1/*
2 * Copyright 2006 The Android Open Source Project
3 *
4 * Use of this source code is governed by a BSD-style license that can be
5 * found in the LICENSE file.
6 */
7
8#ifndef SkFloatingPoint_DEFINED
9#define SkFloatingPoint_DEFINED
10
11#include "include/core/SkTypes.h"
12#include "include/private/SkFloatBits.h"
13#include "include/private/SkSafe_math.h"
14#include <float.h>
15#include <math.h>
16#include <cmath>
17#include <cstring>
18#include <limits>
19
20
21#if defined(SK_LEGACY_FLOAT_RSQRT)
22#if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
23    #include <xmmintrin.h>
24#elif defined(SK_ARM_HAS_NEON)
25    #include <arm_neon.h>
26#endif
27#endif
28
29// For _POSIX_VERSION
30#if defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
31#include <unistd.h>
32#endif
33
34constexpr float SK_FloatSqrt2 = 1.41421356f;
35constexpr float SK_FloatPI    = 3.14159265f;
36constexpr double SK_DoublePI  = 3.14159265358979323846264338327950288;
37
38// C++98 cmath std::pow seems to be the earliest portable way to get float pow.
39// However, on Linux including cmath undefines isfinite.
40// http://gcc.gnu.org/bugzilla/show_bug.cgi?id=14608
41static inline float sk_float_pow(float base, float exp) {
42    return powf(base, exp);
43}
44
45#define sk_float_sqrt(x)        sqrtf(x)
46#define sk_float_sin(x)         sinf(x)
47#define sk_float_cos(x)         cosf(x)
48#define sk_float_tan(x)         tanf(x)
49#define sk_float_floor(x)       floorf(x)
50#define sk_float_ceil(x)        ceilf(x)
51#define sk_float_trunc(x)       truncf(x)
52#ifdef SK_BUILD_FOR_MAC
53#    define sk_float_acos(x)    static_cast<float>(acos(x))
54#    define sk_float_asin(x)    static_cast<float>(asin(x))
55#else
56#    define sk_float_acos(x)    acosf(x)
57#    define sk_float_asin(x)    asinf(x)
58#endif
59#define sk_float_atan2(y,x)     atan2f(y,x)
60#define sk_float_abs(x)         fabsf(x)
61#define sk_float_copysign(x, y) copysignf(x, y)
62#define sk_float_mod(x,y)       fmodf(x,y)
63#define sk_float_exp(x)         expf(x)
64#define sk_float_log(x)         logf(x)
65
66constexpr float sk_float_degrees_to_radians(float degrees) {
67    return degrees * (SK_FloatPI / 180);
68}
69
70constexpr float sk_float_radians_to_degrees(float radians) {
71    return radians * (180 / SK_FloatPI);
72}
73
74#define sk_float_round(x) sk_float_floor((x) + 0.5f)
75
76// can't find log2f on android, but maybe that just a tool bug?
77#ifdef SK_BUILD_FOR_ANDROID
78    static inline float sk_float_log2(float x) {
79        const double inv_ln_2 = 1.44269504088896;
80        return (float)(log(x) * inv_ln_2);
81    }
82#else
83    #define sk_float_log2(x)        log2f(x)
84#endif
85
86static inline bool sk_float_isfinite(float x) {
87    return SkFloatBits_IsFinite(SkFloat2Bits(x));
88}
89
90static inline bool sk_floats_are_finite(float a, float b) {
91    return sk_float_isfinite(a) && sk_float_isfinite(b);
92}
93
94// warning: comparing floating point with == or != is unsafe
95// storing and comparing against same constants ok.
