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/*
* Copyright 2006 The Android Open Source Project
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#ifndef SkFloatingPoint_DEFINED
#define SkFloatingPoint_DEFINED
#include "SkTypes.h"
#include <math.h>
#include <float.h>
// For _POSIX_VERSION
#if defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
#include <unistd.h>
#endif
#include "SkFloatBits.h"
// C++98 cmath std::pow seems to be the earliest portable way to get float pow.
// However, on Linux including cmath undefines isfinite.
// http://gcc.gnu.org/bugzilla/show_bug.cgi?id=14608
static inline float sk_float_pow(float base, float exp) {
return powf(base, exp);
}
static inline float sk_float_copysign(float x, float y) {
// c++11 contains a 'float copysign(float, float)' function in <cmath>.
#if __cplusplus >= 201103L || (defined(_MSC_VER) && _MSC_VER >= 1800)
return copysign(x, y);
// Posix has demanded 'float copysignf(float, float)' (from C99) since Issue 6.
#elif defined(_POSIX_VERSION) && _POSIX_VERSION >= 200112L
return copysignf(x, y);
// Visual studio prior to 13 only has 'double _copysign(double, double)'.
#elif defined(_MSC_VER)
return (float)_copysign(x, y);
// Otherwise convert to bits and extract sign.
#else
int32_t xbits = SkFloat2Bits(x);
int32_t ybits = SkFloat2Bits(y);
return SkBits2Float((xbits & 0x7FFFFFFF) | (ybits & 0x80000000));
#endif
}
#ifdef SK_BUILD_FOR_WINCE
#define sk_float_sqrt(x) (float)::sqrt(x)
#define sk_float_sin(x) (float)::sin(x)
#define sk_float_cos(x) (float)::cos(x)
#define sk_float_tan(x) (float)::tan(x)
#define sk_float_acos(x) (float)::acos(x)
#define sk_float_asin(x) (float)::asin(x)
#define sk_float_atan2(y,x) (float)::atan2(y,x)
#define sk_float_abs(x) (float)::fabs(x)
#define sk_float_mod(x,y) (float)::fmod(x,y)
#define sk_float_exp(x) (float)::exp(x)
#define sk_float_log(x) (float)::log(x)
#define sk_float_floor(x) (float)::floor(x)
#define sk_float_ceil(x) (float)::ceil(x)
#else
#define sk_float_sqrt(x) sqrtf(x)
#define sk_float_sin(x) sinf(x)
#define sk_float_cos(x) cosf(x)
#define sk_float_tan(x) tanf(x)
#define sk_float_floor(x) floorf(x)
#define sk_float_ceil(x) ceilf(x)
#ifdef SK_BUILD_FOR_MAC
#define sk_float_acos(x) static_cast<float>(acos(x))
#define sk_float_asin(x) static_cast<float>(asin(x))
#else
#define sk_float_acos(x) acosf(x)
#define sk_float_asin(x) asinf(x)
#endif
#define sk_float_atan2(y,x) atan2f(y,x)
#define sk_float_abs(x) fabsf(x)
#define sk_float_mod(x,y) fmodf(x,y)
#define sk_float_exp(x) expf(x)
#define sk_float_log(x) logf(x)
#endif
#ifdef SK_BUILD_FOR_WIN
#define sk_float_isfinite(x) _finite(x)
#define sk_float_isnan(x) _isnan(x)
static inline int sk_float_isinf(float x) {
int32_t bits = SkFloat2Bits(x);
return (bits << 1) == (0xFF << 24);
}
#else
#define sk_float_isfinite(x) isfinite(x)
#define sk_float_isnan(x) isnan(x)
#define sk_float_isinf(x) isinf(x)
#endif
#define sk_double_isnan(a) sk_float_isnan(a)
#ifdef SK_USE_FLOATBITS
#define sk_float_floor2int(x) SkFloatToIntFloor(x)
#define sk_float_round2int(x) SkFloatToIntRound(x)
#define sk_float_ceil2int(x) SkFloatToIntCeil(x)
#else
#define sk_float_floor2int(x) (int)sk_float_floor(x)
#define sk_float_round2int(x) (int)sk_float_floor((x) + 0.5f)
#define sk_float_ceil2int(x) (int)sk_float_ceil(x)
#endif
extern const uint32_t gIEEENotANumber;
extern const uint32_t gIEEEInfinity;
extern const uint32_t gIEEENegativeInfinity;
#define SK_FloatNaN (*SkTCast<const float*>(&gIEEENotANumber))
#define SK_FloatInfinity (*SkTCast<const float*>(&gIEEEInfinity))
#define SK_FloatNegativeInfinity (*SkTCast<const float*>(&gIEEENegativeInfinity))
#if defined(__SSE__)
#include <xmmintrin.h>
#elif defined(SK_ARM_HAS_NEON)
#include <arm_neon.h>
#endif
// Fast, approximate inverse square root.
// Compare to name-brand "1.0f / sk_float_sqrt(x)". Should be around 10x faster on SSE, 2x on NEON.
static inline float sk_float_rsqrt(const float x) {
// We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got
// it at compile time. This is going to be too fast to productively hide behind a function pointer.
//
// We do one step of Newton's method to refine the estimates in the NEON and null paths. No
// refinement is faster, but very innacurate. Two steps is more accurate, but slower than 1/sqrt.
#if defined(__SSE__)
float result;
_mm_store_ss(&result, _mm_rsqrt_ss(_mm_set_ss(x)));
return result;
#elif defined(SK_ARM_HAS_NEON)
// Get initial estimate.
const float32x2_t xx = vdup_n_f32(x); // Clever readers will note we're doing everything 2x.
float32x2_t estimate = vrsqrte_f32(xx);
// One step of Newton's method to refine.
const float32x2_t estimate_sq = vmul_f32(estimate, estimate);
estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq));
return vget_lane_f32(estimate, 0); // 1 will work fine too; the answer's in both places.
#else
// Get initial estimate.
int i = *SkTCast<int*>(&x);
i = 0x5f3759df - (i>>1);
float estimate = *SkTCast<float*>(&i);
// One step of Newton's method to refine.
const float estimate_sq = estimate*estimate;
estimate *= (1.5f-0.5f*x*estimate_sq);
return estimate;
#endif
}
#endif
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