atan2.h

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#pragma once
#include "ftz/config.h"
#include "ftz/math/approx.h"
#include "ftz/math/float.h"
 
// Altered coefficient use from SLEEF 3.9.0 atan2kf, under Boost 1.0 below.
// Our normalized division, serial FMA Horner, tiny mask, finite admission and
// bit quadrant folds define a separate graph, not SLEEF's accuracy contract.
namespace ftz { namespace detail { namespace math {
  struct atan2_result { unsigned int bits, valid; };
  struct atan2_value { float radians; unsigned int valid; };
  // All finite inputs are accepted except (signed-FTZ(y), signed-FTZ(x))=(0,0).
  template <bool Hardware = FTZ_FP32_HARDWARE_FTZ != 0>
  native_constexpr inline atan2_result atan2_words(unsigned int y, unsigned int x) {
    atan2_result result; result.bits=result.valid=0u;
    if (!approx_finite(y) || !approx_finite(x)) return result;
    y=approx_flush(y); x=approx_flush(x);
    unsigned int ay=y&0x7fffffffu, ax=x&0x7fffffffu;
    if ((ay|ax)==0u) return result;
    bool swap=ay>ax, negative_x=(x&0x80000000u)!=0u;
    if (ay==0u || ax==0u) {
      unsigned int magnitude=ax==0u ? 0x3fc90fdbu : (negative_x ? 0x40490fdbu : 0u);
      result.bits=magnitude|(y&0x80000000u); result.valid=1u;
      return result;
    }
    approx_result quotient=approx_divide(swap?ax:ay,swap?ay:ax);
    if (quotient.valid==0u) return result;
    // The true ratio is at most one. Remove possible reciprocal overshoot.
    unsigned int ratio_bits=quotient.bits>0x3f800000u ? 0x3f800000u : quotient.bits;
    bool tiny=ratio_bits<=0x39800000u;
    // Hardware mode may evaluate unobserved tiny stages.
    unsigned int masked=Hardware ? ratio_bits : (tiny?0u:ratio_bits);
    float ratio=fp32_decode(ratio_bits), t=fp32_decode(masked);
    float z=fp32_mul<false>(t,t);
    float h=fp32_decode(0x3b390ccdu);
    h=fp32_fma<false>(h,z,fp32_decode(0xbc82b80du));
    h=fp32_fma<false>(h,z,fp32_decode(0x3d2e19b6u));
    h=fp32_fma<false>(h,z,fp32_decode(0xbd995ffau));
    h=fp32_fma<false>(h,z,fp32_decode(0x3dd9ccf2u));
    h=fp32_fma<false>(h,z,fp32_decode(0xbe116f9fu));
    h=fp32_fma<false>(h,z,fp32_decode(0x3e4cb9a7u));
    h=fp32_fma<false>(h,z,fp32_decode(0xbeaaaa5du));
    float q=fp32_mul<false>(z,h);
    float angle=fp32_fma<false>(q,t,ratio);
    angle=fp32_decode(tiny?ratio_bits:fp32_encode(angle));
    if (swap) angle=fp32_fma<false>(-1.0f,angle,fp32_decode(0x3fc90fdbu));
    if (negative_x) angle=fp32_fma<false>(-1.0f,angle,fp32_decode(0x40490fdbu));
    result.bits=fp32_encode(angle)|(y&0x80000000u); result.valid=1u;
    return result;
  }
  template <bool Hardware = FTZ_FP32_HARDWARE_FTZ != 0>
  native_constexpr inline atan2_value atan2_checked(float y,float x) {
    atan2_result r=atan2_words<Hardware>(fp32_encode(y),fp32_encode(x));
    atan2_value result;result.radians=fp32_decode(r.bits);result.valid=r.valid;return result;
  }
}}}
 
/*
Copyright Naoki Shibata and contributors 2010 - 2025.
Boost Software License - Version 1.0 - August 17th, 2003
 
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the above license grant, this restriction and the following disclaimer,
must be included in all copies of the Software, in whole or in part, and
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