From c6e6991b376658976b123053174618d63a7ada22 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Albin=20Ahlb=C3=A4ck?= <albin.ahlback@gmail.com>
Date: Mon, 27 May 2024 02:13:50 +0200
Subject: [PATCH 1/4] Start on tuning suite

---
 Makefile.in                       |  78 +++++---
 src/limb_types.h                  |   2 +
 src/tune/README.md                |  58 ++++++
 src/tune/clock.h                  |  67 +++++++
 src/tune/n_mod_vec/aors_0.c       |  25 +++
 src/tune/n_mod_vec/aors_1.c       |  25 +++
 src/tune/n_mod_vec/param.c        |  59 ++++++
 src/tune/n_mod_vec/tune_aors.c    |  47 +++++
 src/tune/tune.c                   | 300 ++++++++++++++++++++++++++++++
 src/tune/tune.h                   |  67 +++++++
 src/tune/ulong_extras/param.c     |  59 ++++++
 src/tune/ulong_extras/tune_xgcd.c |  42 +++++
 src/tune/ulong_extras/xgcd_0.c    |  22 +++
 src/tune/ulong_extras/xgcd_1.c    |  22 +++
 src/ulong_extras.h                |  11 +-
 src/ulong_extras/gcdinv.c         |  48 ++++-
 src/ulong_extras/xgcd.c           |  44 +++++
 17 files changed, 946 insertions(+), 30 deletions(-)
 create mode 100644 src/tune/README.md
 create mode 100644 src/tune/clock.h
 create mode 100644 src/tune/n_mod_vec/aors_0.c
 create mode 100644 src/tune/n_mod_vec/aors_1.c
 create mode 100644 src/tune/n_mod_vec/param.c
 create mode 100644 src/tune/n_mod_vec/tune_aors.c
 create mode 100644 src/tune/tune.c
 create mode 100644 src/tune/tune.h
 create mode 100644 src/tune/ulong_extras/param.c
 create mode 100644 src/tune/ulong_extras/tune_xgcd.c
 create mode 100644 src/tune/ulong_extras/xgcd_0.c
 create mode 100644 src/tune/ulong_extras/xgcd_1.c

diff --git a/Makefile.in b/Makefile.in
index 832e95da91..775c11ba86 100644
--- a/Makefile.in
+++ b/Makefile.in
@@ -12,9 +12,11 @@
 FLINT_DIR:=.
 SRC_DIR:=src
 BUILD_DIR:=build
+TUNE_DIR:=src/tune
 ABS_FLINT_DIR:='$(patsubst %/,%, $(dir $(abspath $(lastword $(MAKEFILE_LIST)))))'
 ABS_SRC_DIR:=$(ABS_FLINT_DIR)/$(SRC_DIR)
 ABS_BUILD_DIR:=$(ABS_FLINT_DIR)/$(SRC_DIR)
+ABS_TUNE_DIR:=$(ABS_FLINT_DIR)/$(TUNE_DIR)
 
 FLINT_VERSION:=@FLINT_VERSION_FULL@
 FLINT_MAJOR_SO:=@FLINT_MAJOR_SO@
@@ -81,6 +83,7 @@ CFLAGS:=@CFLAGS@
 TESTCFLAGS:=@TESTCFLAGS@
 CPPFLAGS:=@CPPFLAGS@ -DBUILDING_FLINT
 CPPFLAGS2:=-L$(FLINT_DIR) $(CPPFLAGS)
+CPPFLAGS3:=-I$(TUNE_DIR) $(CPPFLAGS2)
 LIB_CPPFLAGS:=@LIB_CPPFLAGS@
 CXXFLAGS:=@CXXFLAGS@
 LIBS:=@LIBS@
@@ -218,8 +221,15 @@ TEMPLATE_DIRS :=                                                            \
         fq_poly_templates               fq_poly_factor_templates            \
         fq_embed_templates              fq_templates
 
+_TUNE_DIRS :=                                                                \
+        ulong_extras
+
+TUNE_DIRS := $(patsubst %, $(TUNE_DIR)/%, $(_TUNE_DIRS))
+TUNE_BUILD_DIRS := $(patsubst %, $(BUILD_DIR)/tune/%, $(_TUNE_DIRS))
+
 BUILD_DIRS :=                                                               \
         $(BUILD_DIR)                                                        \
+        $(TUNE_BUILD_DIRS)                                                  \
         $(patsubst %, $(BUILD_DIR)/%, $(DIRS))                              \
         $(patsubst %, $(BUILD_DIR)/%/profile, $(DIRS))                      \
         $(patsubst %, $(BUILD_DIR)/%/test, $(DIRS))                         \
@@ -299,12 +309,12 @@ ifneq ($(WANT_NTL), 0)
 interfaces_TEST_SOURCES := $(SRC_DIR)/interfaces/test/t-NTL-interface.cpp
 endif
 
-define xxx_TUNE_SOURCES
-$(1)_TUNE_SOURCES := $(wildcard $(SRC_DIR)/$(1)/tune/*.c)
+define xxx_OLD_TUNE_SOURCES
+$(1)_OLD_TUNE_SOURCES := $(wildcard $(SRC_DIR)/$(1)/tune/*.c)
 endef
-_TUNE_SOURCES := $(wildcard $(SRC_DIR)/tune/*.c)
-$(foreach dir, $(DIRS), $(eval $(call xxx_TUNE_SOURCES,$(dir))))
-TUNE_SOURCES := $(foreach dir,$(DIRS),$($(dir)_TUNE_SOURCES)) $(_TUNE_SOURCES)
+_OLD_TUNE_SOURCES := $(wildcard $(SRC_DIR)/tune/*.c)
+$(foreach dir, $(DIRS), $(eval $(call xxx_OLD_TUNE_SOURCES,$(dir))))
+OLD_TUNE_SOURCES := $(foreach dir,$(DIRS),$($(dir)_OLD_TUNE_SOURCES)) $(_OLD_TUNE_SOURCES)
 
 EXMP_SOURCES := $(wildcard $(FLINT_DIR)/examples/*.c)
 
@@ -359,12 +369,12 @@ interfaces_TESTS := $(BUILD_DIR)/interfaces/test/t-NTL-interface$(EXEEXT)
 endif
 TESTS := $(_TESTS) $(foreach dir,$(DIRS),$($(dir)_TESTS)) $(interfaces_TESTS)
 
-define xxx_TUNES
-$(1)_TUNES := $(patsubst $(SRC_DIR)/%.c,$(BUILD_DIR)/%$(EXEEXT),$($(1)_TUNE_SOURCES))
+define xxx_OLD_TUNES
+$(1)_OLD_TUNES := $(patsubst $(SRC_DIR)/%.c,$(BUILD_DIR)/%$(EXEEXT),$($(1)_OLD_TUNE_SOURCES))
 endef
-_TUNES := $(patsubst $(SRC_DIR)/%.c,$(BUILD_DIR)/%$(EXEEXT),$(_TUNE_SOURCES))
-$(foreach dir, $(DIRS), $(eval $(call xxx_TUNES,$(dir))))
-TUNES := $(foreach dir,$(DIRS),$($(dir)_TUNES)) $(_TUNES)
+_OLD_TUNES := $(patsubst $(SRC_DIR)/%.c,$(BUILD_DIR)/%$(EXEEXT),$(_OLD_TUNE_SOURCES))
+$(foreach dir, $(DIRS), $(eval $(call xxx_OLD_TUNES,$(dir))))
+OLD_TUNES := $(foreach dir,$(DIRS),$($(dir)_OLD_TUNES)) $(_OLD_TUNES)
 
 EXMPS := $(patsubst $(FLINT_DIR)/%.c,$(BUILD_DIR)/%$(EXEEXT),$(EXMP_SOURCES))
 
@@ -675,30 +685,20 @@ endif
 endif
 
 ifeq ($(SHARED), 0)
-$(BUILD_DIR)/tune/%$(EXEEXT): $(SRC_DIR)/tune/%.c $(FLINT_DIR)/$(FLINT_LIB_STATIC) | $(BUILD_DIR)/tune
-	@echo "  CC  $(<:$(SRC_DIR)/%=%)"
-	@$(CC) $(TESTCFLAGS) $(CPPFLAGS2) $< -o $@ $(EXE_LDFLAGS) $(LIBS2) $(DEPFLAGS)
-else
-$(BUILD_DIR)/tune/%$(EXEEXT): $(SRC_DIR)/tune/%.c | $(FLINT_DIR)/$(FLINT_LIB_FULL) $(BUILD_DIR)/tune
-	@echo "  CC  $(<:$(SRC_DIR)/%=%)"
-	@$(CC) $(TESTCFLAGS) $(CPPFLAGS2) $< -o $@ $(EXE_LDFLAGS) $(LIBS2) $(DEPFLAGS)
-endif
-
-ifeq ($(SHARED), 0)
-define xxx_TUNES_rule
+define xxx_OLD_TUNES_rule
 $(BUILD_DIR)/$(1)/tune/%$(EXEEXT): $(SRC_DIR)/$(1)/tune/%.c $(FLINT_DIR)/$(FLINT_LIB_STATIC) | $(BUILD_DIR)/$(1)/tune
 	@echo "  CC  $$(<:$(SRC_DIR)/%=%)"
 	@$(CC) $(TESTCFLAGS) $(CPPFLAGS2) $$< -o $$@ $(EXE_LDFLAGS) $(LIBS2) $$(DEPFLAGS)
 endef
 else
-define xxx_TUNES_rule
+define xxx_OLD_TUNES_rule
 $(BUILD_DIR)/$(1)/tune/%$(EXEEXT): $(SRC_DIR)/$(1)/tune/%.c | $(FLINT_DIR)/$(FLINT_LIB_FULL) $(BUILD_DIR)/$(1)/tune
 	@echo "  CC  $$(<:$(SRC_DIR)/%=%)"
 	@$(CC) $(TESTCFLAGS) $(CPPFLAGS2) $$< -o $$@ $(EXE_LDFLAGS) $(LIBS2) $$(DEPFLAGS)
 endef
 endif
 
-$(foreach dir, $(DIRS), $(eval $(call xxx_TUNES_rule,$(dir))))
+$(foreach dir, $(DIRS), $(eval $(call xxx_OLD_TUNES_rule,$(dir))))
 
 ifeq ($(SHARED), 0)
 $(BUILD_DIR)/examples/%$(EXEEXT): $(FLINT_DIR)/examples/%.c $(FLINT_DIR)/$(FLINT_LIB_STATIC) | $(BUILD_DIR)/examples $(BUILD_DIR)/include
@@ -834,7 +834,35 @@ endif
 # tuning
 ################################################################################
 
-tune: library $(TUNES)
+# Only old tunes, i.e. under src/MOD/tune/
+old_tune: library $(OLD_TUNES)
+
+TUNE_SOURCE:=$(TUNE_DIR)/tune.c
+TUNE_DEPS_SOURCES:=$(foreach dir,$(TUNE_DIRS),$(wildcard $(dir)/*.c))
+
+_TUNE_HEADERS:=tune.h clock.h
+TUNE_HEADERS:=$(patsubst %,$(TUNE_DIR)/%,$(_TUNE_HEADERS))
+
+TUNE_DEPS_OBJS:=$(patsubst $(TUNE_DIR)/%.c,$(BUILD_DIR)/tune/%.o,$(TUNE_DEPS_SOURCES))
+
+TUNE_EXE:=$(BUILD_DIR)/tuneup$(EXEEXT)
+
+# Sloppy to say that all TUNE_BUILD_DIRS have to be built.
+$(BUILD_DIR)/tune/%.o: $(TUNE_DIR)/%.c $(TUNE_HEADERS) | $(TUNE_BUILD_DIRS)
+	@echo "  CC  $(<:$(SRC_DIR)/%=%)"
+	@$(CC) $(CFLAGS) $(CPPFLAGS3) $(LIB_CPPFLAGS) -c $< -o $@ $(DEPFLAGS)
+
+ifeq ($(SHARED), 0)
+$(TUNE_EXE): $(TUNE_SOURCE) $(TUNE_DEPS_OBJS) $(TUNE_HEADERS) $(FLINT_DIR)/$(FLINT_LIB_STATIC) | $(BUILD_DIR)
+	@echo "  CC  $(<:$(SRC_DIR)/%=%)"
+	@$(CC) $(CFLAGS) $(CPPFLAGS3) $(LIB_CPPFLAGS) $(TUNE_DEPS_OBJS) $< -o $@ $(EXE_LDFLAGS) $(LIBS2) $(DEPFLAGS)
+else
+$(TUNE_EXE): $(TUNE_SOURCE) $(TUNE_DEPS_OBJS) $(TUNE_HEADERS) | $(FLINT_DIR)/$(FLINT_LIB_FULL) $(BUILD_DIR)
+	@echo "  CC  $(<:$(SRC_DIR)/%=%)"
+	@$(CC) $(CFLAGS) $(CPPFLAGS3) $(LIB_CPPFLAGS) $(TUNE_DEPS_OBJS) $< -o $@ $(EXE_LDFLAGS) $(LIBS2) $(DEPFLAGS)
+endif
+
+tune: $(TUNE_EXE)
 
 ################################################################################
 # valgrind
@@ -988,5 +1016,5 @@ dist:
 print-%:
 	@echo "$*=$($*)"
 
-.PHONY: all library shared static examples checkexamples profile tests check tune valgrind clean distclean install uninstall dist %_TEST_RUN %_TEST_RUN_% %_TEST_DGB_RUN_ARGS %_VALGRIND_RUN print-% coverage coverage_html debug
+.PHONY: all library shared static examples checkexamples profile tests check tune old_tune valgrind clean distclean install uninstall dist %_TEST_RUN %_TEST_RUN_% %_TEST_DGB_RUN_ARGS %_VALGRIND_RUN print-% coverage coverage_html debug
 .PRECIOUS: $(mpn_extras_PIC_S_SOURCES) $(mpn_extras_S_SOURCES)
diff --git a/src/limb_types.h b/src/limb_types.h
index 05d52238ad..0c6131f653 100644
--- a/src/limb_types.h
+++ b/src/limb_types.h
@@ -18,6 +18,8 @@
 extern "C" {
 #endif
 
+typedef struct { ulong m0, m1; } nn_pair_t;
+
 #define FLINT_MAX_FACTORS_IN_LIMB 15
 
 typedef struct
diff --git a/src/tune/README.md b/src/tune/README.md
new file mode 100644
index 0000000000..f2ebb5685c
--- /dev/null
+++ b/src/tune/README.md
@@ -0,0 +1,58 @@
+# Tuning-suite
+
+Currently working-in-progress, but feedback is much appreciated.
+
+## Usage
+
+Run `make tune` followed by `./build/tuneup`. This pushes all the optimized
+parameters into `stdout`. These can then be used to optimize the parameter file
+`flint-mparam.h` for your system.
+
+### Set CPU frequency
+
+If tuner is using clock ticks (currently only for x86-64), you can specify your
+clock frequency by pushing `export FLINT_CPU_FREQUENCY=3.1e9` to tell the tuner
+that your CPU frequency is 3.1 GHz.
+
+### Options
+
+Currently, no command-line options are allowed apart from `-h` and `--help` to
+display the usual help message.
+
+However, it would be optimal to be able to specify:
+
+- Functions intended to benchmark (currently does all available)
+- Minimum number of runs
+- Warmup runs (currently, 10 is the default)
+- Minimum amount of time to run each function (?)
+- Precision required to terminate successfully (currently 1.25 %)
+- Percentage of runs required to be within said precision (currently 13.5 %)
+
+## Issues
+
+Please open up any issues at <https://github.com/flintlib/flint/issues>.
+
+## Requirements
+
+- FLINT was built with Autotools.
+- Either that
+  * `clock_gettime` is available on the system, or that
+  * compiler is GCC compatible and architecture is x86.
+
+## How it works
+
+The program works in the following order:
+
+1. Parses options
+2. Sets default values
+3. For each function (that is, each variant of each function) tested:
+   a. Run a couple of warmups, which are trashed
+   b. Run hotlaps, of which the time is saved
+   c. Check if there is a smallest time elapsed $t$ for running a function of
+      which at least $k$ of the runs have a time in the interval
+      $[t, (1 + p) t]$, where $p$ is the precision and $k / n$ is the percentage
+      of runs required to be within said precision, where $n$ is the total
+      number of runs. If no such $t$ was found, abort.
+4. With all $t$ obtained from each families of functions, determine cutoff
+   points, methods used, etc.
+5. Print the associated `#define` into `stdout`.
diff --git a/src/tune/clock.h b/src/tune/clock.h
new file mode 100644
index 0000000000..83f447bf3d
--- /dev/null
+++ b/src/tune/clock.h
@@ -0,0 +1,67 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#ifndef FLINT_CLOCK_H
+#define FLINT_CLOCK_H
+
+#include <stdlib.h>
+#include <time.h>
+#include "flint.h"
+
+#define FLINT_CPU_FREQUENCY_DEFAULT 3.2e9
+
+#if FLINT64 && defined(__amd64__)
+typedef ulong flint_time_t[1];
+
+FLINT_FORCE_INLINE
+double flint_time_nsec_diff(flint_time_t t1, flint_time_t t0)
+{
+    char * str = getenv("FLINT_CPU_FREQUENCY");
+    double freq;
+    double seconds;
+
+    if (str == NULL)
+        freq = FLINT_CPU_FREQUENCY_DEFAULT;
+    else
+        freq = strtod(str, NULL);
+
+    seconds = (double) (*t1 - *t0) / freq;
+
+    return seconds * 10e9;
+}
+
+FLINT_FORCE_INLINE
+void flint_time_get(flint_time_t t0)
+{
+    __asm__ volatile (
+            "rdtsc\n\t"
+            "shl $32, %%rdx\n\t"
+            "or %%rdx, %0"
+            : "=a" (*t0) : : "rdx");
+}
+#else
+typedef struct timespec flint_time_t[1];
+
+FLINT_FORCE_INLINE
+double flint_time_nsec_diff(flint_time_t t1, flint_time_t t0)
+{
+    return 1000000000.0 * (t1->tv_sec - t0->tv_sec)
+        + (double) (t1->tv_nsec - t0->tv_nsec);
+}
+
+FLINT_FORCE_INLINE
+void flint_time_get(flint_time_t t0)
+{
+    return clock_gettime(CLOCK_PROCESS_CPUTIME_ID, t0);
+}
+#endif
+
+#endif /* FLINT_CLOCK_H */
diff --git a/src/tune/n_mod_vec/aors_0.c b/src/tune/n_mod_vec/aors_0.c
new file mode 100644
index 0000000000..f5197c3a2a
--- /dev/null
+++ b/src/tune/n_mod_vec/aors_0.c
@@ -0,0 +1,25 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "flint-mparam.h"
+#include "n_mod_vec.h"
+
+#undef N_MOD_VEC_ADD_METHOD
+#undef N_MOD_VEC_SUB_METHOD
+#define TUNE_PROGRAM 1
+
+#define N_MOD_VEC_ADD_METHOD 0
+#define N_MOD_VEC_SUB_METHOD 0
+
+#define _n_mod_vec_add _n_mod_vec_add_0
+#define _n_mod_vec_sub _n_mod_vec_sub_0
+
+#include "n_mod_vec/aors.c"
diff --git a/src/tune/n_mod_vec/aors_1.c b/src/tune/n_mod_vec/aors_1.c
new file mode 100644
index 0000000000..2c17b0d6c1
--- /dev/null
+++ b/src/tune/n_mod_vec/aors_1.c
@@ -0,0 +1,25 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "flint-mparam.h"
+#include "n_mod_vec.h"
+
+#undef N_MOD_VEC_ADD_METHOD
+#undef N_MOD_VEC_SUB_METHOD
+#define TUNE_PROGRAM 1
+
+#define N_MOD_VEC_ADD_METHOD 1
+#define N_MOD_VEC_SUB_METHOD 1
+
+#define _n_mod_vec_add _n_mod_vec_add_1
+#define _n_mod_vec_sub _n_mod_vec_sub_1
+
+#include "n_mod_vec/aors.c"
diff --git a/src/tune/n_mod_vec/param.c b/src/tune/n_mod_vec/param.c
new file mode 100644
index 0000000000..cf7f00f56d
--- /dev/null
+++ b/src/tune/n_mod_vec/param.c
@@ -0,0 +1,59 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "tune.h"
+#include "n_mod.h"
+#include "n_mod_vec.h"
+
+#if FLINT64
+# define N_0 UWORD(7365182178263871635)
+#else
+# define N_0 UWORD(1236571635)
+#endif
+
+void * n_mod_vec_param_init_generate_0(void)
+{
+    struct n_mod_vec_param_0 * param;
+    nn_ptr rp, ap, bp;
+    slong len;
+    flint_rand_t state;
+
+    param = flint_malloc(sizeof(struct n_mod_vec_param_0));
+    flint_rand_init(state);
+
+    len = 1000;
+    rp = flint_malloc(sizeof(ulong) * len);
+    ap = flint_malloc(sizeof(ulong) * len);
+    bp = flint_malloc(sizeof(ulong) * len);
+    n_mod_ctx_init(param->ctx, N_0);
+
+    _n_mod_vec_rand(ap, state, len, param->ctx);
+    _n_mod_vec_rand(bp, state, len, param->ctx);
+
+    param->rp = rp;
+    param->ap = ap;
+    param->bp = bp;
+    param->len = len;
+    flint_rand_clear(state);
+
+    return param;
+}
+
+void n_mod_vec_param_clear(void * vparam)
+{
+    struct n_mod_vec_param_0 * param = vparam;
+
+    flint_free(param->rp);
+    flint_free(param->ap);
+    flint_free(param->bp);
+    n_mod_ctx_clear(param->ctx);
+    flint_free(param);
+}
diff --git a/src/tune/n_mod_vec/tune_aors.c b/src/tune/n_mod_vec/tune_aors.c
new file mode 100644
index 0000000000..52ee2575f1
--- /dev/null
+++ b/src/tune/n_mod_vec/tune_aors.c
@@ -0,0 +1,47 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "clock.h"
+#include "tune.h"
+#include "n_mod.h"
+#include "n_mod_vec.h"
+
+void _n_mod_vec_add_0(nn_ptr, nn_srcptr, nn_srcptr, slong, ulong);
+void _n_mod_vec_sub_0(nn_ptr, nn_srcptr, nn_srcptr, slong, ulong);
+void _n_mod_vec_add_1(nn_ptr, nn_srcptr, nn_srcptr, slong, ulong);
+void _n_mod_vec_sub_1(nn_ptr, nn_srcptr, nn_srcptr, slong, ulong);
+
+#define DEFINE_IT(name, func)                   \
+double name(void * vparam)                      \
+{                                               \
+    struct n_mod_vec_param_0 * param = vparam;  \
+    nn_ptr rp, ap, bp;                          \
+    slong len;                                  \
+    ulong nu;                                   \
+    flint_time_t t0, t1;                        \
+                                                \
+    rp = param->rp;                             \
+    ap = param->ap;                             \
+    bp = param->bp;                             \
+    len = param->len;                           \
+    nu = param->ctx->nu;                        \
+                                                \
+    flint_time_get(t0);                         \
+    func(rp, ap, bp, len, nu);                  \
+    flint_time_get(t1);                         \
+                                                \
+    return flint_time_nsec_diff(t1, t0);        \
+}
+
+DEFINE_IT(_tune_n_mod_vec_add_0, _n_mod_vec_add_0)
+DEFINE_IT(_tune_n_mod_vec_add_1, _n_mod_vec_add_1)
+DEFINE_IT(_tune_n_mod_vec_sub_0, _n_mod_vec_sub_0)
+DEFINE_IT(_tune_n_mod_vec_sub_1, _n_mod_vec_sub_1)
diff --git a/src/tune/tune.c b/src/tune/tune.c
new file mode 100644
index 0000000000..f336535342
--- /dev/null
+++ b/src/tune/tune.c
@@ -0,0 +1,300 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+/* TODO:
+    * Allow to pass function inputs.
+    * Allow to pass number of warmup runs.
+    * Allow to pass number of runs.
+    * Allow to pass minimum amount of milliseconds each function has to run.
+    * Support considering other things than simply the mean run time.
+*/
+
+/* NOT-TODO:
+    * Do not allow passing inputs of a specific kind.
+*/
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+#include <getopt.h>
+#include "tune.h"
+
+#if 0
+static void print_copyright(void)
+{
+    printf("/*\n"
+           "    Copyright (C) 2024 Albin Ahlbäck\n"
+           "\n"
+           "    This file is part of FLINT.\n"
+           "\n"
+           "    FLINT is free software: you can redistribute it and/or modify it under\n"
+           "    the terms of the GNU Lesser General Public License (LGPL) as published\n"
+           "    by the Free Software Foundation; either version 3 of the License, or\n"
+           "    (at your option) any later version.  See <https://www.gnu.org/licenses/>.\n"
+           "*/\n"
+           "\n");
+}
+#endif
+
+int compare_doubles(const void * ap, const void * bp)
+{
+    double a = *((const double *) ap);
+    double b = *((const double *) bp);
+
+    return (a < b) ? -1 : (a > b) ? 1 : 0;
+}
+
+static double measure_func(tune_func_t fun, void * params, int runs, int warmups)
+{
+    double * times = malloc(sizeof(double) * runs);
+    int ix;
+    const double deviation = 1.0125; /* 1.25 % larger */
+    const double percentage_within_deviation = 0.135; /* 13.5 % */
+    const int check_step = percentage_within_deviation * runs;
+    double ret;
+
+    for (ix = 0; ix < warmups; ix++)
+        fun(params);
+
+    for (ix = 0; ix < runs; ix++)
+        times[ix] = fun(params);
+
+    qsort(times, runs, sizeof(double), compare_doubles);
+
+    for (ix = 0; ix + check_step < runs; ix++)
+    {
+        if (deviation * times[ix] >= times[ix + check_step])
+        {
+            ret = times[ix];
+            break;
+        }
+    }
+
+    if (ix + check_step == runs)
+    {
+        fprintf(stderr, "Could not find appropriate measurements.\n");
+        exit(1);
+    }
+
+    free(times);
+
+    return ret;
+}
+
+#define SPEEDUP(more_time, less_time) ((double) (more_time) / (double) (less_time) - 1.0)
+
+#if 0
+static void print_define(const char * str, int val)
+{
+    printf("#define %-36 %4d\n", str, val);
+}
+#endif
+
+static void
+print_define_with_speedup(const char * str, int val, int other_val, double speedup)
+{
+    printf("#define %-36s %4d /* %.2f%% faster than %d */\n",
+            str, val, speedup, other_val);
+}
+
+static void tune_n_xgcd(int warmups, int min_runs)
+{
+    void * params = n_param_init_generate_0();
+    double t0, t1;
+    int chosen_method, other_method;
+    double speedup;
+
+    t0 = measure_func(_tune_n_xgcd_0, params, warmups, min_runs);
+    t1 = measure_func(_tune_n_xgcd_1, params, warmups, min_runs);
+
+    if (t0 <= t1)
+    {
+        chosen_method = 0;
+        other_method = 1;
+        speedup = SPEEDUP(t1, t0);
+    }
+    else
+    {
+        chosen_method = 1;
+        other_method = 0;
+        speedup = SPEEDUP(t0, t1);
+    }
+
+    print_define_with_speedup("N_GCDEXT_METHOD", chosen_method, other_method, speedup);
+
+    n_param_clear(params);
+}
+
+#if WANT_N_MOD
+static void tune_n_mod_vec_add(int warmups, int min_runs)
+{
+    void * params = n_mod_vec_param_init_generate_0();
+    double t0, t1;
+    int chosen_method, other_method;
+    double speedup;
+
+    t0 = measure_func(_tune_n_mod_vec_add_0, params, warmups, min_runs);
+    t1 = measure_func(_tune_n_mod_vec_add_1, params, warmups, min_runs);
+
+    if (t0 <= t1)
+    {
+        chosen_method = 0;
+        other_method = 1;
+        speedup = SPEEDUP(t1, t0);
+    }
+    else
+    {
+        chosen_method = 1;
+        other_method = 0;
+        speedup = SPEEDUP(t0, t1);
+    }
+
+    print_define_with_speedup("N_MOD_VEC_ADD_METHOD", chosen_method, other_method, speedup);
+
+    n_mod_vec_param_clear(params);
+}
+
+static void tune_n_mod_vec_sub(int warmups, int min_runs)
+{
+    void * params = n_mod_vec_param_init_generate_0();
+    double t0, t1;
+    int chosen_method, other_method;
+    double speedup;
+
+    t0 = measure_func(_tune_n_mod_vec_sub_0, params, warmups, min_runs);
+    t1 = measure_func(_tune_n_mod_vec_sub_1, params, warmups, min_runs);
+
+    if (t0 <= t1)
+    {
+        chosen_method = 0;
+        other_method = 1;
+        speedup = SPEEDUP(t1, t0);
+    }
+    else
+    {
+        chosen_method = 1;
+        other_method = 0;
+        speedup = SPEEDUP(t0, t1);
+    }
+
+    print_define_with_speedup("N_MOD_VEC_SUB_METHOD", chosen_method, other_method, speedup);
+
+    n_mod_vec_param_clear(params);
+}
+#endif
+
+struct tune_t
+{
+    char * name;
+    void (* tune_function)(int, int);
+};
+
+static const struct tune_t tunes[] =
+{
+    {"n_xgcd",         tune_n_xgcd},
+#if WANT_N_MOD
+    {"_n_mod_vec_add", tune_n_mod_vec_add},
+    {"_n_mod_vec_sub", tune_n_mod_vec_sub},
+#endif
+};
+
+#define DEFAULT(x, val) do { if ((x) <= 0) (x) = (val); } while (0)
+#define numberof(x) (sizeof(x) / sizeof((x)[0]))
+
+/* FIXME: Use funcs if funcs != NULL */
+static void
+distribute_tune(int num, const char ** funcs, int warmups, int min_runs)
+{
+    int ix;
+
+    DEFAULT(warmups, 10);
+    DEFAULT(min_runs, 1000);
+
+    if (funcs == NULL)
+    {
+        for (ix = 0; ix < numberof(tunes); ix++)
+            tunes[ix].tune_function(warmups, min_runs);
+    }
+    else
+    {
+        for (ix = 0; ix < num; ix++)
+        {
+            int jx;
+
+            for (jx = 0; jx < numberof(tunes); jx++)
+                if (strcmp(funcs[ix], tunes[jx].name) == 0)
+                {
+                    tunes[jx].tune_function(warmups, min_runs);
+                    break;
+                }
+
+            if (jx == numberof(tunes))
+            {
+                printf("Unknown function %s.\n", funcs[ix]);
+                exit(1);
+            }
+        }
+    }
+}
+
+static void usage(int argc, char ** argv)
+{
+    /* FIXME: Write something more nice */
+    printf("Usage:  %s [options]\n"
+           "\n"
+           "Tunes the parameters, that could then be pushed into flint-mparam.h\n"
+           "\n"
+           "Options:\n"
+           "  -h, --help   Display this help message\n"
+           "\n", argv[0]);
+}
+
+int main(int argc, char ** argv)
+{
+    int c;
+
+    while (1)
+    {
+        int option_index = 0;
+        static struct option long_options[] =
+        {
+            {"help", no_argument, NULL, 'h'},
+            {  NULL,           0, NULL,   0}
+        };
+
+        c = getopt_long(argc, argv, "h", long_options, &option_index);
+        if (c == -1)
+            break;
+
+        switch (c)
+        {
+            case 'h':
+                usage(argc, argv);
+                exit(0);
+
+            default:
+                usage(argc, argv);
+                exit(1);
+        }
+    }
+
+    if (optind < argc)
+    {
+        /* distribute_tune(argc - optind, argv + optind); */
+        printf("Currently does not support arguments.\n\n");
+        usage(argc, argv);
+        exit(1);
+    }
+    else
+        distribute_tune(0, NULL, -1, -1);
+
+    exit(0);
+}
diff --git a/src/tune/tune.h b/src/tune/tune.h
new file mode 100644
index 0000000000..4aac8012fc
--- /dev/null
+++ b/src/tune/tune.h
@@ -0,0 +1,67 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#ifndef FLINT_TUNE_H
+#define FLINT_TUNE_H
+
+#define WANT_N_MOD 0
+
+#include "flint.h"
+#if WANT_N_MOD
+# include "n_mod.h"
+#endif
+
+/* tune_func_t
+
+   Should run a function once and return the time to run the main function. */
+typedef double (* tune_func_t)(void *);
+
+/* ulong_extras **************************************************************/
+
+struct n_param_0
+{
+    nn_ptr ap;
+    nn_ptr bp;
+    nn_ptr xp;
+    nn_ptr yp;
+    slong len;
+};
+
+/* Only sets xp and yp, and orders xp[ix] >= yp[ix] */
+void * n_param_init_generate_0(void);
+void n_param_clear(void *);
+
+double _tune_n_xgcd_0(void *);
+double _tune_n_xgcd_1(void *);
+
+/* n_mod_vec *****************************************************************/
+#if WANT_N_MOD
+struct n_mod_vec_param_0
+{
+    nn_ptr rp;
+    nn_ptr ap;
+    nn_ptr bp;
+    slong len;
+    n_mod_ctx_t ctx;
+};
+
+/* Only sets ap and bp */
+void * n_mod_vec_param_init_generate_0(void);
+void n_mod_vec_param_clear(void *);
+
+double _tune_n_mod_vec_add_0(void *);
+double _tune_n_mod_vec_add_1(void *);
+
+double _tune_n_mod_vec_sub_0(void *);
+double _tune_n_mod_vec_sub_1(void *);
+#endif
+
+#endif /* FLINT_TUNE_H */
diff --git a/src/tune/ulong_extras/param.c b/src/tune/ulong_extras/param.c
new file mode 100644
index 0000000000..d4edb7ccd1
--- /dev/null
+++ b/src/tune/ulong_extras/param.c
@@ -0,0 +1,59 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "tune.h"
+
+void * n_param_init_generate_0(void)
+{
+    struct n_param_0 * param;
+    nn_ptr ap, bp, xp, yp;
+    slong len;
+    slong ix;
+    flint_rand_t state;
+
+    param = flint_malloc(sizeof(struct n_param_0));
+    flint_rand_init(state);
+
+    len = 100;
+    ap = flint_malloc(sizeof(ulong) * len);
+    bp = flint_malloc(sizeof(ulong) * len);
+    xp = flint_malloc(sizeof(ulong) * len);
+    yp = flint_malloc(sizeof(ulong) * len);
+
+    for (ix = 0; ix < len; ix++)
+    {
+        xp[ix] = n_randlimb(state);
+        yp[ix] = n_randlimb(state);
+        if (xp[ix] < yp[ix])
+            FLINT_SWAP(ulong, xp[ix], yp[ix]);
+    }
+
+    param->ap = ap;
+    param->bp = bp;
+    param->xp = xp;
+    param->yp = yp;
+    param->len = len;
+
+    flint_rand_clear(state);
+
+    return param;
+}
+
+void n_param_clear(void * vparam)
+{
+    struct n_param_0 * param = vparam;
+
+    flint_free(param->ap);
+    flint_free(param->bp);
+    flint_free(param->xp);
+    flint_free(param->yp);
+    flint_free(param);
+}
diff --git a/src/tune/ulong_extras/tune_xgcd.c b/src/tune/ulong_extras/tune_xgcd.c
new file mode 100644
index 0000000000..95999e0522
--- /dev/null
+++ b/src/tune/ulong_extras/tune_xgcd.c
@@ -0,0 +1,42 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "clock.h"
+#include "tune.h"
+
+ulong n_xgcd_0(nn_ptr, nn_ptr, ulong, ulong);
+ulong n_xgcd_1(nn_ptr, nn_ptr, ulong, ulong);
+
+#define DEFINE_IT(name, func)                   \
+double name(void * vparam)                      \
+{                                               \
+    struct n_param_0 * param = vparam;          \
+    nn_ptr ap, bp, xp, yp;                      \
+    slong len;                                  \
+    flint_time_t t0, t1;                        \
+    slong ix;                                   \
+                                                \
+    ap = param->ap;                             \
+    bp = param->bp;                             \
+    xp = param->xp;                             \
+    yp = param->yp;                             \
+    len = param->len;                           \
+                                                \
+    flint_time_get(t0);                         \
+    for (ix = 0; ix < len; ix++)                \
+        func(ap, bp, xp[ix], yp[ix]);           \
+    flint_time_get(t1);                         \
+                                                \
+    return flint_time_nsec_diff(t1, t0);        \
+}
+
+DEFINE_IT(_tune_n_xgcd_0, n_xgcd_0)
+DEFINE_IT(_tune_n_xgcd_1, n_xgcd_0)
diff --git a/src/tune/ulong_extras/xgcd_0.c b/src/tune/ulong_extras/xgcd_0.c
new file mode 100644
index 0000000000..9a622af929
--- /dev/null
+++ b/src/tune/ulong_extras/xgcd_0.c
@@ -0,0 +1,22 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "flint-mparam.h"
+#include "ulong_extras.h"
+
+#undef N_GCDEXT_METHOD
+#define TUNE_PROGRAM 1
+
+#define N_GCDEXT_METHOD 0
+
+#define n_xgcd n_xgcd_0
+
+#include "ulong_extras/xgcd.c"
diff --git a/src/tune/ulong_extras/xgcd_1.c b/src/tune/ulong_extras/xgcd_1.c
new file mode 100644
index 0000000000..9cdd58cd4c
--- /dev/null
+++ b/src/tune/ulong_extras/xgcd_1.c
@@ -0,0 +1,22 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "flint-mparam.h"
+#include "ulong_extras.h"
+
+#undef N_GCDEXT_METHOD
+#define TUNE_PROGRAM 1
+
+#define N_GCDEXT_METHOD 1
+
+#define n_xgcd n_xgcd_1
+
+#include "ulong_extras/xgcd.c"
diff --git a/src/ulong_extras.h b/src/ulong_extras.h
index 729e83dbec..38f56f7cde 100644
--- a/src/ulong_extras.h
+++ b/src/ulong_extras.h
@@ -110,7 +110,16 @@ ulong n_gcd(ulong x, ulong y)
 }
 
 ulong n_xgcd(ulong * a, ulong * b, ulong x, ulong y);
-ulong n_gcdinv(ulong * a, ulong x, ulong y);
+
+nn_pair_t _n_gcdinv(ulong x, ulong y);
+
+ULONG_EXTRAS_INLINE ulong n_gcdinv(ulong * a, ulong x, ulong y)
+{
+    nn_pair_t ret = _n_gcdinv(x, y);
+    *a = ret.m0;
+    return ret.m1;
+}
+
 ulong n_CRT(ulong r1, ulong m1, ulong r2, ulong m2);
 
