Fix: Avoid LibC symbols

Closes #229

Co-authored-by: kukugpt <[email protected]>

Author: ashvardanian

c/lib.c

@@ -7,6 +7,12 @@
 #define SIMSIMD_NATIVE_F16 0
 #define SIMSIMD_NATIVE_BF16 0
 
+/*  Override the primary serial operations to avoid the LibC dependency.
+ */
+#define SIMSIMD_SQRT(x) simsimd_approximate_square_root(x)
+#define SIMSIMD_RSQRT(x) simsimd_approximate_inverse_square_root(x)
+#define SIMSIMD_LOG(x) simsimd_approximate_log(x)
+
 /*  Depending on the Operating System, the following intrinsics are available
  *  on recent compiler toolchains:
  *

include/simsimd/types.h

@@ -34,7 +34,7 @@
 #elif defined(__GNUC__) || defined(__clang__)
 #define SIMSIMD_DYNAMIC __attribute__((visibility("default")))
 #define SIMSIMD_PUBLIC __attribute__((unused)) inline static
-#define SIMSIMD_INTERNAL __attribute__((always_inline)) inline static
+#define SIMSIMD_INTERNAL inline static
 #else
 #define SIMSIMD_DYNAMIC
 #define SIMSIMD_PUBLIC inline static
@@ -436,16 +436,20 @@ SIMSIMD_STATIC_ASSERT(sizeof(simsimd_bf16_t) == 2, simsimd_bf16_t_must_be_2_byte
 #endif
 
 #if !defined(SIMSIMD_F32_TO_I8)
-#define SIMSIMD_F32_TO_I8(x, y) *(y) = (simsimd_i8_t)fminf(fmaxf(roundf(x), -128), 127)
+#define SIMSIMD_F32_TO_I8(x, y) \
+    *(y) = (simsimd_i8_t)((x) > 127 ? 127 : ((x) < -128 ? -128 : (int)((x) + ((x) < 0 ? -0.5f : 0.5f))))
 #endif
 #if !defined(SIMSIMD_F32_TO_U8)
-#define SIMSIMD_F32_TO_U8(x, y) *(y) = (simsimd_u8_t)fminf(fmaxf(roundf(x), 0), 255)
+#define SIMSIMD_F32_TO_U8(x, y) \
+    *(y) = (simsimd_u8_t)((x) > 255 ? 255 : ((x) < 0 ? 0 : (int)((x) + ((x) < 0 ? -0.5f : 0.5f))))
 #endif
 #if !defined(SIMSIMD_F64_TO_I8)
-#define SIMSIMD_F64_TO_I8(x, y) *(y) = (simsimd_i8_t)fmin(fmax(round(x), -128), 127)
+#define SIMSIMD_F64_TO_I8(x, y) \
+    *(y) = (simsimd_i8_t)((x) > 127 ? 127 : ((x) < -128 ? -128 : (int)((x) + ((x) < 0 ? -0.5 : 0.5))))
 #endif
 #if !defined(SIMSIMD_F64_TO_U8)
-#define SIMSIMD_F64_TO_U8(x, y) *(y) = (simsimd_u8_t)fmin(fmax(round(x), 0), 255)
+#define SIMSIMD_F64_TO_U8(x, y) \
+    *(y) = (simsimd_u8_t)((x) > 255 ? 255 : ((x) < 0 ? 0 : (int)((x) + ((x) < 0 ? -0.5 : 0.5))))
 #endif
 
 /** @brief  Convenience type for half-precision floating-point type conversions. */
@@ -467,20 +471,33 @@ typedef union {
  *  https://web.archive.org/web/20210208132927/http://assemblyrequired.crashworks.org/timing-square-root/
  *  https://stackoverflow.com/a/41460625/2766161
  */
-SIMSIMD_PUBLIC simsimd_f32_t simsimd_approximate_inverse_square_root(simsimd_f32_t number) {
+SIMSIMD_INTERNAL simsimd_f32_t simsimd_approximate_inverse_square_root(simsimd_f32_t number) {
     simsimd_f32i32_t conv;
     conv.f = number;
     conv.i = 0x5F1FFFF9 - (conv.i >> 1);
+    // Refine using a Newton-Raphson step for better accuracy
     conv.f *= 0.703952253f * (2.38924456f - number * conv.f * conv.f);
     return conv.f;
 }
 
