mirror of
https://github.com/bkaradzic/bx.git
synced 2026-02-19 21:43:00 +01:00
Removed reliance on libm/math.h CRT functions.
This commit is contained in:
Branimir Karadžić
199
src/math.cpp
199
src/math.cpp
@@ -5,8 +5,7 @@
|
||||
|
||||
#include "bx_p.h"
|
||||
#include <bx/math.h>
|
||||
|
||||
#include <math.h>
|
||||
#include <bx/uint32_t.h>
|
||||
|
||||
namespace bx
|
||||
{
|
||||
@@ -14,18 +13,17 @@ namespace bx
|
||||
const float kPi2 = 6.2831853071795864769252867665590f;
|
||||
const float kInvPi = 1.0f/kPi;
|
||||
const float kPiHalf = 1.5707963267948966192313216916398f;
|
||||
const float kPiQuarter = 0.7853981633974483096156608458199f;
|
||||
const float kSqrt2 = 1.4142135623730950488016887242097f;
|
||||
const float kLogNat10 = 2.3025850929940456840179914546844f;
|
||||
const float kInvLogNat2 = 1.4426950408889634073599246810019f;
|
||||
#if BX_COMPILER_MSVC
|
||||
const float kHuge = float(HUGE_VAL);
|
||||
#else
|
||||
const float kHuge = HUGE_VALF;
|
||||
#endif // BX_COMPILER_MSVC
|
||||
|
||||
float asin(float _a)
|
||||
{
|
||||
return ::asinf(_a);
|
||||
}
|
||||
const float kLogNat2Hi = 0.6931471805599453094172321214582f;
|
||||
const float kLogNat2Lo = 1.90821492927058770002e-10f;
|
||||
const float kE = 2.7182818284590452353602874713527f;
|
||||
const float kNearZero = 1.0f/float(1 << 28);
|
||||
const float kFloatMin = 1.175494e-38f;
|
||||
const float kFloatMax = 3.402823e+38f;
|
||||
const float kInfinity = bitsToFloat(UINT32_C(0x7f800000) );
|
||||
|
||||
namespace
|
||||
{
|
||||
@@ -72,14 +70,13 @@ namespace bx
|
||||
c10 = kSinC10;
|
||||
}
|
||||
|
||||
const float xsq = square(xx);
|
||||
float result;
|
||||
result = xsq * c10 + c8;
|
||||
result = xsq * result + c6;
|
||||
result = xsq * result + c4;
|
||||
result = xsq * result + c2;
|
||||
result = xsq * result + 1.0f;
|
||||
result *= c0;
|
||||
const float xsq = square(xx);
|
||||
const float tmp0 = mad(c10, xsq, c8 );
|
||||
const float tmp1 = mad(tmp0, xsq, c6 );
|
||||
const float tmp2 = mad(tmp1, xsq, c4 );
|
||||
const float tmp3 = mad(tmp2, xsq, c2 );
|
||||
const float tmp4 = mad(tmp3, xsq, 1.0);
|
||||
const float result = tmp4 * c0;
|
||||
|
||||
return bits == 1 || bits == 2
|
||||
? -result
|
||||
@@ -87,38 +84,168 @@ namespace bx
|
||||
;
|
||||
}
|
||||
|
||||
float tan(float _a)
|
||||
namespace
|
||||
{
|
||||
#if 0
|
||||
return sin(_a) / cos(_a);
|
||||
#else
|
||||
return ::tanf(_a);
|
||||
#endif
|
||||
}
|
||||
static const float kAcosC0 = 1.5707288f;
|
||||
static const float kAcosC1 = -0.2121144f;
|
||||
static const float kAcosC2 = 0.0742610f;
|
||||
static const float kAcosC3 = -0.0187293f;
|
||||
|
||||
} // namespace
|
||||
|
||||
float acos(float _a)
|
||||
{
|
||||
return ::acosf(_a);
|
||||
const float absa = abs(_a);
|
||||
const float tmp0 = mad(kAcosC3, absa, kAcosC2);
|
||||
