////  AudioHelpers.h//  libraries/shared/src////  Created by Ken Cooke on 1/4/17.//  Copyright 2017 High Fidelity, Inc.////  Distributed under the Apache License, Version 2.0.//  See the accompanying file LICENSE or http://www.apache.org/licenses/LICENSE-2.0.html// #ifndef hifi_AudioHelpers_h#define hifi_AudioHelpers_h #include <stdint.h> #include <NumericalConstants.h>#include <cmath> const int IEEE754_MANT_BITS = 23;const int IEEE754_EXPN_BIAS = 127; //// for x  > 0.0f, returns log2(x)// for x <= 0.0f, returns large negative value//// abs |error| < 2e-4, smooth (exact for x=2^N)// rel |error| < 0.4 from precision loss very close to 1.0f//static inline float fastLog2f(float x) {     union { float f; int32_t i; } mant, bits = { x };     // split into mantissa and exponent    mant.i = (bits.i & ((1 << IEEE754_MANT_BITS) - 1)) | (IEEE754_EXPN_BIAS << IEEE754_MANT_BITS);    int32_t expn = (bits.i >> IEEE754_MANT_BITS) - IEEE754_EXPN_BIAS;     mant.f -= 1.0f;     // polynomial for log2(1+x) over x=[0,1]    x = (((-0.0821307180f * mant.f + 0.321188984f) * mant.f - 0.677784014f) * mant.f + 1.43872575f) * mant.f;     return x + expn;} //// for -126 <= x < 128, returns exp2(x)// for x < -126, returns 0// for x >= 128, returns undefined//// rel |error| < 9e-6, smooth (exact for x=N)//static inline float fastExp2f(float x) {     union { float f; int32_t i; } xi;     // bias such that x > 0    x += IEEE754_EXPN_BIAS;     // split into integer and fraction    xi.i = (int32_t)x;    x -= xi.i;     // construct exp2(xi) as a float    xi.i &= ~(xi.i >> 31);  // MAX(xi.i, 0)    xi.i <<= IEEE754_MANT_BITS;     // polynomial for exp2(x) over x=[0,1]    x = (((0.0135557472f * x + 0.0520323690f) * x + 0.241379763f) * x + 0.693032121f) * x + 1.0f;     return x * xi.f;} //// on x86 architecture, assume that SSE2 is present//#if defined(_M_IX86) || defined(_M_X64) || defined(__i386__) || defined(__x86_64__) #include <xmmintrin.h>// inline sqrtss, without requiring /fp:faststatic inline float fastSqrtf(float x) {       return _mm_cvtss_f32(_mm_sqrt_ss(_mm_set_ss(x)));} #else  static inline float fastSqrtf(float x) {       return sqrtf(x);} #endif //// for -1 <= x <= 1, returns acos(x)// otherwise, returns NaN//// abs |error| < 7e-5, smooth//static inline float fastAcosf(float x) {     union { float f; int32_t i; } xi = { x };     int32_t sign = xi.i & 0x80000000;    xi.i ^= sign;   // fabs(x)     // compute sqrt(1-x) in parallel    float r = fastSqrtf(1.0f - xi.f);     // polynomial for acos(x)/sqrt(1-x) over x=[0,1]    xi.f = ((-0.0198439236f * xi.f + 0.0762021306f) * xi.f + -0.212940971f) * xi.f + 1.57079633f;     xi.f *= r;    return (sign ? PI - xi.f : xi.f);} //// Quantize a non-negative gain value to the nearest 0.5dB, and pack to a byte.//// Values above +30dB are clamped to +30dB// Values below -97dB are clamped to -inf// Value of 1.0 (+0dB) is reconstructed exactly//const float GAIN_CONVERSION_RATIO = 2.0f * 6.02059991f; // scale log2 to 0.5dBconst float GAIN_CONVERSION_OFFSET = 255 - 60.0f;       // translate +30dB to max static inline uint8_t packFloatGainToByte(float gain) {    float f = fastLog2f(gain) * GAIN_CONVERSION_RATIO + GAIN_CONVERSION_OFFSET;    int32_t i = std::lround(f);  // quantize     uint8_t byte = std::clamp(i, 0, 255);    return byte;} static inline float unpackFloatGainFromByte(uint8_t byte) {     float gain = (byte == 0) ? 0.0f : fastExp2f((byte - GAIN_CONVERSION_OFFSET) * (1.0f/GAIN_CONVERSION_RATIO));    return gain;} #endif  // hifi_AudioHelpers_h