 /* Checked arithmetic ********************************************************/
diff --git a/src/ulong_extras/gcdinv.c b/src/ulong_extras/gcdinv.c
index 0ae711ca86..d87cd03786 100644
--- a/src/ulong_extras/gcdinv.c
+++ b/src/ulong_extras/gcdinv.c
@@ -11,9 +11,11 @@
 
 #include "ulong_extras.h"
 
-ulong
-n_gcdinv(ulong * s, ulong x, ulong y)
+#if N_GCDEXT_METHOD == 0
+nn_pair_t
+_n_gcdinv(ulong x, ulong y)
 {
+    nn_pair_t ret;
     slong v1, v2, t2;
     ulong d, r, quot, rem;
 
@@ -111,7 +113,45 @@ n_gcdinv(ulong * s, ulong x, ulong y)
     if (v1 < WORD(0))
         v1 += y;
 
-    (*s) = v1;
+    ret.m0 = v1;
+    ret.m1 = x;
 
-    return x;
+    return ret;
 }
+#elif N_GCDEXT_METHOD == 1
+nn_pair_t
+_n_gcdinv(ulong x, ulong y)
+{
+    nn_pair_t ret;
+    slong v1, v2, t2;
+    ulong d, r, quot, rem;
+
+    FLINT_ASSERT(y > x);
+
+    v1 = 0;
+    v2 = 1;
+    r = x;
+    x = y;
+
+    while (r)
+    {
+        quot = x / r;
+        rem = x - r * quot;
+        x = r;
+        t2 = v2;
+        v2 = v1 - quot * v2;
+        v1 = t2;
+        r = rem;
+    }
+
+    if (v1 < WORD(0))
+        v1 += y;
+
+    ret.m0 = v1;
+    ret.m1 = x;
+
+    return ret;
+}
+#else
+# error
+#endif
diff --git a/src/ulong_extras/xgcd.c b/src/ulong_extras/xgcd.c
index 18f19e6eba..61482b8f97 100644
--- a/src/ulong_extras/xgcd.c
+++ b/src/ulong_extras/xgcd.c
@@ -11,6 +11,7 @@
 
 #include "ulong_extras.h"
 
+#if N_GCDEXT_METHOD == 0
 ulong
 n_xgcd(ulong * a, ulong * b, ulong x, ulong y)
 {
@@ -145,3 +146,46 @@ n_xgcd(ulong * a, ulong * b, ulong x, ulong y)
 
     return u3;
 }
+#elif N_GCDEXT_METHOD == 1
+ulong
+n_xgcd(ulong * a, ulong * b, ulong x, ulong y)
+{
+    slong u1, u2, v1, v2, t1, t2;
+    ulong u3, v3, quot, rem;
+
+    FLINT_ASSERT(x >= y);
+
+    u1 = v2 = 1;
+    u2 = v1 = 0;
+    u3 = x;
+    v3 = y;
+
+    while (v3)
+    {
+        quot = u3 / v3;
+        rem = u3 - v3 * quot;
+        t1 = u2;
+        u2 = u1 - quot * u2;
+        u1 = t1;
+        u3 = v3;
+        t2 = v2;
+        v2 = v1 - quot * v2;
+        v1 = t2;
+        v3 = rem;
+    }
+
+    /* Remarkably, |u1| < x/2, thus comparison with 0 is valid */
+    if (u1 <= WORD(0))
+    {
+        u1 += y;
+        v1 -= x;
+    }
+
+    *a = u1;
+    *b = -v1;
+
+    return u3;
+}
+#else
+# error
+#endif

From b6905965d9ea617d21b66722481e29e8aee9d380 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Albin=20Ahlb=C3=A4ck?= <albin.ahlback@gmail.com>
Date: Mon, 27 May 2024 20:58:02 +0200
Subject: [PATCH 2/4] Prepare flint_mpn_(mul|sqr)high_n for tuning

Move related parameters to flint-mparam.h
---
 src/mpn_extras.h                              |  13 +-
 src/mpn_extras/arm64/applem1/flint-mparam.h   | 152 ++++++++++++++++++
 src/mpn_extras/arm64/flint-mparam.h           | 152 ++++++++++++++++++
 src/mpn_extras/generic/flint-mparam.h         | 152 ++++++++++++++++++
 src/mpn_extras/mulhigh.c                      |  78 +--------
 src/mpn_extras/sqrhigh.c                      |  72 +--------
 .../x86_64/broadwell/flint-mparam.h           | 152 ++++++++++++++++++
 src/mpn_extras/x86_64/flint-mparam.h          | 152 ++++++++++++++++++
 src/mpn_extras/x86_64/skylake/flint-mparam.h  | 152 ++++++++++++++++++
 src/mpn_extras/x86_64/zen3/flint-mparam.h     | 152 ++++++++++++++++++
 10 files changed, 1074 insertions(+), 153 deletions(-)

diff --git a/src/mpn_extras.h b/src/mpn_extras.h
index 365776e11f..68e997ffea 100644
--- a/src/mpn_extras.h
+++ b/src/mpn_extras.h
@@ -22,6 +22,7 @@
 #endif
 
 #include <gmp.h>
+#include "flint-mparam.h"
 #include "longlong.h"
 
 #ifdef __cplusplus
@@ -594,13 +595,7 @@ FLINT_DLL extern const flint_mpn_sqrhigh_normalised_func_t flint_mpn_sqrhigh_nor
 
 #endif
 
-/* FIXME: this tuning is for x86_64_adx with fft_small */
-/* NOTE: we assume that the same cutoff is optimal for both mulhigh and mullow */
-#define FLINT_MPN_MULHIGH_MULDERS_CUTOFF 50
-#define FLINT_MPN_MULHIGH_MUL_CUTOFF 2000
-#define FLINT_MPN_MULHIGH_K_TAB_SIZE 2048
-
-FLINT_DLL extern const signed short flint_mpn_mulhigh_k_tab[FLINT_MPN_MULHIGH_K_TAB_SIZE];
+FLINT_DLL extern const short flint_mpn_mulhigh_k_tab[];
 
 mp_limb_t flint_mpn_mullow_basecase(mp_ptr res, mp_srcptr u, mp_srcptr v, mp_size_t n);
 void _flint_mpn_mullow_n_mulders_recursive(mp_ptr rp, mp_srcptr np, mp_srcptr mp, mp_size_t n);
@@ -667,10 +662,6 @@ void flint_mpn_mul_or_mulhigh_n(mp_ptr rp, mp_srcptr xp, mp_srcptr yp, mp_size_t
         flint_mpn_mul_n(rp, xp, yp, n);
 }
 
-#define FLINT_MPN_SQRHIGH_MULDERS_CUTOFF 90
-#define FLINT_MPN_SQRHIGH_SQR_CUTOFF 2000
-#define FLINT_MPN_SQRHIGH_K_TAB_SIZE 2048
-
 #if FLINT_HAVE_ASSEMBLY_x86_64_adx
 mp_limb_t _flint_mpn_sqrhigh_basecase_even(mp_ptr, mp_srcptr, mp_size_t);
 mp_limb_t _flint_mpn_sqrhigh_basecase_odd(mp_ptr, mp_srcptr, mp_size_t);
diff --git a/src/mpn_extras/arm64/applem1/flint-mparam.h b/src/mpn_extras/arm64/applem1/flint-mparam.h
index 2e739d4f77..77ca7e07c7 100644
--- a/src/mpn_extras/arm64/applem1/flint-mparam.h
+++ b/src/mpn_extras/arm64/applem1/flint-mparam.h
@@ -27,4 +27,156 @@
 #define FFT_N_NUM                                 19
 #define FFT_MULMOD_2EXPP1_CUTOFF                 128
 
+/* FIXME: This tuning is for x86_64_adx with fft_small */
+/* NOTE: We assume that the same cutoff is optimal for both mulhigh and mullow */
+#define FLINT_MPN_MULHIGH_MULDERS_CUTOFF 50
+#define FLINT_MPN_MULHIGH_MUL_CUTOFF 2000
+#define FLINT_MPN_MULHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_SQRHIGH_MULDERS_CUTOFF 90
+#define FLINT_MPN_SQRHIGH_SQR_CUTOFF 2000
+#define FLINT_MPN_SQRHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_MULHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 16, 15, 15, 18, 18, \
+  18, 19, 20, 18, 22, 22, 20, 20, 26, 22, 22, 22, 24, 24, 24, 26, 25, 26, 30, 30, 28, 30, 31, 32, 32, 30, 36, 36, 36, 36, \
+  38, 39, 39, 38, 39, 40, 40, 40, 44, 40, 44, 44, 40, 44, 44, 48, 44, 48, 44, 48, 48, 52, 52, 52, 44, 52, 52, 52, 52, 56, \
+  60, 60, 52, 60, 60, 52, 52, 60, 64, 72, 56, 60, 72, 60, 60, 60, 76, 64, 60, 60, 72, 60, 72, 80, 72, 72, 80, 72, 68, 76, \
+  88, 76, 68, 76, 72, 72, 80, 88, 72, 72, 88, 72, 80, 76, 76, 80, 80, 88, 80, 88, 84, 88, 80, 96, 80, 80, 88, 80, 88, 88, \
+  80, 88, 96, 96, 88, 96, 92, 96, 96, 92, 100, 88, 96, 104, 88, 108, 96, 104, 104, 104, 112, 112, 108, 104, 104, 112, 112, 120, 104, 112, \
+  120, 112, 112, 120, 124, 124, 116, 124, 108, 120, 124, 116, 120, 120, 116, 120, 124, 120, 120, 140, 120, 120, 120, 120, 144, 120, 132, 144, 136, 140, \
+  144, 144, 144, 144, 144, 144, 144, 144, 140, 156, 140, 140, 144, 144, 144, 160, 144, 144, 156, 156, 144, 160, 160, 160, 160, 152, 160, 156, 156, 156, \
+  160, 160, 144, 160, 164, 156, 156, 156, 172, 156, 156, 160, 176, 160, 160, 164, 176, 156, 160, 160, 156, 156, 160, 160, 156, 160, 172, 160, 188, 172, \
+  172, 172, 160, 172, 176, 160, 160, 176, 180, 176, 164, 188, 192, 176, 172, 188, 188, 188, 172, 188, 192, 188, 180, 192, 192, 188, 188, 192, 188, 188, \
+  188, 188, 192, 160, 156, 204, 160, 164, 164, 164, 164, 176, 180, 168, 172, 184, 188, 200, 216, 188, 164, 188, 220, 188, 208, 176, 180, 188, 172, 188, \
+  184, 188, 204, 208, 220, 196, 220, 196, 208, 212, 188, 220, 176, 176, 184, 192, 208, 184, 188, 196, 204, 244, 208, 212, 212, 228, 256, 188, 204, 196, \
+  188, 192, 192, 192, 212, 188, 292, 212, 220, 236, 228, 248, 260, 224, 264, 196, 200, 196, 212, 208, 204, 216, 208, 228, 216, 220, 252, 220, 268, 264, \
+  284, 268, 300, 220, 208, 212, 220, 236, 244, 224, 252, 252, 260, 264, 256, 256, 292, 272, 288, 292, 328, 224, 256, 236, 252, 268, 256, 252, 260, 272, \
+  284, 296, 300, 280, 300, 284, 252, 236, 328, 324, 264, 264, 256, 264, 280, 268, 284, 284, 292, 304, 260, 304, 264, 256, 328, 328, 260, 276, 328, 284, \
+  276, 296, 300, 320, 320, 304, 328, 304, 272, 268, 280, 268, 288, 292, 288, 284, 316, 288, 328, 328, 300, 328, 328, 280, 264, 328, 300, 328, 316, 324, \
+  300, 324, 300, 324, 316, 316, 328, 348, 276, 376, 288, 296, 296, 304, 320, 316, 328, 328, 324, 328, 340, 384, 348, 376, 300, 396, 304, 300, 304, 324, \
+  300, 324, 328, 328, 328, 440, 448, 384, 376, 456, 464, 384, 376, 472, 480, 376, 352, 328, 376, 352, 376, 392, 392, 384, 456, 456, 480, 448, 456, 456, \
+  472, 472, 472, 352, 464, 472, 472, 472, 480, 440, 480, 480, 480, 480, 456, 472, 472, 464, 464, 464, 456, 472, 480, 472, 480, 480, 480, 480, 448, 456, \
+  480, 448, 456, 464, 456, 464, 456, 480, 472, 464, 464, 472, 472, 472, 480, 472, 480, 480, 472, 480, 480, 480, 480, 464, 464, 464, 456, 472, 464, 480, \
+  472, 472, 480, 472, 480, 480, 464, 464, 472, 464, 472, 472, 480, 464, 480, 472, 480, 480, 576, 576, 560, 480, 472, 480, 568, 480, 480, 464, 480, 472, \
+  480, 576, 480, 552, 560, 560, 560, 560, 568, 560, 560, 576, 576, 560, 568, 472, 480, 480, 544, 568, 552, 544, 560, 544, 560, 568, 552, 576, 568, 560, \
+  576, 576, 568, 576, 560, 576, 568, 536, 576, 568, 560, 544, 560, 552, 560, 568, 560, 576, 568, 560, 560, 560, 568, 576, 568, 576, 576, 576, 576, 544, \
+  576, 576, 568, 576, 560, 576, 576, 576, 544, 552, 568, 576, 552, 560, 576, 560, 568, 560, 576, 560, 544, 576, 576, 576, 576, 568, 576, 568, 560, 576, \
+  552, 552, 576, 560, 568, 568, 568, 576, 576, 576, 560, 552, 576, 560, 568, 560, 576, 560, 568, 560, 568, 568, 568, 576, 552, 576, 560, 576, 576, 560, \
+  568, 576, 568, 576, 576, 576, 576, 560, 576, 568, 568, 568, 560, 560, 576, 576, 568, 568, 576, 560, 576, 576, 568, 576, 560, 576, 576, 568, 576, 568, \
+  576, 568, 576, 576, 568, 576, 576, 576, 576, 568, 576, 576, 568, 568, 576, 576, 784, 576, 776, 576, 568, 576, 576, 576, 576, 576, 576, 576, 776, 776, \
+  776, 776, 776, 776, 776, 784, 776, 776, 784, 776, 776, 776, 800, 776, 776, 776, 776, 776, 776, 800, 776, 808, 792, 800, 776, 792, 776, 776, 776, 776, \
+  792, 776, 776, 784, 792, 784, 800, 776, 784, 808, 784, 776, 776, 776, 808, 784, 792, 776, 792, 832, 800, 800, 816, 792, 816, 816, 856, 808, 848, 824, \
+  870, 832, 792, 776, 784, 784, 784, 784, 800, 792, 800, 792, 784, 800, 800, 800, 816, 824, 824, 824, 832, 816, 816, 832, 824, 824, 848, 832, 856, 856, \
+  840, 872, 864, 872, 872, 880, 880, 880, 872, 888, 880, 880, 872, 880, 880, 880, 840, 872, 872, 848, 880, 848, 856, 840, 848, 840, 880, 872, 856, 872, \
+  856, 888, 880, 872, 888, 880, 872, 920, 888, 872, 880, 872, 888, 888, 888, 880, 880, 928, 880, 928, 928, 928, 920, 920, 904, 912, 880, 904, 928, 872, \
+  872, 880, 888, 880, 896, 880, 872, 896, 888, 896, 896, 928, 904, 896, 896, 912, 904, 904, 920, 880, 912, 920, 928, 928, 880, 920, 920, 880, 888, 904, \
+  896, 904, 928, 896, 912, 896, 912, 920, 912, 912, 928, 928, 928, 920, 928, 928, 928, 928, 928, 928, 912, 904, 912, 896, 904, 904, 920, 920, 920, 928, \
+  928, 920, 928, 928, 928, 912, 928, 912, 928, 928, 928, 912, 912, 912, 928, 928, 928, 896, 928, 928, 912, 928, 928, 928, 912, 928, 912, 928, 928, 912, \
+  928, 912, 928, 928, 928, 928, 928, 912, 928, 928, 928, 928, 912, 912, 928, 912, 928, 1024, 928, 928, 928, 928, 928, 928, 1056, 912, 928, 928, 1024, 1024, \
+  928, 928, 1024, 928, 928, 928, 928, 928, 928, 1040, 1040, 928, 1056, 1024, 1072, 1024, 1040, 1040, 1040, 1024, 1088, 1056, 1056, 1088, 1040, 1056, 1072, 1072, 1056, 1056, \
+  1024, 1088, 1040, 1024, 1040, 1040, 1024, 1056, 1056, 1056, 1040, 1072, 1056, 1040, 1056, 1056, 1056, 1056, 1056, 1056, 1056, 1120, 1056, 1088, 1056, 1120, 1088, 1072, 1104, 1104, \
+  1104, 1120, 1088, 1088, 1072, 1088, 1120, 1104, 1088, 1104, 1088, 1072, 1104, 1088, 1120, 1088, 1072, 1072, 1072, 1088, 1088, 1072, 1072, 1088, 1104, 1152, 1104, 1104, 1088, 1104, \
+  1136, 1088, 1104, 1152, 1152, 1152, 1136, 1120, 1136, 1152, 1120, 1152, 1088, 1120, 1104, 1120, 1136, 1104, 1136, 1088, 1136, 1104, 1088, 1104, 1120, 1104, 1104, 1120, 1136, 1136, \
+  1120, 1136, 1136, 1136, 1120, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1104, 1152, 1120, 1136, 1120, 1120, 1152, 1120, 1136, 1152, 1136, 1152, 1120, 1152, 1136, 1136, 1136, 1136, \
+  1136, 1152, 1152, 1152, 1152, 1120, 1120, 1152, 1136, 1136, 1136, 1152, 1152, 1120, 1152, 1152, 1152, 1152, 1152, 1104, 1152, 1152, 1120, 1136, 1152, 1120, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1344, 1152, 1344, 1344, 1344, 1152, 1152, 1152, 1152, 1344, 1328, 1328, 1328, 1152, 1344, 1152, 1344, 1152, 1344, 1152, 1152, 1328, 1152, 1328, 1344, 1328, 1344, 1328, 1344, \
+  1344, 1312, 1328, 1328, 1328, 1344, 1344, 1344, 1328, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, \
+  1328, 1344, 1344, 1344, 1344, 1328, 1344, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1573, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1583, 1568, 1568, 1552, 1568, 1552, 1568, \
+  1568, 1568, 1584, 1568, 1584, 1568, 1568, 1568, 1552, 1552, 1552, 1568, 1552, 1584, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1584, 1552, 1584, 1552, 1617, 1568, 1584, \
+  1552, 1552, 1584, 1584, 1552, 1625, 1626, 1627, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1632, 1636, 1632, 1638, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1648, 1669, 1648, 1671, 1632, 1664, 1648, 1632, 1648, 1648, 1648, 1632, \
+  1632, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1648, 1664, 1648, 1648, 1648, 1648, 1648, 1648, \
+  1680, 1664, 1680, 1696, 1680, 1680, 1664, 1680, 1680, 1648, 1632, 1680, 1696, 1632, 1648, 1648, 1632, 1680, 1680, 1664, 1664, 1664, 1648, 1680, 1664, 1680, 1664, 1680, 1664, 1664, \
+  1680, 1696, 1664, 1696, 1712, 1712, 1696, 1680, 1712, 1696, 1728, 1712, 1696, 1728, 1728, 1712, 1728, 1648, 1680, 1696, 1712, 1696, 1712, 1696, 1696, 1680, 1696, 1696, 1696, 1712, \
+  1696, 1696, 1696, 1696, 1712, 1728, 1696, 1728, 1696, 1696, 1712, 1728, 1712, 1728, 1712, 1680, 1696, 1728, 1712, 1696, 1696, 1696, 1712, 1712, 1728, 1696, 1728, 1712, 1712, 1728, \
+  1696, 1696, 1696, 1712, 1696, 1728, 1712, 1712, 1712, 1728, 1696, 1712, 1728, 1728, 1696, 1728, 1728, 1728, 1728, 1728, 1680, 1712, 1728, 1696, 1728, 1728, 1728, 1728, 1696, 1728, \
+  1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1728, 1696, 1728, 1712, 1712, 1712, 1712, 1728, 1712, 1712, 1712, 1728, 1712, 1728, 1728, 1728, \
+  1728, 1712, 1728, 1728, 1712, 1728, 1728, 1712, 1712, 1728, 1712, 1712, 1728, 1728, 1712, 1728, 1712, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1712, \
+  1728, 1712, 1712, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, \
+  1728, 1728, 1712, 1728, 1728, 1824, 1728, 1728, 1728, 1728, 1824, 1728, 1840, 1728, 1728, 1728, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1728, 1728, 1856, 1856, 1856, 1856, 1728, \
+  1728, 1856, 1856, 1728, 1856, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1856, 1856, 1856, 1840, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1840, 1904, 1856, 1856, 1840, 1840, 1856, \
+  1856, 1840, 1856, 1840, 1856, 1856, 1856, 1856, 1952, 1856, 1856, 1856, 1856, 1952, 1904, 1904, 1856, 1856, 1856, 1920, 1952, 2001, 1952, 1984, 1952, 1936, 1952, 1904, 1968, 1920, \
+  1984, 1920, 1968, 1920, 1936, 1856, 2000, 1920, 1936, 1952, 2000, 1968, 1984, 1968, 1984, 2000, 1952, 2000, 2016, 1984, 2000, 2016, 1984, 1664, 2016, 1984, 2016, 1968, 2016, 2016, \
+  1744, 2016, 2016, 1968, 2000, 1728, 1712, 1696
+
+#define FLINT_MPN_SQRHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 29, 0, 0, 31, 0, 31, \
+  0, 32, 0, 34, 0, 36, 36, 40, 0, 40, 40, 40, 0, 44, 0, 44, 44, 48, 0, 52, 48, 52, 44, 44, 48, 48, 48, 48, 48, 48, \
+  48, 48, 48, 48, 52, 52, 52, 52, 52, 56, 56, 52, 56, 56, 56, 56, 56, 56, 56, 56, 60, 60, 68, 64, 60, 60, 60, 60, 64, 64, \
+  64, 68, 68, 68, 64, 64, 68, 68, 72, 72, 68, 68, 68, 72, 76, 80, 72, 72, 72, 88, 76, 76, 80, 80, 76, 80, 76, 80, 84, 80, \
+  88, 88, 80, 84, 88, 80, 80, 84, 92, 88, 92, 88, 88, 88, 88, 96, 88, 108, 100, 92, 88, 88, 104, 100, 100, 92, 104, 108, 100, 92, \
+  104, 100, 104, 96, 108, 104, 96, 96, 104, 100, 100, 104, 112, 116, 108, 104, 104, 116, 108, 104, 104, 120, 116, 104, 108, 132, 116, 108, 120, 108, \
+  108, 108, 132, 108, 120, 112, 112, 116, 132, 128, 116, 124, 128, 116, 132, 120, 132, 120, 124, 120, 132, 120, 124, 128, 120, 128, 128, 132, 144, 124, \
+  128, 124, 140, 128, 128, 124, 136, 132, 128, 128, 140, 144, 128, 128, 140, 136, 132, 144, 148, 152, 144, 132, 160, 156, 140, 144, 156, 144, 140, 144, \
+  140, 156, 156, 156, 140, 144, 168, 156, 156, 164, 168, 156, 156, 160, 144, 144, 180, 156, 152, 168, 156, 160, 156, 148, 180, 168, 180, 156, 164, 156, \
+  156, 172, 156, 156, 156, 180, 180, 172, 180, 168, 164, 172, 164, 172, 176, 176, 168, 176, 172, 176, 180, 168, 176, 180, 180, 180, 192, 184, 180, 176, \
+  204, 176, 188, 180, 188, 180, 204, 180, 192, 204, 180, 192, 180, 204, 228, 192, 188, 192, 204, 180, 192, 216, 200, 216, 228, 216, 204, 216, 188, 216, \
+  216, 204, 216, 192, 204, 212, 228, 204, 228, 216, 204, 216, 192, 204, 204, 212, 204, 216, 204, 216, 228, 228, 224, 212, 204, 216, 216, 224, 228, 212, \
+  216, 228, 212, 204, 204, 216, 216, 216, 228, 216, 220, 224, 228, 220, 228, 228, 236, 224, 260, 224, 228, 228, 260, 228, 248, 252, 264, 248, 216, 212, \
+  212, 212, 220, 216, 216, 220, 216, 224, 216, 228, 232, 224, 220, 224, 240, 244, 236, 244, 232, 256, 288, 240, 236, 288, 260, 260, 264, 232, 228, 228, \
+  228, 236, 236, 228, 236, 236, 236, 248, 256, 260, 232, 236, 264, 256, 260, 252, 284, 252, 264, 276, 244, 296, 244, 240, 244, 248, 240, 252, 256, 260, \
+  260, 252, 252, 272, 252, 272, 260, 296, 268, 260, 256, 276, 272, 264, 312, 284, 256, 252, 252, 252, 264, 252, 256, 260, 264, 276, 292, 268, 264, 276, \
+  264, 260, 264, 304, 288, 296, 296, 296, 288, 296, 272, 280, 264, 264, 272, 264, 288, 288, 280, 288, 272, 280, 296, 296, 280, 288, 296, 320, 344, 320, \
+  344, 272, 344, 344, 304, 288, 280, 280, 312, 280, 280, 304, 304, 312, 304, 296, 288, 328, 320, 352, 320, 320, 328, 360, 344, 344, 360, 288, 288, 304, \
+  288, 296, 320, 320, 312, 312, 304, 328, 336, 312, 312, 360, 336, 344, 344, 336, 360, 360, 296, 296, 304, 360, 328, 328, 312, 320, 320, 328, 312, 344, \
+  344, 328, 344, 344, 368, 360, 352, 360, 392, 392, 368, 320, 312, 392, 312, 328, 344, 336, 344, 328, 360, 352, 352, 360, 360, 360, 368, 408, 360, 376, \
+  392, 392, 376, 336, 344, 352, 360, 352, 344, 344, 384, 344, 360, 376, 392, 368, 360, 408, 408, 448, 432, 384, 392, 336, 360, 344, 360, 360, 368, 376, \
+  376, 360, 368, 408, 368, 376, 376, 376, 432, 376, 384, 464, 432, 344, 432, 376, 344, 344, 384, 344, 384, 376, 400, 432, 456, 432, 456, 392, 432, 392, \
+  448, 456, 360, 376, 456, 408, 384, 368, 376, 432, 376, 472, 464, 504, 448, 360, 408, 456, 376, 408, 424, 424, 448, 440, 456, 392, 408, 384, 408, 392, \
+  384, 416, 424, 432, 400, 472, 480, 408, 432, 432, 464, 456, 504, 464, 456, 472, 496, 416, 392, 424, 504, 400, 440, 432, 472, 448, 456, 456, 432, 448, \
+  456, 504, 504, 512, 496, 504, 424, 416, 408, 432, 544, 432, 440, 456, 448, 448, 464, 472, 480, 552, 552, 544, 552, 560, 552, 544, 544, 544, 552, 552, \
+  552, 552, 552, 552, 552, 560, 552, 552, 560, 560, 560, 560, 568, 576, 568, 592, 576, 560, 560, 560, 560, 568, 568, 576, 568, 568, 576, 568, 568, 576, \
+  568, 568, 600, 592, 576, 608, 576, 576, 576, 576, 584, 584, 576, 592, 592, 600, 584, 592, 584, 600, 600, 600, 584, 624, 584, 592, 600, 592, 616, 592, \
+  592, 592, 592, 592, 592, 592, 600, 608, 600, 608, 600, 600, 600, 624, 616, 608, 616, 600, 632, 608, 608, 608, 616, 608, 608, 608, 608, 616, 608, 664, \
+  664, 632, 656, 616, 664, 624, 616, 632, 632, 616, 624, 624, 624, 632, 624, 624, 624, 624, 648, 632, 624, 624, 872, 872, 656, 664, 696, 872, 872, 872, \
+  632, 872, 872, 896, 872, 896, 872, 896, 880, 872, 896, 872, 888, 872, 872, 872, 872, 872, 888, 872, 880, 824, 872, 856, 880, 888, 800, 848, 800, 880, \
+  848, 800, 808, 872, 872, 864, 824, 840, 872, 872, 872, 872, 872, 872, 872, 872, 872, 872, 880, 928, 872, 920, 872, 920, 888, 880, 872, 880, 872, 872, \
+  872, 888, 880, 888, 888, 872, 888, 872, 880, 896, 920, 920, 880, 928, 904, 872, 888, 904, 872, 872, 872, 872, 880, 888, 872, 872, 872, 880, 872, 904, \
+  920, 888, 888, 872, 880, 880, 888, 896, 896, 880, 872, 904, 880, 912, 896, 872, 904, 904, 912, 880, 880, 920, 912, 896, 928, 928, 872, 872, 872, 872, \
+  880, 880, 888, 888, 888, 912, 880, 880, 880, 912, 896, 896, 928, 896, 912, 912, 896, 928, 928, 928, 928, 912, 880, 928, 880, 880, 896, 880, 896, 880, \
+  896, 880, 880, 912, 912, 880, 896, 880, 896, 912, 880, 880, 928, 912, 912, 928, 928, 896, 928, 912, 928, 928, 928, 928, 928, 928, 880, 880, 880, 880, \
+  880, 912, 896, 912, 912, 896, 928, 896, 928, 896, 928, 928, 928, 928, 912, 880, 928, 912, 896, 928, 896, 880, 912, 896, 912, 896, 896, 896, 928, 896, \
+  912, 928, 912, 928, 912, 928, 912, 880, 928, 928, 880, 928, 928, 880, 896, 928, 880, 896, 912, 928, 928, 896, 912, 928, 912, 928, 1024, 928, 928, 1040, \
+  912, 928, 1024, 1024, 928, 928, 928, 928, 912, 1040, 1072, 912, 1072, 1072, 1056, 1040, 1072, 1088, 1104, 1040, 1040, 928, 1024, 928, 928, 1056, 928, 928, 1056, 1040, \
+  928, 1056, 1024, 1056, 1056, 1056, 1104, 1024, 1056, 1072, 1056, 1056, 1088, 1072, 1120, 1104, 1072, 1072, 1072, 1104, 1120, 1024, 1120, 1120, 1056, 1024, 1040, 1024, 1040, 1040, \
+  1040, 1024, 1040, 1056, 1040, 1088, 1040, 1056, 1120, 1040, 1040, 1072, 1072, 1088, 1104, 1088, 1104, 1088, 1088, 1056, 1120, 1104, 1152, 1104, 1088, 1120, 1104, 1120, 1024, 1120, \
+  1152, 1136, 1152, 1056, 1056, 1072, 1056, 1152, 1088, 1056, 1104, 1072, 1104, 1088, 1120, 1072, 1104, 1088, 1088, 1120, 1120, 1120, 1152, 1136, 1120, 1120, 1152, 1120, 1136, 1152, \
+  1152, 1072, 1136, 1136, 1088, 1152, 1136, 1136, 1104, 1056, 1072, 1088, 1104, 1104, 1120, 1120, 1104, 1104, 1104, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1136, 1072, \
+  1152, 1136, 1152, 1152, 1104, 1152, 1104, 1152, 1152, 1088, 1120, 1152, 1136, 1136, 1120, 1136, 1120, 1152, 1136, 1136, 1120, 1136, 1152, 1136, 1152, 1136, 1136, 1120, 1152, 1152, \
+  1104, 1152, 1152, 1152, 1104, 1120, 1104, 1120, 1120, 1120, 1120, 1136, 1136, 1136, 1136, 1152, 1120, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1104, \
+  1120, 1152, 1136, 1136, 1136, 1136, 1136, 1136, 1120, 1152, 1152, 1152, 1136, 1104, 1152, 1136, 1136, 1152, 1136, 1120, 1136, 1152, 1152, 1136, 1136, 1120, 1136, 1136, 1136, 1120, \
+  1152, 1152, 1152, 1136, 1136, 1136, 1152, 1104, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1152, \
+  1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, \
+  1120, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1136, \
+  1152, 1152, 1152, 1104, 1120, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1152, 1120, 1152, 1136, 1152, 1152, 1120, 1152, 1120, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1120, 1152, 1152, 1136, 1152, 1136, 1552, 1552, 1136, 1136, 1152, 1552, 1136, 1136, 1584, 1552, 1552, 1552, \
+  1152, 1552, 1552, 1152, 1584, 1552, 1152, 1152, 1552, 1584, 1152, 1152, 1552, 1584, 1568, 1552, 1552, 1552, 1152, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1625, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1568, 1632, 1552, 1632, 1568, 1584, 1568, 1568, 1584, 1600, 1552, 1552, 1632, 1600, 1632, 1632, 1632, \
+  1632, 1568, 1584, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1552, 1662, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1568, 1600, 1632, 1552, 1616, 1632, 1632, 1632, 1584, 1632, \
+  1632, 1552, 1632, 1632, 1632, 1568, 1600, 1632, 1648, 1616, 1632, 1648, 1632, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1632, 1664, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1648, 1648, 1648, 1616, 1632, 1680, 1632, 1680, 1648, 1632, 1664, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1648, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1648, 1664, 1648, 1648, 1632, 1648, 1632, 1680, 1664, 1648, 1680, 1664, 1696, 1632, 1664, 1680, 1632, 1648, 1696, \
+  1680, 1632, 1632, 1648, 1648, 1648, 1632, 1664, 1632, 1648, 1648, 1632, 1648, 1648, 1632, 1664, 1664, 1680, 1680, 1632, 1664, 1664, 1648, 1648, 1712, 1728, 1664, 1712, 1696, 1712, \
+  1680, 1632, 1728, 1648, 1728, 1728, 1712, 1648, 1632, 1632, 1664, 1648, 1664, 1664, 1680, 1712, 1664, 1632, 1696, 1664, 1712, 1696, 1680, 1680, 1696, 1680, 1680, 1712, 1648, 1712, \
+  1632, 1728, 1696, 1648, 1712, 1632, 1712, 1696, 1648, 1680, 1648, 1664, 1648, 1696, 1712, 1648, 1648, 1680, 1664, 1696, 1728, 1696, 1712, 1728, 1696, 1728, 1712, 1664, 1680, 1728, \
+  1712, 1712, 1712, 1728, 1728, 1712, 1728, 1696, 1728, 1712, 1696, 1728, 1728, 1680, 1728, 1712, 1664, 1680, 1680, 1696, 1712, 1696, 1696, 1696, 1728, 1696, 1728, 1728, 1696, 1712, \
+  1712, 1664, 1712, 1680, 1664, 1728, 1728, 1664, 1696, 1696, 1680, 1712, 1680, 1712, 1696, 1728, 1696, 1696, 1728, 1696, 1712, 1696, 1712, 1712, 1712, 1728, 1712, 1696, 1728, 1680, \
+  1696, 1712, 1712, 1728, 1712, 1728, 1696, 1728, 1776, 1728, 1696, 1776, 1728, 1728, 1712, 1712, 1824, 1856, 1728, 1824, 1728, 1728, 1712, 1728, 1728, 1728, 1856, 1696, 1728, 1840, \
+  1712, 1712, 1824, 1856, 1792, 1712, 1840, 1728, 1808, 1728, 1824, 1824, 1840, 1824, 1824, 1856, 1856, 1824, 1856, 1840, 1696, 1856, 1840, 1840, 1856, 1856, 1824, 1712, 1792, 1856, \
+  1824, 1728, 1808, 1792, 1856, 1728, 1792, 1840, 1808, 1808, 1712, 1808, 1840, 1808, 1824, 1824, 1824, 1840, 1824, 1840, 1856, 1824, 1728, 1856, 1856, 1824, 1856, 1856, 1792, 1792, \
+  1856, 1824, 1856, 1824, 1824, 1856, 1808, 1824, 1856, 1856, 1840, 1840, 1840, 1840, 1856, 1840, 1840, 1856, 1824, 1840, 1808, 1824, 1840, 1856, 1856, 1824, 1856, 1840, 1840, 1840, \
+  1824, 1824, 1840, 1840, 1840, 1856, 1856, 1856
+
 #endif
diff --git a/src/mpn_extras/arm64/flint-mparam.h b/src/mpn_extras/arm64/flint-mparam.h
index 0112747333..8c5e03d736 100644
--- a/src/mpn_extras/arm64/flint-mparam.h
+++ b/src/mpn_extras/arm64/flint-mparam.h
@@ -29,4 +29,156 @@
 #define FFT_N_NUM                                 19
 #define FFT_MULMOD_2EXPP1_CUTOFF                 128
 
