src/libc-shim/include/math.h

@@ -82,6 +82,7 @@ double log2(double);
 float log2f(float);
 
 double pow(double, double);
+float powf(float, float);
 
 double scalbn(double, int);
 

src/libc-shim/src/__math_oflowf.c

@@ -0,0 +1,6 @@
+#include "libm.h"
+
+float __math_oflowf(uint32_t sign)
+{
+	return __math_xflowf(sign, 0x1p97f);
+}

src/libc-shim/src/__math_uflowf.c

@@ -0,0 +1,6 @@
+#include "libm.h"
+
+float __math_uflowf(uint32_t sign)
+{
+	return __math_xflowf(sign, 0x1p-95f);
+}

src/libc-shim/src/exp2f_data.c

@@ -0,0 +1,35 @@
+/*
+ * Shared data between expf, exp2f and powf.
+ *
+ * Copyright (c) 2017-2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include "exp2f_data.h"
+
+#define N (1 << EXP2F_TABLE_BITS)
+
+const struct exp2f_data __exp2f_data = {
+  /* tab[i] = uint(2^(i/N)) - (i << 52-BITS)
+     used for computing 2^(k/N) for an int |k| < 150 N as
+     double(tab[k%N] + (k << 52-BITS)) */
+  .tab = {
+0x3ff0000000000000, 0x3fefd9b0d3158574, 0x3fefb5586cf9890f, 0x3fef9301d0125b51,
+0x3fef72b83c7d517b, 0x3fef54873168b9aa, 0x3fef387a6e756238, 0x3fef1e9df51fdee1,
+0x3fef06fe0a31b715, 0x3feef1a7373aa9cb, 0x3feedea64c123422, 0x3feece086061892d,
+0x3feebfdad5362a27, 0x3feeb42b569d4f82, 0x3feeab07dd485429, 0x3feea47eb03a5585,
+0x3feea09e667f3bcd, 0x3fee9f75e8ec5f74, 0x3feea11473eb0187, 0x3feea589994cce13,
+0x3feeace5422aa0db, 0x3feeb737b0cdc5e5, 0x3feec49182a3f090, 0x3feed503b23e255d,
+0x3feee89f995ad3ad, 0x3feeff76f2fb5e47, 0x3fef199bdd85529c, 0x3fef3720dcef9069,
+0x3fef5818dcfba487, 0x3fef7c97337b9b5f, 0x3fefa4afa2a490da, 0x3fefd0765b6e4540,
+  },
+  .shift_scaled = 0x1.8p+52 / N,
+  .poly = {
+  0x1.c6af84b912394p-5, 0x1.ebfce50fac4f3p-3, 0x1.62e42ff0c52d6p-1,
+  },
+  .shift = 0x1.8p+52,
+  .invln2_scaled = 0x1.71547652b82fep+0 * N,
+  .poly_scaled = {
+  0x1.c6af84b912394p-5/N/N/N, 0x1.ebfce50fac4f3p-3/N/N, 0x1.62e42ff0c52d6p-1/N,
+  },
+};

src/libc-shim/src/exp2f_data.h

@@ -0,0 +1,23 @@
+/*
+ * Copyright (c) 2017-2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+#ifndef _EXP2F_DATA_H
+#define _EXP2F_DATA_H
+
+#include <features.h>
+#include <stdint.h>
+
+/* Shared between expf, exp2f and powf.  */
+#define EXP2F_TABLE_BITS 5
+#define EXP2F_POLY_ORDER 3
+extern const struct exp2f_data {
+	uint64_t tab[1 << EXP2F_TABLE_BITS];
+	double shift_scaled;
+	double poly[EXP2F_POLY_ORDER];
+	double shift;
+	double invln2_scaled;
+	double poly_scaled[EXP2F_POLY_ORDER];
+} __exp2f_data;
+
+#endif

src/libc-shim/src/libm.h

@@ -1,3 +1,6 @@
+#ifndef _LIBM_H
+#define _LIBM_H
+
 #include <float.h>
 #include <math.h>
 #include <stdint.h>
@@ -144,8 +147,13 @@ int __rem_pio2f(float, double*);
 float __sindf(double);
 float __cosdf(double);
 
+float __math_xflowf(uint32_t, float);
+float __math_uflowf(uint32_t);
+float __math_oflowf(uint32_t);
 float __math_invalidf(float);
 double __math_xflow(uint32_t, double);
 double __math_uflow(uint32_t);
 double __math_oflow(uint32_t);
 double __math_invalid(double);
+
+#endif // _LIBM_H

