skia2/include/private/SkFloatingPoint.h

/*
 * 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 "../private/SkFloatBits.h"
#include "SkTypes.h"
#include "SkSafe_math.h"
#include <float.h>
#include <math.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

// 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

static inline bool sk_float_isfinite(float x) {
    return SkFloatBits_IsFinite(SkFloat2Bits(x));
}

static inline bool sk_float_isinf(float x) {
    return SkFloatBits_IsInf(SkFloat2Bits(x));
}

static inline bool sk_float_isnan(float x) {
    return !(x == x);
}

#define sk_double_isnan(a)          sk_float_isnan(a)

#define SK_MaxS32FitsInFloat    2147483520
#define SK_MinS32FitsInFloat    -SK_MaxS32FitsInFloat

#define SK_MaxS64FitsInFloat    (SK_MaxS64 >> (63-24) << (63-24))   // 0x7fffff8000000000
#define SK_MinS64FitsInFloat    -SK_MaxS64FitsInFloat

/**
 *  Return the closest int for the given float. Returns SK_MaxS32FitsInFloat for NaN.
 */
static inline int sk_float_saturate2int(float x) {
    x = SkTMin<float>(x, SK_MaxS32FitsInFloat);
    x = SkTMax<float>(x, SK_MinS32FitsInFloat);
    return (int)x;
}

/**
 *  Return the closest int for the given double. Returns SK_MaxS32 for NaN.
 */
static inline int sk_double_saturate2int(double x) {
    x = SkTMin<double>(x, SK_MaxS32);
    x = SkTMax<double>(x, SK_MinS32);
    return (int)x;
}

/**
 *  Return the closest int64_t for the given float. Returns SK_MaxS64FitsInFloat for NaN.
 */
static inline int64_t sk_float_saturate2int64(float x) {
    x = SkTMin<float>(x, SK_MaxS64FitsInFloat);
    x = SkTMax<float>(x, SK_MinS64FitsInFloat);
    return (int64_t)x;
}

#define sk_float_floor2int(x)   sk_float_saturate2int(sk_float_floor(x))
#define sk_float_round2int(x)   sk_float_saturate2int(sk_float_floor((x) + 0.5f))
#define sk_float_ceil2int(x)    sk_float_saturate2int(sk_float_ceil(x))

#define sk_float_floor2int_no_saturate(x)   (int)sk_float_floor(x)
#define sk_float_round2int_no_saturate(x)   (int)sk_float_floor((x) + 0.5f)
#define sk_float_ceil2int_no_saturate(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)

// Cast double to float, ignoring any warning about too-large finite values being cast to float.
// Clang thinks this is undefined, but it's actually implementation defined to return either
// the largest float or infinity (one of the two bracketing representable floats).  Good enough!
#if defined(__clang__) && (__clang_major__ * 1000 + __clang_minor__) >= 3007
__attribute__((no_sanitize("float-cast-overflow")))
#endif
static inline float sk_double_to_float(double x) {
    return static_cast<float>(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

// IEEE defines how float divide behaves for non-finite values and zero-denoms, but C does not
// so we have a helper that suppresses the possible undefined-behavior warnings.

#ifdef __clang__
__attribute__((no_sanitize("float-divide-by-zero")))
#endif
static inline float sk_ieee_float_divide(float numer, float denom) {
    return numer / denom;
}

#ifdef __clang__
__attribute__((no_sanitize("float-divide-by-zero")))
#endif
static inline double sk_ieee_double_divide(double numer, double denom) {
    return numer / denom;
}

#endif