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- +1 −1 configure
- +1 −1 configure.in
- +3 −0 include/SDL_config.h.cmake
- +3 −0 include/SDL_config.h.in
- +3 −0 include/SDL_config_android.h
- +3 −0 include/SDL_config_iphoneos.h
- +3 −0 include/SDL_config_macosx.h
- +3 −0 include/SDL_config_pandora.h
- +3 −0 include/SDL_config_psp.h
- +3 −0 include/SDL_config_windows.h
- +3 −0 include/SDL_config_winrt.h
- +3 −0 include/SDL_config_wiz.h
- +3 −0 include/SDL_stdinc.h
- +3 −0 src/dynapi/SDL_dynapi_overrides.h
- +3 −0 src/dynapi/SDL_dynapi_procs.h
- +118 −0 src/libm/k_tan.c
- +1 −0 src/libm/math_libm.h
- +1 −0 src/libm/math_private.h
- +67 −0 src/libm/s_tan.c
- +30 −0 src/stdlib/SDL_stdlib.c
| @@ -0,0 +1,118 @@ | ||
| /* | ||
| * ==================================================== | ||
| * 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); | ||
| } | ||
| } |
| @@ -0,0 +1,67 @@ | ||
| /* | ||
| * ==================================================== | ||
| * 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.h" | ||
| #include "math_private.h" | ||
|
|
||
| double tan(double x) | ||
| { | ||
| double y[2],z=0.0; | ||
| int32_t n, ix; | ||
|
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| /* High word of x. */ | ||
| GET_HIGH_WORD(ix,x); | ||
|
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| /* |x| ~< pi/4 */ | ||
| ix &= 0x7fffffff; | ||
| if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); | ||
|
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||
| /* tan(Inf or NaN) is NaN */ | ||
| else if (ix>=0x7ff00000) return x-x; /* NaN */ | ||
|
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||
| /* 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) |