+/* FIXME: This tuning is for x86_64_adx with fft_small */
+/* NOTE: We assume that the same cutoff is optimal for both mulhigh and mullow */
+#define FLINT_MPN_MULHIGH_MULDERS_CUTOFF 50
+#define FLINT_MPN_MULHIGH_MUL_CUTOFF 2000
+#define FLINT_MPN_MULHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_SQRHIGH_MULDERS_CUTOFF 90
+#define FLINT_MPN_SQRHIGH_SQR_CUTOFF 2000
+#define FLINT_MPN_SQRHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_MULHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 16, 15, 15, 18, 18, \
+  18, 19, 20, 18, 22, 22, 20, 20, 26, 22, 22, 22, 24, 24, 24, 26, 25, 26, 30, 30, 28, 30, 31, 32, 32, 30, 36, 36, 36, 36, \
+  38, 39, 39, 38, 39, 40, 40, 40, 44, 40, 44, 44, 40, 44, 44, 48, 44, 48, 44, 48, 48, 52, 52, 52, 44, 52, 52, 52, 52, 56, \
+  60, 60, 52, 60, 60, 52, 52, 60, 64, 72, 56, 60, 72, 60, 60, 60, 76, 64, 60, 60, 72, 60, 72, 80, 72, 72, 80, 72, 68, 76, \
+  88, 76, 68, 76, 72, 72, 80, 88, 72, 72, 88, 72, 80, 76, 76, 80, 80, 88, 80, 88, 84, 88, 80, 96, 80, 80, 88, 80, 88, 88, \
+  80, 88, 96, 96, 88, 96, 92, 96, 96, 92, 100, 88, 96, 104, 88, 108, 96, 104, 104, 104, 112, 112, 108, 104, 104, 112, 112, 120, 104, 112, \
+  120, 112, 112, 120, 124, 124, 116, 124, 108, 120, 124, 116, 120, 120, 116, 120, 124, 120, 120, 140, 120, 120, 120, 120, 144, 120, 132, 144, 136, 140, \
+  144, 144, 144, 144, 144, 144, 144, 144, 140, 156, 140, 140, 144, 144, 144, 160, 144, 144, 156, 156, 144, 160, 160, 160, 160, 152, 160, 156, 156, 156, \
+  160, 160, 144, 160, 164, 156, 156, 156, 172, 156, 156, 160, 176, 160, 160, 164, 176, 156, 160, 160, 156, 156, 160, 160, 156, 160, 172, 160, 188, 172, \
+  172, 172, 160, 172, 176, 160, 160, 176, 180, 176, 164, 188, 192, 176, 172, 188, 188, 188, 172, 188, 192, 188, 180, 192, 192, 188, 188, 192, 188, 188, \
+  188, 188, 192, 160, 156, 204, 160, 164, 164, 164, 164, 176, 180, 168, 172, 184, 188, 200, 216, 188, 164, 188, 220, 188, 208, 176, 180, 188, 172, 188, \
+  184, 188, 204, 208, 220, 196, 220, 196, 208, 212, 188, 220, 176, 176, 184, 192, 208, 184, 188, 196, 204, 244, 208, 212, 212, 228, 256, 188, 204, 196, \
+  188, 192, 192, 192, 212, 188, 292, 212, 220, 236, 228, 248, 260, 224, 264, 196, 200, 196, 212, 208, 204, 216, 208, 228, 216, 220, 252, 220, 268, 264, \
+  284, 268, 300, 220, 208, 212, 220, 236, 244, 224, 252, 252, 260, 264, 256, 256, 292, 272, 288, 292, 328, 224, 256, 236, 252, 268, 256, 252, 260, 272, \
+  284, 296, 300, 280, 300, 284, 252, 236, 328, 324, 264, 264, 256, 264, 280, 268, 284, 284, 292, 304, 260, 304, 264, 256, 328, 328, 260, 276, 328, 284, \
+  276, 296, 300, 320, 320, 304, 328, 304, 272, 268, 280, 268, 288, 292, 288, 284, 316, 288, 328, 328, 300, 328, 328, 280, 264, 328, 300, 328, 316, 324, \
+  300, 324, 300, 324, 316, 316, 328, 348, 276, 376, 288, 296, 296, 304, 320, 316, 328, 328, 324, 328, 340, 384, 348, 376, 300, 396, 304, 300, 304, 324, \
+  300, 324, 328, 328, 328, 440, 448, 384, 376, 456, 464, 384, 376, 472, 480, 376, 352, 328, 376, 352, 376, 392, 392, 384, 456, 456, 480, 448, 456, 456, \
+  472, 472, 472, 352, 464, 472, 472, 472, 480, 440, 480, 480, 480, 480, 456, 472, 472, 464, 464, 464, 456, 472, 480, 472, 480, 480, 480, 480, 448, 456, \
+  480, 448, 456, 464, 456, 464, 456, 480, 472, 464, 464, 472, 472, 472, 480, 472, 480, 480, 472, 480, 480, 480, 480, 464, 464, 464, 456, 472, 464, 480, \
+  472, 472, 480, 472, 480, 480, 464, 464, 472, 464, 472, 472, 480, 464, 480, 472, 480, 480, 576, 576, 560, 480, 472, 480, 568, 480, 480, 464, 480, 472, \
+  480, 576, 480, 552, 560, 560, 560, 560, 568, 560, 560, 576, 576, 560, 568, 472, 480, 480, 544, 568, 552, 544, 560, 544, 560, 568, 552, 576, 568, 560, \
+  576, 576, 568, 576, 560, 576, 568, 536, 576, 568, 560, 544, 560, 552, 560, 568, 560, 576, 568, 560, 560, 560, 568, 576, 568, 576, 576, 576, 576, 544, \
+  576, 576, 568, 576, 560, 576, 576, 576, 544, 552, 568, 576, 552, 560, 576, 560, 568, 560, 576, 560, 544, 576, 576, 576, 576, 568, 576, 568, 560, 576, \
+  552, 552, 576, 560, 568, 568, 568, 576, 576, 576, 560, 552, 576, 560, 568, 560, 576, 560, 568, 560, 568, 568, 568, 576, 552, 576, 560, 576, 576, 560, \
+  568, 576, 568, 576, 576, 576, 576, 560, 576, 568, 568, 568, 560, 560, 576, 576, 568, 568, 576, 560, 576, 576, 568, 576, 560, 576, 576, 568, 576, 568, \
+  576, 568, 576, 576, 568, 576, 576, 576, 576, 568, 576, 576, 568, 568, 576, 576, 784, 576, 776, 576, 568, 576, 576, 576, 576, 576, 576, 576, 776, 776, \
+  776, 776, 776, 776, 776, 784, 776, 776, 784, 776, 776, 776, 800, 776, 776, 776, 776, 776, 776, 800, 776, 808, 792, 800, 776, 792, 776, 776, 776, 776, \
+  792, 776, 776, 784, 792, 784, 800, 776, 784, 808, 784, 776, 776, 776, 808, 784, 792, 776, 792, 832, 800, 800, 816, 792, 816, 816, 856, 808, 848, 824, \
+  870, 832, 792, 776, 784, 784, 784, 784, 800, 792, 800, 792, 784, 800, 800, 800, 816, 824, 824, 824, 832, 816, 816, 832, 824, 824, 848, 832, 856, 856, \
+  840, 872, 864, 872, 872, 880, 880, 880, 872, 888, 880, 880, 872, 880, 880, 880, 840, 872, 872, 848, 880, 848, 856, 840, 848, 840, 880, 872, 856, 872, \
+  856, 888, 880, 872, 888, 880, 872, 920, 888, 872, 880, 872, 888, 888, 888, 880, 880, 928, 880, 928, 928, 928, 920, 920, 904, 912, 880, 904, 928, 872, \
+  872, 880, 888, 880, 896, 880, 872, 896, 888, 896, 896, 928, 904, 896, 896, 912, 904, 904, 920, 880, 912, 920, 928, 928, 880, 920, 920, 880, 888, 904, \
+  896, 904, 928, 896, 912, 896, 912, 920, 912, 912, 928, 928, 928, 920, 928, 928, 928, 928, 928, 928, 912, 904, 912, 896, 904, 904, 920, 920, 920, 928, \
+  928, 920, 928, 928, 928, 912, 928, 912, 928, 928, 928, 912, 912, 912, 928, 928, 928, 896, 928, 928, 912, 928, 928, 928, 912, 928, 912, 928, 928, 912, \
+  928, 912, 928, 928, 928, 928, 928, 912, 928, 928, 928, 928, 912, 912, 928, 912, 928, 1024, 928, 928, 928, 928, 928, 928, 1056, 912, 928, 928, 1024, 1024, \
+  928, 928, 1024, 928, 928, 928, 928, 928, 928, 1040, 1040, 928, 1056, 1024, 1072, 1024, 1040, 1040, 1040, 1024, 1088, 1056, 1056, 1088, 1040, 1056, 1072, 1072, 1056, 1056, \
+  1024, 1088, 1040, 1024, 1040, 1040, 1024, 1056, 1056, 1056, 1040, 1072, 1056, 1040, 1056, 1056, 1056, 1056, 1056, 1056, 1056, 1120, 1056, 1088, 1056, 1120, 1088, 1072, 1104, 1104, \
+  1104, 1120, 1088, 1088, 1072, 1088, 1120, 1104, 1088, 1104, 1088, 1072, 1104, 1088, 1120, 1088, 1072, 1072, 1072, 1088, 1088, 1072, 1072, 1088, 1104, 1152, 1104, 1104, 1088, 1104, \
+  1136, 1088, 1104, 1152, 1152, 1152, 1136, 1120, 1136, 1152, 1120, 1152, 1088, 1120, 1104, 1120, 1136, 1104, 1136, 1088, 1136, 1104, 1088, 1104, 1120, 1104, 1104, 1120, 1136, 1136, \
+  1120, 1136, 1136, 1136, 1120, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1104, 1152, 1120, 1136, 1120, 1120, 1152, 1120, 1136, 1152, 1136, 1152, 1120, 1152, 1136, 1136, 1136, 1136, \
+  1136, 1152, 1152, 1152, 1152, 1120, 1120, 1152, 1136, 1136, 1136, 1152, 1152, 1120, 1152, 1152, 1152, 1152, 1152, 1104, 1152, 1152, 1120, 1136, 1152, 1120, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1344, 1152, 1344, 1344, 1344, 1152, 1152, 1152, 1152, 1344, 1328, 1328, 1328, 1152, 1344, 1152, 1344, 1152, 1344, 1152, 1152, 1328, 1152, 1328, 1344, 1328, 1344, 1328, 1344, \
+  1344, 1312, 1328, 1328, 1328, 1344, 1344, 1344, 1328, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, \
+  1328, 1344, 1344, 1344, 1344, 1328, 1344, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1573, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1583, 1568, 1568, 1552, 1568, 1552, 1568, \
+  1568, 1568, 1584, 1568, 1584, 1568, 1568, 1568, 1552, 1552, 1552, 1568, 1552, 1584, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1584, 1552, 1584, 1552, 1617, 1568, 1584, \
+  1552, 1552, 1584, 1584, 1552, 1625, 1626, 1627, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1632, 1636, 1632, 1638, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1648, 1669, 1648, 1671, 1632, 1664, 1648, 1632, 1648, 1648, 1648, 1632, \
+  1632, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1648, 1664, 1648, 1648, 1648, 1648, 1648, 1648, \
+  1680, 1664, 1680, 1696, 1680, 1680, 1664, 1680, 1680, 1648, 1632, 1680, 1696, 1632, 1648, 1648, 1632, 1680, 1680, 1664, 1664, 1664, 1648, 1680, 1664, 1680, 1664, 1680, 1664, 1664, \
+  1680, 1696, 1664, 1696, 1712, 1712, 1696, 1680, 1712, 1696, 1728, 1712, 1696, 1728, 1728, 1712, 1728, 1648, 1680, 1696, 1712, 1696, 1712, 1696, 1696, 1680, 1696, 1696, 1696, 1712, \
+  1696, 1696, 1696, 1696, 1712, 1728, 1696, 1728, 1696, 1696, 1712, 1728, 1712, 1728, 1712, 1680, 1696, 1728, 1712, 1696, 1696, 1696, 1712, 1712, 1728, 1696, 1728, 1712, 1712, 1728, \
+  1696, 1696, 1696, 1712, 1696, 1728, 1712, 1712, 1712, 1728, 1696, 1712, 1728, 1728, 1696, 1728, 1728, 1728, 1728, 1728, 1680, 1712, 1728, 1696, 1728, 1728, 1728, 1728, 1696, 1728, \
+  1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1728, 1696, 1728, 1712, 1712, 1712, 1712, 1728, 1712, 1712, 1712, 1728, 1712, 1728, 1728, 1728, \
+  1728, 1712, 1728, 1728, 1712, 1728, 1728, 1712, 1712, 1728, 1712, 1712, 1728, 1728, 1712, 1728, 1712, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1712, \
+  1728, 1712, 1712, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, \
+  1728, 1728, 1712, 1728, 1728, 1824, 1728, 1728, 1728, 1728, 1824, 1728, 1840, 1728, 1728, 1728, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1728, 1728, 1856, 1856, 1856, 1856, 1728, \
+  1728, 1856, 1856, 1728, 1856, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1856, 1856, 1856, 1840, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1840, 1904, 1856, 1856, 1840, 1840, 1856, \
+  1856, 1840, 1856, 1840, 1856, 1856, 1856, 1856, 1952, 1856, 1856, 1856, 1856, 1952, 1904, 1904, 1856, 1856, 1856, 1920, 1952, 2001, 1952, 1984, 1952, 1936, 1952, 1904, 1968, 1920, \
+  1984, 1920, 1968, 1920, 1936, 1856, 2000, 1920, 1936, 1952, 2000, 1968, 1984, 1968, 1984, 2000, 1952, 2000, 2016, 1984, 2000, 2016, 1984, 1664, 2016, 1984, 2016, 1968, 2016, 2016, \
+  1744, 2016, 2016, 1968, 2000, 1728, 1712, 1696
+
+#define FLINT_MPN_SQRHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 29, 0, 0, 31, 0, 31, \
+  0, 32, 0, 34, 0, 36, 36, 40, 0, 40, 40, 40, 0, 44, 0, 44, 44, 48, 0, 52, 48, 52, 44, 44, 48, 48, 48, 48, 48, 48, \
+  48, 48, 48, 48, 52, 52, 52, 52, 52, 56, 56, 52, 56, 56, 56, 56, 56, 56, 56, 56, 60, 60, 68, 64, 60, 60, 60, 60, 64, 64, \
+  64, 68, 68, 68, 64, 64, 68, 68, 72, 72, 68, 68, 68, 72, 76, 80, 72, 72, 72, 88, 76, 76, 80, 80, 76, 80, 76, 80, 84, 80, \
+  88, 88, 80, 84, 88, 80, 80, 84, 92, 88, 92, 88, 88, 88, 88, 96, 88, 108, 100, 92, 88, 88, 104, 100, 100, 92, 104, 108, 100, 92, \
+  104, 100, 104, 96, 108, 104, 96, 96, 104, 100, 100, 104, 112, 116, 108, 104, 104, 116, 108, 104, 104, 120, 116, 104, 108, 132, 116, 108, 120, 108, \
+  108, 108, 132, 108, 120, 112, 112, 116, 132, 128, 116, 124, 128, 116, 132, 120, 132, 120, 124, 120, 132, 120, 124, 128, 120, 128, 128, 132, 144, 124, \
+  128, 124, 140, 128, 128, 124, 136, 132, 128, 128, 140, 144, 128, 128, 140, 136, 132, 144, 148, 152, 144, 132, 160, 156, 140, 144, 156, 144, 140, 144, \
+  140, 156, 156, 156, 140, 144, 168, 156, 156, 164, 168, 156, 156, 160, 144, 144, 180, 156, 152, 168, 156, 160, 156, 148, 180, 168, 180, 156, 164, 156, \
+  156, 172, 156, 156, 156, 180, 180, 172, 180, 168, 164, 172, 164, 172, 176, 176, 168, 176, 172, 176, 180, 168, 176, 180, 180, 180, 192, 184, 180, 176, \
+  204, 176, 188, 180, 188, 180, 204, 180, 192, 204, 180, 192, 180, 204, 228, 192, 188, 192, 204, 180, 192, 216, 200, 216, 228, 216, 204, 216, 188, 216, \
+  216, 204, 216, 192, 204, 212, 228, 204, 228, 216, 204, 216, 192, 204, 204, 212, 204, 216, 204, 216, 228, 228, 224, 212, 204, 216, 216, 224, 228, 212, \
+  216, 228, 212, 204, 204, 216, 216, 216, 228, 216, 220, 224, 228, 220, 228, 228, 236, 224, 260, 224, 228, 228, 260, 228, 248, 252, 264, 248, 216, 212, \
+  212, 212, 220, 216, 216, 220, 216, 224, 216, 228, 232, 224, 220, 224, 240, 244, 236, 244, 232, 256, 288, 240, 236, 288, 260, 260, 264, 232, 228, 228, \
+  228, 236, 236, 228, 236, 236, 236, 248, 256, 260, 232, 236, 264, 256, 260, 252, 284, 252, 264, 276, 244, 296, 244, 240, 244, 248, 240, 252, 256, 260, \
+  260, 252, 252, 272, 252, 272, 260, 296, 268, 260, 256, 276, 272, 264, 312, 284, 256, 252, 252, 252, 264, 252, 256, 260, 264, 276, 292, 268, 264, 276, \
+  264, 260, 264, 304, 288, 296, 296, 296, 288, 296, 272, 280, 264, 264, 272, 264, 288, 288, 280, 288, 272, 280, 296, 296, 280, 288, 296, 320, 344, 320, \
+  344, 272, 344, 344, 304, 288, 280, 280, 312, 280, 280, 304, 304, 312, 304, 296, 288, 328, 320, 352, 320, 320, 328, 360, 344, 344, 360, 288, 288, 304, \
+  288, 296, 320, 320, 312, 312, 304, 328, 336, 312, 312, 360, 336, 344, 344, 336, 360, 360, 296, 296, 304, 360, 328, 328, 312, 320, 320, 328, 312, 344, \
+  344, 328, 344, 344, 368, 360, 352, 360, 392, 392, 368, 320, 312, 392, 312, 328, 344, 336, 344, 328, 360, 352, 352, 360, 360, 360, 368, 408, 360, 376, \
+  392, 392, 376, 336, 344, 352, 360, 352, 344, 344, 384, 344, 360, 376, 392, 368, 360, 408, 408, 448, 432, 384, 392, 336, 360, 344, 360, 360, 368, 376, \
+  376, 360, 368, 408, 368, 376, 376, 376, 432, 376, 384, 464, 432, 344, 432, 376, 344, 344, 384, 344, 384, 376, 400, 432, 456, 432, 456, 392, 432, 392, \
+  448, 456, 360, 376, 456, 408, 384, 368, 376, 432, 376, 472, 464, 504, 448, 360, 408, 456, 376, 408, 424, 424, 448, 440, 456, 392, 408, 384, 408, 392, \
+  384, 416, 424, 432, 400, 472, 480, 408, 432, 432, 464, 456, 504, 464, 456, 472, 496, 416, 392, 424, 504, 400, 440, 432, 472, 448, 456, 456, 432, 448, \
+  456, 504, 504, 512, 496, 504, 424, 416, 408, 432, 544, 432, 440, 456, 448, 448, 464, 472, 480, 552, 552, 544, 552, 560, 552, 544, 544, 544, 552, 552, \
+  552, 552, 552, 552, 552, 560, 552, 552, 560, 560, 560, 560, 568, 576, 568, 592, 576, 560, 560, 560, 560, 568, 568, 576, 568, 568, 576, 568, 568, 576, \
+  568, 568, 600, 592, 576, 608, 576, 576, 576, 576, 584, 584, 576, 592, 592, 600, 584, 592, 584, 600, 600, 600, 584, 624, 584, 592, 600, 592, 616, 592, \
+  592, 592, 592, 592, 592, 592, 600, 608, 600, 608, 600, 600, 600, 624, 616, 608, 616, 600, 632, 608, 608, 608, 616, 608, 608, 608, 608, 616, 608, 664, \
+  664, 632, 656, 616, 664, 624, 616, 632, 632, 616, 624, 624, 624, 632, 624, 624, 624, 624, 648, 632, 624, 624, 872, 872, 656, 664, 696, 872, 872, 872, \
+  632, 872, 872, 896, 872, 896, 872, 896, 880, 872, 896, 872, 888, 872, 872, 872, 872, 872, 888, 872, 880, 824, 872, 856, 880, 888, 800, 848, 800, 880, \
+  848, 800, 808, 872, 872, 864, 824, 840, 872, 872, 872, 872, 872, 872, 872, 872, 872, 872, 880, 928, 872, 920, 872, 920, 888, 880, 872, 880, 872, 872, \
+  872, 888, 880, 888, 888, 872, 888, 872, 880, 896, 920, 920, 880, 928, 904, 872, 888, 904, 872, 872, 872, 872, 880, 888, 872, 872, 872, 880, 872, 904, \
+  920, 888, 888, 872, 880, 880, 888, 896, 896, 880, 872, 904, 880, 912, 896, 872, 904, 904, 912, 880, 880, 920, 912, 896, 928, 928, 872, 872, 872, 872, \
+  880, 880, 888, 888, 888, 912, 880, 880, 880, 912, 896, 896, 928, 896, 912, 912, 896, 928, 928, 928, 928, 912, 880, 928, 880, 880, 896, 880, 896, 880, \
+  896, 880, 880, 912, 912, 880, 896, 880, 896, 912, 880, 880, 928, 912, 912, 928, 928, 896, 928, 912, 928, 928, 928, 928, 928, 928, 880, 880, 880, 880, \
+  880, 912, 896, 912, 912, 896, 928, 896, 928, 896, 928, 928, 928, 928, 912, 880, 928, 912, 896, 928, 896, 880, 912, 896, 912, 896, 896, 896, 928, 896, \
+  912, 928, 912, 928, 912, 928, 912, 880, 928, 928, 880, 928, 928, 880, 896, 928, 880, 896, 912, 928, 928, 896, 912, 928, 912, 928, 1024, 928, 928, 1040, \
+  912, 928, 1024, 1024, 928, 928, 928, 928, 912, 1040, 1072, 912, 1072, 1072, 1056, 1040, 1072, 1088, 1104, 1040, 1040, 928, 1024, 928, 928, 1056, 928, 928, 1056, 1040, \
+  928, 1056, 1024, 1056, 1056, 1056, 1104, 1024, 1056, 1072, 1056, 1056, 1088, 1072, 1120, 1104, 1072, 1072, 1072, 1104, 1120, 1024, 1120, 1120, 1056, 1024, 1040, 1024, 1040, 1040, \
+  1040, 1024, 1040, 1056, 1040, 1088, 1040, 1056, 1120, 1040, 1040, 1072, 1072, 1088, 1104, 1088, 1104, 1088, 1088, 1056, 1120, 1104, 1152, 1104, 1088, 1120, 1104, 1120, 1024, 1120, \
+  1152, 1136, 1152, 1056, 1056, 1072, 1056, 1152, 1088, 1056, 1104, 1072, 1104, 1088, 1120, 1072, 1104, 1088, 1088, 1120, 1120, 1120, 1152, 1136, 1120, 1120, 1152, 1120, 1136, 1152, \
+  1152, 1072, 1136, 1136, 1088, 1152, 1136, 1136, 1104, 1056, 1072, 1088, 1104, 1104, 1120, 1120, 1104, 1104, 1104, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1136, 1072, \
+  1152, 1136, 1152, 1152, 1104, 1152, 1104, 1152, 1152, 1088, 1120, 1152, 1136, 1136, 1120, 1136, 1120, 1152, 1136, 1136, 1120, 1136, 1152, 1136, 1152, 1136, 1136, 1120, 1152, 1152, \
+  1104, 1152, 1152, 1152, 1104, 1120, 1104, 1120, 1120, 1120, 1120, 1136, 1136, 1136, 1136, 1152, 1120, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1104, \
+  1120, 1152, 1136, 1136, 1136, 1136, 1136, 1136, 1120, 1152, 1152, 1152, 1136, 1104, 1152, 1136, 1136, 1152, 1136, 1120, 1136, 1152, 1152, 1136, 1136, 1120, 1136, 1136, 1136, 1120, \
+  1152, 1152, 1152, 1136, 1136, 1136, 1152, 1104, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1152, \
+  1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, \
+  1120, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1136, \
+  1152, 1152, 1152, 1104, 1120, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1152, 1120, 1152, 1136, 1152, 1152, 1120, 1152, 1120, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1120, 1152, 1152, 1136, 1152, 1136, 1552, 1552, 1136, 1136, 1152, 1552, 1136, 1136, 1584, 1552, 1552, 1552, \
+  1152, 1552, 1552, 1152, 1584, 1552, 1152, 1152, 1552, 1584, 1152, 1152, 1552, 1584, 1568, 1552, 1552, 1552, 1152, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1625, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1568, 1632, 1552, 1632, 1568, 1584, 1568, 1568, 1584, 1600, 1552, 1552, 1632, 1600, 1632, 1632, 1632, \
+  1632, 1568, 1584, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1552, 1662, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1568, 1600, 1632, 1552, 1616, 1632, 1632, 1632, 1584, 1632, \
+  1632, 1552, 1632, 1632, 1632, 1568, 1600, 1632, 1648, 1616, 1632, 1648, 1632, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1632, 1664, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1648, 1648, 1648, 1616, 1632, 1680, 1632, 1680, 1648, 1632, 1664, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1648, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1648, 1664, 1648, 1648, 1632, 1648, 1632, 1680, 1664, 1648, 1680, 1664, 1696, 1632, 1664, 1680, 1632, 1648, 1696, \
+  1680, 1632, 1632, 1648, 1648, 1648, 1632, 1664, 1632, 1648, 1648, 1632, 1648, 1648, 1632, 1664, 1664, 1680, 1680, 1632, 1664, 1664, 1648, 1648, 1712, 1728, 1664, 1712, 1696, 1712, \
+  1680, 1632, 1728, 1648, 1728, 1728, 1712, 1648, 1632, 1632, 1664, 1648, 1664, 1664, 1680, 1712, 1664, 1632, 1696, 1664, 1712, 1696, 1680, 1680, 1696, 1680, 1680, 1712, 1648, 1712, \
+  1632, 1728, 1696, 1648, 1712, 1632, 1712, 1696, 1648, 1680, 1648, 1664, 1648, 1696, 1712, 1648, 1648, 1680, 1664, 1696, 1728, 1696, 1712, 1728, 1696, 1728, 1712, 1664, 1680, 1728, \
+  1712, 1712, 1712, 1728, 1728, 1712, 1728, 1696, 1728, 1712, 1696, 1728, 1728, 1680, 1728, 1712, 1664, 1680, 1680, 1696, 1712, 1696, 1696, 1696, 1728, 1696, 1728, 1728, 1696, 1712, \
+  1712, 1664, 1712, 1680, 1664, 1728, 1728, 1664, 1696, 1696, 1680, 1712, 1680, 1712, 1696, 1728, 1696, 1696, 1728, 1696, 1712, 1696, 1712, 1712, 1712, 1728, 1712, 1696, 1728, 1680, \
+  1696, 1712, 1712, 1728, 1712, 1728, 1696, 1728, 1776, 1728, 1696, 1776, 1728, 1728, 1712, 1712, 1824, 1856, 1728, 1824, 1728, 1728, 1712, 1728, 1728, 1728, 1856, 1696, 1728, 1840, \
+  1712, 1712, 1824, 1856, 1792, 1712, 1840, 1728, 1808, 1728, 1824, 1824, 1840, 1824, 1824, 1856, 1856, 1824, 1856, 1840, 1696, 1856, 1840, 1840, 1856, 1856, 1824, 1712, 1792, 1856, \
+  1824, 1728, 1808, 1792, 1856, 1728, 1792, 1840, 1808, 1808, 1712, 1808, 1840, 1808, 1824, 1824, 1824, 1840, 1824, 1840, 1856, 1824, 1728, 1856, 1856, 1824, 1856, 1856, 1792, 1792, \
+  1856, 1824, 1856, 1824, 1824, 1856, 1808, 1824, 1856, 1856, 1840, 1840, 1840, 1840, 1856, 1840, 1840, 1856, 1824, 1840, 1808, 1824, 1840, 1856, 1856, 1824, 1856, 1840, 1840, 1840, \
+  1824, 1824, 1840, 1840, 1840, 1856, 1856, 1856
+
 #endif
diff --git a/src/mpn_extras/generic/flint-mparam.h b/src/mpn_extras/generic/flint-mparam.h
index 0112747333..8c5e03d736 100644
--- a/src/mpn_extras/generic/flint-mparam.h
+++ b/src/mpn_extras/generic/flint-mparam.h
@@ -29,4 +29,156 @@
 #define FFT_N_NUM                                 19
 #define FFT_MULMOD_2EXPP1_CUTOFF                 128
 
