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-rw-r--r--3rdparty/SDL2/src/libm/e_atan2.c116
-rw-r--r--3rdparty/SDL2/src/libm/e_log.c167
-rw-r--r--3rdparty/SDL2/src/libm/e_pow.c342
-rw-r--r--3rdparty/SDL2/src/libm/e_rem_pio2.c201
-rw-r--r--3rdparty/SDL2/src/libm/e_sqrt.c464
-rw-r--r--3rdparty/SDL2/src/libm/k_cos.c100
-rw-r--r--3rdparty/SDL2/src/libm/k_rem_pio2.c363
-rw-r--r--3rdparty/SDL2/src/libm/k_sin.c87
-rw-r--r--3rdparty/SDL2/src/libm/k_tan.c118
-rw-r--r--3rdparty/SDL2/src/libm/math_libm.h38
-rw-r--r--3rdparty/SDL2/src/libm/math_private.h221
-rw-r--r--3rdparty/SDL2/src/libm/s_atan.c115
-rw-r--r--3rdparty/SDL2/src/libm/s_copysign.c42
-rw-r--r--3rdparty/SDL2/src/libm/s_cos.c91
-rw-r--r--3rdparty/SDL2/src/libm/s_fabs.c39
-rw-r--r--3rdparty/SDL2/src/libm/s_floor.c96
-rw-r--r--3rdparty/SDL2/src/libm/s_scalbn.c79
-rw-r--r--3rdparty/SDL2/src/libm/s_sin.c91
-rw-r--r--3rdparty/SDL2/src/libm/s_tan.c67
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)