+/**
+ *  @brief  Approximates `sqrt(x)` using the fast inverse square root trick
+ *          with adjustments for direct square root approximation.
+ *
+ *  Similar to `rsqrt` approximation but multiplies by `number` to get `sqrt`.
+ *  This technique is useful where `sqrt` approximation is needed in performance-critical code,
+ *  though modern hardware provides optimized alternatives.
+ */
+SIMSIMD_INTERNAL simsimd_f32_t simsimd_approximate_square_root(simsimd_f32_t number) {
+    return number * simsimd_approximate_inverse_square_root(number);
+}
+
 /**
  *  @brief  Computes `log(x)` using the Mercator series.
  *          The series converges to the natural logarithm for args between -1 and 1.
  *          Published in 1668 in "Logarithmotechnia".
  */
-SIMSIMD_PUBLIC simsimd_f32_t simsimd_approximate_log(simsimd_f32_t number) {
+SIMSIMD_INTERNAL simsimd_f32_t simsimd_approximate_log(simsimd_f32_t number) {
     simsimd_f32_t x = number - 1;
     simsimd_f32_t x2 = x * x;
     simsimd_f32_t x3 = x * x * x;
@@ -497,7 +514,7 @@ SIMSIMD_PUBLIC simsimd_f32_t simsimd_approximate_log(simsimd_f32_t number) {
  *  https://gist.github.com/milhidaka/95863906fe828198f47991c813dbe233
  *  https://github.com/OpenCyphal/libcanard/blob/636795f4bc395f56af8d2c61d3757b5e762bb9e5/canard.c#L811-L834
  */
-SIMSIMD_PUBLIC simsimd_f32_t simsimd_f16_to_f32(simsimd_f16_t const *x_ptr) {
+SIMSIMD_INTERNAL simsimd_f32_t simsimd_f16_to_f32(simsimd_f16_t const *x_ptr) {
     unsigned short x = *(unsigned short const *)x_ptr;
     unsigned int exponent = (x & 0x7C00) >> 10;
     unsigned int mantissa = (x & 0x03FF) << 13;
@@ -519,7 +536,7 @@ SIMSIMD_PUBLIC simsimd_f32_t simsimd_f16_to_f32(simsimd_f16_t const *x_ptr) {
  *  https://gist.github.com/milhidaka/95863906fe828198f47991c813dbe233
  *  https://github.com/OpenCyphal/libcanard/blob/636795f4bc395f56af8d2c61d3757b5e762bb9e5/canard.c#L811-L834
  */
-SIMSIMD_PUBLIC void simsimd_f32_to_f16(simsimd_f32_t x, simsimd_f16_t *result_ptr) {
+SIMSIMD_INTERNAL void simsimd_f32_to_f16(simsimd_f32_t x, simsimd_f16_t *result_ptr) {
     simsimd_f32i32_t conv;
     conv.f = x;
     unsigned int b = conv.i + 0x00001000;
@@ -538,7 +555,7 @@ SIMSIMD_PUBLIC void simsimd_f32_to_f16(simsimd_f32_t x, simsimd_f16_t *result_pt
  *  https://stackoverflow.com/questions/55253233/convert-fp32-to-bfloat16-in-c/55254307#55254307
  *  https://cloud.google.com/blog/products/ai-machine-learning/bfloat16-the-secret-to-high-performance-on-cloud-tpus
  */
-SIMSIMD_PUBLIC simsimd_f32_t simsimd_bf16_to_f32(simsimd_bf16_t const *x_ptr) {
+SIMSIMD_INTERNAL simsimd_f32_t simsimd_bf16_to_f32(simsimd_bf16_t const *x_ptr) {
     unsigned short x = *(unsigned short const *)x_ptr;
     simsimd_f32i32_t conv;
     conv.i = x << 16; // Zero extends the mantissa
@@ -551,7 +568,7 @@ SIMSIMD_PUBLIC simsimd_f32_t simsimd_bf16_to_f32(simsimd_bf16_t const *x_ptr) {
  *  https://stackoverflow.com/questions/55253233/convert-fp32-to-bfloat16-in-c/55254307#55254307
  *  https://cloud.google.com/blog/products/ai-machine-learning/bfloat16-the-secret-to-high-performance-on-cloud-tpus
  */
-SIMSIMD_PUBLIC void simsimd_f32_to_bf16(simsimd_f32_t x, simsimd_bf16_t *result_ptr) {
+SIMSIMD_INTERNAL void simsimd_f32_to_bf16(simsimd_f32_t x, simsimd_bf16_t *result_ptr) {
     simsimd_f32i32_t conv;
     conv.f = x;
     conv.i += 0x8000; // Rounding is optional
@@ -561,12 +578,12 @@ SIMSIMD_PUBLIC void simsimd_f32_to_bf16(simsimd_f32_t x, simsimd_bf16_t *result_
     *(unsigned short *)result_ptr = (unsigned short)conv.i;
 }
 
-SIMSIMD_PUBLIC simsimd_u32_t simsimd_u32_rol(simsimd_u32_t x, int n) { return (x << n) | (x >> (32 - n)); }
-SIMSIMD_PUBLIC simsimd_u16_t simsimd_u16_rol(simsimd_u16_t x, int n) { return (x << n) | (x >> (16 - n)); }
-SIMSIMD_PUBLIC simsimd_u8_t simsimd_u8_rol(simsimd_u8_t x, int n) { return (x << n) | (x >> (8 - n)); }
-SIMSIMD_PUBLIC simsimd_u32_t simsimd_u32_ror(simsimd_u32_t x, int n) { return (x >> n) | (x << (32 - n)); }
-SIMSIMD_PUBLIC simsimd_u16_t simsimd_u16_ror(simsimd_u16_t x, int n) { return (x >> n) | (x << (16 - n)); }
-SIMSIMD_PUBLIC simsimd_u8_t simsimd_u8_ror(simsimd_u8_t x, int n) { return (x >> n) | (x << (8 - n)); }
+SIMSIMD_INTERNAL simsimd_u32_t simsimd_u32_rol(simsimd_u32_t x, int n) { return (x << n) | (x >> (32 - n)); }
+SIMSIMD_INTERNAL simsimd_u16_t simsimd_u16_rol(simsimd_u16_t x, int n) { return (x << n) | (x >> (16 - n)); }
+SIMSIMD_INTERNAL simsimd_u8_t simsimd_u8_rol(simsimd_u8_t x, int n) { return (x << n) | (x >> (8 - n)); }
+SIMSIMD_INTERNAL simsimd_u32_t simsimd_u32_ror(simsimd_u32_t x, int n) { return (x >> n) | (x << (32 - n)); }
+SIMSIMD_INTERNAL simsimd_u16_t simsimd_u16_ror(simsimd_u16_t x, int n) { return (x >> n) | (x << (16 - n)); }
+SIMSIMD_INTERNAL simsimd_u8_t simsimd_u8_ror(simsimd_u8_t x, int n) { return (x >> n) | (x << (8 - n)); }
 
 #ifdef __cplusplus
 } // extern "C"