Scalar EXPM1MINUS evaluation stubs
PiperOrigin-RevId: 343906379
diff --git a/src/math/expm1minus-scalar-rr2-lut16-p4.c b/src/math/expm1minus-scalar-rr2-lut16-p4.c
new file mode 100644
index 0000000..dcc6c81
--- /dev/null
+++ b/src/math/expm1minus-scalar-rr2-lut16-p4.c
@@ -0,0 +1,101 @@
+// 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.
+
+#include <assert.h>
+#include <stddef.h>
+
+#include <xnnpack/common.h>
+#include <xnnpack/math-stubs.h>
+
+#include <fp16/bitcasts.h>
+
+
+// Table of exp2(k / 16) values decremented (as integer) by (k << 19), k = 0..15
+extern XNN_INTERNAL const uint32_t xnn_table_exp2minus_k_over_16[16];
+
+void xnn_math_f32_expm1minus__scalar_rr2_lut16_p4(
+ size_t n,
+ const float* input,
+ float* output)
+{
+ assert(n % (4 * sizeof(float)) == 0);
+
+ // Large number such that ulp(magic bias) == exp2(-4)
+ const float vmagic_bias = 0x1.800000p19f;
+ const float vlog2e = 0x1.715476p+0f;
+ // Mask for the lowest 4 bits
+ const uint32_t vindex_mask = UINT32_C(0xF);
+ // The largest x for which expm1f(x) is saturated at -1.0f.
+ const float vsat_cutoff = -0x1.154246p+4f;
+ // Last 11 bits are zeroes
+ const float vminus_ln2_hi = -0x1.62E000p-1f;
+ const float vminus_ln2_lo = -0x1.0BFBE8p-15f;
+ // Coefficient of polynomial approximation
+ // exp(t) - 1 ~ t * (1 + t * (c2 + t * (c3 + t * c4)))
+ // on [-log(2)/32, log(2)/32]
+ const float vc4 = 0x1.55563Ap-5f;
+ const float vc3 = 0x1.555708p-3f;
+ const float vc2 = 0x1.000000p-1f;
+ const float vone = 1.0f;
+
+ for (; n != 0; n -= sizeof(float)) {
+ float vx = *input++;
+
+ // Compute reduced argument n := round(x / log(2), 4).
+ // We do it by adding a large number (magic bias), which cause rounding of the result to 4 fractional bits, then
+ // subtracing the large number back. The trick with adding large number is valid only within certain bounds
+ // (|x / log(2)| <= 2**18, i.e. |x| <= 0x1.62E43p+17 = 181704.375), but that is acceptable, because inputs x are
+ // restricted to [-17.328680, 0].
+ // Note that addition-subtraction of the large number doesn't cause overflow for inputs in this range.
+ float vn = vx * vlog2e + vmagic_bias;
+
+ // Create a floating-point number s (scale) such that s := 2**n for valid inputs, i.e. -17.328680 <= x <= 0.0. As n
+ // has 4 fractional bits, we split s == 2**n = 2**int(n) * 2**frac(n). We create s in two steps:
+ // 1. Fetch 2**frac(n) from the table using the 4 low bits of n, as integer. Note that the fetched values are in
+ // the [1.0, 2.0) range, i.e. their floating-point exponent is 0.
+ // 2. Adjust fecthed value by addition of int(n) to its floating-point exponent. The result is always a normalized
+ // number, because for -17.328680 <= x <= 0.0 we have -25 <= int(n) <= 0, and thus the adjusted exponent is not
+ // lower than -25.
+ //
+ // Shift bits 4:12 into 23:31 (position of floating-point exponent).
+ const uint32_t ve = fp32_to_bits(vn) << 19;
+
+ // Use bits 0:4 bits of n, as integer, as an index for table lookup of l := 2**frac(n).
+ const uint32_t vidx = fp32_to_bits(vn) & vindex_mask;
+ // Adjust exponent of the value l fetched from the table to get the final s value.
+ float vs = fp32_from_bits(xnn_table_exp2minus_k_over_16[vidx] + ve);
+
+ // Subtract the large number back to get final n := round(x / log(2), 4).
+ vn -= vmagic_bias;
+
+ // The function saturates at -1 for large negative inputs: expm1f(x) == -1.0f for x <= sat_cutoff ~= -17.328680.
+ // To guarantee this behaviour, we zero out s (scale) for x <= sat_cutoff.
+ if XNN_UNPREDICTABLE(vx <= vsat_cutoff) {
+ vs = 0.0f;
+ }
+
+ // Compute reduced argument t := x - n * log(2).
+ // Use Cody-Waite range reduction method (note two constants to represent log(2)) to improve accuracy.
+ float vt = vn * vminus_ln2_hi + vx;
+ vt = vn * vminus_ln2_lo + vt;
+
+ // Compute degree-4 polynomial approximation for exp(t) - 1 on [-log(2)/32, log(2)/32].
+ // P(t) = t * (1 + t * (c2 + t * (c3 + t * c4))) = t + t * (t * (c2 + t * (c3 + t * c4))) = t + t * p
+ float vp = vc4 * vt + vc3;
+ vp = vp * vt + vc2;
+ vp *= vt;
+
+ // Reconstruct the exp(x) - 1 value:
+ // exp(x) - 1 = s * (1 + t * (1 + t * (c2 + t * c3))) - 1
+ // = (s - 1) + s * (t + t * p)
+ // = ((t * s) + (t * s) * p) + (s - 1)
+ vt *= vs;
+ const float vsm1 = vs - vone;
+ vp = vp * vt + vt;
+ const float vf = vp + vsm1;
+
+ *output++ = vf;
+ }
+}