+/* FIXME: This tuning is for x86_64_adx with fft_small */
+/* NOTE: We assume that the same cutoff is optimal for both mulhigh and mullow */
+#define FLINT_MPN_MULHIGH_MULDERS_CUTOFF 50
+#define FLINT_MPN_MULHIGH_MUL_CUTOFF 2000
+#define FLINT_MPN_MULHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_SQRHIGH_MULDERS_CUTOFF 90
+#define FLINT_MPN_SQRHIGH_SQR_CUTOFF 2000
+#define FLINT_MPN_SQRHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_MULHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 16, 15, 15, 18, 18, \
+  18, 19, 20, 18, 22, 22, 20, 20, 26, 22, 22, 22, 24, 24, 24, 26, 25, 26, 30, 30, 28, 30, 31, 32, 32, 30, 36, 36, 36, 36, \
+  38, 39, 39, 38, 39, 40, 40, 40, 44, 40, 44, 44, 40, 44, 44, 48, 44, 48, 44, 48, 48, 52, 52, 52, 44, 52, 52, 52, 52, 56, \
+  60, 60, 52, 60, 60, 52, 52, 60, 64, 72, 56, 60, 72, 60, 60, 60, 76, 64, 60, 60, 72, 60, 72, 80, 72, 72, 80, 72, 68, 76, \
+  88, 76, 68, 76, 72, 72, 80, 88, 72, 72, 88, 72, 80, 76, 76, 80, 80, 88, 80, 88, 84, 88, 80, 96, 80, 80, 88, 80, 88, 88, \
+  80, 88, 96, 96, 88, 96, 92, 96, 96, 92, 100, 88, 96, 104, 88, 108, 96, 104, 104, 104, 112, 112, 108, 104, 104, 112, 112, 120, 104, 112, \
+  120, 112, 112, 120, 124, 124, 116, 124, 108, 120, 124, 116, 120, 120, 116, 120, 124, 120, 120, 140, 120, 120, 120, 120, 144, 120, 132, 144, 136, 140, \
+  144, 144, 144, 144, 144, 144, 144, 144, 140, 156, 140, 140, 144, 144, 144, 160, 144, 144, 156, 156, 144, 160, 160, 160, 160, 152, 160, 156, 156, 156, \
+  160, 160, 144, 160, 164, 156, 156, 156, 172, 156, 156, 160, 176, 160, 160, 164, 176, 156, 160, 160, 156, 156, 160, 160, 156, 160, 172, 160, 188, 172, \
+  172, 172, 160, 172, 176, 160, 160, 176, 180, 176, 164, 188, 192, 176, 172, 188, 188, 188, 172, 188, 192, 188, 180, 192, 192, 188, 188, 192, 188, 188, \
+  188, 188, 192, 160, 156, 204, 160, 164, 164, 164, 164, 176, 180, 168, 172, 184, 188, 200, 216, 188, 164, 188, 220, 188, 208, 176, 180, 188, 172, 188, \
+  184, 188, 204, 208, 220, 196, 220, 196, 208, 212, 188, 220, 176, 176, 184, 192, 208, 184, 188, 196, 204, 244, 208, 212, 212, 228, 256, 188, 204, 196, \
+  188, 192, 192, 192, 212, 188, 292, 212, 220, 236, 228, 248, 260, 224, 264, 196, 200, 196, 212, 208, 204, 216, 208, 228, 216, 220, 252, 220, 268, 264, \
+  284, 268, 300, 220, 208, 212, 220, 236, 244, 224, 252, 252, 260, 264, 256, 256, 292, 272, 288, 292, 328, 224, 256, 236, 252, 268, 256, 252, 260, 272, \
+  284, 296, 300, 280, 300, 284, 252, 236, 328, 324, 264, 264, 256, 264, 280, 268, 284, 284, 292, 304, 260, 304, 264, 256, 328, 328, 260, 276, 328, 284, \
+  276, 296, 300, 320, 320, 304, 328, 304, 272, 268, 280, 268, 288, 292, 288, 284, 316, 288, 328, 328, 300, 328, 328, 280, 264, 328, 300, 328, 316, 324, \
+  300, 324, 300, 324, 316, 316, 328, 348, 276, 376, 288, 296, 296, 304, 320, 316, 328, 328, 324, 328, 340, 384, 348, 376, 300, 396, 304, 300, 304, 324, \
+  300, 324, 328, 328, 328, 440, 448, 384, 376, 456, 464, 384, 376, 472, 480, 376, 352, 328, 376, 352, 376, 392, 392, 384, 456, 456, 480, 448, 456, 456, \
+  472, 472, 472, 352, 464, 472, 472, 472, 480, 440, 480, 480, 480, 480, 456, 472, 472, 464, 464, 464, 456, 472, 480, 472, 480, 480, 480, 480, 448, 456, \
+  480, 448, 456, 464, 456, 464, 456, 480, 472, 464, 464, 472, 472, 472, 480, 472, 480, 480, 472, 480, 480, 480, 480, 464, 464, 464, 456, 472, 464, 480, \
+  472, 472, 480, 472, 480, 480, 464, 464, 472, 464, 472, 472, 480, 464, 480, 472, 480, 480, 576, 576, 560, 480, 472, 480, 568, 480, 480, 464, 480, 472, \
+  480, 576, 480, 552, 560, 560, 560, 560, 568, 560, 560, 576, 576, 560, 568, 472, 480, 480, 544, 568, 552, 544, 560, 544, 560, 568, 552, 576, 568, 560, \
+  576, 576, 568, 576, 560, 576, 568, 536, 576, 568, 560, 544, 560, 552, 560, 568, 560, 576, 568, 560, 560, 560, 568, 576, 568, 576, 576, 576, 576, 544, \
+  576, 576, 568, 576, 560, 576, 576, 576, 544, 552, 568, 576, 552, 560, 576, 560, 568, 560, 576, 560, 544, 576, 576, 576, 576, 568, 576, 568, 560, 576, \
+  552, 552, 576, 560, 568, 568, 568, 576, 576, 576, 560, 552, 576, 560, 568, 560, 576, 560, 568, 560, 568, 568, 568, 576, 552, 576, 560, 576, 576, 560, \
+  568, 576, 568, 576, 576, 576, 576, 560, 576, 568, 568, 568, 560, 560, 576, 576, 568, 568, 576, 560, 576, 576, 568, 576, 560, 576, 576, 568, 576, 568, \
+  576, 568, 576, 576, 568, 576, 576, 576, 576, 568, 576, 576, 568, 568, 576, 576, 784, 576, 776, 576, 568, 576, 576, 576, 576, 576, 576, 576, 776, 776, \
+  776, 776, 776, 776, 776, 784, 776, 776, 784, 776, 776, 776, 800, 776, 776, 776, 776, 776, 776, 800, 776, 808, 792, 800, 776, 792, 776, 776, 776, 776, \
+  792, 776, 776, 784, 792, 784, 800, 776, 784, 808, 784, 776, 776, 776, 808, 784, 792, 776, 792, 832, 800, 800, 816, 792, 816, 816, 856, 808, 848, 824, \
+  870, 832, 792, 776, 784, 784, 784, 784, 800, 792, 800, 792, 784, 800, 800, 800, 816, 824, 824, 824, 832, 816, 816, 832, 824, 824, 848, 832, 856, 856, \
+  840, 872, 864, 872, 872, 880, 880, 880, 872, 888, 880, 880, 872, 880, 880, 880, 840, 872, 872, 848, 880, 848, 856, 840, 848, 840, 880, 872, 856, 872, \
+  856, 888, 880, 872, 888, 880, 872, 920, 888, 872, 880, 872, 888, 888, 888, 880, 880, 928, 880, 928, 928, 928, 920, 920, 904, 912, 880, 904, 928, 872, \
+  872, 880, 888, 880, 896, 880, 872, 896, 888, 896, 896, 928, 904, 896, 896, 912, 904, 904, 920, 880, 912, 920, 928, 928, 880, 920, 920, 880, 888, 904, \
+  896, 904, 928, 896, 912, 896, 912, 920, 912, 912, 928, 928, 928, 920, 928, 928, 928, 928, 928, 928, 912, 904, 912, 896, 904, 904, 920, 920, 920, 928, \
+  928, 920, 928, 928, 928, 912, 928, 912, 928, 928, 928, 912, 912, 912, 928, 928, 928, 896, 928, 928, 912, 928, 928, 928, 912, 928, 912, 928, 928, 912, \
+  928, 912, 928, 928, 928, 928, 928, 912, 928, 928, 928, 928, 912, 912, 928, 912, 928, 1024, 928, 928, 928, 928, 928, 928, 1056, 912, 928, 928, 1024, 1024, \
+  928, 928, 1024, 928, 928, 928, 928, 928, 928, 1040, 1040, 928, 1056, 1024, 1072, 1024, 1040, 1040, 1040, 1024, 1088, 1056, 1056, 1088, 1040, 1056, 1072, 1072, 1056, 1056, \
+  1024, 1088, 1040, 1024, 1040, 1040, 1024, 1056, 1056, 1056, 1040, 1072, 1056, 1040, 1056, 1056, 1056, 1056, 1056, 1056, 1056, 1120, 1056, 1088, 1056, 1120, 1088, 1072, 1104, 1104, \
+  1104, 1120, 1088, 1088, 1072, 1088, 1120, 1104, 1088, 1104, 1088, 1072, 1104, 1088, 1120, 1088, 1072, 1072, 1072, 1088, 1088, 1072, 1072, 1088, 1104, 1152, 1104, 1104, 1088, 1104, \
+  1136, 1088, 1104, 1152, 1152, 1152, 1136, 1120, 1136, 1152, 1120, 1152, 1088, 1120, 1104, 1120, 1136, 1104, 1136, 1088, 1136, 1104, 1088, 1104, 1120, 1104, 1104, 1120, 1136, 1136, \
+  1120, 1136, 1136, 1136, 1120, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1104, 1152, 1120, 1136, 1120, 1120, 1152, 1120, 1136, 1152, 1136, 1152, 1120, 1152, 1136, 1136, 1136, 1136, \
+  1136, 1152, 1152, 1152, 1152, 1120, 1120, 1152, 1136, 1136, 1136, 1152, 1152, 1120, 1152, 1152, 1152, 1152, 1152, 1104, 1152, 1152, 1120, 1136, 1152, 1120, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1344, 1152, 1344, 1344, 1344, 1152, 1152, 1152, 1152, 1344, 1328, 1328, 1328, 1152, 1344, 1152, 1344, 1152, 1344, 1152, 1152, 1328, 1152, 1328, 1344, 1328, 1344, 1328, 1344, \
+  1344, 1312, 1328, 1328, 1328, 1344, 1344, 1344, 1328, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, \
+  1328, 1344, 1344, 1344, 1344, 1328, 1344, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1573, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1583, 1568, 1568, 1552, 1568, 1552, 1568, \
+  1568, 1568, 1584, 1568, 1584, 1568, 1568, 1568, 1552, 1552, 1552, 1568, 1552, 1584, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1584, 1552, 1584, 1552, 1617, 1568, 1584, \
+  1552, 1552, 1584, 1584, 1552, 1625, 1626, 1627, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1632, 1636, 1632, 1638, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1648, 1669, 1648, 1671, 1632, 1664, 1648, 1632, 1648, 1648, 1648, 1632, \
+  1632, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1648, 1664, 1648, 1648, 1648, 1648, 1648, 1648, \
+  1680, 1664, 1680, 1696, 1680, 1680, 1664, 1680, 1680, 1648, 1632, 1680, 1696, 1632, 1648, 1648, 1632, 1680, 1680, 1664, 1664, 1664, 1648, 1680, 1664, 1680, 1664, 1680, 1664, 1664, \
+  1680, 1696, 1664, 1696, 1712, 1712, 1696, 1680, 1712, 1696, 1728, 1712, 1696, 1728, 1728, 1712, 1728, 1648, 1680, 1696, 1712, 1696, 1712, 1696, 1696, 1680, 1696, 1696, 1696, 1712, \
+  1696, 1696, 1696, 1696, 1712, 1728, 1696, 1728, 1696, 1696, 1712, 1728, 1712, 1728, 1712, 1680, 1696, 1728, 1712, 1696, 1696, 1696, 1712, 1712, 1728, 1696, 1728, 1712, 1712, 1728, \
+  1696, 1696, 1696, 1712, 1696, 1728, 1712, 1712, 1712, 1728, 1696, 1712, 1728, 1728, 1696, 1728, 1728, 1728, 1728, 1728, 1680, 1712, 1728, 1696, 1728, 1728, 1728, 1728, 1696, 1728, \
+  1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1728, 1696, 1728, 1712, 1712, 1712, 1712, 1728, 1712, 1712, 1712, 1728, 1712, 1728, 1728, 1728, \
+  1728, 1712, 1728, 1728, 1712, 1728, 1728, 1712, 1712, 1728, 1712, 1712, 1728, 1728, 1712, 1728, 1712, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1712, \
+  1728, 1712, 1712, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, \
+  1728, 1728, 1712, 1728, 1728, 1824, 1728, 1728, 1728, 1728, 1824, 1728, 1840, 1728, 1728, 1728, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1728, 1728, 1856, 1856, 1856, 1856, 1728, \
+  1728, 1856, 1856, 1728, 1856, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1856, 1856, 1856, 1840, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1840, 1904, 1856, 1856, 1840, 1840, 1856, \
+  1856, 1840, 1856, 1840, 1856, 1856, 1856, 1856, 1952, 1856, 1856, 1856, 1856, 1952, 1904, 1904, 1856, 1856, 1856, 1920, 1952, 2001, 1952, 1984, 1952, 1936, 1952, 1904, 1968, 1920, \
+  1984, 1920, 1968, 1920, 1936, 1856, 2000, 1920, 1936, 1952, 2000, 1968, 1984, 1968, 1984, 2000, 1952, 2000, 2016, 1984, 2000, 2016, 1984, 1664, 2016, 1984, 2016, 1968, 2016, 2016, \
+  1744, 2016, 2016, 1968, 2000, 1728, 1712, 1696
+
+#define FLINT_MPN_SQRHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 29, 0, 0, 31, 0, 31, \
+  0, 32, 0, 34, 0, 36, 36, 40, 0, 40, 40, 40, 0, 44, 0, 44, 44, 48, 0, 52, 48, 52, 44, 44, 48, 48, 48, 48, 48, 48, \
+  48, 48, 48, 48, 52, 52, 52, 52, 52, 56, 56, 52, 56, 56, 56, 56, 56, 56, 56, 56, 60, 60, 68, 64, 60, 60, 60, 60, 64, 64, \
+  64, 68, 68, 68, 64, 64, 68, 68, 72, 72, 68, 68, 68, 72, 76, 80, 72, 72, 72, 88, 76, 76, 80, 80, 76, 80, 76, 80, 84, 80, \
+  88, 88, 80, 84, 88, 80, 80, 84, 92, 88, 92, 88, 88, 88, 88, 96, 88, 108, 100, 92, 88, 88, 104, 100, 100, 92, 104, 108, 100, 92, \
+  104, 100, 104, 96, 108, 104, 96, 96, 104, 100, 100, 104, 112, 116, 108, 104, 104, 116, 108, 104, 104, 120, 116, 104, 108, 132, 116, 108, 120, 108, \
+  108, 108, 132, 108, 120, 112, 112, 116, 132, 128, 116, 124, 128, 116, 132, 120, 132, 120, 124, 120, 132, 120, 124, 128, 120, 128, 128, 132, 144, 124, \
+  128, 124, 140, 128, 128, 124, 136, 132, 128, 128, 140, 144, 128, 128, 140, 136, 132, 144, 148, 152, 144, 132, 160, 156, 140, 144, 156, 144, 140, 144, \
+  140, 156, 156, 156, 140, 144, 168, 156, 156, 164, 168, 156, 156, 160, 144, 144, 180, 156, 152, 168, 156, 160, 156, 148, 180, 168, 180, 156, 164, 156, \
+  156, 172, 156, 156, 156, 180, 180, 172, 180, 168, 164, 172, 164, 172, 176, 176, 168, 176, 172, 176, 180, 168, 176, 180, 180, 180, 192, 184, 180, 176, \
+  204, 176, 188, 180, 188, 180, 204, 180, 192, 204, 180, 192, 180, 204, 228, 192, 188, 192, 204, 180, 192, 216, 200, 216, 228, 216, 204, 216, 188, 216, \
+  216, 204, 216, 192, 204, 212, 228, 204, 228, 216, 204, 216, 192, 204, 204, 212, 204, 216, 204, 216, 228, 228, 224, 212, 204, 216, 216, 224, 228, 212, \
+  216, 228, 212, 204, 204, 216, 216, 216, 228, 216, 220, 224, 228, 220, 228, 228, 236, 224, 260, 224, 228, 228, 260, 228, 248, 252, 264, 248, 216, 212, \
+  212, 212, 220, 216, 216, 220, 216, 224, 216, 228, 232, 224, 220, 224, 240, 244, 236, 244, 232, 256, 288, 240, 236, 288, 260, 260, 264, 232, 228, 228, \
+  228, 236, 236, 228, 236, 236, 236, 248, 256, 260, 232, 236, 264, 256, 260, 252, 284, 252, 264, 276, 244, 296, 244, 240, 244, 248, 240, 252, 256, 260, \
+  260, 252, 252, 272, 252, 272, 260, 296, 268, 260, 256, 276, 272, 264, 312, 284, 256, 252, 252, 252, 264, 252, 256, 260, 264, 276, 292, 268, 264, 276, \
+  264, 260, 264, 304, 288, 296, 296, 296, 288, 296, 272, 280, 264, 264, 272, 264, 288, 288, 280, 288, 272, 280, 296, 296, 280, 288, 296, 320, 344, 320, \
+  344, 272, 344, 344, 304, 288, 280, 280, 312, 280, 280, 304, 304, 312, 304, 296, 288, 328, 320, 352, 320, 320, 328, 360, 344, 344, 360, 288, 288, 304, \
+  288, 296, 320, 320, 312, 312, 304, 328, 336, 312, 312, 360, 336, 344, 344, 336, 360, 360, 296, 296, 304, 360, 328, 328, 312, 320, 320, 328, 312, 344, \
+  344, 328, 344, 344, 368, 360, 352, 360, 392, 392, 368, 320, 312, 392, 312, 328, 344, 336, 344, 328, 360, 352, 352, 360, 360, 360, 368, 408, 360, 376, \
+  392, 392, 376, 336, 344, 352, 360, 352, 344, 344, 384, 344, 360, 376, 392, 368, 360, 408, 408, 448, 432, 384, 392, 336, 360, 344, 360, 360, 368, 376, \
+  376, 360, 368, 408, 368, 376, 376, 376, 432, 376, 384, 464, 432, 344, 432, 376, 344, 344, 384, 344, 384, 376, 400, 432, 456, 432, 456, 392, 432, 392, \
+  448, 456, 360, 376, 456, 408, 384, 368, 376, 432, 376, 472, 464, 504, 448, 360, 408, 456, 376, 408, 424, 424, 448, 440, 456, 392, 408, 384, 408, 392, \
+  384, 416, 424, 432, 400, 472, 480, 408, 432, 432, 464, 456, 504, 464, 456, 472, 496, 416, 392, 424, 504, 400, 440, 432, 472, 448, 456, 456, 432, 448, \
+  456, 504, 504, 512, 496, 504, 424, 416, 408, 432, 544, 432, 440, 456, 448, 448, 464, 472, 480, 552, 552, 544, 552, 560, 552, 544, 544, 544, 552, 552, \
+  552, 552, 552, 552, 552, 560, 552, 552, 560, 560, 560, 560, 568, 576, 568, 592, 576, 560, 560, 560, 560, 568, 568, 576, 568, 568, 576, 568, 568, 576, \
+  568, 568, 600, 592, 576, 608, 576, 576, 576, 576, 584, 584, 576, 592, 592, 600, 584, 592, 584, 600, 600, 600, 584, 624, 584, 592, 600, 592, 616, 592, \
+  592, 592, 592, 592, 592, 592, 600, 608, 600, 608, 600, 600, 600, 624, 616, 608, 616, 600, 632, 608, 608, 608, 616, 608, 608, 608, 608, 616, 608, 664, \
+  664, 632, 656, 616, 664, 624, 616, 632, 632, 616, 624, 624, 624, 632, 624, 624, 624, 624, 648, 632, 624, 624, 872, 872, 656, 664, 696, 872, 872, 872, \
+  632, 872, 872, 896, 872, 896, 872, 896, 880, 872, 896, 872, 888, 872, 872, 872, 872, 872, 888, 872, 880, 824, 872, 856, 880, 888, 800, 848, 800, 880, \
+  848, 800, 808, 872, 872, 864, 824, 840, 872, 872, 872, 872, 872, 872, 872, 872, 872, 872, 880, 928, 872, 920, 872, 920, 888, 880, 872, 880, 872, 872, \
+  872, 888, 880, 888, 888, 872, 888, 872, 880, 896, 920, 920, 880, 928, 904, 872, 888, 904, 872, 872, 872, 872, 880, 888, 872, 872, 872, 880, 872, 904, \
+  920, 888, 888, 872, 880, 880, 888, 896, 896, 880, 872, 904, 880, 912, 896, 872, 904, 904, 912, 880, 880, 920, 912, 896, 928, 928, 872, 872, 872, 872, \
+  880, 880, 888, 888, 888, 912, 880, 880, 880, 912, 896, 896, 928, 896, 912, 912, 896, 928, 928, 928, 928, 912, 880, 928, 880, 880, 896, 880, 896, 880, \
+  896, 880, 880, 912, 912, 880, 896, 880, 896, 912, 880, 880, 928, 912, 912, 928, 928, 896, 928, 912, 928, 928, 928, 928, 928, 928, 880, 880, 880, 880, \
+  880, 912, 896, 912, 912, 896, 928, 896, 928, 896, 928, 928, 928, 928, 912, 880, 928, 912, 896, 928, 896, 880, 912, 896, 912, 896, 896, 896, 928, 896, \
+  912, 928, 912, 928, 912, 928, 912, 880, 928, 928, 880, 928, 928, 880, 896, 928, 880, 896, 912, 928, 928, 896, 912, 928, 912, 928, 1024, 928, 928, 1040, \
+  912, 928, 1024, 1024, 928, 928, 928, 928, 912, 1040, 1072, 912, 1072, 1072, 1056, 1040, 1072, 1088, 1104, 1040, 1040, 928, 1024, 928, 928, 1056, 928, 928, 1056, 1040, \
+  928, 1056, 1024, 1056, 1056, 1056, 1104, 1024, 1056, 1072, 1056, 1056, 1088, 1072, 1120, 1104, 1072, 1072, 1072, 1104, 1120, 1024, 1120, 1120, 1056, 1024, 1040, 1024, 1040, 1040, \
+  1040, 1024, 1040, 1056, 1040, 1088, 1040, 1056, 1120, 1040, 1040, 1072, 1072, 1088, 1104, 1088, 1104, 1088, 1088, 1056, 1120, 1104, 1152, 1104, 1088, 1120, 1104, 1120, 1024, 1120, \
+  1152, 1136, 1152, 1056, 1056, 1072, 1056, 1152, 1088, 1056, 1104, 1072, 1104, 1088, 1120, 1072, 1104, 1088, 1088, 1120, 1120, 1120, 1152, 1136, 1120, 1120, 1152, 1120, 1136, 1152, \
+  1152, 1072, 1136, 1136, 1088, 1152, 1136, 1136, 1104, 1056, 1072, 1088, 1104, 1104, 1120, 1120, 1104, 1104, 1104, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1136, 1072, \
+  1152, 1136, 1152, 1152, 1104, 1152, 1104, 1152, 1152, 1088, 1120, 1152, 1136, 1136, 1120, 1136, 1120, 1152, 1136, 1136, 1120, 1136, 1152, 1136, 1152, 1136, 1136, 1120, 1152, 1152, \
+  1104, 1152, 1152, 1152, 1104, 1120, 1104, 1120, 1120, 1120, 1120, 1136, 1136, 1136, 1136, 1152, 1120, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1104, \
+  1120, 1152, 1136, 1136, 1136, 1136, 1136, 1136, 1120, 1152, 1152, 1152, 1136, 1104, 1152, 1136, 1136, 1152, 1136, 1120, 1136, 1152, 1152, 1136, 1136, 1120, 1136, 1136, 1136, 1120, \
+  1152, 1152, 1152, 1136, 1136, 1136, 1152, 1104, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1152, \
+  1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, \
+  1120, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1136, \
+  1152, 1152, 1152, 1104, 1120, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1152, 1120, 1152, 1136, 1152, 1152, 1120, 1152, 1120, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1120, 1152, 1152, 1136, 1152, 1136, 1552, 1552, 1136, 1136, 1152, 1552, 1136, 1136, 1584, 1552, 1552, 1552, \
+  1152, 1552, 1552, 1152, 1584, 1552, 1152, 1152, 1552, 1584, 1152, 1152, 1552, 1584, 1568, 1552, 1552, 1552, 1152, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1625, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1568, 1632, 1552, 1632, 1568, 1584, 1568, 1568, 1584, 1600, 1552, 1552, 1632, 1600, 1632, 1632, 1632, \
+  1632, 1568, 1584, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1552, 1662, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1568, 1600, 1632, 1552, 1616, 1632, 1632, 1632, 1584, 1632, \
+  1632, 1552, 1632, 1632, 1632, 1568, 1600, 1632, 1648, 1616, 1632, 1648, 1632, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1632, 1664, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1648, 1648, 1648, 1616, 1632, 1680, 1632, 1680, 1648, 1632, 1664, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1648, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1648, 1664, 1648, 1648, 1632, 1648, 1632, 1680, 1664, 1648, 1680, 1664, 1696, 1632, 1664, 1680, 1632, 1648, 1696, \
+  1680, 1632, 1632, 1648, 1648, 1648, 1632, 1664, 1632, 1648, 1648, 1632, 1648, 1648, 1632, 1664, 1664, 1680, 1680, 1632, 1664, 1664, 1648, 1648, 1712, 1728, 1664, 1712, 1696, 1712, \
+  1680, 1632, 1728, 1648, 1728, 1728, 1712, 1648, 1632, 1632, 1664, 1648, 1664, 1664, 1680, 1712, 1664, 1632, 1696, 1664, 1712, 1696, 1680, 1680, 1696, 1680, 1680, 1712, 1648, 1712, \
+  1632, 1728, 1696, 1648, 1712, 1632, 1712, 1696, 1648, 1680, 1648, 1664, 1648, 1696, 1712, 1648, 1648, 1680, 1664, 1696, 1728, 1696, 1712, 1728, 1696, 1728, 1712, 1664, 1680, 1728, \
+  1712, 1712, 1712, 1728, 1728, 1712, 1728, 1696, 1728, 1712, 1696, 1728, 1728, 1680, 1728, 1712, 1664, 1680, 1680, 1696, 1712, 1696, 1696, 1696, 1728, 1696, 1728, 1728, 1696, 1712, \
+  1712, 1664, 1712, 1680, 1664, 1728, 1728, 1664, 1696, 1696, 1680, 1712, 1680, 1712, 1696, 1728, 1696, 1696, 1728, 1696, 1712, 1696, 1712, 1712, 1712, 1728, 1712, 1696, 1728, 1680, \
+  1696, 1712, 1712, 1728, 1712, 1728, 1696, 1728, 1776, 1728, 1696, 1776, 1728, 1728, 1712, 1712, 1824, 1856, 1728, 1824, 1728, 1728, 1712, 1728, 1728, 1728, 1856, 1696, 1728, 1840, \
+  1712, 1712, 1824, 1856, 1792, 1712, 1840, 1728, 1808, 1728, 1824, 1824, 1840, 1824, 1824, 1856, 1856, 1824, 1856, 1840, 1696, 1856, 1840, 1840, 1856, 1856, 1824, 1712, 1792, 1856, \
+  1824, 1728, 1808, 1792, 1856, 1728, 1792, 1840, 1808, 1808, 1712, 1808, 1840, 1808, 1824, 1824, 1824, 1840, 1824, 1840, 1856, 1824, 1728, 1856, 1856, 1824, 1856, 1856, 1792, 1792, \
+  1856, 1824, 1856, 1824, 1824, 1856, 1808, 1824, 1856, 1856, 1840, 1840, 1840, 1840, 1856, 1840, 1840, 1856, 1824, 1840, 1808, 1824, 1840, 1856, 1856, 1824, 1856, 1840, 1840, 1840, \
+  1824, 1824, 1840, 1840, 1840, 1856, 1856, 1856
+
 #endif
diff --git a/src/mpn_extras/mulhigh.c b/src/mpn_extras/mulhigh.c
index cd6b738818..7362da4b93 100644
--- a/src/mpn_extras/mulhigh.c
+++ b/src/mpn_extras/mulhigh.c
@@ -18,77 +18,11 @@
 #include <string.h>
 #include "mpn_extras.h"
 
-/* Generated by tune-mulhigh.c */
-const signed short flint_mpn_mulhigh_k_tab[FLINT_MPN_MULHIGH_K_TAB_SIZE] =
-{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 16, 15, 15, 18, 18, 
-18, 19, 20, 18, 22, 22, 20, 20, 26, 22, 22, 22, 24, 24, 24, 26, 25, 26, 30, 30, 28, 30, 31, 32, 32, 30, 36, 36, 36, 36, 
-38, 39, 39, 38, 39, 40, 40, 40, 44, 40, 44, 44, 40, 44, 44, 48, 44, 48, 44, 48, 48, 52, 52, 52, 44, 52, 52, 52, 52, 56, 
-60, 60, 52, 60, 60, 52, 52, 60, 64, 72, 56, 60, 72, 60, 60, 60, 76, 64, 60, 60, 72, 60, 72, 80, 72, 72, 80, 72, 68, 76, 
-88, 76, 68, 76, 72, 72, 80, 88, 72, 72, 88, 72, 80, 76, 76, 80, 80, 88, 80, 88, 84, 88, 80, 96, 80, 80, 88, 80, 88, 88, 
-80, 88, 96, 96, 88, 96, 92, 96, 96, 92, 100, 88, 96, 104, 88, 108, 96, 104, 104, 104, 112, 112, 108, 104, 104, 112, 112, 120, 104, 112, 
-120, 112, 112, 120, 124, 124, 116, 124, 108, 120, 124, 116, 120, 120, 116, 120, 124, 120, 120, 140, 120, 120, 120, 120, 144, 120, 132, 144, 136, 140, 
-144, 144, 144, 144, 144, 144, 144, 144, 140, 156, 140, 140, 144, 144, 144, 160, 144, 144, 156, 156, 144, 160, 160, 160, 160, 152, 160, 156, 156, 156, 
-160, 160, 144, 160, 164, 156, 156, 156, 172, 156, 156, 160, 176, 160, 160, 164, 176, 156, 160, 160, 156, 156, 160, 160, 156, 160, 172, 160, 188, 172, 
-172, 172, 160, 172, 176, 160, 160, 176, 180, 176, 164, 188, 192, 176, 172, 188, 188, 188, 172, 188, 192, 188, 180, 192, 192, 188, 188, 192, 188, 188, 
-188, 188, 192, 160, 156, 204, 160, 164, 164, 164, 164, 176, 180, 168, 172, 184, 188, 200, 216, 188, 164, 188, 220, 188, 208, 176, 180, 188, 172, 188, 
-184, 188, 204, 208, 220, 196, 220, 196, 208, 212, 188, 220, 176, 176, 184, 192, 208, 184, 188, 196, 204, 244, 208, 212, 212, 228, 256, 188, 204, 196, 
-188, 192, 192, 192, 212, 188, 292, 212, 220, 236, 228, 248, 260, 224, 264, 196, 200, 196, 212, 208, 204, 216, 208, 228, 216, 220, 252, 220, 268, 264, 
-284, 268, 300, 220, 208, 212, 220, 236, 244, 224, 252, 252, 260, 264, 256, 256, 292, 272, 288, 292, 328, 224, 256, 236, 252, 268, 256, 252, 260, 272, 
-284, 296, 300, 280, 300, 284, 252, 236, 328, 324, 264, 264, 256, 264, 280, 268, 284, 284, 292, 304, 260, 304, 264, 256, 328, 328, 260, 276, 328, 284, 
-276, 296, 300, 320, 320, 304, 328, 304, 272, 268, 280, 268, 288, 292, 288, 284, 316, 288, 328, 328, 300, 328, 328, 280, 264, 328, 300, 328, 316, 324, 
-300, 324, 300, 324, 316, 316, 328, 348, 276, 376, 288, 296, 296, 304, 320, 316, 328, 328, 324, 328, 340, 384, 348, 376, 300, 396, 304, 300, 304, 324, 
-300, 324, 328, 328, 328, 440, 448, 384, 376, 456, 464, 384, 376, 472, 480, 376, 352, 328, 376, 352, 376, 392, 392, 384, 456, 456, 480, 448, 456, 456, 
-472, 472, 472, 352, 464, 472, 472, 472, 480, 440, 480, 480, 480, 480, 456, 472, 472, 464, 464, 464, 456, 472, 480, 472, 480, 480, 480, 480, 448, 456, 
-480, 448, 456, 464, 456, 464, 456, 480, 472, 464, 464, 472, 472, 472, 480, 472, 480, 480, 472, 480, 480, 480, 480, 464, 464, 464, 456, 472, 464, 480, 
-472, 472, 480, 472, 480, 480, 464, 464, 472, 464, 472, 472, 480, 464, 480, 472, 480, 480, 576, 576, 560, 480, 472, 480, 568, 480, 480, 464, 480, 472, 
-480, 576, 480, 552, 560, 560, 560, 560, 568, 560, 560, 576, 576, 560, 568, 472, 480, 480, 544, 568, 552, 544, 560, 544, 560, 568, 552, 576, 568, 560, 
-576, 576, 568, 576, 560, 576, 568, 536, 576, 568, 560, 544, 560, 552, 560, 568, 560, 576, 568, 560, 560, 560, 568, 576, 568, 576, 576, 576, 576, 544, 
-576, 576, 568, 576, 560, 576, 576, 576, 544, 552, 568, 576, 552, 560, 576, 560, 568, 560, 576, 560, 544, 576, 576, 576, 576, 568, 576, 568, 560, 576, 
-552, 552, 576, 560, 568, 568, 568, 576, 576, 576, 560, 552, 576, 560, 568, 560, 576, 560, 568, 560, 568, 568, 568, 576, 552, 576, 560, 576, 576, 560, 
-568, 576, 568, 576, 576, 576, 576, 560, 576, 568, 568, 568, 560, 560, 576, 576, 568, 568, 576, 560, 576, 576, 568, 576, 560, 576, 576, 568, 576, 568, 
-576, 568, 576, 576, 568, 576, 576, 576, 576, 568, 576, 576, 568, 568, 576, 576, 784, 576, 776, 576, 568, 576, 576, 576, 576, 576, 576, 576, 776, 776, 
-776, 776, 776, 776, 776, 784, 776, 776, 784, 776, 776, 776, 800, 776, 776, 776, 776, 776, 776, 800, 776, 808, 792, 800, 776, 792, 776, 776, 776, 776, 
-792, 776, 776, 784, 792, 784, 800, 776, 784, 808, 784, 776, 776, 776, 808, 784, 792, 776, 792, 832, 800, 800, 816, 792, 816, 816, 856, 808, 848, 824, 
-870, 832, 792, 776, 784, 784, 784, 784, 800, 792, 800, 792, 784, 800, 800, 800, 816, 824, 824, 824, 832, 816, 816, 832, 824, 824, 848, 832, 856, 856, 
-840, 872, 864, 872, 872, 880, 880, 880, 872, 888, 880, 880, 872, 880, 880, 880, 840, 872, 872, 848, 880, 848, 856, 840, 848, 840, 880, 872, 856, 872, 
-856, 888, 880, 872, 888, 880, 872, 920, 888, 872, 880, 872, 888, 888, 888, 880, 880, 928, 880, 928, 928, 928, 920, 920, 904, 912, 880, 904, 928, 872, 
-872, 880, 888, 880, 896, 880, 872, 896, 888, 896, 896, 928, 904, 896, 896, 912, 904, 904, 920, 880, 912, 920, 928, 928, 880, 920, 920, 880, 888, 904, 
-896, 904, 928, 896, 912, 896, 912, 920, 912, 912, 928, 928, 928, 920, 928, 928, 928, 928, 928, 928, 912, 904, 912, 896, 904, 904, 920, 920, 920, 928, 
-928, 920, 928, 928, 928, 912, 928, 912, 928, 928, 928, 912, 912, 912, 928, 928, 928, 896, 928, 928, 912, 928, 928, 928, 912, 928, 912, 928, 928, 912, 
-928, 912, 928, 928, 928, 928, 928, 912, 928, 928, 928, 928, 912, 912, 928, 912, 928, 1024, 928, 928, 928, 928, 928, 928, 1056, 912, 928, 928, 1024, 1024, 
-928, 928, 1024, 928, 928, 928, 928, 928, 928, 1040, 1040, 928, 1056, 1024, 1072, 1024, 1040, 1040, 1040, 1024, 1088, 1056, 1056, 1088, 1040, 1056, 1072, 1072, 1056, 1056, 
-1024, 1088, 1040, 1024, 1040, 1040, 1024, 1056, 1056, 1056, 1040, 1072, 1056, 1040, 1056, 1056, 1056, 1056, 1056, 1056, 1056, 1120, 1056, 1088, 1056, 1120, 1088, 1072, 1104, 1104, 
-1104, 1120, 1088, 1088, 1072, 1088, 1120, 1104, 1088, 1104, 1088, 1072, 1104, 1088, 1120, 1088, 1072, 1072, 1072, 1088, 1088, 1072, 1072, 1088, 1104, 1152, 1104, 1104, 1088, 1104, 
-1136, 1088, 1104, 1152, 1152, 1152, 1136, 1120, 1136, 1152, 1120, 1152, 1088, 1120, 1104, 1120, 1136, 1104, 1136, 1088, 1136, 1104, 1088, 1104, 1120, 1104, 1104, 1120, 1136, 1136, 
-1120, 1136, 1136, 1136, 1120, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1104, 1152, 1120, 1136, 1120, 1120, 1152, 1120, 1136, 1152, 1136, 1152, 1120, 1152, 1136, 1136, 1136, 1136, 
-1136, 1152, 1152, 1152, 1152, 1120, 1120, 1152, 1136, 1136, 1136, 1152, 1152, 1120, 1152, 1152, 1152, 1152, 1152, 1104, 1152, 1152, 1120, 1136, 1152, 1120, 1152, 1136, 1152, 1152, 
-1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 
-1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 
-1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 
-1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 
-1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 
-1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 
-1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 
-1152, 1344, 1152, 1344, 1344, 1344, 1152, 1152, 1152, 1152, 1344, 1328, 1328, 1328, 1152, 1344, 1152, 1344, 1152, 1344, 1152, 1152, 1328, 1152, 1328, 1344, 1328, 1344, 1328, 1344, 
-1344, 1312, 1328, 1328, 1328, 1344, 1344, 1344, 1328, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, 
-1328, 1344, 1344, 1344, 1344, 1328, 1344, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 
-1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1573, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1583, 1568, 1568, 1552, 1568, 1552, 1568, 
-1568, 1568, 1584, 1568, 1584, 1568, 1568, 1568, 1552, 1552, 1552, 1568, 1552, 1584, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1584, 1552, 1584, 1552, 1617, 1568, 1584, 
-1552, 1552, 1584, 1584, 1552, 1625, 1626, 1627, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1632, 1636, 1632, 1638, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 
-1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1648, 1669, 1648, 1671, 1632, 1664, 1648, 1632, 1648, 1648, 1648, 1632, 
-1632, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1648, 1664, 1648, 1648, 1648, 1648, 1648, 1648, 
-1680, 1664, 1680, 1696, 1680, 1680, 1664, 1680, 1680, 1648, 1632, 1680, 1696, 1632, 1648, 1648, 1632, 1680, 1680, 1664, 1664, 1664, 1648, 1680, 1664, 1680, 1664, 1680, 1664, 1664, 
-1680, 1696, 1664, 1696, 1712, 1712, 1696, 1680, 1712, 1696, 1728, 1712, 1696, 1728, 1728, 1712, 1728, 1648, 1680, 1696, 1712, 1696, 1712, 1696, 1696, 1680, 1696, 1696, 1696, 1712, 
-1696, 1696, 1696, 1696, 1712, 1728, 1696, 1728, 1696, 1696, 1712, 1728, 1712, 1728, 1712, 1680, 1696, 1728, 1712, 1696, 1696, 1696, 1712, 1712, 1728, 1696, 1728, 1712, 1712, 1728, 
-1696, 1696, 1696, 1712, 1696, 1728, 1712, 1712, 1712, 1728, 1696, 1712, 1728, 1728, 1696, 1728, 1728, 1728, 1728, 1728, 1680, 1712, 1728, 1696, 1728, 1728, 1728, 1728, 1696, 1728, 
-1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1728, 1696, 1728, 1712, 1712, 1712, 1712, 1728, 1712, 1712, 1712, 1728, 1712, 1728, 1728, 1728, 
-1728, 1712, 1728, 1728, 1712, 1728, 1728, 1712, 1712, 1728, 1712, 1712, 1728, 1728, 1712, 1728, 1712, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1712, 
-1728, 1712, 1712, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 
-1728, 1728, 1712, 1728, 1728, 1824, 1728, 1728, 1728, 1728, 1824, 1728, 1840, 1728, 1728, 1728, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1728, 1728, 1856, 1856, 1856, 1856, 1728, 
-1728, 1856, 1856, 1728, 1856, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1856, 1856, 1856, 1840, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1840, 1904, 1856, 1856, 1840, 1840, 1856, 
-1856, 1840, 1856, 1840, 1856, 1856, 1856, 1856, 1952, 1856, 1856, 1856, 1856, 1952, 1904, 1904, 1856, 1856, 1856, 1920, 1952, 2001, 1952, 1984, 1952, 1936, 1952, 1904, 1968, 1920, 
-1984, 1920, 1968, 1920, 1936, 1856, 2000, 1920, 1936, 1952, 2000, 1968, 1984, 1968, 1984, 2000, 1952, 2000, 2016, 1984, 2000, 2016, 1984, 1664, 2016, 1984, 2016, 1968, 2016, 2016, 
-1744, 2016, 2016, 1968, 2000, 1728, 1712, 1696, };
+#if TUNE_PROGRAM
+short flint_mpn_mulhigh_k_tab[FLINT_MPN_MULHIGH_K_TAB_SIZE];
+#else
+const short flint_mpn_mulhigh_k_tab[FLINT_MPN_MULHIGH_K_TAB_SIZE] = {FLINT_MPN_MULHIGH_K_TAB};
+#endif
 
 void
 _flint_mpn_mulhigh_n_mulders_recursive(mp_ptr rp, mp_srcptr np, mp_srcptr mp, mp_size_t n)
@@ -168,6 +102,7 @@ _flint_mpn_mulhigh_n_mul(mp_ptr res, mp_srcptr u, mp_srcptr v, mp_size_t n)
     return bot;
 }
 
