828 lines
22 KiB
C
828 lines
22 KiB
C
/*
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* This file is part of the MicroPython project, http://micropython.org/
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*
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* The MIT License (MIT)
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*
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* Copyright (c) 2013, 2014 Damien P. George
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*
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* Permission is hereby granted, free of charge, to any person obtaining a copy
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* of this software and associated documentation files (the "Software"), to deal
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* in the Software without restriction, including without limitation the rights
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* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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* copies of the Software, and to permit persons to whom the Software is
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* furnished to do so, subject to the following conditions:
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*
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* The above copyright notice and this permission notice shall be included in
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* all copies or substantial portions of the Software.
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*
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* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
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* THE SOFTWARE.
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*/
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#include "libm.h"
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typedef float float_t;
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typedef union {
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float f;
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struct {
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uint64_t m : 23;
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uint64_t e : 8;
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uint64_t s : 1;
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};
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} float_s_t;
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#ifndef NDEBUG
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float copysignf(float x, float y) {
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float_s_t fx={.f = x};
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float_s_t fy={.f = y};
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// copy sign bit;
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fx.s = fy.s;
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return fx.f;
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}
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#endif
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// some compilers define log2f in terms of logf
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#ifdef log2f
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#undef log2f
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#endif
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// some compilers have _M_LN2 defined in math.h, some don't
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#ifndef _M_LN2
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#define _M_LN2 (0.69314718055994530942)
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#endif
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float log2f(float x) { return logf(x) / (float)_M_LN2; }
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static const float _M_LN10 = 2.30258509299404; // 0x40135d8e
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float log10f(float x) { return logf(x) / (float)_M_LN10; }
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float tanhf(float x) {
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if (isinf(x)) {
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return copysignf(1, x);
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}
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return sinhf(x) / coshf(x);
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}
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/*****************************************************************************/
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/*****************************************************************************/
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// __fpclassifyf from musl-0.9.15
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/*****************************************************************************/
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/*****************************************************************************/
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int __fpclassifyf(float x)
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{
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union {float f; uint32_t i;} u = {x};
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int e = u.i>>23 & 0xff;
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if (!e) return u.i<<1 ? FP_SUBNORMAL : FP_ZERO;
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if (e==0xff) return u.i<<9 ? FP_NAN : FP_INFINITE;
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return FP_NORMAL;
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}
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/*****************************************************************************/
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/*****************************************************************************/
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// scalbnf from musl-0.9.15
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/*****************************************************************************/
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/*****************************************************************************/
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float scalbnf(float x, int n)
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{
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union {float f; uint32_t i;} u;
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float_t y = x;
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if (n > 127) {
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y *= 0x1p127f;
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n -= 127;
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if (n > 127) {
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y *= 0x1p127f;
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n -= 127;
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if (n > 127)
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n = 127;
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}
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} else if (n < -126) {
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y *= 0x1p-126f;
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n += 126;
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if (n < -126) {
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y *= 0x1p-126f;
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n += 126;
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if (n < -126)
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n = -126;
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}
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}
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u.i = (uint32_t)(0x7f+n)<<23;
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x = y * u.f;
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return x;
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}
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/*****************************************************************************/
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/*****************************************************************************/
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// powf from musl-0.9.15
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/*****************************************************************************/
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/*****************************************************************************/
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/* origin: FreeBSD /usr/src/lib/msun/src/e_powf.c */
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/*
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* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
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*/
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/*
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* ====================================================
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* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
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*
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* Developed at SunPro, a Sun Microsystems, Inc. business.
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* Permission to use, copy, modify, and distribute this
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* software is freely granted, provided that this notice
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* is preserved.
