/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-│
│ vi: set noet ft=c ts=8 tw=8 fenc=utf-8                                   :vi │
╚──────────────────────────────────────────────────────────────────────────────╝
│                                                                              │
│  Musl Libc                                                                   │
│  Copyright © 2005-2014 Rich Felker, et al.                                   │
│                                                                              │
│  Permission is hereby granted, free of charge, to any person obtaining       │
│  a copy of this software and associated documentation files (the             │
│  "Software"), to deal in the Software without restriction, including         │
│  without limitation the rights to use, copy, modify, merge, publish,         │
│  distribute, sublicense, and/or sell copies of the Software, and to          │
│  permit persons to whom the Software is furnished to do so, subject to       │
│  the following conditions:                                                   │
│                                                                              │
│  The above copyright notice and this permission notice shall be              │
│  included in all copies or substantial portions of the Software.             │
│                                                                              │
│  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,             │
│  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF          │
│  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.      │
│  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY        │
│  CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,        │
│  TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE           │
│  SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                      │
│                                                                              │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/intrin/likely.h"
#include "libc/math.h"
#include "libc/tinymath/exp2f_data.internal.h"
#include "libc/tinymath/internal.h"

asm(".ident\t\"\\n\\n\
Double-precision math functions (MIT License)\\n\
Copyright 2018 ARM Limited\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off

/*
 * Single-precision e^x function.
 *
 * Copyright (c) 2017-2018, Arm Limited.
 * SPDX-License-Identifier: MIT
 */

/*
EXP2F_TABLE_BITS = 5
EXP2F_POLY_ORDER = 3

ULP error: 0.502 (nearest rounding.)
Relative error: 1.69 * 2^-34 in [-ln2/64, ln2/64] (before rounding.)
Wrong count: 170635 (all nearest rounding wrong results with fma.)
Non-nearest ULP error: 1 (rounded ULP error)
*/

#define N (1 << EXP2F_TABLE_BITS)
#define InvLn2N __exp2f_data.invln2_scaled
#define T __exp2f_data.tab
#define C __exp2f_data.poly_scaled

static inline uint32_t top12(float x)
{
	return asuint(x) >> 20;
}

/**
 * Returns 𝑒^x.
 */
float expf(float x)
{
	uint32_t abstop;
	uint64_t ki, t;
	double_t kd, xd, z, r, r2, y, s;

	xd = (double_t)x;
	abstop = top12(x) & 0x7ff;
	if (UNLIKELY(abstop >= top12(88.0f))) {
		/* |x| >= 88 or x is nan.  */
		if (asuint(x) == asuint(-INFINITY))
			return 0.0f;
		if (abstop >= top12(INFINITY))
			return x + x;
		if (x > 0x1.62e42ep6f) /* x > log(0x1p128) ~= 88.72 */
			return __math_oflowf(0);
		if (x < -0x1.9fe368p6f) /* x < log(0x1p-150) ~= -103.97 */
			return __math_uflowf(0);
	}

	/* x*N/Ln2 = k + r with r in [-1/2, 1/2] and int k.  */
	z = InvLn2N * xd;

	/* Round and convert z to int, the result is in [-150*N, 128*N] and
	   ideally ties-to-even rule is used, otherwise the magnitude of r
	   can be bigger which gives larger approximation error.  */
#if TOINT_INTRINSICS
	kd = roundtoint(z);
	ki = converttoint(z);
#else
# define SHIFT __exp2f_data.shift
	kd = eval_as_double(z + SHIFT);
	ki = asuint64(kd);
	kd -= SHIFT;
#endif
	r = z - kd;

	/* exp(x) = 2^(k/N) * 2^(r/N) ~= s * (C0*r^3 + C1*r^2 + C2*r + 1) */
	t = T[ki % N];
	t += ki << (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);
}