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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 "SkSafe_math.h"
#include <float.h>
#if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
#include <xmmintrin.h>
#elif defined(SK_ARM_HAS_NEON)
#include <arm_neon.h>
#endif
// 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);
}
#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)
#define sk_float_trunc(x) truncf(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_copysign(x, y) copysignf(x, y)
#define sk_float_mod(x,y) fmodf(x,y)
#define sk_float_exp(x) expf(x)
#define sk_float_log(x) logf(x)
#define sk_float_round(x) sk_float_floor((x) + 0.5f)
// can't find log2f on android, but maybe that just a tool bug?
#ifdef SK_BUILD_FOR_ANDROID
static inline float sk_float_log2(float x) {
const double inv_ln_2 = 1.44269504088896;
return (float)(log(x) * inv_ln_2);
}
#else
#define sk_float_log2(x) log2f(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)
#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)
#define sk_double_floor(x) floor(x)
#define sk_double_round(x) floor((x) + 0.5)
#define sk_double_ceil(x) ceil(x)
#define sk_double_floor2int(x) (int)floor(x)
#define sk_double_round2int(x) (int)floor((x) + 0.5f)
#define sk_double_ceil2int(x) (int)ceil(x)
static const uint32_t kIEEENotANumber = 0x7fffffff;
#define SK_FloatNaN (*SkTCast<const float*>(&kIEEENotANumber))
#define SK_FloatInfinity (+(float)INFINITY)
#define SK_FloatNegativeInfinity (-(float)INFINITY)
static inline float sk_float_rsqrt_portable(float x) {
// Get initial estimate.
int i;
memcpy(&i, &x, 4);
i = 0x5F1FFFF9 - (i>>1);
float estimate;
memcpy(&estimate, &i, 4);
// One step of Newton's method to refine.
const float estimate_sq = estimate*estimate;
estimate *= 0.703952253f*(2.38924456f-x*estimate_sq);
return estimate;
}
// 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(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 portable paths. No
// refinement is faster, but very innacurate. Two steps is more accurate, but slower than 1/sqrt.
//
// Optimized constants in the portable path courtesy of http://rrrola.wz.cz/inv_sqrt.html
#if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(x)));
#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
return sk_float_rsqrt_portable(x);
#endif
}
// This is the number of significant digits we can print in a string such that when we read that
// string back we get the floating point number we expect. The minimum value C requires is 6, but
// most compilers support 9
#ifdef FLT_DECIMAL_DIG
#define SK_FLT_DECIMAL_DIG FLT_DECIMAL_DIG
#else
#define SK_FLT_DECIMAL_DIG 9
#endif
#endif
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