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* ====================================================
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*/
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static const float
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bp[] = {1.0, 1.5,},
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dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
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dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
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two24 = 16777216.0, /* 0x4b800000 */
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huge = 1.0e30,
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tiny = 1.0e-30,
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/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
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L1 = 6.0000002384e-01, /* 0x3f19999a */
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L2 = 4.2857143283e-01, /* 0x3edb6db7 */
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L3 = 3.3333334327e-01, /* 0x3eaaaaab */
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L4 = 2.7272811532e-01, /* 0x3e8ba305 */
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L5 = 2.3066075146e-01, /* 0x3e6c3255 */
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L6 = 2.0697501302e-01, /* 0x3e53f142 */
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P1 = 1.6666667163e-01, /* 0x3e2aaaab */
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P2 = -2.7777778450e-03, /* 0xbb360b61 */
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P3 = 6.6137559770e-05, /* 0x388ab355 */
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P4 = -1.6533901999e-06, /* 0xb5ddea0e */
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P5 = 4.1381369442e-08, /* 0x3331bb4c */
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lg2 = 6.9314718246e-01, /* 0x3f317218 */
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lg2_h = 6.93145752e-01, /* 0x3f317200 */
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lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
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ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
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cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
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cp_h = 9.6191406250e-01, /* 0x3f764000 =12b cp */
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cp_l = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */
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ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
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ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
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ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
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float powf(float x, float y)
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{
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float z,ax,z_h,z_l,p_h,p_l;
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float y1,t1,t2,r,s,sn,t,u,v,w;
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int32_t i,j,k,yisint,n;
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int32_t hx,hy,ix,iy,is;
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GET_FLOAT_WORD(hx, x);
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GET_FLOAT_WORD(hy, y);
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ix = hx & 0x7fffffff;
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iy = hy & 0x7fffffff;
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/* x**0 = 1, even if x is NaN */
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if (iy == 0)
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return 1.0f;
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/* 1**y = 1, even if y is NaN */
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if (hx == 0x3f800000)
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return 1.0f;
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/* NaN if either arg is NaN */
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if (ix > 0x7f800000 || iy > 0x7f800000)
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return x + y;
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/* determine if y is an odd int when x < 0
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* yisint = 0 ... y is not an integer
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* yisint = 1 ... y is an odd int
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* yisint = 2 ... y is an even int
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*/
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yisint = 0;
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if (hx < 0) {
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if (iy >= 0x4b800000)
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yisint = 2; /* even integer y */
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else if (iy >= 0x3f800000) {
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k = (iy>>23) - 0x7f; /* exponent */
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j = iy>>(23-k);
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if ((j<<(23-k)) == iy)
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yisint = 2 - (j & 1);
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}
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}
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/* special value of y */
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if (iy == 0x7f800000) { /* y is +-inf */
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if (ix == 0x3f800000) /* (-1)**+-inf is 1 */
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return 1.0f;
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else if (ix > 0x3f800000) /* (|x|>1)**+-inf = inf,0 */