+#if !TUNE_PROGRAM
 mp_limb_t
 _flint_mpn_mulhigh_n(mp_ptr res, mp_srcptr u, mp_srcptr v, mp_size_t n)
 {
@@ -203,3 +138,4 @@ mp_limb_pair_t _flint_mpn_mulhigh_normalised(mp_ptr rp, mp_srcptr xp, mp_srcptr
 
     return ret;
 }
+#endif
diff --git a/src/mpn_extras/sqrhigh.c b/src/mpn_extras/sqrhigh.c
index d1578e3c5d..c5f77c0abf 100644
--- a/src/mpn_extras/sqrhigh.c
+++ b/src/mpn_extras/sqrhigh.c
@@ -17,77 +17,7 @@
 
 #include "mpn_extras.h"
 
-/* Generated by tune-sqrhigh.c */
-static const signed short flint_mpn_sqrhigh_k_tab[FLINT_MPN_SQRHIGH_K_TAB_SIZE] = 
-{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
-0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 29, 0, 0, 31, 0, 31, 
-0, 32, 0, 34, 0, 36, 36, 40, 0, 40, 40, 40, 0, 44, 0, 44, 44, 48, 0, 52, 48, 52, 44, 44, 48, 48, 48, 48, 48, 48, 
-48, 48, 48, 48, 52, 52, 52, 52, 52, 56, 56, 52, 56, 56, 56, 56, 56, 56, 56, 56, 60, 60, 68, 64, 60, 60, 60, 60, 64, 64, 
-64, 68, 68, 68, 64, 64, 68, 68, 72, 72, 68, 68, 68, 72, 76, 80, 72, 72, 72, 88, 76, 76, 80, 80, 76, 80, 76, 80, 84, 80, 
-88, 88, 80, 84, 88, 80, 80, 84, 92, 88, 92, 88, 88, 88, 88, 96, 88, 108, 100, 92, 88, 88, 104, 100, 100, 92, 104, 108, 100, 92, 
-104, 100, 104, 96, 108, 104, 96, 96, 104, 100, 100, 104, 112, 116, 108, 104, 104, 116, 108, 104, 104, 120, 116, 104, 108, 132, 116, 108, 120, 108, 
-108, 108, 132, 108, 120, 112, 112, 116, 132, 128, 116, 124, 128, 116, 132, 120, 132, 120, 124, 120, 132, 120, 124, 128, 120, 128, 128, 132, 144, 124, 
-128, 124, 140, 128, 128, 124, 136, 132, 128, 128, 140, 144, 128, 128, 140, 136, 132, 144, 148, 152, 144, 132, 160, 156, 140, 144, 156, 144, 140, 144, 
-140, 156, 156, 156, 140, 144, 168, 156, 156, 164, 168, 156, 156, 160, 144, 144, 180, 156, 152, 168, 156, 160, 156, 148, 180, 168, 180, 156, 164, 156, 
-156, 172, 156, 156, 156, 180, 180, 172, 180, 168, 164, 172, 164, 172, 176, 176, 168, 176, 172, 176, 180, 168, 176, 180, 180, 180, 192, 184, 180, 176, 
-204, 176, 188, 180, 188, 180, 204, 180, 192, 204, 180, 192, 180, 204, 228, 192, 188, 192, 204, 180, 192, 216, 200, 216, 228, 216, 204, 216, 188, 216, 
-216, 204, 216, 192, 204, 212, 228, 204, 228, 216, 204, 216, 192, 204, 204, 212, 204, 216, 204, 216, 228, 228, 224, 212, 204, 216, 216, 224, 228, 212, 
-216, 228, 212, 204, 204, 216, 216, 216, 228, 216, 220, 224, 228, 220, 228, 228, 236, 224, 260, 224, 228, 228, 260, 228, 248, 252, 264, 248, 216, 212, 
-212, 212, 220, 216, 216, 220, 216, 224, 216, 228, 232, 224, 220, 224, 240, 244, 236, 244, 232, 256, 288, 240, 236, 288, 260, 260, 264, 232, 228, 228, 
-228, 236, 236, 228, 236, 236, 236, 248, 256, 260, 232, 236, 264, 256, 260, 252, 284, 252, 264, 276, 244, 296, 244, 240, 244, 248, 240, 252, 256, 260, 
-260, 252, 252, 272, 252, 272, 260, 296, 268, 260, 256, 276, 272, 264, 312, 284, 256, 252, 252, 252, 264, 252, 256, 260, 264, 276, 292, 268, 264, 276, 
-264, 260, 264, 304, 288, 296, 296, 296, 288, 296, 272, 280, 264, 264, 272, 264, 288, 288, 280, 288, 272, 280, 296, 296, 280, 288, 296, 320, 344, 320, 
-344, 272, 344, 344, 304, 288, 280, 280, 312, 280, 280, 304, 304, 312, 304, 296, 288, 328, 320, 352, 320, 320, 328, 360, 344, 344, 360, 288, 288, 304, 
-288, 296, 320, 320, 312, 312, 304, 328, 336, 312, 312, 360, 336, 344, 344, 336, 360, 360, 296, 296, 304, 360, 328, 328, 312, 320, 320, 328, 312, 344, 
-344, 328, 344, 344, 368, 360, 352, 360, 392, 392, 368, 320, 312, 392, 312, 328, 344, 336, 344, 328, 360, 352, 352, 360, 360, 360, 368, 408, 360, 376, 
-392, 392, 376, 336, 344, 352, 360, 352, 344, 344, 384, 344, 360, 376, 392, 368, 360, 408, 408, 448, 432, 384, 392, 336, 360, 344, 360, 360, 368, 376, 
-376, 360, 368, 408, 368, 376, 376, 376, 432, 376, 384, 464, 432, 344, 432, 376, 344, 344, 384, 344, 384, 376, 400, 432, 456, 432, 456, 392, 432, 392, 
-448, 456, 360, 376, 456, 408, 384, 368, 376, 432, 376, 472, 464, 504, 448, 360, 408, 456, 376, 408, 424, 424, 448, 440, 456, 392, 408, 384, 408, 392, 
-384, 416, 424, 432, 400, 472, 480, 408, 432, 432, 464, 456, 504, 464, 456, 472, 496, 416, 392, 424, 504, 400, 440, 432, 472, 448, 456, 456, 432, 448, 
-456, 504, 504, 512, 496, 504, 424, 416, 408, 432, 544, 432, 440, 456, 448, 448, 464, 472, 480, 552, 552, 544, 552, 560, 552, 544, 544, 544, 552, 552, 
-552, 552, 552, 552, 552, 560, 552, 552, 560, 560, 560, 560, 568, 576, 568, 592, 576, 560, 560, 560, 560, 568, 568, 576, 568, 568, 576, 568, 568, 576, 
-568, 568, 600, 592, 576, 608, 576, 576, 576, 576, 584, 584, 576, 592, 592, 600, 584, 592, 584, 600, 600, 600, 584, 624, 584, 592, 600, 592, 616, 592, 
-592, 592, 592, 592, 592, 592, 600, 608, 600, 608, 600, 600, 600, 624, 616, 608, 616, 600, 632, 608, 608, 608, 616, 608, 608, 608, 608, 616, 608, 664, 
-664, 632, 656, 616, 664, 624, 616, 632, 632, 616, 624, 624, 624, 632, 624, 624, 624, 624, 648, 632, 624, 624, 872, 872, 656, 664, 696, 872, 872, 872, 
-632, 872, 872, 896, 872, 896, 872, 896, 880, 872, 896, 872, 888, 872, 872, 872, 872, 872, 888, 872, 880, 824, 872, 856, 880, 888, 800, 848, 800, 880, 
-848, 800, 808, 872, 872, 864, 824, 840, 872, 872, 872, 872, 872, 872, 872, 872, 872, 872, 880, 928, 872, 920, 872, 920, 888, 880, 872, 880, 872, 872, 
-872, 888, 880, 888, 888, 872, 888, 872, 880, 896, 920, 920, 880, 928, 904, 872, 888, 904, 872, 872, 872, 872, 880, 888, 872, 872, 872, 880, 872, 904, 
-920, 888, 888, 872, 880, 880, 888, 896, 896, 880, 872, 904, 880, 912, 896, 872, 904, 904, 912, 880, 880, 920, 912, 896, 928, 928, 872, 872, 872, 872, 
-880, 880, 888, 888, 888, 912, 880, 880, 880, 912, 896, 896, 928, 896, 912, 912, 896, 928, 928, 928, 928, 912, 880, 928, 880, 880, 896, 880, 896, 880, 
-896, 880, 880, 912, 912, 880, 896, 880, 896, 912, 880, 880, 928, 912, 912, 928, 928, 896, 928, 912, 928, 928, 928, 928, 928, 928, 880, 880, 880, 880, 
-880, 912, 896, 912, 912, 896, 928, 896, 928, 896, 928, 928, 928, 928, 912, 880, 928, 912, 896, 928, 896, 880, 912, 896, 912, 896, 896, 896, 928, 896, 
-912, 928, 912, 928, 912, 928, 912, 880, 928, 928, 880, 928, 928, 880, 896, 928, 880, 896, 912, 928, 928, 896, 912, 928, 912, 928, 1024, 928, 928, 1040, 
-912, 928, 1024, 1024, 928, 928, 928, 928, 912, 1040, 1072, 912, 1072, 1072, 1056, 1040, 1072, 1088, 1104, 1040, 1040, 928, 1024, 928, 928, 1056, 928, 928, 1056, 1040, 
-928, 1056, 1024, 1056, 1056, 1056, 1104, 1024, 1056, 1072, 1056, 1056, 1088, 1072, 1120, 1104, 1072, 1072, 1072, 1104, 1120, 1024, 1120, 1120, 1056, 1024, 1040, 1024, 1040, 1040, 
-1040, 1024, 1040, 1056, 1040, 1088, 1040, 1056, 1120, 1040, 1040, 1072, 1072, 1088, 1104, 1088, 1104, 1088, 1088, 1056, 1120, 1104, 1152, 1104, 1088, 1120, 1104, 1120, 1024, 1120, 
-1152, 1136, 1152, 1056, 1056, 1072, 1056, 1152, 1088, 1056, 1104, 1072, 1104, 1088, 1120, 1072, 1104, 1088, 1088, 1120, 1120, 1120, 1152, 1136, 1120, 1120, 1152, 1120, 1136, 1152, 
-1152, 1072, 1136, 1136, 1088, 1152, 1136, 1136, 1104, 1056, 1072, 1088, 1104, 1104, 1120, 1120, 1104, 1104, 1104, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1136, 1072, 
-1152, 1136, 1152, 1152, 1104, 1152, 1104, 1152, 1152, 1088, 1120, 1152, 1136, 1136, 1120, 1136, 1120, 1152, 1136, 1136, 1120, 1136, 1152, 1136, 1152, 1136, 1136, 1120, 1152, 1152, 
-1104, 1152, 1152, 1152, 1104, 1120, 1104, 1120, 1120, 1120, 1120, 1136, 1136, 1136, 1136, 1152, 1120, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1104, 
-1120, 1152, 1136, 1136, 1136, 1136, 1136, 1136, 1120, 1152, 1152, 1152, 1136, 1104, 1152, 1136, 1136, 1152, 1136, 1120, 1136, 1152, 1152, 1136, 1136, 1120, 1136, 1136, 1136, 1120, 
-1152, 1152, 1152, 1136, 1136, 1136, 1152, 1104, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1152, 
-1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 
-1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 
-1120, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 
-1136, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1136, 
-1152, 1152, 1152, 1104, 1120, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1152, 1120, 1152, 1136, 1152, 1152, 1120, 1152, 1120, 1136, 1152, 1152, 
-1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1120, 1152, 1152, 1136, 1152, 1136, 1552, 1552, 1136, 1136, 1152, 1552, 1136, 1136, 1584, 1552, 1552, 1552, 
-1152, 1552, 1552, 1152, 1584, 1552, 1152, 1152, 1552, 1584, 1152, 1152, 1552, 1584, 1568, 1552, 1552, 1552, 1152, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 
-1552, 1552, 1552, 1552, 1552, 1625, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1568, 1632, 1552, 1632, 1568, 1584, 1568, 1568, 1584, 1600, 1552, 1552, 1632, 1600, 1632, 1632, 1632, 
-1632, 1568, 1584, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1552, 1662, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1568, 1600, 1632, 1552, 1616, 1632, 1632, 1632, 1584, 1632, 
-1632, 1552, 1632, 1632, 1632, 1568, 1600, 1632, 1648, 1616, 1632, 1648, 1632, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1632, 1664, 1632, 1632, 
-1632, 1632, 1632, 1632, 1632, 1648, 1648, 1648, 1616, 1632, 1680, 1632, 1680, 1648, 1632, 1664, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, 
-1648, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1648, 1664, 1648, 1648, 1632, 1648, 1632, 1680, 1664, 1648, 1680, 1664, 1696, 1632, 1664, 1680, 1632, 1648, 1696, 
-1680, 1632, 1632, 1648, 1648, 1648, 1632, 1664, 1632, 1648, 1648, 1632, 1648, 1648, 1632, 1664, 1664, 1680, 1680, 1632, 1664, 1664, 1648, 1648, 1712, 1728, 1664, 1712, 1696, 1712, 
-1680, 1632, 1728, 1648, 1728, 1728, 1712, 1648, 1632, 1632, 1664, 1648, 1664, 1664, 1680, 1712, 1664, 1632, 1696, 1664, 1712, 1696, 1680, 1680, 1696, 1680, 1680, 1712, 1648, 1712, 
-1632, 1728, 1696, 1648, 1712, 1632, 1712, 1696, 1648, 1680, 1648, 1664, 1648, 1696, 1712, 1648, 1648, 1680, 1664, 1696, 1728, 1696, 1712, 1728, 1696, 1728, 1712, 1664, 1680, 1728, 
-1712, 1712, 1712, 1728, 1728, 1712, 1728, 1696, 1728, 1712, 1696, 1728, 1728, 1680, 1728, 1712, 1664, 1680, 1680, 1696, 1712, 1696, 1696, 1696, 1728, 1696, 1728, 1728, 1696, 1712, 
-1712, 1664, 1712, 1680, 1664, 1728, 1728, 1664, 1696, 1696, 1680, 1712, 1680, 1712, 1696, 1728, 1696, 1696, 1728, 1696, 1712, 1696, 1712, 1712, 1712, 1728, 1712, 1696, 1728, 1680, 
-1696, 1712, 1712, 1728, 1712, 1728, 1696, 1728, 1776, 1728, 1696, 1776, 1728, 1728, 1712, 1712, 1824, 1856, 1728, 1824, 1728, 1728, 1712, 1728, 1728, 1728, 1856, 1696, 1728, 1840, 
-1712, 1712, 1824, 1856, 1792, 1712, 1840, 1728, 1808, 1728, 1824, 1824, 1840, 1824, 1824, 1856, 1856, 1824, 1856, 1840, 1696, 1856, 1840, 1840, 1856, 1856, 1824, 1712, 1792, 1856, 
-1824, 1728, 1808, 1792, 1856, 1728, 1792, 1840, 1808, 1808, 1712, 1808, 1840, 1808, 1824, 1824, 1824, 1840, 1824, 1840, 1856, 1824, 1728, 1856, 1856, 1824, 1856, 1856, 1792, 1792, 
-1856, 1824, 1856, 1824, 1824, 1856, 1808, 1824, 1856, 1856, 1840, 1840, 1840, 1840, 1856, 1840, 1840, 1856, 1824, 1840, 1808, 1824, 1840, 1856, 1856, 1824, 1856, 1840, 1840, 1840, 
-1824, 1824, 1840, 1840, 1840, 1856, 1856, 1856, };
+static const short flint_mpn_sqrhigh_k_tab[FLINT_MPN_SQRHIGH_K_TAB_SIZE] = {FLINT_MPN_SQRHIGH_K_TAB};
 
 void
 _flint_mpn_sqrhigh_mulders_recursive(mp_ptr rp, mp_srcptr np, mp_size_t n)
diff --git a/src/mpn_extras/x86_64/broadwell/flint-mparam.h b/src/mpn_extras/x86_64/broadwell/flint-mparam.h
index 0112747333..8c5e03d736 100644
--- a/src/mpn_extras/x86_64/broadwell/flint-mparam.h
+++ b/src/mpn_extras/x86_64/broadwell/flint-mparam.h
@@ -29,4 +29,156 @@
 #define FFT_N_NUM                                 19
 #define FFT_MULMOD_2EXPP1_CUTOFF                 128
 
+/* FIXME: This tuning is for x86_64_adx with fft_small */
+/* NOTE: We assume that the same cutoff is optimal for both mulhigh and mullow */
+#define FLINT_MPN_MULHIGH_MULDERS_CUTOFF 50
+#define FLINT_MPN_MULHIGH_MUL_CUTOFF 2000
+#define FLINT_MPN_MULHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_SQRHIGH_MULDERS_CUTOFF 90
+#define FLINT_MPN_SQRHIGH_SQR_CUTOFF 2000
+#define FLINT_MPN_SQRHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_MULHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 16, 15, 15, 18, 18, \
+  18, 19, 20, 18, 22, 22, 20, 20, 26, 22, 22, 22, 24, 24, 24, 26, 25, 26, 30, 30, 28, 30, 31, 32, 32, 30, 36, 36, 36, 36, \
+  38, 39, 39, 38, 39, 40, 40, 40, 44, 40, 44, 44, 40, 44, 44, 48, 44, 48, 44, 48, 48, 52, 52, 52, 44, 52, 52, 52, 52, 56, \
+  60, 60, 52, 60, 60, 52, 52, 60, 64, 72, 56, 60, 72, 60, 60, 60, 76, 64, 60, 60, 72, 60, 72, 80, 72, 72, 80, 72, 68, 76, \
+  88, 76, 68, 76, 72, 72, 80, 88, 72, 72, 88, 72, 80, 76, 76, 80, 80, 88, 80, 88, 84, 88, 80, 96, 80, 80, 88, 80, 88, 88, \
+  80, 88, 96, 96, 88, 96, 92, 96, 96, 92, 100, 88, 96, 104, 88, 108, 96, 104, 104, 104, 112, 112, 108, 104, 104, 112, 112, 120, 104, 112, \
+  120, 112, 112, 120, 124, 124, 116, 124, 108, 120, 124, 116, 120, 120, 116, 120, 124, 120, 120, 140, 120, 120, 120, 120, 144, 120, 132, 144, 136, 140, \
+  144, 144, 144, 144, 144, 144, 144, 144, 140, 156, 140, 140, 144, 144, 144, 160, 144, 144, 156, 156, 144, 160, 160, 160, 160, 152, 160, 156, 156, 156, \
+  160, 160, 144, 160, 164, 156, 156, 156, 172, 156, 156, 160, 176, 160, 160, 164, 176, 156, 160, 160, 156, 156, 160, 160, 156, 160, 172, 160, 188, 172, \
+  172, 172, 160, 172, 176, 160, 160, 176, 180, 176, 164, 188, 192, 176, 172, 188, 188, 188, 172, 188, 192, 188, 180, 192, 192, 188, 188, 192, 188, 188, \
+  188, 188, 192, 160, 156, 204, 160, 164, 164, 164, 164, 176, 180, 168, 172, 184, 188, 200, 216, 188, 164, 188, 220, 188, 208, 176, 180, 188, 172, 188, \
+  184, 188, 204, 208, 220, 196, 220, 196, 208, 212, 188, 220, 176, 176, 184, 192, 208, 184, 188, 196, 204, 244, 208, 212, 212, 228, 256, 188, 204, 196, \
+  188, 192, 192, 192, 212, 188, 292, 212, 220, 236, 228, 248, 260, 224, 264, 196, 200, 196, 212, 208, 204, 216, 208, 228, 216, 220, 252, 220, 268, 264, \
+  284, 268, 300, 220, 208, 212, 220, 236, 244, 224, 252, 252, 260, 264, 256, 256, 292, 272, 288, 292, 328, 224, 256, 236, 252, 268, 256, 252, 260, 272, \
+  284, 296, 300, 280, 300, 284, 252, 236, 328, 324, 264, 264, 256, 264, 280, 268, 284, 284, 292, 304, 260, 304, 264, 256, 328, 328, 260, 276, 328, 284, \
+  276, 296, 300, 320, 320, 304, 328, 304, 272, 268, 280, 268, 288, 292, 288, 284, 316, 288, 328, 328, 300, 328, 328, 280, 264, 328, 300, 328, 316, 324, \
+  300, 324, 300, 324, 316, 316, 328, 348, 276, 376, 288, 296, 296, 304, 320, 316, 328, 328, 324, 328, 340, 384, 348, 376, 300, 396, 304, 300, 304, 324, \
+  300, 324, 328, 328, 328, 440, 448, 384, 376, 456, 464, 384, 376, 472, 480, 376, 352, 328, 376, 352, 376, 392, 392, 384, 456, 456, 480, 448, 456, 456, \
+  472, 472, 472, 352, 464, 472, 472, 472, 480, 440, 480, 480, 480, 480, 456, 472, 472, 464, 464, 464, 456, 472, 480, 472, 480, 480, 480, 480, 448, 456, \
+  480, 448, 456, 464, 456, 464, 456, 480, 472, 464, 464, 472, 472, 472, 480, 472, 480, 480, 472, 480, 480, 480, 480, 464, 464, 464, 456, 472, 464, 480, \
+  472, 472, 480, 472, 480, 480, 464, 464, 472, 464, 472, 472, 480, 464, 480, 472, 480, 480, 576, 576, 560, 480, 472, 480, 568, 480, 480, 464, 480, 472, \
+  480, 576, 480, 552, 560, 560, 560, 560, 568, 560, 560, 576, 576, 560, 568, 472, 480, 480, 544, 568, 552, 544, 560, 544, 560, 568, 552, 576, 568, 560, \
+  576, 576, 568, 576, 560, 576, 568, 536, 576, 568, 560, 544, 560, 552, 560, 568, 560, 576, 568, 560, 560, 560, 568, 576, 568, 576, 576, 576, 576, 544, \
+  576, 576, 568, 576, 560, 576, 576, 576, 544, 552, 568, 576, 552, 560, 576, 560, 568, 560, 576, 560, 544, 576, 576, 576, 576, 568, 576, 568, 560, 576, \
+  552, 552, 576, 560, 568, 568, 568, 576, 576, 576, 560, 552, 576, 560, 568, 560, 576, 560, 568, 560, 568, 568, 568, 576, 552, 576, 560, 576, 576, 560, \
+  568, 576, 568, 576, 576, 576, 576, 560, 576, 568, 568, 568, 560, 560, 576, 576, 568, 568, 576, 560, 576, 576, 568, 576, 560, 576, 576, 568, 576, 568, \
+  576, 568, 576, 576, 568, 576, 576, 576, 576, 568, 576, 576, 568, 568, 576, 576, 784, 576, 776, 576, 568, 576, 576, 576, 576, 576, 576, 576, 776, 776, \
+  776, 776, 776, 776, 776, 784, 776, 776, 784, 776, 776, 776, 800, 776, 776, 776, 776, 776, 776, 800, 776, 808, 792, 800, 776, 792, 776, 776, 776, 776, \
+  792, 776, 776, 784, 792, 784, 800, 776, 784, 808, 784, 776, 776, 776, 808, 784, 792, 776, 792, 832, 800, 800, 816, 792, 816, 816, 856, 808, 848, 824, \
+  870, 832, 792, 776, 784, 784, 784, 784, 800, 792, 800, 792, 784, 800, 800, 800, 816, 824, 824, 824, 832, 816, 816, 832, 824, 824, 848, 832, 856, 856, \
+  840, 872, 864, 872, 872, 880, 880, 880, 872, 888, 880, 880, 872, 880, 880, 880, 840, 872, 872, 848, 880, 848, 856, 840, 848, 840, 880, 872, 856, 872, \
+  856, 888, 880, 872, 888, 880, 872, 920, 888, 872, 880, 872, 888, 888, 888, 880, 880, 928, 880, 928, 928, 928, 920, 920, 904, 912, 880, 904, 928, 872, \
+  872, 880, 888, 880, 896, 880, 872, 896, 888, 896, 896, 928, 904, 896, 896, 912, 904, 904, 920, 880, 912, 920, 928, 928, 880, 920, 920, 880, 888, 904, \
+  896, 904, 928, 896, 912, 896, 912, 920, 912, 912, 928, 928, 928, 920, 928, 928, 928, 928, 928, 928, 912, 904, 912, 896, 904, 904, 920, 920, 920, 928, \
+  928, 920, 928, 928, 928, 912, 928, 912, 928, 928, 928, 912, 912, 912, 928, 928, 928, 896, 928, 928, 912, 928, 928, 928, 912, 928, 912, 928, 928, 912, \
+  928, 912, 928, 928, 928, 928, 928, 912, 928, 928, 928, 928, 912, 912, 928, 912, 928, 1024, 928, 928, 928, 928, 928, 928, 1056, 912, 928, 928, 1024, 1024, \
+  928, 928, 1024, 928, 928, 928, 928, 928, 928, 1040, 1040, 928, 1056, 1024, 1072, 1024, 1040, 1040, 1040, 1024, 1088, 1056, 1056, 1088, 1040, 1056, 1072, 1072, 1056, 1056, \
+  1024, 1088, 1040, 1024, 1040, 1040, 1024, 1056, 1056, 1056, 1040, 1072, 1056, 1040, 1056, 1056, 1056, 1056, 1056, 1056, 1056, 1120, 1056, 1088, 1056, 1120, 1088, 1072, 1104, 1104, \
+  1104, 1120, 1088, 1088, 1072, 1088, 1120, 1104, 1088, 1104, 1088, 1072, 1104, 1088, 1120, 1088, 1072, 1072, 1072, 1088, 1088, 1072, 1072, 1088, 1104, 1152, 1104, 1104, 1088, 1104, \
+  1136, 1088, 1104, 1152, 1152, 1152, 1136, 1120, 1136, 1152, 1120, 1152, 1088, 1120, 1104, 1120, 1136, 1104, 1136, 1088, 1136, 1104, 1088, 1104, 1120, 1104, 1104, 1120, 1136, 1136, \
+  1120, 1136, 1136, 1136, 1120, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1104, 1152, 1120, 1136, 1120, 1120, 1152, 1120, 1136, 1152, 1136, 1152, 1120, 1152, 1136, 1136, 1136, 1136, \
+  1136, 1152, 1152, 1152, 1152, 1120, 1120, 1152, 1136, 1136, 1136, 1152, 1152, 1120, 1152, 1152, 1152, 1152, 1152, 1104, 1152, 1152, 1120, 1136, 1152, 1120, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1344, 1152, 1344, 1344, 1344, 1152, 1152, 1152, 1152, 1344, 1328, 1328, 1328, 1152, 1344, 1152, 1344, 1152, 1344, 1152, 1152, 1328, 1152, 1328, 1344, 1328, 1344, 1328, 1344, \
+  1344, 1312, 1328, 1328, 1328, 1344, 1344, 1344, 1328, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, \
+  1328, 1344, 1344, 1344, 1344, 1328, 1344, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1573, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1583, 1568, 1568, 1552, 1568, 1552, 1568, \
+  1568, 1568, 1584, 1568, 1584, 1568, 1568, 1568, 1552, 1552, 1552, 1568, 1552, 1584, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1584, 1552, 1584, 1552, 1617, 1568, 1584, \
+  1552, 1552, 1584, 1584, 1552, 1625, 1626, 1627, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1632, 1636, 1632, 1638, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1648, 1669, 1648, 1671, 1632, 1664, 1648, 1632, 1648, 1648, 1648, 1632, \
+  1632, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1648, 1664, 1648, 1648, 1648, 1648, 1648, 1648, \
+  1680, 1664, 1680, 1696, 1680, 1680, 1664, 1680, 1680, 1648, 1632, 1680, 1696, 1632, 1648, 1648, 1632, 1680, 1680, 1664, 1664, 1664, 1648, 1680, 1664, 1680, 1664, 1680, 1664, 1664, \
+  1680, 1696, 1664, 1696, 1712, 1712, 1696, 1680, 1712, 1696, 1728, 1712, 1696, 1728, 1728, 1712, 1728, 1648, 1680, 1696, 1712, 1696, 1712, 1696, 1696, 1680, 1696, 1696, 1696, 1712, \
+  1696, 1696, 1696, 1696, 1712, 1728, 1696, 1728, 1696, 1696, 1712, 1728, 1712, 1728, 1712, 1680, 1696, 1728, 1712, 1696, 1696, 1696, 1712, 1712, 1728, 1696, 1728, 1712, 1712, 1728, \
+  1696, 1696, 1696, 1712, 1696, 1728, 1712, 1712, 1712, 1728, 1696, 1712, 1728, 1728, 1696, 1728, 1728, 1728, 1728, 1728, 1680, 1712, 1728, 1696, 1728, 1728, 1728, 1728, 1696, 1728, \
+  1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1728, 1696, 1728, 1712, 1712, 1712, 1712, 1728, 1712, 1712, 1712, 1728, 1712, 1728, 1728, 1728, \
+  1728, 1712, 1728, 1728, 1712, 1728, 1728, 1712, 1712, 1728, 1712, 1712, 1728, 1728, 1712, 1728, 1712, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1712, \
+  1728, 1712, 1712, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, \
+  1728, 1728, 1712, 1728, 1728, 1824, 1728, 1728, 1728, 1728, 1824, 1728, 1840, 1728, 1728, 1728, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1728, 1728, 1856, 1856, 1856, 1856, 1728, \
+  1728, 1856, 1856, 1728, 1856, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1856, 1856, 1856, 1840, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1840, 1904, 1856, 1856, 1840, 1840, 1856, \
+  1856, 1840, 1856, 1840, 1856, 1856, 1856, 1856, 1952, 1856, 1856, 1856, 1856, 1952, 1904, 1904, 1856, 1856, 1856, 1920, 1952, 2001, 1952, 1984, 1952, 1936, 1952, 1904, 1968, 1920, \
+  1984, 1920, 1968, 1920, 1936, 1856, 2000, 1920, 1936, 1952, 2000, 1968, 1984, 1968, 1984, 2000, 1952, 2000, 2016, 1984, 2000, 2016, 1984, 1664, 2016, 1984, 2016, 1968, 2016, 2016, \
+  1744, 2016, 2016, 1968, 2000, 1728, 1712, 1696
+
+#define FLINT_MPN_SQRHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 29, 0, 0, 31, 0, 31, \
+  0, 32, 0, 34, 0, 36, 36, 40, 0, 40, 40, 40, 0, 44, 0, 44, 44, 48, 0, 52, 48, 52, 44, 44, 48, 48, 48, 48, 48, 48, \
+  48, 48, 48, 48, 52, 52, 52, 52, 52, 56, 56, 52, 56, 56, 56, 56, 56, 56, 56, 56, 60, 60, 68, 64, 60, 60, 60, 60, 64, 64, \
+  64, 68, 68, 68, 64, 64, 68, 68, 72, 72, 68, 68, 68, 72, 76, 80, 72, 72, 72, 88, 76, 76, 80, 80, 76, 80, 76, 80, 84, 80, \
+  88, 88, 80, 84, 88, 80, 80, 84, 92, 88, 92, 88, 88, 88, 88, 96, 88, 108, 100, 92, 88, 88, 104, 100, 100, 92, 104, 108, 100, 92, \
+  104, 100, 104, 96, 108, 104, 96, 96, 104, 100, 100, 104, 112, 116, 108, 104, 104, 116, 108, 104, 104, 120, 116, 104, 108, 132, 116, 108, 120, 108, \
+  108, 108, 132, 108, 120, 112, 112, 116, 132, 128, 116, 124, 128, 116, 132, 120, 132, 120, 124, 120, 132, 120, 124, 128, 120, 128, 128, 132, 144, 124, \
+  128, 124, 140, 128, 128, 124, 136, 132, 128, 128, 140, 144, 128, 128, 140, 136, 132, 144, 148, 152, 144, 132, 160, 156, 140, 144, 156, 144, 140, 144, \
+  140, 156, 156, 156, 140, 144, 168, 156, 156, 164, 168, 156, 156, 160, 144, 144, 180, 156, 152, 168, 156, 160, 156, 148, 180, 168, 180, 156, 164, 156, \
+  156, 172, 156, 156, 156, 180, 180, 172, 180, 168, 164, 172, 164, 172, 176, 176, 168, 176, 172, 176, 180, 168, 176, 180, 180, 180, 192, 184, 180, 176, \
+  204, 176, 188, 180, 188, 180, 204, 180, 192, 204, 180, 192, 180, 204, 228, 192, 188, 192, 204, 180, 192, 216, 200, 216, 228, 216, 204, 216, 188, 216, \
+  216, 204, 216, 192, 204, 212, 228, 204, 228, 216, 204, 216, 192, 204, 204, 212, 204, 216, 204, 216, 228, 228, 224, 212, 204, 216, 216, 224, 228, 212, \
+  216, 228, 212, 204, 204, 216, 216, 216, 228, 216, 220, 224, 228, 220, 228, 228, 236, 224, 260, 224, 228, 228, 260, 228, 248, 252, 264, 248, 216, 212, \
+  212, 212, 220, 216, 216, 220, 216, 224, 216, 228, 232, 224, 220, 224, 240, 244, 236, 244, 232, 256, 288, 240, 236, 288, 260, 260, 264, 232, 228, 228, \
+  228, 236, 236, 228, 236, 236, 236, 248, 256, 260, 232, 236, 264, 256, 260, 252, 284, 252, 264, 276, 244, 296, 244, 240, 244, 248, 240, 252, 256, 260, \
+  260, 252, 252, 272, 252, 272, 260, 296, 268, 260, 256, 276, 272, 264, 312, 284, 256, 252, 252, 252, 264, 252, 256, 260, 264, 276, 292, 268, 264, 276, \
+  264, 260, 264, 304, 288, 296, 296, 296, 288, 296, 272, 280, 264, 264, 272, 264, 288, 288, 280, 288, 272, 280, 296, 296, 280, 288, 296, 320, 344, 320, \
+  344, 272, 344, 344, 304, 288, 280, 280, 312, 280, 280, 304, 304, 312, 304, 296, 288, 328, 320, 352, 320, 320, 328, 360, 344, 344, 360, 288, 288, 304, \
+  288, 296, 320, 320, 312, 312, 304, 328, 336, 312, 312, 360, 336, 344, 344, 336, 360, 360, 296, 296, 304, 360, 328, 328, 312, 320, 320, 328, 312, 344, \
+  344, 328, 344, 344, 368, 360, 352, 360, 392, 392, 368, 320, 312, 392, 312, 328, 344, 336, 344, 328, 360, 352, 352, 360, 360, 360, 368, 408, 360, 376, \
+  392, 392, 376, 336, 344, 352, 360, 352, 344, 344, 384, 344, 360, 376, 392, 368, 360, 408, 408, 448, 432, 384, 392, 336, 360, 344, 360, 360, 368, 376, \
+  376, 360, 368, 408, 368, 376, 376, 376, 432, 376, 384, 464, 432, 344, 432, 376, 344, 344, 384, 344, 384, 376, 400, 432, 456, 432, 456, 392, 432, 392, \
+  448, 456, 360, 376, 456, 408, 384, 368, 376, 432, 376, 472, 464, 504, 448, 360, 408, 456, 376, 408, 424, 424, 448, 440, 456, 392, 408, 384, 408, 392, \
+  384, 416, 424, 432, 400, 472, 480, 408, 432, 432, 464, 456, 504, 464, 456, 472, 496, 416, 392, 424, 504, 400, 440, 432, 472, 448, 456, 456, 432, 448, \
+  456, 504, 504, 512, 496, 504, 424, 416, 408, 432, 544, 432, 440, 456, 448, 448, 464, 472, 480, 552, 552, 544, 552, 560, 552, 544, 544, 544, 552, 552, \
+  552, 552, 552, 552, 552, 560, 552, 552, 560, 560, 560, 560, 568, 576, 568, 592, 576, 560, 560, 560, 560, 568, 568, 576, 568, 568, 576, 568, 568, 576, \
+  568, 568, 600, 592, 576, 608, 576, 576, 576, 576, 584, 584, 576, 592, 592, 600, 584, 592, 584, 600, 600, 600, 584, 624, 584, 592, 600, 592, 616, 592, \
+  592, 592, 592, 592, 592, 592, 600, 608, 600, 608, 600, 600, 600, 624, 616, 608, 616, 600, 632, 608, 608, 608, 616, 608, 608, 608, 608, 616, 608, 664, \
+  664, 632, 656, 616, 664, 624, 616, 632, 632, 616, 624, 624, 624, 632, 624, 624, 624, 624, 648, 632, 624, 624, 872, 872, 656, 664, 696, 872, 872, 872, \
+  632, 872, 872, 896, 872, 896, 872, 896, 880, 872, 896, 872, 888, 872, 872, 872, 872, 872, 888, 872, 880, 824, 872, 856, 880, 888, 800, 848, 800, 880, \
+  848, 800, 808, 872, 872, 864, 824, 840, 872, 872, 872, 872, 872, 872, 872, 872, 872, 872, 880, 928, 872, 920, 872, 920, 888, 880, 872, 880, 872, 872, \
+  872, 888, 880, 888, 888, 872, 888, 872, 880, 896, 920, 920, 880, 928, 904, 872, 888, 904, 872, 872, 872, 872, 880, 888, 872, 872, 872, 880, 872, 904, \
+  920, 888, 888, 872, 880, 880, 888, 896, 896, 880, 872, 904, 880, 912, 896, 872, 904, 904, 912, 880, 880, 920, 912, 896, 928, 928, 872, 872, 872, 872, \
+  880, 880, 888, 888, 888, 912, 880, 880, 880, 912, 896, 896, 928, 896, 912, 912, 896, 928, 928, 928, 928, 912, 880, 928, 880, 880, 896, 880, 896, 880, \
+  896, 880, 880, 912, 912, 880, 896, 880, 896, 912, 880, 880, 928, 912, 912, 928, 928, 896, 928, 912, 928, 928, 928, 928, 928, 928, 880, 880, 880, 880, \
+  880, 912, 896, 912, 912, 896, 928, 896, 928, 896, 928, 928, 928, 928, 912, 880, 928, 912, 896, 928, 896, 880, 912, 896, 912, 896, 896, 896, 928, 896, \
+  912, 928, 912, 928, 912, 928, 912, 880, 928, 928, 880, 928, 928, 880, 896, 928, 880, 896, 912, 928, 928, 896, 912, 928, 912, 928, 1024, 928, 928, 1040, \
+  912, 928, 1024, 1024, 928, 928, 928, 928, 912, 1040, 1072, 912, 1072, 1072, 1056, 1040, 1072, 1088, 1104, 1040, 1040, 928, 1024, 928, 928, 1056, 928, 928, 1056, 1040, \
+  928, 1056, 1024, 1056, 1056, 1056, 1104, 1024, 1056, 1072, 1056, 1056, 1088, 1072, 1120, 1104, 1072, 1072, 1072, 1104, 1120, 1024, 1120, 1120, 1056, 1024, 1040, 1024, 1040, 1040, \
+  1040, 1024, 1040, 1056, 1040, 1088, 1040, 1056, 1120, 1040, 1040, 1072, 1072, 1088, 1104, 1088, 1104, 1088, 1088, 1056, 1120, 1104, 1152, 1104, 1088, 1120, 1104, 1120, 1024, 1120, \
+  1152, 1136, 1152, 1056, 1056, 1072, 1056, 1152, 1088, 1056, 1104, 1072, 1104, 1088, 1120, 1072, 1104, 1088, 1088, 1120, 1120, 1120, 1152, 1136, 1120, 1120, 1152, 1120, 1136, 1152, \
+  1152, 1072, 1136, 1136, 1088, 1152, 1136, 1136, 1104, 1056, 1072, 1088, 1104, 1104, 1120, 1120, 1104, 1104, 1104, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1136, 1072, \
+  1152, 1136, 1152, 1152, 1104, 1152, 1104, 1152, 1152, 1088, 1120, 1152, 1136, 1136, 1120, 1136, 1120, 1152, 1136, 1136, 1120, 1136, 1152, 1136, 1152, 1136, 1136, 1120, 1152, 1152, \
+  1104, 1152, 1152, 1152, 1104, 1120, 1104, 1120, 1120, 1120, 1120, 1136, 1136, 1136, 1136, 1152, 1120, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1104, \
+  1120, 1152, 1136, 1136, 1136, 1136, 1136, 1136, 1120, 1152, 1152, 1152, 1136, 1104, 1152, 1136, 1136, 1152, 1136, 1120, 1136, 1152, 1152, 1136, 1136, 1120, 1136, 1136, 1136, 1120, \
+  1152, 1152, 1152, 1136, 1136, 1136, 1152, 1104, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1152, \
+  1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, \
+  1120, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1136, \
+  1152, 1152, 1152, 1104, 1120, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1152, 1120, 1152, 1136, 1152, 1152, 1120, 1152, 1120, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1120, 1152, 1152, 1136, 1152, 1136, 1552, 1552, 1136, 1136, 1152, 1552, 1136, 1136, 1584, 1552, 1552, 1552, \
+  1152, 1552, 1552, 1152, 1584, 1552, 1152, 1152, 1552, 1584, 1152, 1152, 1552, 1584, 1568, 1552, 1552, 1552, 1152, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1625, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1568, 1632, 1552, 1632, 1568, 1584, 1568, 1568, 1584, 1600, 1552, 1552, 1632, 1600, 1632, 1632, 1632, \
+  1632, 1568, 1584, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1552, 1662, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1568, 1600, 1632, 1552, 1616, 1632, 1632, 1632, 1584, 1632, \
+  1632, 1552, 1632, 1632, 1632, 1568, 1600, 1632, 1648, 1616, 1632, 1648, 1632, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1632, 1664, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1648, 1648, 1648, 1616, 1632, 1680, 1632, 1680, 1648, 1632, 1664, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1648, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1648, 1664, 1648, 1648, 1632, 1648, 1632, 1680, 1664, 1648, 1680, 1664, 1696, 1632, 1664, 1680, 1632, 1648, 1696, \
+  1680, 1632, 1632, 1648, 1648, 1648, 1632, 1664, 1632, 1648, 1648, 1632, 1648, 1648, 1632, 1664, 1664, 1680, 1680, 1632, 1664, 1664, 1648, 1648, 1712, 1728, 1664, 1712, 1696, 1712, \
+  1680, 1632, 1728, 1648, 1728, 1728, 1712, 1648, 1632, 1632, 1664, 1648, 1664, 1664, 1680, 1712, 1664, 1632, 1696, 1664, 1712, 1696, 1680, 1680, 1696, 1680, 1680, 1712, 1648, 1712, \
+  1632, 1728, 1696, 1648, 1712, 1632, 1712, 1696, 1648, 1680, 1648, 1664, 1648, 1696, 1712, 1648, 1648, 1680, 1664, 1696, 1728, 1696, 1712, 1728, 1696, 1728, 1712, 1664, 1680, 1728, \
+  1712, 1712, 1712, 1728, 1728, 1712, 1728, 1696, 1728, 1712, 1696, 1728, 1728, 1680, 1728, 1712, 1664, 1680, 1680, 1696, 1712, 1696, 1696, 1696, 1728, 1696, 1728, 1728, 1696, 1712, \
+  1712, 1664, 1712, 1680, 1664, 1728, 1728, 1664, 1696, 1696, 1680, 1712, 1680, 1712, 1696, 1728, 1696, 1696, 1728, 1696, 1712, 1696, 1712, 1712, 1712, 1728, 1712, 1696, 1728, 1680, \
+  1696, 1712, 1712, 1728, 1712, 1728, 1696, 1728, 1776, 1728, 1696, 1776, 1728, 1728, 1712, 1712, 1824, 1856, 1728, 1824, 1728, 1728, 1712, 1728, 1728, 1728, 1856, 1696, 1728, 1840, \
+  1712, 1712, 1824, 1856, 1792, 1712, 1840, 1728, 1808, 1728, 1824, 1824, 1840, 1824, 1824, 1856, 1856, 1824, 1856, 1840, 1696, 1856, 1840, 1840, 1856, 1856, 1824, 1712, 1792, 1856, \
+  1824, 1728, 1808, 1792, 1856, 1728, 1792, 1840, 1808, 1808, 1712, 1808, 1840, 1808, 1824, 1824, 1824, 1840, 1824, 1840, 1856, 1824, 1728, 1856, 1856, 1824, 1856, 1856, 1792, 1792, \
+  1856, 1824, 1856, 1824, 1824, 1856, 1808, 1824, 1856, 1856, 1840, 1840, 1840, 1840, 1856, 1840, 1840, 1856, 1824, 1840, 1808, 1824, 1840, 1856, 1856, 1824, 1856, 1840, 1840, 1840, \
+  1824, 1824, 1840, 1840, 1840, 1856, 1856, 1856
+
 #endif
diff --git a/src/mpn_extras/x86_64/flint-mparam.h b/src/mpn_extras/x86_64/flint-mparam.h
index 0112747333..8c5e03d736 100644
--- a/src/mpn_extras/x86_64/flint-mparam.h
+++ b/src/mpn_extras/x86_64/flint-mparam.h
@@ -29,4 +29,156 @@
 #define FFT_N_NUM                                 19
 #define FFT_MULMOD_2EXPP1_CUTOFF                 128
 
