Neon equivalent of mm_madd_epi16 and mm_maddubs_epi16

You might want to look at the implementations is SIMDe for _mm_madd_epi16 and _mm_maddubs_epi16 (note to future readers: you might want to check the latest version of those files since implementations in SIMDe get improved sometimes and it's very unlikely I'll remember to update this answer). These implementations are just copied from there.

If you're on AArch64, for _mm_madd_epi16 you probably want to use an vmull_s16+vget_low_s16 for the low half, a vmull_high_s16 for the high half, then use vpaddq_s32 to add them together into a 128-bit result. Without AArch64 you'll need two vmull_s16 calls (one with vget_low_s16 and one with vget_high_s16), but since vpaddq_s32 isn't supported you'll need two vpadd_s32 calls with a vcombine_s32:

#if defined(SIMDE_ARM_NEON_A64V8_NATIVE)
  int32x4_t pl = vmull_s16(vget_low_s16(a_.neon_i16),  vget_low_s16(b_.neon_i16));
  int32x4_t ph = vmull_high_s16(a_.neon_i16, b_.neon_i16);
  r_.neon_s32 = vpaddq_s32(pl, ph);
#elif defined(SIMDE_ARM_NEON_A32V7_NATIVE)
  int32x4_t pl = vmull_s16(vget_low_s16(a_.neon_i16),  vget_low_s16(b_.neon_i16));
  int32x4_t ph = vmull_s16(vget_high_s16(a_.neon_i16), vget_high_s16(b_.neon_i16));
  int32x2_t rl = vpadd_s32(vget_low_s32(pl), vget_high_s32(pl));
  int32x2_t rh = vpadd_s32(vget_low_s32(ph), vget_high_s32(ph));
  r_.neon_i32 = vcombine_s32(rl, rh);
#endif

For _mm_maddubs_epi16 it's a little more complicated, but I don't think an AArch64-specific version will do much good:

/* Zero extend a */
int16x8_t a_odd = vreinterpretq_s16_u16(vshrq_n_u16(a_.neon_u16, 8));
int16x8_t a_even = vreinterpretq_s16_u16(vbicq_u16(a_.neon_u16, vdupq_n_u16(0xff00)));

/* Sign extend by shifting left then shifting right. */
int16x8_t b_even = vshrq_n_s16(vshlq_n_s16(b_.neon_i16, 8), 8);
int16x8_t b_odd = vshrq_n_s16(b_.neon_i16, 8);

/* multiply */
int16x8_t prod1 = vmulq_s16(a_even, b_even);
int16x8_t prod2 = vmulq_s16(a_odd, b_odd);

/* saturated add */
r_.neon_i16 = vqaddq_s16(prod1, prod2);