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circuitpython/stmhal/math.c
Damien George 04b9147e15 Add license header to (almost) all files. 
Blanket wide to all .c and .h files.  Some files originating from ST are
difficult to deal with (license wise) so it was left out of those.

Also merged modpyb.h, modos.h, modstm.h and modtime.h in stmhal/.
2014-05-03 23:27:38 +01:00

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/*
* This file is part of the Micro Python project, http://micropython.org/
*
* The MIT License (MIT)
*
* Copyright (c) 2013, 2014 Damien P. George
*
* 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 <stdint.h>
#include <math.h>
typedef float float_t;
typedef union {
float f;
struct {
uint64_t m : 23;
uint64_t e : 8;
uint64_t s : 1;
};
} float_s_t;
typedef union {
double d;
struct {
uint64_t m : 52;
uint64_t e : 11;
uint64_t s : 1;
};
} double_s_t;
double __attribute__((pcs("aapcs"))) __aeabi_i2d(int32_t x) {
return (float)x;
}
double __attribute__((pcs("aapcs"))) __aeabi_f2d(float x) {
float_s_t fx={0};
double_s_t dx={0};
fx.f = x;
dx.s = (fx.s);
dx.e = (fx.e-127+1023) & 0x7FF;
dx.m = fx.m;
dx.m <<=(52-23); // left justify
return dx.d;
}
float __attribute__((pcs("aapcs"))) __aeabi_d2f(double x) {
float_s_t fx={0};
double_s_t dx={0};
dx.d = x;
fx.s = (dx.s);
fx.e = (dx.e-1023+127) & 0xFF;
fx.m = (dx.m>>(52-23)); // right justify
return fx.f;
}
double __aeabi_dmul(double x , double y) {
return 0.0;
}
float sqrtf(float x) {
asm volatile (
"vsqrt.f32 %[r], %[x]\n"
: [r] "=t" (x)
: [x] "t" (x));
return x;
}
// some compilers define log2f in terms of logf
#ifdef log2f
#undef log2f
#endif
float log2f(float x) { return logf(x) / (float)_M_LN2; }
static const float _M_LN10 = 2.30258509299404; // 0x40135d8e
float log10f(float x) { return logf(x) / (float)_M_LN10; }
float tanhf(float x) { return sinhf(x) / coshf(x); }
// TODO we need import these functions from some library (eg musl or newlib)
float acoshf(float x) { return 0.0; }
float asinhf(float x) { return 0.0; }
float atanhf(float x) { return 0.0; }
float tanf(float x) { return 0.0; }
float acosf(float x) { return 0.0; }
float asinf(float x) { return 0.0; }
float atanf(float x) { return 0.0; }
float atan2f(float x, float y) { return 0.0; }
float fmodf(float x, float y) { return 0.0; }
float tgammaf(float x) { return 0.0; }
float lgammaf(float x) { return 0.0; }
float erff(float x) { return 0.0; }
float erfcf(float x) { return 0.0; }
float modff(float x, float *y) { return 0.0; }
float frexpf(float x, int *exp) { return 0.0; }
float ldexpf(float x, int exp) { return 0.0; }
/*****************************************************************************/
/*****************************************************************************/
// from musl-0.9.15 libm.h
/*****************************************************************************/
/*****************************************************************************/
/* origin: FreeBSD /usr/src/lib/msun/src/math_private.h */
/*
* ====================================================
* 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.
* ====================================================
*/
#define FORCE_EVAL(x) do { \
if (sizeof(x) == sizeof(float)) { \
volatile float __x; \
__x = (x); \
(void)__x; \
} else if (sizeof(x) == sizeof(double)) { \
volatile double __x; \
__x = (x); \
(void)__x; \
} else { \
volatile long double __x; \
__x = (x); \
(void)__x; \
} \
} while(0)
/* Get a 32 bit int from a float. */
#define GET_FLOAT_WORD(w,d) \
do { \
union {float f; uint32_t i;} __u; \
__u.f = (d); \
(w) = __u.i; \
} while (0)
/* Set a float from a 32 bit int. */
#define SET_FLOAT_WORD(d,w) \
do { \
union {float f; uint32_t i;} __u; \
__u.i = (w); \
(d) = __u.f; \
} while (0)
/*****************************************************************************/
/*****************************************************************************/
// __fpclassifyf from musl-0.9.15
/*****************************************************************************/
/*****************************************************************************/
int __fpclassifyf(float x)