+/* FIXME: This tuning is for x86_64_adx with fft_small */
+/* NOTE: We assume that the same cutoff is optimal for both mulhigh and mullow */
+#define FLINT_MPN_MULHIGH_MULDERS_CUTOFF 50
+#define FLINT_MPN_MULHIGH_MUL_CUTOFF 2000
+#define FLINT_MPN_MULHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_SQRHIGH_MULDERS_CUTOFF 90
+#define FLINT_MPN_SQRHIGH_SQR_CUTOFF 2000
+#define FLINT_MPN_SQRHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_MULHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 16, 15, 15, 18, 18, \
+  18, 19, 20, 18, 22, 22, 20, 20, 26, 22, 22, 22, 24, 24, 24, 26, 25, 26, 30, 30, 28, 30, 31, 32, 32, 30, 36, 36, 36, 36, \
+  38, 39, 39, 38, 39, 40, 40, 40, 44, 40, 44, 44, 40, 44, 44, 48, 44, 48, 44, 48, 48, 52, 52, 52, 44, 52, 52, 52, 52, 56, \
+  60, 60, 52, 60, 60, 52, 52, 60, 64, 72, 56, 60, 72, 60, 60, 60, 76, 64, 60, 60, 72, 60, 72, 80, 72, 72, 80, 72, 68, 76, \
+  88, 76, 68, 76, 72, 72, 80, 88, 72, 72, 88, 72, 80, 76, 76, 80, 80, 88, 80, 88, 84, 88, 80, 96, 80, 80, 88, 80, 88, 88, \
+  80, 88, 96, 96, 88, 96, 92, 96, 96, 92, 100, 88, 96, 104, 88, 108, 96, 104, 104, 104, 112, 112, 108, 104, 104, 112, 112, 120, 104, 112, \
+  120, 112, 112, 120, 124, 124, 116, 124, 108, 120, 124, 116, 120, 120, 116, 120, 124, 120, 120, 140, 120, 120, 120, 120, 144, 120, 132, 144, 136, 140, \
+  144, 144, 144, 144, 144, 144, 144, 144, 140, 156, 140, 140, 144, 144, 144, 160, 144, 144, 156, 156, 144, 160, 160, 160, 160, 152, 160, 156, 156, 156, \
+  160, 160, 144, 160, 164, 156, 156, 156, 172, 156, 156, 160, 176, 160, 160, 164, 176, 156, 160, 160, 156, 156, 160, 160, 156, 160, 172, 160, 188, 172, \
+  172, 172, 160, 172, 176, 160, 160, 176, 180, 176, 164, 188, 192, 176, 172, 188, 188, 188, 172, 188, 192, 188, 180, 192, 192, 188, 188, 192, 188, 188, \
+  188, 188, 192, 160, 156, 204, 160, 164, 164, 164, 164, 176, 180, 168, 172, 184, 188, 200, 216, 188, 164, 188, 220, 188, 208, 176, 180, 188, 172, 188, \
+  184, 188, 204, 208, 220, 196, 220, 196, 208, 212, 188, 220, 176, 176, 184, 192, 208, 184, 188, 196, 204, 244, 208, 212, 212, 228, 256, 188, 204, 196, \
+  188, 192, 192, 192, 212, 188, 292, 212, 220, 236, 228, 248, 260, 224, 264, 196, 200, 196, 212, 208, 204, 216, 208, 228, 216, 220, 252, 220, 268, 264, \
+  284, 268, 300, 220, 208, 212, 220, 236, 244, 224, 252, 252, 260, 264, 256, 256, 292, 272, 288, 292, 328, 224, 256, 236, 252, 268, 256, 252, 260, 272, \
+  284, 296, 300, 280, 300, 284, 252, 236, 328, 324, 264, 264, 256, 264, 280, 268, 284, 284, 292, 304, 260, 304, 264, 256, 328, 328, 260, 276, 328, 284, \
+  276, 296, 300, 320, 320, 304, 328, 304, 272, 268, 280, 268, 288, 292, 288, 284, 316, 288, 328, 328, 300, 328, 328, 280, 264, 328, 300, 328, 316, 324, \
+  300, 324, 300, 324, 316, 316, 328, 348, 276, 376, 288, 296, 296, 304, 320, 316, 328, 328, 324, 328, 340, 384, 348, 376, 300, 396, 304, 300, 304, 324, \
+  300, 324, 328, 328, 328, 440, 448, 384, 376, 456, 464, 384, 376, 472, 480, 376, 352, 328, 376, 352, 376, 392, 392, 384, 456, 456, 480, 448, 456, 456, \
+  472, 472, 472, 352, 464, 472, 472, 472, 480, 440, 480, 480, 480, 480, 456, 472, 472, 464, 464, 464, 456, 472, 480, 472, 480, 480, 480, 480, 448, 456, \
+  480, 448, 456, 464, 456, 464, 456, 480, 472, 464, 464, 472, 472, 472, 480, 472, 480, 480, 472, 480, 480, 480, 480, 464, 464, 464, 456, 472, 464, 480, \
+  472, 472, 480, 472, 480, 480, 464, 464, 472, 464, 472, 472, 480, 464, 480, 472, 480, 480, 576, 576, 560, 480, 472, 480, 568, 480, 480, 464, 480, 472, \
+  480, 576, 480, 552, 560, 560, 560, 560, 568, 560, 560, 576, 576, 560, 568, 472, 480, 480, 544, 568, 552, 544, 560, 544, 560, 568, 552, 576, 568, 560, \
+  576, 576, 568, 576, 560, 576, 568, 536, 576, 568, 560, 544, 560, 552, 560, 568, 560, 576, 568, 560, 560, 560, 568, 576, 568, 576, 576, 576, 576, 544, \
+  576, 576, 568, 576, 560, 576, 576, 576, 544, 552, 568, 576, 552, 560, 576, 560, 568, 560, 576, 560, 544, 576, 576, 576, 576, 568, 576, 568, 560, 576, \
+  552, 552, 576, 560, 568, 568, 568, 576, 576, 576, 560, 552, 576, 560, 568, 560, 576, 560, 568, 560, 568, 568, 568, 576, 552, 576, 560, 576, 576, 560, \
+  568, 576, 568, 576, 576, 576, 576, 560, 576, 568, 568, 568, 560, 560, 576, 576, 568, 568, 576, 560, 576, 576, 568, 576, 560, 576, 576, 568, 576, 568, \
+  576, 568, 576, 576, 568, 576, 576, 576, 576, 568, 576, 576, 568, 568, 576, 576, 784, 576, 776, 576, 568, 576, 576, 576, 576, 576, 576, 576, 776, 776, \
+  776, 776, 776, 776, 776, 784, 776, 776, 784, 776, 776, 776, 800, 776, 776, 776, 776, 776, 776, 800, 776, 808, 792, 800, 776, 792, 776, 776, 776, 776, \
+  792, 776, 776, 784, 792, 784, 800, 776, 784, 808, 784, 776, 776, 776, 808, 784, 792, 776, 792, 832, 800, 800, 816, 792, 816, 816, 856, 808, 848, 824, \
+  870, 832, 792, 776, 784, 784, 784, 784, 800, 792, 800, 792, 784, 800, 800, 800, 816, 824, 824, 824, 832, 816, 816, 832, 824, 824, 848, 832, 856, 856, \
+  840, 872, 864, 872, 872, 880, 880, 880, 872, 888, 880, 880, 872, 880, 880, 880, 840, 872, 872, 848, 880, 848, 856, 840, 848, 840, 880, 872, 856, 872, \
+  856, 888, 880, 872, 888, 880, 872, 920, 888, 872, 880, 872, 888, 888, 888, 880, 880, 928, 880, 928, 928, 928, 920, 920, 904, 912, 880, 904, 928, 872, \
+  872, 880, 888, 880, 896, 880, 872, 896, 888, 896, 896, 928, 904, 896, 896, 912, 904, 904, 920, 880, 912, 920, 928, 928, 880, 920, 920, 880, 888, 904, \
+  896, 904, 928, 896, 912, 896, 912, 920, 912, 912, 928, 928, 928, 920, 928, 928, 928, 928, 928, 928, 912, 904, 912, 896, 904, 904, 920, 920, 920, 928, \
+  928, 920, 928, 928, 928, 912, 928, 912, 928, 928, 928, 912, 912, 912, 928, 928, 928, 896, 928, 928, 912, 928, 928, 928, 912, 928, 912, 928, 928, 912, \
+  928, 912, 928, 928, 928, 928, 928, 912, 928, 928, 928, 928, 912, 912, 928, 912, 928, 1024, 928, 928, 928, 928, 928, 928, 1056, 912, 928, 928, 1024, 1024, \
+  928, 928, 1024, 928, 928, 928, 928, 928, 928, 1040, 1040, 928, 1056, 1024, 1072, 1024, 1040, 1040, 1040, 1024, 1088, 1056, 1056, 1088, 1040, 1056, 1072, 1072, 1056, 1056, \
+  1024, 1088, 1040, 1024, 1040, 1040, 1024, 1056, 1056, 1056, 1040, 1072, 1056, 1040, 1056, 1056, 1056, 1056, 1056, 1056, 1056, 1120, 1056, 1088, 1056, 1120, 1088, 1072, 1104, 1104, \
+  1104, 1120, 1088, 1088, 1072, 1088, 1120, 1104, 1088, 1104, 1088, 1072, 1104, 1088, 1120, 1088, 1072, 1072, 1072, 1088, 1088, 1072, 1072, 1088, 1104, 1152, 1104, 1104, 1088, 1104, \
+  1136, 1088, 1104, 1152, 1152, 1152, 1136, 1120, 1136, 1152, 1120, 1152, 1088, 1120, 1104, 1120, 1136, 1104, 1136, 1088, 1136, 1104, 1088, 1104, 1120, 1104, 1104, 1120, 1136, 1136, \
+  1120, 1136, 1136, 1136, 1120, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1104, 1152, 1120, 1136, 1120, 1120, 1152, 1120, 1136, 1152, 1136, 1152, 1120, 1152, 1136, 1136, 1136, 1136, \
+  1136, 1152, 1152, 1152, 1152, 1120, 1120, 1152, 1136, 1136, 1136, 1152, 1152, 1120, 1152, 1152, 1152, 1152, 1152, 1104, 1152, 1152, 1120, 1136, 1152, 1120, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1344, 1152, 1344, 1344, 1344, 1152, 1152, 1152, 1152, 1344, 1328, 1328, 1328, 1152, 1344, 1152, 1344, 1152, 1344, 1152, 1152, 1328, 1152, 1328, 1344, 1328, 1344, 1328, 1344, \
+  1344, 1312, 1328, 1328, 1328, 1344, 1344, 1344, 1328, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, \
+  1328, 1344, 1344, 1344, 1344, 1328, 1344, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1573, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1583, 1568, 1568, 1552, 1568, 1552, 1568, \
+  1568, 1568, 1584, 1568, 1584, 1568, 1568, 1568, 1552, 1552, 1552, 1568, 1552, 1584, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1584, 1552, 1584, 1552, 1617, 1568, 1584, \
+  1552, 1552, 1584, 1584, 1552, 1625, 1626, 1627, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1632, 1636, 1632, 1638, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1648, 1669, 1648, 1671, 1632, 1664, 1648, 1632, 1648, 1648, 1648, 1632, \
+  1632, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1648, 1664, 1648, 1648, 1648, 1648, 1648, 1648, \
+  1680, 1664, 1680, 1696, 1680, 1680, 1664, 1680, 1680, 1648, 1632, 1680, 1696, 1632, 1648, 1648, 1632, 1680, 1680, 1664, 1664, 1664, 1648, 1680, 1664, 1680, 1664, 1680, 1664, 1664, \
+  1680, 1696, 1664, 1696, 1712, 1712, 1696, 1680, 1712, 1696, 1728, 1712, 1696, 1728, 1728, 1712, 1728, 1648, 1680, 1696, 1712, 1696, 1712, 1696, 1696, 1680, 1696, 1696, 1696, 1712, \
+  1696, 1696, 1696, 1696, 1712, 1728, 1696, 1728, 1696, 1696, 1712, 1728, 1712, 1728, 1712, 1680, 1696, 1728, 1712, 1696, 1696, 1696, 1712, 1712, 1728, 1696, 1728, 1712, 1712, 1728, \
+  1696, 1696, 1696, 1712, 1696, 1728, 1712, 1712, 1712, 1728, 1696, 1712, 1728, 1728, 1696, 1728, 1728, 1728, 1728, 1728, 1680, 1712, 1728, 1696, 1728, 1728, 1728, 1728, 1696, 1728, \
+  1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1728, 1696, 1728, 1712, 1712, 1712, 1712, 1728, 1712, 1712, 1712, 1728, 1712, 1728, 1728, 1728, \
+  1728, 1712, 1728, 1728, 1712, 1728, 1728, 1712, 1712, 1728, 1712, 1712, 1728, 1728, 1712, 1728, 1712, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1712, \
+  1728, 1712, 1712, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, \
+  1728, 1728, 1712, 1728, 1728, 1824, 1728, 1728, 1728, 1728, 1824, 1728, 1840, 1728, 1728, 1728, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1728, 1728, 1856, 1856, 1856, 1856, 1728, \
+  1728, 1856, 1856, 1728, 1856, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1856, 1856, 1856, 1840, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1840, 1904, 1856, 1856, 1840, 1840, 1856, \
+  1856, 1840, 1856, 1840, 1856, 1856, 1856, 1856, 1952, 1856, 1856, 1856, 1856, 1952, 1904, 1904, 1856, 1856, 1856, 1920, 1952, 2001, 1952, 1984, 1952, 1936, 1952, 1904, 1968, 1920, \
+  1984, 1920, 1968, 1920, 1936, 1856, 2000, 1920, 1936, 1952, 2000, 1968, 1984, 1968, 1984, 2000, 1952, 2000, 2016, 1984, 2000, 2016, 1984, 1664, 2016, 1984, 2016, 1968, 2016, 2016, \
+  1744, 2016, 2016, 1968, 2000, 1728, 1712, 1696
+
+#define FLINT_MPN_SQRHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 29, 0, 0, 31, 0, 31, \
+  0, 32, 0, 34, 0, 36, 36, 40, 0, 40, 40, 40, 0, 44, 0, 44, 44, 48, 0, 52, 48, 52, 44, 44, 48, 48, 48, 48, 48, 48, \
+  48, 48, 48, 48, 52, 52, 52, 52, 52, 56, 56, 52, 56, 56, 56, 56, 56, 56, 56, 56, 60, 60, 68, 64, 60, 60, 60, 60, 64, 64, \
+  64, 68, 68, 68, 64, 64, 68, 68, 72, 72, 68, 68, 68, 72, 76, 80, 72, 72, 72, 88, 76, 76, 80, 80, 76, 80, 76, 80, 84, 80, \
+  88, 88, 80, 84, 88, 80, 80, 84, 92, 88, 92, 88, 88, 88, 88, 96, 88, 108, 100, 92, 88, 88, 104, 100, 100, 92, 104, 108, 100, 92, \
+  104, 100, 104, 96, 108, 104, 96, 96, 104, 100, 100, 104, 112, 116, 108, 104, 104, 116, 108, 104, 104, 120, 116, 104, 108, 132, 116, 108, 120, 108, \
+  108, 108, 132, 108, 120, 112, 112, 116, 132, 128, 116, 124, 128, 116, 132, 120, 132, 120, 124, 120, 132, 120, 124, 128, 120, 128, 128, 132, 144, 124, \
+  128, 124, 140, 128, 128, 124, 136, 132, 128, 128, 140, 144, 128, 128, 140, 136, 132, 144, 148, 152, 144, 132, 160, 156, 140, 144, 156, 144, 140, 144, \
+  140, 156, 156, 156, 140, 144, 168, 156, 156, 164, 168, 156, 156, 160, 144, 144, 180, 156, 152, 168, 156, 160, 156, 148, 180, 168, 180, 156, 164, 156, \
+  156, 172, 156, 156, 156, 180, 180, 172, 180, 168, 164, 172, 164, 172, 176, 176, 168, 176, 172, 176, 180, 168, 176, 180, 180, 180, 192, 184, 180, 176, \
+  204, 176, 188, 180, 188, 180, 204, 180, 192, 204, 180, 192, 180, 204, 228, 192, 188, 192, 204, 180, 192, 216, 200, 216, 228, 216, 204, 216, 188, 216, \
+  216, 204, 216, 192, 204, 212, 228, 204, 228, 216, 204, 216, 192, 204, 204, 212, 204, 216, 204, 216, 228, 228, 224, 212, 204, 216, 216, 224, 228, 212, \
+  216, 228, 212, 204, 204, 216, 216, 216, 228, 216, 220, 224, 228, 220, 228, 228, 236, 224, 260, 224, 228, 228, 260, 228, 248, 252, 264, 248, 216, 212, \
+  212, 212, 220, 216, 216, 220, 216, 224, 216, 228, 232, 224, 220, 224, 240, 244, 236, 244, 232, 256, 288, 240, 236, 288, 260, 260, 264, 232, 228, 228, \
+  228, 236, 236, 228, 236, 236, 236, 248, 256, 260, 232, 236, 264, 256, 260, 252, 284, 252, 264, 276, 244, 296, 244, 240, 244, 248, 240, 252, 256, 260, \
+  260, 252, 252, 272, 252, 272, 260, 296, 268, 260, 256, 276, 272, 264, 312, 284, 256, 252, 252, 252, 264, 252, 256, 260, 264, 276, 292, 268, 264, 276, \
+  264, 260, 264, 304, 288, 296, 296, 296, 288, 296, 272, 280, 264, 264, 272, 264, 288, 288, 280, 288, 272, 280, 296, 296, 280, 288, 296, 320, 344, 320, \
+  344, 272, 344, 344, 304, 288, 280, 280, 312, 280, 280, 304, 304, 312, 304, 296, 288, 328, 320, 352, 320, 320, 328, 360, 344, 344, 360, 288, 288, 304, \
+  288, 296, 320, 320, 312, 312, 304, 328, 336, 312, 312, 360, 336, 344, 344, 336, 360, 360, 296, 296, 304, 360, 328, 328, 312, 320, 320, 328, 312, 344, \
+  344, 328, 344, 344, 368, 360, 352, 360, 392, 392, 368, 320, 312, 392, 312, 328, 344, 336, 344, 328, 360, 352, 352, 360, 360, 360, 368, 408, 360, 376, \
+  392, 392, 376, 336, 344, 352, 360, 352, 344, 344, 384, 344, 360, 376, 392, 368, 360, 408, 408, 448, 432, 384, 392, 336, 360, 344, 360, 360, 368, 376, \
+  376, 360, 368, 408, 368, 376, 376, 376, 432, 376, 384, 464, 432, 344, 432, 376, 344, 344, 384, 344, 384, 376, 400, 432, 456, 432, 456, 392, 432, 392, \
+  448, 456, 360, 376, 456, 408, 384, 368, 376, 432, 376, 472, 464, 504, 448, 360, 408, 456, 376, 408, 424, 424, 448, 440, 456, 392, 408, 384, 408, 392, \
+  384, 416, 424, 432, 400, 472, 480, 408, 432, 432, 464, 456, 504, 464, 456, 472, 496, 416, 392, 424, 504, 400, 440, 432, 472, 448, 456, 456, 432, 448, \
+  456, 504, 504, 512, 496, 504, 424, 416, 408, 432, 544, 432, 440, 456, 448, 448, 464, 472, 480, 552, 552, 544, 552, 560, 552, 544, 544, 544, 552, 552, \
+  552, 552, 552, 552, 552, 560, 552, 552, 560, 560, 560, 560, 568, 576, 568, 592, 576, 560, 560, 560, 560, 568, 568, 576, 568, 568, 576, 568, 568, 576, \
+  568, 568, 600, 592, 576, 608, 576, 576, 576, 576, 584, 584, 576, 592, 592, 600, 584, 592, 584, 600, 600, 600, 584, 624, 584, 592, 600, 592, 616, 592, \
+  592, 592, 592, 592, 592, 592, 600, 608, 600, 608, 600, 600, 600, 624, 616, 608, 616, 600, 632, 608, 608, 608, 616, 608, 608, 608, 608, 616, 608, 664, \
+  664, 632, 656, 616, 664, 624, 616, 632, 632, 616, 624, 624, 624, 632, 624, 624, 624, 624, 648, 632, 624, 624, 872, 872, 656, 664, 696, 872, 872, 872, \
+  632, 872, 872, 896, 872, 896, 872, 896, 880, 872, 896, 872, 888, 872, 872, 872, 872, 872, 888, 872, 880, 824, 872, 856, 880, 888, 800, 848, 800, 880, \
+  848, 800, 808, 872, 872, 864, 824, 840, 872, 872, 872, 872, 872, 872, 872, 872, 872, 872, 880, 928, 872, 920, 872, 920, 888, 880, 872, 880, 872, 872, \
+  872, 888, 880, 888, 888, 872, 888, 872, 880, 896, 920, 920, 880, 928, 904, 872, 888, 904, 872, 872, 872, 872, 880, 888, 872, 872, 872, 880, 872, 904, \
+  920, 888, 888, 872, 880, 880, 888, 896, 896, 880, 872, 904, 880, 912, 896, 872, 904, 904, 912, 880, 880, 920, 912, 896, 928, 928, 872, 872, 872, 872, \
+  880, 880, 888, 888, 888, 912, 880, 880, 880, 912, 896, 896, 928, 896, 912, 912, 896, 928, 928, 928, 928, 912, 880, 928, 880, 880, 896, 880, 896, 880, \
+  896, 880, 880, 912, 912, 880, 896, 880, 896, 912, 880, 880, 928, 912, 912, 928, 928, 896, 928, 912, 928, 928, 928, 928, 928, 928, 880, 880, 880, 880, \
+  880, 912, 896, 912, 912, 896, 928, 896, 928, 896, 928, 928, 928, 928, 912, 880, 928, 912, 896, 928, 896, 880, 912, 896, 912, 896, 896, 896, 928, 896, \
+  912, 928, 912, 928, 912, 928, 912, 880, 928, 928, 880, 928, 928, 880, 896, 928, 880, 896, 912, 928, 928, 896, 912, 928, 912, 928, 1024, 928, 928, 1040, \
+  912, 928, 1024, 1024, 928, 928, 928, 928, 912, 1040, 1072, 912, 1072, 1072, 1056, 1040, 1072, 1088, 1104, 1040, 1040, 928, 1024, 928, 928, 1056, 928, 928, 1056, 1040, \
+  928, 1056, 1024, 1056, 1056, 1056, 1104, 1024, 1056, 1072, 1056, 1056, 1088, 1072, 1120, 1104, 1072, 1072, 1072, 1104, 1120, 1024, 1120, 1120, 1056, 1024, 1040, 1024, 1040, 1040, \
+  1040, 1024, 1040, 1056, 1040, 1088, 1040, 1056, 1120, 1040, 1040, 1072, 1072, 1088, 1104, 1088, 1104, 1088, 1088, 1056, 1120, 1104, 1152, 1104, 1088, 1120, 1104, 1120, 1024, 1120, \
+  1152, 1136, 1152, 1056, 1056, 1072, 1056, 1152, 1088, 1056, 1104, 1072, 1104, 1088, 1120, 1072, 1104, 1088, 1088, 1120, 1120, 1120, 1152, 1136, 1120, 1120, 1152, 1120, 1136, 1152, \
+  1152, 1072, 1136, 1136, 1088, 1152, 1136, 1136, 1104, 1056, 1072, 1088, 1104, 1104, 1120, 1120, 1104, 1104, 1104, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1136, 1072, \
+  1152, 1136, 1152, 1152, 1104, 1152, 1104, 1152, 1152, 1088, 1120, 1152, 1136, 1136, 1120, 1136, 1120, 1152, 1136, 1136, 1120, 1136, 1152, 1136, 1152, 1136, 1136, 1120, 1152, 1152, \
+  1104, 1152, 1152, 1152, 1104, 1120, 1104, 1120, 1120, 1120, 1120, 1136, 1136, 1136, 1136, 1152, 1120, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1104, \
+  1120, 1152, 1136, 1136, 1136, 1136, 1136, 1136, 1120, 1152, 1152, 1152, 1136, 1104, 1152, 1136, 1136, 1152, 1136, 1120, 1136, 1152, 1152, 1136, 1136, 1120, 1136, 1136, 1136, 1120, \
+  1152, 1152, 1152, 1136, 1136, 1136, 1152, 1104, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1152, \
+  1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, \
+  1120, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1136, \
+  1152, 1152, 1152, 1104, 1120, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1152, 1120, 1152, 1136, 1152, 1152, 1120, 1152, 1120, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1120, 1152, 1152, 1136, 1152, 1136, 1552, 1552, 1136, 1136, 1152, 1552, 1136, 1136, 1584, 1552, 1552, 1552, \
+  1152, 1552, 1552, 1152, 1584, 1552, 1152, 1152, 1552, 1584, 1152, 1152, 1552, 1584, 1568, 1552, 1552, 1552, 1152, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1625, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1568, 1632, 1552, 1632, 1568, 1584, 1568, 1568, 1584, 1600, 1552, 1552, 1632, 1600, 1632, 1632, 1632, \
+  1632, 1568, 1584, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1552, 1662, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1568, 1600, 1632, 1552, 1616, 1632, 1632, 1632, 1584, 1632, \
+  1632, 1552, 1632, 1632, 1632, 1568, 1600, 1632, 1648, 1616, 1632, 1648, 1632, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1632, 1664, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1648, 1648, 1648, 1616, 1632, 1680, 1632, 1680, 1648, 1632, 1664, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1648, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1648, 1664, 1648, 1648, 1632, 1648, 1632, 1680, 1664, 1648, 1680, 1664, 1696, 1632, 1664, 1680, 1632, 1648, 1696, \
+  1680, 1632, 1632, 1648, 1648, 1648, 1632, 1664, 1632, 1648, 1648, 1632, 1648, 1648, 1632, 1664, 1664, 1680, 1680, 1632, 1664, 1664, 1648, 1648, 1712, 1728, 1664, 1712, 1696, 1712, \
+  1680, 1632, 1728, 1648, 1728, 1728, 1712, 1648, 1632, 1632, 1664, 1648, 1664, 1664, 1680, 1712, 1664, 1632, 1696, 1664, 1712, 1696, 1680, 1680, 1696, 1680, 1680, 1712, 1648, 1712, \
+  1632, 1728, 1696, 1648, 1712, 1632, 1712, 1696, 1648, 1680, 1648, 1664, 1648, 1696, 1712, 1648, 1648, 1680, 1664, 1696, 1728, 1696, 1712, 1728, 1696, 1728, 1712, 1664, 1680, 1728, \
+  1712, 1712, 1712, 1728, 1728, 1712, 1728, 1696, 1728, 1712, 1696, 1728, 1728, 1680, 1728, 1712, 1664, 1680, 1680, 1696, 1712, 1696, 1696, 1696, 1728, 1696, 1728, 1728, 1696, 1712, \
+  1712, 1664, 1712, 1680, 1664, 1728, 1728, 1664, 1696, 1696, 1680, 1712, 1680, 1712, 1696, 1728, 1696, 1696, 1728, 1696, 1712, 1696, 1712, 1712, 1712, 1728, 1712, 1696, 1728, 1680, \
+  1696, 1712, 1712, 1728, 1712, 1728, 1696, 1728, 1776, 1728, 1696, 1776, 1728, 1728, 1712, 1712, 1824, 1856, 1728, 1824, 1728, 1728, 1712, 1728, 1728, 1728, 1856, 1696, 1728, 1840, \
+  1712, 1712, 1824, 1856, 1792, 1712, 1840, 1728, 1808, 1728, 1824, 1824, 1840, 1824, 1824, 1856, 1856, 1824, 1856, 1840, 1696, 1856, 1840, 1840, 1856, 1856, 1824, 1712, 1792, 1856, \
+  1824, 1728, 1808, 1792, 1856, 1728, 1792, 1840, 1808, 1808, 1712, 1808, 1840, 1808, 1824, 1824, 1824, 1840, 1824, 1840, 1856, 1824, 1728, 1856, 1856, 1824, 1856, 1856, 1792, 1792, \
+  1856, 1824, 1856, 1824, 1824, 1856, 1808, 1824, 1856, 1856, 1840, 1840, 1840, 1840, 1856, 1840, 1840, 1856, 1824, 1840, 1808, 1824, 1840, 1856, 1856, 1824, 1856, 1840, 1840, 1840, \
+  1824, 1824, 1840, 1840, 1840, 1856, 1856, 1856
+
 #endif
diff --git a/src/mpn_extras/x86_64/skylake/flint-mparam.h b/src/mpn_extras/x86_64/skylake/flint-mparam.h
index 4ddf1efd71..6e8652f1cd 100644
--- a/src/mpn_extras/x86_64/skylake/flint-mparam.h
+++ b/src/mpn_extras/x86_64/skylake/flint-mparam.h
@@ -27,4 +27,156 @@
 #define FFT_N_NUM                                 19
 #define FFT_MULMOD_2EXPP1_CUTOFF                 128
 
