diff options
Diffstat (limited to '3rdparty/SDL2/src/libm')
-rw-r--r-- | 3rdparty/SDL2/src/libm/e_atan2.c | 116 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/e_log.c | 167 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/e_pow.c | 342 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/e_rem_pio2.c | 201 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/e_sqrt.c | 464 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/k_cos.c | 100 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/k_rem_pio2.c | 363 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/k_sin.c | 87 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/k_tan.c | 118 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/math_libm.h | 38 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/math_private.h | 221 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/s_atan.c | 115 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/s_copysign.c | 42 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/s_cos.c | 91 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/s_fabs.c | 39 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/s_floor.c | 96 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/s_scalbn.c | 79 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/s_sin.c | 91 | ||||
-rw-r--r-- | 3rdparty/SDL2/src/libm/s_tan.c | 67 |
19 files changed, 0 insertions, 2837 deletions
diff --git a/3rdparty/SDL2/src/libm/e_atan2.c b/3rdparty/SDL2/src/libm/e_atan2.c deleted file mode 100644 index f7b91a3e1b6..00000000000 --- a/3rdparty/SDL2/src/libm/e_atan2.c +++ /dev/null @@ -1,116 +0,0 @@ -/* - * ==================================================== - * 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_atan2(y,x) - * Method : - * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). - * 2. Reduce x to positive by (if x and y are unexceptional): - * ARG (x+iy) = arctan(y/x) ... if x > 0, - * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, - * - * Special cases: - * - * ATAN2((anything), NaN ) is NaN; - * ATAN2(NAN , (anything) ) is NaN; - * ATAN2(+-0, +(anything but NaN)) is +-0 ; - * ATAN2(+-0, -(anything but NaN)) is +-pi ; - * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; - * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; - * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; - * ATAN2(+-INF,+INF ) is +-pi/4 ; - * ATAN2(+-INF,-INF ) is +-3pi/4; - * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; - * - * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ - -#include "math_libm.h" -#include "math_private.h" - -static const double -tiny = 1.0e-300, -zero = 0.0, -pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ -pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ -pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ -pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ - -double attribute_hidden __ieee754_atan2(double y, double x) -{ - double z; - int32_t k,m,hx,hy,ix,iy; - u_int32_t lx,ly; - - EXTRACT_WORDS(hx,lx,x); - ix = hx&0x7fffffff; - EXTRACT_WORDS(hy,ly,y); - iy = hy&0x7fffffff; - if(((ix|((lx|-(int32_t)lx)>>31))>0x7ff00000)|| - ((iy|((ly|-(int32_t)ly)>>31))>0x7ff00000)) /* x or y is NaN */ - return x+y; - if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ - m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ - - /* when y = 0 */ - if((iy|ly)==0) { - switch(m) { - case 0: - case 1: return y; /* atan(+-0,+anything)=+-0 */ - case 2: return pi+tiny;/* atan(+0,-anything) = pi */ - case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ - } - } - /* when x = 0 */ - if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; - - /* when x is INF */ - if(ix==0x7ff00000) { - if(iy==0x7ff00000) { - switch(m) { - case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ - case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ - case 2: return 3.0*pi_o_4+tiny;/* atan(+INF,-INF) */ - case 3: return -3.0*pi_o_4-tiny;/* atan(-INF,-INF) */ - } - } else { - switch(m) { - case 0: return zero ; /* atan(+...,+INF) */ - case 1: return -zero ; /* atan(-...,+INF) */ - case 2: return pi+tiny ; /* atan(+...,-INF) */ - case 3: return -pi-tiny ; /* atan(-...,-INF) */ - } - } - } - /* when y is INF */ - if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; - - /* compute y/x */ - k = (iy-ix)>>20; - if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ - else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ - else z=atan(fabs(y/x)); /* safe to do y/x */ - switch (m) { - case 0: return z ; /* atan(+,+) */ - case 1: { - u_int32_t zh; - GET_HIGH_WORD(zh,z); - SET_HIGH_WORD(z,zh ^ 0x80000000); - } - return z ; /* atan(-,+) */ - case 2: return pi-(z-pi_lo);/* atan(+,-) */ - default: /* case 3 */ - return (z-pi_lo)-pi;/* atan(-,-) */ - } -} diff --git a/3rdparty/SDL2/src/libm/e_log.c b/3rdparty/SDL2/src/libm/e_log.c deleted file mode 100644 index da64138cd18..00000000000 --- a/3rdparty/SDL2/src/libm/e_log.c +++ /dev/null @@ -1,167 +0,0 @@ -/* @(#)e_log.c 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. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: e_log.c,v 1.8 1995/05/10 20:45:49 jtc Exp $"; -#endif - -/* __ieee754_log(x) - * Return the logrithm of x - * - * Method : - * 1. Argument Reduction: find k and f such that - * x = 2^k * (1+f), - * where sqrt(2)/2 < 1+f < sqrt(2) . - * - * 2. Approximation of log(1+f). - * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) - * = 2s + 2/3 s**3 + 2/5 s**5 + ....., - * = 2s + s*R - * We use a special Reme algorithm on [0,0.1716] to generate - * a polynomial of degree 14 to approximate R The maximum error - * of this polynomial approximation is bounded by 2**-58.45. In - * other words, - * 2 4 6 8 10 12 14 - * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s - * (the values of Lg1 to Lg7 are listed in the program) - * and - * | 2 14 | -58.45 - * | Lg1*s +...+Lg7*s - R(z) | <= 2 - * | | - * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. - * In order to guarantee error in log below 1ulp, we compute log - * by - * log(1+f) = f - s*(f - R) (if f is not too large) - * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) - * - * 3. Finally, log(x) = k*ln2 + log(1+f). - * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) - * Here ln2 is split into two floating point number: - * ln2_hi + ln2_lo, - * where n*ln2_hi is always exact for |n| < 2000. - * - * Special cases: - * log(x) is NaN with signal if x < 0 (including -INF) ; - * log(+INF) is +INF; log(0) is -INF with signal; - * log(NaN) is that NaN with no signal. - * - * Accuracy: - * according to an error analysis, the error is always less than - * 1 ulp (unit in the last place). - * - * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ - -#include "math_libm.h" -#include "math_private.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif - ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ - ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ - two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ - Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ - Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ - Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ - Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ - Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ - Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ - Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ - -#ifdef __STDC__ -static const double zero = 0.0; -#else -static double zero = 0.0; -#endif - -#ifdef __STDC__ -double attribute_hidden -__ieee754_log(double x) -#else -double attribute_hidden -__ieee754_log(x) - double x; -#endif -{ - double hfsq, f, s, z, R, w, t1, t2, dk; - int32_t k, hx, i, j; - u_int32_t lx; - - EXTRACT_WORDS(hx, lx, x); - - k = 0; - if (hx < 0x00100000) { /* x < 2**-1022 */ - if (((hx & 0x7fffffff) | lx) == 0) - return -two54 / zero; /* log(+-0)=-inf */ - if (hx < 0) - return (x - x) / zero; /* log(-#) = NaN */ - k -= 54; - x *= two54; /* subnormal number, scale up x */ - GET_HIGH_WORD(hx, x); - } - if (hx >= 0x7ff00000) - return x + x; - k += (hx >> 20) - 1023; - hx &= 0x000fffff; - i = (hx + 0x95f64) & 0x100000; - SET_HIGH_WORD(x, hx | (i ^ 0x3ff00000)); /* normalize x or x/2 */ - k += (i >> 20); - f = x - 1.0; - if ((0x000fffff & (2 + hx)) < 3) { /* |f| < 2**-20 */ - if (f == zero) { - if (k == 0) - return zero; - else { - dk = (double) k; - return dk * ln2_hi + dk * ln2_lo; - } - } - R = f * f * (0.5 - 0.33333333333333333 * f); - if (k == 0) - return f - R; - else { - dk = (double) k; - return dk * ln2_hi - ((R - dk * ln2_lo) - f); - } - } - s = f / (2.0 + f); - dk = (double) k; - z = s * s; - i = hx - 0x6147a; - w = z * z; - j = 0x6b851 - hx; - t1 = w * (Lg2 + w * (Lg4 + w * Lg6)); - t2 = z * (Lg1 + w * (Lg3 + w * (Lg5 + w * Lg7))); - i |= j; - R = t2 + t1; - if (i > 0) { - hfsq = 0.5 * f * f; - if (k == 0) - return f - (hfsq - s * (hfsq + R)); - else - return dk * ln2_hi - ((hfsq - (s * (hfsq + R) + dk * ln2_lo)) - - f); - } else { - if (k == 0) - return f - s * (f - R); - else - return dk * ln2_hi - ((s * (f - R) - dk * ln2_lo) - f); - } -} diff --git a/3rdparty/SDL2/src/libm/e_pow.c b/3rdparty/SDL2/src/libm/e_pow.c deleted file mode 100644 index 686da2e5564..00000000000 --- a/3rdparty/SDL2/src/libm/e_pow.c +++ /dev/null @@ -1,342 +0,0 @@ -/* @(#)e_pow.c 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. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static char rcsid[] = "$NetBSD: e_pow.c,v 1.9 1995/05/12 04:57:32 jtc Exp $"; -#endif - -/* __ieee754_pow(x,y) return x**y - * - * n - * Method: Let x = 2 * (1+f) - * 1. Compute and return log2(x) in two pieces: - * log2(x) = w1 + w2, - * where w1 has 53-24 = 29 bit trailing zeros. - * 2. Perform y*log2(x) = n+y' by simulating muti-precision - * arithmetic, where |y'|<=0.5. - * 3. Return x**y = 2**n*exp(y'*log2) - * - * Special cases: - * 1. (anything) ** 0 is 1 - * 2. (anything) ** 1 is itself - * 3. (anything) ** NAN is NAN - * 4. NAN ** (anything except 0) is NAN - * 5. +-(|x| > 1) ** +INF is +INF - * 6. +-(|x| > 1) ** -INF is +0 - * 7. +-(|x| < 1) ** +INF is +0 - * 8. +-(|x| < 1) ** -INF is +INF - * 9. +-1 ** +-INF is NAN - * 10. +0 ** (+anything except 0, NAN) is +0 - * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 - * 12. +0 ** (-anything except 0, NAN) is +INF - * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF - * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) - * 15. +INF ** (+anything except 0,NAN) is +INF - * 16. +INF ** (-anything except 0,NAN) is +0 - * 17. -INF ** (anything) = -0 ** (-anything) - * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) - * 19. (-anything except 0 and inf) ** (non-integer) is NAN - * - * Accuracy: - * pow(x,y) returns x**y nearly rounded. In particular - * pow(integer,integer) - * always returns the correct integer provided it is - * representable. - * - * Constants : - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ - -#include "math_libm.h" -#include "math_private.h" - -libm_hidden_proto(scalbn) - libm_hidden_proto(fabs) -#ifdef __STDC__ - static const double -#else - static double -#endif - bp[] = { 1.0, 1.5, }, dp_h[] = { - 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ - - dp_l[] = { - 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ - - zero = 0.0, one = 1.0, two = 2.0, two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ - huge_val = 1.0e300, tiny = 1.0e-300, - /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ - L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ - L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ - L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ - L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ - L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ - L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ - P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ - P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ - P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ - P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ - P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ - lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ - lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ - lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ - ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ - cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ - cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ - cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h */ - ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ - ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2 */ - ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail */ - -#ifdef __STDC__ - double attribute_hidden __ieee754_pow(double x, double y) -#else - double attribute_hidden __ieee754_pow(x, y) - double x, y; -#endif - { - double z, ax, z_h, z_l, p_h, p_l; - double y1, t1, t2, r, s, t, u, v, w; - int32_t i, j, k, yisint, n; - int32_t hx, hy, ix, iy; - u_int32_t lx, ly; - - EXTRACT_WORDS(hx, lx, x); - EXTRACT_WORDS(hy, ly, y); - ix = hx & 0x7fffffff; - iy = hy & 0x7fffffff; - - /* y==zero: x**0 = 1 */ - if ((iy | ly) == 0) - return one; - - /* +-NaN return x+y */ - if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) || - iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0))) - 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 >= 0x43400000) - yisint = 2; /* even integer y */ - else if (iy >= 0x3ff00000) { - k = (iy >> 20) - 0x3ff; /* exponent */ - if (k > 20) { - j = ly >> (52 - k); - if ((j << (52 - k)) == ly) - yisint = 2 - (j & 1); - } else if (ly == 0) { - j = iy >> (20 - k); - if ((j << (20 - k)) == iy) - yisint = 2 - (j & 1); - } - } - } - - /* special value of y */ - if (ly == 0) { - if (iy == 0x7ff00000) { /* y is +-inf */ - if (((ix - 0x3ff00000) | lx) == 0) - return y - y; /* inf**+-1 is NaN */ - else if (ix >= 0x3ff00000) /* (|x|>1)**+-inf = inf,0 */ - return (hy >= 0) ? y : zero; - else /* (|x|<1)**-,+inf = inf,0 */ - return (hy < 0) ? -y : zero; - } - if (iy == 0x3ff00000) { /* y is +-1 */ - if (hy < 0) - return one / x; - else - return x; - } - if (hy == 0x40000000) - return x * x; /* y is 2 */ - if (hy == 0x3fe00000) { /* y is 0.5 */ - if (hx >= 0) /* x >= +0 */ - return __ieee754_sqrt(x); - } - } - - ax = fabs(x); - /* special value of x */ - if (lx == 0) { - if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) { - z = ax; /* x is +-0,+-inf,+-1 */ - if (hy < 0) - z = one / z; /* z = (1/|x|) */ - if (hx < 0) { - if (((ix - 0x3ff00000) | 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; - } - } - - /* (x<0)**(non-int) is NaN */ - if (((((u_int32_t) hx >> 31) - 1) | yisint) == 0) - return (x - x) / (x - x); - - /* |y| is huge */ - if (iy > 0x41e00000) { /* if |y| > 2**31 */ - if (iy > 0x43f00000) { /* if |y| > 2**64, must o/uflow */ - if (ix <= 0x3fefffff) - return (hy < 0) ? huge_val * huge_val : tiny * tiny; - if (ix >= 0x3ff00000) - return (hy > 0) ? huge_val * huge_val : tiny * tiny; - } - /* over/underflow if x is not close to one */ - if (ix < 0x3fefffff) - return (hy < 0) ? huge_val * huge_val : tiny * tiny; - if (ix > 0x3ff00000) - return (hy > 0) ? huge_val * huge_val : 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 = x - 1; /* t has 20 trailing zeros */ - w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25)); - u = ivln2_h * t; /* ivln2_h has 21 sig. bits */ - v = t * ivln2_l - w * ivln2; - t1 = u + v; - SET_LOW_WORD(t1, 0); - t2 = v - (t1 - u); - } else { - double s2, s_h, s_l, t_h, t_l; - n = 0; - /* take care subnormal number */ - if (ix < 0x00100000) { - ax *= two53; - n -= 53; - GET_HIGH_WORD(ix, ax); - } - n += ((ix) >> 20) - 0x3ff; - j = ix & 0x000fffff; - /* determine interval */ - ix = j | 0x3ff00000; /* normalize ix */ - if (j <= 0x3988E) - k = 0; /* |x|<sqrt(3/2) */ - else if (j < 0xBB67A) - k = 1; /* |x|<sqrt(3) */ - else { - k = 0; - n += 1; - ix -= 0x00100000; - } - SET_HIGH_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 = one / (ax + bp[k]); - s = u * v; - s_h = s; - SET_LOW_WORD(s_h, 0); - /* t_h=ax+bp[k] High */ - t_h = zero; - SET_HIGH_WORD(t_h, - ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18)); - 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 = 3.0 + s2 + r; - SET_LOW_WORD(t_h, 0); - t_l = r - ((t_h - 3.0) - 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; - SET_LOW_WORD(p_h, 0); - 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 = (double) n; - t1 = (((z_h + z_l) + dp_h[k]) + t); - SET_LOW_WORD(t1, 0); - t2 = z_l - (((t1 - t) - dp_h[k]) - z_h); - } - - s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ - if (((((u_int32_t) hx >> 31) - 1) | (yisint - 1)) == 0) - s = -one; /* (-ve)**(odd int) */ - - /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ - y1 = y; - SET_LOW_WORD(y1, 0); - p_l = (y - y1) * t1 + y * t2; - p_h = y1 * t1; - z = p_l + p_h; - EXTRACT_WORDS(j, i, z); - if (j >= 0x40900000) { /* z >= 1024 */ - if (((j - 0x40900000) | i) != 0) /* if z > 1024 */ - return s * huge_val * huge_val; /* overflow */ - else { - if (p_l + ovt > z - p_h) - return s * huge_val * huge_val; /* overflow */ - } - } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */ - if (((j - 0xc090cc00) | i) != 0) /* z < -1075 */ - return s * tiny * tiny; /* underflow */ - else { - if (p_l <= z - p_h) - return s * tiny * tiny; /* underflow */ - } - } - /* - * compute 2**(p_h+p_l) - */ - i = j & 0x7fffffff; - k = (i >> 20) - 0x3ff; - n = 0; - if (i > 0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ - n = j + (0x00100000 >> (k + 1)); - k = ((n & 0x7fffffff) >> 20) - 0x3ff; /* new k for n */ - t = zero; - SET_HIGH_WORD(t, n & ~(0x000fffff >> k)); - n = ((n & 0x000fffff) | 0x00100000) >> (20 - k); - if (j < 0) - n = -n; - p_h -= t; - } - t = p_l + p_h; - SET_LOW_WORD(t, 0); - 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 - two) - (w + z * w); - z = one - (r - z); - GET_HIGH_WORD(j, z); - j += (n << 20); - if ((j >> 20) <= 0) - z = scalbn(z, n); /* subnormal output */ - else - SET_HIGH_WORD(z, j); - return s * z; - } diff --git a/3rdparty/SDL2/src/libm/e_rem_pio2.c b/3rdparty/SDL2/src/libm/e_rem_pio2.c deleted file mode 100644 index a8ffe31421b..00000000000 --- a/3rdparty/SDL2/src/libm/e_rem_pio2.c +++ /dev/null @@ -1,201 +0,0 @@ -/* @(#)e_rem_pio2.c 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. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: e_rem_pio2.c,v 1.8 1995/05/10 20:46:02 jtc Exp $"; -#endif - -/* __ieee754_rem_pio2(x,y) - * - * return the remainder of x rem pi/2 in y[0]+y[1] - * use __kernel_rem_pio2() - */ - -#include "math_libm.h" -#include "math_private.h" - -libm_hidden_proto(fabs) - -/* - * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi - */ -#ifdef __STDC__ - static const int32_t two_over_pi[] = { -#else - static int32_t two_over_pi[] = { -#endif - 0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, - 0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, - 0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, - 0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, - 0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, - 0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, - 0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, - 0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, - 0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, - 0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, - 0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, - }; - -#ifdef __STDC__ -static const int32_t npio2_hw[] = { -#else -static int32_t npio2_hw[] = { -#endif - 0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, - 0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, - 0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, - 0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, - 0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, - 0x404858EB, 0x404921FB, -}; - -/* - * invpio2: 53 bits of 2/pi - * pio2_1: first 33 bit of pi/2 - * pio2_1t: pi/2 - pio2_1 - * pio2_2: second 33 bit of pi/2 - * pio2_2t: pi/2 - (pio2_1+pio2_2) - * pio2_3: third 33 bit of pi/2 - * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) - */ - -#ifdef __STDC__ -static const double -#else -static double -#endif - zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ - half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ - two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ - invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ - pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ - pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ - pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ - pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ - pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ - pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ - -#ifdef __STDC__ -int32_t attribute_hidden -__ieee754_rem_pio2(double x, double *y) -#else -int32_t attribute_hidden -__ieee754_rem_pio2(x, y) - double x, y[]; -#endif -{ - double z = 0.0, w, t, r, fn; - double tx[3]; - int32_t e0, i, j, nx, n, ix, hx; - u_int32_t low; - - GET_HIGH_WORD(hx, x); /* high word of x */ - ix = hx & 0x7fffffff; - if (ix <= 0x3fe921fb) { /* |x| ~<= pi/4 , no need for reduction */ - y[0] = x; - y[1] = 0; - return 0; - } - if (ix < 0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ - if (hx > 0) { - z = x - pio2_1; - if (ix != 0x3ff921fb) { /* 33+53 bit pi is good enough */ - y[0] = z - pio2_1t; - y[1] = (z - y[0]) - pio2_1t; - } else { /* near pi/2, use 33+33+53 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 != 0x3ff921fb) { /* 33+53 bit pi is good enough */ - y[0] = z + pio2_1t; - y[1] = (z - y[0]) + pio2_1t; - } else { /* near pi/2, use 33+33+53 bit pi */ - z += pio2_2; - y[0] = z + pio2_2t; - y[1] = (z - y[0]) + pio2_2t; - } - return -1; - } - } - if (ix <= 0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ - t = fabs(x); - n = (int32_t) (t * invpio2 + half); - fn = (double) n; - r = t - fn * pio2_1; - w = fn * pio2_1t; /* 1st round good to 85 bit */ - if (n < 32 && ix != npio2_hw[n - 1]) { - y[0] = r - w; /* quick check no cancellation */ - } else { - u_int32_t high; - j = ix >> 20; - y[0] = r - w; - GET_HIGH_WORD(high, y[0]); - i = j - ((high >> 20) & 0x7ff); - if (i > 16) { /* 2nd iteration needed, good to 118 */ - t = r; - w = fn * pio2_2; - r = t - w; - w = fn * pio2_2t - ((t - r) - w); - y[0] = r - w; - GET_HIGH_WORD(high, y[0]); - i = j - ((high >> 20) & 0x7ff); - if (i > 49) { /* 3rd iteration need, 151 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 (ix >= 0x7ff00000) { /* x is inf or NaN */ - y[0] = y[1] = x - x; - return 0; - } - /* set z = scalbn(|x|,ilogb(x)-23) */ - GET_LOW_WORD(low, x); - SET_LOW_WORD(z, low); - e0 = (ix >> 20) - 1046; /* e0 = ilogb(z)-23; */ - SET_HIGH_WORD(z, ix - ((int32_t) (e0 << 20))); - for (i = 0; i < 2; i++) { - tx[i] = (double) ((int32_t) (z)); - z = (z - tx[i]) * two24; - } - tx[2] = z; - nx = 3; - while (tx[nx - 1] == zero) - nx--; /* skip zero term */ - n = __kernel_rem_pio2(tx, y, e0, nx, 2, two_over_pi); - if (hx < 0) { - y[0] = -y[0]; - y[1] = -y[1]; - return -n; - } - return n; -} diff --git a/3rdparty/SDL2/src/libm/e_sqrt.c b/3rdparty/SDL2/src/libm/e_sqrt.c deleted file mode 100644 index b8b8bec6fab..00000000000 --- a/3rdparty/SDL2/src/libm/e_sqrt.c +++ /dev/null @@ -1,464 +0,0 @@ -/* @(#)e_sqrt.c 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. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: e_sqrt.c,v 1.8 1995/05/10 20:46:17 jtc Exp $"; -#endif - -/* __ieee754_sqrt(x) - * Return correctly rounded sqrt. - * ------------------------------------------ - * | Use the hardware sqrt if you have one | - * ------------------------------------------ - * Method: - * Bit by bit method using integer arithmetic. (Slow, but portable) - * 1. Normalization - * Scale x to y in [1,4) with even powers of 2: - * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then - * sqrt(x) = 2^k * sqrt(y) - * 2. Bit by bit computation - * Let q = sqrt(y) truncated to i bit after binary point (q = 1), - * i 0 - * i+1 2 - * s = 2*q , and y = 2 * ( y - q ). (1) - * i i i i - * - * To compute q from q , one checks whether - * i+1 i - * - * -(i+1) 2 - * (q + 2 ) <= y. (2) - * i - * -(i+1) - * If (2) is false, then q = q ; otherwise q = q + 2 . - * i+1 i i+1 i - * - * With some algebric manipulation, it is not difficult to see - * that (2) is equivalent to - * -(i+1) - * s + 2 <= y (3) - * i i - * - * The advantage of (3) is that s and y can be computed by - * i i - * the following recurrence formula: - * if (3) is false - * - * s = s , y = y ; (4) - * i+1 i i+1 i - * - * otherwise, - * -i -(i+1) - * s = s + 2 , y = y - s - 2 (5) - * i+1 i i+1 i i - * - * One may easily use induction to prove (4) and (5). - * Note. Since the left hand side of (3) contain only i+2 bits, - * it does not necessary to do a full (53-bit) comparison - * in (3). - * 3. Final rounding - * After generating the 53 bits result, we compute one more bit. - * Together with the remainder, we can decide whether the - * result is exact, bigger than 1/2ulp, or less than 1/2ulp - * (it will never equal to 1/2ulp). - * The rounding mode can be detected by checking whether - * huge + tiny is equal to huge, and whether huge - tiny is - * equal to huge for some floating point number "huge" and "tiny". - * - * Special cases: - * sqrt(+-0) = +-0 ... exact - * sqrt(inf) = inf - * sqrt(-ve) = NaN ... with invalid signal - * sqrt(NaN) = NaN ... with invalid signal for signaling NaN - * - * Other methods : see the appended file at the end of the program below. - *--------------- - */ - -#include "math_libm.h" -#include "math_private.h" - -#ifdef __STDC__ -static const double one = 1.0, tiny = 1.0e-300; -#else -static double one = 1.0, tiny = 1.0e-300; -#endif - -#ifdef __STDC__ -double attribute_hidden -__ieee754_sqrt(double x) -#else -double attribute_hidden -__ieee754_sqrt(x) - double x; -#endif -{ - double z; - int32_t sign = (int) 0x80000000; - int32_t ix0, s0, q, m, t, i; - u_int32_t r, t1, s1, ix1, q1; - - EXTRACT_WORDS(ix0, ix1, x); - - /* take care of Inf and NaN */ - if ((ix0 & 0x7ff00000) == 0x7ff00000) { - return x * x + x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf - sqrt(-inf)=sNaN */ - } - /* take care of zero */ - if (ix0 <= 0) { - if (((ix0 & (~sign)) | ix1) == 0) - return x; /* sqrt(+-0) = +-0 */ - else if (ix0 < 0) - return (x - x) / (x - x); /* sqrt(-ve) = sNaN */ - } - /* normalize x */ - m = (ix0 >> 20); - if (m == 0) { /* subnormal x */ - while (ix0 == 0) { - m -= 21; - ix0 |= (ix1 >> 11); - ix1 <<= 21; - } - for (i = 0; (ix0 & 0x00100000) == 0; i++) - ix0 <<= 1; - m -= i - 1; - ix0 |= (ix1 >> (32 - i)); - ix1 <<= i; - } - m -= 1023; /* unbias exponent */ - ix0 = (ix0 & 0x000fffff) | 0x00100000; - if (m & 1) { /* odd m, double x to make it even */ - ix0 += ix0 + ((ix1 & sign) >> 31); - ix1 += ix1; - } - m >>= 1; /* m = [m/2] */ - - /* generate sqrt(x) bit by bit */ - ix0 += ix0 + ((ix1 & sign) >> 31); - ix1 += ix1; - q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ - r = 0x00200000; /* r = moving bit from right to left */ - - while (r != 0) { - t = s0 + r; - if (t <= ix0) { - s0 = t + r; - ix0 -= t; - q += r; - } - ix0 += ix0 + ((ix1 & sign) >> 31); - ix1 += ix1; - r >>= 1; - } - - r = sign; - while (r != 0) { - t1 = s1 + r; - t = s0; - if ((t < ix0) || ((t == ix0) && (t1 <= ix1))) { - s1 = t1 + r; - if (((t1 & sign) == sign) && (s1 & sign) == 0) - s0 += 1; - ix0 -= t; - if (ix1 < t1) - ix0 -= 1; - ix1 -= t1; - q1 += r; - } - ix0 += ix0 + ((ix1 & sign) >> 31); - ix1 += ix1; - r >>= 1; - } - - /* use floating add to find out rounding direction */ - if ((ix0 | ix1) != 0) { - z = one - tiny; /* trigger inexact flag */ - if (z >= one) { - z = one + tiny; - if (q1 == (u_int32_t) 0xffffffff) { - q1 = 0; - q += 1; - } else if (z > one) { - if (q1 == (u_int32_t) 0xfffffffe) - q += 1; - q1 += 2; - } else - q1 += (q1 & 1); - } - } - ix0 = (q >> 1) + 0x3fe00000; - ix1 = q1 >> 1; - if ((q & 1) == 1) - ix1 |= sign; - ix0 += (m << 20); - INSERT_WORDS(z, ix0, ix1); - return z; -} - -/* -Other methods (use floating-point arithmetic) -------------- -(This is a copy of a drafted paper by Prof W. Kahan -and K.C. Ng, written in May, 1986) - - Two algorithms are given here to implement sqrt(x) - (IEEE double precision arithmetic) in