Initial import

libc/math/exp.c

@@ -0,0 +1,133 @@
+/*
+ * Double-precision e^x function.
+ *
+ * Copyright (c) 2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include "libc/math/math.h"
+#include "libc/math/libm.h"
+#include "libc/math/exp_data.h"
+
+#define N (1 << EXP_TABLE_BITS)
+#define InvLn2N __exp_data.invln2N
+#define NegLn2hiN __exp_data.negln2hiN
+#define NegLn2loN __exp_data.negln2loN
+#define Shift __exp_data.shift
+#define T __exp_data.tab
+#define C2 __exp_data.poly[5 - EXP_POLY_ORDER]
+#define C3 __exp_data.poly[6 - EXP_POLY_ORDER]
+#define C4 __exp_data.poly[7 - EXP_POLY_ORDER]
+#define C5 __exp_data.poly[8 - EXP_POLY_ORDER]
+
+/* Handle cases that may overflow or underflow when computing the result that
+   is scale*(1+TMP) without intermediate rounding.  The bit representation of
+   scale is in SBITS, however it has a computed exponent that may have
+   overflown into the sign bit so that needs to be adjusted before using it as
+   a double.  (int32_t)KI is the k used in the argument reduction and exponent
+   adjustment of scale, positive k here means the result may overflow and
+   negative k means the result may underflow.  */
+static inline double specialcase(double_t tmp, uint64_t sbits, uint64_t ki)
+{
+	double_t scale, y;
+
+	if ((ki & 0x80000000) == 0) {
+		/* k > 0, the exponent of scale might have overflowed by <= 460.  */
+		sbits -= 1009ull << 52;
+		scale = asdouble(sbits);
+		y = 0x1p1009 * (scale + scale * tmp);
+		return eval_as_double(y);
+	}
+	/* k < 0, need special care in the subnormal range.  */
+	sbits += 1022ull << 52;
+	scale = asdouble(sbits);
+	y = scale + scale * tmp;
+	if (y < 1.0) {
+		/* Round y to the right precision before scaling it into the subnormal
+		 range to avoid double rounding that can cause 0.5+E/2 ulp error where
+		 E is the worst-case ulp error outside the subnormal range.  So this
+		 is only useful if the goal is better than 1 ulp worst-case error.  */
+		double_t hi, lo;
+		lo = scale - y + scale * tmp;
+		hi = 1.0 + y;
+		lo = 1.0 - hi + y + lo;
+		y = eval_as_double(hi + lo) - 1.0;
+		/* Avoid -0.0 with downward rounding.  */
+		if (WANT_ROUNDING && y == 0.0)
+			y = 0.0;
+		/* The underflow exception needs to be signaled explicitly.  */
+		fp_force_eval(fp_barrier(0x1p-1022) * 0x1p-1022);
+	}
+	y = 0x1p-1022 * y;
+	return eval_as_double(y);
+}
+
+/* Top 12 bits of a double (sign and exponent bits).  */
+static inline uint32_t top12(double x)
+{
+	return asuint64(x) >> 52;
+}
+
+double exp(double x)
+{
+	uint32_t abstop;
+	uint64_t ki, idx, top, sbits;
+	double_t kd, z, r, r2, scale, tail, tmp;
+
+	abstop = top12(x) & 0x7ff;
+	if (predict_false(abstop - top12(0x1p-54) >= top12(512.0) - top12(0x1p-54))) {
+		if (abstop - top12(0x1p-54) >= 0x80000000)
+			/* Avoid spurious underflow for tiny x.  */
+			/* Note: 0 is common input.  */
+			return WANT_ROUNDING ? 1.0 + x : 1.0;
+		if (abstop >= top12(1024.0)) {
+			if (asuint64(x) == asuint64(-INFINITY))
+				return 0.0;
+			if (abstop >= top12(INFINITY))
+				return 1.0 + x;
+			if (asuint64(x) >> 63)
+				return __math_uflow(0);
+			else
+				return __math_oflow(0);
+		}
+		/* Large x is special cased below.  */
+		abstop = 0;
+	}
+
+	/* exp(x) = 2^(k/N) * exp(r), with exp(r) in [2^(-1/2N),2^(1/2N)].  */
+	/* x = ln2/N*k + r, with int k and r in [-ln2/2N, ln2/2N].  */
+	z = InvLn2N * x;
+#if TOINT_INTRINSICS
+	kd = roundtoint(z);
+	ki = converttoint(z);
+#elif EXP_USE_TOINT_NARROW
+	/* z - kd is in [-0.5-2^-16, 0.5] in all rounding modes.  */
+	kd = eval_as_double(z + Shift);
+	ki = asuint64(kd) >> 16;
+	kd = (double_t)(int32_t)ki;
+#else
+	/* z - kd is in [-1, 1] in non-nearest rounding modes.  */
+	kd = eval_as_double(z + Shift);
+	ki = asuint64(kd);
+	kd -= Shift;
+#endif
+	r = x + kd * NegLn2hiN + kd * NegLn2loN;
+	/* 2^(k/N) ~= scale * (1 + tail).  */
+	idx = 2 * (ki % N);
+	top = ki << (52 - EXP_TABLE_BITS);
+	tail = asdouble(T[idx]);
+	/* This is only a valid scale when -1023*N < k < 1024*N.  */
+	sbits = T[idx + 1] + top;
+	/* exp(x) = 2^(k/N) * exp(r) ~= scale + scale * (tail + exp(r) - 1).  */
+	/* Evaluation is optimized assuming superscalar pipelined execution.  */
+	r2 = r * r;
+	/* Without fma the worst case error is 0.25/N ulp larger.  */
+	/* Worst case error is less than 0.5+1.11/N+(abs poly error * 2^53) ulp.  */
+	tmp = tail + r + r2 * (C2 + r * C3) + r2 * r2 * (C4 + r * C5);
+	if (predict_false(abstop == 0))
+		return specialcase(tmp, sbits, ki);
+	scale = asdouble(sbits);
+	/* Note: tmp == 0 or |tmp| > 2^-200 and scale > 2^-739, so there
+	   is no spurious underflow here even without fma.  */
+	return eval_as_double(scale + scale * tmp);
+}