const float tmp1 = mad(tmp0, absa, kAcosC1);
|
||||
const float tmp2 = mad(tmp1, absa, kAcosC0);
|
||||
const float tmp3 = tmp2 * sqrt(1.0 - absa);
|
||||
const float negate = float(_a < 0.0f);
|
||||
const float tmp4 = tmp3 - 2.0f*negate*tmp3;
|
||||
const float result = negate*kPi + tmp4;
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
namespace
|
||||
{
|
||||
static const float kAtan2C0 = -0.013480470f;
|
||||
static const float kAtan2C1 = 0.057477314f;
|
||||
static const float kAtan2C2 = -0.121239071f;
|
||||
static const float kAtan2C3 = 0.195635925f;
|
||||
static const float kAtan2C4 = -0.332994597f;
|
||||
static const float kAtan2C5 = 0.999995630f;
|
||||
|
||||
} // namespace
|
||||
|
||||
float atan2(float _y, float _x)
|
||||
{
|
||||
return ::atan2f(_y, _x);
|
||||
const float ax = abs(_x);
|
||||
const float ay = abs(_y);
|
||||
const float maxaxy = max(ax, ay);
|
||||
const float minaxy = min(ax, ay);
|
||||
const float mxy = minaxy / maxaxy;
|
||||
const float mxysq = square(mxy);
|
||||
const float tmp0 = mad(kAtan2C0, mxysq, kAtan2C1);
|
||||
const float tmp1 = mad(tmp0, mxysq, kAtan2C2);
|
||||
const float tmp2 = mad(tmp1, mxysq, kAtan2C3);
|
||||
const float tmp3 = mad(tmp2, mxysq, kAtan2C4);
|
||||
const float tmp4 = mad(tmp3, mxysq, kAtan2C5);
|
||||
const float tmp5 = tmp4 * mxy;
|
||||
const float tmp6 = ay > ax ? kPiHalf - tmp5 : tmp5;
|
||||
const float tmp7 = _x < 0.0f ? kPi - tmp6 : tmp6;
|
||||
const float result = sign(_y)*tmp7;
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
float ldexp(float _a, int32_t _b)
|
||||
{
|
||||
const uint32_t ftob = floatToBits(_a);
|
||||
const uint32_t masked = uint32_and(ftob, UINT32_C(0xff800000) );
|
||||
const uint32_t expsign0 = uint32_sra(masked, 23);
|
||||
const uint32_t tmp = uint32_iadd(expsign0, _b);
|
||||
const uint32_t expsign1 = uint32_sll(tmp, 23);
|
||||
const uint32_t mantissa = uint32_and(ftob, UINT32_C(0x007fffff) );
|
||||
const uint32_t bits = uint32_or(mantissa, expsign1);
|
||||
const float result = bitsToFloat(bits);
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
float frexp(float _a, int32_t* _exp)
|
||||
{
|
||||
const uint32_t ftob = floatToBits(_a);
|
||||
const uint32_t masked0 = uint32_and(ftob, UINT32_C(0x7f800000) );
|
||||
const uint32_t exp0 = uint32_srl(masked0, 23);
|
||||
const uint32_t masked1 = uint32_and(ftob, UINT32_C(0x807fffff) );
|
||||
const uint32_t bits = uint32_or(masked1, UINT32_C(0x3f000000) );
|
||||
const float result = bitsToFloat(bits);
|
||||
|
||||
*_exp = int32_t(exp0 - 0x7e);
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
namespace
|
||||
{
|
||||
static const float kExpC0 = 1.66666666666666019037e-01f;
|
||||
static const float kExpC1 = -2.77777777770155933842e-03f;
|
||||
static const float kExpC2 = 6.61375632143793436117e-05f;
|
||||
static const float kExpC3 = -1.65339022054652515390e-06f;