+/* FIXME: This tuning is for x86_64_adx with fft_small */
+/* NOTE: We assume that the same cutoff is optimal for both mulhigh and mullow */
+#define FLINT_MPN_MULHIGH_MULDERS_CUTOFF 50
+#define FLINT_MPN_MULHIGH_MUL_CUTOFF 2000
+#define FLINT_MPN_MULHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_SQRHIGH_MULDERS_CUTOFF 90
+#define FLINT_MPN_SQRHIGH_SQR_CUTOFF 2000
+#define FLINT_MPN_SQRHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_MULHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 16, 15, 15, 18, 18, \
+  18, 19, 20, 18, 22, 22, 20, 20, 26, 22, 22, 22, 24, 24, 24, 26, 25, 26, 30, 30, 28, 30, 31, 32, 32, 30, 36, 36, 36, 36, \
+  38, 39, 39, 38, 39, 40, 40, 40, 44, 40, 44, 44, 40, 44, 44, 48, 44, 48, 44, 48, 48, 52, 52, 52, 44, 52, 52, 52, 52, 56, \
+  60, 60, 52, 60, 60, 52, 52, 60, 64, 72, 56, 60, 72, 60, 60, 60, 76, 64, 60, 60, 72, 60, 72, 80, 72, 72, 80, 72, 68, 76, \
+  88, 76, 68, 76, 72, 72, 80, 88, 72, 72, 88, 72, 80, 76, 76, 80, 80, 88, 80, 88, 84, 88, 80, 96, 80, 80, 88, 80, 88, 88, \
+  80, 88, 96, 96, 88, 96, 92, 96, 96, 92, 100, 88, 96, 104, 88, 108, 96, 104, 104, 104, 112, 112, 108, 104, 104, 112, 112, 120, 104, 112, \
+  120, 112, 112, 120, 124, 124, 116, 124, 108, 120, 124, 116, 120, 120, 116, 120, 124, 120, 120, 140, 120, 120, 120, 120, 144, 120, 132, 144, 136, 140, \
+  144, 144, 144, 144, 144, 144, 144, 144, 140, 156, 140, 140, 144, 144, 144, 160, 144, 144, 156, 156, 144, 160, 160, 160, 160, 152, 160, 156, 156, 156, \
+  160, 160, 144, 160, 164, 156, 156, 156, 172, 156, 156, 160, 176, 160, 160, 164, 176, 156, 160, 160, 156, 156, 160, 160, 156, 160, 172, 160, 188, 172, \
+  172, 172, 160, 172, 176, 160, 160, 176, 180, 176, 164, 188, 192, 176, 172, 188, 188, 188, 172, 188, 192, 188, 180, 192, 192, 188, 188, 192, 188, 188, \
+  188, 188, 192, 160, 156, 204, 160, 164, 164, 164, 164, 176, 180, 168, 172, 184, 188, 200, 216, 188, 164, 188, 220, 188, 208, 176, 180, 188, 172, 188, \
+  184, 188, 204, 208, 220, 196, 220, 196, 208, 212, 188, 220, 176, 176, 184, 192, 208, 184, 188, 196, 204, 244, 208, 212, 212, 228, 256, 188, 204, 196, \
+  188, 192, 192, 192, 212, 188, 292, 212, 220, 236, 228, 248, 260, 224, 264, 196, 200, 196, 212, 208, 204, 216, 208, 228, 216, 220, 252, 220, 268, 264, \
+  284, 268, 300, 220, 208, 212, 220, 236, 244, 224, 252, 252, 260, 264, 256, 256, 292, 272, 288, 292, 328, 224, 256, 236, 252, 268, 256, 252, 260, 272, \
+  284, 296, 300, 280, 300, 284, 252, 236, 328, 324, 264, 264, 256, 264, 280, 268, 284, 284, 292, 304, 260, 304, 264, 256, 328, 328, 260, 276, 328, 284, \
+  276, 296, 300, 320, 320, 304, 328, 304, 272, 268, 280, 268, 288, 292, 288, 284, 316, 288, 328, 328, 300, 328, 328, 280, 264, 328, 300, 328, 316, 324, \
+  300, 324, 300, 324, 316, 316, 328, 348, 276, 376, 288, 296, 296, 304, 320, 316, 328, 328, 324, 328, 340, 384, 348, 376, 300, 396, 304, 300, 304, 324, \
+  300, 324, 328, 328, 328, 440, 448, 384, 376, 456, 464, 384, 376, 472, 480, 376, 352, 328, 376, 352, 376, 392, 392, 384, 456, 456, 480, 448, 456, 456, \
+  472, 472, 472, 352, 464, 472, 472, 472, 480, 440, 480, 480, 480, 480, 456, 472, 472, 464, 464, 464, 456, 472, 480, 472, 480, 480, 480, 480, 448, 456, \
+  480, 448, 456, 464, 456, 464, 456, 480, 472, 464, 464, 472, 472, 472, 480, 472, 480, 480, 472, 480, 480, 480, 480, 464, 464, 464, 456, 472, 464, 480, \
+  472, 472, 480, 472, 480, 480, 464, 464, 472, 464, 472, 472, 480, 464, 480, 472, 480, 480, 576, 576, 560, 480, 472, 480, 568, 480, 480, 464, 480, 472, \
+  480, 576, 480, 552, 560, 560, 560, 560, 568, 560, 560, 576, 576, 560, 568, 472, 480, 480, 544, 568, 552, 544, 560, 544, 560, 568, 552, 576, 568, 560, \
+  576, 576, 568, 576, 560, 576, 568, 536, 576, 568, 560, 544, 560, 552, 560, 568, 560, 576, 568, 560, 560, 560, 568, 576, 568, 576, 576, 576, 576, 544, \
+  576, 576, 568, 576, 560, 576, 576, 576, 544, 552, 568, 576, 552, 560, 576, 560, 568, 560, 576, 560, 544, 576, 576, 576, 576, 568, 576, 568, 560, 576, \
+  552, 552, 576, 560, 568, 568, 568, 576, 576, 576, 560, 552, 576, 560, 568, 560, 576, 560, 568, 560, 568, 568, 568, 576, 552, 576, 560, 576, 576, 560, \
+  568, 576, 568, 576, 576, 576, 576, 560, 576, 568, 568, 568, 560, 560, 576, 576, 568, 568, 576, 560, 576, 576, 568, 576, 560, 576, 576, 568, 576, 568, \
+  576, 568, 576, 576, 568, 576, 576, 576, 576, 568, 576, 576, 568, 568, 576, 576, 784, 576, 776, 576, 568, 576, 576, 576, 576, 576, 576, 576, 776, 776, \
+  776, 776, 776, 776, 776, 784, 776, 776, 784, 776, 776, 776, 800, 776, 776, 776, 776, 776, 776, 800, 776, 808, 792, 800, 776, 792, 776, 776, 776, 776, \
+  792, 776, 776, 784, 792, 784, 800, 776, 784, 808, 784, 776, 776, 776, 808, 784, 792, 776, 792, 832, 800, 800, 816, 792, 816, 816, 856, 808, 848, 824, \
+  870, 832, 792, 776, 784, 784, 784, 784, 800, 792, 800, 792, 784, 800, 800, 800, 816, 824, 824, 824, 832, 816, 816, 832, 824, 824, 848, 832, 856, 856, \
+  840, 872, 864, 872, 872, 880, 880, 880, 872, 888, 880, 880, 872, 880, 880, 880, 840, 872, 872, 848, 880, 848, 856, 840, 848, 840, 880, 872, 856, 872, \
+  856, 888, 880, 872, 888, 880, 872, 920, 888, 872, 880, 872, 888, 888, 888, 880, 880, 928, 880, 928, 928, 928, 920, 920, 904, 912, 880, 904, 928, 872, \
+  872, 880, 888, 880, 896, 880, 872, 896, 888, 896, 896, 928, 904, 896, 896, 912, 904, 904, 920, 880, 912, 920, 928, 928, 880, 920, 920, 880, 888, 904, \
+  896, 904, 928, 896, 912, 896, 912, 920, 912, 912, 928, 928, 928, 920, 928, 928, 928, 928, 928, 928, 912, 904, 912, 896, 904, 904, 920, 920, 920, 928, \
+  928, 920, 928, 928, 928, 912, 928, 912, 928, 928, 928, 912, 912, 912, 928, 928, 928, 896, 928, 928, 912, 928, 928, 928, 912, 928, 912, 928, 928, 912, \
+  928, 912, 928, 928, 928, 928, 928, 912, 928, 928, 928, 928, 912, 912, 928, 912, 928, 1024, 928, 928, 928, 928, 928, 928, 1056, 912, 928, 928, 1024, 1024, \
+  928, 928, 1024, 928, 928, 928, 928, 928, 928, 1040, 1040, 928, 1056, 1024, 1072, 1024, 1040, 1040, 1040, 1024, 1088, 1056, 1056, 1088, 1040, 1056, 1072, 1072, 1056, 1056, \
+  1024, 1088, 1040, 1024, 1040, 1040, 1024, 1056, 1056, 1056, 1040, 1072, 1056, 1040, 1056, 1056, 1056, 1056, 1056, 1056, 1056, 1120, 1056, 1088, 1056, 1120, 1088, 1072, 1104, 1104, \
+  1104, 1120, 1088, 1088, 1072, 1088, 1120, 1104, 1088, 1104, 1088, 1072, 1104, 1088, 1120, 1088, 1072, 1072, 1072, 1088, 1088, 1072, 1072, 1088, 1104, 1152, 1104, 1104, 1088, 1104, \
+  1136, 1088, 1104, 1152, 1152, 1152, 1136, 1120, 1136, 1152, 1120, 1152, 1088, 1120, 1104, 1120, 1136, 1104, 1136, 1088, 1136, 1104, 1088, 1104, 1120, 1104, 1104, 1120, 1136, 1136, \
+  1120, 1136, 1136, 1136, 1120, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1104, 1152, 1120, 1136, 1120, 1120, 1152, 1120, 1136, 1152, 1136, 1152, 1120, 1152, 1136, 1136, 1136, 1136, \
+  1136, 1152, 1152, 1152, 1152, 1120, 1120, 1152, 1136, 1136, 1136, 1152, 1152, 1120, 1152, 1152, 1152, 1152, 1152, 1104, 1152, 1152, 1120, 1136, 1152, 1120, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1344, 1152, 1344, 1344, 1344, 1152, 1152, 1152, 1152, 1344, 1328, 1328, 1328, 1152, 1344, 1152, 1344, 1152, 1344, 1152, 1152, 1328, 1152, 1328, 1344, 1328, 1344, 1328, 1344, \
+  1344, 1312, 1328, 1328, 1328, 1344, 1344, 1344, 1328, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, \
+  1328, 1344, 1344, 1344, 1344, 1328, 1344, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1573, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1583, 1568, 1568, 1552, 1568, 1552, 1568, \
+  1568, 1568, 1584, 1568, 1584, 1568, 1568, 1568, 1552, 1552, 1552, 1568, 1552, 1584, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1584, 1552, 1584, 1552, 1617, 1568, 1584, \
+  1552, 1552, 1584, 1584, 1552, 1625, 1626, 1627, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1632, 1636, 1632, 1638, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1648, 1669, 1648, 1671, 1632, 1664, 1648, 1632, 1648, 1648, 1648, 1632, \
+  1632, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1648, 1664, 1648, 1648, 1648, 1648, 1648, 1648, \
+  1680, 1664, 1680, 1696, 1680, 1680, 1664, 1680, 1680, 1648, 1632, 1680, 1696, 1632, 1648, 1648, 1632, 1680, 1680, 1664, 1664, 1664, 1648, 1680, 1664, 1680, 1664, 1680, 1664, 1664, \
+  1680, 1696, 1664, 1696, 1712, 1712, 1696, 1680, 1712, 1696, 1728, 1712, 1696, 1728, 1728, 1712, 1728, 1648, 1680, 1696, 1712, 1696, 1712, 1696, 1696, 1680, 1696, 1696, 1696, 1712, \
+  1696, 1696, 1696, 1696, 1712, 1728, 1696, 1728, 1696, 1696, 1712, 1728, 1712, 1728, 1712, 1680, 1696, 1728, 1712, 1696, 1696, 1696, 1712, 1712, 1728, 1696, 1728, 1712, 1712, 1728, \
+  1696, 1696, 1696, 1712, 1696, 1728, 1712, 1712, 1712, 1728, 1696, 1712, 1728, 1728, 1696, 1728, 1728, 1728, 1728, 1728, 1680, 1712, 1728, 1696, 1728, 1728, 1728, 1728, 1696, 1728, \
+  1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1728, 1696, 1728, 1712, 1712, 1712, 1712, 1728, 1712, 1712, 1712, 1728, 1712, 1728, 1728, 1728, \
+  1728, 1712, 1728, 1728, 1712, 1728, 1728, 1712, 1712, 1728, 1712, 1712, 1728, 1728, 1712, 1728, 1712, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1712, \
+  1728, 1712, 1712, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, \
+  1728, 1728, 1712, 1728, 1728, 1824, 1728, 1728, 1728, 1728, 1824, 1728, 1840, 1728, 1728, 1728, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1728, 1728, 1856, 1856, 1856, 1856, 1728, \
+  1728, 1856, 1856, 1728, 1856, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1856, 1856, 1856, 1840, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1840, 1904, 1856, 1856, 1840, 1840, 1856, \
+  1856, 1840, 1856, 1840, 1856, 1856, 1856, 1856, 1952, 1856, 1856, 1856, 1856, 1952, 1904, 1904, 1856, 1856, 1856, 1920, 1952, 2001, 1952, 1984, 1952, 1936, 1952, 1904, 1968, 1920, \
+  1984, 1920, 1968, 1920, 1936, 1856, 2000, 1920, 1936, 1952, 2000, 1968, 1984, 1968, 1984, 2000, 1952, 2000, 2016, 1984, 2000, 2016, 1984, 1664, 2016, 1984, 2016, 1968, 2016, 2016, \
+  1744, 2016, 2016, 1968, 2000, 1728, 1712, 1696
+
+#define FLINT_MPN_SQRHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 29, 0, 0, 31, 0, 31, \
+  0, 32, 0, 34, 0, 36, 36, 40, 0, 40, 40, 40, 0, 44, 0, 44, 44, 48, 0, 52, 48, 52, 44, 44, 48, 48, 48, 48, 48, 48, \
+  48, 48, 48, 48, 52, 52, 52, 52, 52, 56, 56, 52, 56, 56, 56, 56, 56, 56, 56, 56, 60, 60, 68, 64, 60, 60, 60, 60, 64, 64, \
+  64, 68, 68, 68, 64, 64, 68, 68, 72, 72, 68, 68, 68, 72, 76, 80, 72, 72, 72, 88, 76, 76, 80, 80, 76, 80, 76, 80, 84, 80, \
+  88, 88, 80, 84, 88, 80, 80, 84, 92, 88, 92, 88, 88, 88, 88, 96, 88, 108, 100, 92, 88, 88, 104, 100, 100, 92, 104, 108, 100, 92, \
+  104, 100, 104, 96, 108, 104, 96, 96, 104, 100, 100, 104, 112, 116, 108, 104, 104, 116, 108, 104, 104, 120, 116, 104, 108, 132, 116, 108, 120, 108, \
+  108, 108, 132, 108, 120, 112, 112, 116, 132, 128, 116, 124, 128, 116, 132, 120, 132, 120, 124, 120, 132, 120, 124, 128, 120, 128, 128, 132, 144, 124, \
+  128, 124, 140, 128, 128, 124, 136, 132, 128, 128, 140, 144, 128, 128, 140, 136, 132, 144, 148, 152, 144, 132, 160, 156, 140, 144, 156, 144, 140, 144, \
+  140, 156, 156, 156, 140, 144, 168, 156, 156, 164, 168, 156, 156, 160, 144, 144, 180, 156, 152, 168, 156, 160, 156, 148, 180, 168, 180, 156, 164, 156, \
+  156, 172, 156, 156, 156, 180, 180, 172, 180, 168, 164, 172, 164, 172, 176, 176, 168, 176, 172, 176, 180, 168, 176, 180, 180, 180, 192, 184, 180, 176, \
+  204, 176, 188, 180, 188, 180, 204, 180, 192, 204, 180, 192, 180, 204, 228, 192, 188, 192, 204, 180, 192, 216, 200, 216, 228, 216, 204, 216, 188, 216, \
+  216, 204, 216, 192, 204, 212, 228, 204, 228, 216, 204, 216, 192, 204, 204, 212, 204, 216, 204, 216, 228, 228, 224, 212, 204, 216, 216, 224, 228, 212, \
+  216, 228, 212, 204, 204, 216, 216, 216, 228, 216, 220, 224, 228, 220, 228, 228, 236, 224, 260, 224, 228, 228, 260, 228, 248, 252, 264, 248, 216, 212, \
+  212, 212, 220, 216, 216, 220, 216, 224, 216, 228, 232, 224, 220, 224, 240, 244, 236, 244, 232, 256, 288, 240, 236, 288, 260, 260, 264, 232, 228, 228, \
+  228, 236, 236, 228, 236, 236, 236, 248, 256, 260, 232, 236, 264, 256, 260, 252, 284, 252, 264, 276, 244, 296, 244, 240, 244, 248, 240, 252, 256, 260, \
+  260, 252, 252, 272, 252, 272, 260, 296, 268, 260, 256, 276, 272, 264, 312, 284, 256, 252, 252, 252, 264, 252, 256, 260, 264, 276, 292, 268, 264, 276, \
+  264, 260, 264, 304, 288, 296, 296, 296, 288, 296, 272, 280, 264, 264, 272, 264, 288, 288, 280, 288, 272, 280, 296, 296, 280, 288, 296, 320, 344, 320, \
+  344, 272, 344, 344, 304, 288, 280, 280, 312, 280, 280, 304, 304, 312, 304, 296, 288, 328, 320, 352, 320, 320, 328, 360, 344, 344, 360, 288, 288, 304, \
+  288, 296, 320, 320, 312, 312, 304, 328, 336, 312, 312, 360, 336, 344, 344, 336, 360, 360, 296, 296, 304, 360, 328, 328, 312, 320, 320, 328, 312, 344, \
+  344, 328, 344, 344, 368, 360, 352, 360, 392, 392, 368, 320, 312, 392, 312, 328, 344, 336, 344, 328, 360, 352, 352, 360, 360, 360, 368, 408, 360, 376, \
+  392, 392, 376, 336, 344, 352, 360, 352, 344, 344, 384, 344, 360, 376, 392, 368, 360, 408, 408, 448, 432, 384, 392, 336, 360, 344, 360, 360, 368, 376, \
+  376, 360, 368, 408, 368, 376, 376, 376, 432, 376, 384, 464, 432, 344, 432, 376, 344, 344, 384, 344, 384, 376, 400, 432, 456, 432, 456, 392, 432, 392, \
+  448, 456, 360, 376, 456, 408, 384, 368, 376, 432, 376, 472, 464, 504, 448, 360, 408, 456, 376, 408, 424, 424, 448, 440, 456, 392, 408, 384, 408, 392, \
+  384, 416, 424, 432, 400, 472, 480, 408, 432, 432, 464, 456, 504, 464, 456, 472, 496, 416, 392, 424, 504, 400, 440, 432, 472, 448, 456, 456, 432, 448, \
+  456, 504, 504, 512, 496, 504, 424, 416, 408, 432, 544, 432, 440, 456, 448, 448, 464, 472, 480, 552, 552, 544, 552, 560, 552, 544, 544, 544, 552, 552, \
+  552, 552, 552, 552, 552, 560, 552, 552, 560, 560, 560, 560, 568, 576, 568, 592, 576, 560, 560, 560, 560, 568, 568, 576, 568, 568, 576, 568, 568, 576, \
+  568, 568, 600, 592, 576, 608, 576, 576, 576, 576, 584, 584, 576, 592, 592, 600, 584, 592, 584, 600, 600, 600, 584, 624, 584, 592, 600, 592, 616, 592, \
+  592, 592, 592, 592, 592, 592, 600, 608, 600, 608, 600, 600, 600, 624, 616, 608, 616, 600, 632, 608, 608, 608, 616, 608, 608, 608, 608, 616, 608, 664, \
+  664, 632, 656, 616, 664, 624, 616, 632, 632, 616, 624, 624, 624, 632, 624, 624, 624, 624, 648, 632, 624, 624, 872, 872, 656, 664, 696, 872, 872, 872, \
+  632, 872, 872, 896, 872, 896, 872, 896, 880, 872, 896, 872, 888, 872, 872, 872, 872, 872, 888, 872, 880, 824, 872, 856, 880, 888, 800, 848, 800, 880, \
+  848, 800, 808, 872, 872, 864, 824, 840, 872, 872, 872, 872, 872, 872, 872, 872, 872, 872, 880, 928, 872, 920, 872, 920, 888, 880, 872, 880, 872, 872, \
+  872, 888, 880, 888, 888, 872, 888, 872, 880, 896, 920, 920, 880, 928, 904, 872, 888, 904, 872, 872, 872, 872, 880, 888, 872, 872, 872, 880, 872, 904, \
+  920, 888, 888, 872, 880, 880, 888, 896, 896, 880, 872, 904, 880, 912, 896, 872, 904, 904, 912, 880, 880, 920, 912, 896, 928, 928, 872, 872, 872, 872, \
+  880, 880, 888, 888, 888, 912, 880, 880, 880, 912, 896, 896, 928, 896, 912, 912, 896, 928, 928, 928, 928, 912, 880, 928, 880, 880, 896, 880, 896, 880, \
+  896, 880, 880, 912, 912, 880, 896, 880, 896, 912, 880, 880, 928, 912, 912, 928, 928, 896, 928, 912, 928, 928, 928, 928, 928, 928, 880, 880, 880, 880, \
+  880, 912, 896, 912, 912, 896, 928, 896, 928, 896, 928, 928, 928, 928, 912, 880, 928, 912, 896, 928, 896, 880, 912, 896, 912, 896, 896, 896, 928, 896, \
+  912, 928, 912, 928, 912, 928, 912, 880, 928, 928, 880, 928, 928, 880, 896, 928, 880, 896, 912, 928, 928, 896, 912, 928, 912, 928, 1024, 928, 928, 1040, \
+  912, 928, 1024, 1024, 928, 928, 928, 928, 912, 1040, 1072, 912, 1072, 1072, 1056, 1040, 1072, 1088, 1104, 1040, 1040, 928, 1024, 928, 928, 1056, 928, 928, 1056, 1040, \
+  928, 1056, 1024, 1056, 1056, 1056, 1104, 1024, 1056, 1072, 1056, 1056, 1088, 1072, 1120, 1104, 1072, 1072, 1072, 1104, 1120, 1024, 1120, 1120, 1056, 1024, 1040, 1024, 1040, 1040, \
+  1040, 1024, 1040, 1056, 1040, 1088, 1040, 1056, 1120, 1040, 1040, 1072, 1072, 1088, 1104, 1088, 1104, 1088, 1088, 1056, 1120, 1104, 1152, 1104, 1088, 1120, 1104, 1120, 1024, 1120, \
+  1152, 1136, 1152, 1056, 1056, 1072, 1056, 1152, 1088, 1056, 1104, 1072, 1104, 1088, 1120, 1072, 1104, 1088, 1088, 1120, 1120, 1120, 1152, 1136, 1120, 1120, 1152, 1120, 1136, 1152, \
+  1152, 1072, 1136, 1136, 1088, 1152, 1136, 1136, 1104, 1056, 1072, 1088, 1104, 1104, 1120, 1120, 1104, 1104, 1104, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1136, 1072, \
+  1152, 1136, 1152, 1152, 1104, 1152, 1104, 1152, 1152, 1088, 1120, 1152, 1136, 1136, 1120, 1136, 1120, 1152, 1136, 1136, 1120, 1136, 1152, 1136, 1152, 1136, 1136, 1120, 1152, 1152, \
+  1104, 1152, 1152, 1152, 1104, 1120, 1104, 1120, 1120, 1120, 1120, 1136, 1136, 1136, 1136, 1152, 1120, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1104, \
+  1120, 1152, 1136, 1136, 1136, 1136, 1136, 1136, 1120, 1152, 1152, 1152, 1136, 1104, 1152, 1136, 1136, 1152, 1136, 1120, 1136, 1152, 1152, 1136, 1136, 1120, 1136, 1136, 1136, 1120, \
+  1152, 1152, 1152, 1136, 1136, 1136, 1152, 1104, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1152, \
+  1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, \
+  1120, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1136, \
+  1152, 1152, 1152, 1104, 1120, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1152, 1120, 1152, 1136, 1152, 1152, 1120, 1152, 1120, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1120, 1152, 1152, 1136, 1152, 1136, 1552, 1552, 1136, 1136, 1152, 1552, 1136, 1136, 1584, 1552, 1552, 1552, \
+  1152, 1552, 1552, 1152, 1584, 1552, 1152, 1152, 1552, 1584, 1152, 1152, 1552, 1584, 1568, 1552, 1552, 1552, 1152, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1625, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1568, 1632, 1552, 1632, 1568, 1584, 1568, 1568, 1584, 1600, 1552, 1552, 1632, 1600, 1632, 1632, 1632, \
+  1632, 1568, 1584, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1552, 1662, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1568, 1600, 1632, 1552, 1616, 1632, 1632, 1632, 1584, 1632, \
+  1632, 1552, 1632, 1632, 1632, 1568, 1600, 1632, 1648, 1616, 1632, 1648, 1632, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1632, 1664, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1648, 1648, 1648, 1616, 1632, 1680, 1632, 1680, 1648, 1632, 1664, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1648, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1648, 1664, 1648, 1648, 1632, 1648, 1632, 1680, 1664, 1648, 1680, 1664, 1696, 1632, 1664, 1680, 1632, 1648, 1696, \
+  1680, 1632, 1632, 1648, 1648, 1648, 1632, 1664, 1632, 1648, 1648, 1632, 1648, 1648, 1632, 1664, 1664, 1680, 1680, 1632, 1664, 1664, 1648, 1648, 1712, 1728, 1664, 1712, 1696, 1712, \
+  1680, 1632, 1728, 1648, 1728, 1728, 1712, 1648, 1632, 1632, 1664, 1648, 1664, 1664, 1680, 1712, 1664, 1632, 1696, 1664, 1712, 1696, 1680, 1680, 1696, 1680, 1680, 1712, 1648, 1712, \
+  1632, 1728, 1696, 1648, 1712, 1632, 1712, 1696, 1648, 1680, 1648, 1664, 1648, 1696, 1712, 1648, 1648, 1680, 1664, 1696, 1728, 1696, 1712, 1728, 1696, 1728, 1712, 1664, 1680, 1728, \
+  1712, 1712, 1712, 1728, 1728, 1712, 1728, 1696, 1728, 1712, 1696, 1728, 1728, 1680, 1728, 1712, 1664, 1680, 1680, 1696, 1712, 1696, 1696, 1696, 1728, 1696, 1728, 1728, 1696, 1712, \
+  1712, 1664, 1712, 1680, 1664, 1728, 1728, 1664, 1696, 1696, 1680, 1712, 1680, 1712, 1696, 1728, 1696, 1696, 1728, 1696, 1712, 1696, 1712, 1712, 1712, 1728, 1712, 1696, 1728, 1680, \
+  1696, 1712, 1712, 1728, 1712, 1728, 1696, 1728, 1776, 1728, 1696, 1776, 1728, 1728, 1712, 1712, 1824, 1856, 1728, 1824, 1728, 1728, 1712, 1728, 1728, 1728, 1856, 1696, 1728, 1840, \
+  1712, 1712, 1824, 1856, 1792, 1712, 1840, 1728, 1808, 1728, 1824, 1824, 1840, 1824, 1824, 1856, 1856, 1824, 1856, 1840, 1696, 1856, 1840, 1840, 1856, 1856, 1824, 1712, 1792, 1856, \
+  1824, 1728, 1808, 1792, 1856, 1728, 1792, 1840, 1808, 1808, 1712, 1808, 1840, 1808, 1824, 1824, 1824, 1840, 1824, 1840, 1856, 1824, 1728, 1856, 1856, 1824, 1856, 1856, 1792, 1792, \
+  1856, 1824, 1856, 1824, 1824, 1856, 1808, 1824, 1856, 1856, 1840, 1840, 1840, 1840, 1856, 1840, 1840, 1856, 1824, 1840, 1808, 1824, 1840, 1856, 1856, 1824, 1856, 1840, 1840, 1840, \
+  1824, 1824, 1840, 1840, 1840, 1856, 1856, 1856
+
 #endif
diff --git a/src/mpn_extras/x86_64/zen3/flint-mparam.h b/src/mpn_extras/x86_64/zen3/flint-mparam.h
index d1e50ebe30..373cdd7f32 100644
--- a/src/mpn_extras/x86_64/zen3/flint-mparam.h
+++ b/src/mpn_extras/x86_64/zen3/flint-mparam.h
@@ -27,4 +27,156 @@
 #define FFT_N_NUM                                 19
 #define FFT_MULMOD_2EXPP1_CUTOFF                 128
 