src/libc-shim/src/powf.c

@@ -0,0 +1,187 @@
+/*
+ * Copyright (c) 2017-2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include <math.h>
+#include <stdint.h>
+#include "libm.h"
+#include "exp2f_data.h"
+#include "powf_data.h"
+
+/*
+POWF_LOG2_POLY_ORDER = 5
+EXP2F_TABLE_BITS = 5
+
+ULP error: 0.82 (~ 0.5 + relerr*2^24)
+relerr: 1.27 * 2^-26 (Relative error ~= 128*Ln2*relerr_log2 + relerr_exp2)
+relerr_log2: 1.83 * 2^-33 (Relative error of logx.)
+relerr_exp2: 1.69 * 2^-34 (Relative error of exp2(ylogx).)
+*/
+
+#define N (1 << POWF_LOG2_TABLE_BITS)
+#define T __powf_log2_data.tab
+#define A __powf_log2_data.poly
+#define OFF 0x3f330000
+
+/* Subnormal input is normalized so ix has negative biased exponent.
+   Output is multiplied by N (POWF_SCALE) if TOINT_INTRINICS is set.  */
+static inline double_t log2_inline(uint32_t ix)
+{
+	double_t z, r, r2, r4, p, q, y, y0, invc, logc;
+	uint32_t iz, top, 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 >> (23 - POWF_LOG2_TABLE_BITS)) % N;
+	top = tmp & 0xff800000;
+	iz = ix - top;
+	k = (int32_t)top >> (23 - POWF_SCALE_BITS); /* arithmetic shift */
+	invc = T[i].invc;
+	logc = T[i].logc;
+	z = (double_t)asfloat(iz);
+
+	/* log2(x) = log1p(z/c-1)/ln2 + log2(c) + k */
+	r = z * invc - 1;
+	y0 = logc + (double_t)k;
+
+	/* Pipelined polynomial evaluation to approximate log1p(r)/ln2.  */
+	r2 = r * r;
+	y = A[0] * r + A[1];
+	p = A[2] * r + A[3];
+	r4 = r2 * r2;
+	q = A[4] * r + y0;
+	q = p * r2 + q;
+	y = y * r4 + q;
+	return y;
+}
+
+#undef N
+#undef T
+#define N (1 << EXP2F_TABLE_BITS)
+#define T __exp2f_data.tab
+#define SIGN_BIAS (1 << (EXP2F_TABLE_BITS + 11))
+
+/* The output of log2 and thus the input of exp2 is either scaled by N
+   (in case of fast toint intrinsics) or not.  The unscaled xd must be
+   in [-1021,1023], sign_bias sets the sign of the result.  */
+static inline float exp2_inline(double_t xd, uint32_t sign_bias)
+{
+	uint64_t ki, ski, t;
+	double_t kd, z, r, r2, y, s;
+
+#if TOINT_INTRINSICS
+#define C __exp2f_data.poly_scaled
+	/* N*x = k + r with r in [-1/2, 1/2] */
+	kd = roundtoint(xd); /* k */
+	ki = converttoint(xd);
+#else
+#define C __exp2f_data.poly
+#define SHIFT __exp2f_data.shift_scaled
+	/* x = k/N + r with r in [-1/(2N), 1/(2N)] */
+	kd = eval_as_double(xd + SHIFT);
+	ki = asuint64(kd);
+	kd -= SHIFT; /* k/N */
+#endif
+	r = xd - kd;
+
+	/* exp2(x) = 2^(k/N) * 2^r ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
+	t = T[ki % N];
+	ski = ki + sign_bias;
+	t += ski << (52 - EXP2F_TABLE_BITS);
+	s = asdouble(t);
+	z = C[0] * r + C[1];
+	r2 = r * r;
+	y = C[2] * r + 1;
+	y = z * r2 + y;
+	y = y * s;
+	return eval_as_float(y);
+}
+
+/* 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(uint32_t iy)
+{
+	int e = iy >> 23 & 0xff;
+	if (e < 0x7f)
+		return 0;
+	if (e > 0x7f + 23)
+		return 2;
+	if (iy & ((1 << (0x7f + 23 - e)) - 1))
+		return 0;
+	if (iy & (1 << (0x7f + 23 - e)))
+		return 1;
+	return 2;
+}
+
+static inline int zeroinfnan(uint32_t ix)
+{
+	return 2 * ix - 1 >= 2u * 0x7f800000 - 1;
+}
+
+float powf(float x, float y)
+{
+	uint32_t sign_bias = 0;
+	uint32_t ix, iy;
+
+	ix = asuint(x);
+	iy = asuint(y);
+	if (predict_false(ix - 0x00800000 >= 0x7f800000 - 0x00800000 ||
+			  zeroinfnan(iy))) {
+		/* Either (x < 0x1p-126 or inf or nan) or (y is 0 or inf or nan).  */
+		if (predict_false(zeroinfnan(iy))) {
+			if (2 * iy == 0)
+				return issignalingf_inline(x) ? x + y : 1.0f;
+			if (ix == 0x3f800000)
+				return issignalingf_inline(y) ? x + y : 1.0f;
+			if (2 * ix > 2u * 0x7f800000 ||
+			    2 * iy > 2u * 0x7f800000)
+				return x + y;
+			if (2 * ix == 2 * 0x3f800000)
+				return 1.0f;
+			if ((2 * ix < 2 * 0x3f800000) == !(iy & 0x80000000))
+				return 0.0f; /* |x|<1 && y==inf or |x|>1 && y==-inf.  */
+			return y * y;
+		}
+		if (predict_false(zeroinfnan(ix))) {
+			float_t x2 = x * x;
+			if (ix & 0x80000000 && 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.  */
+			// NOTE(orca): no fp barriers
+			//return iy & 0x80000000 ? fp_barrierf(1 / x2) : x2;
+			return iy & 0x80000000 ? (1 / x2) : x2;
+		}
+		/* x and y are non-zero finite.  */
+		if (ix & 0x80000000) {
+			/* Finite x < 0.  */
+			int yint = checkint(iy);
+			if (yint == 0)
+				return __math_invalidf(x);
+			if (yint == 1)
+				sign_bias = SIGN_BIAS;
+			ix &= 0x7fffffff;
+		}
+		if (ix < 0x00800000) {
+			/* Normalize subnormal x so exponent becomes negative.  */
+			ix = asuint(x * 0x1p23f);
+			ix &= 0x7fffffff;
+			ix -= 23 << 23;
+		}
+	}
+	double_t logx = log2_inline(ix);
+	double_t ylogx = y * logx; /* cannot overflow, y is single prec.  */
+	if (predict_false((asuint64(ylogx) >> 47 & 0xffff) >=
+			  asuint64(126.0 * POWF_SCALE) >> 47)) {
+		/* |y*log(x)| >= 126.  */
+		if (ylogx > 0x1.fffffffd1d571p+6 * POWF_SCALE)
+			return __math_oflowf(sign_bias);
+		if (ylogx <= -150.0 * POWF_SCALE)
+			return __math_uflowf(sign_bias);
+	}
+	return exp2_inline(ylogx, sign_bias);
+}