|
||||
static const float kExpC4 = 4.13813679705723846039e-08f;
|
||||
static const float kExpMax = 7.09782712893383973096e+02f;
|
||||
|
||||
} // namespace
|
||||
|
||||
float exp(float _a)
|
||||
{
|
||||
return ::expf(_a);
|
||||
if (abs(_a) <= kNearZero)
|
||||
{
|
||||
return _a + 1.0f;
|
||||
}
|
||||
|
||||
const float kk = round(_a*kInvLogNat2);
|
||||
const float hi = _a - kk*kLogNat2Hi;
|
||||
const float lo = kk*kLogNat2Lo;
|
||||
const float hml = hi - lo;
|
||||
const float hmlsq = square(hml);
|
||||
const float tmp0 = mad(kExpC4, hmlsq, kExpC3);
|
||||
const float tmp1 = mad(tmp0, hmlsq, kExpC2);
|
||||
const float tmp2 = mad(tmp1, hmlsq, kExpC1);
|
||||
const float tmp3 = mad(tmp2, hmlsq, kExpC0);
|
||||
const float tmp4 = hml - hmlsq * tmp3;
|
||||
const float tmp5 = hml*tmp4/(2.0f-tmp4);
|
||||
const float tmp6 = 1.0f - ( (lo - tmp5) - hi);
|
||||
const float result = ldexp(tmp6, int32_t(kk) );
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
namespace
|
||||
{
|
||||
static const float kLogC0 = 6.666666666666735130e-01f;
|
||||
static const float kLogC1 = 3.999999999940941908e-01f;
|
||||
static const float kLogC2 = 2.857142874366239149e-01f;
|
||||
static const float kLogC3 = 2.222219843214978396e-01f;
|
||||
static const float kLogC4 = 1.818357216161805012e-01f;
|
||||
static const float kLogC5 = 1.531383769920937332e-01f;
|
||||
static const float kLogC6 = 1.479819860511658591e-01f;
|
||||
|
||||
} // namespace
|
||||
|
||||
float log(float _a)
|
||||
{
|
||||
return ::logf(_a);
|
||||
}
|
||||
int32_t exp;
|
||||
float ff = frexp(_a, &exp);
|
||||
if (ff < kSqrt2*0.5f)
|
||||
{
|
||||
ff *= 2.0f;
|
||||
--exp;
|
||||
}
|
||||
|
||||
float sqrt(float _a)
|
||||
{
|
||||
return ::sqrtf(_a);
|
||||
ff -= 1.0f;
|
||||
const float kk = float(exp);
|
||||
const float hi = kk*kLogNat2Hi;
|
||||
const float lo = kk*kLogNat2Lo;
|
||||
const float ss = ff / (2.0f + ff);
|
||||
const float s2 = square(ss);
|
||||
const float s4 = square(s2);
|
||||
|
||||
const float tmp0 = mad(kLogC6, s4, kLogC4);
|
||||
const float tmp1 = mad(tmp0, s4, kLogC2);
|
||||
const float tmp2 = mad(tmp1, s4, kLogC0);
|
||||
const float t1 = s2*tmp2;
|
||||
|
||||
const float tmp3 = mad(kLogC5, s4, kLogC3);
|
||||
const float tmp4 = mad(tmp3, s4, kLogC1);
|
||||
const float t2 = s4*tmp4;
|
||||
|
||||
const float t12 = t1 + t2;
|
||||
const float hfsq = 0.5*square(ff);
|
||||
const float result = hi - ( (hfsq - (ss*(hfsq+t12) + lo) ) - ff);
|
||||
|
||||
return result;
|
||||
}
|
||||
|
||||
float floor(float _a)
|
||||
@@ -126,7 +253,7 @@ namespace bx
|
||||
if (_a < 0.0f)
|
||||
{
|
||||
const float fr = fract(-_a);
|
||||
float result = -_a - fr;
|
||||
const float result = -_a - fr;
|
||||
|
||||
return -(0.0f != fr
|
||||
? result + 1.0f
|
||||
|
||||
Reference in New Issue
Block a user