+/* FIXME: This tuning is for x86_64_adx with fft_small */
+/* NOTE: We assume that the same cutoff is optimal for both mulhigh and mullow */
+#define FLINT_MPN_MULHIGH_MULDERS_CUTOFF 50
+#define FLINT_MPN_MULHIGH_MUL_CUTOFF 2000
+#define FLINT_MPN_MULHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_SQRHIGH_MULDERS_CUTOFF 90
+#define FLINT_MPN_SQRHIGH_SQR_CUTOFF 2000
+#define FLINT_MPN_SQRHIGH_K_TAB_SIZE 2048
+
+#define FLINT_MPN_MULHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 16, 15, 15, 18, 18, \
+  18, 19, 20, 18, 22, 22, 20, 20, 26, 22, 22, 22, 24, 24, 24, 26, 25, 26, 30, 30, 28, 30, 31, 32, 32, 30, 36, 36, 36, 36, \
+  38, 39, 39, 38, 39, 40, 40, 40, 44, 40, 44, 44, 40, 44, 44, 48, 44, 48, 44, 48, 48, 52, 52, 52, 44, 52, 52, 52, 52, 56, \
+  60, 60, 52, 60, 60, 52, 52, 60, 64, 72, 56, 60, 72, 60, 60, 60, 76, 64, 60, 60, 72, 60, 72, 80, 72, 72, 80, 72, 68, 76, \
+  88, 76, 68, 76, 72, 72, 80, 88, 72, 72, 88, 72, 80, 76, 76, 80, 80, 88, 80, 88, 84, 88, 80, 96, 80, 80, 88, 80, 88, 88, \
+  80, 88, 96, 96, 88, 96, 92, 96, 96, 92, 100, 88, 96, 104, 88, 108, 96, 104, 104, 104, 112, 112, 108, 104, 104, 112, 112, 120, 104, 112, \
+  120, 112, 112, 120, 124, 124, 116, 124, 108, 120, 124, 116, 120, 120, 116, 120, 124, 120, 120, 140, 120, 120, 120, 120, 144, 120, 132, 144, 136, 140, \
+  144, 144, 144, 144, 144, 144, 144, 144, 140, 156, 140, 140, 144, 144, 144, 160, 144, 144, 156, 156, 144, 160, 160, 160, 160, 152, 160, 156, 156, 156, \
+  160, 160, 144, 160, 164, 156, 156, 156, 172, 156, 156, 160, 176, 160, 160, 164, 176, 156, 160, 160, 156, 156, 160, 160, 156, 160, 172, 160, 188, 172, \
+  172, 172, 160, 172, 176, 160, 160, 176, 180, 176, 164, 188, 192, 176, 172, 188, 188, 188, 172, 188, 192, 188, 180, 192, 192, 188, 188, 192, 188, 188, \
+  188, 188, 192, 160, 156, 204, 160, 164, 164, 164, 164, 176, 180, 168, 172, 184, 188, 200, 216, 188, 164, 188, 220, 188, 208, 176, 180, 188, 172, 188, \
+  184, 188, 204, 208, 220, 196, 220, 196, 208, 212, 188, 220, 176, 176, 184, 192, 208, 184, 188, 196, 204, 244, 208, 212, 212, 228, 256, 188, 204, 196, \
+  188, 192, 192, 192, 212, 188, 292, 212, 220, 236, 228, 248, 260, 224, 264, 196, 200, 196, 212, 208, 204, 216, 208, 228, 216, 220, 252, 220, 268, 264, \
+  284, 268, 300, 220, 208, 212, 220, 236, 244, 224, 252, 252, 260, 264, 256, 256, 292, 272, 288, 292, 328, 224, 256, 236, 252, 268, 256, 252, 260, 272, \
+  284, 296, 300, 280, 300, 284, 252, 236, 328, 324, 264, 264, 256, 264, 280, 268, 284, 284, 292, 304, 260, 304, 264, 256, 328, 328, 260, 276, 328, 284, \
+  276, 296, 300, 320, 320, 304, 328, 304, 272, 268, 280, 268, 288, 292, 288, 284, 316, 288, 328, 328, 300, 328, 328, 280, 264, 328, 300, 328, 316, 324, \
+  300, 324, 300, 324, 316, 316, 328, 348, 276, 376, 288, 296, 296, 304, 320, 316, 328, 328, 324, 328, 340, 384, 348, 376, 300, 396, 304, 300, 304, 324, \
+  300, 324, 328, 328, 328, 440, 448, 384, 376, 456, 464, 384, 376, 472, 480, 376, 352, 328, 376, 352, 376, 392, 392, 384, 456, 456, 480, 448, 456, 456, \
+  472, 472, 472, 352, 464, 472, 472, 472, 480, 440, 480, 480, 480, 480, 456, 472, 472, 464, 464, 464, 456, 472, 480, 472, 480, 480, 480, 480, 448, 456, \
+  480, 448, 456, 464, 456, 464, 456, 480, 472, 464, 464, 472, 472, 472, 480, 472, 480, 480, 472, 480, 480, 480, 480, 464, 464, 464, 456, 472, 464, 480, \
+  472, 472, 480, 472, 480, 480, 464, 464, 472, 464, 472, 472, 480, 464, 480, 472, 480, 480, 576, 576, 560, 480, 472, 480, 568, 480, 480, 464, 480, 472, \
+  480, 576, 480, 552, 560, 560, 560, 560, 568, 560, 560, 576, 576, 560, 568, 472, 480, 480, 544, 568, 552, 544, 560, 544, 560, 568, 552, 576, 568, 560, \
+  576, 576, 568, 576, 560, 576, 568, 536, 576, 568, 560, 544, 560, 552, 560, 568, 560, 576, 568, 560, 560, 560, 568, 576, 568, 576, 576, 576, 576, 544, \
+  576, 576, 568, 576, 560, 576, 576, 576, 544, 552, 568, 576, 552, 560, 576, 560, 568, 560, 576, 560, 544, 576, 576, 576, 576, 568, 576, 568, 560, 576, \
+  552, 552, 576, 560, 568, 568, 568, 576, 576, 576, 560, 552, 576, 560, 568, 560, 576, 560, 568, 560, 568, 568, 568, 576, 552, 576, 560, 576, 576, 560, \
+  568, 576, 568, 576, 576, 576, 576, 560, 576, 568, 568, 568, 560, 560, 576, 576, 568, 568, 576, 560, 576, 576, 568, 576, 560, 576, 576, 568, 576, 568, \
+  576, 568, 576, 576, 568, 576, 576, 576, 576, 568, 576, 576, 568, 568, 576, 576, 784, 576, 776, 576, 568, 576, 576, 576, 576, 576, 576, 576, 776, 776, \
+  776, 776, 776, 776, 776, 784, 776, 776, 784, 776, 776, 776, 800, 776, 776, 776, 776, 776, 776, 800, 776, 808, 792, 800, 776, 792, 776, 776, 776, 776, \
+  792, 776, 776, 784, 792, 784, 800, 776, 784, 808, 784, 776, 776, 776, 808, 784, 792, 776, 792, 832, 800, 800, 816, 792, 816, 816, 856, 808, 848, 824, \
+  870, 832, 792, 776, 784, 784, 784, 784, 800, 792, 800, 792, 784, 800, 800, 800, 816, 824, 824, 824, 832, 816, 816, 832, 824, 824, 848, 832, 856, 856, \
+  840, 872, 864, 872, 872, 880, 880, 880, 872, 888, 880, 880, 872, 880, 880, 880, 840, 872, 872, 848, 880, 848, 856, 840, 848, 840, 880, 872, 856, 872, \
+  856, 888, 880, 872, 888, 880, 872, 920, 888, 872, 880, 872, 888, 888, 888, 880, 880, 928, 880, 928, 928, 928, 920, 920, 904, 912, 880, 904, 928, 872, \
+  872, 880, 888, 880, 896, 880, 872, 896, 888, 896, 896, 928, 904, 896, 896, 912, 904, 904, 920, 880, 912, 920, 928, 928, 880, 920, 920, 880, 888, 904, \
+  896, 904, 928, 896, 912, 896, 912, 920, 912, 912, 928, 928, 928, 920, 928, 928, 928, 928, 928, 928, 912, 904, 912, 896, 904, 904, 920, 920, 920, 928, \
+  928, 920, 928, 928, 928, 912, 928, 912, 928, 928, 928, 912, 912, 912, 928, 928, 928, 896, 928, 928, 912, 928, 928, 928, 912, 928, 912, 928, 928, 912, \
+  928, 912, 928, 928, 928, 928, 928, 912, 928, 928, 928, 928, 912, 912, 928, 912, 928, 1024, 928, 928, 928, 928, 928, 928, 1056, 912, 928, 928, 1024, 1024, \
+  928, 928, 1024, 928, 928, 928, 928, 928, 928, 1040, 1040, 928, 1056, 1024, 1072, 1024, 1040, 1040, 1040, 1024, 1088, 1056, 1056, 1088, 1040, 1056, 1072, 1072, 1056, 1056, \
+  1024, 1088, 1040, 1024, 1040, 1040, 1024, 1056, 1056, 1056, 1040, 1072, 1056, 1040, 1056, 1056, 1056, 1056, 1056, 1056, 1056, 1120, 1056, 1088, 1056, 1120, 1088, 1072, 1104, 1104, \
+  1104, 1120, 1088, 1088, 1072, 1088, 1120, 1104, 1088, 1104, 1088, 1072, 1104, 1088, 1120, 1088, 1072, 1072, 1072, 1088, 1088, 1072, 1072, 1088, 1104, 1152, 1104, 1104, 1088, 1104, \
+  1136, 1088, 1104, 1152, 1152, 1152, 1136, 1120, 1136, 1152, 1120, 1152, 1088, 1120, 1104, 1120, 1136, 1104, 1136, 1088, 1136, 1104, 1088, 1104, 1120, 1104, 1104, 1120, 1136, 1136, \
+  1120, 1136, 1136, 1136, 1120, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1104, 1152, 1120, 1136, 1120, 1120, 1152, 1120, 1136, 1152, 1136, 1152, 1120, 1152, 1136, 1136, 1136, 1136, \
+  1136, 1152, 1152, 1152, 1152, 1120, 1120, 1152, 1136, 1136, 1136, 1152, 1152, 1120, 1152, 1152, 1152, 1152, 1152, 1104, 1152, 1152, 1120, 1136, 1152, 1120, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1344, 1152, 1344, 1344, 1344, 1152, 1152, 1152, 1152, 1344, 1328, 1328, 1328, 1152, 1344, 1152, 1344, 1152, 1344, 1152, 1152, 1328, 1152, 1328, 1344, 1328, 1344, 1328, 1344, \
+  1344, 1312, 1328, 1328, 1328, 1344, 1344, 1344, 1328, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1344, 1328, 1344, \
+  1328, 1344, 1344, 1344, 1344, 1328, 1344, 1537, 1538, 1539, 1540, 1541, 1542, 1543, 1544, 1545, 1546, 1547, 1548, 1549, 1550, 1551, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1573, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1583, 1568, 1568, 1552, 1568, 1552, 1568, \
+  1568, 1568, 1584, 1568, 1584, 1568, 1568, 1568, 1552, 1552, 1552, 1568, 1552, 1584, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1584, 1552, 1584, 1552, 1617, 1568, 1584, \
+  1552, 1552, 1584, 1584, 1552, 1625, 1626, 1627, 1628, 1629, 1630, 1631, 1632, 1633, 1634, 1632, 1636, 1632, 1638, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1648, 1669, 1648, 1671, 1632, 1664, 1648, 1632, 1648, 1648, 1648, 1632, \
+  1632, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1632, 1648, 1664, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1648, 1664, 1648, 1648, 1648, 1648, 1648, 1648, \
+  1680, 1664, 1680, 1696, 1680, 1680, 1664, 1680, 1680, 1648, 1632, 1680, 1696, 1632, 1648, 1648, 1632, 1680, 1680, 1664, 1664, 1664, 1648, 1680, 1664, 1680, 1664, 1680, 1664, 1664, \
+  1680, 1696, 1664, 1696, 1712, 1712, 1696, 1680, 1712, 1696, 1728, 1712, 1696, 1728, 1728, 1712, 1728, 1648, 1680, 1696, 1712, 1696, 1712, 1696, 1696, 1680, 1696, 1696, 1696, 1712, \
+  1696, 1696, 1696, 1696, 1712, 1728, 1696, 1728, 1696, 1696, 1712, 1728, 1712, 1728, 1712, 1680, 1696, 1728, 1712, 1696, 1696, 1696, 1712, 1712, 1728, 1696, 1728, 1712, 1712, 1728, \
+  1696, 1696, 1696, 1712, 1696, 1728, 1712, 1712, 1712, 1728, 1696, 1712, 1728, 1728, 1696, 1728, 1728, 1728, 1728, 1728, 1680, 1712, 1728, 1696, 1728, 1728, 1728, 1728, 1696, 1728, \
+  1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1728, 1696, 1728, 1712, 1712, 1712, 1712, 1728, 1712, 1712, 1712, 1728, 1712, 1728, 1728, 1728, \
+  1728, 1712, 1728, 1728, 1712, 1728, 1728, 1712, 1712, 1728, 1712, 1712, 1728, 1728, 1712, 1728, 1712, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1712, \
+  1728, 1712, 1712, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1712, 1712, 1728, 1728, 1728, 1712, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, 1728, \
+  1728, 1728, 1712, 1728, 1728, 1824, 1728, 1728, 1728, 1728, 1824, 1728, 1840, 1728, 1728, 1728, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1728, 1728, 1856, 1856, 1856, 1856, 1728, \
+  1728, 1856, 1856, 1728, 1856, 1728, 1856, 1728, 1840, 1856, 1856, 1840, 1856, 1856, 1856, 1840, 1856, 1856, 1856, 1856, 1856, 1856, 1856, 1840, 1904, 1856, 1856, 1840, 1840, 1856, \
+  1856, 1840, 1856, 1840, 1856, 1856, 1856, 1856, 1952, 1856, 1856, 1856, 1856, 1952, 1904, 1904, 1856, 1856, 1856, 1920, 1952, 2001, 1952, 1984, 1952, 1936, 1952, 1904, 1968, 1920, \
+  1984, 1920, 1968, 1920, 1936, 1856, 2000, 1920, 1936, 1952, 2000, 1968, 1984, 1968, 1984, 2000, 1952, 2000, 2016, 1984, 2000, 2016, 1984, 1664, 2016, 1984, 2016, 1968, 2016, 2016, \
+  1744, 2016, 2016, 1968, 2000, 1728, 1712, 1696
+
+#define FLINT_MPN_SQRHIGH_K_TAB \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
+  0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 28, 29, 0, 0, 31, 0, 31, \
+  0, 32, 0, 34, 0, 36, 36, 40, 0, 40, 40, 40, 0, 44, 0, 44, 44, 48, 0, 52, 48, 52, 44, 44, 48, 48, 48, 48, 48, 48, \
+  48, 48, 48, 48, 52, 52, 52, 52, 52, 56, 56, 52, 56, 56, 56, 56, 56, 56, 56, 56, 60, 60, 68, 64, 60, 60, 60, 60, 64, 64, \
+  64, 68, 68, 68, 64, 64, 68, 68, 72, 72, 68, 68, 68, 72, 76, 80, 72, 72, 72, 88, 76, 76, 80, 80, 76, 80, 76, 80, 84, 80, \
+  88, 88, 80, 84, 88, 80, 80, 84, 92, 88, 92, 88, 88, 88, 88, 96, 88, 108, 100, 92, 88, 88, 104, 100, 100, 92, 104, 108, 100, 92, \
+  104, 100, 104, 96, 108, 104, 96, 96, 104, 100, 100, 104, 112, 116, 108, 104, 104, 116, 108, 104, 104, 120, 116, 104, 108, 132, 116, 108, 120, 108, \
+  108, 108, 132, 108, 120, 112, 112, 116, 132, 128, 116, 124, 128, 116, 132, 120, 132, 120, 124, 120, 132, 120, 124, 128, 120, 128, 128, 132, 144, 124, \
+  128, 124, 140, 128, 128, 124, 136, 132, 128, 128, 140, 144, 128, 128, 140, 136, 132, 144, 148, 152, 144, 132, 160, 156, 140, 144, 156, 144, 140, 144, \
+  140, 156, 156, 156, 140, 144, 168, 156, 156, 164, 168, 156, 156, 160, 144, 144, 180, 156, 152, 168, 156, 160, 156, 148, 180, 168, 180, 156, 164, 156, \
+  156, 172, 156, 156, 156, 180, 180, 172, 180, 168, 164, 172, 164, 172, 176, 176, 168, 176, 172, 176, 180, 168, 176, 180, 180, 180, 192, 184, 180, 176, \
+  204, 176, 188, 180, 188, 180, 204, 180, 192, 204, 180, 192, 180, 204, 228, 192, 188, 192, 204, 180, 192, 216, 200, 216, 228, 216, 204, 216, 188, 216, \
+  216, 204, 216, 192, 204, 212, 228, 204, 228, 216, 204, 216, 192, 204, 204, 212, 204, 216, 204, 216, 228, 228, 224, 212, 204, 216, 216, 224, 228, 212, \
+  216, 228, 212, 204, 204, 216, 216, 216, 228, 216, 220, 224, 228, 220, 228, 228, 236, 224, 260, 224, 228, 228, 260, 228, 248, 252, 264, 248, 216, 212, \
+  212, 212, 220, 216, 216, 220, 216, 224, 216, 228, 232, 224, 220, 224, 240, 244, 236, 244, 232, 256, 288, 240, 236, 288, 260, 260, 264, 232, 228, 228, \
+  228, 236, 236, 228, 236, 236, 236, 248, 256, 260, 232, 236, 264, 256, 260, 252, 284, 252, 264, 276, 244, 296, 244, 240, 244, 248, 240, 252, 256, 260, \
+  260, 252, 252, 272, 252, 272, 260, 296, 268, 260, 256, 276, 272, 264, 312, 284, 256, 252, 252, 252, 264, 252, 256, 260, 264, 276, 292, 268, 264, 276, \
+  264, 260, 264, 304, 288, 296, 296, 296, 288, 296, 272, 280, 264, 264, 272, 264, 288, 288, 280, 288, 272, 280, 296, 296, 280, 288, 296, 320, 344, 320, \
+  344, 272, 344, 344, 304, 288, 280, 280, 312, 280, 280, 304, 304, 312, 304, 296, 288, 328, 320, 352, 320, 320, 328, 360, 344, 344, 360, 288, 288, 304, \
+  288, 296, 320, 320, 312, 312, 304, 328, 336, 312, 312, 360, 336, 344, 344, 336, 360, 360, 296, 296, 304, 360, 328, 328, 312, 320, 320, 328, 312, 344, \
+  344, 328, 344, 344, 368, 360, 352, 360, 392, 392, 368, 320, 312, 392, 312, 328, 344, 336, 344, 328, 360, 352, 352, 360, 360, 360, 368, 408, 360, 376, \
+  392, 392, 376, 336, 344, 352, 360, 352, 344, 344, 384, 344, 360, 376, 392, 368, 360, 408, 408, 448, 432, 384, 392, 336, 360, 344, 360, 360, 368, 376, \
+  376, 360, 368, 408, 368, 376, 376, 376, 432, 376, 384, 464, 432, 344, 432, 376, 344, 344, 384, 344, 384, 376, 400, 432, 456, 432, 456, 392, 432, 392, \
+  448, 456, 360, 376, 456, 408, 384, 368, 376, 432, 376, 472, 464, 504, 448, 360, 408, 456, 376, 408, 424, 424, 448, 440, 456, 392, 408, 384, 408, 392, \
+  384, 416, 424, 432, 400, 472, 480, 408, 432, 432, 464, 456, 504, 464, 456, 472, 496, 416, 392, 424, 504, 400, 440, 432, 472, 448, 456, 456, 432, 448, \
+  456, 504, 504, 512, 496, 504, 424, 416, 408, 432, 544, 432, 440, 456, 448, 448, 464, 472, 480, 552, 552, 544, 552, 560, 552, 544, 544, 544, 552, 552, \
+  552, 552, 552, 552, 552, 560, 552, 552, 560, 560, 560, 560, 568, 576, 568, 592, 576, 560, 560, 560, 560, 568, 568, 576, 568, 568, 576, 568, 568, 576, \
+  568, 568, 600, 592, 576, 608, 576, 576, 576, 576, 584, 584, 576, 592, 592, 600, 584, 592, 584, 600, 600, 600, 584, 624, 584, 592, 600, 592, 616, 592, \
+  592, 592, 592, 592, 592, 592, 600, 608, 600, 608, 600, 600, 600, 624, 616, 608, 616, 600, 632, 608, 608, 608, 616, 608, 608, 608, 608, 616, 608, 664, \
+  664, 632, 656, 616, 664, 624, 616, 632, 632, 616, 624, 624, 624, 632, 624, 624, 624, 624, 648, 632, 624, 624, 872, 872, 656, 664, 696, 872, 872, 872, \
+  632, 872, 872, 896, 872, 896, 872, 896, 880, 872, 896, 872, 888, 872, 872, 872, 872, 872, 888, 872, 880, 824, 872, 856, 880, 888, 800, 848, 800, 880, \
+  848, 800, 808, 872, 872, 864, 824, 840, 872, 872, 872, 872, 872, 872, 872, 872, 872, 872, 880, 928, 872, 920, 872, 920, 888, 880, 872, 880, 872, 872, \
+  872, 888, 880, 888, 888, 872, 888, 872, 880, 896, 920, 920, 880, 928, 904, 872, 888, 904, 872, 872, 872, 872, 880, 888, 872, 872, 872, 880, 872, 904, \
+  920, 888, 888, 872, 880, 880, 888, 896, 896, 880, 872, 904, 880, 912, 896, 872, 904, 904, 912, 880, 880, 920, 912, 896, 928, 928, 872, 872, 872, 872, \
+  880, 880, 888, 888, 888, 912, 880, 880, 880, 912, 896, 896, 928, 896, 912, 912, 896, 928, 928, 928, 928, 912, 880, 928, 880, 880, 896, 880, 896, 880, \
+  896, 880, 880, 912, 912, 880, 896, 880, 896, 912, 880, 880, 928, 912, 912, 928, 928, 896, 928, 912, 928, 928, 928, 928, 928, 928, 880, 880, 880, 880, \
+  880, 912, 896, 912, 912, 896, 928, 896, 928, 896, 928, 928, 928, 928, 912, 880, 928, 912, 896, 928, 896, 880, 912, 896, 912, 896, 896, 896, 928, 896, \
+  912, 928, 912, 928, 912, 928, 912, 880, 928, 928, 880, 928, 928, 880, 896, 928, 880, 896, 912, 928, 928, 896, 912, 928, 912, 928, 1024, 928, 928, 1040, \
+  912, 928, 1024, 1024, 928, 928, 928, 928, 912, 1040, 1072, 912, 1072, 1072, 1056, 1040, 1072, 1088, 1104, 1040, 1040, 928, 1024, 928, 928, 1056, 928, 928, 1056, 1040, \
+  928, 1056, 1024, 1056, 1056, 1056, 1104, 1024, 1056, 1072, 1056, 1056, 1088, 1072, 1120, 1104, 1072, 1072, 1072, 1104, 1120, 1024, 1120, 1120, 1056, 1024, 1040, 1024, 1040, 1040, \
+  1040, 1024, 1040, 1056, 1040, 1088, 1040, 1056, 1120, 1040, 1040, 1072, 1072, 1088, 1104, 1088, 1104, 1088, 1088, 1056, 1120, 1104, 1152, 1104, 1088, 1120, 1104, 1120, 1024, 1120, \
+  1152, 1136, 1152, 1056, 1056, 1072, 1056, 1152, 1088, 1056, 1104, 1072, 1104, 1088, 1120, 1072, 1104, 1088, 1088, 1120, 1120, 1120, 1152, 1136, 1120, 1120, 1152, 1120, 1136, 1152, \
+  1152, 1072, 1136, 1136, 1088, 1152, 1136, 1136, 1104, 1056, 1072, 1088, 1104, 1104, 1120, 1120, 1104, 1104, 1104, 1136, 1152, 1136, 1152, 1136, 1136, 1152, 1152, 1152, 1136, 1072, \
+  1152, 1136, 1152, 1152, 1104, 1152, 1104, 1152, 1152, 1088, 1120, 1152, 1136, 1136, 1120, 1136, 1120, 1152, 1136, 1136, 1120, 1136, 1152, 1136, 1152, 1136, 1136, 1120, 1152, 1152, \
+  1104, 1152, 1152, 1152, 1104, 1120, 1104, 1120, 1120, 1120, 1120, 1136, 1136, 1136, 1136, 1152, 1120, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1104, \
+  1120, 1152, 1136, 1136, 1136, 1136, 1136, 1136, 1120, 1152, 1152, 1152, 1136, 1104, 1152, 1136, 1136, 1152, 1136, 1120, 1136, 1152, 1152, 1136, 1136, 1120, 1136, 1136, 1136, 1120, \
+  1152, 1152, 1152, 1136, 1136, 1136, 1152, 1104, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1136, 1120, 1152, \
+  1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1152, 1120, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, \
+  1120, 1152, 1136, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1152, 1152, 1152, 1152, 1152, 1152, \
+  1136, 1152, 1152, 1152, 1152, 1152, 1136, 1136, 1152, 1136, 1152, 1120, 1152, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1136, 1136, 1136, 1152, 1152, 1152, 1136, \
+  1152, 1152, 1152, 1104, 1120, 1152, 1136, 1152, 1152, 1136, 1152, 1136, 1152, 1152, 1152, 1136, 1136, 1152, 1152, 1120, 1152, 1136, 1152, 1152, 1120, 1152, 1120, 1136, 1152, 1152, \
+  1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1152, 1120, 1152, 1152, 1136, 1152, 1136, 1552, 1552, 1136, 1136, 1152, 1552, 1136, 1136, 1584, 1552, 1552, 1552, \
+  1152, 1552, 1552, 1152, 1584, 1552, 1152, 1152, 1552, 1584, 1152, 1152, 1552, 1584, 1568, 1552, 1552, 1552, 1152, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1552, \
+  1552, 1552, 1552, 1552, 1552, 1625, 1552, 1552, 1552, 1552, 1552, 1552, 1552, 1568, 1632, 1552, 1632, 1568, 1584, 1568, 1568, 1584, 1600, 1552, 1552, 1632, 1600, 1632, 1632, 1632, \
+  1632, 1568, 1584, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1552, 1662, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1568, 1600, 1632, 1552, 1616, 1632, 1632, 1632, 1584, 1632, \
+  1632, 1552, 1632, 1632, 1632, 1568, 1600, 1632, 1648, 1616, 1632, 1648, 1632, 1632, 1632, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1680, 1664, 1632, 1664, 1632, 1632, \
+  1632, 1632, 1632, 1632, 1632, 1648, 1648, 1648, 1616, 1632, 1680, 1632, 1680, 1648, 1632, 1664, 1632, 1648, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1632, 1632, 1632, 1632, 1632, \
+  1648, 1648, 1632, 1632, 1632, 1632, 1632, 1632, 1632, 1664, 1632, 1648, 1664, 1648, 1648, 1632, 1648, 1632, 1680, 1664, 1648, 1680, 1664, 1696, 1632, 1664, 1680, 1632, 1648, 1696, \
+  1680, 1632, 1632, 1648, 1648, 1648, 1632, 1664, 1632, 1648, 1648, 1632, 1648, 1648, 1632, 1664, 1664, 1680, 1680, 1632, 1664, 1664, 1648, 1648, 1712, 1728, 1664, 1712, 1696, 1712, \
+  1680, 1632, 1728, 1648, 1728, 1728, 1712, 1648, 1632, 1632, 1664, 1648, 1664, 1664, 1680, 1712, 1664, 1632, 1696, 1664, 1712, 1696, 1680, 1680, 1696, 1680, 1680, 1712, 1648, 1712, \
+  1632, 1728, 1696, 1648, 1712, 1632, 1712, 1696, 1648, 1680, 1648, 1664, 1648, 1696, 1712, 1648, 1648, 1680, 1664, 1696, 1728, 1696, 1712, 1728, 1696, 1728, 1712, 1664, 1680, 1728, \
+  1712, 1712, 1712, 1728, 1728, 1712, 1728, 1696, 1728, 1712, 1696, 1728, 1728, 1680, 1728, 1712, 1664, 1680, 1680, 1696, 1712, 1696, 1696, 1696, 1728, 1696, 1728, 1728, 1696, 1712, \
+  1712, 1664, 1712, 1680, 1664, 1728, 1728, 1664, 1696, 1696, 1680, 1712, 1680, 1712, 1696, 1728, 1696, 1696, 1728, 1696, 1712, 1696, 1712, 1712, 1712, 1728, 1712, 1696, 1728, 1680, \
+  1696, 1712, 1712, 1728, 1712, 1728, 1696, 1728, 1776, 1728, 1696, 1776, 1728, 1728, 1712, 1712, 1824, 1856, 1728, 1824, 1728, 1728, 1712, 1728, 1728, 1728, 1856, 1696, 1728, 1840, \
+  1712, 1712, 1824, 1856, 1792, 1712, 1840, 1728, 1808, 1728, 1824, 1824, 1840, 1824, 1824, 1856, 1856, 1824, 1856, 1840, 1696, 1856, 1840, 1840, 1856, 1856, 1824, 1712, 1792, 1856, \
+  1824, 1728, 1808, 1792, 1856, 1728, 1792, 1840, 1808, 1808, 1712, 1808, 1840, 1808, 1824, 1824, 1824, 1840, 1824, 1840, 1856, 1824, 1728, 1856, 1856, 1824, 1856, 1856, 1792, 1792, \
+  1856, 1824, 1856, 1824, 1824, 1856, 1808, 1824, 1856, 1856, 1840, 1840, 1840, 1840, 1856, 1840, 1840, 1856, 1824, 1840, 1808, 1824, 1840, 1856, 1856, 1824, 1856, 1840, 1840, 1840, \
+  1824, 1824, 1840, 1840, 1840, 1856, 1856, 1856
+
 #endif

From 83de09070720263ef1c0d6cd37def3f01ecde708 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Albin=20Ahlb=C3=A4ck?= <albin.ahlback@gmail.com>
Date: Mon, 27 May 2024 23:55:08 +0200
Subject: [PATCH 3/4] Start on tuning flint_mpn_mulhigh_n

---
 src/tune/mpn_extras/mulhigh_0.c      |  25 +++++++
 src/tune/mpn_extras/tune_mulhigh_n.c | 108 +++++++++++++++++++++++++++
 src/tune/tune.c                      |   2 +-
 src/tune/tune.h                      |   4 +
 4 files changed, 138 insertions(+), 1 deletion(-)
 create mode 100644 src/tune/mpn_extras/mulhigh_0.c
 create mode 100644 src/tune/mpn_extras/tune_mulhigh_n.c

diff --git a/src/tune/mpn_extras/mulhigh_0.c b/src/tune/mpn_extras/mulhigh_0.c
new file mode 100644
index 0000000000..e38740df2a
--- /dev/null
+++ b/src/tune/mpn_extras/mulhigh_0.c
@@ -0,0 +1,25 @@
+/*
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "flint-mparam.h"
+#include "mpn_extras.h"
+#include "tune.h"
+
+#undef FLINT_MPN_MULHIGH_K_TAB_SIZE
+#undef FLINT_MPN_MULHIGH_K_TAB
+#define TUNE_PROGRAM 1
+
+#define FLINT_MPN_MULHIGH_K_TAB_SIZE FLINT_MPN_MULHIGH_K_TAB_MAX_SIZE
+#define flint_mpn_mulhigh_k_tab flint_mpn_mulhigh_k_tab_0
+#define _flint_mpn_mulhigh_n_mulders_recursive _flint_mpn_mulhigh_n_mulders_recursive_0
+#define _flint_mpn_mulhigh_n_mulders _flint_mpn_mulhigh_n_mulders_0
+
+#include "mpn_extras/mulhigh.c"
diff --git a/src/tune/mpn_extras/tune_mulhigh_n.c b/src/tune/mpn_extras/tune_mulhigh_n.c
new file mode 100644
index 0000000000..a1fdcb95a7
--- /dev/null
+++ b/src/tune/mpn_extras/tune_mulhigh_n.c
@@ -0,0 +1,108 @@
+/*
+    Copyright (C) 2024 Fredrik Johansson
+    Copyright (C) 2024 Albin Ahlbäck
+
+    This file is part of FLINT.
+
+    FLINT is free software: you can redistribute it and/or modify it under
+    the terms of the GNU Lesser General Public License (LGPL) as published
+    by the Free Software Foundation; either version 3 of the License, or
+    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
+*/
+
+#include "mpn_extras.h"
+#include "tune.h"
+
+#undef FLINT_MPN_MULHIGH_K_TAB_SIZE
+#define FLINT_MPN_MULHIGH_K_TAB_SIZE FLINT_MPN_MULHIGH_K_TAB_MAX_SIZE
+
+#define flint_mpn_mulhigh_k_tab flint_mpn_mulhigh_k_tab_0
+#define _flint_mpn_mulhigh_n_mulders _flint_mpn_mulhigh_n_mulders_0
+
+FLINT_DLL extern short flint_mpn_mulhigh_k_tab[FLINT_MPN_MULHIGH_K_TAB_SIZE];
+mp_limb_t _flint_mpn_mulhigh_n_mulders(mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
+
+/* IDEA:
+
+    1. Set all entries in flint_mpn_mulhigh_k_tab to zeroes.
+    2. Skip any further altering of those entries having a corresponding
+       hardcoded version.
+    3. When reasonable, check if basecase is faster.
+    4. The sequence of k should be weakly increasing. We only need to consider k
+       between n / 2 and n.
+       TODO: How can we prune the search with this information?
+    5. Run some warmups and run some hotlaps for each k. Only use the fastest
+       consistent time (see tune.c).
+    6. Use the k that corresponds to the fastest time and push that to
+       flint_mpn_mulhigh_k_tab so that it can be used in consecutive runs.
+    7. For large enough n, check if _flint_mpn_mulhigh_n_mul is faster. When we
+       have 50 consecutive runs of full multiplication that are faster high
+       multiplication, we exit.
+*/
+
+#define BASECASE_REASONABLE(n) ((n) < 200)
+
+double measure_func(tune_func_t, void *, int, int);
+
+#if 0
+void _tune_flint_mpn_mulhigh_n(void * vparam)
+{
+    struct mulhigh__param_0 * param = vparam;
+    nn_ptr ap, bp, xp, yp;
+    slong len;
+    flint_time_t t0, t1;
+    slong ix;
+
+    ap = param->ap;
+    bp = param->bp;
+    xp = param->xp;
+    yp = param->yp;
+    len = param->len;
+
+    flint_time_get(t0);
+    for (ix = 0; ix < len; ix++)
+        func(ap, bp, xp[ix], yp[ix]);
+    flint_time_get(t1);
+
+    return flint_time_nsec_diff(t1, t0);
+}
+
+void
+tune_flint_mpn_mulhigh_n(int FLINT_UNUSED(warmups), int FLINT_UNUSED(min_runs))
+{
+    slong n;
+    mp_ptr rp, xp, yp;
+    flint_rand_t state;
+
+    /* Initialize flint_mpn_mulhigh_k_tab */
+    for (n = 0; n < FLINT_MPN_MULHIGH_K_TAB_MAX_SIZE; n++)
+        flint_mpn_mulhigh_k_tab[n] = 0;
+
+    rp = flint_malloc(2 * sizeof(mp_limb_t) * FLINT_MPN_MULHIGH_K_TAB_MAX_SIZE);
+    xp = flint_malloc(sizeof(mp_limb_t) * FLINT_MPN_MULHIGH_K_TAB_MAX_SIZE);
+    yp = flint_malloc(sizeof(mp_limb_t) * FLINT_MPN_MULHIGH_K_TAB_MAX_SIZE);
+
+    flint_rand_init(state);
+    flint_mpn_rrandom(xp, state, FLINT_MPN_MULHIGH_K_TAB_MAX_SIZE);
+    flint_mpn_rrandom(yp, state, FLINT_MPN_MULHIGH_K_TAB_MAX_SIZE);
+    flint_rand_clear(state);
+
+    for (n = 1; n < FLINT_MPN_MULHIGH_K_TAB_MAX_SIZE; n++)
+    {
+        if (FLINT_HAVE_MULHIGH_FUNC(n))
+            continue;
+
+        if (BASECASE_REASONABLE(n))
+        {
+
+        }
+        else
+        {
+        }
+    }
+
+    flint_free(rp);
+    flint_free(xp);
+    flint_free(yp);
+}
+#endif
diff --git a/src/tune/tune.c b/src/tune/tune.c
index f336535342..b95394252b 100644
--- a/src/tune/tune.c
+++ b/src/tune/tune.c
@@ -52,7 +52,7 @@ int compare_doubles(const void * ap, const void * bp)
     return (a < b) ? -1 : (a > b) ? 1 : 0;
 }
 
-static double measure_func(tune_func_t fun, void * params, int runs, int warmups)
+double measure_func(tune_func_t fun, void * params, int runs, int warmups)
 {
     double * times = malloc(sizeof(double) * runs);
     int ix;
diff --git a/src/tune/tune.h b/src/tune/tune.h
index 4aac8012fc..e56fbcabc3 100644
--- a/src/tune/tune.h
+++ b/src/tune/tune.h
@@ -42,6 +42,10 @@ void n_param_clear(void *);
 double _tune_n_xgcd_0(void *);
 double _tune_n_xgcd_1(void *);
 
+/* mpn_extras ****************************************************************/
+
+#define FLINT_MPN_MULHIGH_K_TAB_MAX_SIZE 4096
+
 /* n_mod_vec *****************************************************************/
 #if WANT_N_MOD
 struct n_mod_vec_param_0

From 43059067eeb285435346f7a37971e045f4babba2 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Albin=20Ahlb=C3=A4ck?= <albin.ahlback@gmail.com>
Date: Mon, 17 Jun 2024 13:37:50 +0200
Subject: [PATCH 4/4] Stash IDK

---
 src/tune/mpn_extras/tune_mulhigh_n.c | 4 +---
 1 file changed, 1 insertion(+), 3 deletions(-)

diff --git a/src/tune/mpn_extras/tune_mulhigh_n.c b/src/tune/mpn_extras/tune_mulhigh_n.c
index a1fdcb95a7..3afe77825a 100644
--- a/src/tune/mpn_extras/tune_mulhigh_n.c
+++ b/src/tune/mpn_extras/tune_mulhigh_n.c
@@ -44,10 +44,9 @@ mp_limb_t _flint_mpn_mulhigh_n_mulders(mp_ptr, mp_srcptr, mp_srcptr, mp_size_t);
 
 double measure_func(tune_func_t, void *, int, int);
 
-#if 0
 void _tune_flint_mpn_mulhigh_n(void * vparam)
 {
-    struct mulhigh__param_0 * param = vparam;
+    struct mulhigh_param_0 * param = vparam;
     nn_ptr ap, bp, xp, yp;
     slong len;
     flint_time_t t0, t1;
@@ -105,4 +104,3 @@ tune_flint_mpn_mulhigh_n(int FLINT_UNUSED(warmups), int FLINT_UNUSED(min_runs))
     flint_free(xp);
     flint_free(yp);
 }
-#endif