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-rw-r--r--stmhal/Makefile10
-rw-r--r--stmhal/math.c940
-rw-r--r--stmhal/mathsincos.c627
3 files changed, 8 insertions, 1569 deletions
diff --git a/stmhal/Makefile b/stmhal/Makefile
index ba965481a3..707b898a52 100644
--- a/stmhal/Makefile
+++ b/stmhal/Makefile
@@ -60,6 +60,13 @@ endif
# uncomment this if you want libgcc
#LIBS += $(shell $(CC) -print-libgcc-file-name)
+SRC_LIB = $(addprefix lib/,\
+ libm/math.c \
+ libm/mathsincos.c \
+ libm/atanf.c \
+ libm/atan2f.c \
+ )
+
SRC_C = \
main.c \
string0.c \
@@ -84,8 +91,6 @@ SRC_C = \
uart.c \
usb.c \
printf.c \
- math.c \
- mathsincos.c \
gccollect.c \
pybstdio.c \
readline.c \
@@ -193,6 +198,7 @@ SRC_CC3K = $(addprefix $(CC3K_DIR)/,\
OBJ =
OBJ += $(PY_O)
+OBJ += $(addprefix $(BUILD)/, $(SRC_LIB:.c=.o))
OBJ += $(addprefix $(BUILD)/, $(SRC_C:.c=.o))
OBJ += $(addprefix $(BUILD)/, $(SRC_S:.s=.o))
OBJ += $(addprefix $(BUILD)/, $(SRC_HAL:.c=.o))
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;
-}
diff --git a/stmhal/mathsincos.c b/stmhal/mathsincos.c
deleted file mode 100644
index 9ea08e6c87..0000000000
--- a/stmhal/mathsincos.c
+++ /dev/null
@@ -1,627 +0,0 @@
-/*
- * This file is part of the Micro Python project, http://micropython.org/
- *
- * These math functions are taken from newlib 2.1.0, the newlib/libm directory.
- * Appropriate copyright headers are reproduced below.
- *
- * 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>
-
-/* @(#)fdlibm.h 5.1 93/09/24 */
-/*
- * ====================================================
- * 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 FLT_UWORD_IS_FINITE(x) ((x)<0x7f800000L)
-
-/* A union which permits us to convert between a float and a 32 bit
- int. */
-
-typedef union
-{
- float value;
- __uint32_t word;
-} ieee_float_shape_type;
-
-
-/* Get a 32 bit int from a float. */
-
-#define GET_FLOAT_WORD(i,d) \
-do { \
- ieee_float_shape_type gf_u; \
- gf_u.value = (d); \
- (i) = gf_u.word; \
-} while (0)
-
-/* Set a float from a 32 bit int. */
-
-#define SET_FLOAT_WORD(d,i) \
-do { \
- ieee_float_shape_type sf_u; \
- sf_u.word = (i); \
- (d) = sf_u.value; \
-} while (0)
-
-
-
-/* kf_rem_pio2.c -- float version of k_rem_pio2.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.
- * ====================================================
- */
-
-/* In the float version, the input parameter x contains 8 bit
- integers, not 24 bit integers. 113 bit precision is not supported. */
-
-#ifdef __STDC__
-static const int init_jk[] = {4,7,9}; /* initial value for jk */
-#else
-static int init_jk[] = {4,7,9};
-#endif
-
-#ifdef __STDC__
-static const float PIo2[] = {
-#else
-static float PIo2[] = {
-#endif
- 1.5703125000e+00, /* 0x3fc90000 */
- 4.5776367188e-04, /* 0x39f00000 */
- 2.5987625122e-05, /* 0x37da0000 */
- 7.5437128544e-08, /* 0x33a20000 */
- 6.0026650317e-11, /* 0x2e840000 */
- 7.3896444519e-13, /* 0x2b500000 */
- 5.3845816694e-15, /* 0x27c20000 */
- 5.6378512969e-18, /* 0x22d00000 */
- 8.3009228831e-20, /* 0x1fc40000 */
- 3.2756352257e-22, /* 0x1bc60000 */
- 6.3331015649e-25, /* 0x17440000 */
-};
-
-static const float
-zero = 0.0000000000e+00, /* 0x00000000 */
-one = 1.0000000000e+00, /* 0x3f800000 */
-two8 = 2.5600000000e+02, /* 0x43800000 */
-twon8 = 3.9062500000e-03; /* 0x3b800000 */
-
-int __kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const __int32_t *ipio2)
-{
