Adding upstream version 0.0~git20221206.8b7148f.upstream/0.0_git20221206.8b7148f

Signed-off-by: Daniel Baumann <daniel.baumann@progress-linux.org>

1 files changed, 343 insertions, 0 deletions

diff --git a/libc-top-half/musl/src/math/pow.c b/libc-top-half/musl/src/math/pow.c
new file mode 100644
index 0000000..694c2ef
--- /dev/null
+++ b/libc-top-half/musl/src/math/pow.c
@@ -0,0 +1,343 @@
+/*
+ * Double-precision x^y function.
+ *
+ * Copyright (c) 2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include <math.h>
+#include <stdint.h>
+#include "libm.h"
+#include "exp_data.h"
+#include "pow_data.h"
+
+/*
+Worst-case error: 0.54 ULP (~= ulperr_exp + 1024*Ln2*relerr_log*2^53)
+relerr_log: 1.3 * 2^-68 (Relative error of log, 1.5 * 2^-68 without fma)
+ulperr_exp: 0.509 ULP (ULP error of exp, 0.511 ULP without fma)
+*/
+
+#define T __pow_log_data.tab
+#define A __pow_log_data.poly
+#define Ln2hi __pow_log_data.ln2hi
+#define Ln2lo __pow_log_data.ln2lo
+#define N (1 << POW_LOG_TABLE_BITS)
+#define OFF 0x3fe6955500000000
+
+/* Top 12 bits of a double (sign and exponent bits).  */
+static inline uint32_t top12(double x)
+{
+	return asuint64(x) >> 52;
+}
+
+/* Compute y+TAIL = log(x) where the rounded result is y and TAIL has about
+   additional 15 bits precision.  IX is the bit representation of x, but
+   normalized in the subnormal range using the sign bit for the exponent.  */
+static inline double_t log_inline(uint64_t ix, double_t *tail)
+{
+	/* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+	double_t z, r, y, invc, logc, logctail, kd, hi, t1, t2, lo, lo1, lo2, p;
+	uint64_t iz, tmp;
+	int k, i;
+
+	/* x = 2^k z; where z is in range [OFF,2*OFF) and exact.
+	   The range is split into N subintervals.
+	   The ith subinterval contains z and c is near its center.  */
+	tmp = ix - OFF;
+	i = (tmp >> (52 - POW_LOG_TABLE_BITS)) % N;
+	k = (int64_t)tmp >> 52; /* arithmetic shift */
+	iz = ix - (tmp & 0xfffULL << 52);
+	z = asdouble(iz);
+	kd = (double_t)k;
+
+	/* log(x) = k*Ln2 + log(c) + log1p(z/c-1).  */
+	invc = T[i].invc;
+	logc = T[i].logc;
+	logctail = T[i].logctail;
+
+	/* Note: 1/c is j/N or j/N/2 where j is an integer in [N,2N) and
+     |z/c - 1| < 1/N, so r = z/c - 1 is exactly representible.  */
+#if __FP_FAST_FMA
+	r = __builtin_fma(z, invc, -1.0);
+#else
+	/* Split z such that rhi, rlo and rhi*rhi are exact and |rlo| <= |r|.  */
+	double_t zhi = asdouble((iz + (1ULL << 31)) & (-1ULL << 32));
+	double_t zlo = z - zhi;
+	double_t rhi = zhi * invc - 1.0;
+	double_t rlo = zlo * invc;
+	r = rhi + rlo;
+#endif
+
+	/* k*Ln2 + log(c) + r.  */
+	t1 = kd * Ln2hi + logc;
+	t2 = t1 + r;
+	lo1 = kd * Ln2lo + logctail;
+	lo2 = t1 - t2 + r;
+
+	/* Evaluation is optimized assuming superscalar pipelined execution.  */