96#if defined(__clang__)
97#pragma clang diagnostic ignored "-Wfloat-equal"
98#elif defined(__GNUC__)
99#pragma GCC diagnostic ignored "-Wfloat-equal"
100#endif
101static inline bool sk_floats_are_finite(const float array[], int count) {
102    float prod = 0;
103    for (int i = 0; i < count; ++i) {
104        prod *= array[i];
105    }
106    // At this point, prod will either be NaN or 0
107    return prod == 0;   // if prod is NaN, this check will return false
108}
109
110static inline bool sk_float_isinf(float x) {
111    return SkFloatBits_IsInf(SkFloat2Bits(x));
112}
113
114static inline bool sk_float_isnan(float x) {
115    return !(x == x);
116}
117
118#define sk_double_isnan(a)          sk_float_isnan(a)
119
120#define SK_MaxS32FitsInFloat    2147483520
121#define SK_MinS32FitsInFloat    -SK_MaxS32FitsInFloat
122
123#define SK_MaxS64FitsInFloat    (SK_MaxS64 >> (63-24) << (63-24))   // 0x7fffff8000000000
124#define SK_MinS64FitsInFloat    -SK_MaxS64FitsInFloat
125
126/**
127 *  Return the closest int for the given float. Returns SK_MaxS32FitsInFloat for NaN.
128 */
129static inline int sk_float_saturate2int(float x) {
130    x = x < SK_MaxS32FitsInFloat ? x : SK_MaxS32FitsInFloat;
131    x = x > SK_MinS32FitsInFloat ? x : SK_MinS32FitsInFloat;
132    return (int)x;
133}
134
135/**
136 *  Return the closest int for the given double. Returns SK_MaxS32 for NaN.
137 */
138static inline int sk_double_saturate2int(double x) {
139    x = x < SK_MaxS32 ? x : SK_MaxS32;
140    x = x > SK_MinS32 ? x : SK_MinS32;
141    return (int)x;
142}
143
144/**
145 *  Return the closest int64_t for the given float. Returns SK_MaxS64FitsInFloat for NaN.
146 */
147static inline int64_t sk_float_saturate2int64(float x) {
148    x = x < SK_MaxS64FitsInFloat ? x : SK_MaxS64FitsInFloat;
149    x = x > SK_MinS64FitsInFloat ? x : SK_MinS64FitsInFloat;
150    return (int64_t)x;
151}
152
153#define sk_float_floor2int(x)   sk_float_saturate2int(sk_float_floor(x))
154#define sk_float_round2int(x)   sk_float_saturate2int(sk_float_floor((x) + 0.5f))
155#define sk_float_ceil2int(x)    sk_float_saturate2int(sk_float_ceil(x))
156
157#define sk_float_floor2int_no_saturate(x)   (int)sk_float_floor(x)
158#define sk_float_round2int_no_saturate(x)   (int)sk_float_floor((x) + 0.5f)
159#define sk_float_ceil2int_no_saturate(x)    (int)sk_float_ceil(x)
160
161#define sk_double_floor(x)          floor(x)
162#define sk_double_round(x)          floor((x) + 0.5)
163#define sk_double_ceil(x)           ceil(x)
164#define sk_double_floor2int(x)      (int)floor(x)
165#define sk_double_round2int(x)      (int)floor((x) + 0.5)
166#define sk_double_ceil2int(x)       (int)ceil(x)
167
168// Cast double to float, ignoring any warning about too-large finite values being cast to float.
169// Clang thinks this is undefined, but it's actually implementation defined to return either
170// the largest float or infinity (one of the two bracketing representable floats).  Good enough!
171SK_ATTRIBUTE(no_sanitize("float-cast-overflow"))
172static inline float sk_double_to_float(double x) {
173    return static_cast<float>(x);
174}
175
176#define SK_FloatNaN                 std::numeric_limits<float>::quiet_NaN()
177#define SK_FloatInfinity            (+std::numeric_limits<float>::infinity())
178#define SK_FloatNegativeInfinity    (-std::numeric_limits<float>::infinity())
179
180#define SK_DoubleNaN                std::numeric_limits<double>::quiet_NaN()
181
182// Returns false if any of the floats are outside of [0...1]
183// Returns true if count is 0
184bool sk_floats_are_unit(const float array[], size_t count);
185
186#if defined(SK_LEGACY_FLOAT_RSQRT)
187static inline float sk_float_rsqrt_portable(float x) {
188    // Get initial estimate.
189    int i;
190    memcpy(&i, &x, 4);
191    i = 0x5F1FFFF9 - (i>>1);
192    float estimate;
193    memcpy(&estimate, &i, 4);
194
195    // One step of Newton's method to refine.