- __int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih;
- float z,fw,f[20],fq[20],q[20];
-
- /* initialize jk*/
- jk = init_jk[prec];
- jp = jk;
-
- /* determine jx,jv,q0, note that 3>q0 */
- jx = nx-1;
- jv = (e0-3)/8; if(jv<0) jv=0;
- q0 = e0-8*(jv+1);
-
- /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */
- j = jv-jx; m = jx+jk;
- for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j];
-
- /* compute q[0],q[1],...q[jk] */
- for (i=0;i<=jk;i++) {
- for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw;
- }
-
- jz = jk;
-recompute:
- /* distill q[] into iq[] reversingly */
- for(i=0,j=jz,z=q[jz];j>0;i++,j--) {
- fw = (float)((__int32_t)(twon8* z));
- iq[i] = (__int32_t)(z-two8*fw);
- z = q[j-1]+fw;
- }
-
- /* compute n */
- z = scalbnf(z,(int)q0); /* actual value of z */
- z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */
- n = (__int32_t) z;
- z -= (float)n;
- ih = 0;
- if(q0>0) { /* need iq[jz-1] to determine n */
- i = (iq[jz-1]>>(8-q0)); n += i;
- iq[jz-1] -= i<<(8-q0);
- ih = iq[jz-1]>>(7-q0);
- }
- else if(q0==0) ih = iq[jz-1]>>8;
- else if(z>=(float)0.5) ih=2;
-
- if(ih>0) { /* q > 0.5 */
- n += 1; carry = 0;
- for(i=0;i<jz ;i++) { /* compute 1-q */
- j = iq[i];
- if(carry==0) {
- if(j!=0) {
- carry = 1; iq[i] = 0x100- j;
- }
- } else iq[i] = 0xff - j;
- }
- if(q0>0) { /* rare case: chance is 1 in 12 */
- switch(q0) {
- case 1:
- iq[jz-1] &= 0x7f; break;
- case 2:
- iq[jz-1] &= 0x3f; break;
- }
- }
- if(ih==2) {
- z = one - z;
- if(carry!=0) z -= scalbnf(one,(int)q0);
- }
- }
-
- /* check if recomputation is needed */
- if(z==zero) {
- j = 0;
- for (i=jz-1;i>=jk;i--) j |= iq[i];
- if(j==0) { /* need recomputation */
- for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */
-
- for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */
- f[jx+i] = (float) ipio2[jv+i];
- for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j];
- q[i] = fw;
- }
- jz += k;
- goto recompute;
- }
- }
-
- /* chop off zero terms */
- if(z==(float)0.0) {
- jz -= 1; q0 -= 8;
- while(iq[jz]==0) { jz--; q0-=8;}
- } else { /* break z into 8-bit if necessary */
- z = scalbnf(z,-(int)q0);
- if(z>=two8) {
- fw = (float)((__int32_t)(twon8*z));
- iq[jz] = (__int32_t)(z-two8*fw);
- jz += 1; q0 += 8;
- iq[jz] = (__int32_t) fw;
- } else iq[jz] = (__int32_t) z ;
- }
-
- /* convert integer "bit" chunk to floating-point value */
- fw = scalbnf(one,(int)q0);
- for(i=jz;i>=0;i--) {
- q[i] = fw*(float)iq[i]; fw*=twon8;
- }
-
- /* compute PIo2[0,...,jp]*q[jz,...,0] */
- for(i=jz;i>=0;i--) {
- for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k];
- fq[jz-i] = fw;
- }
-
- /* compress fq[] into y[] */
- switch(prec) {
- case 0:
- fw = 0.0;
- for (i=jz;i>=0;i--) fw += fq[i];
- y[0] = (ih==0)? fw: -fw;
- break;
- case 1:
- case 2:
- fw = 0.0;
- for (i=jz;i>=0;i--) fw += fq[i];
- y[0] = (ih==0)? fw: -fw;
- fw = fq[0]-fw;
- for (i=1;i<=jz;i++) fw += fq[i];
- y[1] = (ih==0)? fw: -fw;
- break;
- case 3: /* painful */
- for (i=jz;i>0;i--) {
- fw = fq[i-1]+fq[i];
- fq[i] += fq[i-1]-fw;
- fq[i-1] = fw;
- }
- for (i=jz;i>1;i--) {
- fw = fq[i-1]+fq[i];
- fq[i] += fq[i-1]-fw;
- fq[i-1] = fw;
- }
- for (fw=0.0,i=jz;i>=2;i--) fw += fq[i];
- if(ih==0) {
- y[0] = fq[0]; y[1] = fq[1]; y[2] = fw;
- } else {
- y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw;
- }
- }
- return n&7;
-}
-
-
-/* ef_rem_pio2.c -- float version of e_rem_pio2.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.