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return hy >= 0 ? y : 0.0f;
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else if (ix != 0) /* (|x|<1)**+-inf = 0,inf if x!=0 */
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return hy >= 0 ? 0.0f: -y;
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}
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if (iy == 0x3f800000) /* y is +-1 */
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return hy >= 0 ? x : 1.0f/x;
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if (hy == 0x40000000) /* y is 2 */
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return x*x;
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if (hy == 0x3f000000) { /* y is 0.5 */
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if (hx >= 0) /* x >= +0 */
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return sqrtf(x);
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}
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ax = fabsf(x);
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/* special value of x */
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if (ix == 0x7f800000 || ix == 0 || ix == 0x3f800000) { /* x is +-0,+-inf,+-1 */
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z = ax;
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if (hy < 0) /* z = (1/|x|) */
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z = 1.0f/z;
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if (hx < 0) {
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if (((ix-0x3f800000)|yisint) == 0) {
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z = (z-z)/(z-z); /* (-1)**non-int is NaN */
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} else if (yisint == 1)
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z = -z; /* (x<0)**odd = -(|x|**odd) */
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}
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return z;
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}
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sn = 1.0f; /* sign of result */
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if (hx < 0) {
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if (yisint == 0) /* (x<0)**(non-int) is NaN */
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return (x-x)/(x-x);
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if (yisint == 1) /* (x<0)**(odd int) */
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sn = -1.0f;
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}
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/* |y| is huge */
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if (iy > 0x4d000000) { /* if |y| > 2**27 */
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/* over/underflow if x is not close to one */
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if (ix < 0x3f7ffff8)
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return hy < 0 ? sn*huge*huge : sn*tiny*tiny;
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if (ix > 0x3f800007)
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return hy > 0 ? sn*huge*huge : sn*tiny*tiny;
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/* now |1-x| is tiny <= 2**-20, suffice to compute
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log(x) by x-x^2/2+x^3/3-x^4/4 */
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t = ax - 1; /* t has 20 trailing zeros */
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w = (t*t)*(0.5f - t*(0.333333333333f - t*0.25f));
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u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
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v = t*ivln2_l - w*ivln2;
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t1 = u + v;
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GET_FLOAT_WORD(is, t1);
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SET_FLOAT_WORD(t1, is & 0xfffff000);
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t2 = v - (t1-u);
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} else {
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float s2,s_h,s_l,t_h,t_l;
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n = 0;
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/* take care subnormal number */
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if (ix < 0x00800000) {
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ax *= two24;
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n -= 24;
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GET_FLOAT_WORD(ix, ax);
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}
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n += ((ix)>>23) - 0x7f;
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j = ix & 0x007fffff;
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/* determine interval */
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ix = j | 0x3f800000; /* normalize ix */
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if (j <= 0x1cc471) /* |x|<sqrt(3/2) */
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k = 0;
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else if (j < 0x5db3d7) /* |x|<sqrt(3) */
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k = 1;
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else {
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k = 0;
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n += 1;
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ix -= 0x00800000;
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}
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SET_FLOAT_WORD(ax, ix);
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/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
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u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
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v = 1.0f/(ax+bp[k]);
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s = u*v;
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s_h = s;
