stmhal: Add powf, logf, log2f, log10f.
This commit is contained in:
Damien George
parent
aba9f51fef
commit
769b23a9c6
385
stmhal/math.c
385
stmhal/math.c
@ -46,12 +46,6 @@ double __aeabi_dmul(double x , double y) {
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return 0.0;
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}
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/*
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double sqrt(double x) {
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// TODO
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return 0.0;
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}
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*/
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float sqrtf(float x) {
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asm volatile (
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@ -61,16 +55,18 @@ float sqrtf(float x) {
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return x;
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}
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// TODO we need import these functions from some library (eg musl or newlib)
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float powf(float x, float y) { return 0.0; }
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float logf(float x) { return 0.0; }
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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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float log2f(float x) { return 0.0; }
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float log10f(float x) { return 0.0; }
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float tanhf(float x) { return 0.0; }
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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) { return sinhf(x) / coshf(x); }
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// TODO we need import these functions from some library (eg musl or newlib)
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float acoshf(float x) { return 0.0; }
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float asinhf(float x) { return 0.0; }
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float atanhf(float x) { return 0.0; }
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@ -93,8 +89,11 @@ float modff(float x, float *y) { return 0.0; }
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float frexpf(float x, int *exp) { return 0.0; }
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float ldexpf(float x, int exp) { return 0.0; }
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/*****************************************************************************/
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/*****************************************************************************/
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// from musl-0.9.15 libm.h
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/*****************************************************************************/
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/*****************************************************************************/
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/* origin: FreeBSD /usr/src/lib/msun/src/math_private.h */
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/*
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@ -140,8 +139,11 @@ do { \
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(d) = __u.f; \
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} while (0)
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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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@ -152,8 +154,11 @@ int __fpclassifyf(float x)
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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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@ -184,8 +189,275 @@ float scalbnf(float x, int n)
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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 == 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);
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GET_FLOAT_WORD(j, z);
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j += n<<23;
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if ((j>>23) <= 0) /* subnormal output */
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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;
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}
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/*****************************************************************************/
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/*****************************************************************************/
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// expf 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_expf.c */
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/*
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@ -211,8 +483,8 @@ invln2 = 1.4426950216e+0f, /* 0x3fb8aa3b */
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* Domain [-0.34568, 0.34568], range ~[-4.278e-9, 4.447e-9]:
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* |x*(exp(x)+1)/(exp(x)-1) - p(x)| < 2**-27.74
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*/
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P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */
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P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
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expf_P1 = 1.6666625440e-1f, /* 0xaaaa8f.0p-26 */
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expf_P2 = -2.7667332906e-3f; /* -0xb55215.0p-32 */
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float expf(float x)
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{
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@ -260,15 +532,18 @@ float expf(float x)
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/* x is now in primary range */
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xx = x*x;
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c = x - xx*(P1+xx*P2);
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c = x - xx*(expf_P1+xx*expf_P2);
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y = 1 + (x*c/(2-c) - lo + hi);
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if (k == 0)
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return y;
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return scalbnf(y, k);
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}
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/*****************************************************************************/
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/*****************************************************************************/
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// expm1f from musl-0.9.15
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/*****************************************************************************/
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/*****************************************************************************/
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/* origin: FreeBSD /usr/src/lib/msun/src/s_expm1f.c */
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/*
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@ -380,8 +655,11 @@ float expm1f(float x)
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return y;
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}
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/*****************************************************************************/
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/*****************************************************************************/
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// __expo2f from musl-0.9.15
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/*****************************************************************************/
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/*****************************************************************************/
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/* k is such that k*ln2 has minimal relative error and x - kln2 > log(FLT_MIN) */
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static const int k = 235;
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@ -398,8 +676,82 @@ float __expo2f(float x)
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return expf(x - kln2) * scale * scale;
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}
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/*****************************************************************************/
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/*****************************************************************************/
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// logf from musl-0.9.15
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/*****************************************************************************/
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/*****************************************************************************/
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|
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/* 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)
|
||||
{
|
||||
@ -433,8 +785,11 @@ float coshf(float x)
|
||||
return t;
|
||||
}
|
||||
|
||||
/*****************************************************************************/
|
||||
/*****************************************************************************/
|
||||
// sinhf from musl-0.9.15
|
||||
/*****************************************************************************/
|
||||
/*****************************************************************************/
|
||||
|
||||
float sinhf(float x)
|
||||
{
|
||||
|
||||
Loading…
x
Reference in New Issue
Block a user