summaryrefslogtreecommitdiffstatshomepage
path: root/stmhal/math.c
diff options
context:
space:
mode:
Diffstat (limited to 'stmhal/math.c')
-rw-r--r--stmhal/math.c940
1 files changed, 0 insertions, 940 deletions
diff --git a/stmhal/math.c b/stmhal/math.c
deleted file mode 100644
index 9f0d312488..0000000000
--- a/stmhal/math.c
+++ /dev/null
@@ -1,940 +0,0 @@
-/*
- * 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;
-}
-
-#ifndef NDEBUG
-float copysignf(float x, float y) {
- float_s_t fx={.f = x};
- float_s_t fy={.f = y};
-
- // copy sign bit;
- fx.s = fy.s;
-
- return fx.f;
-}
-#endif
-
-// some compilers define log2f in terms of logf
-#ifdef log2f
-#undef log2f
-#endif
-// some compilers have _M_LN2 defined in math.h, some don't
-#ifndef _M_LN2
-#define _M_LN2 (0.69314718055994530942)
-#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;
-}
generated by cgit v1.2.3 (git 2.39.1) at 2025-06-06 07:38:18 +0000