{
union {float f; uint32_t i;} u = {x};
int e = u.i>>23 & 0xff;
if (!e) return u.i<<1 ? FP_SUBNORMAL : FP_ZERO;
if (e==0xff) return u.i<<9 ? FP_NAN : FP_INFINITE;
return FP_NORMAL;
}
/*****************************************************************************/
/*****************************************************************************/
// scalbnf from musl-0.9.15
/*****************************************************************************/
/*****************************************************************************/
float scalbnf(float x, int n)
{
union {float f; uint32_t i;} u;
float_t y = x;
if (n > 127) {
y *= 0x1p127f;
n -= 127;
if (n > 127) {
y *= 0x1p127f;
n -= 127;
if (n > 127)
n = 127;
}
} else if (n < -126) {
y *= 0x1p-126f;
n += 126;
if (n < -126) {
y *= 0x1p-126f;
n += 126;
if (n < -126)
n = -126;
}
}
u.i = (uint32_t)(0x7f+n)<<23;
x = y * u.f;
return x;
}
/*****************************************************************************/
/*****************************************************************************/
// powf from musl-0.9.15
/*****************************************************************************/
/*****************************************************************************/
/* origin: FreeBSD /usr/src/lib/msun/src/e_powf.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
bp[] = {1.0, 1.5,},
dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */
dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */
two24 = 16777216.0, /* 0x4b800000 */
huge = 1.0e30,
tiny = 1.0e-30,
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1 = 6.0000002384e-01, /* 0x3f19999a */
L2 = 4.2857143283e-01, /* 0x3edb6db7 */
L3 = 3.3333334327e-01, /* 0x3eaaaaab */
L4 = 2.7272811532e-01, /* 0x3e8ba305 */
L5 = 2.3066075146e-01, /* 0x3e6c3255 */
L6 = 2.0697501302e-01, /* 0x3e53f142 */
P1 = 1.6666667163e-01, /* 0x3e2aaaab */
P2 = -2.7777778450e-03, /* 0xbb360b61 */
P3 = 6.6137559770e-05, /* 0x388ab355 */
P4 = -1.6533901999e-06, /* 0xb5ddea0e */
P5 = 4.1381369442e-08, /* 0x3331bb4c */
lg2 = 6.9314718246e-01, /* 0x3f317218 */
lg2_h = 6.93145752e-01, /* 0x3f317200 */
lg2_l = 1.42860654e-06, /* 0x35bfbe8c */
ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */
cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */
cp_h = 9.6191406250e-01, /* 0x3f764000 =12b cp */
cp_l = -1.1736857402e-04, /* 0xb8f623c6 =tail of cp_h */
ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */
ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/
ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/
float powf(float x, float y)
{
float z,ax,z_h,z_l,p_h,p_l;
float y1,t1,t2,r,s,sn,t,u,v,w;
int32_t i,j,k,yisint,n;
int32_t hx,hy,ix,iy,is;
GET_FLOAT_WORD(hx, x);
GET_FLOAT_WORD(hy, y);
ix = hx & 0x7fffffff;
iy = hy & 0x7fffffff;
/* x**0 = 1, even if x is NaN */
if (iy == 0)
return 1.0f;
/* 1**y = 1, even if y is NaN */
if (hx == 0x3f800000)
return 1.0f;
/* NaN if either arg is NaN */
if (ix > 0x7f800000 || iy > 0x7f800000)
return x + y;
/* determine if y is an odd int when x < 0
* yisint = 0 ... y is not an integer
* yisint = 1 ... y is an odd int
* yisint = 2 ... y is an even int
*/
yisint = 0;
if (hx < 0) {
if (iy >= 0x4b800000)
yisint = 2; /* even integer y */
else if (iy >= 0x3f800000) {
k = (iy>>23) - 0x7f; /* exponent */
j = iy>>(23-k);
if ((j<<(23-k)) == iy)
yisint = 2 - (j & 1);
}
}
/* special value of y */
if (iy == 0x7f800000) { /* y is +-inf */
if (ix == 0x3f800000) /* (-1)**+-inf is 1 */
return 1.0f;
else if (ix > 0x3f800000) /* (|x|>1)**+-inf = inf,0 */
return hy >= 0 ? y : 0.0f;
else if (ix != 0) /* (|x|<1)**+-inf = 0,inf if x!=0 */
return hy >= 0 ? 0.0f: -y;
}
if (iy == 0x3f800000) /* y is +-1 */
return hy >= 0 ? x : 1.0f/x;
if (hy == 0x40000000) /* y is 2 */
return x*x;
if (hy == 0x3f000000) { /* y is 0.5 */
if (hx >= 0) /* x >= +0 */
return sqrtf(x);
}
ax = fabsf(x);
/* special value of x */
if (ix == 0x7f800000 || ix == 0 || ix == 0x3f800000) { /* x is +-0,+-inf,+-1 */
z = ax;
if (hy < 0) /* z = (1/|x|) */
z = 1.0f/z;
if (hx < 0) {
if (((ix-0x3f800000)|yisint) == 0) {
z = (z-z)/(z-z); /* (-1)**non-int is NaN */
} else if (yisint == 1)
