#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;
}