- * ====================================================
- *
- */
-
-/* __ieee754_rem_pio2f(x,y)
- *
- * return the remainder of x rem pi/2 in y[0]+y[1]
- * use __kernel_rem_pio2f()
- */
-
-
-/*
- * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi
- */
-static const __int32_t two_over_pi[] = {
-0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC,
-0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62,
-0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63,
-0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A,
-0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09,
-0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29,
-0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44,
-0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41,
-0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C,
-0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8,
-0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11,
-0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF,
-0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E,
-0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5,
-0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92,
-0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08,
-0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0,
-0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3,
-0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85,
-0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80,
-0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA,
-0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B,
-};
-
-/* This array is like the one in e_rem_pio2.c, but the numbers are
- single precision and the last 8 bits are forced to 0. */
-static const __int32_t npio2_hw[] = {
-0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00,
-0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00,
-0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100,
-0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00,
-0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00,
-0x4242c700, 0x42490f00
-};
-
-/*
- * invpio2: 24 bits of 2/pi
- * pio2_1: first 17 bit of pi/2
- * pio2_1t: pi/2 - pio2_1
- * pio2_2: second 17 bit of pi/2
- * pio2_2t: pi/2 - (pio2_1+pio2_2)
- * pio2_3: third 17 bit of pi/2
- * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3)
- */
-
-static const float
-half = 5.0000000000e-01, /* 0x3f000000 */
-invpio2 = 6.3661980629e-01, /* 0x3f22f984 */
-pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */
-pio2_1t = 1.0804334124e-05, /* 0x37354443 */
-pio2_2 = 1.0804273188e-05, /* 0x37354400 */
-pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */
-pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */
-pio2_3t = 6.1232342629e-17; /* 0x248d3132 */
-
-__int32_t __ieee754_rem_pio2f(float x, float *y)
-{
- float z,w,t,r,fn;
- float tx[3];
- __int32_t i,j,n,ix,hx;
- int e0,nx;
-
- GET_FLOAT_WORD(hx,x);
- ix = hx&0x7fffffff;
- if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */
- {y[0] = x; y[1] = 0; return 0;}
- if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */
- if(hx>0) {
- z = x - pio2_1;
- if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
- y[0] = z - pio2_1t;
- y[1] = (z-y[0])-pio2_1t;
- } else { /* near pi/2, use 24+24+24 bit pi */
- z -= pio2_2;
- y[0] = z - pio2_2t;
- y[1] = (z-y[0])-pio2_2t;
- }
- return 1;
- } else { /* negative x */
- z = x + pio2_1;
- if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */
- y[0] = z + pio2_1t;
- y[1] = (z-y[0])+pio2_1t;
- } else { /* near pi/2, use 24+24+24 bit pi */
- z += pio2_2;
- y[0] = z + pio2_2t;
- y[1] = (z-y[0])+pio2_2t;
- }
- return -1;
- }
- }
- if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */
- t = fabsf(x);
- n = (__int32_t) (t*invpio2+half);
- fn = (float)n;
- r = t-fn*pio2_1;
- w = fn*pio2_1t; /* 1st round good to 40 bit */
- if(n<32&&(ix&0xffffff00)!=npio2_hw[n-1]) {
- y[0] = r-w; /* quick check no cancellation */
- } else {
- __uint32_t high;
- j = ix>>23;
- y[0] = r-w;
- GET_FLOAT_WORD(high,y[0]);
- i = j-((high>>23)&0xff);
- if(i>8) { /* 2nd iteration needed, good to 57 */
- t = r;
- w = fn*pio2_2;