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GET_FLOAT_WORD(is, s_h);
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SET_FLOAT_WORD(s_h, is & 0xfffff000);
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/* t_h=ax+bp[k] High */
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is = ((ix>>1) & 0xfffff000) | 0x20000000;
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SET_FLOAT_WORD(t_h, is + 0x00400000 + (k<<21));
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t_l = ax - (t_h - bp[k]);
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s_l = v*((u - s_h*t_h) - s_h*t_l);
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/* compute log(ax) */
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s2 = s*s;
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r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
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r += s_l*(s_h+s);
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s2 = s_h*s_h;
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t_h = 3.0f + s2 + r;
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GET_FLOAT_WORD(is, t_h);
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SET_FLOAT_WORD(t_h, is & 0xfffff000);
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t_l = r - ((t_h - 3.0f) - s2);
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/* u+v = s*(1+...) */
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u = s_h*t_h;
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v = s_l*t_h + t_l*s;
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/* 2/(3log2)*(s+...) */
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p_h = u + v;
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GET_FLOAT_WORD(is, p_h);
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SET_FLOAT_WORD(p_h, is & 0xfffff000);
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p_l = v - (p_h - u);
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z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
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z_l = cp_l*p_h + p_l*cp+dp_l[k];
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/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
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t = (float)n;
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t1 = (((z_h + z_l) + dp_h[k]) + t);
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GET_FLOAT_WORD(is, t1);
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SET_FLOAT_WORD(t1, is & 0xfffff000);
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t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
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}
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/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
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GET_FLOAT_WORD(is, y);
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SET_FLOAT_WORD(y1, is & 0xfffff000);
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p_l = (y-y1)*t1 + y*t2;
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p_h = y1*t1;
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z = p_l + p_h;
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GET_FLOAT_WORD(j, z);
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if (j > 0x43000000) /* if z > 128 */
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return sn*huge*huge; /* overflow */
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else if (j == 0x43000000) { /* if z == 128 */
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if (p_l + ovt > z - p_h)
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return sn*huge*huge; /* overflow */
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} else if ((j&0x7fffffff) > 0x43160000) /* z < -150 */ // FIXME: check should be (uint32_t)j > 0xc3160000
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return sn*tiny*tiny; /* underflow */
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else if (j == (int32_t) 0xc3160000) { /* z == -150 */
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if (p_l <= z-p_h)
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return sn*tiny*tiny; /* underflow */
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}
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/*
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* compute 2**(p_h+p_l)
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*/
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i = j & 0x7fffffff;
|
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k = (i>>23) - 0x7f;
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n = 0;
|
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if (i > 0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
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n = j + (0x00800000>>(k+1));
|
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k = ((n&0x7fffffff)>>23) - 0x7f; /* new k for n */
|
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SET_FLOAT_WORD(t, n & ~(0x007fffff>>k));
|
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n = ((n&0x007fffff)|0x00800000)>>(23-k);
|
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if (j < 0)
|
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n = -n;
|
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p_h -= t;
|
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}
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t = p_l + p_h;
|
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GET_FLOAT_WORD(is, t);
|
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SET_FLOAT_WORD(t, is & 0xffff8000);
|
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u = t*lg2_h;
|
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v = (p_l-(t-p_h))*lg2 + t*lg2_l;
|
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z = u + v;
|
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w = v - (z - u);
|
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t = z*z;
|