software. - Both supply sqrt(x) correctly rounded. The first algorithm (in - Section A) uses newton iterations and involves four divisions. - The second one uses reciproot iterations to avoid division, but - requires more multiplications. Both algorithms need the ability - to chop results of arithmetic operations instead of round them, - and the INEXACT flag to indicate when an arithmetic operation - is executed exactly with no roundoff error, all part of the - standard (IEEE 754-1985). The ability to perform shift, add, - subtract and logical AND operations upon 32-bit words is needed - too, though not part of the standard. - -A. sqrt(x) by Newton Iteration - - (1) Initial approximation - - Let x0 and x1 be the leading and the trailing 32-bit words of - a floating point number x (in IEEE double format) respectively - - 1 11 52 ...widths - ------------------------------------------------------ - x: |s| e | f | - ------------------------------------------------------ - msb lsb msb lsb ...order - - - ------------------------ ------------------------ - x0: |s| e | f1 | x1: | f2 | - ------------------------ ------------------------ - - By performing shifts and subtracts on x0 and x1 (both regarded - as integers), we obtain an 8-bit approximation of sqrt(x) as - follows. - - k := (x0>>1) + 0x1ff80000; - y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits - Here k is a 32-bit integer and T1[] is an integer array containing - correction terms. Now magically the floating value of y (y's - leading 32-bit word is y0, the value of its trailing word is 0) - approximates sqrt(x) to almost 8-bit. - - Value of T1: - static int T1[32]= { - 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592, - 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215, - 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581, - 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,}; - - (2) Iterative refinement - - Apply Heron's rule three times to y, we have y approximates - sqrt(x) to within 1 ulp (Unit in the Last Place): - - y := (y+x/y)/2 ... almost 17 sig. bits - y := (y+x/y)/2 ... almost 35 sig. bits - y := y-(y-x/y)/2 ... within 1 ulp - - - Remark 1. - Another way to improve y to within 1 ulp is: - - y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x) - y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x) - - 2 - (x-y )*y - y := y + 2* ---------- ...within 1 ulp - 2 - 3y + x - - - This formula has one division fewer than the one above; however, - it requires more multiplications and additions. Also x must be - scaled in advance to avoid spurious overflow in evaluating the - expression 3y*y+x. Hence it is not recommended uless division - is slow. If division is very slow, then one should use the - reciproot algorithm given in section B. - - (3) Final adjustment - - By twiddling y's last bit it is possible to force y to be - correctly rounded according to the prevailing rounding mode - as follows. Let r and i be copies of the rounding mode and - inexact flag before entering the square root program. Also we - use the expression y+-ulp for the next representable floating - numbers (up and down) of y. Note that y+-ulp = either fixed - point y+-1, or multiply y by nextafter(1,+-inf) in chopped - mode. - - I := FALSE; ... reset INEXACT flag I - R := RZ; ... set rounding mode to round-toward-zero - z := x/y; ... chopped quotient, possibly inexact - If(not I) then { ... if the quotient is exact - if(z=y) { - I := i; ... restore inexact flag - R := r; ... restore rounded mode - return sqrt(x):=y. - } else { - z := z - ulp; ... special rounding - } - } - i := TRUE; ... sqrt(x) is inexact - If (r=RN) then z=z+ulp ... rounded-to-nearest - If (r=RP) then { ... round-toward-+inf - y = y+ulp; z=z+ulp; - } - y := y+z; ... chopped sum - y0:=y0-0x00100000; ... y := y/2 is correctly rounded. - I := i; ... restore inexact flag - R := r; ... restore rounded mode - return sqrt(x):=y. - - (4) Special cases - - Square root of +inf, +-0, or NaN is itself; - Square root of a negative number is NaN with invalid signal. - - -B. sqrt(x) by Reciproot Iteration - - (1) Initial approximation - - Let x0 and x1 be the leading and the trailing 32-bit words of - a floating point number x (in IEEE double format) respectively - (see section A). By performing shifs and subtracts on x0 and y0, - we obtain a 7.8-bit approximation of 1/sqrt(x) as follows. - - k := 0x5fe80000 - (x0>>1); - y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits - - Here k is a 32-bit integer and T2[] is an integer array - containing correction terms. Now magically the floating - value of y (y's leading 32-bit word is y0, the value of - its trailing word y1 is set to zero) approximates 1/sqrt(x) - to almost 7.8-bit. - - Value of T2: - static int T2[64]= { - 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866, - 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f, - 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d, - 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0, - 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989, - 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd, - 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e, - 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,}; - - (2) Iterative refinement - - Apply Reciproot iteration three times to y and multiply the - result by x to get an approximation z that matches sqrt(x) - to about 1 ulp. To be exact, we will have - -1ulp < sqrt(x)-z<1.0625ulp. - - ... set rounding mode to Round-to-nearest - y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x) - y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x) - ... special arrangement for better accuracy - z := x*y ... 29 bits to sqrt(x), with z*y<1 - z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x) - - Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that - (a) the term z*y in the final iteration is always less than 1; - (b) the error in the final result is biased upward so that - -1 ulp < sqrt(x) - z < 1.0625 ulp - instead of |sqrt(x)-z|<1.03125ulp. - - (3) Final adjustment - - By twiddling y's last bit it is possible to force y to be - correctly rounded according to the prevailing rounding mode - as follows. Let r and i be copies of the rounding mode and - inexact flag before entering the square root program. Also we - use the expression y+-ulp for the next representable floating - numbers (up and down) of y. Note that y+-ulp = either fixed - point y+-1, or multiply y by nextafter(1,+-inf) in chopped - mode. - - R := RZ; ... set rounding mode to round-toward-zero - switch(r) { - case RN: ... round-to-nearest - if(x<= z*(z-ulp)...chopped) z = z - ulp; else - if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp; - break; - case RZ:case RM: ... round-to-zero or round-to--inf - R:=RP; ... reset rounding mod to round-to-+inf - if(x<z*z ... rounded up) z = z - ulp; else - if(x>=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp; - break; - case RP: ... round-to-+inf - if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else - if(x>z*z ...chopped) z = z+ulp; - break; - } - - Remark 3. The above comparisons can be done in fixed point. For - example, to compare x and w=z*z chopped, it suffices to compare - x1 and w1 (the trailing parts of x and w), regarding them as - two's complement integers. - - ...Is z an exact square root? - To determine whether z is an exact square root of x, let z1 be the - trailing part of z, and also let x0 and x1 be the leading and - trailing parts of x. - - If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0 - I := 1; ... Raise Inexact flag: z is not exact - else { - j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2 - k := z1 >> 26; ... get z's 25-th and 26-th - fraction bits - I := i or (k&j) or ((k&(j+j+1))!=(x1&3)); - } - R:= r ... restore rounded mode - return sqrt(x):=z. - - If multiplication is cheaper then the foregoing red tape, the - Inexact flag can be evaluated by - - I := i; - I := (z*z!=x) or I. - - Note that z*z can overwrite I; this value must be sensed if it is - True. - - Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be - zero. - - -------------------- - z1: | f2 | - -------------------- - bit 31 bit 0 - - Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd - or even of logb(x) have the following relations: - - ------------------------------------------------- - bit 27,26 of z1 bit 1,0 of x1 logb(x) - ------------------------------------------------- - 00 00 odd and even - 01 01 even - 10 10 odd - 10 00 even - 11 01 even - ------------------------------------------------- - - (4) Special cases (see (4) of Section A). - - */ diff --git a/3rdparty/SDL2/src/libm/k_cos.c b/3rdparty/SDL2/src/libm/k_cos.c deleted file mode 100644 index 64c50e3fb94..00000000000 --- a/3rdparty/SDL2/src/libm/k_cos.c +++ /dev/null @@ -1,100 +0,0 @@ -/* @(#)k_cos.c 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. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: k_cos.c,v 1.8 1995/05/10 20:46:22 jtc Exp $"; -#endif - -/* - * __kernel_cos( x, y ) - * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * - * Algorithm - * 1. Since cos(-x) = cos(x), we need only to consider positive x. - * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. - * 3. cos(x) is approximated by a polynomial of degree 14 on - * [0,pi/4] - * 4 14 - * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x - * where the remez error is - * - * | 2 4 6 8 10 12 14 | -58 - * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 - * | | - * - * 4 6 8 10 12 14 - * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then - * cos(x) = 1 - x*x/2 + r - * since cos(x+y) ~ cos(x) - sin(x)*y - * ~ cos(x) - x*y, - * a correction term is necessary in cos(x) and hence - * cos(x+y) = 1 - (x*x/2 - (r - x*y)) - * For better accuracy when x > 0.3, let qx = |x|/4 with - * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. - * Then - * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). - * Note that 1-qx and (x*x/2-qx) is EXACT here, and the - * magnitude of the latter is at least a quarter of x*x/2, - * thus, reducing the rounding error in the subtraction. - */ - -#include "math_libm.h" -#include "math_private.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif - one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ - C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ - C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ - C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ - C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ - C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ - C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ - -#ifdef __STDC__ -double attribute_hidden -__kernel_cos(double x, double y) -#else -double attribute_hidden -__kernel_cos(x, y) - double x, y; -#endif -{ - double a, hz, z, r, qx; - int32_t ix; - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; /* ix = |x|'s high word */ - if (ix < 0x3e400000) { /* 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 < 0x3FD33333) /* if |x| < 0.3 */ - return one - (0.5 * z - (z * r - x * y)); - else { - if (ix > 0x3fe90000) { /* x > 0.78125 */ - qx = 0.28125; - } else { - INSERT_WORDS(qx, ix - 0x00200000, 0); /* x/4 */ - } - hz = 0.5 * z - qx; - a = one - qx; - return a - (hz - (z * r - x * y)); - } -} diff --git a/3rdparty/SDL2/src/libm/k_rem_pio2.c b/3rdparty/SDL2/src/libm/k_rem_pio2.c deleted file mode 100644 index 23c2b61dd91..00000000000 --- a/3rdparty/SDL2/src/libm/k_rem_pio2.c +++ /dev/null @@ -1,363 +0,0 @@ -/* @(#)k_rem_pio2.c 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. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: k_rem_pio2.c,v 1.7 1995/05/10 20:46:25 jtc Exp $"; -#endif - -/* - * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) - * double x[],y[]; int e0,nx,prec; int ipio2[]; - * - * __kernel_rem_pio2 return the last three digits of N with - * y = x - N*pi/2 - * so that |y| < pi/2. - * - * The method is to compute the integer (mod 8) and fraction parts of - * (2/pi)*x without doing the full multiplication. In general we - * skip the part of the product that are known to be a huge integer ( - * more accurately, = 0 mod 8 ). Thus the number of operations are - * independent of the exponent of the input. - * - * (2/pi) is represented by an array of 24-bit integers in ipio2[]. - * - * Input parameters: - * x[] The input value (must be positive) is broken into nx - * pieces of 24-bit integers in double precision format. - * x[i] will be the i-th 24 bit of x. The scaled exponent - * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 - * match x's up to 24 bits. - * - * Example of breaking a double positive z into x[0]+x[1]+x[2]: - * e0 = ilogb(z)-23 - * z = scalbn(z,-e0) - * for i = 0,1,2 - * x[i] = floor(z) - * z = (z-x[i])*2**24 - * - * - * y[] ouput result in an array of double precision numbers. - * The dimension of y[] is: - * 24-bit precision 1 - * 53-bit precision 2 - * 64-bit precision 2 - * 113-bit precision 3 - * The actual value is the sum of them. Thus for 113-bit - * precison, one may have to do something like: - * - * long double t,w,r_head, r_tail; - * t = (long double)y[2] + (long double)y[1]; - * w = (long double)y[0]; - * r_head = t+w; - * r_tail = w - (r_head - t); - * - * e0 The exponent of x[0] - * - * nx dimension of x[] - * - * prec an integer indicating the precision: - * 0 24 bits (single) - * 1 53 bits (double) - * 2 64 bits (extended) - * 3 113 bits (quad) - * - * ipio2[] - * integer array, contains the (24*i)-th to (24*i+23)-th - * bit of 2/pi after binary point. The corresponding - * floating value is - * - * ipio2[i] * 2^(-24(i+1)). - * - * External function: - * double scalbn(), floor(); - * - * - * Here is the description of some local variables: - * - * jk jk+1 is the initial number of terms of ipio2[] needed - * in the computation. The recommended value is 2,3,4, - * 6 for single, double, extended,and quad. - * - * jz local integer variable indicating the number of - * terms of ipio2[] used. - * - * jx nx - 1 - * - * jv index for pointing to the suitable ipio2[] for the - * computation. In general, we want - * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 - * is an integer. Thus - * e0-3-24*jv >= 0 or (e0-3)/24 >= jv - * Hence jv = max(0,(e0-3)/24). - * - * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. - * - * q[] double array with integral value, representing the - * 24-bits chunk of the product of x and 2/pi. - * - * q0 the corresponding exponent of q[0]. Note that the - * exponent for q[i] would be q0-24*i. - * - * PIo2[] double precision array, obtained by cutting pi/2 - * into 24 bits chunks. - * - * f[] ipio2[] in floating point - * - * iq[] integer array by breaking up q[] in 24-bits chunk. - * - * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] - * - * ih integer. If >0 it indicates q[] is >= 0.5, hence - * it also indicates the *sign* of the result. - * - */ - - -/* - * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ - -#include "math_libm.h" -#include "math_private.h" - -#include "SDL_assert.h" - -libm_hidden_proto(scalbn) - libm_hidden_proto(floor) -#ifdef __STDC__ - static const int init_jk[] = { 2, 3, 4, 6 }; /* initial value for jk */ -#else - static int init_jk[] = { 2, 3, 4, 6 }; -#endif - -#ifdef __STDC__ -static const double PIo2[] = { -#else -static double PIo2[] = { -#endif - 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ - 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ - 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ - 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ - 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ - 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ - 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ - 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ -}; - -#ifdef __STDC__ -static const double -#else -static double -#endif - zero = 0.0, one = 1.0, two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ - twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ - -#ifdef __STDC__ -int attribute_hidden -__kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, - const int32_t * ipio2) -#else -int attribute_hidden -__kernel_rem_pio2(x, y, e0, nx, prec, ipio2) - double x[], y[]; - int e0, nx, prec; - int32_t ipio2[]; -#endif -{ - int32_t jz, jx, jv, jp, jk, carry, n, iq[20], i, j, k, m, q0, ih; - double z, fw, f[20], fq[20], q[20]; - - /* initialize jk */ - SDL_assert((prec >= 0) && (prec < SDL_arraysize(init_jk))); - jk = init_jk[prec]; - SDL_assert((jk >= 2) && (jk <= 6)); - jp = jk; - - /* determine jx,jv,q0, note that 3>q0 */ - SDL_assert(nx > 0); - jx = nx - 1; - jv = (e0 - 3) / 24; - if (jv < 0) - jv = 0; - q0 = e0 - 24 * (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 : (double) 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 = (double) ((int32_t) (twon24 * z)); - iq[i] = (int32_t) (z - two24 * fw); - z = q[j - 1] + fw; - } - - /* compute n */ - z = scalbn(z, q0); /* actual value of z */ - z -= 8.0 * floor(z * 0.125); /* trim off integer >= 8 */ - n = (int32_t) z; - z -= (double) n; - ih = 0; - if (q0 > 0) { /* need iq[jz-1] to determine n */ - i = (iq[jz - 1] >> (24 - q0)); - n += i; - iq[jz - 1] -= i << (24 - q0); - ih = iq[jz - 1] >> (23 - q0); - } else if (q0 == 0) - ih = iq[jz - 1] >> 23; - else if (z >= 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] = 0x1000000 - j; - } - } else - iq[i] = 0xffffff - j; - } - if (q0 > 0) { /* rare case: chance is 1 in 12 */ - switch (q0) { - case 1: - iq[jz - 1] &= 0x7fffff; - break; - case 2: - iq[jz - 1] &= 0x3fffff; - break; - } - } - if (ih == 2) { - z = one - z; - if (carry != 0) - z -= scalbn(one, 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] = (double) 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 == 0.0) { - jz -= 1; - q0 -= 24; - while (iq[jz] == 0) { - jz--; - q0 -= 24; - } - } else { /* break z into 24-bit if necessary */ - z = scalbn(z, -q0); - if (z >= two24) { - fw = (double) ((int32_t) (twon24 * z)); - iq[jz] = (int32_t) (z - two24 * fw); - jz += 1; - q0 += 24; - iq[jz] = (int32_t) fw; - } else - iq[jz] = (int32_t) z; - } - - /* convert integer "bit" chunk to floating-point value */ - fw = scalbn(one, q0); - for (i = jz; i >= 0; i--) { - q[i] = fw * (double) iq[i]; - fw *= twon24; - } - - /* 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; -} diff --git a/3rdparty/SDL2/src/libm/k_sin.c b/3rdparty/SDL2/src/libm/k_sin.c deleted file mode 100644 index 60881575a54..00000000000 --- a/3rdparty/SDL2/src/libm/k_sin.c +++ /dev/null @@ -1,87 +0,0 @@ -/* @(#)k_sin.c 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. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: k_sin.c,v 1.8 1995/05/10 20:46:31 jtc Exp $"; -#endif - -/* __kernel_sin( x, y, iy) - * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). - * - * Algorithm - * 1. Since sin(-x) = -sin(x), we need only to consider positive x. - * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. - * 3. sin(x) is approximated by a polynomial of degree 13 on - * [0,pi/4] - * 3 13 - * sin(x) ~ x + S1*x + ... + S6*x - * where - * - * |sin(x) 2 4 6 8 10 12 | -58 - * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 - * | x | - * - * 4. sin(x+y) = sin(x) + sin'(x')*y - * ~ sin(x) + (1-x*x/2)*y - * For better accuracy, let - * 3 2 2 2 2 - * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) - * then 3 2 - * sin(x) = x + (S1*x + (x *(r-y/2)+y)) - */ - -#include "math_libm.h" -#include "math_private.h" - -#ifdef __STDC__ -static const double -#else -static double -#endif - half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ - S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ - S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ - S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ - S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ - S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ - S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ - -#ifdef __STDC__ -double attribute_hidden -__kernel_sin(double x, double y, int iy) -#else -double attribute_hidden -__kernel_sin(x, y, iy) - double x, y; - int iy; /* iy=0 if y is zero */ -#endif -{ - double z, r, v; - int32_t ix; - GET_HIGH_WORD(ix, x); - ix &= 0x7fffffff; /* high word of x */ - if (ix < 0x3e400000) { /* |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); -} diff --git a/3rdparty/SDL2/src/libm/k_tan.c b/3rdparty/SDL2/src/libm/k_tan.c deleted file mode 100644 index 27e6639b0c7..00000000000 --- a/3rdparty/SDL2/src/libm/k_tan.c +++ /dev/null @@ -1,118 +0,0 @@ -/* - * ==================================================== - * 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. - * ==================================================== - */ - -/* __kernel_tan( x, y, k ) - * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 - * Input x is assumed to be bounded by ~pi/4 in magnitude. - * Input y is the tail of x. - * Input k indicates whether tan (if k=1) or - * -1/tan (if k= -1) is returned. - * - * Algorithm - * 1. Since tan(-x) = -tan(x), we need only to consider positive x. - * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. - * 3. tan(x) is approximated by a odd polynomial of degree 27 on - * [0,0.67434] - * 3 27 - * tan(x) ~ x + T1*x + ... + T13*x - * where - * - * |tan(x) 2 4 26 | -59.2 - * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 - * | x | - * - * Note: tan(x+y) = tan(x) + tan'(x)*y - * ~ tan(x) + (1+x*x)*y - * Therefore, for better accuracy in computing tan(x+y), let - * 3 2 2 2 2 - * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) - * then - * 3 2 - * tan(x+y) = x + (T1*x + (x *(r+y)+y)) - * - * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then - * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) - * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) - */ - -#include "math_libm.h" -#include "math_private.h" - -static const double -one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ -pio4 = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ -pio4lo= 3.06161699786838301793e-17, /* 0x3C81A626, 0x33145C07 */ -T[] = { - 3.33333333333334091986e-01, /* 0x3FD55555, 0x55555563 */ - 1.33333333333201242699e-01, /* 0x3FC11111, 0x1110FE7A */ - 5.39682539762260521377e-02, /* 0x3FABA1BA, 0x1BB341FE */ - 2.18694882948595424599e-02, /* 0x3F9664F4, 0x8406D637 */ - 8.86323982359930005737e-03, /* 0x3F8226E3, 0xE96E8493 */ - 3.59207910759131235356e-03, /* 0x3F6D6D22, 0xC9560328 */ - 1.45620945432529025516e-03, /* 0x3F57DBC8, 0xFEE08315 */ - 5.88041240820264096874e-04, /* 0x3F4344D8, 0xF2F26501 */ - 2.46463134818469906812e-04, /* 0x3F3026F7, 0x1A8D1068 */ - 7.81794442939557092300e-05, /* 0x3F147E88, 0xA03792A6 */ - 7.14072491382608190305e-05, /* 0x3F12B80F, 0x32F0A7E9 */ - -1.85586374855275456654e-05, /* 0xBEF375CB, 0xDB605373 */ - 2.59073051863633712884e-05, /* 0x3EFB2A70, 0x74BF7AD4 */ -}; - -double __kernel_tan(double x, double y, int iy) -{ - double z,r,v,w,s; - int32_t ix,hx; - GET_HIGH_WORD(hx,x); - ix = hx&0x7fffffff; /* high word of |x| */ - if(ix<0x3e300000) /* x < 2**-28 */ - {if((int)x==0) { /* generate inexact */ - u_int32_t low; - GET_LOW_WORD(low,x); - if(((ix|low)|(iy+1))==0) return one/fabs(x); - else return (iy==1)? x: -one/x; - } - } - if(ix>=0x3FE59428) { /* |x|>=0.6744 */ - if(hx<0) {x = -x; y = -y;} - z = pio4-x; - w = pio4lo-y; - x = z+w; y = 0.0; - } - z = x*x; - w = z*z; - /* Break x^5*(T[1]+x^2*T[2]+...) into - * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + - * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) - */ - r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); - v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); - s = z*x; - r = y + z*(s*(r+v)+y); - r += T[0]*s; - w = x+r; - if(ix>=0x3FE59428) { - v = (double)iy; - return (double)(1-((hx>>30)&2))*(v-2.0*(x-(w*w/(w+v)-r))); - } - if(iy==1) return w; - else { /* if allow error up to 2 ulp, - simply return -1.0/(x+r) here */ - /* compute -1.0/(x+r) accurately */ - double a,t; - z = w; - SET_LOW_WORD(z,0); - v = r-(z - x); /* z+v = r+x */ - t = a = -1.0/w; /* a = -1.0/w */ - SET_LOW_WORD(t,0); - s = 1.0+t*z; - return t+a*(s+t*v); - } -} diff --git a/3rdparty/SDL2/src/libm/math_libm.h b/3rdparty/SDL2/src/libm/math_libm.h deleted file mode 100644 index 3fe1727a3b5..00000000000 --- a/3rdparty/SDL2/src/libm/math_libm.h +++ /dev/null @@ -1,38 +0,0 @@ -/* - Simple DirectMedia Layer - Copyright (C) 1997-2016 Sam Lantinga <slouken@libsdl.org> - - This software is provided 'as-is', without any express or implied - warranty. In no event will the authors be held liable for any damages - arising from the use of this software. - - Permission is granted to anyone to use this software for any purpose, - including commercial applications, and to alter it and redistribute it - freely, subject to the following restrictions: - - 1. The origin of this software must not be misrepresented; you must not - claim that you wrote the original software. If you use this software - in a product, an acknowledgment in the product documentation would be - appreciated but is not required. - 2. Altered source versions must be plainly marked as such, and must not be - misrepresented as being the original software. - 3. This notice may not be removed or altered from any source distribution. -*/ -#include "../SDL_internal.h" - -/* Math routines from uClibc: http://www.uclibc.org */ - -double SDL_uclibc_atan(double x); -double SDL_uclibc_atan2(double y, double x); -double SDL_uclibc_copysign(double x, double y); -double SDL_uclibc_cos(double x); -double SDL_uclibc_fabs(double x); -double SDL_uclibc_floor(double x); -double SDL_uclibc_log(double x); -double SDL_uclibc_pow(double x, double y); -double SDL_uclibc_scalbn(double x, int n); -double SDL_uclibc_sin(double x); -double SDL_uclibc_sqrt(double x); -double SDL_uclibc_tan(double x); - -/* vi: set ts=4 sw=4 expandtab: */ diff --git a/3rdparty/SDL2/src/libm/math_private.h b/3rdparty/SDL2/src/libm/math_private.h deleted file mode 100644 index 74c8b3d45f5..00000000000 --- a/3rdparty/SDL2/src/libm/math_private.h +++ /dev/null @@ -1,221 +0,0 @@ -/* - * ==================================================== - * 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. - * ==================================================== - */ - -/* - * from: @(#)fdlibm.h 5.1 93/09/24 - * $Id: math_private.h,v 1.3 2004/02/09 07:10:38 andersen Exp $ - */ - -#ifndef _MATH_PRIVATE_H_ -#define _MATH_PRIVATE_H_ - -/* #include <endian.h> */ -#include "SDL_endian.h" -/* #include <sys/types.h> */ - -#define attribute_hidden -#define libm_hidden_proto(x) -#define libm_hidden_def(x) - -#ifndef __HAIKU__ /* already defined in a system header. */ -typedef unsigned int u_int32_t; -#endif - -#define atan SDL_uclibc_atan -#define __ieee754_atan2 SDL_uclibc_atan2 -#define copysign SDL_uclibc_copysign -#define cos SDL_uclibc_cos -#define fabs SDL_uclibc_fabs -#define floor SDL_uclibc_floor -#define __ieee754_log SDL_uclibc_log -#define __ieee754_pow SDL_uclibc_pow -#define scalbn SDL_uclibc_scalbn -#define sin SDL_uclibc_sin -#define __ieee754_sqrt SDL_uclibc_sqrt -#define tan SDL_uclibc_tan - -/* The original fdlibm code used statements like: - n0 = ((*(int*)&one)>>29)^1; * index of high word * - ix0 = *(n0+(int*)&x); * high word of x * - ix1 = *((1-n0)+(int*)&x); * low word of x * - to dig two 32 bit words out of the 64 bit IEEE floating point - value. That is non-ANSI, and, moreover, the gcc instruction - scheduler gets it wrong. We instead use the following macros. - Unlike the original code, we determine the endianness at compile - time, not at run time; I don't see much benefit to selecting - endianness at run time. */ - -/* A union which permits us to convert between a double and two 32 bit - ints. */ - -/* - * Math on arm is special: - * For FPA, float words are always big-endian. - * For VFP, floats words follow the memory system mode. - */ - -#if (SDL_BYTEORDER == SDL_BIG_ENDIAN) - -typedef union -{ - double value; - struct - { - u_int32_t msw; - u_int32_t lsw; - } parts; -} ieee_double_shape_type; - -#else - -typedef union -{ - double value; - struct - { - u_int32_t lsw; - u_int32_t msw; - } parts; -} ieee_double_shape_type; - -#endif - -/* Get two 32 bit ints from a double. */ - -#define EXTRACT_WORDS(ix0,ix1,d) \ -do { \ - ieee_double_shape_type ew_u; \ - ew_u.value = (d); \ - (ix0) = ew_u.parts.msw; \ - (ix1) = ew_u.parts.lsw; \ -} while (0) - -/* Get the more significant 32 bit int from a double. */ - -#define GET_HIGH_WORD(i,d) \ -do { \ - ieee_double_shape_type gh_u; \ - gh_u.value = (d); \ - (i) = gh_u.parts.msw; \ -} while (0) - -/* Get the less significant 32 bit int from a double. */ - -#define GET_LOW_WORD(i,d) \ -do { \ - ieee_double_shape_type gl_u; \ - gl_u.value = (d); \ - (i) = gl_u.parts.lsw; \ -} while (0) - -/* Set a double from two 32 bit ints. */ - -#define INSERT_WORDS(d,ix0,ix1) \ -do { \ - ieee_double_shape_type iw_u; \ - iw_u.parts.msw = (ix0); \ - iw_u.parts.lsw = (ix1); \ - (d) = iw_u.value; \ -} while (0) - -/* Set the more significant 32 bits of a double from an int. */ - -#define SET_HIGH_WORD(d,v) \ -do { \ - ieee_double_shape_type sh_u; \ - sh_u.value = (d); \ - sh_u.parts.msw = (v); \ - (d) = sh_u.value; \ -} while (0) - -/* Set the less significant 32 bits of a double from an int. */ - -#define SET_LOW_WORD(d,v) \ -do { \ - ieee_double_shape_type sl_u; \ - sl_u.value = (d); \ - sl_u.parts.lsw = (v); \ - (d) = sl_u.value; \ -} while (0) - -/* A union which permits us to convert between a float and a 32 bit - int. */ - -typedef union -{ - float value; - u_int32_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) - -/* ieee style elementary functions */ -extern double -__ieee754_sqrt(double) - attribute_hidden; - extern double __ieee754_acos(double) attribute_hidden; - extern double __ieee754_acosh(double) attribute_hidden; - extern double __ieee754_log(double) attribute_hidden; - extern double __ieee754_atanh(double) attribute_hidden; - extern double __ieee754_asin(double) attribute_hidden; - extern double __ieee754_atan2(double, double) attribute_hidden; - extern double __ieee754_exp(double) attribute_hidden; - extern double __ieee754_cosh(double) attribute_hidden; - extern double __ieee754_fmod(double, double) attribute_hidden; - extern double __ieee754_pow(double, double) attribute_hidden; - extern double __ieee754_lgamma_r(double, int *) attribute_hidden; - extern double __ieee754_gamma_r(double, int *) attribute_hidden; - extern double __ieee754_lgamma(double) attribute_hidden; - extern double __ieee754_gamma(double) attribute_hidden; - extern double __ieee754_log10(double) attribute_hidden; - extern double __ieee754_sinh(double) attribute_hidden; - extern double __ieee754_hypot(double, double) attribute_hidden; - extern double __ieee754_j0(double) attribute_hidden; - extern double __ieee754_j1(double) attribute_hidden; - extern double __ieee754_y0(double) attribute_hidden; - extern double __ieee754_y1(double) attribute_hidden; - extern double __ieee754_jn(int, double) attribute_hidden; - extern double __ieee754_yn(int, double) attribute_hidden; - extern double __ieee754_remainder(double, double) attribute_hidden; - extern int __ieee754_rem_pio2(double, double *) attribute_hidden; -#if defined(_SCALB_INT) - extern double __ieee754_scalb(double, int) attribute_hidden; -#else - extern double __ieee754_scalb(double, double) attribute_hidden; -#endif - -/* fdlibm kernel function */ -#ifndef _IEEE_LIBM - extern double __kernel_standard(double, double, int) attribute_hidden; -#endif - extern double __kernel_sin(double, double, int) attribute_hidden; - extern double __kernel_cos(double, double) attribute_hidden; - extern double __kernel_tan(double, double, int) attribute_hidden; - extern int __kernel_rem_pio2(double *, double *, int, int, int, - const int *) attribute_hidden; - -#endif /* _MATH_PRIVATE_H_ */ diff --git a/3rdparty/SDL2/src/libm/s_atan.c b/3rdparty/SDL2/src/libm/s_atan.c deleted file mode 100644 index 970ea4dbfad..00000000000 --- a/3rdparty/SDL2/src/libm/s_atan.c +++ /dev/null @@ -1,115 +0,0 @@ -/* - * ==================================================== - * 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. - * ==================================================== - */ - -/* atan(x) - * Method - * 1. Reduce x to positive by atan(x) = -atan(-x). - * 2. According to the integer k=4t+0.25 chopped, t=x, the argument - * is further reduced to one of the following intervals and the - * arctangent of t is evaluated by the corresponding formula: - * - * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) - * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) - * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) - * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) - * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) - * - * Constants: - * The hexadecimal values are the intended ones for the following - * constants. The decimal values may be used, provided that the - * compiler will convert from decimal to binary accurately enough - * to produce the hexadecimal values shown. - */ - -#include "math_libm.h" -#include "math_private.h" - -static const double atanhi[] = { - 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ - 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ - 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ - 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ -}; - -static const double atanlo[] = { - 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ - 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ - 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ - 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ -}; - -static const double aT[] = { - 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ - -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ - 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ - -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ - 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ - -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ - 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ - -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ - 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ - -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ - 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ -}; - -static const double -one = 1.0, -huge = 1.0e300; - -double atan(double x) -{ - double w,s1,s2,z; - int32_t ix,hx,id; - - GET_HIGH_WORD(hx,x); - ix = hx&0x7fffffff; - if(ix>=0x44100000) { /* if |x| >= 2^66 */ - u_int32_t low; - GET_LOW_WORD(low,x); - if(ix>0x7ff00000|| - (ix==0x7ff00000&&(low!=0))) - return x+x; /* NaN */ - if(hx>0) return atanhi[3]+atanlo[3]; - else return -atanhi[3]-atanlo[3]; - } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ - if (ix < 0x3e200000) { /* |x| < 2^-29 */ - if(huge+x>one) return x; /* raise inexact */ - } - id = -1; - } else { - x = fabs(x); - if (ix < 0x3ff30000) { /* |x| < 1.1875 */ - if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ - id = 0; x = (2.0*x-one)/(2.0+x); - } else { /* 11/16<=|x|< 19/16 */ - id = 1; x = (x-one)/(x+one); - } - } else { - if (ix < 0x40038000) { /* |x| < 2.4375 */ - id = 2; x = (x-1.5)/(one+1.5*x); - } else { /* 2.4375 <= |x| < 2^66 */ - id = 3; x = -1.0/x; - } - }} - /* end of argument reduction */ - z = x*x; - w = z*z; - /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ - s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); - s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); - if (id<0) return x - x*(s1+s2); - else { - z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); - return (hx<0)? -z:z; - } -} -libm_hidden_def(atan) - diff --git a/3rdparty/SDL2/src/libm/s_copysign.c b/3rdparty/SDL2/src/libm/s_copysign.c deleted file mode 100644 index afd43e9a724..00000000000 --- a/3rdparty/SDL2/src/libm/s_copysign.c +++ /dev/null @@ -1,42 +0,0 @@ -/* @(#)s_copysign.c 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. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: s_copysign.c,v 1.8 1995/05/10 20:46:57 jtc Exp $"; -#endif - -/* - * copysign(double x, double y) - * copysign(x,y) returns a value with the magnitude of x and - * with the sign bit of y. - */ - -#include "math_libm.h" -#include "math_private.h" - -libm_hidden_proto(copysign) -#ifdef __STDC__ - double copysign(double x, double y) -#else - double copysign(x, y) - double x, y; -#endif -{ - u_int32_t hx, hy; - GET_HIGH_WORD(hx, x); - GET_HIGH_WORD(hy, y); - SET_HIGH_WORD(x, (hx & 0x7fffffff) | (hy & 0x80000000)); - return x; -} - -libm_hidden_def(copysign) diff --git a/3rdparty/SDL2/src/libm/s_cos.c b/3rdparty/SDL2/src/libm/s_cos.c deleted file mode 100644 index 66b156c9f52..00000000000 --- a/3rdparty/SDL2/src/libm/s_cos.c +++ /dev/null @@ -1,91 +0,0 @@ -/* @(#)s_cos.c 5.1 93/09/24 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: s_cos.c,v 1.7 1995/05/10 20:47:02 jtc Exp $"; -#endif - -/* cos(x) - * Return cosine function of x. - * - * kernel function: - * __kernel_sin ... sine function on [-pi/4,pi/4] - * __kernel_cos ... cosine function on [-pi/4,pi/4] - * __ieee754_rem_pio2 ... argument reduction routine - * - * Method. - * Let S,C and T denote the sin, cos and tan respectively on - * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 - * in [-pi/4 , +pi/4], and let n = k mod 4. - * We have - * - * n sin(x) cos(x) tan(x) - * ---------------------------------------------------------- - * 0 S C T - * 1 C -S -1/T - * 2 -S -C T - * 3 -C S -1/T - * ---------------------------------------------------------- - * - * Special cases: - * Let trig be any of sin, cos, or tan. - * trig(+-INF) is NaN, with signals; - * trig(NaN) is that NaN; - * - * Accuracy: - * TRIG(x) returns trig(x) nearly rounded - */ - -#include "math_libm.h" -#include "math_private.h" - -libm_hidden_proto(cos) -#ifdef __STDC__ - double cos(double x) -#else - double cos(x) - double x; -#endif -{ - double y[2], z = 0.0; - int32_t n, ix; - - /* High word of x. */ - GET_HIGH_WORD(ix, x); - - /* |x| ~< pi/4 */ - ix &= 0x7fffffff; - if (ix <= 0x3fe921fb) - return __kernel_cos(x, z); - - /* cos(Inf or NaN) is NaN */ - else if (ix >= 0x7ff00000) - return x - x; - - /* argument reduction needed */ - else { - n = __ieee754_rem_pio2(x, y); - switch (n & 3) { - case 0: - return __kernel_cos(y[0], y[1]); - case 1: - return -__kernel_sin(y[0], y[1], 1); - case 2: - return -__kernel_cos(y[0], y[1]); - default: - return __kernel_sin(y[0], y[1], 1); - } - } -} - -libm_hidden_def(cos) diff --git a/3rdparty/SDL2/src/libm/s_fabs.c b/3rdparty/SDL2/src/libm/s_fabs.c deleted file mode 100644 index 5cf0c3977bb..00000000000 --- a/3rdparty/SDL2/src/libm/s_fabs.c +++ /dev/null @@ -1,39 +0,0 @@ -/* @(#)s_fabs.c 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. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: s_fabs.c,v 1.7 1995/05/10 20:47:13 jtc Exp $"; -#endif - -/* - * fabs(x) returns the absolute value of x. - */ - -#include "math_libm.h" -#include "math_private.h" - -libm_hidden_proto(fabs) -#ifdef __STDC__ - double fabs(double x) -#else - double fabs(x) - double x; -#endif -{ - u_int32_t high; - GET_HIGH_WORD(high, x); - SET_HIGH_WORD(x, high & 0x7fffffff); - return x; -} - -libm_hidden_def(fabs) diff --git a/3rdparty/SDL2/src/libm/s_floor.c b/3rdparty/SDL2/src/libm/s_floor.c deleted file mode 100644 index b553d303828..00000000000 --- a/3rdparty/SDL2/src/libm/s_floor.c +++ /dev/null @@ -1,96 +0,0 @@ -/* @(#)s_floor.c 5.1 93/09/24 */ -/* - * ==================================================== - * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. - * - * Developed at SunPro, a Sun Microsystems, Inc. business. - * Permission to use, copy, modify, and distribute this - * software is freely granted, provided that this notice - * is preserved. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: s_floor.c,v 1.8 1995/05/10 20:47:20 jtc Exp $"; -#endif - -/* - * floor(x) - * Return x rounded toward -inf to integral value - * Method: - * Bit twiddling. - * Exception: - * Inexact flag raised if x not equal to floor(x). - */ - -#include "math_libm.h" -#include "math_private.h" - -#ifdef __STDC__ -static const double huge_val = 1.0e300; -#else -static double huge_val = 1.0e300; -#endif - -libm_hidden_proto(floor) -#ifdef __STDC__ - double floor(double x) -#else - double floor(x) - double x; -#endif -{ - int32_t i0, i1, j0; - u_int32_t i, j; - EXTRACT_WORDS(i0, i1, x); - j0 = ((i0 >> 20) & 0x7ff) - 0x3ff; - if (j0 < 20) { - if (j0 < 0) { /* raise inexact if x != 0 */ - if (huge_val + x > 0.0) { /* return 0*sign(x) if |x|<1 */ - if (i0 >= 0) { - i0 = i1 = 0; - } else if (((i0 & 0x7fffffff) | i1) != 0) { - i0 = 0xbff00000; - i1 = 0; - } - } - } else { - i = (0x000fffff) >> j0; - if (((i0 & i) | i1) == 0) - return x; /* x is integral */ - if (huge_val + x > 0.0) { /* raise inexact flag */ - if (i0 < 0) - i0 += (0x00100000) >> j0; - i0 &= (~i); - i1 = 0; - } - } - } else if (j0 > 51) { - if (j0 == 0x400) - return x + x; /* inf or NaN */ - else - return x; /* x is integral */ - } else { - i = ((u_int32_t) (0xffffffff)) >> (j0 - 20); - if ((i1 & i) == 0) - return x; /* x is integral */ - if (huge_val + x > 0.0) { /* raise inexact flag */ - if (i0 < 0) { - if (j0 == 20) - i0 += 1; - else { - j = i1 + (1 << (52 - j0)); - if (j < (u_int32_t) i1) - i0 += 1; /* got a carry */ - i1 = j; - } - } - i1 &= (~i); - } - } - INSERT_WORDS(x, i0, i1); - return x; -} - -libm_hidden_def(floor) diff --git a/3rdparty/SDL2/src/libm/s_scalbn.c b/3rdparty/SDL2/src/libm/s_scalbn.c deleted file mode 100644 index f824e926d70..00000000000 --- a/3rdparty/SDL2/src/libm/s_scalbn.c +++ /dev/null @@ -1,79 +0,0 @@ -/* @(#)s_scalbn.c 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. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: s_scalbn.c,v 1.8 1995/05/10 20:48:08 jtc Exp $"; -#endif - -/* - * scalbn (double x, int n) - * scalbn(x,n) returns x* 2**n computed by exponent - * manipulation rather than by actually performing an - * exponentiation or a multiplication. - */ - -#include "math_libm.h" -#include "math_private.h" - -libm_hidden_proto(copysign) -#ifdef __STDC__ - static const double -#else - static double -#endif - two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ - twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ - huge_val = 1.0e+300, tiny = 1.0e-300; - -libm_hidden_proto(scalbn) -#ifdef __STDC__ - double scalbn(double x, int n) -#else - double scalbn(x, n) - double x; - int n; -#endif -{ - int32_t k, hx, lx; - EXTRACT_WORDS(hx, lx, x); - k = (hx & 0x7ff00000) >> 20; /* extract exponent */ - if (k == 0) { /* 0 or subnormal x */ - if ((lx | (hx & 0x7fffffff)) == 0) - return x; /* +-0 */ - x *= two54; - GET_HIGH_WORD(hx, x); - k = ((hx & 0x7ff00000) >> 20) - 54; - if (n < -50000) - return tiny * x; /* underflow */ - } - if (k == 0x7ff) - return x + x; /* NaN or Inf */ - k = k + n; - if (k > 0x7fe) - return huge_val * copysign(huge_val, x); /* overflow */ - if (k > 0) { /* normal result */ - SET_HIGH_WORD(x, (hx & 0x800fffff) | (k << 20)); - return x; - } - if (k <= -54) { - if (n > 50000) /* in case integer overflow in n+k */ - return huge_val * copysign(huge_val, x); /* overflow */ - else - return tiny * copysign(tiny, x); /* underflow */ - } - k += 54; /* subnormal result */ - SET_HIGH_WORD(x, (hx & 0x800fffff) | (k << 20)); - return x * twom54; -} - -libm_hidden_def(scalbn) diff --git a/3rdparty/SDL2/src/libm/s_sin.c b/3rdparty/SDL2/src/libm/s_sin.c deleted file mode 100644 index 771176619f8..00000000000 --- a/3rdparty/SDL2/src/libm/s_sin.c +++ /dev/null @@ -1,91 +0,0 @@ -/* @(#)s_sin.c 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. - * ==================================================== - */ - -#if defined(LIBM_SCCS) && !defined(lint) -static const char rcsid[] = - "$NetBSD: s_sin.c,v 1.7 1995/05/10 20:48:15 jtc Exp $"; -#endif - -/* sin(x) - * Return sine function of x. - * - * kernel function: - * __kernel_sin ... sine function on [-pi/4,pi/4] - * __kernel_cos ... cose function on [-pi/4,pi/4] - * __ieee754_rem_pio2 ... argument reduction routine - * - * Method. - * Let S,C and T denote the sin, cos and tan respectively on - * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 - * in [-pi/4 , +pi/4], and let n = k mod 4. - * We have - * - * n sin(x) cos(x) tan(x) - * ---------------------------------------------------------- - * 0 S C T - * 1 C -S -1/T - * 2 -S -C T - * 3 -C S -1/T - * ---------------------------------------------------------- - * - * Special cases: - * Let trig be any of sin, cos, or tan. - * trig(+-INF) is NaN, with signals; - * trig(NaN) is that NaN; - * - * Accuracy: - * TRIG(x) returns trig(x) nearly rounded - */ - -#include "math_libm.h" -#include "math_private.h" - -libm_hidden_proto(sin) -#ifdef __STDC__ - double sin(double x) -#else - double sin(x) - double x; -#endif -{ - double y[2], z = 0.0; - int32_t n, ix; - - /* High word of x. */ - GET_HIGH_WORD(ix, x); - - /* |x| ~< pi/4 */ - ix &= 0x7fffffff; - if (ix <= 0x3fe921fb) - return __kernel_sin(x, z, 0); - - /* sin(Inf or NaN) is NaN */ - else if (ix >= 0x7ff00000) - return x - x; - - /* argument reduction needed */ - else { - n = __ieee754_rem_pio2(x, y); - switch (n & 3) { - case 0: - return __kernel_sin(y[0], y[1], 1); - case 1: - return __kernel_cos(y[0], y[1]); - case 2: - return -__kernel_sin(y[0], y[1], 1); - default: - return -__kernel_cos(y[0], y[1]); - } - } -} - -libm_hidden_def(sin) diff --git a/3rdparty/SDL2/src/libm/s_tan.c b/3rdparty/SDL2/src/libm/s_tan.c deleted file mode 100644 index 18c8f5b0601..00000000000 --- a/3rdparty/SDL2/src/libm/s_tan.c +++ /dev/null @@ -1,67 +0,0 @@ -/* - * ==================================================== - * 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. - * ==================================================== - */ - -/* tan(x) - * Return tangent function of x. - * - * kernel function: - * __kernel_tan ... tangent function on [-pi/4,pi/4] - * __ieee754_rem_pio2 ... argument reduction routine - * - * Method. - * Let S,C and T denote the sin, cos and tan respectively on - * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 - * in [-pi/4 , +pi/4], and let n = k mod 4. - * We have - * - * n sin(x) cos(x) tan(x) - * ---------------------------------------------------------- - * 0 S C T - * 1 C -S -1/T - * 2 -S -C T - * 3 -C S -1/T - * ---------------------------------------------------------- - * - * Special cases: - * Let trig be any of sin, cos, or tan. - * trig(+-INF) is NaN, with signals; - * trig(NaN) is that NaN; - * - * Accuracy: - * TRIG(x) returns trig(x) nearly rounded - */ - -#include "math_libm.h" -#include "math_private.h" - -double tan(double x) -{ - double y[2],z=0.0; - int32_t n, ix; - - /* High word of x. */ - GET_HIGH_WORD(ix,x); - - /* |x| ~< pi/4 */ - ix &= 0x7fffffff; - if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); - - /* tan(Inf or NaN) is NaN */ - else if (ix>=0x7ff00000) return x-x; /* NaN */ - - /* argument reduction needed */ - else { - n = __ieee754_rem_pio2(x,y); - return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even - -1 -- n odd */ - } -} -libm_hidden_def(tan) |