- r = t-w;
- w = fn*pio2_2t-((t-r)-w);
- y[0] = r-w;
- GET_FLOAT_WORD(high,y[0]);
- i = j-((high>>23)&0xff);
- if(i>25) { /* 3rd iteration need, 74 bits acc */
- t = r; /* will cover all possible cases */
- w = fn*pio2_3;
- r = t-w;
- w = fn*pio2_3t-((t-r)-w);
- y[0] = r-w;
- }
- }
- }
- y[1] = (r-y[0])-w;
- if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
- else return n;
- }
- /*
- * all other (large) arguments
- */
- if(!FLT_UWORD_IS_FINITE(ix)) {
- y[0]=y[1]=x-x; return 0;
- }
- /* set z = scalbn(|x|,ilogb(x)-7) */
- e0 = (int)((ix>>23)-134); /* e0 = ilogb(z)-7; */
- SET_FLOAT_WORD(z, ix - ((__int32_t)e0<<23));
- for(i=0;i<2;i++) {
- tx[i] = (float)((__int32_t)(z));
- z = (z-tx[i])*two8;
- }
- tx[2] = z;
- nx = 3;
- while(tx[nx-1]==zero) nx--; /* skip zero term */
- n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi);
- if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;}
- return n;
-}
-
-
-/* kf_sin.c -- float version of k_sin.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
-S1 = -1.6666667163e-01, /* 0xbe2aaaab */
-S2 = 8.3333337680e-03, /* 0x3c088889 */
-S3 = -1.9841270114e-04, /* 0xb9500d01 */
-S4 = 2.7557314297e-06, /* 0x3638ef1b */
-S5 = -2.5050759689e-08, /* 0xb2d72f34 */
-S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */
-
-float __kernel_sinf(float x, float y, int iy) /* iy=0 if y is zero */
-{
- float z,r,v;
- __int32_t ix;
- GET_FLOAT_WORD(ix,x);
- ix &= 0x7fffffff; /* high word of x */
- if(ix<0x32000000) /* |x| < 2**-27 */
- {if((int)x==0) return x;} /* generate inexact */
- z = x*x;
- v = z*x;
- r = S2+z*(S3+z*(S4+z*(S5+z*S6)));
- if(iy==0) return x+v*(S1+z*r);
- else return x-((z*(half*y-v*r)-y)-v*S1);
-}
-
-
-
-/* kf_cos.c -- float version of k_cos.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
-C1 = 4.1666667908e-02, /* 0x3d2aaaab */
-C2 = -1.3888889225e-03, /* 0xbab60b61 */
-C3 = 2.4801587642e-05, /* 0x37d00d01 */
-C4 = -2.7557314297e-07, /* 0xb493f27c */
-C5 = 2.0875723372e-09, /* 0x310f74f6 */
-C6 = -1.1359647598e-11; /* 0xad47d74e */
-
-float __kernel_cosf(float x, float y)
-{
- float a,hz,z,r,qx;
- __int32_t ix;
- GET_FLOAT_WORD(ix,x);
- ix &= 0x7fffffff; /* ix = |x|'s high word*/
- if(ix<0x32000000) { /* if x < 2**27 */
- if(((int)x)==0) return one; /* generate inexact */
- }
- z = x*x;
- r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
- if(ix < 0x3e99999a) /* if |x| < 0.3 */
- return one - ((float)0.5*z - (z*r - x*y));
- else {
- if(ix > 0x3f480000) { /* x > 0.78125 */
- qx = (float)0.28125;
- } else {
- SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */
- }
- hz = (float)0.5*z-qx;
- a = one-qx;
- return a - (hz - (z*r-x*y));
- }
-}
-
-
-/* sf_sin.c -- float version of s_sin.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.
- * ====================================================
- */
-
-
-float sinf(float x)
-{
- float y[2],z=0.0;
- __int32_t n,ix;
-
- GET_FLOAT_WORD(ix,x);
-
- /* |x| ~< pi/4 */
- ix &= 0x7fffffff;
- if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0);
-
- /* sin(Inf or NaN) is NaN */
- else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;
-
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2f(x,y);
- switch(n&3) {
- case 0: return __kernel_sinf(y[0],y[1],1);
- case 1: return __kernel_cosf(y[0],y[1]);
- case 2: return -__kernel_sinf(y[0],y[1],1);
- default:
- return -__kernel_cosf(y[0],y[1]);
- }
- }
-}
-
-
-/* sf_cos.c -- float version of s_cos.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.
- * ====================================================
- */
-
-
-float cosf(float x)
-{
- float y[2],z=0.0;
- __int32_t n,ix;
-
- GET_FLOAT_WORD(ix,x);
-
- /* |x| ~< pi/4 */
- ix &= 0x7fffffff;
- if(ix <= 0x3f490fd8) return __kernel_cosf(x,z);
-
- /* cos(Inf or NaN) is NaN */
- else if (!FLT_UWORD_IS_FINITE(ix)) return x-x;
-
- /* argument reduction needed */
- else {
- n = __ieee754_rem_pio2f(x,y);
- switch(n&3) {
- case 0: return __kernel_cosf(y[0],y[1]);
- case 1: return -__kernel_sinf(y[0],y[1],1);
- case 2: return -__kernel_cosf(y[0],y[1]);
- default:
- return __kernel_sinf(y[0],y[1],1);
- }
- }
-}
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