NEON/NEONFMA RAddStoreExpMinusMax micro-kernels
PiperOrigin-RevId: 291547227
diff --git a/src/f32-raddstoreexpminusmax/neon-p5.c.in b/src/f32-raddstoreexpminusmax/neon-p5.c.in
new file mode 100644
index 0000000..2bceff0
--- /dev/null
+++ b/src/f32-raddstoreexpminusmax/neon-p5.c.in
@@ -0,0 +1,267 @@
+// Copyright 2020 Google LLC
+//
+// This source code is licensed under the BSD-style license found in the
+// LICENSE file in the root directory of this source tree.
+
+$assert ELEMENTS_TILE % 4 == 0
+$assert ELEMENTS_TILE >= 4
+$SIMD_TILE = ELEMENTS_TILE // 4
+$ABC = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+$VMULADDQ_F32 = "vfmaq_f32" if FMA else "vmlaq_f32"
+#include <assert.h>
+
+#include <arm_neon.h>
+
+#include <xnnpack/common.h>
+#include <xnnpack/raddstoreexpminusmax.h>
+
+
+void xnn_f32_raddstoreexpminusmax_ukernel__${"neonfma" if FMA else "neon"}_p5_x${ELEMENTS_TILE}${"" if ACCUMULATORS == 1 else "_acc%d" % ACCUMULATORS}(
+ size_t elements,
+ const float* input,
+ float* output,
+ float* sum,
+ float max)
+{
+ assert(elements % sizeof(float) == 0);
+
+ const float32x4_t vmagic_bias = vmovq_n_f32(0x1.8000FEp23f);
+ // The smallest x for which expf(x) is normalized.
+ const float32x4_t vdenorm_cutoff = vmovq_n_f32(-0x1.5D589Ep6f);
+ const float32x4_t vlog2e = vmovq_n_f32(0x1.715476p+0f);
+ $if FMA:
+ const float32x4_t vminus_ln2_hi = vmovq_n_f32(-0x1.62E43p-1f);
+ const float32x4_t vminus_ln2_lo = vmovq_n_f32(0x1.05C61p-29f);
+ $else:
+ // Last 7 bits are zeroes
+ const float32x4_t vminus_ln2_hi = vmovq_n_f32(-0x1.62E400p-1f);
+ const float32x4_t vminus_ln2_lo = vmovq_n_f32(-0x1.7F7D1Cp-20f);
+
+ const float32x4_t vc1 = vmovq_n_f32(0x1.FFFFF6p-1f);
+ const float32x4_t vc2 = vmovq_n_f32(0x1.FFFDC6p-2f);
+ const float32x4_t vc3 = vmovq_n_f32(0x1.555A80p-3f);
+ const float32x4_t vc4 = vmovq_n_f32(0x1.573A1Ap-5f);
+ const float32x4_t vc5 = vmovq_n_f32(0x1.0F9F9Cp-7f);
+
+ const float32x4_t vi_max = vdupq_n_f32(max);
+
+ $if ELEMENTS_TILE > 4:
+ $for K in range(ACCUMULATORS):
+ float32x4_t vacc${K} = vmovq_n_f32(0.0f);
+ for (; elements >= ${ELEMENTS_TILE} * sizeof(float); elements -= ${ELEMENTS_TILE} * sizeof(float)) {
+ // Load ${ELEMENTS_TILE} (${SIMD_TILE}x4) inputs at a time.
+ $for N in range(0, ELEMENTS_TILE, 4):
+ const float32x4_t vi${ABC[N:N+4]} = vld1q_f32(input); input += 4;
+
+ // Subtract maximum input x := i - i_max. This implies x <= 0.
+ $for N in range(0, ELEMENTS_TILE, 4):
+ const float32x4_t vx${ABC[N:N+4]} = vsubq_f32(vi${ABC[N:N+4]}, vi_max);
+
+ // Compute reduced argument n := round(x / log(2)).
+ // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the
+ // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
+ // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because
+ // inputs outside of [-87.336540, 0.0] underflow expf(x) anyway. We fixup the result for such inputs at the very end
+ // of the algorithm.
+ $for N in range(0, ELEMENTS_TILE, 4):
+ float32x4_t vn${ABC[N:N+4]} = ${VMULADDQ_F32}(vmagic_bias, vx${ABC[N:N+4]}, vlog2e);
+
+ // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
+ // -87.33642 <= x <= 0.0, and -126 <= n <= 0 accordingly.
+ $for N in range(0, ELEMENTS_TILE, 4):
+ const float32x4_t vs${ABC[N:N+4]} = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn${ABC[N:N+4]}), 23));
+
+ // Subtract the large number back to get final n := round(x / log(2)).
+ $for N in range(0, ELEMENTS_TILE, 4):
+ vn${ABC[N:N+4]} = vsubq_f32(vn${ABC[N:N+4]}, vmagic_bias);
+
+ // Compute reduced argument t := z - n * log(2).
+ // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
+ $for N in range(0, ELEMENTS_TILE, 4):
+ float32x4_t vt${ABC[N:N+4]} = ${VMULADDQ_F32}(vx${ABC[N:N+4]}, vn${ABC[N:N+4]}, vminus_ln2_hi);
+
+ $for N in range(0, ELEMENTS_TILE, 4):
+ vt${ABC[N:N+4]} = ${VMULADDQ_F32}(vt${ABC[N:N+4]}, vn${ABC[N:N+4]}, vminus_ln2_lo);
+
+ // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
+ $for N in range(0, ELEMENTS_TILE, 4):
+ float32x4_t vp${ABC[N:N+4]} = ${VMULADDQ_F32}(vc4, vc5, vt${ABC[N:N+4]});
+
+ $for N in range(0, ELEMENTS_TILE, 4):
+ vp${ABC[N:N+4]} = ${VMULADDQ_F32}(vc3, vp${ABC[N:N+4]}, vt${ABC[N:N+4]});
+
+ $for N in range(0, ELEMENTS_TILE, 4):
+ vp${ABC[N:N+4]} = ${VMULADDQ_F32}(vc2, vp${ABC[N:N+4]}, vt${ABC[N:N+4]});
+
+ $for N in range(0, ELEMENTS_TILE, 4):
+ vp${ABC[N:N+4]} = ${VMULADDQ_F32}(vc1, vp${ABC[N:N+4]}, vt${ABC[N:N+4]});
+
+ // Reconstruct the final f value:
+ // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
+ // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
+ // = s + (t * s) * p
+ $for N in range(0, ELEMENTS_TILE, 4):
+ vt${ABC[N:N+4]} = vmulq_f32(vt${ABC[N:N+4]}, vs${ABC[N:N+4]});
+
+ $for N in range(0, ELEMENTS_TILE, 4):
+ float32x4_t vf${ABC[N:N+4]} = ${VMULADDQ_F32}(vs${ABC[N:N+4]}, vp${ABC[N:N+4]}, vt${ABC[N:N+4]});
+
+ // For inputs below denormal cutoff, replace output with +0.0f.
+ // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
+ $for N in range(0, ELEMENTS_TILE, 4):
+ vf${ABC[N:N+4]} = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf${ABC[N:N+4]}), vcltq_f32(vx${ABC[N:N+4]}, vdenorm_cutoff)));
+
+ // Store ${ELEMENTS_TILE} (${SIMD_TILE}x4) outputs at a time.
+ $for N in range(0, ELEMENTS_TILE, 4):
+ vst1q_f32(output, vf${ABC[N:N+4]}); output += 4;
+
+ // Accumulate computed exponents.
+ $for N in range(0, ELEMENTS_TILE, 4):
+ vacc${N % ACCUMULATORS} = vaddq_f32(vacc${N % ACCUMULATORS}, vf${ABC[N:N+4]});
+ }
+ $if ACCUMULATORS > 1:
+ // Add up all accumulators to vacc0
+ $ACC_SLICE = 1
+ $while ACC_SLICE < ACCUMULATORS:
+ $for A in range(0, ACCUMULATORS, ACC_SLICE * 2):
+ $if A + ACC_SLICE < ACCUMULATORS:
+ vacc${A} = vaddq_f32(vacc${A}, vacc${A + ACC_SLICE});
+ $ACC_SLICE *= 2
+
+ float32x4_t vacc = vacc0;
+ $else:
+ float32x4_t vacc = vmovq_n_f32(0.0f);
+ for (; elements >= 4 * sizeof(float); elements -= 4 * sizeof(float)) {
+ // Load 4 inputs at a time.
+ const float32x4_t vi = vld1q_f32(input); input += 4;
+
+ // Subtract maximum input x := i - i_max. This implies x <= 0.
+ const float32x4_t vx = vsubq_f32(vi, vi_max);
+
+ // Compute reduced argument n := round(x / log(2)).
+ // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the
+ // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
+ // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because
+ // inputs outside of [-87.336540, 0.0] underflow expf(x) anyway. We fixup the result for such inputs at the very end
+ // of the algorithm.
+ float32x4_t vn = ${VMULADDQ_F32}(vmagic_bias, vx, vlog2e);
+
+ // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
+ // -87.33642 <= x <= 0.0, and -126 <= n <= 0 accordingly.
+ const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23));
+
+ // Subtract the large number back to get final n := round(x / log(2)).
+ vn = vsubq_f32(vn, vmagic_bias);
+
+ // Compute reduced argument t := z - n * log(2).
+ // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
+ float32x4_t vt = ${VMULADDQ_F32}(vx, vn, vminus_ln2_hi);
+ vt = ${VMULADDQ_F32}(vt, vn, vminus_ln2_lo);
+
+ // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
+ float32x4_t vp = ${VMULADDQ_F32}(vc4, vc5, vt);
+ vp = ${VMULADDQ_F32}(vc3, vp, vt);
+ vp = ${VMULADDQ_F32}(vc2, vp, vt);
+ vp = ${VMULADDQ_F32}(vc1, vp, vt);
+
+ // Reconstruct the final f value:
+ // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
+ // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
+ // = s + (t * s) * p
+ vt = vmulq_f32(vt, vs);
+ float32x4_t vf = ${VMULADDQ_F32}(vs, vp, vt);
+
+ // For inputs below denormal cutoff, replace output with +0.0f.
+ // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
+ vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff)));
+
+ // Store 4 outputs at a time.
+ vst1q_f32(output, vf); output += 4;
+
+ // Accumulate computed exponents.
+ vacc = vaddq_f32(vacc, vf);
+ }
+#if XNN_ARCH_ARM64
+ float vacc_lo = vaddvq_f32(vacc);
+#else
+ float32x2_t vacc_lo = vadd_f32(vget_high_f32(vacc), vget_low_f32(vacc));
+#endif
+ if (elements != 0) {
+ assert(elements >= 1 * sizeof(float));
+ assert(elements <= 3 * sizeof(float));
+ // Load 4 inputs at a time.
+ const float32x4_t vi = vld1q_f32(input); input += 4;
+
+ // Subtract maximum input x := i - i_max. This implies x <= 0.
+ const float32x4_t vx = vsubq_f32(vi, vi_max);
+
+ // Compute reduced argument n := round(x / log(2)).
+ // We do it by adding a large number (magic bias), which cause rounding of result to an integer, then subtracing the
+ // large number back. The first addition is combined with multiplication by log2e into a single FMA instruction.
+ // The trick with adding large number is valid only within certain bounds (|x| <= 2**22), but thats ok, because
+ // inputs outside of [-87.336540, 0.0] underflow expf(x) anyway. We fixup the result for such inputs at the very end
+ // of the algorithm.
+ float32x4_t vn = ${VMULADDQ_F32}(vmagic_bias, vx, vlog2e);
+
+ // Create a floating-point number s (scale) such that s == 2**n for inputs which don't cause underflow, i.e.
+ // -87.33642 <= x <= 0.0, and -126 <= n <= 0 accordingly.
+ const float32x4_t vs = vreinterpretq_f32_s32(vshlq_n_s32(vreinterpretq_s32_f32(vn), 23));
+
+ // Subtract the large number back to get final n := round(x / log(2)).
+ vn = vsubq_f32(vn, vmagic_bias);
+
+ // Compute reduced argument t := z - n * log(2).
+ // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
+ float32x4_t vt = ${VMULADDQ_F32}(vx, vn, vminus_ln2_hi);
+ vt = ${VMULADDQ_F32}(vt, vn, vminus_ln2_lo);
+
+ // Compute degree-5 polynomial approxiatmion for exp(t) on [-log(2)/2, log(2)/2].
+ float32x4_t vp = ${VMULADDQ_F32}(vc4, vc5, vt);
+ vp = ${VMULADDQ_F32}(vc3, vp, vt);
+ vp = ${VMULADDQ_F32}(vc2, vp, vt);
+ vp = ${VMULADDQ_F32}(vc1, vp, vt);
+
+ // Reconstruct the final f value:
+ // f = s * (1 + t * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5)))))
+ // = s + (t * s) * (c1 + t * (c2 + t * (c3 + t * (c4 + t * c5))))
+ // = s + (t * s) * p
+ vt = vmulq_f32(vt, vs);
+ float32x4_t vf = ${VMULADDQ_F32}(vs, vp, vt);
+
+ // For inputs below denormal cutoff, replace output with +0.0f.
+ // Note that for NaN inputs, comparison result is false, and outputs are left unchanged.
+ vf = vreinterpretq_f32_u32(vbicq_u32(vreinterpretq_u32_f32(vf), vcltq_f32(vx, vdenorm_cutoff)));
+
+ float32x2_t vf_lo = vget_low_f32(vf);
+ if (elements & (2 * sizeof(float))) {
+ // Store 2 outputs at a time.
+ vst1_f32(output, vf_lo); output += 2;
+
+ // Accumulate 2 computed exponents.
+ #if XNN_ARCH_ARM64
+ vacc_lo += vaddv_f32(vf_lo);
+ #else
+ vacc_lo = vadd_f32(vacc_lo, vf_lo);
+ #endif
+
+ vf_lo = vget_high_f32(vf);
+ }
+ if (elements & (1 * sizeof(float))) {
+ // Store 1 output at a time.
+ vst1_lane_f32(output, vf_lo, 0);
+
+ // Accumulate 1 computed exponent.
+ #if XNN_ARCH_ARM64
+ vacc_lo += vget_lane_f32(vf_lo, 0);
+ #else
+ vacc_lo = vadd_f32(vacc_lo, vreinterpret_f32_u64(vshl_n_u64(vreinterpret_u64_f32(vf_lo), 32)));
+ #endif
+ }
+ }
+ // Reduce 4 elements in the SIMD register
+#if XNN_ARCH_ARM64
+ *sum = vacc_lo;
+#else
+ vst1_lane_f32(sum, vpadd_f32(vacc_lo, vacc_lo), 0);
+#endif
+}