z = -z; /* (x<0)**odd = -(|x|**odd) */
}
return z;
}
sn = 1.0f; /* sign of result */
if (hx < 0) {
if (yisint == 0) /* (x<0)**(non-int) is NaN */
return (x-x)/(x-x);
if (yisint == 1) /* (x<0)**(odd int) */
sn = -1.0f;
}
/* |y| is huge */
if (iy > 0x4d000000) { /* if |y| > 2**27 */
/* over/underflow if x is not close to one */
if (ix < 0x3f7ffff8)
return hy < 0 ? sn*huge*huge : sn*tiny*tiny;
if (ix > 0x3f800007)
return hy > 0 ? sn*huge*huge : sn*tiny*tiny;
/* now |1-x| is tiny <= 2**-20, suffice to compute
log(x) by x-x^2/2+x^3/3-x^4/4 */
t = ax - 1; /* t has 20 trailing zeros */
w = (t*t)*(0.5f - t*(0.333333333333f - t*0.25f));
u = ivln2_h*t; /* ivln2_h has 16 sig. bits */
v = t*ivln2_l - w*ivln2;
t1 = u + v;
GET_FLOAT_WORD(is, t1);
SET_FLOAT_WORD(t1, is & 0xfffff000);
t2 = v - (t1-u);
} else {
float s2,s_h,s_l,t_h,t_l;
n = 0;
/* take care subnormal number */
if (ix < 0x00800000) {
ax *= two24;
n -= 24;
GET_FLOAT_WORD(ix, ax);
}
n += ((ix)>>23) - 0x7f;
j = ix & 0x007fffff;
/* determine interval */
ix = j | 0x3f800000; /* normalize ix */
if (j <= 0x1cc471) /* |x|<sqrt(3/2) */
k = 0;
else if (j < 0x5db3d7) /* |x|<sqrt(3) */
k = 1;
else {
k = 0;
n += 1;
ix -= 0x00800000;
}
SET_FLOAT_WORD(ax, ix);
/* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
u = ax - bp[k]; /* bp[0]=1.0, bp[1]=1.5 */
v = 1.0f/(ax+bp[k]);
s = u*v;
s_h = s;
GET_FLOAT_WORD(is, s_h);
SET_FLOAT_WORD(s_h, is & 0xfffff000);
/* t_h=ax+bp[k] High */
is = ((ix>>1) & 0xfffff000) | 0x20000000;
SET_FLOAT_WORD(t_h, is + 0x00400000 + (k<<21));
t_l = ax - (t_h - bp[k]);
s_l = v*((u - s_h*t_h) - s_h*t_l);
/* compute log(ax) */
s2 = s*s;
r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6)))));
r += s_l*(s_h+s);
s2 = s_h*s_h;
t_h = 3.0f + s2 + r;
GET_FLOAT_WORD(is, t_h);
SET_FLOAT_WORD(t_h, is & 0xfffff000);
t_l = r - ((t_h - 3.0f) - s2);
/* u+v = s*(1+...) */
u = s_h*t_h;
v = s_l*t_h + t_l*s;
/* 2/(3log2)*(s+...) */
p_h = u + v;
GET_FLOAT_WORD(is, p_h);
SET_FLOAT_WORD(p_h, is & 0xfffff000);
p_l = v - (p_h - u);
z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */
z_l = cp_l*p_h + p_l*cp+dp_l[k];
/* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
t = (float)n;
t1 = (((z_h + z_l) + dp_h[k]) + t);
GET_FLOAT_WORD(is, t1);
SET_FLOAT_WORD(t1, is & 0xfffff000);
t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
}
/* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */
GET_FLOAT_WORD(is, y);
SET_FLOAT_WORD(y1, is & 0xfffff000);
p_l = (y-y1)*t1 + y*t2;
p_h = y1*t1;
z = p_l + p_h;
GET_FLOAT_WORD(j, z);
if (j > 0x43000000) /* if z > 128 */
return sn*huge*huge; /* overflow */
else if (j == 0x43000000) { /* if z == 128 */
if (p_l + ovt > z - p_h)
return sn*huge*huge; /* overflow */
} else if ((j&0x7fffffff) > 0x43160000) /* z < -150 */ // FIXME: check should be (uint32_t)j > 0xc3160000
return sn*tiny*tiny; /* underflow */
else if (j == 0xc3160000) { /* z == -150 */
if (p_l <= z-p_h)
return sn*tiny*tiny; /* underflow */
}
/*
* compute 2**(p_h+p_l)
*/
i = j & 0x7fffffff;
k = (i>>23) - 0x7f;
n = 0;
if (i > 0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */
n = j + (0x00800000>>(k+1));
k = ((n&0x7fffffff)>>23) - 0x7f; /* new k for n */
SET_FLOAT_WORD(t, n & ~(0x007fffff>>k));
n = ((n&0x007fffff)|0x00800000)>>(23-k);
if (j < 0)
n = -n;
p_h -= t;
}
t = p_l + p_h;
GET_FLOAT_WORD(is, t);
SET_FLOAT_WORD(t, is & 0xffff8000);
u = t*lg2_h;
v = (p_l-(t-p_h))*lg2 + t*lg2_l;
z = u + v;
w = v - (z - u);
t = z*z;
t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
r = (z*t1)/(t1-2.0f) - (w+z*w);
z = 1.0f - (r - z);
GET_FLOAT_WORD(j, z);
j += n<<23;
if ((j>>23) <= 0) /* subnormal output */
z = scalbnf(z, n);
else
SET_FLOAT_WORD(z, j);
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
/*****************************************************************************/
/*****************************************************************************/
/* 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;
/* expf(x)/2 for x >= log(FLT_MAX), slightly better than 0.5f*expf(x/2)*expf(x/2) */
float __expo2f(float x)
{
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;
}
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