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