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257 lines
7.6 KiB
C++
257 lines
7.6 KiB
C++
// This code is in the public domain -- castano@gmail.com
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#pragma once
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#ifndef NV_MATH_FTOI_H
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#define NV_MATH_FTOI_H
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#include "nvmath/nvmath.h"
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#include <math.h>
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namespace nv
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{
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// Optimized float to int conversions. See:
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// http://cbloomrants.blogspot.com/2009/01/01-17-09-float-to-int.html
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// http://www.stereopsis.com/sree/fpu2006.html
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// http://assemblyrequired.crashworks.org/2009/01/12/why-you-should-never-cast-floats-to-ints/
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// http://chrishecker.com/Miscellaneous_Technical_Articles#Floating_Point
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union DoubleAnd64 {
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uint64 i;
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double d;
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};
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static const double floatutil_xs_doublemagic = (6755399441055744.0); // 2^52 * 1.5
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static const double floatutil_xs_doublemagicdelta = (1.5e-8); // almost .5f = .5f + 1e^(number of exp bit)
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static const double floatutil_xs_doublemagicroundeps = (0.5f - floatutil_xs_doublemagicdelta); // almost .5f = .5f - 1e^(number of exp bit)
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NV_FORCEINLINE int ftoi_round_xs(double val, double magic) {
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#if 1
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DoubleAnd64 dunion;
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dunion.d = val + magic;
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return (int32) dunion.i; // just cast to grab the bottom bits
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#else
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val += magic;
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return ((int*)&val)[0]; // @@ Assumes little endian.
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#endif
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}
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NV_FORCEINLINE int ftoi_round_xs(float val) {
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return ftoi_round_xs(val, floatutil_xs_doublemagic);
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}
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NV_FORCEINLINE int ftoi_floor_xs(float val) {
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return ftoi_round_xs(val - floatutil_xs_doublemagicroundeps, floatutil_xs_doublemagic);
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}
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NV_FORCEINLINE int ftoi_ceil_xs(float val) {
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return ftoi_round_xs(val + floatutil_xs_doublemagicroundeps, floatutil_xs_doublemagic);
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}
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NV_FORCEINLINE int ftoi_trunc_xs(float val) {
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return (val<0) ? ftoi_ceil_xs(val) : ftoi_floor_xs(val);
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}
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#if NV_CPU_X86 || NV_CPU_X86_64
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NV_FORCEINLINE int ftoi_round_sse(float f) {
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return _mm_cvt_ss2si(_mm_set_ss(f));
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}
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NV_FORCEINLINE int ftoi_trunc_sse(float f) {
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return _mm_cvtt_ss2si(_mm_set_ss(f));
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}
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#endif
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#if NV_USE_SSE
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NV_FORCEINLINE int ftoi_round(float val) {
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return ftoi_round_sse(val);
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}
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NV_FORCEINLINE int ftoi_trunc(float f) {
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return ftoi_trunc_sse(f);
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}
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// We can probably do better than this. See for example:
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// http://dss.stephanierct.com/DevBlog/?p=8
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NV_FORCEINLINE int ftoi_floor(float val) {
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return ftoi_round(floorf(val));
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}
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NV_FORCEINLINE int ftoi_ceil(float val) {
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return ftoi_round(ceilf(val));
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}
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#else
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// In theory this should work with any double floating point math implementation, but it appears that MSVC produces incorrect code
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// when SSE2 is targeted and fast math is enabled (/arch:SSE2 & /fp:fast). These problems go away with /fp:precise, which is the default mode.
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NV_FORCEINLINE int ftoi_round(float val) {
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return ftoi_round_xs(val);
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}
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NV_FORCEINLINE int ftoi_floor(float val) {
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return ftoi_floor_xs(val);
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}
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NV_FORCEINLINE int ftoi_ceil(float val) {
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return ftoi_ceil_xs(val);
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}
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NV_FORCEINLINE int ftoi_trunc(float f) {
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return ftoi_trunc_xs(f);
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}
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#endif
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inline void test_ftoi() {
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// Round to nearest integer.
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nvCheck(ftoi_round(0.1f) == 0);
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nvCheck(ftoi_round(0.6f) == 1);
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nvCheck(ftoi_round(-0.2f) == 0);
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nvCheck(ftoi_round(-0.7f) == -1);
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nvCheck(ftoi_round(10.1f) == 10);
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nvCheck(ftoi_round(10.6f) == 11);
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nvCheck(ftoi_round(-90.1f) == -90);
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nvCheck(ftoi_round(-90.6f) == -91);
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nvCheck(ftoi_round(0) == 0);
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nvCheck(ftoi_round(1) == 1);
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nvCheck(ftoi_round(-1) == -1);
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nvCheck(ftoi_round(0.5f) == 0); // How are midpoints rounded? Bankers rounding.