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t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
|
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r = (z*t1)/(t1-2.0f) - (w+z*w);
|
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z = 1.0f - (r - z);
|
|
GET_FLOAT_WORD(j, z);
|
|
j += n<<23;
|
|
if ((j>>23) <= 0) /* subnormal output */
|
|
z = scalbnf(z, n);
|
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else
|
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SET_FLOAT_WORD(z, j);
|
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return sn*z;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
// expf from musl-0.9.15
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
|
|
/* origin: FreeBSD /usr/src/lib/msun/src/e_expf.c */
|
|
/*
|
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
|
|
static const float
|
|
half[2] = {0.5,-0.5},
|
|
ln2hi = 6.9314575195e-1f, /* 0x3f317200 */
|
|
ln2lo = 1.4286067653e-6f, /* 0x35bfbe8e */
|
|
invln2 = 1.4426950216e+0f, /* 0x3fb8aa3b */
|
|
/*
|
|
* Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
|
|
* |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
|
|
*/
|
|
expf_P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */
|
|
expf_P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
|
|
|
|
float expf(float x)
|
|
{
|
|
float_t hi, lo, c, xx, y;
|
|
int k, sign;
|
|
uint32_t hx;
|
|
|
|
GET_FLOAT_WORD(hx, x);
|
|
sign = hx >> 31; /* sign bit of x */
|
|
hx &= 0x7fffffff; /* high word of |x| */
|
|
|
|
/* special cases */
|
|
if (hx >= 0x42aeac50) { /* if |x| >= -87.33655f or NaN */
|
|
if (hx >= 0x42b17218 && !sign) { /* x >= 88.722839f */
|
|
/* overflow */
|
|
x *= 0x1p127f;
|
|
return x;
|
|
}
|
|
if (sign) {
|
|
/* underflow */
|
|
FORCE_EVAL(-0x1p-149f/x);
|
|
if (hx >= 0x42cff1b5) /* x <= -103.972084f */
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
/* argument reduction */
|
|
if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
|
|
if (hx > 0x3f851592) /* if |x| > 1.5 ln2 */
|
|
k = invln2*x + half[sign];
|
|
else
|
|
k = 1 - sign - sign;
|
|
hi = x - k*ln2hi; /* k*ln2hi is exact here */
|
|
lo = k*ln2lo;
|
|
x = hi - lo;
|
|
} else if (hx > 0x39000000) { /* |x| > 2**-14 */
|
|
k = 0;
|
|
hi = x;
|
|
lo = 0;
|
|
} else {
|
|
/* raise inexact */
|
|
FORCE_EVAL(0x1p127f + x);
|
|
return 1 + x;
|
|
}
|
|
|
|
/* x is now in primary range */
|
|
xx = x*x;
|
|
c = x - xx*(expf_P1+xx*expf_P2);
|
|
y = 1 + (x*c/(2-c) - lo + hi);
|
|
if (k == 0)
|
|
return y;
|
|
return scalbnf(y, k);
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
// expm1f from musl-0.9.15
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
|
|
/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
|
|
/*
|
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
|
|
static const float
|
|
o_threshold = 8.8721679688e+01, /* 0x42b17180 */
|
|
ln2_hi = 6.9313812256e-01, /* 0x3f317180 */
|
|
ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */
|
|
//invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */
|
|
/*
|
|
* Domain [-0.34568, 0.34568], range ~[-6.694e-10, 6.696e-10]:
|
|
* |6 / x * (1 + 2 * (1 / (exp(x) - 1) - 1 / x)) - q(x)| < 2**-30.04
|
|
* Scaled coefficients: Qn_here = 2**n * Qn_for_q (see s_expm1.c):
|
|
*/
|
|
Q1 = -3.3333212137e-2, /* -0x888868.0p-28 */
|
|
Q2 = 1.5807170421e-3; /* 0xcf3010.0p-33 */
|
|
|
|
float expm1f(float x)
|
|
{
|
|
float_t y,hi,lo,c,t,e,hxs,hfx,r1,twopk;
|
|
union {float f; uint32_t i;} u = {x};
|
|
uint32_t hx = u.i & 0x7fffffff;
|
|
int k, sign = u.i >> 31;
|
|
|
|
/* filter out huge and non-finite argument */
|
|
if (hx >= 0x4195b844) { /* if |x|>=27*ln2 */
|
|
if (hx > 0x7f800000) /* NaN */
|
|
return x;
|
|
if (sign)
|
|
return -1;
|
|
if (x > o_threshold) {
|
|
x *= 0x1p127f;
|
|
return x;
|
|
}
|
|
}
|
|
|
|
/* argument reduction */
|
|
if (hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */
|
|
if (hx < 0x3F851592) { /* and |x| < 1.5 ln2 */
|
|
if (!sign) {
|
|
hi = x - ln2_hi;
|
|
lo = ln2_lo;
|
|
k = 1;
|
|
} else {
|
|
hi = x + ln2_hi;
|
|
lo = -ln2_lo;
|
|
k = -1;
|
|
}
|
|
} else {
|
|
k = invln2*x + (sign ? -0.5f : 0.5f);
|
|
t = k;
|
|
hi = x - t*ln2_hi; /* t*ln2_hi is exact here */
|
|
lo = t*ln2_lo;
|
|
}
|
|
x = hi-lo;
|
|
c = (hi-x)-lo;
|
|
} else if (hx < 0x33000000) { /* when |x|<2**-25, return x */
|
|
if (hx < 0x00800000)
|
|
FORCE_EVAL(x*x);
|
|
return x;
|
|
} else
|
|
k = 0;
|
|
|
|
/* x is now in primary range */
|
|
hfx = 0.5f*x;
|
|
hxs = x*hfx;
|
|
r1 = 1.0f+hxs*(Q1+hxs*Q2);
|
|
t = 3.0f - r1*hfx;
|
|
e = hxs*((r1-t)/(6.0f - x*t));
|
|
if (k == 0) /* c is 0 */
|
|
return x - (x*e-hxs);
|
|
e = x*(e-c) - c;
|
|
e -= hxs;
|
|
/* exp(x) ~ 2^k (x_reduced - e + 1) */
|
|
if (k == -1)
|
|
return 0.5f*(x-e) - 0.5f;
|
|
if (k == 1) {
|
|
if (x < -0.25f)
|
|
return -2.0f*(e-(x+0.5f));
|
|
return 1.0f + 2.0f*(x-e);
|
|
}
|
|
u.i = (0x7f+k)<<23; /* 2^k */
|
|
twopk = u.f;
|
|
if (k < 0 || k > 56) { /* suffice to return exp(x)-1 */
|
|
y = x - e + 1.0f;
|
|
if (k == 128)
|
|
y = y*2.0f*0x1p127f;
|
|
else
|
|
y = y*twopk;
|
|
return y - 1.0f;
|
|
}
|
|
u.i = (0x7f-k)<<23; /* 2^-k */
|
|
if (k < 23)
|
|
y = (x-e+(1-u.f))*twopk;
|
|
else
|
|
y = (x-(e+u.f)+1)*twopk;
|
|
return y;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
// __expo2f from musl-0.9.15
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
|
|
|
|
/* expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5f*expf(x/2)*expf(x/2) */
|
|
float __expo2f(float x)
|
|
{
|
|
/* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */
|
|
static const int k = 235;
|
|
static const float kln2 = 0x1.45c778p+7f;
|
|
float scale;
|
|
|
|
/* note that k is odd and scale*scale overflows */
|
|
SET_FLOAT_WORD(scale, (uint32_t)(0x7f + k/2) << 23);
|
|
/* exp(x - k ln2) * 2**(k-1) */
|
|
return expf(x - kln2) * scale * scale;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
// logf from musl-0.9.15
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
|
|
/* origin: FreeBSD /usr/src/lib/msun/src/e_logf.c */
|
|
/*
|
|
* Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com.
