qd_real &a, int &flag) {
++  /* Uses Heron's method, see:
++     https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Babylonian_method
+ 
+-       x' = x + (1 - a * x^2) * x / 2;
+-       
+-     which converges to 1/sqrt(a), starting with the
+-     double precision approximation to 1/sqrt(a).
+-     Since Newton's iteration more or less doubles the
+-     number of correct digits, we only need to perform it 
+-     twice.
++     1. x0 = approximate sqrt(a);
++     2. x_{n+1} = (1/2) * (x_n + a / x_n);
++     3. repeat 2 until corrections are small
+   */
+ 
++  int i;
++  double e, eps;
++
++  qd_real r, diff;
++  qd_real half = "0.5000000000000000000000000000000000"
++                 "000000000000000000000000000000000000";
++
+   if (a.is_zero())
+-    return 0.0;
++    return (qd_real) 0.0;
+ 
+   if (a.is_negative()) {
+     qd_real::error("(qd_real::sqrt): Negative argument.");
+     return qd_real::_nan;
+   }
+ 
+-  qd_real r = (1.0 / std::sqrt(a[0]));
+-  qd_real h = mul_pwr2(a, 0.5);
++  eps = std::numeric_limits<qd_real>::epsilon();
+ 
+-  r += ((0.5 - h * sqr(r)) * r);
+-  r += ((0.5 - h * sqr(r)) * r);
+-  r += ((0.5 - h * sqr(r)) * r);
++  qd_real x = std::sqrt(a[0]);
++  qd_real y;
+ 
+-  r *= a;
+-  return r;
++  for (i=0; i < 10; i++) {
++      y = half * (x + a / x);
++      diff = x - y;
++      x = y;
++      e = fabs(((diff[3] + diff[2]) + diff[1]) + diff[0]);
++      if (e < fabs(x.x[0]) * eps) {
++          flag = 0; // convergence achieved
++          return x;
++      }
++  }
++
++  flag = 1; // failed to converge
++  return x;
++}
++
++QD_API qd_real sqrt(const qd_real &a) {
++  int flag;
++  return fsqrt(a, flag);
+ }
+ 
+ 
+-- 
+2.41.0
+
