kopia lustrzana https://github.com/micropython/micropython
451 wiersze
11 KiB
C
451 wiersze
11 KiB
C
#include <stdint.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_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;
|
|
|
|
}
|
|
/*
|
|
double sqrt(double x) {
|
|
// TODO
|
|
return 0.0;
|
|
}
|
|
*/
|
|
|
|
float sqrtf(float x) {
|
|
asm volatile (
|
|
"vsqrt.f32 %[r], %[x]\n"
|
|
: [r] "=t" (x)
|
|
: [x] "t" (x));
|
|
return x;
|
|
}
|
|
|
|
// TODO we need import these functions from some library (eg musl or newlib)
|
|
float powf(float x, float y) { return 0.0; }
|
|
float logf(float x) { return 0.0; }
|
|
float log2f(float x) { return 0.0; }
|
|
float log10f(float x) { return 0.0; }
|
|
float tanhf(float x) { return 0.0; }
|
|
float acoshf(float x) { return 0.0; }
|
|
float asinhf(float x) { return 0.0; }
|
|
float atanhf(float x) { return 0.0; }
|
|
float cosf(float x) { return 0.0; }
|
|
float sinf(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 ceilf(float x) { return 0.0; }
|
|
float floorf(float x) { return 0.0; }
|
|
float truncf(float x) { 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; }
|
|
int __fpclassifyf(float x) { return 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)
|
|
|
|
/*****************************************************************************/
|
|
// 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;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
// 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
|
|
*/
|
|
P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */
|
|
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*(P1+xx*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;
|
|
}
|
|
|
|
/*****************************************************************************/
|
|
// 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;
|
|
}
|