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nvCheck(ftoi_round(1.5f) == 2);
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nvCheck(ftoi_round(2.5f) == 2);
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nvCheck(ftoi_round(3.5f) == 4);
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nvCheck(ftoi_round(4.5f) == 4);
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nvCheck(ftoi_round(-0.5f) == 0);
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nvCheck(ftoi_round(-1.5f) == -2);
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// Truncation (round down if > 0, round up if < 0).
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nvCheck(ftoi_trunc(0.1f) == 0);
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nvCheck(ftoi_trunc(0.6f) == 0);
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nvCheck(ftoi_trunc(-0.2f) == 0);
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nvCheck(ftoi_trunc(-0.7f) == 0); // @@ When using /arch:SSE2 in Win32, msvc produce wrong code for this one. It is skipping the addition.
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nvCheck(ftoi_trunc(1.99f) == 1);
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nvCheck(ftoi_trunc(-1.2f) == -1);
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// Floor (round down).
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nvCheck(ftoi_floor(0.1f) == 0);
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nvCheck(ftoi_floor(0.6f) == 0);
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nvCheck(ftoi_floor(-0.2f) == -1);
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nvCheck(ftoi_floor(-0.7f) == -1);
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nvCheck(ftoi_floor(1.99f) == 1);
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nvCheck(ftoi_floor(-1.2f) == -2);
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nvCheck(ftoi_floor(0) == 0);
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nvCheck(ftoi_floor(1) == 1);
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nvCheck(ftoi_floor(-1) == -1);
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nvCheck(ftoi_floor(2) == 2);
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nvCheck(ftoi_floor(-2) == -2);
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// Ceil (round up).
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nvCheck(ftoi_ceil(0.1f) == 1);
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nvCheck(ftoi_ceil(0.6f) == 1);
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nvCheck(ftoi_ceil(-0.2f) == 0);
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nvCheck(ftoi_ceil(-0.7f) == 0);
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nvCheck(ftoi_ceil(1.99f) == 2);
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nvCheck(ftoi_ceil(-1.2f) == -1);
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nvCheck(ftoi_ceil(0) == 0);
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nvCheck(ftoi_ceil(1) == 1);
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nvCheck(ftoi_ceil(-1) == -1);
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nvCheck(ftoi_ceil(2) == 2);
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nvCheck(ftoi_ceil(-2) == -2);
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}
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// Safe versions using standard casts.
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inline int iround(float f)
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{
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return int(floorf(f + 0.5f));
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}
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inline int iround(double f)
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{
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return int(::floor(f + 0.5));
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}
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inline int ifloor(float f)
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{
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return int(floorf(f));
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}
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inline int iceil(float f)
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{
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return int(ceilf(f));
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}
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// I'm always confused about which quantizer to use. I think we should choose a quantizer based on how the values are expanded later and this is generally using the 'exact endpoints' rule.
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// Some notes from cbloom: http://cbloomrants.blogspot.com/2011/07/07-26-11-pixel-int-to-float-options.html
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// Quantize a float in the [0,1] range, using exact end points or uniform bins.
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inline float quantizeFloat(float x, uint bits, bool exactEndPoints = true) {
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nvDebugCheck(bits <= 16);
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float range = float(1 << bits);
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if (exactEndPoints) {
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return floorf(x * (range-1) + 0.5f) / (range-1);
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}
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else {
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return (floorf(x * range) + 0.5f) / range;
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}
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}
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// This is the most common rounding mode:
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//
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// 0 1 2 3
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// |___|_______|_______|___|
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// 0 1
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//
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// You get that if you take the unit floating point number multiply by 'N-1' and round to nearest. That is, `i = round(f * (N-1))`.
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// You reconstruct the original float dividing by 'N-1': `f = i / (N-1)`
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// 0 1 2 3
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// |_____|_____|_____|_____|
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// 0 1
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/*enum BinningMode {
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RoundMode_ExactEndPoints,
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RoundMode_UniformBins,
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};*/
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template <int N>
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inline uint unitFloatToFixed(float f) {
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return ftoi_round(f * ((1<<N)-1));
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}
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inline uint8 unitFloatToFixed8(float f) {
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return (uint8)unitFloatToFixed<8>(f);
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}
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inline uint16 unitFloatToFixed16(float f) {
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return (uint16)unitFloatToFixed<16>(f);
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}
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} // nv
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#endif // NV_MATH_FTOI_H
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