summaryrefslogtreecommitdiff
path: root/Source/3rdParty/SDL2/src/libm/e_exp.c
diff options
context:
space:
mode:
authorchai <chaifix@163.com>2019-03-19 23:06:27 +0800
committerchai <chaifix@163.com>2019-03-19 23:06:27 +0800
commit1497dccd63a84b7ee2b229b1ad9c5c02718f2a78 (patch)
treef8d1bff50da13e126d08c7345653e002e293202d /Source/3rdParty/SDL2/src/libm/e_exp.c
parent5e2a973516e0729b225da9de0b03015dc5854ac4 (diff)
*rename
Diffstat (limited to 'Source/3rdParty/SDL2/src/libm/e_exp.c')
-rw-r--r--Source/3rdParty/SDL2/src/libm/e_exp.c187
1 files changed, 0 insertions, 187 deletions
diff --git a/Source/3rdParty/SDL2/src/libm/e_exp.c b/Source/3rdParty/SDL2/src/libm/e_exp.c
deleted file mode 100644
index d8cd4a4..0000000
--- a/Source/3rdParty/SDL2/src/libm/e_exp.c
+++ /dev/null
@@ -1,187 +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_exp(x)
- * Returns the exponential of x.
- *
- * Method
- * 1. Argument reduction:
- * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658.
- * Given x, find r and integer k such that
- *
- * x = k*ln2 + r, |r| <= 0.5*ln2.
- *
- * Here r will be represented as r = hi-lo for better
- * accuracy.
- *
- * 2. Approximation of exp(r) by a special rational function on
- * the interval [0,0.34658]:
- * Write
- * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ...
- * We use a special Reme algorithm on [0,0.34658] to generate
- * a polynomial of degree 5 to approximate R. The maximum error
- * of this polynomial approximation is bounded by 2**-59. In
- * other words,
- * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5
- * (where z=r*r, and the values of P1 to P5 are listed below)
- * and
- * | 5 | -59
- * | 2.0+P1*z+...+P5*z - R(z) | <= 2
- * | |
- * The computation of exp(r) thus becomes
- * 2*r
- * exp(r) = 1 + -------
- * R - r
- * r*R1(r)
- * = 1 + r + ----------- (for better accuracy)
- * 2 - R1(r)
- * where
- * 2 4 10
- * R1(r) = r - (P1*r + P2*r + ... + P5*r ).
- *
- * 3. Scale back to obtain exp(x):
- * From step 1, we have
- * exp(x) = 2^k * exp(r)
- *
- * Special cases:
- * exp(INF) is INF, exp(NaN) is NaN;
- * exp(-INF) is 0, and
- * for finite argument, only exp(0)=1 is exact.
- *
- * Accuracy:
- * according to an error analysis, the error is always less than
- * 1 ulp (unit in the last place).
- *
- * Misc. info.
- * For IEEE double
- * if x > 7.09782712893383973096e+02 then exp(x) overflow
- * if x < -7.45133219101941108420e+02 then exp(x) underflow
- *
- * 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
-one = 1.0,
-halF[2] = {0.5,-0.5,},
-huge = 1.0e+300,
-twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/
-o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */
-u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */
-ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */
- -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */
-ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */
- -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */
-invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */
-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 */
-
-double __ieee754_exp(double x) /* default IEEE double exp */
-{
- double y;
- double hi = 0.0;
- double lo = 0.0;
- double c;
- double t;
- int32_t k=0;
- int32_t xsb;
- u_int32_t hx;
-
- GET_HIGH_WORD(hx,x);
- xsb = (hx>>31)&1; /* sign bit of x */
- hx &= 0x7fffffff; /* high word of |x| */
-
- /* filter out non-finite argument */
- if(hx >= 0x40862E42) { /* if |x|>=709.78... */
- if(hx>=0x7ff00000) {
- u_int32_t lx;
- GET_LOW_WORD(lx,x);
- if(((hx&0xfffff)|lx)!=0)
- return x+x; /* NaN */
- else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */
- }
- #if 1
- if(x > o_threshold) return huge*huge; /* overflow */
- #else /* !!! FIXME: check this: "huge * huge" is a compiler warning, maybe they wanted +Inf? */
- if(x > o_threshold) return INFINITY; /* overflow */
- #endif
-
- if(x < u_threshold) return twom1000*twom1000; /* underflow */
- }
-
- /* argument reduction */
- if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */
- if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */
- hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb;
- } else {
- k = (int32_t) (invln2*x+halF[xsb]);
- t = k;
- hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */
- lo = t*ln2LO[0];
- }
- x = hi - lo;
- }
- else if(hx < 0x3e300000) { /* when |x|<2**-28 */
- if(huge+x>one) return one+x;/* trigger inexact */
- }
- else k = 0;
-
- /* x is now in primary range */
- t = x*x;
- c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5))));
- if(k==0) return one-((x*c)/(c-2.0)-x);
- else y = one-((lo-(x*c)/(2.0-c))-hi);
- if(k >= -1021) {
- u_int32_t hy;
- GET_HIGH_WORD(hy,y);
- SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */
- return y;
- } else {
- u_int32_t hy;
- GET_HIGH_WORD(hy,y);
- SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */
- return y*twom1000;
- }
-}
-
-/*
- * wrapper exp(x)
- */
-#ifndef _IEEE_LIBM
-double exp(double x)
-{
- static const double o_threshold = 7.09782712893383973096e+02; /* 0x40862E42, 0xFEFA39EF */
- static const double u_threshold = -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */
-
- double z = __ieee754_exp(x);
- if (_LIB_VERSION == _IEEE_)
- return z;
- if (isfinite(x)) {
- if (x > o_threshold)
- return __kernel_standard(x, x, 6); /* exp overflow */
- if (x < u_threshold)
- return __kernel_standard(x, x, 7); /* exp underflow */
- }
- return z;
-}
-#else
-strong_alias(__ieee754_exp, exp)
-#endif
-libm_hidden_def(exp)