src/libc-shim/src/powf_data.c

@@ -0,0 +1,34 @@
+/*
+ * Data definition for powf.
+ *
+ * Copyright (c) 2017-2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+
+#include "powf_data.h"
+
+const struct powf_log2_data __powf_log2_data = {
+  .tab = {
+  { 0x1.661ec79f8f3bep+0, -0x1.efec65b963019p-2 * POWF_SCALE },
+  { 0x1.571ed4aaf883dp+0, -0x1.b0b6832d4fca4p-2 * POWF_SCALE },
+  { 0x1.49539f0f010bp+0, -0x1.7418b0a1fb77bp-2 * POWF_SCALE },
+  { 0x1.3c995b0b80385p+0, -0x1.39de91a6dcf7bp-2 * POWF_SCALE },
+  { 0x1.30d190c8864a5p+0, -0x1.01d9bf3f2b631p-2 * POWF_SCALE },
+  { 0x1.25e227b0b8eap+0, -0x1.97c1d1b3b7afp-3 * POWF_SCALE },
+  { 0x1.1bb4a4a1a343fp+0, -0x1.2f9e393af3c9fp-3 * POWF_SCALE },
+  { 0x1.12358f08ae5bap+0, -0x1.960cbbf788d5cp-4 * POWF_SCALE },
+  { 0x1.0953f419900a7p+0, -0x1.a6f9db6475fcep-5 * POWF_SCALE },
+  { 0x1p+0, 0x0p+0 * POWF_SCALE },
+  { 0x1.e608cfd9a47acp-1, 0x1.338ca9f24f53dp-4 * POWF_SCALE },
+  { 0x1.ca4b31f026aap-1, 0x1.476a9543891bap-3 * POWF_SCALE },
+  { 0x1.b2036576afce6p-1, 0x1.e840b4ac4e4d2p-3 * POWF_SCALE },
+  { 0x1.9c2d163a1aa2dp-1, 0x1.40645f0c6651cp-2 * POWF_SCALE },
+  { 0x1.886e6037841edp-1, 0x1.88e9c2c1b9ff8p-2 * POWF_SCALE },
+  { 0x1.767dcf5534862p-1, 0x1.ce0a44eb17bccp-2 * POWF_SCALE },
+  },
+  .poly = {
+  0x1.27616c9496e0bp-2 * POWF_SCALE, -0x1.71969a075c67ap-2 * POWF_SCALE,
+  0x1.ec70a6ca7baddp-2 * POWF_SCALE, -0x1.7154748bef6c8p-1 * POWF_SCALE,
+  0x1.71547652ab82bp0 * POWF_SCALE,
+  }
+};

src/libc-shim/src/powf_data.h

@@ -0,0 +1,26 @@
+/*
+ * Copyright (c) 2017-2018, Arm Limited.
+ * SPDX-License-Identifier: MIT
+ */
+#ifndef _POWF_DATA_H
+#define _POWF_DATA_H
+
+#include "libm.h"
+#include "exp2f_data.h"
+
+#define POWF_LOG2_TABLE_BITS 4
+#define POWF_LOG2_POLY_ORDER 5
+#if TOINT_INTRINSICS
+#define POWF_SCALE_BITS EXP2F_TABLE_BITS
+#else
+#define POWF_SCALE_BITS 0
+#endif
+#define POWF_SCALE ((double)(1 << POWF_SCALE_BITS))
+extern const struct powf_log2_data {
+	struct {
+		double invc, logc;
+	} tab[1 << POWF_LOG2_TABLE_BITS];
+	double poly[POWF_LOG2_POLY_ORDER];
+} __powf_log2_data;
+
+#endif