196    const float estimate_sq = estimate*estimate;
197    estimate *= 0.703952253f*(2.38924456f-x*estimate_sq);
198    return estimate;
199}
200
201// Fast, approximate inverse square root.
202// Compare to name-brand "1.0f / sk_float_sqrt(x)".  Should be around 10x faster on SSE, 2x on NEON.
203static inline float sk_float_rsqrt(float x) {
204// We want all this inlined, so we'll inline SIMD and just take the hit when we don't know we've got
205// it at compile time.  This is going to be too fast to productively hide behind a function pointer.
206//
207// We do one step of Newton's method to refine the estimates in the NEON and portable paths.  No
208// refinement is faster, but very innacurate.  Two steps is more accurate, but slower than 1/sqrt.
209//
210// Optimized constants in the portable path courtesy of http://rrrola.wz.cz/inv_sqrt.html
211#if SK_CPU_SSE_LEVEL >= SK_CPU_SSE_LEVEL_SSE1
212    return _mm_cvtss_f32(_mm_rsqrt_ss(_mm_set_ss(x)));
213#elif defined(SK_ARM_HAS_NEON)
214    // Get initial estimate.
215    const float32x2_t xx = vdup_n_f32(x);  // Clever readers will note we're doing everything 2x.
216    float32x2_t estimate = vrsqrte_f32(xx);
217
218    // One step of Newton's method to refine.
219    const float32x2_t estimate_sq = vmul_f32(estimate, estimate);
220    estimate = vmul_f32(estimate, vrsqrts_f32(xx, estimate_sq));
221    return vget_lane_f32(estimate, 0);  // 1 will work fine too; the answer's in both places.
222#else
223    return sk_float_rsqrt_portable(x);
224#endif
225}
226#else
227
228static inline float sk_float_rsqrt_portable(float x) { return 1.0f / sk_float_sqrt(x); }
229static inline float sk_float_rsqrt         (float x) { return 1.0f / sk_float_sqrt(x); }
230
231#endif
232
233// Returns the log2 of the provided value, were that value to be rounded up to the next power of 2.
234// Returns 0 if value <= 0:
235// Never returns a negative number, even if value is NaN.
236//
237//     sk_float_nextlog2((-inf..1]) -> 0
238//     sk_float_nextlog2((1..2]) -> 1
239//     sk_float_nextlog2((2..4]) -> 2
240//     sk_float_nextlog2((4..8]) -> 3
241//     ...
242static inline int sk_float_nextlog2(float x) {
243    uint32_t bits = (uint32_t)SkFloat2Bits(x);
244    bits += (1u << 23) - 1u;  // Increment the exponent for non-powers-of-2.
245    int exp = ((int32_t)bits >> 23) - 127;
246    return exp & ~(exp >> 31);  // Return 0 for negative or denormalized floats, and exponents < 0.
247}
248
249// This is the number of significant digits we can print in a string such that when we read that
250// string back we get the floating point number we expect.  The minimum value C requires is 6, but
251// most compilers support 9
252#ifdef FLT_DECIMAL_DIG
253#define SK_FLT_DECIMAL_DIG FLT_DECIMAL_DIG
254#else
255#define SK_FLT_DECIMAL_DIG 9
256#endif
257
258// IEEE defines how float divide behaves for non-finite values and zero-denoms, but C does not
259// so we have a helper that suppresses the possible undefined-behavior warnings.
260
261SK_ATTRIBUTE(no_sanitize("float-divide-by-zero"))
262static inline float sk_ieee_float_divide(float numer, float denom) {
263    return numer / denom;
264}
265
266SK_ATTRIBUTE(no_sanitize("float-divide-by-zero"))
267static inline double sk_ieee_double_divide(double numer, double denom) {
268    return numer / denom;
269}
270
271// While we clean up divide by zero, we'll replace places that do divide by zero with this TODO.
272static inline float sk_ieee_float_divide_TODO_IS_DIVIDE_BY_ZERO_SAFE_HERE(float n, float d) {
273    return sk_ieee_float_divide(n,d);
274}
275
276static inline float sk_fmaf(float f, float m, float a) {
277#if defined(FP_FAST_FMA)
278    return std::fmaf(f,m,a);
279#else
280    return f*m+a;
281#endif
282}
283
284#endif
285