+	double_t ar, ar2, ar3, lo3, lo4;
+	ar = A[0] * r; /* A[0] = -0.5.  */
+	ar2 = r * ar;
+	ar3 = r * ar2;
+	/* k*Ln2 + log(c) + r + A[0]*r*r.  */
+#if __FP_FAST_FMA
+	hi = t2 + ar2;
+	lo3 = __builtin_fma(ar, r, -ar2);
+	lo4 = t2 - hi + ar2;
+#else
+	double_t arhi = A[0] * rhi;
+	double_t arhi2 = rhi * arhi;
+	hi = t2 + arhi2;
+	lo3 = rlo * (ar + arhi);
+	lo4 = t2 - hi + arhi2;
+#endif
+	/* p = log1p(r) - r - A[0]*r*r.  */
+	p = (ar3 * (A[1] + r * A[2] +
+		    ar2 * (A[3] + r * A[4] + ar2 * (A[5] + r * A[6]))));
+	lo = lo1 + lo2 + lo3 + lo4 + p;
+	y = hi + lo;
+	*tail = hi - y + lo;
+	return y;
+}
+
+#undef N
+#undef T
+#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]
+#define C6 __exp_data.poly[9 - 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;
+	/* Note: sbits is signed scale.  */
+	scale = asdouble(sbits);
+	y = scale + scale * tmp;
+	if (fabs(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, one = 1.0;
+		if (y < 0.0)
+			one = -1.0;
+		lo = scale - y + scale * tmp;
+		hi = one + y;
+		lo = one - hi + y + lo;
+		y = eval_as_double(hi + lo) - one;
+		/* Fix the sign of 0.  */
+		if (y == 0.0)
+			y = asdouble(sbits & 0x8000000000000000);
+		/* 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);
+}
+
+#define SIGN_BIAS (0x800 << EXP_TABLE_BITS)
+
+/* Computes sign*exp(x+xtail) where |xtail| < 2^-8/N and |xtail| <= |x|.
+   The sign_bias argument is SIGN_BIAS or 0 and sets the sign to -1 or 1.  */
+static inline double exp_inline(double_t x, double_t xtail, uint32_t sign_bias)
+{
+	uint32_t abstop;
+	uint64_t ki, idx, top, sbits;
+	/* double_t for better performance on targets with FLT_EVAL_METHOD==2.  */
+	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.  */
+			double_t one = WANT_ROUNDING ? 1.0 + x : 1.0;
+			return sign_bias ? -one : one;
+		}
+		if (abstop >= top12(1024.0)) {
+			/* Note: inf and nan are already handled.  */
+			if (asuint64(x) >> 63)
+				return __math_uflow(sign_bias);
+			else
+				return __math_oflow(sign_bias);
+		}
+		/* 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;
+	/* The code assumes 2^-200 < |xtail| < 2^-8/N.  */
+	r += xtail;
+	/* 2^(k/N) ~= scale * (1 + tail).  */
+	idx = 2 * (ki % N);
+	top = (ki + sign_bias) << (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);
+}
+
+/* Returns 0 if not int, 1 if odd int, 2 if even int.  The argument is
+   the bit representation of a non-zero finite floating-point value.  */
+static inline int checkint(uint64_t iy)
+{
+	int e = iy >> 52 & 0x7ff;
+	if (e < 0x3ff)
+		return 0;
+	if (e > 0x3ff + 52)
+		return 2;
+	if (iy & ((1ULL << (0x3ff + 52 - e)) - 1))
+		return 0;
+	if (iy & (1ULL << (0x3ff + 52 - e)))
+		return 1;
+	return 2;
+}
+
+/* Returns 1 if input is the bit representation of 0, infinity or nan.  */
