From 88b31ff8a43c105dc3ed123b6f4af7ff27286c37 Mon Sep 17 00:00:00 2001
From: ckormanyos <ckormanyos@yahoo.com>
Date: Fri, 20 Feb 2026 21:30:07 +0100
Subject: [PATCH] Use the global small data pointer

---
 .../math/functions/math_functions_bessel.h    | 19 ++++++++++++++++---
 .../xtensa_esp32_p4/make/xtensa_esp32_p4.ld   | 16 ++++++++++------
 .../make/xtensa_esp32_p4_flags.gmk            |  4 ++++
 .../startup/Code/Startup/boot.s               |  4 ++++
 4 files changed, 34 insertions(+), 9 deletions(-)

diff --git a/ref_app/src/math/functions/math_functions_bessel.h b/ref_app/src/math/functions/math_functions_bessel.h
index 20bf91a1c..2f376b606 100644
--- a/ref_app/src/math/functions/math_functions_bessel.h
+++ b/ref_app/src/math/functions/math_functions_bessel.h
@@ -1,5 +1,5 @@
 ///////////////////////////////////////////////////////////////////////////////
-//  Copyright Christopher Kormanyos 2014 - 2025.
+//  Copyright Christopher Kormanyos 2014 - 2026.
 //  Distributed under the Boost Software License,
 //  Version 1.0. (See accompanying file LICENSE_1_0.txt
 //  or copy at http://www.boost.org/LICENSE_1_0.txt)
@@ -22,11 +22,24 @@
         // Compute the Taylor series representation of cyl_bessel_j.
         // There are no checks on input range or parameter boundaries.
 
+        // The following low-precision analysis has been carried out
+        // for another perspective on small arguments.
+
+        //   Series[BesselJ[n, x], {x, 0, 7}]
+        //   Normal[%]
+        //   FullSimplify[%]
+        // Then explicitly take the polynomial part and run it through HornerForm[...].
+        // The result is the following.
+        // (1/(3 Gamma[4 + n])) 2^(-7 - n) x^n (384 (1 + n) (2 + n) (3 + n) - x^2 (576 + n (480 + 96 n) + x^2 (36 + 12 n - x^2)))
+        // This should provide good precision for 32-bit float for arguments having (x/n) <= 3/10.
+
         const T x_half     = x / 2;
         const T v_plus_one = v + 1;
 
-        const T hypergeometric_0f1_term =
-          math::functions::hypergeometric_0f1(v_plus_one, -(x_half * x_half));
+        const T hypergeometric_0f1_term
+        {
+          math::functions::hypergeometric_0f1(v_plus_one, -(x_half * x_half))
+        };
 
         using std::pow;
         using std::tgamma;
diff --git a/ref_app/target/micros/xtensa_esp32_p4/make/xtensa_esp32_p4.ld b/ref_app/target/micros/xtensa_esp32_p4/make/xtensa_esp32_p4.ld
index ac1a7b1c4..ce2830aec 100644
--- a/ref_app/target/micros/xtensa_esp32_p4/make/xtensa_esp32_p4.ld
+++ b/ref_app/target/micros/xtensa_esp32_p4/make/xtensa_esp32_p4.ld
@@ -122,6 +122,7 @@ SECTIONS
     *(.data*)
     . = ALIGN(4);
     KEEP (*(.data*))
+    _small_ram_begin = .;
     *(.sdata)
     . = ALIGN(4);
     KEEP (*(.sdata))
@@ -135,18 +136,19 @@ SECTIONS
   .bss : ALIGN(4)
   {
     _bss_begin = .;
-    *(.bss)
-    . = ALIGN(4);
-    KEEP (*(.bss))
-    *(.bss*)
-    . = ALIGN(4);
-    KEEP (*(.bss*))
     *(.sbss)
     . = ALIGN(4);
     KEEP (*(.sbss))
     *(.sbss*)
     . = ALIGN(4);
     KEEP (*(.sbss*))
+    _small_ram_end = .;
+    *(.bss)
+    . = ALIGN(4);
+    KEEP (*(.bss))
+    *(.bss*)
+    . = ALIGN(4);
+    KEEP (*(.bss*))
     _bss_end = .;
   } > RAM
 
@@ -174,4 +176,6 @@ SECTIONS
   printf = 0x4fc00024;
 
   _rom_data_begin = LOADADDR(.data);
+
+  _global_pointer = _small_ram_begin + (_small_ram_end - _small_ram_begin) / 2;
 }
diff --git a/ref_app/target/micros/xtensa_esp32_p4/make/xtensa_esp32_p4_flags.gmk b/ref_app/target/micros/xtensa_esp32_p4/make/xtensa_esp32_p4_flags.gmk
index 221ac7ebd..72dc8f211 100644
--- a/ref_app/target/micros/xtensa_esp32_p4/make/xtensa_esp32_p4_flags.gmk
+++ b/ref_app/target/micros/xtensa_esp32_p4/make/xtensa_esp32_p4_flags.gmk
@@ -21,6 +21,9 @@ TGT_ALLFLAGS  = -O2
                 -march=rv32imafc_zicsr_zifencei_xesppie                           \
                 -mabi=ilp32f                                                      \
                 -msmall-data-limit=32                                             \
+                -mrelax                                                           \
+                -mrelax                                                           \
+                -fno-common                                                       \
                 -falign-functions=4                                               \
                 -fomit-frame-pointer                                              \
                 -DHP_CORES_SMP_MODE
@@ -40,6 +43,7 @@ TGT_AFLAGS    =
 
 TGT_LDFLAGS   = -nostdlib                                                         \
                 -nostartfiles                                                     \
+                $(TGT_ALLFLAGS)                                                   \
                 -Wl,--no-warn-rwx-segments                                        \
                 -Wl,-z,max-page-size=4096                                         \
                 -Wl,-Map,$(APP).map                                               \
diff --git a/ref_app/target/micros/xtensa_esp32_p4/startup/Code/Startup/boot.s b/ref_app/target/micros/xtensa_esp32_p4/startup/Code/Startup/boot.s
index 2af61f36c..bca56bd30 100644
--- a/ref_app/target/micros/xtensa_esp32_p4/startup/Code/Startup/boot.s
+++ b/ref_app/target/micros/xtensa_esp32_p4/startup/Code/Startup/boot.s
@@ -38,6 +38,7 @@
 .align 2
 .globl _start
 .extern main_x
+.extern _global_pointer
 
 .set mtvt, 0x307
 .set msip, 0x20000000
@@ -56,6 +57,9 @@ _start:
         csrs mstatus, t0
         fscsr x0
 
+        /* Set/enable the global pointer for small ram */
+        la gp, _global_pointer
+
          /* Read machine hart ID */
          csrr a0, mhartid
          bnez a0, .L_core1