|
|
*/
|
|
/*
|
|
* ====================================================
|
|
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
|
|
*
|
|
* Developed at SunPro, a Sun Microsystems, Inc. business.
|
|
* Permission to use, copy, modify, and distribute this
|
|
* software is freely granted, provided that this notice
|
|
* is preserved.
|
|
* ====================================================
|
|
*/
|
|
|
|
static const float
|
|
/* |(log(1+s)-log(1-s))/s - Lg(s)| < 2**-34.24 (~[-4.95e-11, 4.97e-11]). */
|
|
Lg1 = 0xaaaaaa.0p-24, /* 0.66666662693 */
|
|
Lg2 = 0xccce13.0p-25, /* 0.40000972152 */
|
|
Lg3 = 0x91e9ee.0p-25, /* 0.28498786688 */
|
|
Lg4 = 0xf89e26.0p-26; /* 0.24279078841 */
|
|
|
|
float logf(float x)
|
|
{
|
|
union {float f; uint32_t i;} u = {x};
|
|
float_t hfsq,f,s,z,R,w,t1,t2,dk;
|
|
uint32_t ix;
|
|
int k;
|
|
|
|
ix = u.i;
|
|
k = 0;
|
|
if (ix < 0x00800000 || ix>>31) { /* x < 2**-126 */
|
|
if (ix<<1 == 0)
|
|
return -1/(x*x); /* log(+-0)=-inf */
|
|
if (ix>>31)
|
|
return (x-x)/0.0f; /* log(-#) = NaN */
|
|
/* subnormal number, scale up x */
|
|
k -= 25;
|
|
x *= 0x1p25f;
|
|
u.f = x;
|
|
ix = u.i;
|
|
} else if (ix >= 0x7f800000) {
|
|
return x;
|
|
} else if (ix == 0x3f800000)
|
|
return 0;
|
|
|
|
/* reduce x into [sqrt(2)/2, sqrt(2)] */
|
|
ix += 0x3f800000 - 0x3f3504f3;
|
|
k += (int)(ix>>23) - 0x7f;
|
|
ix = (ix&0x007fffff) + 0x3f3504f3;
|
|
u.i = ix;
|
|
x = u.f;
|
|
|
|
f = x - 1.0f;
|
|
s = f/(2.0f + f);
|
|
z = s*s;
|
|
w = z*z;
|
|
t1= w*(Lg2+w*Lg4);
|
|
t2= z*(Lg1+w*Lg3);
|
|
R = t2 + t1;
|
|
hfsq = 0.5f*f*f;
|
|
dk = k;
|
|
return s*(hfsq+R) + dk*ln2_lo - hfsq + f + dk*ln2_hi;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
// coshf from musl-0.9.15
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
|
|
float coshf(float x)
|
|
{
|
|
union {float f; uint32_t i;} u = {.f = x};
|
|
uint32_t w;
|
|
float t;
|
|
|
|
/* |x| */
|
|
u.i &= 0x7fffffff;
|
|
x = u.f;
|
|
w = u.i;
|
|
|
|
/* |x| < log(2) */
|
|
if (w < 0x3f317217) {
|
|
if (w < 0x3f800000 - (12<<23)) {
|
|
FORCE_EVAL(x + 0x1p120f);
|
|
return 1;
|
|
}
|
|
t = expm1f(x);
|
|
return 1 + t*t/(2*(1+t));
|
|
}
|
|
|
|
/* |x| < log(FLT_MAX) */
|
|
if (w < 0x42b17217) {
|
|
t = expf(x);
|
|
return 0.5f*(t + 1/t);
|
|
}
|
|
|
|
/* |x| > log(FLT_MAX) or nan */