+static inline int zeroinfnan(uint64_t i)
+{
+	return 2 * i - 1 >= 2 * asuint64(INFINITY) - 1;
+}
+
+double pow(double x, double y)
+{
+	uint32_t sign_bias = 0;
+	uint64_t ix, iy;
+	uint32_t topx, topy;
+
+	ix = asuint64(x);
+	iy = asuint64(y);
+	topx = top12(x);
+	topy = top12(y);
+	if (predict_false(topx - 0x001 >= 0x7ff - 0x001 ||
+			  (topy & 0x7ff) - 0x3be >= 0x43e - 0x3be)) {
+		/* Note: if |y| > 1075 * ln2 * 2^53 ~= 0x1.749p62 then pow(x,y) = inf/0
+		   and if |y| < 2^-54 / 1075 ~= 0x1.e7b6p-65 then pow(x,y) = +-1.  */
+		/* Special cases: (x < 0x1p-126 or inf or nan) or
+		   (|y| < 0x1p-65 or |y| >= 0x1p63 or nan).  */
+		if (predict_false(zeroinfnan(iy))) {
+			if (2 * iy == 0)
+				return issignaling_inline(x) ? x + y : 1.0;
+			if (ix == asuint64(1.0))
+				return issignaling_inline(y) ? x + y : 1.0;
+			if (2 * ix > 2 * asuint64(INFINITY) ||
+			    2 * iy > 2 * asuint64(INFINITY))
+				return x + y;
+			if (2 * ix == 2 * asuint64(1.0))
+				return 1.0;
+			if ((2 * ix < 2 * asuint64(1.0)) == !(iy >> 63))
+				return 0.0; /* |x|<1 && y==inf or |x|>1 && y==-inf.  */
+			return y * y;
+		}
+		if (predict_false(zeroinfnan(ix))) {
+			double_t x2 = x * x;
+			if (ix >> 63 && checkint(iy) == 1)
+				x2 = -x2;
+			/* Without the barrier some versions of clang hoist the 1/x2 and
+			   thus division by zero exception can be signaled spuriously.  */
+			return iy >> 63 ? fp_barrier(1 / x2) : x2;
+		}
+		/* Here x and y are non-zero finite.  */
+		if (ix >> 63) {
+			/* Finite x < 0.  */
+			int yint = checkint(iy);
+			if (yint == 0)
+				return __math_invalid(x);
+			if (yint == 1)
+				sign_bias = SIGN_BIAS;
+			ix &= 0x7fffffffffffffff;
+			topx &= 0x7ff;
+		}
+		if ((topy & 0x7ff) - 0x3be >= 0x43e - 0x3be) {
+			/* Note: sign_bias == 0 here because y is not odd.  */
+			if (ix == asuint64(1.0))
+				return 1.0;
+			if ((topy & 0x7ff) < 0x3be) {
+				/* |y| < 2^-65, x^y ~= 1 + y*log(x).  */
+				if (WANT_ROUNDING)
+					return ix > asuint64(1.0) ? 1.0 + y :
+								    1.0 - y;
+				else
+					return 1.0;
+			}
+			return (ix > asuint64(1.0)) == (topy < 0x800) ?
+				       __math_oflow(0) :
+				       __math_uflow(0);
+		}
+		if (topx == 0) {
+			/* Normalize subnormal x so exponent becomes negative.  */
+			ix = asuint64(x * 0x1p52);
+			ix &= 0x7fffffffffffffff;
+			ix -= 52ULL << 52;
+		}
+	}
+
+	double_t lo;
+	double_t hi = log_inline(ix, &lo);
+	double_t ehi, elo;
+#if __FP_FAST_FMA
+	ehi = y * hi;
+	elo = y * lo + __builtin_fma(y, hi, -ehi);
+#else
+	double_t yhi = asdouble(iy & -1ULL << 27);
+	double_t ylo = y - yhi;
+	double_t lhi = asdouble(asuint64(hi) & -1ULL << 27);
+	double_t llo = hi - lhi + lo;
+	ehi = yhi * lhi;
+	elo = ylo * lhi + y * llo; /* |elo| < |ehi| * 2^-25.  */
+#endif
+	return exp_inline(ehi, elo, sign_bias);
+}