|
|
t = __expo2f(x);
|
|
return t;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
// sinhf from musl-0.9.15
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
|
|
float sinhf(float x)
|
|
{
|
|
union {float f; uint32_t i;} u = {.f = x};
|
|
uint32_t w;
|
|
float t, h, absx;
|
|
|
|
h = 0.5;
|
|
if (u.i >> 31)
|
|
h = -h;
|
|
/* |x| */
|
|
u.i &= 0x7fffffff;
|
|
absx = u.f;
|
|
w = u.i;
|
|
|
|
/* |x| < log(FLT_MAX) */
|
|
if (w < 0x42b17217) {
|
|
t = expm1f(absx);
|
|
if (w < 0x3f800000) {
|
|
if (w < 0x3f800000 - (12<<23))
|
|
return x;
|
|
return h*(2*t - t*t/(t+1));
|
|
}
|
|
return h*(t + t/(t+1));
|
|
}
|
|
|
|
/* |x| > logf(FLT_MAX) or nan */
|
|
t = 2*h*__expo2f(absx);
|
|
return t;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
// ceilf, floorf and truncf from musl-0.9.15
|
|
/*****************************************************************************/
|
|
/*****************************************************************************/
|
|
|
|
float ceilf(float x)
|
|
{
|
|
union {float f; uint32_t i;} u = {x};
|
|
int e = (int)(u.i >> 23 & 0xff) - 0x7f;
|
|
uint32_t m;
|
|
|
|
if (e >= 23)
|
|
return x;
|
|
if (e >= 0) {
|
|
m = 0x007fffff >> e;
|
|
if ((u.i & m) == 0)
|
|
return x;
|
|
FORCE_EVAL(x + 0x1p120f);
|
|
if (u.i >> 31 == 0)
|
|
u.i += m;
|
|
u.i &= ~m;
|
|
} else {
|
|
FORCE_EVAL(x + 0x1p120f);
|
|
if (u.i >> 31)
|
|
u.f = -0.0;
|
|
else if (u.i << 1)
|
|
u.f = 1.0;
|
|
}
|
|
return u.f;
|
|
}
|
|
|
|
float floorf(float x)
|
|
{
|
|
union {float f; uint32_t i;} u = {x};
|
|
int e = (int)(u.i >> 23 & 0xff) - 0x7f;
|
|
uint32_t m;
|
|
|
|
if (e >= 23)
|
|
return x;
|
|
if (e >= 0) {
|
|
m = 0x007fffff >> e;
|
|
if ((u.i & m) == 0)
|
|
return x;
|
|
FORCE_EVAL(x + 0x1p120f);
|
|
if (u.i >> 31)
|
|
u.i += m;
|
|
u.i &= ~m;
|
|
} else {
|
|
FORCE_EVAL(x + 0x1p120f);
|
|
if (u.i >> 31 == 0)
|
|
u.i = 0;
|
|
else if (u.i << 1)
|
|
u.f = -1.0;
|
|
}
|
|
return u.f;
|
|
}
|
|
|
|
float truncf(float x)
|
|
{
|
|
union {float f; uint32_t i;} u = {x};
|
|
int e = (int)(u.i >> 23 & 0xff) - 0x7f + 9;
|
|
uint32_t m;
|
|
|
|
if (e >= 23 + 9)
|
|
return x;
|
|
if (e < 9)
|
|
e = 1;
|
|
m = -1U >> e;
|
|
if ((u.i & m) == 0)
|
|
return x;
|
|
FORCE_EVAL(x + 0x1p120f);
|
|
u.i &= ~m;
|
|
return u.f;
|
|
}
|